RESEARCH ON LOBSTER AGE-SIZE RELATIONSHIPS: DEVELOPING
REGIONALLY SPECIFIED GROWTH MODELS FROM META-ANALYSIS OF
EXISTING DATA
By
Charlene Emma Bergeron
B.A. Marine Biology, University of California, Santa Cruz 1998
A THESIS
Submitted in Partial Fulfillment of the
Requirements for the Degree of
Master of Science
(in Marine Biology)
The Graduate School
The University of Maine
December, 2011
Advisory Committee:
Richard Wahle, Research Associate Professor, School of Marine Science, Co-Advisor
Yong Chen, Professor, School of Marine Science, Co-Advisor
Andrew Pershing, Research Associate Professor, School of Marine Science
Copyright 2011 Charlene Bergeron
All Rights Reserved
iii
RESEARCH ON LOBSTER AGE-SIZE RELATIONSHIPS: DEVELOPING
REGIONALLY SPECIFIED GROWTH MODELS FROM META-ANALYSIS OF
EXISTING DATA
By Charlene Emma Bergeron
Thesis Advisors: Dr. Richard A. Wahle & Dr. Yong Chen
An Abstract of the Thesis Presented
in Partial Fulfillment of the Requirements for the
Degree of Master of Science
(in Marine Biology)
December, 2011
Understanding age-to-body size relationships and their variability in the American
lobster is critical to our ability to assess the impact of harvesting on yield, as well as to
forecast trends in future recruitment. Crustaceans lack conspicuous age markers and are
ectothermic, therefore estimating growth and size-at-age is especially challenging.
Because the American lobster’s geographic range spans one of the steepest north-to-south
gradients in ocean temperature on earth, variability due to environmental factors is
especially important to consider when modeling growth. To date, the effects of
temperature on lobster biological rates, particularly growth, have not been incorporated
into growth models used by stock assessments.
In this study I developed a step-wise growth model for three oceanographically
contrasting regions: southern New England, Gulf of Maine, and the Bay of Fundy. These
regions span a thermal gradient from a warm, summer-stratified regime in the south, to a
cool, well-mixed regime in the north. In Chapter 1, regionally specified step-wise
probabilistic growth models were developed from empirical juvenile size-frequency
distributions and tagging data. In Chapter 2, I modified this model to incorporate
temperature in terms of growing degree-days, a method based on thermal requirements of
growth. Both models provide regionally specified estimates of lobster size-at-age and its
variability. Additionally, the growing degree-day model can predict how a changing
climate would alter growth trajectories.
In Chapter 1 considerable regional differences in lobster growth were evident. In
southern New England, growth is initially fastest, but an early onset of maturity slows
growth dramatically at a relatively small size. In contrast, in the Gulf of Maine and Bay
of Fundy, growth is initially slower than in the south, but maturity is delayed to a larger
size and the subsequent decline in growth rate is less severe. The resulting regional
growth curves give the mean and 95% confidence interval for the age lobsters recruit to
the fishery.
The growing degree-day model described in Chapter 2 attempted to use
temperature to explain regional differences in growth. If temperature was the dominant
factor determining regional growth differences, I would expect the three regional growth
trajectories to converge when expressed on a scale of growing degree-days. Such
convergence was only partly realized. However, back-calculating these results to a scale
of calendar-days gave only slightly slower growth trajectories than the original model
developed in Chapter 1. When using this model to make predictions for changing climate
scenarios, varying the size-at-maturity along with temperature helped to explain regional
growth trajectories. Future model development would benefit from an understanding of
why the onset of maturity affects body growth more severely under warmer conditions.
Thus, while regionally-specified models have advanced our ability to account for
regional differences in lobster growth, they have yet to adequately include the
environmental factors that determine those differences. Temperature surely plays an
important role in the observed regional differences in both the onset of sexual maturity
and growth, however, I cannot rule out other factors that may also be important, such as
food availability, population density, or local adaptation.
ACKNOWLEDGEMENTS
I would like to thank my co-advisors Dr. Richard Wahle and Dr. Yong
Chen for giving me the opportunity to be involved in this project. Thanks to their
combined support and encouragement I was able to complete this project. Also,
thank you to my committee member, Dr. Andrew Pershing, for his insightful
input into this project.
Thanks to everyone who provided the large amounts of data used in this
project: Dr Peter Lawton and the Canadian department of Fisheries and Oceans;
Carl Wilson, Robert Russell and Maine Department of Marine Resources,
University of Rhode Island, Rhode Island Department of Marine Fisheries, and
the American Lobster Settlement Index Collaborative.
I am grateful that on my first day working on this project Dr. Chen
introduced me to Yi-Jay Chang (now Dr. Chang). I never would have been able to
get through the coding, debugging, and modifying of these models in R without
Yi-Jay’s help. He was always willing to spend time with me discussing R, growth
modeling, lobsters, underwater cameras, and Taiwanese cuisine.
Last, but definitely not least, thank you to my family, friends, fellow
graduate students and my dog, Maliko. Thank you for the endless support,
encouragement, incentives to finish, and many needed play sessions including
hikes, dinners, drinks, swims, surfs, runs… Without this I could not have finished
and still be mostly sane. 
iv
TABLE OF CONTENTS
ACKNOWLEDGEMENTS ............................................................................................... iv LIST OF TABLES ........................................................................................................... viii LIST OF FIGURES ............................................................................................................. x Chapter
1. LINKING TAGGING-BASED AND SIZE-FREQUENCY-BASED
APPROACHES TO GROWTH MODELING IN CRUSTACEANS FOR
THREE OCEANOGRAPHICALLY DISTINCT REGIONS ........................................ 1 Abstract ....................................................................................................................... 1 Introduction ................................................................................................................. 2 Methods ....................................................................................................................... 8 Study regions ........................................................................................................... 8 Regional difference in oceanography ...................................................................... 9 Length-frequency analysis to determine size-at-age of early juveniles ................ 13 Analysis of tagging data for older lobsters ............................................................ 15 von Bertalanffy growth parameters ........................................................... 17 Molt increment .......................................................................................... 19 Molt probability ......................................................................................... 21 Probabalistic step-wise growth model ................................................................... 22 Size transition matrix............................................................................................. 24 Results ....................................................................................................................... 26 Estimating von Bertalanffy Growth Parameters ................................................... 26 Estimating size-at-age of juvenile lobsters ............................................................ 27 Molt increment ...................................................................................................... 29 Molt probability ..................................................................................................... 33
v
Stepwise growth model ......................................................................................... 35 Growth transition matrix ....................................................................................... 38 Discussion ................................................................................................................. 41 2. DEVELOPING A DEGREE-DAY MODEL FOR LOBSTER GROWTH ................. 47 Abstract ..................................................................................................................... 47 Introduction ............................................................................................................... 48 Methods ..................................................................................................................... 52 Study regions and oceanography ........................................................................... 53 Temperature time series ........................................................................................ 55 Modeled temperature ................................................................................. 56 Growing degree days ................................................................................. 59 Evaluating growth in early juveniles: length-frequency analysis ......................... 60 Evaluating growth in older juveniles and adults: mark-recapture data ................. 61 Growth increment ...................................................................................... 61 Molt probability ......................................................................................... 62 Probabilistic step-wise degree day growth model ................................................. 64 Results ....................................................................................................................... 67 Cumulative degree days ........................................................................................ 67 Molt Probability .................................................................................................... 68 Probabilistic step-wise degree-day growth model................................................. 72 Climate Change Predictions .................................................................................. 77 Discussion ................................................................................................................. 83 REFERENCES .................................................................................................................. 89 vi
APPENDIX. Size transition matrices by sex and region ................................................ 100 BIOGRAPHY OF THE AUTHOR ................................................................................. 104 vii
LIST OF TABLES
Table 1.1.
Sources of suction sampling data, number of sites sampled,
number of quadrats and quadrat size used for each region. ...................... 13 Table 1.2.
Sources of tagging data for each region and corresponding years,
size ranges of lobsters caught and recaptured, and maximum daysat-large. ...................................................................................................... 17 Table 1.3.
Parameters for size-at-maturity ogives and inflection point used in
describing growth increment for each region. ........................................... 21 Table 1.4.
Mean, standard deviation, and coefficient of variation for first 4
age-classes of lobsters in 3 thermal regions as determined by
modal analysis of size frequency data by MULTIFAN. ........................... 29 Table 1.5.
The mean and 95% confidence intervals for growth factor and
growth increment by size group and sex for lobsters with one molt. ........ 30 Table 1.6.
Average growth factor by region before and after maturity. ..................... 30 Table 1.7.
Parameters for the relationship of growth factor to pre-molt
carapace length for size groups greater than and less than the size
at 10% maturity. ........................................................................................ 31 Table 1.8.
Molt probability parameters by size class, sex and region. ....................... 35 Table 1.9.
Mean age-at-recruitment to fishery and upper and lower
confidence intervals for all regions by sex.. .............................................. 37 Table 1.10.
von Bertalanffy growth function parameter estimates for American
lobsters from north to south including estimates from this study
compared to those of other studies in the same geographic region.. ......... 42 viii
Table 2.1
Mean carapace length, standard deviation, and coefficient of
variation for first four age-classes of lobsters in three thermal
regions as determined by modal analysis of size frequency data by
MULTIFAN. ............................................................................................. 61 Table 2.2.
Analysis of temperature data for each region. ........................................... 68 Table 2.3.
Molt probability parameters by region, sex and size group as
calculated by growing degree-day. ............................................................ 69 Table 2.4.
Results of Kolmogorov-Smirnov test to compare cumulative
degree-day distribution required for male lobsters to reach 50 mm
and harvestable size between regions.. ..................................................... 74 Table 2.5.
Estimated age at harvestable size. ............................................................. 76 Table 2.6.
Results of Kolmogorov-Smirnov test to compare age distributions
required for male lobsters to reach 50 mm and harvestable size
within regions by calendar day and growing degree-day models. ............ 77 Table 2.7.
Results of Kolmogorov-Smirnov test to compare growing degreeday distributions required for male lobsters to reach 50 mm and
harvestable size within regions by three models ...................................... 83 Table A1.
Size transition matrix for male and female lobsters in SNE. .................. 101 Table A2.
Size transition matrix for male and female lobsters in GOM.................. 102
Table A3.
Size transition matrix for male and female lobsters in BOF. .................. 103 ix
LIST OF FIGURES
Figure 1.1.
Map of the Gulf of Maine and southern New England showing
study regions defined by boxes.. ................................................................. 9 Figure 1.2.
Seasonal changes in thermal stratification for Bay of Fundy, Gulf
of Maine, and southern New England.. ..................................................... 12 Figure 1.3.
Flow diagram of individual-based stepwise growth model....................... 24 Figure 1.4.
Schematic diagram of size transition matrix shows the probability
that an individual in one size class will transition to subsequent
size classes within a year. .......................................................................... 25 Figure 1.5.
von Bertalanffy growth curves from tagging data in three regions ........... 26 Figure 1.6.
Size frequency histograms of lobsters from suction sampling with
best fitting curves in red corresponding to age classes 0+ to 3+ for
Bay of Fundy, Gulf of Maine, and southern New England. ...................... 28 Figure 1.7.
Relationship between growth factor and carapace length measured
at time of tagging. ...................................................................................... 32 Figure 1.8.
Molt probability curves as a function of days at large for Bay of
Fundy, Gulf of Maine, and southern New England by size class
and sex. ...................................................................................................... 34 Figure 1.9.
Results of the stepwise growth model simulations for BOF, GOM,
and SNE regions.. ...................................................................................... 36 Figure 1.10.
Annual probabilities of male and female American lobsters
growing from one size class to another for BOF, GOM, and SNE
x
from an initial carapace lengths of 7.5 mm, 42.5 mm, 82.5 mm,
and 122.2 mm. ........................................................................................... 40 Figure 2.1.
Study regions from north to south: Bay of Fundy, Gulf of Maine,
and southern New England........................................................................ 54 Figure 2.2.
Seasonal changes in thermal stratification within boundaries of
study regions denoted in Fig. 2.1.. ............................................................ 57 Figure 2.3.
Annual temperature cycles for each region were produced by
fitting a sine function to observed temperature time series and were
then used to calculate cumulative growing degree-days.. ......................... 59 Figure 2.4.
Relationship of growth factor to carapace length from tagging data
in Bay of Fundy, Gulf of Maine, and southern New England for
males and females.. ................................................................................... 62 Figure 2.5.
Flow diagram of individual-based stepwise growth model by
growing degree-day. .................................................................................. 66 Figure 2.6.
Molt probability curves plotted as a function of growing degreedays for Bay of Fundy, Gulf of Maine 10 m, Gulf of Maine 20 m
and southern New England from top to bottom by size class and
sex. ............................................................................................................. 70 Figure 2.7.
Comparison of molt probability curves plotted against calendar
days and growing degree-days for the same size classes; 20 – 39
mm and 40-65 mm in southern New England and Gulf of Maine.. ......... 71 Figure 2.8.
Stepwise model results by degree-day for Bay of Fundy, two
depths in the Gulf of Maine, and southern New England.. ....................... 73 xi
Figure 2.9.
Regional curves produced by the original probabilistic step-wise
model based on calendar day compare more favorably to the
growth curves from the degree-day model back calculated to a
calendar day scale. ..................................................................................... 75 Figure 2.10.
Size at 10% maturity for female lobsters from locations of different
average yearly cumulative degree days greater than 8°C.......................... 79 Figure 2.11.
Growth trajectories as a function of degree-days modeled for
temperature regimes 2°C warmer than current conditions. ....................... 80 Figure 2.12.
Predicted size-at-age curves for temperature regimes 2°C warmer
than current conditions.. ............................................................................ 81 xii
Chapter 1
LINKING TAGGING-BASED AND SIZE-FREQUENCY-BASED APPROACHES
TO GROWTH MODELING IN CRUSTACEANS FOR THREE
OCEANOGRAPHICALLY DISTINCT REGIONS
Abstract
Understanding growth and size-at-age is key to modeling the dynamics and
sustainable management of exploited populations. Because crustaceans have no
morphological age markers, estimating growth and size-at-age is a complex process made
ever more challenging by individual and environmentally induced growth variability.
Current growth models usually fail to incorporate these components of variability and
therefore are of limited generality. The stepwise growth model for the American lobster,
Homarus americanus, presented here offers a novel approach to age estimation and its
variability by integrating two growth analysis methods traditionally used independently:
(1) modal analysis of early juvenile size-frequency distributions, for which accurate
estimates of absolute age exist, and (2) mark-recapture studies of older juveniles and
adults, giving estimates of relative age and growth. In this study, the former is used to
confirm age estimates in the latter. Growth curves are developed for three
oceanographically contrasting regions for which juvenile size-frequency and markrecapture for older lobsters are available. The study encompasses three oceanographically
contrasting regions that span the thermal gradient along a significant segment of the
species’ range. From north to south they are, the cool, well-mixed Bay of Fundy,
1
Canada; the summer stratified mid-coastal Gulf of Maine; and a more strongly summerstratified southern New England shelf, USA. The models resulted in differing growth
trajectories for lobsters in the three regions. In southern New England growth during the
juvenile years was considerably faster than in the other regions, but because lobsters
mature at a smaller size than in the two northern regions, growth slowed sooner and more
dramatically. In contrast, in the other two regions growth started off more slowly,
maturity was delayed to a larger size, and the subsequent decline in growth rate was less
severe. In general, males grew faster than females. While temperature is likely to play an
important role in explaining the observed regional differences in growth, other
environmental conditions, such as food availability or density dependence, may also play
a key role in lobster growth.
Introduction
Somatic growth of marine organisms is a key variable in our understanding of
population and ecosystem processes because of its influence on the flow of energy,
population productivity, and the accumulation of biomass. The rate of individual growth
has important implications for yields and sustainable management of fisheries (Hilborn
and Walters 1992, Chen et al. 2005, Neuheimer and Taggart 2007). Furthermore, because
mortality, reproduction and trophic interactions are often size-dependent (Peters 1983,
Werner et al. 1983), temporal and spatial variability in body growth can have important
implications for recruitment and abundance trends (Wahle et al. 2004, Ehrhardt 2008).
Large-bodied decapod crustaceans, such as lobsters and crabs, have posed a particular
challenge to population modeling because the absence of morphological age markers
2
limits our understanding of the age-size relationship (Wahle and Fogarty 2006). While
the search for a practical age marker continues, it is necessary to take innovative
approaches to modeling growth that take advantage of conventional data generated by
population surveys and mark-recapture studies.
Lobsters of the genus Homarus are among the largest and longest living marine
crustaceans (Wolff 1978, Sheehy et al. 1999, Wahle and Fogarty 2006). In the coastal and
shelf areas of the NW Atlantic, Homarus americanus is a conspicuous, abundant and
ecologically important species (Miller 1985, Worm and Myers 2003). It also supports one
of the most productive lobster fisheries in the world, and the most valuable single-species
fishery in the Northeast US and Atlantic Canada (NEFSC 1996, Steneck and Wilson
2001, Chen et al. 2005, ASMFC 2006)
The benthic life phase of lobsters can live for decades and achieve body sizes
exceeding 20 kg (Wolff 1978?). As a result there is tremendous scope for growth.
Growth rates depend on both heritable and environmental factors (Aiken and Waddy
1976, Hedgecock 1986, Waddy et al. 1995, Wahle and Fogarty 2006). While this study
develops specified growth models for three geographic regions, I do not attempt to
discriminate heritable and environmental components.
Crustaceans grow discontinuously by molting; the complete shedding of the
hardened exoskeleton and the formation of a new larger one. Variability in growth is
therefore manifested as more or less frequent molting, depending on intrinsic and
extrinsic conditions. Environmental factors that affect growth can include dissolved
oxygen, salinity, light intensity, photoperiod, density of con-specifics, and food supply;
however, as with most ectotherms temperature is the principal factor (Waddy et al. 1995,
3
Angilletta et al. 2002). Warmer temperatures, to a physiological limit, generally increase
molt frequency, as well as affect the growth increment between molts (Hughes and
Mathiessen 1962, MacKenzie and Moring 1985).
Intrinsic factors that affect lobster growth include size, sex, and the onset of
sexual maturity. With increased size, growth rate decreases (Templeman 1940). Before
the onset of sexual maturity, there is little difference in growth rate between males and
females, but after maturity female growth slows considerably (Herrick 1895, Hadley
1906, Waddy et al. 1995). The onset of maturity itself is influenced by the environment,
and tends to occur at a smaller size, and earlier age, in warmer water temperatures
(Waddy et al. 1995).
Biochemical age markers, such as lipofuscin, have shown some promise in
identifying age classes in lobsters, although the reliability of this method remains in
question (Sheehy 1990, Wahle and Fogarty 2006). This fluorescing pigment has been
shown to accumulate with age in the neural tissue of the brain or eyestalks of freshwater
crayfish Cherax spp. (Sheehy 1989, Sheehy 1990, Sheehy 1992), and marine decapods,
such as Nephrops norvegicus (Belchier 1994), Penaeus monodon (Sheehy 1995),
Callinectes sapidus (Ju et al. 1999), and Homarus gammarus (Sheehy and Wickens 1994,
O’Donovan and Tully 1996) and more recently, Homarus americanus (Wahle et al. 1996,
Giannini 2008). However, there are several shortcomings to this method. Accumulation
of lipofuscin can be dependent on temperature or other environmental factors because it
is a metabolic by-product, thus age estimates derived from lipofuscin need to be
calibrated to local conditions (Sheehy et al. 1998, Ehrhardt 2008). This method remains
relatively costly and labor intensive, and may not be practical for long-term monitoring or
4
large geographic comparisons spanning a wide range of environmental conditions. While
the search for direct age markers continues, researchers studying crustaceans largely
resort to one of two long-standing methods of evaluating size-at-age and growth: the
analysis of size-frequency distributions, and growth increment from mark-recapture.
However, to date, few growth studies have integrated the two methods.
Lobster recruitment occurs in annual summer pulses; therefore, length frequency
data can reveal annual cohorts as peaks in the size distribution (MacDonald and Pitcher
1979, Grant et al. 1987). Within a single sample multiple age classes can be detected and
with annual sampling, one can follow the progression of cohorts through time (Hartnoll
2001). Length-frequency analysis assumes that multiple modes in the size distribution
correspond to probable age groups that can be identified with a statistical goodness of fit
approach (MacDonald and Pitcher 1979, Grant et al. 1987). This technique has been used
successfully in decapods including Nephrops norvegicus (Mytilineou and Sardi 1995),
Panulirus argus (Ehrhardt 2008), and Chionocetes opilio (Sainte-Marie et al. 1995,
Comeau et al. 1998). Length frequency analysis is best applied in cases where modes
corresponding to age groups are conspicuous in the size distribution. But for many
species and particularly for older age groups, it is difficult or impossible to resolve age
groups because of variable growth rates. For these larger individuals other methods such
as mark-recapture become more appropriate to determine growth.
Mark-recapture approaches provide valuable information on growth and relative
age through the direct assessment of change in size of tagged animals over the time
elapsed between marking and recapture. The development of a tag that is retained
through the molt was a breakthrough for field studies of crustacean growth and
5
movement (Wilder 1963, Wahle and Fogarty 2006). Individually identified tags enable
the determination of individual growth increment over a time interval. Still, unless the
age of the individual is known at the time of tagging, only relative age can be determined.
Another limitation of tagging is the heightened risk of injury or death associated with
tagging, especially for the smallest individuals. However, as will be shown in this study,
coupling length-frequency analysis of the younger stages with mark-recapture analysis of
older stages may be useful approach to the development and validation of growth models.
The von Bertalanffy growth function (VBGF) (von Bertalanffy 1938), has been
used extensively in growth modeling for many fisheries species (Chen et al. 1992). This
model assumes continuous growth that slows over time and approaches an asymptote as
age goes to infinity. Using a continuous function to describe the discontinuous growth of
crustaceans has been debated (Breen 1994, Stewart and Kennelly 2000). Nonetheless, it
is still useful for modeling crustacean growth because the von Bertalanffy growth
parameters can readily be compared among species or location (Stewart and Kennelly
2000) and used in stock assessment models (Cobb and Caddy 1989, Wahle and Fogarty
2006).
A more realistic method for describing discontinuous growth is a stepwise model
that incorporates the length of time between molts; molt frequency, and the increase in
length between molts; molt increment (Melville-Smith 1989). Most often a probabilistic
stepwise growth curve (Chen and Kennelly 1999) simulation model is used to describe
stepwise growth simply by combining information of molt increment and molt
probability. This method has been used to describe growth of red king crab Paralithodes
camtschatica (McCaughran and Powell 1977), southern rock lobster, Jasus edwardsii
6
(Annala and Bycroft 1988), spanner crab Ranina ranina (Chen and Kennelly 1999), and
two species of scyllarid lobsters Ibacus peronii and I. chacei (Stewart and Kennelly
2000).
The probabilistic stepwise growth model results in a growth transition matrix
giving the probability that lobsters in one size class grow into subsequent size classes.
Past studies have suggested that the large errors in the estimation of growth transition
matrix tend to yield biased results in estimates of lobster population dynamics (Chen et
al. 2005). Thus, it is important to derive regionally specified growth transition matrices
that may result from regional differences in environmental and heritable effects.
Growth is an important life-history process for understanding population structure
and is a central part of various models used for stock assessment. Currently the American
lobster stock assessment employs a length-based model for quantifying the dynamics of
lobster population size structure (ASMFC 2009). This model requires a growth transition
matrix as an input. However, there is large uncertainty the growth transition matrix
because of our still poor understanding of size-specific lobster molting frequency and
molt increment (ASMFC 2009). Improving the estimation of growth transition matrix
was therefore a major recommendation of the US lobster stock assessment review panel
(ASMFC 2009).
The aim of this project was to develop a stepwise growth model for the American
lobster starting from the time of postlarval settlement, by coupling the results of lengthfrequency analysis of the youngest benthic lobsters with the results of mark-recapture
studies of older lobsters. I used lobster size-frequency and mark-recapture data available
from separate studies conducted in New England, USA, and Atlantic Canada and from
7
contrasting thermal regimes. For early juveniles for which size modes are useful in age
determination, but for which tagging data are scarce, I used a length-frequency based
modeling approach, to estimate mean size at age and its variation. For older juveniles
and adult lobsters, for which the opposite is true, I used growth data from tagging studies
to estimate growth increment and molt probability. An individual-based stepwise growth
model for the full size range was developed by using size and region-specific parameters
described by these two methods. Individual-based stepwise results were then used in the
construction of a growth transition matrix for each region.
Methods
Study regions
This study incorporated suction sampling and tagging study data from three
oceanographically contrasting regions encompassing different fishery statistical areas
(Figure 1.1 and 1.2).

Bay of Fundy (BOF): Cool, well-mixed throughout the summer growing season National Marine Fisheries Service (NMFS) statistical area 511 and Canadian
Lobster Fishery Areas 34, 35, 36, 37 and 38;

Gulf of Maine (GOM): Summer stratified with shallow thermocline - NMFS
statistical areas 512 and 513, and

Southern New England (SNE): Summer stratified with deep thermocline - NMFS
statistical areas 538, 539, and 611.
8
Figure 1.1. Map of the Gulf of Maine and southern New England showing study regions
defined by boxes. Regions from north to south are: Bay of Fundy (BOF), Gulf of Maine
(GOM), and southern New England (SNE). Tag-recapture release locations and lengthfrequency data from settlement index sites used in this study are indicated by black
squares and empty circles respectively.
Regional difference in oceanography
The Gulf of Maine is partially enclosed by the shores of Nova Scotia, New
Brunswick, and New England. Circulation in the Gulf of Maine is generally cyclonic. At
the north end of the Gulf of Maine is the large inlet of the Bay of Fundy. The head of the
Bay of Fundy is shallow while the mouth is a deep, steep-sided trench lined by coastal
shelves and shallower rocky ledges (Brown and Gaskin 1988). Circulation is dominated
by strong tidal streams which create turbulence as they pass over ledges, forcing cold
bottom water to the surface. Because of this tidal mixing, the Bay of Fundy is a well
9
mixed regime that does not become strongly stratified thermally, and only warms slightly
above 10°C from July into October. In contrast, the other two regions both develop a
strong thermocline during the warm season.
Coastal Gulf of Maine waters are strongly influenced by the southwest flowing
Gulf of Maine Coastal Current (GMCC). The GMCC splits into two components around
Penobscot Bay in mid-coast Maine. The two resulting currents differ in physical
properties, flow dynamics, (Lynch et al. 1997) and vary annually in relative strength
(Pettigrew et al. 1998). East of Penobscot Bay, the Eastern Maine Coastal Current
(EMCC) draws cold water from the Bay of Fundy and remains well mixed by the
region’s strong tidal forces. While west of Penobscot Bay, the Western Maine Coastal
Current (WMCC) continues down the coast and maintains vertical stratification in the
summer and autumn (Townsend et al. 1987). Surface temperatures in the Gulf of Maine
region rise to 16-18 °C during the summer, whereas bottom temperatures rarely exceed 7
°C.
Outside of the Gulf of Maine, south of Cape Cod, the southern New England
continental shelf is wide, gently sloped, and relatively shallow. The large shallow shelf
area is strongly influenced by the warm Gulf Stream and is strongly stratified in the
summer and autumn (Townsend et al. 2004). The stratified layer here is correspondingly
deeper and the growing season is more extended than in the Gulf of Maine. Surface
temperatures in southern New England can rise well above 20°C and can approach
physiological stressful levels for lobsters in protected bays and estuaries, such as Long
Island Sound.
10
The thermal properties of these regions are reflected by averaged regional
seasonal temperature depth profiles (Figure 1.2). Paradoxically, however, by virtue of the
differences in vertical mixing, mid-summer temperatures are warmer at 50 m in the Bay
of Fundy than they are at the same depth in the Gulf of Maine. In short, lobsters living at
different depths in the Fundy region would be likely to encounter little difference in
temperature during up- or downslope movements in the summer, whereas those in the
Gulf of Maine and southern New England would experience greater extremes. To the
extent temperature is a determinant of growth rates, therefore, it would be reasonable to
expect lobsters to exhibit greater variability in size-at-age in regions that become
thermally stratified during the growing season than in regions that do not.
11
Figure 1.2. Seasonal changes in thermal stratification for Bay of Fundy (BOF) (44.5° N
to 45.5° N and 64.75° W to 67.25° W), Gulf of Maine (GOM) (43.33° N to 44.07° N and
69.22° W to 70.62° W), and southern New England (SNE) (40.87° N to 41.6° N and
70.43° W to 73.55° W). Data represent 10 year mean from 1995 – 2004. No temperature
data were available below 60 m in SNE because of the shallower shelf area. (Source:
Canada Department of Fisheries and Oceans (DFO), Hydrographic Climate Database
http://www2.mar.dfo-mpo.gc.ca/science/ocean/sci/sci-e.html taken at 1m (± 0.5m)
intervals).
12
Length-frequency analysis to determine size-at-age of early juveniles
Length frequency data from diver-based suction sampling in lobster nurseries
were used to estimate size-at-age for the smallest juvenile lobsters between 5 and 40 mm
carapace length. At these sizes relatively clear modes corresponding to age classes were
evident in size distributions. Annual suction sampling began in 1989 in midcoast Maine
(8-10 sites), 1990 in Rhode Island (3-6 sites) and 1993 in New Brunswick (2-9 sites)
(Table 1.1) (Wahle et al. 2004). Surveys are conducted annually at the end of the
postlarval settlement season in late August to early September in Rhode Island, late
September to mid-October in midcoast Maine, and mid to late October in Beaver
Harbour, New Brunswick. At each site divers collected samples from 12 – 18 quadrats.
Quadrat size is 0.25 m2 in Beaver Harbour and 0.5m2 in the other two regions. Lobsters
were measured and sex recorded where possible. Sexes were not separated for the
smallest lobsters due to difficulty in distinguishing them at such small sizes. However, at
these sizes there is no difference in growth rates between females and males, and
therefore, it is reasonable to combine the data for analysis. For further details on the
suction sampling method, see Incze and Wahle (1991) and Incze et al. (1997).
Table 1.1. Sources of suction sampling data, number of sites sampled, number of
quadrats and quadrat size used for each region.
Number Number of Size of Region Suction Sampling
of sites
quadrats per site quadrat
BOF DFO 1991‐2008 2‐9 12‐14 0.25 m2 10 12 0.5 m2 6 12 0.5 m2 GOM SNE Wahle 1989‐2005 ME DMR 2006‐2008 Wahle 1990‐2005 RI DFW 2006 ‐2008 13
The program, MULTIFAN (Fournier and Sibert 1990), was used to analyze
annual length frequency data from all available years from each of the three regions. This
approach uses a maximum likelihood method to analyze a time series of length frequency
distributions to estimate the number of age classes present, the mean size at age and
associated standard deviation for each age class, as well as the von Bertalanffy growth
parameters. Length frequency distributions were divided into 1 mm size bins up to 60
mm. The MULTIFAN model assumed: (1) lengths of individuals in an age class are
normally distributed about the mean, (2) the mean length at age lies on or near the von
Bertalanffy growth curve, and (3) the standard deviation about the mean length-at-age is
a simple function of length-at-age (Fournier and Sibert 1990). In this case I also assumed
that the first mode represents young-of-year lobsters, or age 0+ (Wahle and Steneck
1991). In MULTIFAN, an initial systematic search was conducted with VBGF growth
coefficient, K, values ranging from 0.02 to 0.14 and number of age classes from 4 to 10.
To find the best fitting model, I tested the hypotheses that the standard deviation in length
is: (1) constant for all age classes; (2) variable for all age classes; and (3) variable for all
age classes and values of the growth parameter, K. Because all the sampling was
conducted at the same time of year, no seasonal parameters were estimated. Log
likelihood tests were used to select the most parsimonious fit to the data following the
method of Fournier and Sibert (1990) and Francis et al. (1999) packaged as MULTIFAN
Sigtest.
14
Analysis of tagging data for older lobsters
Data were compiled from several tagging studies to estimate growth parameters in
each region for lobsters greater than 20 mm in carapace length (Table 1.2). Lobsters were
caught either by trap, trawl, or by divers and tagged with a sphyrion tag inserted dorsally
in the gap between the carapace and first abdominal segment. Tags inserted in this
location were retained through the molt, protected from abrasion, and were conspicuous
for recapture (Moriyasu et al. 1995, Comeau and Mallet 2003). Tags were printed with a
unique number and the relevant telephone number for reporting by harvesters. Lobsters
less than 20 mm could not be tagged because of high mortality and tag loss. The
information essential in this analysis were the date of capture and recapture, carapace
length, and sex. Lobsters were released as close to the capture site as possible. Although a
considerable fraction of lobsters were recaptured more than once, for this study, I only
used data from the first recapture to keep observations independent.
In the Bay of Fundy and southwest Nova Scotia, Canada Department of Fisheries
and Oceans tagged lobsters between 1977 and 1993 in 15 locations (Campbell 1983,
Campbell and Stasko 1985, Campbell and Pezzack 1986, Robichaud and Campbell
1995). I selected lobsters that were both tagged and recaptured in eight areas within the
Bay of Fundy (Figure 1.1). Lobsters that emigrated from these areas were not included in
this analysis.
Data for the Gulf of Maine region originated from five tagging studies (Figure
1.1): (1) in 1975, tag-recapture data were collected by Krouse (1981) in the Boothbay and
Kennebunkport, Maine areas. Approximately 1000 harvestable size lobsters were bought
from wholesalers, tagged and released. (2) Between 1978 and 1987, and again in 1991
15
lobsters were tagged by DFO Canada in southern Nova Scotia (Cambell and Stasko
1985). I justify the use of these lobsters because the thermal regime along the
southeastern coast of Nova Scotia is similar to that of the Gulf of Maine. (3) From 1983
to 1992 Maine Department of Marine Resources (DMR) tagged lobsters Boothbay
Harbor, Maine (43°48.132 N, 69° 41.252 W) (Krouse 1983). (4) Between 1999 and
2002, a Sea Grant-supported mark-recapture study was conducted by divers at five sites
in midcoast Maine, with some recaptures being called in by fishermen over the ensuing
years (Wahle unpublished). (5) Between 2001 and 2003, in another Maine Sea Grant
study, lobsters were tagged from commercial lobster traps with escape vents blocked to
prevent the loss of sublegal lobsters for research purposes (Dunnington et al. 2005,
Geraldi et al. 2009).
In southern New England, I used data generated by several tagging studies
conducted between 1993 and 2004 (Figure 1.1, Table 1.2). Between 1993 and 2003,
University of Rhode Island and Rhode Island Department of Fish and Wildlife tagged
lobsters in Narragansett Bay on weekly trawl and trap surveys (Castro et al. 2001). Diverbased tagging was conducted in Rhode Island between 1999 and 2000 at two sites on the
outer coast of Rhode Island (Wahle unpublished). In 2000-2001, the Rhode Island
Lobsterman’s Association tagged lobsters in Narragansett Bay, Rhode Island Sound, and
Block Island Sound, and the North Cape Lobster Restoration project tagged and released
lobsters in a 10 mile radius off Point Judith. Connecticut Department of Environmental
Protection also had a lobster tagging program from 2001-2004 with lobsters released in
Block Island Sound and four areas in Long Island Sound (Simpson unpublished).
For all three regions, cases with missing data on recapture size and sex were
16
removed. It is reasonable to expect normally distributed positive and negative
measurement error of a few mm, therefore I excluded only cases in which the recapture
size was >5 mm less than the original size, assuming negative growth is not possible.
However, it is reasonable for lobster to grow more than 5 mm. The data was also filtered
for number of days at large. If a growth increment was detected in less than 20 days, it
was not included for the molt probability analysis because, although a lobster may molt
within this time from tagging, such a short period between molts for lobsters greater than
2 years old is not expected.
Table 1.2. Sources of tagging data for each region and corresponding years, size ranges
of lobsters caught and recaptured, and maximum days-at-large.
Size range Size range Days at large (max tagged recaptured (median))
(mm)
(mm)
Region
Source
# of sites
BOF
DFO 1977 ‐ 1993
8
20‐197
21‐204
2947 (117)
Krouse 1975‐1977
DFO 1977 ‐ 1993
ME DMR 1983‐1994
Wahle 1999‐2000
Wahle 2001‐2003
URI / RI DFW 1993 ‐2001
Wahle 1999‐2000
RILA 2000‐2001
NCRM 2000‐2001
CT DEP 2001‐2004
2
6
1
9
4
2
2
5
1
5
81‐107
20‐133
25‐80
21‐91
51‐110
45‐95
23‐80
69‐103
83‐103
58‐110
81‐96
21‐146
25‐100
24‐94
53‐111
45‐105
23‐81
73‐103
73‐103
63‐93
738(397)
1295(67)
4109(192)
1094(8)
379(19)
781(29)
127(13)
591(81)
67(14)
687(111)
GOM
SNE
von Bertalanffy growth parameters
Tagging data were used in a modified version of the von Bertalanffy equation,
referred to as the Fabens method (Fabens 1965). This method estimates L∞ and K by
17
predicting the length at recapture (Lr) based on estimated parameters and the length at
tagging (Lm):
1
,
[1.1]
where Lm is the carapace length at tagging, L∞, is the average size at infinite age, K is the
Brody growth parameter and t0 is the hypothetical age when the carapace length is zero.
The equation can be rearranged to predict the molt increment, LΔn:
1
∆
,
[1.2]
The growth parameters can then be estimated using the least squares method. This
method has been used in a number of studies on crustaceans (e.g., Homarus americanus:
Ennis 1980, Jasus edwardsii: Annala and Bycroft 1988, Panulirus cygnus: James 1991,
Cheng and Kuk 2002).
A second method to obtain von Bertalanffy growth parameters from tagging data
is the Ford-Walford plot. The Ford-Walford plot assumes equal time intervals between
sampling, therefore tagging data are limited to lobsters exhibiting one molt and
recaptured near the one year anniversary of tagging. With t0 set equal to zero the VBGF
equation is linearized, and the length at age t (Lt) can be plotted against its length one
year later (Lt+1) (King 1995). All lobsters recaptured after one year, with a buffer of 30
days, are used whether or not growth is indicated as not to overestimate parameters
(Wahle and Fogarty 2006). From this plot the slope, b, and y-axis intercept, a, of the
straight line fitting the data are written as:
exp
and,
1
exp
[1.3]
,
[1.4]
respectively. Thus the parameters can be estimated as:
18
ln
[1.5]
[1.6]
Molt increment
To determine molt increment, it was first necessary to distinguish measurement
error from molt-related changes in size. Measurement error was evaluated with lobsters
recaptured before they would have had time to molt (i.e., ≤5 days, Ehrhardt 2008). By
this method I found measurement error to be within the range of ±4% and consistent with
previous such estimates (Campbell 1983, Idoine and Finn 1985). Molt increments
typically exceeded 4% of the original size.
To distinguish lobsters that have experienced only one molt from those that have
experienced more than one molt during their time at large, recaptured lobsters were first
grouped into size classes by sex. Lobsters with one molt were distinguished by examining
a frequency distribution of growth factor by size group (Fogarty and Idoine 1988). Clear
modes were evident in these distributions at one molt and two molts. For each size group,
I calculated the 95% confidence interval for the growth factor corresponding to one molt.
The relationship between premolt size and either the absolute molt increment or
molt increment as a proportion of premolt size (growth factor) can be described by a
linear equation (Kurata 1962, Mauchline 1976). This method often reveals important
changes in growth with increasing body size, and particularly with the onset of maturity
(Hiatt 1948, Mauchline 1976, Cooper and Uzmann 1980, Somerton 1980, Fogarty and
Idoine 1988, Wahle and Fogarty 2006). I therefore conducted separate regressions for
juveniles and sexually mature lobsters. I found that a linear function could be applied to
19
immature sizes but a non-linear function was more appropriate after maturity (ASMFC
2006, Cadrin 1995). The linear equation with slope, b, and y-intercept, a, was used to
evaluate the proportional change in length, ∆ , as a function of initial size,
, for
immature lobsters:
∆
[1.7]
A power function was applied to sexually mature lobsters:
∆
[1.8]
Either equation can then be used to describe molt increment ∆ by:
∆
∆
[1.9]
To set the maturity thresholds I used previously reported female size-at-maturity ogives
derived from of ovarian and cement gland staging (Campbell and Robinson 1983,
ASMFC 2006) (Table 1.3). Ogives were defined by the logistic function:
,
[1.10]
where PmatCL is the proportion mature at length CL, and a and b are estimated
parameters.
For females I used the size at which 10% of the females were mature as the
switch point from linear to non-linear curve fitting. Since size-at-maturity was estimated
on the basis of visible evidence of egg-bearing, it was expected that changes in growth
rate occurred prior to such evidence as more energy is directed to preparation for
reproduction. For males an inflection point 16% larger than that of the females in the
same region, was used to reflect the functional maturity of males (Aiken and Waddy
1989, Waddy et al. 1995). This method was also used in current lobster stock assessment
models (ASMFC 2009).
20
Table 1.3. Parameters for size-at-maturity ogives and inflection point used in describing
growth increment for each region.
Female size‐of‐
maturity parameters Region Female size at 10% maturity Male inflection CL a
b
BOF 23.23 ‐0.214 98 114 GOM 21.21 ‐0.232 82 95 SNE 15.28 ‐0.206 64 74 Molt probability
Molt probability was estimated using the method of Chen and Kennelly
(1999). Estimates were partitioned by sex and size (Templeman 1940, Waddy et al.
1995). Lobsters were further grouped by days-at-large; immature lobsters were grouped
in 30 day bins; sexually mature lobsters in 365 day bins reflecting reduced molt
frequency. I calculated the proportion of each group molting over the period. The logistic
model below was used to describe the relationship between number of days-at-large and
proportion molting.
,
[1.11]
where Di is the number of days at large for the day group i, and a and b are parameters to
be estimated. Parameters, a and b, were estimated using the general linear model
function. The error structure is binomial because proportions are constrained between 0
and 1, and the logistic model link function “logit” was used. The number of days at large
at which 50% of the lobsters have molted can be estimated as:
21
D
,
[1.12]
where a and b are the estimated logistics curve parameters (Chen and Paloheimo 1994).
If there was no difference in molt probability between males and females, sexes
were combined. In the Gulf of Maine sexes were combined for size classes 20-39 and 4065 mm; in southern New England sexes were combined in the 20-39 mm size class. From
the smallest size classes (20-39 and 40-59 mm) in Gulf of Maine and Bay of Fundy, I
also excluded from the analysis lobsters that were tagged after the molting season had
ended and recaptured before the next one began. Including them would have rendered
unrealistically low growth rates.
The question of bias introduced by including or
removing these lobsters is examined further in the Discussion.
Probabalistic step-wise growth model
I initiated the step-wise growth model by assigning an age of 0 to lobsters at the
time of hatching. Hatching typically occurs in June in southern New England (Lund and
Stewart 1970, Bibb et al. 1983, Fogarty et al. 1983), July in the Gulf of Maine (Sherman
and Lewis 1967), and August in the Bay of Fundy (Campbell and Pezzack 1986, Cobb
and Wahle 1994). Young-of-year lobsters were collected and measured in the late
summer and fall. Thus lobsters of age class 0+ were assumed to be approximately 65
days old in southern New England, and 75 days in both Gulf of Maine and Bay of Fundy,
because of the longer development time in the cooler waters.
The individual-based modeling approach of Chen and Kennelly (1999) was used
to construct probabilistic step-wise growth curves (PSCG). This approach results in a
22
distribution of growth curves for which a mean, median, and confidence interval can be
calculated. The algorithm proceeds as follows (Figure 1.3):
(1) Choose a random start size from a normal distribution with the mean and
standard deviation defined by the length frequency analysis of age 0+ lobsters, Li, where i
is 1 to n and n is the number of molts by one lobster;
(2) Define age at sampling of 0+ lobsters at time of settlement survey;
(3) Choose a time step, D (in this study, if L<= size-of-maturity (SOM), D=30
days; if L>SOM, D=365) and determine whether or not D falls in a molting season
(summer and fall). If it is not in molt season, D is increased by time step until a molt
season is reached.
(4) When molt season is reached, the algorithm calculates the corresponding molt
probability, Pi, by the logistic molt probability equation [Eq. 1.11].
(5) Select a random number, q, from a normal distribution between 0 and 1. If q ≤
Pi, a molt occurs. If q>Pi a molt does not occur; D is then increased by a time step until a
molt occurs.
(6) Calculate the size increment for an individual of size Li based on size specific
growth factor [Eq. 1.7] if before maturity or [Eq. 1.8] after maturity, and with [Eq. 1.9] to
decide the size increment, ΔLi.
(7) Calculate the new size after the molt; Li+1 = Li + ΔLi and
(8) Replace Li with Li+1.
Repeat steps 2 through 6 until a maximum number of molts, n, is reached.
Because the start age of the first size is known, the growth curves estimated by this
method are expressed in terms of actual age instead of relative age.
23
Figure 1.3. Flow diagram of individual-based stepwise growth model. See text for
explanation of symbols.
Size transition matrix
Finally, a size transition matrix was estimated by using the results of the
individual-based probabilistic stepwise growth curve model. This was done by recording
the number of lobsters that molted from one size class to another after a specified amount
of time – in this case one year (Figure 1.4) . The matrix includes 300 5-mm size bins. The
17th size bin has a midpoint of 82.5 mm, which is harvestable size for all three regions.
The sizes of lobster were tallied for each size bin at the beginning and end of each year,
and transitional probabilities were taken as the proportion of the total number of lobsters
that have transitioned to each size bin.
24
Figure 1.4. Schematic diagram of size transition matrix shows the probability that an
individual in one size class will transition to subsequent size classes (S) within a year.
25
Results
Estimating von Bertalanffy Growth Parameters
Regional estimates of the von Bertalanffy growth curves by the Fabens or FordWalford method within the data size range are shown in Figure 1.5. Overall, the
estimated growth curves by these methods often result in extremely large size-at-infiniteage, Linf, and biologically unrealistic growth rates; for example very fast growth
compared to hatchery studies and conventional knowledge of lobster growth.
Figure 1.5. von Bertalanffy growth curves from tagging data in three regions. All curves
are derived by the Fabens method except the ones for males in SNE. Dashed lines are
females and solid are male.
In southern New England the Fabens method resulted in extremely fast growth
and unrealistically large size for males (not shown). Meanwhile, Fabens method
estimates for females were within the expected range of growth rate. For males, growth
26
curve parameters from the Ford-Walford method resulted in more reasonable results.
However, for males and females by both methods (Figure 1.5), early growth was
extremely fast, with lobsters reaching 50 mm by age 1.5 years. Growth rates for females
in BOF by the Fabens method were also faster than biologically expected. For males in
BOF and GOM growth rates were reasonable in the early years, but have unlikely high
growth rate at large sizes. By the Fabens method, growth rates for females in the GOM
were within the expected range of growth rate.
Estimating size-at-age of juvenile lobsters
Regional differences in lobster growth were evident in the size distribution of the
youngest lobsters. I provide the best fitting size distributions for each of the first four age
groups (age 0+ to 3+) in each of the three regions from the MULTIFAN modal analysis
(Figure 1.6). The best fitting model for each region consistently included age-classes with
variable standard deviation and variable K, Brody growth parameter. It was not possible
to resolve age groups greater than age 3+ by MULTIFAN because of lack of clear modes
in the size distribution.
The separation in size among the resolved age classes increased from north to
south, such that 2+ lobsters in southern New England were estimated to be almost twice
as long as those in the Bay of Fundy (Figure 1.6, Table 1.4). As might be expected of the
region with the longest growing season, the variation in size at a given age was greatest
in southern New England. In general, although the variability in absolute size increased
with age, the coefficient of variation declined as lobsters grew. It must be cautioned that
uncertainty in these estimates of size and variability increases with age.
27
Figure 1.6. Size frequency histograms of lobsters from suction sampling with best fitting
curves in red corresponding to age classes 0+ to 3+ (top to bottom) for Bay of Fundy
(BOF), Gulf of Maine (GOM), and southern New England (SNE). See Table 1.4 for
corresponding statistics.
28
Table 1.4. Mean, standard deviation, and coefficient of variation for first 4 age-classes
(0+, 1+, 2+ and 3+) of lobsters in 3 thermal regions as determined by modal analysis of
size frequency data by MULTIFAN.
Region BOF GOM SNE Age class
0+
1+
2+
3+ Mean 7.73
12.53
17.63
22.59 SD
1.51
1.6
1.69
1.79 CV
0.20
0.13
0.10
0.08 Mean 9.29
14.8
20.19
25.47 SD
1.58
1.68
1.79
1.9 CV
0.17
0.11
0.09
0.07 Mean 9.75
20.96
31.25
40.7 SD
2.25
2.82
3.48
4.23 CV
0.23
0.13
0.11
0.10 Molt increment
From the evaluation of tagged lobsters, the growth factor, growth increment per
molt as a percent of initial size, tended to increase with body size prior to maturity and
declined after maturity (Tables 1.5 and 1.6; Figure 1.7). Sex related differences in molt
increment did not become evident until after maturity, when the growth factor began to
decrease more dramatically in females than males (Tables 1.5 and 1.6). The post-maturity
decline in molt increment occurred at a smaller body size and was most dramatic in
southern New England.
The functional relationship of between initial size and molting growth factor was
generally linear and positive prior to maturity, but non-linear and negative after maturity
(Figure 1.7; Table 1.7). Also, while growth factors were similar between the sexes prior
to maturity, they tended to diverge afterward, although data were especially limited for
reproductive sizes in the Gulf of Maine (Figure 1.7, Table 1.7).
29
Table 1.5. The mean and 95% confidence intervals for growth factor and growth
increment by size group and sex for lobsters with one molt. Size of maturity is indicated
for males and females in each region. Note the size bins differed slightly between regions
due to data constraints
Region
Males
Females
growth factor growth growth factor growth size (%)
increment (mm)
(%)
increment (mm)
groups (mm) mean lower upper mean lower upper mean lower upper mean lower upper SOM
95% 95%
95% 95%
95% 95%
95% 95%
60‐79
80‐99
BOF 100‐119
120‐139
140 +
20‐39
40‐59
GOM
60‐79
80‐99 100 +
20‐39
40‐59
SNE
60‐79
80‐99
18%
17%
16%
17%
15%
12%
14%
16%
15%
16%
14%
15%
14%
11%
11%
10%
8%
11%
10%
8%
7%
10%
13%
13%
9%
10%
8%
7%
23%
22%
22%
23%
21%
19%
19%
20%
16%
18%
19%
20%
20%
15%
13.0
15.3
17.9
21.9
22.7
4.0
6.6
10.8
13.7
17
4.4
8.2
9.9
9.0
8.0
8.7
9.0
14.1
15.0
3.0
3.0
7.0
12.1
14.3
3.0
4.7
6.0
6.0
17.0
20.0
23.1
29.9
31.0
6.0
10.0
14.0
15
18.8
6.0
11.7
14.8
11.7
17%
16%
12%
9%
6%
13%
14%
15%
14%
13%
13%
13%
10%
8%
11%
8%
7%
5%
4%
9%
8%
8%
9%
12%
8%
8%
5%
4%
21%
21%
20%
15%
12%
20%
20%
19%
18%
15%
19%
19%
14%
11%
12.4
13.6
12.8
10.9
9.6
4.2
7.2
10.0
12.2
15.5
4.2
6.7
7.1
6.5
Table 1.6. Average growth factor (%) by region before and after maturity.
Average relative growth before maturity
after maturity (%) M
F
M
F BOF 17% 16% 16% 7% GOM 14% 14% 16% 13% SNE 15% 13% 13% 9% 30
8.8
7.0
7.9
6.0
6.0
3.0
3.9
5.0
7.8
13.0
2.5
3.4
4.0
4.0
16.0
18.7
22.0
19.0
16.8
7.0
11.0
14.0
15.0
17.9
6.6
10.0
10.0
10.0
F = 98
M = 114
F = 82
M = 95
F = 64
M = 74
Table 1.7. Parameters for the relationship of growth factor to pre-molt carapace length
(mm) for size groups greater than and less than the size at 10% maturity. The standard
deviation was used in the step-wise growth model to add variation to the predicted
increment.
Region
Sex
Males
BOF
Females
Males
GOM
Females
Males
SNE
Females
size group
< 114
>=114
< 98
>= 98
< 95
>= 95
< 82
>= 82
< 74
>= 74
< 64
>= 64
N
502
151
488
726
327
15*
311
50*
274
244
73
525
31
a
0.16
2.30
0.15
1176.41
0.09
0.43
0.11
0.41
0.15
876.99
0.09
1645.17
b
0.0001
-0.5422
0.0002
-1.9698
0.0009
-0.2292
0.0006
-0.2329
0.0001
-1.9923
0.0011
-2.2288
SD
0.0306
0.0266
0.0294
0.0235
0.0267
0.0162
0.0251
0.0219
0.0349
0.0293
0.0374
0.0246
2
R
0.0059
0.0821
0.0040
0.4628
0.2337
0.0521
0.1165
0.0060
0.0013
0.0834
0.1132
0.3736
P
0.1015
0.0004
0.1628
<0.0001
<0.0001
0.4131
<0.0001
0.5868
0.5842
<0.0001
0.0036
<0.0001
Figure 1.7. Relationship between growth factor (growth increment/initial size) and
carapace length measured at time of tagging.
32
Molt probability
In general, with increasing body size the probability of molting decreased (Figure
1.8). Parameters of the logistic equation for molt probability as a function of days at large
are presented in Table 1.8 for each sex and size group. After the onset of maturity males
were generally, but not always more likely to molt than females at a given size.
33
Figure 1.8. Molt probability curves as a function of days at large for Bay of Fundy
(BOF), Gulf of Maine (GOM), and southern New England (SNE) by size class (carapace
length in mm) and sex. Curves are separated by sex for reproductively mature size groups
(males solid line, females dashed line, where sexes are combined there is only one solid
line).
34
Table 1.8. Molt probability parameters by size class, sex and region.
Region
BOF
size group
60-99
100 - 129
130 +
GOM
20-39
40-65
66-79
80-99
20-39
40-65
SNE
66-79
80-99
SEX
Males
Females
Males
Females
Males
Females
Combined
Combined
Males
Females
Males
Females
Combined
Males
Females
Males
Females
Males
Females
N
765
693
310
1619
150
1233
468
843
586
557
861
960
132
152
127
368
471
191
1458
a
-2.560
-2.156
-3.654
-3.461
-2.287
-4.392
-1.687
-1.951
-3.556
-3.355
-5.316
-5.177
-1.873
-2.216
-2.358
-2.880
-2.012
-3.542
-3.180
b
0.0147
0.0149
0.0122
0.0107
0.0081
0.0109
0.0183
0.0230
0.0274
0.0200
0.0124
0.0137
0.0480
0.0184
0.0180
0.0131
0.0106
0.0091
0.0069
D50
175
145
299
325
281
404
92
85
130
167
428
378
39
121
131
219
190
389
460
Stepwise growth model
Growth trajectories generated by 1000 simulation runs of the stepwise growth
model for male and female lobsters varied by region (Figure 1.9). Growth rates declined
more dramatically in females after maturity than in males, especially in SNE where
maturity is reached at earlier and at a smaller size than in GOM or BOF. In the BOF
region, there was no change in the growth trajectory for males after maturity. Variation in
growth rate was greatest in the GOM region. The mean size-at-age estimated for the 1+ 3 + age groups from the size frequency analysis compares favorably with the stepwise
growth model-based mean estimates.
35
36
Figure 1.9. Results of the stepwise growth model simulations for BOF, GOM, and SNE regions (left to right). Mean (solid
line) and 95% confidence intervals (shaded area between dashed lines) derived from 1000 simulations are shown for males
(dark grey) and females (light grey).Black points on each graph represent the length-frequency derived mean-size-at-age
estimates for the ages 0+, which was used to start the simulations, 1+, 2+, and 3+. Horizontal lines denoted by “m” and “r”
indicate female size at 10% maturity and harvestable size (82.5 mm) respectively.
My estimates of age-at-recruitment to the fishery by the stepwise growth model
are consistent with previous estimates. Males are estimated to enter the fishery in BOF at
twice the age as they do in SNE. The difference is not as great for females. Within a
region, males and females reach the US harvestable size of 82.5 mm at approximately the
same age (Table 1.9). In the two cooler regions this is likely due to the fact that male and
female functional size-at-maturity is not reached until after 82.5 mm. The size at which
10% of the females are mature in GOM is 82 mm, however the effects of maturity are
only seen in larger lobsters. In SNE, the 10% size-at-maturity for females is 64 mm,
however, males and females reach the 82.5 mm benchmark at the same age because
growth for both sexes significantly slows down by this size. Between regions, lobsters
recruit to the fishery at an earlier age in the warmer southern region and progressively
later towards the cooler north.
Table 1.9.Mean age-at-recruitment to fishery (minimum harvestable size 82.5 mm) and
upper and lower confidence intervals for all regions by sex. The range of years estimated
within the confidence intervals is also shown.
Region
BOF
GOM
SNE
Sex
M
F
M
F
M
F
Average age Lower (years)
95%
9.0
6.1
8.4
5.3
7.7
4.7
7.6
4.7
4.5
2.6
5.5
3.1
37
Upper 95%
12.4
11.7
9.6
10
6.4
7.5
Range (# of years)
6.3
6.4
4.9
5.3
3.8
4.4
Growth transition matrix
The probability of growing from one size category to the next in one year varies
by size class, sex, and region. Examples of the transitions are given below for lobsters at
four different initial sizes (Figure 1.10). The full transition matrix is given in the
Appendix. Lobsters starting at 7.5 mm produced only a single mode representing more
than one molt in all regions (Figure 1.10a-b). Separate probability modes could not be
resolved for the smallest lobsters in any region because the 5 mm size bins exceeded the
size of initial growth increments. In all regions, as lobsters grew larger, the curves spread
out and there were several, usually two, probability modes. Because growth increments
vary, none of the modes were very distinct.
For lobsters starting at 42.5 mm multiple modes began to emerge that likely
correspond to molt increments (Figure 1.10c-d). In Bay of Fundy most lobsters either did
not molt or molted once, with a smaller proportion molting twice or rarely three times a
year. In the Gulf of Maine, in contrast, lobsters mostly molted two or three times a year;
and in southern New England, where lobsters of this size are within a molt or two of
sexual maturity, males molted one to three times, whereas most females molted only once
or twice a year.
At the starting size of 82.5 mm, the modes in the probability curves were more
distinct and were more commonly bi- or trimodal, the first mode corresponding to those
of this size group that did not grow over the year (Figure 1.10e-f). Only in the Bay of
Fundy where 82 mm lobsters were not yet sexually mature, did we see a third mode
corresponding to a second molt during the year.
38
At the largest size, 122.5 mm and for all regions, the two modes strongly
represented no annual molt or one molt, respectively (Figure 1.10g-h). Lobsters in the
Bay of Fundy and the Gulf of Maine were similarly divided about equally between those
that do not molt or molt once a year. In SNE, by contrast only a small proportion of
males and an even smaller proportion of females molted annually. It is important to note
that the probability curves for this size group for the Gulf of Maine and southern New
England are beyond the range of the available data, are purely modeled estimates, and
therefore, must be interpreted with caution.
39
Figure 1.10. Annual probabilities of male and female American lobsters growing from
one size class to another for BOF, GOM, and SNE from an initial carapace lengths of 7.5
mm (a-b), 42.5 mm (c-d), 82.5 mm (e-f), and 122.2 mm (g-h). Curves, based on the size
transition matrix derived from the stepwise growth model, are compared.
40
Discussion
This study is the first to integrate two size-based modeling approaches, modal
analysis and individual based stepwise modeling, to overcome the challenge of modeling
growth for crustaceans which lack morphological age markers. Lobster growth has most
often been modeled using the von Bertalanffy growth function (Table 1.10) (reviewed by
Wahle and Fogarty 2006), but this approach does not realistically describe lobster growth
over the full range of sizes. Observed differences in early growth and the effects of the
onset of maturity in lobsters appear to be the reason for the poor fit.
The von Bertalanffy growth trajectory slows with increasing size. But in the
American lobster growth is initially an increasing function of size prior to maturity and
only declines after maturity (compare Figure 1.5 to Figure 1.9). Despite this difference in
growth trajectory, the von Bertalanffy method is often used for lobsters (e.g. Ennis 1980,
Krouse 1977, Russell 1980). The step-wise growth curve models developed here capture
these differences more realistically.
41
Table 1.10. von Bertalanffy growth function parameter estimates for American lobsters
from north to south including estimates from this study compared to those of other
studies in the same geographic region. Values from earlier studies were used as a range
for estimating parameters in this study.
Location
Sex
Newfoundland
Bay of Fundy
K
Linf
t0
size range
N
Males
0.390
105.0
‐0.800
50‐94
?
Females
0.240
112.0
‐0.690
56‐106
?
Males
0.065
281.0
0.760
67‐175
?
Females
0.089
207.0
0.420
67‐175
?
Males
0.036
476.11
0.08
62‐175
1508
Females
0.14
177.24
0
60‐197
3822
266.77
‐0.7725
80‐129
241
‐0.096
combined 0.04785
Maine
combined
Reference
Fabens
Ennis 1980
product of annual molt increment & probability of molting
Campbell 1983
Fabens
THIS STUDY
13480
polymodal analysis of length frequency data
Thomas 1973
81‐100
26
Ford‐Walford
Krouse 1977
Fabens
THIS STUDY
Males
0.027
500
‐0.019
20‐107
1726
Females
0.136
146.27
‐0.032
21‐111
1675
0.0634
253
‐0.5485
?
?
?
Fair 1976
Males
0.09361
189.55
‐0.29012
?
?
Females
0.09664
184.59
‐0.19756
?
?
polymodal analysis of length frequency data
Russell et al 1978
Males
0.636
99.65
24‐95
16
Ford‐Walford
Females
0.557
93.96
23‐110
2151
Fabens
Massachusetts combined
Rhode Island
0.087
method
‐0.09
THIS STUDY
Modal analysis provided starting estimates of size-at-age for the youngest
lobsters, and produced results consistent with previous studies examining the relationship
of growth rate and temperature. In general, for young lobsters, a longer period of warmer
water results in a prolonged settlement season as well as a prolonged growing season
This leads to differential growth depending on regional temperature regime and a wider
scope for growth. For example, field studies in the SNE region have shown that
postlarvae that settle earlier in the season can grow 30-50% larger in carapace length than
late settlers by the end of the growing season (James-Pirri et al. 1998). Furthermore,
because lobsters grow faster in warm water there is more scope for variation in size
(Aiken 1980, James-Pirri and Cobb 2000). Of the regions in this study, the settlement
season and growing season in SNE are longer than in the northern cooler regions.
42
Although the GOM has a shorter settlement season and a cooler regime than SNE, the
shallow thermocline introduces a wide range of temperatures and therefore more
opportunity for variable growth than in the even cooler and thermally more uniform BOF.
Size-at-age estimates from the modal analysis thus provided a realistic starting point for
the regionally specified stepwise models, as well as an independent comparison of sizeat-age for ages 0+, 1+, 2+ and 3+.
Molt increment was described by a “broken stick” approach due to complex
relationship of intrinsic and extrinsic factors, the most striking of which was maturity. As
shown in other studies, molt increment depends on size, sex, and temperature (Fogarty
1995, Comeau and Savoie 2001) and maturity (Cadrin 1995). Thus a regional “broken
stick” relationship, with a switch from a linear to a non-linear function at the size-atmaturity, was supported by the data and provided the most realistic estimates of molt
increment. This “broken stick” approach was similarly employed in the American
Lobster Stock Assessment (ASMFC 2009).
Molt increment decreased dramatically with the onset of sexual maturity,
especially for females. Upon reaching sexual maturity, females expend a greater
percentage of energy towards reproduction and less towards somatic growth, resulting in
smaller growth increments (Wilder 1963, Ennis 1972, Hartnoll 1982). This was most
apparent for BOF and SNE where mature lobsters were well represented in tagging
studies. In these two regions, females have similar steeply decreasing curves for molt
increment by size, although differing by about 40 mm; the temperature-related betweenregion difference in size-at-maturity. Estimates of this relationship for GOM would
benefit from additional data points for mature lobsters.
43
Growth was not always faster in warmer regimes as might be expected. For
example, despite the cooler temperatures, BOF lobsters boasted the largest average
growth increments, relative to SNE and GOM. Most striking is the regional difference in
growth after the onset of maturity. Despite the warmer temperatures, mature lobsters in
SNE had the longest intermolt periods. This dramatic slowdown of growth may reflect
the high cost of reproduction or increasing cost of larger body size in an environment
nearing physiologically stressful (pejus) temperatures (Pörtner et al. 2007). Growth
slowed more rapidly in southern New England after maturity not only because of longer
intermolt periods, but also because of smaller growth increments per molt. Typically,
after maturity molt increment declines, and the effect is stronger in females than males.
This effect was especially apparent in southern New England, where the two sexes were
more similar in the reduction of growth increment. Similar steeply decreasing molt
increment trajectories for both males and females have been observed in the Gulf of St.
Lawrence (Comeau and Savoie 2001), a region where summer water temperatures are
similar to SNE. The interaction of temperature and sex effects on post-maturity growth
trajectories remains poorly understood, and needs to be incorporated in future growth
modeling.
Estimates of the probability of molting can be greatly affected by the timing of
tagging and recapture. When tagged in the beginning of the molt season and then
recaptured after a short time at large, molt probability may be over-estimated; but when
tagged at the end of the molting season and recaptured before the next opportunity to
molt, molt probability may be greatly under-estimated. For example, for small lobsters in
GOM, the molt probability was greatly increased, well beyond what is biologically
44
expected, when all lobsters were used to model molt probability. This problem was
resolved in two ways: (1) by not including individuals that were tagged immediately after
the molting season and recaptured before the peak of the next molt season, and (2) by
grouping individuals into 30-day bins I assumed this large interval should reduce error
(Chen and Kennelly 1999).
The effects of the regional differences in molt increment and molt probability are
reflected in the resulting growth curves and the size-transition matrix. Growth in
juveniles begins fastest in SNE, where intermolt time is reduced, despite smaller molt
increment. However, an early onset of maturity dramatically slows growth. In contrast, in
GOM and BOF growth starts off slow because the cooler temperatures lead to longer
time between molts, even though the molt increments are larger. In crustaceans it is often
the case that the effect of molt frequency is proportionally greater than the effect of molt
increment (Hartnoll 2001). Because maturity is delayed to a larger size and the
subsequent decline in growth rate is less severe, larger body sizes are seen in the cooler
regions. While the mechanisms are not fully understood (Blackburn et al. 1999¸
Angilletta et al. 2004), larger body size and delayed maturity in higher latitudes and
smaller body size and earlier maturity at lower latitudes is a trend not limited to
crustaceans but one that is observed across taxa (Blackburn et al. 1999, Hartnoll 2001,
Angilletta et al. 2004).
Age estimates are possible with this model because I started with a known size-atage. Since estimates of size-at-age 0+, 1+, 2+, and 3+ derived from modal analysis,
correspond well with model estimates, it is encouraging that estimated growth trajectories
from the stepwise model generally agree with these estimates. Sources of error in
45
estimates of the age-at-recruitment to the fishery can derive from limited numbers of
tagged lobsters in the larger size ranges in GOM and SNE. Growth trajectories of larger
lobsters are therefore less certain. This deficiency of large lobsters in the data is perhaps a
result of harvesting, lobsters moving offshore with larger size, or natural mortality. In the
northernmost region, growth estimates for large lobsters are also to be used with caution
because the molt probability described by available data result in molting more frequently
than might be biologically realistic. In all regions, a better description of molt increment
and molt probability at the smallest sizes would also increase the power of the model, as
here I must extrapolate using parameters based on the larger size classes. From this
model the resulting growth transition matrices describing the transition from one size
class to another can be easily modified by changing the parameters in the model.
Because crustaceans have no known chronological age markers, growth models
are dependent on body size-related measurement such as molt increment and size-specific
molt probability. While further research is in progress to find a morphological age
marker, lobster scientists continue to rely on size-based methods. These methods are
highly dependent on the quality and breadth of the data. The stepwise growth model
presented here is easily to update and provides estimates of size and variability at
absolute age. By using region-specific parameters I examine how differences in sizespecific molt increment and molt probability result in differences in growth. Here I have
shown that growth is very different between the three regions of contrasting
environmental conditions. The exact mechanism that causes this difference is yet to be
determined, although temperature difference is a likely candidate. In the next chapter
environmental forcing by temperature will be further investigated.
46
Chapter 2
DEVELOPING A DEGREE-DAY MODEL FOR LOBSTER GROWTH
Abstract
Growth in ectotherms is highly temperature dependent. In crustaceans the effects
of temperature are readily observed throughout the molt process (Hartnoll 1982, Aiken
and Waddy 1986). Temperature variability therefore adds complexity to the already
challenging task of modeling growth in crustaceans, which, as a group, do not retain
morphological age-markers. A growth model incorporating temperature effects would be
especially valuable to modeling population dynamics of commercially exploited species.
The American lobster, Homarus americanus, is one of the most commercially important
species in the US Northeast and Atlantic Canada.
Ranging from nearshore
Newfoundland to offshore North Carolina, the species spans the steepest latitudinal
gradient in sea surface temperature on earth. Here I build on a probabilistic stepwise
growth model developed in Chapter 1. In this chapter I modified it to include temperature
variability for three thermally distinct regions within this range, from the cool, wellmixed regime of the Bay of Fundy, Canada, to a warm, summer-stratified regime of
southern New England shelf waters, USA. The growth model integrates two approaches
to determining growth rates and size-at-age: (1) a length-frequency approach, which
results in a known size-at-age of the first three year classes of benthic lobsters from long
term diver-based sampling, and (2) a mark-recapture based approach, whereby molt
frequency and molt increment are estimated from tagging studies. Temperature effects
47
are incorporated by determining the probability of molting as a function of growing
degree-days (GDD, ºC*day), based on regional temperature time series and the speciesspecific metabolic requirements of growth. Average daily temperature is incorporated in
the simulation to predict the molt process through time. If temperature were the major
determinant of regional differences in growth, I would expect the molt probability curves
plotted against degree-day to remove differences that are apparent when they are plotted
simply over time. I found, however, that “correcting for” thermal effects by the degreeday method does not entirely explain regional differences in growth, suggesting other
environmental or heritable influences may be at work. However, growth at alternate
temperatures can be predicted by this model assuming that the molt probability
relationships are fixed within a region. Understanding the influence of temperature and
other factors on growth would provide more biological realism and generality to
population dynamic models, and will be especially relevant in the context of a changing
climate
Introduction
Practically all aspects of ectotherm behavior and physiology are affected by
temperature; from locomotion, sensory input, and immune function to rates of feeding
and growth (Huey and Stevenson 1979, Angilletta et al. 2002). For marine decapod
crustaceans, regional differences and variability in growth are most often attributed to
environmental variability. Among environmental factors such as photoperiod, food, and
population density, temperature is cited as having the greatest influence on growth rate
(Waddy et al. 1995, Hartnoll 2001). Thus, for species that experience large gradients in
48
temperature over their geographic range, regional differences in size-at-age can be
dramatic. Because growth varies regionally, it impacts recruitment to the fishery, age at
sexual maturity, and longevity (Hilborn and Walters 1992, King 1995). In turn, growth
variability
has
important
implications
for
sustainable
fisheries
management.
Incorporating temperature into growth models, can therefore refine estimates of
individual growth rate (Brylawski and Miller 2003, Neuheimer and Taggart 2007), and
improve predictions of growth in a changing climate.
The American lobster, Homarus americanus, is a commercially important species
spanning a geographic range from coastal Newfoundland, Canada in the north to the
offshore canyons of the continental shelf off North Carolina, USA (approximately 36 ºN
to 54 ºN). This range crosses the steepest latitudinal gradient in sea surface temperature
on the planet. The gradient is maintained by the confluence of cold polar waters of the
Labrador Current from the north and warm Gulf Stream waters from the south (Colton
and Stoddard 1972, Brown and Gaskin 1988, Townsend et al. 2004). Summer thermal
stratification varies regionally, and can be very pronounced such as areas of the southern
New England shelf and southern Gulf of St Lawrence to near complete vertical mixing,
such as in the Bay of Fundy and Georges Bank. The bathymetric range of the American
lobster varies accordingly from 0 to 50 m in the northern part of its range to as great as
700 m in the south (Lawton and Lavalli 1995).
Growth and behavior of all life stages of lobsters are influenced by temperature
(Waddy et al. 1995, Wahle and Fogarty 2006) For benthic juveniles and adults, molt
frequency increases with increasing temperatures between ~5 ºC and 20-25ºC. At
temperatures below 5ºC, metabolism slows to the point that the molt cycle and therefore
49
growth is inhibited, while temperatures above 25 ºC are physiological stressful and lethal
(Waddy et al. 1995). While molt frequency increases with increasing temperature within
this range, molt increment decreases. This decrease in increment may not be directly
related to temperature so much as the shorter intermolt period limiting the accumulation
of energy reserves that can be dedicated to growth (Hartnoll 1982).
The onset of sexual maturity has a slowing effect on growth and is itself
temperature dependent (Hartnoll 1982, Little and Watson 2003). After maturity growth
slows significantly as more energy goes into reproduction and secondary sex
characteristics such as cheliped and abdomen allometry. For the American lobster,
warmer environments accelerate gonad maturation more than somatic growth; therefore,
in warmer regimes reproductive maturity comes at smaller sizes and an earlier age than in
colder regimes (Estrella and McKiernan 1989, Comeau and Savoie 2001). This
interaction of reproductive development and somatic growth adds to the regional
variation in size-at-age and allometry (MacCormack and DeMont 2003).
In addition to temperature effects, growth rate also varies with size and sex. In
general, growth rate in lobsters declines proportionally with increasing size as molts
become less frequent (Waddy et al. 1995). Prior to maturity there is no difference
between sexes in the intermolt period, however after maturity there is a marked increase
in females, likely reflecting the greater cost of reproduction for females. In general, molt
increment as a percentage of pre-molt size, also referred to as relative growth, either
increases or remains constant with increasing size until maturity, at which time it begins
to decrease dramatically (Hartnoll 1982, Bergeron et al. 2011). The molt increment is
50
also comparable between sexes before maturity, but declines more for females after
maturity (Wilder 1963, Ennis 1972, Hartnoll 1982).
Limitations of current growth models include the exclusion of physiologically
meaningful environmental variables.
Conventional growth models used in stock
assessment, such as the von Bertalanffy growth function and molt-process models, often
ignore environmental influences (Brylawski and Miller 2003, Neuheimer and Taggart
2007). Very few models of lobster growth have incorporated temperature or seasonality
(Tully et al. 2000). On the other hand, temperature has long been included in agriculture
and entomology growth and development modeling as the time-based integral of the heat
available for growth, as measured by growing degree-days (GDD, ºC*day) (Neuheimer
and Taggart 2007). The GDD metric scales growth and development to the underlying
physiological processes (metabolism and enzymatic reactions) that drive ectothermic
growth and development. More recently GDD has been used successfully to describe
growth and development of fish and crustaceans (Neuheimer and Taggart 2007), and has
been incorporated in models of growth (Brylawski and Miller 2003, Smith 1997).
The growing degree-day approach allows for the effects of time and temperature
on growth to be expressed interactively (Neuheimer and Taggart 2007). A growing
degree-day is calculated as the difference between daily average ambient temperature,
Tamb, and the physiological minimum temperature, Tmin, required for growth. Where
temperatures are below the Tmin, no degree days are accumulated. For temperatures above
the physiological maximum, where growth rates slow down or mortality increases,
growing degree day equals the thermal maximum, Tmax. Expressing growth as a function
of degree-days can help differentiate thermal influences. For example, laboratory studies
51
with the blue crab Callinectes sapidus and western rock lobster Panulirus cygnus, have
shown that growth trajectories that diverge under different temperature regimes when
plotted on a scale of calendar days converge when plotted on a scale of degree-days
(Smith 1997).
In this paper I present an individual-based probabilistic stepwise growth model
that was modified to incorporate the growing-degree-day approach. Molt increment and
molt frequency were parameterized from tag-recapture data in the field in conjunction
with daily bottom temperature time series. Molt frequency was expressed in terms of
specific size-dependent molt probability curves, and thus accounts for variability in
individual growth. Because a wide range of size groups was used to parameterize the
model, temperature effects on size-at-maturity are included for both molt probability and
molt increment relationships. A size distribution of lobsters of a known age from field
collected data and length frequency analysis used as starting size allows for estimating
growth rate by true age and includes variation in initial size-at-age.
Recently the degree-day method has been applied to growth of other crustacean
species including Dungeness crab (Metacarcinus formerly Cancer magister), blue crab
(Callinectes sapidus), and pronghorn spiny lobster (Panulirus penicillatus) (Chang et al
2011). The work presented here is the first to apply the degree-day method to growth of
Homarus americanus using empirical data to parameterize the model.
Methods
The algorithm for the growing degree-day model, to a large extent, was the same
as that for the regionally specified growth model presented in Chapter 1. I developed the
52
model for three regions: Bay of Fundy (BOF), Gulf of Maine (GOM), and southern New
England (SNE) (Figure 2.1). Length frequency data from suction sampling of lobster
nurseries were used to determine the mean size-at-age of the earliest benthic lobsters.
Mark-recapture data were used to evaluate molt increment and molt probability of older
lobsters. Bottom temperature time series for each region were used from available
sources to determine molt probability by growing degree-day.
Study regions and oceanography
The oceanographic properties of the three regions of this study contrast markedly
(Figure 2.2). The Bay of Fundy (BOF) is well-mixed throughout the year. This results in
temperatures only slightly above 10°C during the warmest part of the year. The other two
regions become thermally stratified during the warmer months. In Gulf of Maine (GOM)
a strong, shallow thermocline, forms at a depth of 15 – 25 m by late summer and remains
through the fall. Here the surface waters can warm to 16-18°C while below the
thermocline temperatures remain below 8°C. It is important to note that despite the cooler
surface temperatures in the BOF, midsummer temperatures below the thermocline in the
GOM are considerably cooler than the same depth in the BOF. In southern New England
(SNE), surface temperatures can rise above 20°C during the peak of the warm season, and
the thermocline forms at a greater depth of 30 to 40 m. Summer temperatures in southern
New England bays and estuaries regularly approach levels that are thermally stressful to
lobsters.
53
Figure 2.1. Study regions from north to south: Bay of Fundy (BOF), Gulf of Maine
(GOM), and southern New England (SNE). Tagging study and settlement index sites
used in this study indicated by black squares and open circles, respectively. Climatology
(Figure 2.2) was modeled for waters within the three study regions (rectangles).
54
Temperature time series
Seasonal temperature profiles from the Department of Fisheries and Oceans
(DFO),
Canada’s
Hydrographic
Climate
Database
(http://www.mar.dfo-
mpo.gc.ca/science/ocean/database/ doc2006/clim2006app.html) described the average
seasonal thermal properties of each region (Figure 2.2). This database supplied
temperature profile data from various oceanographic cruises from 1985-2004 over a
depth range from 0 to 100 m at 1m (± 0.5m) intervals within defined geographic range
(shown in Figure 2.1: southern New England (SNE); 40°52.2' N to 41° 36.0' N and 70°
25.8' W to 73° 33.0' W, Gulf of Maine (GOM); 43° 19.8' N to 44° 4.2' N and 69° 13.2' W
to 70° 37.2' W, and Bay of Fundy (BOF); 44° 30.0' N to 45° 30.0' N and 64° 45.0' W to
67° 15.0' W).
Additional bottom temperature time series corresponding to the date and
approximate depth of lobster mark-recapture data were used to parameterize the sine
function describing regional annual temperature (Figure 3a). These time series were also
used to calculate cumulative temperature (Figure 3b). In southern New England, bottom
temperature was recorded weekly by the University of Rhode Island bottom trawl survey
conducted weekly at Whale Rock at the mouth of the Narragansett Bay (41°26.3' N,
71°25.4' W) between 15 and 17 m depth from 1977 – 2005. Because daily temperatures
were not available, the single weekly reading was used for all the days of the same week.
For the Gulf of Maine, two temperature regimes were used because the markrecapture data straddled the steep and relatively shallow thermocline. Thus, the
contrasting growth trajectories obtained depending on where lobsters live were
represented. The above-thermocline temperature time series was represented by 10 m
55
depth, and the below-thermocline time series was for 20 m. The 10 m temperature data
were taken from a monitoring station at Maine Department of Marine Resources (DMR)
in Boothbay Harbor, Maine (43°50.67' N, 69°38.50' W), and the 20 m data are from Gulf
of Maine Ocean Observing System (GoMOOS) buoy E01 on the Central Maine Shelf
(43° 42.88' N, 69° 21.47' W) (www. gomoos.org).
Observed temperature data for the mouth of the Bay of Fundy, near Grand
Manan Island, were available for the years 1979-1997. This data set consisted of several
sampling locations within Canadian Lobster Fishing Areas (LFAs) 36, 37 and 38, with an
average depth of 15 m. Gaps in time series were filled by modeling the average yearly
temperature using a fitted sine function. Smaller gaps were filled by using the nearest
previous temperature.
In all regions, the bottom temperature time series at depth compared favorably to
seasonal temperature profiles (Figure 2.2) available from Canada DFO.
Modeled temperature
To model the annual temperature cycle, the observed daily temperature time
series were fitted by the sinusoidal function [Eq. 2.1] to obtain regionally specified
parameters.
[2.1]
The seasonal average minimum and maximum temperature (min and max, respectively)
from the observed temperature time series were used to approximate the amplitude, A,
and the vertical shift, h.
[2.2]
56
Figure 2.2. Seasonal changes in thermal stratification within boundaries of study regions
denoted in Fig. 2.1. In GOM, two depths were used to model lobster growth shown by
arrows, (a) 10 m and (b) 20 m. Data represent 10-year mean from 1995 – 2004. SNE
study area does not extend greater than 60 m. (Source: Canada Department of Fisheries
and Oceans, Hydrographic Climate Database http://www2.mar.dfompo.gc.ca/science/ocean/sci/sci-e.html taken at 1m (± 0.5m) intervals).
57
[2.3]
With period equal to one year (365 days), the angular frequency, k, was calculated.
[2.4]
Then the phase shift, c, was calculated.
[2.5]
These estimated parameters were included in Eq. 2.1 for time, t, in days and compared to
the time series of observed daily temperature over a year averaged over 10 years. A
subroutine in Microsoft Excel Solver was then used to minimize the sum of the least
squares by recalculating A, h, k, c and the day correction factor, cf. The parameters for
this function were included in the growth model to estimate the regionally specified daily
temperature, and thus calculate growing degree-days accumulated since the previous
molt.
58
Figure 2.3. Annual temperature cycles for each region (a) were produced by fitting a sine
function to observed temperature time series and were then used to calculate (b)
cumulative growing degree-days (GDD). Note that the Bay of Fundy cumulative GDD
falls between the shallow and deep GDD for the Gulf of Maine.
Growing degree days
For this study a growing degree-day (GDD) was defined as the daily average
temperature, Tj, expressed as the number of degrees between predetermined minimum
and maximum threshold temperatures (Tmin and Tmax) required for growth [Eq. 2.6]. I
used 5°C as the minimum temperature for lobster growth because below this temperature
molt induction is strongly inhibited (Aiken 1980). I assumed this threshold was the same
for all regions, although this assumption may warrant testing. For the model I assumed a
thermal maximum (Tmax) of 20°C, above which growth rate stays the same. This
assumption also warrants further testing because growth rate may actually begin to
59
decrease at temperatures higher than the maximum or even before the maximum (Pörtner
2001). The growing degree-days is calculated as,
[2.6]
where,
,
,
By this formula, additional degrees above the thermal maximum are not accumulated,
and therefore do not accelerate growth. Cumulative growing degree-days were then
taken as the sum of degree days over the time interval of interest.
Evaluating growth in early juveniles: length-frequency analysis
Length frequency data from annual diver-based suction sampling were analyzed
by modal analysis to give the mean size-at-age and standard deviation for known age
classes of early benthic lobsters up to an age of 3 years (Table 2.1; Chapter I Table 1.4).
This was done using program MULTIFAN which determines the best fitting normal
distribution curve around each of multiple modes in size frequency data. This method
was described in detail in Chapter 1.
60
Table 2.1.Mean carapace length (mm), standard deviation, and coefficient of variation for
first four age-classes (0+, 1+, 2+ and 3+) of lobsters in three thermal regions as
determined by modal analysis of size frequency data by MULTIFAN (from Chapter 1).
Region SNE GOM BOF Age class
0+
1+
2+
3+ Mean 9.75
20.96
31.25
40.7 SD
2.25
2.82
3.48
4.23 CV
0.23
0.13
0.11
0.10 Mean 9.29
14.8
20.19
25.47 SD
1.58
1.68
1.79
1.9 CV
0.17
0.11
0.09
0.07 Mean 7.73
12.53
17.63
22.59 SD
1.51
1.6
1.69
1.79 CV
0.20
0.13
0.10
0.08 Evaluating growth in older juveniles and adults: mark-recapture data
Mark-recapture data used in this study were described in detail in Chapter 1.
These data provide information on growth increment and molt probability for lobsters >
20 mm carapace length.
Growth increment
The relationships between premolt size and the molt increment as a proportion of
the premolt size (growth factor) were derived from the mark-recapture data in Chapter I
(Figure 2.4). Differences in molt increment with size and onset of maturity were taken
into account by using separate regressions for juveniles and sexually mature lobsters. A
linear increasing function was applied before maturity while a nonlinear decreasing
function was applied after maturity. The linear equation with slope b and y-intercept, a,
61
was used to estimate the proportional change in length pΔL as a function of initial size Lt
for immature lobsters:
[2.7]
pΔL = a Lt +b
A power function was applied to sexually mature lobsters:
pΔL = a Lt b
[2.8]
Either equation can then be used to describe molt increment
ΔL = pΔL * Lt
by:
[2.9]
Figure 2.4. Relationship of growth factor to carapace length from tagging data in Bay of
Fundy (BOF), Gulf of Maine (GOM), and southern New England (SNE) for males (solid
line) and females (dashed line). These analyses completed in Chapter 1.
Molt probability
Size specific molt probability curves were estimated by modifying the method of
Chen and Kennelly (1999) to incorporate growing degree-days. As in Chapter I, estimates
were partitioned by sex and size group. Instead of grouping lobsters by days-at-large,
however, tagging data were aligned with available temperature time series data by date.
Note that temperature time series at 10 m and 20 m were used separately in the Gulf of
Maine. The cumulative growing degree-days during the period at large were calculated
62
for each lobster. Individuals were then binned in categories of 50 growing degree-days. I
calculated the proportion of each group molting in each degree-day bin. A logistic model
was then fitted to the observed relationship between the proportions of lobsters molting
against cumulative degree-days by:
[2.10]
where Pi is the probability of one molt for the growing degree-day interval i, GDDi is the
number of growing degree-days at large for the growing degree-day group i, and a and b
are parameters to be estimated. The parameters, a and b, were estimated using the general
linear model function. The number of growing degree-days at which 50% of the lobsters
have molted, D50, can be estimated as:
,
[2.11]
(Chen and Paloheimo 1994).
The predicted molt probability calculated by sex and size-class for each region
was highly dependent on the temperature time series. Here I made several assumptions:
(1) although I did not know at what point in the molt cycle lobsters were tagged and
recaptured, I assumed that the calculated molt probability represented the average molt
probability; (2) since movement, daily locations, and depth of tagged lobsters were not
available for any of the studies, I assumed an average depth and location for the
temperature time series, and likewise, (3) because I did not know the thermal history of
each tagged lobster, I assumed the available temperature time series approximated the
actual temperatures experienced. Because the depth of the thermocline was near the depth
of the mark-recapture data in Gulf of Maine, and lobsters could easily cross though the
63
steep thermocline, I used two thermal regimes, 10 m and 20 m, to produce molt
probability curves.
Probabilistic step-wise degree day growth model
The probabilistic stepwise growth model developed in Chapter I was modified to
incorporate temperature by way of cumulative growing degree-days. To initiate the
stepwise model, lobsters at the time of hatching were assigned an age of 0. Hatching
occurs at different times in each region: June in southern New England (Lund and
Stewart 1970, Bibb et al. 1983, Fogarty et al. 1983), July in the Gulf of Maine, (Sherman
and Lewis 1967, Xue et al 2008, Incze et al. 2010) and August in the Bay of Fundy
(Campbell and Pezzack 1986, Cobb and Wahle 1994). Young-of-year lobsters were
sampled during the late summer and fall, thus age 0+ lobsters were assumed to be
approximately 65 days old in southern New England, and 75 days old in both Gulf of
Maine and Bay of Fundy. The estimated day of the year for the beginning of the model is
also included in order to start the temperature simulation at the corresponding point in the
temperature cycle.
Based on the individual based probabilistic step-wise growth modeling approach
of Chen and Kennelly (1999), this model resulted in a distribution of growth curves for
which I calculated a mean, median, and 95% confidence interval for size-at-age. The
algorithm (Figure 2.5) used to produce the growths curves follows:
(1) Choose a random initial size from a normal distribution with the mean and
standard deviation defined by the length frequency analysis of age 0+ lobsters, Li, where i
is 1 to n, and n is the number of molts by one lobster;
(2) Define age at sampling of 0+ lobsters at time of settlement survey;
64
(3) Assign a day of the year corresponding to time of hatching to begin the
temperature calculations;
(4) Choose the time step, D, that will represent the number of days over which
cumulative growing degree-days are calculated. Here D = 1 day;
(5) Using the sine function and regional parameters, calculate daily temperature
and secondly, calculate daily growing degree-days, starting from 0 at time of start, and
accumulate growing degree-days, GDDacc;
(6) Calculate the molt probability, Pi, corresponding to the accumulated growing
degree-days by the logistic molt probability equation [Eq. 2.10] ;
(7) Select a random number, q, from a normal distribution between 0 and 1. If q
≤Pi a molt occurs. If q>Pi a molt did not occur, D (and thus GDDacc) then increases by a
time step until a molt occurs;
(8) Calculate the size increment for an individual of size Li based on size specific
growth factor [Eq. 2.7] before maturity or [Eq. 2.8] after maturity, and with [Eq 2.9] to
calculate the size increment, ΔLi;
(9) Calculate the new size after the molt Li+1 = Li + ΔLi and
(10) Replace Li with Li+1.
Repeat steps 4 through 10 until a chosen maximum number of molts, n, is
reached. This was repeated for 1000 lobsters. Both calendar days and growing degreedays were recorded, therefore the model results were expressed as growth curves by
actual age in days and by growing degree-days. The three regions were compared with
respect to mean and variability in size as a function of both cumulative degree-days and
actual age in calendar days. Size-at-age estimates from length-frequency data were
65
compared to the mean size-at-age from the modeled growth curve. Additionally, the
results of the regional individual based stepwise growth models presented in Chapter I
were compared to the results of this model by age.
The number of degree-days required to reach a fixed size (before maturity: 50
mm; and harvestable size: 82.5 mm) as estimated from the resulting growing degree-day
growth curves were compared statistically by a Kolmogorov-Smirnov two-sample test
(KS-test) which tests the null hypothesis that the two distributions are the same. Regions
were compared to each other in this manner to determine whether the growth curves
converged when plotted as a function of growing degree-days. Distributions of age-atsize from the original calendar day model results were also compared to growing degreeday model results back calculated to calendar day within a region.
Figure 2.5. Flow diagram of individual-based stepwise growth model by growing degreeday. See text for explanation of symbols.
Finally, to simulate the consequences of climate change, growth curve predictions
were made in each region for alternative thermal regimes assuming an overall 2°C
temperature increase which has been projected for New England coastal waters by 2085
66
(Fogarty et al. 2007) (Figure 2.2). Current conditions were considered the modeled
temperatures, which were based on real temperature time series from the time period of
tagging. I assumed that the relationship between degree-days and molt probability at size
were static within regions. Two scenarios were modeled with increased temperature; (1)
no change in size-at-maturity, and (2) temperature dependant change in size-at-maturity.
Sizes-at-maturity in the predicted warmer thermal regimes were estimated from
the relationship of regional size-at-maturity to regional cumulative degree-days. I
incorporated size-at-maturity from this study with previously published estimates from
other locations (Little and Watson 2005). I then used those estimates to plot regional sizeat-maturity against the regional cumulative degree-days greater than 8° C.
To determine whether differences in temperature and size-at maturity made a
significant difference to growth trajectories in each region, I used K-S tests to statistically
compare size distributions generated by the different model scenarios.
Results
Cumulative degree days
Southern New England had the greatest number of cumulative degree-days, and in
turn, the longest growing season with temperatures in excess of 5°C, beginning in early
April and ending in mid-January (Figure 2.2, Table 2.2). This region was the only one to
approach temperatures near the physiological thermal maximum of 20°C during late
summer. In the Gulf of Maine degree-days are plotted for two depths because of the
steep, relatively shallow thermocline that is likely to affect a large proportion of the
resident lobster population. There, the growing season at 10 m extends from the end of
67
April to early January, whereas at 20 m it starts in mid-May and ends in late January. The
Bay of Fundy had a growing season starting in mid-May and ending in mid-December
(Table 2.2). Thus, the Gulf of Maine below the thermocline at the 20 m experiences the
lowest cumulative GDDs (Table 2.2, Figure 2.3).
Table 2.2. Analysis of temperature data for each region.
Regional description
Latitude
Depth (m)
Approx. growing season (≥5°C)
Minimum/Maximum temperature (°C) Average temperature during growing season (stdev) (°C) Average annual growing degree‐
days (GDD)
Bay of Fundy
Mixed
44° 40'
15
May ‐ December
10
April ‐ January
20
May ‐ January
Southern New England
Stratified warm
41° 20'
15
April ‐ January
0.7/12.5
2.4/14.3
2/13.1
3/19.2
9.6(1.4)
10.6(3.0)
8.8(2.0)
13.3(3.6)
1008.2
1414.1
970.3
2345.4
Gulf of Maine
Stratified cool
43° 50'
Molt Probability
Parameters for the relationship between molt probability and growing degree-day
were calculated by sex and size for each region (Table 2.3). The resulting molt
probability curves shifted to the right with progressively larger size classes, indicating
that larger lobsters require more growing degree-days between molts (Figure 2.7). As
with the calendar-day plots, the molt probability curves were steeper before maturity than
after maturity by degree-day. Curves for sexually mature lobsters were flatter, suggesting
more variability in the timing of the molt.
A direct comparison of degree-day to calendar-day growth curves is best made for
comparable size bins. Thus I used size groups 20-39 mm and 40-65 mm to compare
southern New England and Gulf of Maine (Figure 2.6).
68
Table 2.3. Molt probability parameters by region, sex and size group as calculated by
growing degree-day (GDD) and shown in Figure 2.7. GDD50 is the number of
cumulative GDDs when 50% of lobsters are predicted to have molted (calculated as:
GDD50 = -a/b).
Region
size group
Sex
20-39
Combined
40-65
Males
Females
Southern New
66-79
Males
England
Females
80-99
Males
Females
20-39
Combined
40-65
Combined
66-79
Males
Gulf of Maine 10 m
Females
80-99
Males
Females
20-39
Combined
40-65
Combined
66-79
Males
Gulf of Maine 20 m
Females
80-99
Males
Females
60-99
Males
Females
100 - 129
Males
Bay of Fundy
Females
130 +
Males
Females
69
N
134
154
131
370
470
191
1458
508
875
515
577
868
959
416
719
413
496
859
947
796
714
297
1533
131
1201
a
-2.509
-2.898
-2.889
-3.268
-2.000
-3.383
-3.330
-2.172
-2.477
-4.068
-4.631
-5.927
-5.947
-1.835
-2.252
-3.795
-3.750
-5.525
-5.957
-10.554
-9.875
-4.758
-4.687
-3.226
-4.426
b GDD50
0.007 361
0.005 628
0.003 901
0.003 1088
0.002 1028
0.001 2764
0.001 2271
0.004 565
0.004 580
0.005 778
0.005 890
0.003 2112
0.003 1917
0.005 407
0.006 359
0.006 645
0.006 669
0.004 1295
0.005 1111
0.017 605
0.016 600
0.006 830
0.007 702
0.004 829
0.005 949
Figure 2.6. Molt probability curves plotted as a function of growing degree-days for Bay
of Fundy (BOF), Gulf of Maine (GOM) 10 m, Gulf of Maine (GOM) 20 m and southern
New England (SNE) from top to bottom by size class and sex (males solid line, females
dashed line, where sexes are combined there is only one solid line).
70
Figure 2.7. Comparison of molt probability curves plotted against calendar days (left
panel) and growing degree-days (right panel) for the same size classes; 20 – 39 mm (top
panel) and 40-65 mm (bottom panel) in southern New England (SNE) and Gulf of Maine
(GOM). In GOM two thermal regimes are compared to SNE by growing degree-day;
above the thermocline at a depth of 10 m and below the thermocline at 20 m (right panel).
71
Probabilistic step-wise degree-day growth model
Growth trajectories derived from 1000 simulation runs of the stepwise degree-day
model were expressed on scales of growing degree-days and calendar days (Figures 2.8
and 2.9). If temperature entirely explained regional differences in growth, I would expect
the number of growing degree-days required to reach a given size to be the same across
regions. That is true in the cases of Bay of Fundy and Gulf of Maine (20m) where it takes
approximately an average of 7000 degree days to grow to 50 mm and 10000 degree days
to reach harvestable size (82.5 mm) (Fig. 2.8). The distributions of degree-days at these
sizes were significantly different according to the KS-test, however (Table 2.4). The
distributions of degree-days at 50 mm, where there would most likely be convergence
before maturity is reached, were significantly different between all regions. The only KStest that approached non-significance (p = 0.045), was between southern New England
and Gulf of Maine (10 m) where it takes an average of 10000 degree days to reach 82.5
mm. However, this is most likely due to the extreme slowing of growth in southern New
England as a result of early maturity.
72
73
Figure 2.8. Stepwise model results by degree-day for Bay of Fundy (BOF), two depths in the Gulf of Maine (GOM), and
southern New England (SNE). Solid lines denote mean size at GDD and the dashed lines outline the 95% confidence intervals
with males in dark grey and females in light grey. Horizontal bars labeled “m” and “r” denote size at female maturity and size at
recruitment to the fishery (82.5 mm) respectively. Horizontal and vertical dashed lines aid in comparing the growing degreedays required to reach 50 mm carapace length and harvestable size.
Table 2.4. Results of Kolmogorov-Smirnov test to compare cumulative degree-day
distribution required for male lobsters to reach 50 mm and harvestable size (82.5 mm)
between regions. Note that the two depths in Gulf of Maine were compared between
regions and also to each other.
50 mm
Regions compared
Harvestable size
D
Prob
D
Prob
BOF ‐ GOM 10 m
0.4085
< 0.001
0.5359
< 0.001
BOF ‐ GOM 20 m
0.3103
< 0.001
0.4939
< 0.001
BOF ‐ SNE
0.7674
< 0.001
0.5966
< 0.001
GOM 10 m ‐ SNE
0.7914
< 0.001
0.6955
< 0.001
GOM 20 m ‐ SNE
0.5033
< 0.001
0.1581
0.04514
GOM 10 m ‐ GOM 20 m
0.5126
< 0.001
0.6495
< 0.001
I also plotted growth curves estimated from the degree-day model in terms of
calendar days to facilitate the comparison with curves generated without degree-days in
the original stepwise model of Chapter 1 (Figure 2.9). Resultant growth curves backcalculated to calendar days from the degree-day model tended to estimate slower growth
rates in both the Bay of Fundy and the Gulf of Maine than the original calendar day
model. In the latter region, the curves for the 10 m and 20 m depths were virtually the
same; curves from 10 m and 20 m depth were both shown in Figure 2.9. In contrast, for
southern New England growth was estimated to be slightly faster than in the original
model, so lobsters were estimated to recruit to the fishery at a slightly younger age than
those by the original calendar day model. In the Bay of Fundy and Gulf of Maine the
growing degree-day model estimates lobsters to recruit to the fishery at a somewhat older
age than the original model (Table 2.5).
74
75
Figure 2.9. Regional curves produced by the original probabilistic step-wise model based on calendar day (top panel) compare
more favorably to the growth curves from the degree-day model back calculated to a calendar day scale. Regional size-atmaturity and harvestable size are shown by horizontal lines denoted by “m” and “r” respectively.
Table 2.5. Estimated age at harvestable size. a) calendar day model, b) growing-degreeday model and c) degree day model with warmer temperatures and adjusted maturity for
male and female lobsters in each region
Degree day model Increased temperature Degree day model
Calendar day model
Region
Bay of Fundy
Gulf of Maine
Southern New England
Bay of Fundy
10 m
Gulf of Maine
20 m
Southern New England
Bay of Fundy
10 m
Gulf of Maine
20 m
Southern New England
Sex
M
F
M
F
M
F
Average age Lower (years)
95%
9.0
6.1
8.4
5.3
7.7
4.7
7.6
4.7
4.5
2.6
5.5
3.1
Upper 95%
12.4
11.7
9.6
10
6.4
7.5
Range (# of years)
6.3
6.4
4.9
5.3
3.8
4.4
M
F
M
F
M
F
M
F
10.5
11
9.8
9.1
10.3
9.7
4.1
5.2
8.2
8.7
6.7
6.3
6.5
6.1
2.6
3.4
13
13.6
13.2
12.2
13.6
12.7
6.2
7.2
4.8
4.9
6.5
5.9
7.1
6.6
3.6
3.8
M
F
M
F
M
F
M
F
7.1
7.5
7.3
6.9
6.4
6.1
4
4.5
5.7
6.1
4.6
4.5
3.9
3.8
2.5
3.1
8.9
9
9.3
8.7
8.5
8
6
6.2
3.2
2.9
4.7
4.2
4.6
4.2
3.5
3.1
76
Resulting age-at-size distributions for males at 50 mm and at 82.5 mm by the
calendar day model and the growing degree-day model were compared by K-S test.
Results of these tests, showed that these two models produced significantly different age
distributions within a region in all cases (Table 2.6).
Table 2.6. Results of Kolmogorov-Smirnov test to compare age distributions required for
male lobsters to reach 50 mm and harvestable size (82.5 mm) within regions by calendar
day and growing degree-day models.
Calendar day model vs Growing degree‐day model
Region
50 mm
D
Prob
Harvestable
D
Prob
BOF
0.4825
< 0.001
0.5638
< 0.001
GOM 10 m
0.5295
< 0.001
0.6806
< 0.001
GOM 20 m
0.6568
< 0.001
0.6731
< 0.001
SNE
0.1372
0.01446
0.296
< 0.001
Climate Change Predictions
The change in size at maturity predicted for thermal regimes with an average
daily temperature 2°C warmer than current temperatures (modeled annual temperature
time series) were estimated by assuming temperature dependence of the onset of
maturity. A linear function described the relationship between average annual degreedays (>8°C) and size at 10% maturity (Figure 2.10). The estimated sizes-at-maturity
under the warmer thermal regime were 77.7, 71.5, 78.8, and 56.6 mm carapace length for
females and 90.1, 83.0, 91.4, and 65.6 mm for functionally mature males for the Bay of
Fundy, Gulf of Maine 10m, Gulf of Maine 20m, and southern New England, respectively
(Figure 2.10). Molt increment relationships were then shifted to correspond to the new
size-at-maturity and the break between linear and non-linear molt increment relationships
adjusted in the model. The growth curves produced under predicted warmer temperature
77
by the two scenarios are shown in Figure 2.11 by degree-days and Figure 2.12 by
calendar days. Adjusting the size-at-maturity had little effect on male growth in the Bay
of Fundy and Gulf of Maine and a negative effect on males in southern New England.
There was also no effect of decreasing size-at-maturity for females in Gulf of Maine,
however, there was a marked negative effect on the growth of females in southern New
England and especially in Bay of Fundy.
78
Size at maturity (CL in mm)
110
100
90
y = ‐0.0166x + 91.003
R² = 0.5363
80
70
60
50
40
0
500
1000
Degree days
1500
2000
Figure 2.10. Size at 10% maturity for female lobsters from locations of different average
yearly cumulative degree days greater than 8°C. Left to right: North offshore (Little
&Watson 2005); Gulf of Maine (20 m); Bay of Fundy, Isle of Shoals, New Hampshire
(Little &Watson 2003); Gulf of Maine (10 m); South offshore (Little &Watson 2005);
Middle offshore (Little &Watson 2005); Great Bay, New Hampshire (Little &Watson
2003); and southern New England. This relationship was best fit by a linear function.
This relationship was used to estimate size-at-maturity under warmed bottom water
conditions.
79
80
Figure 2.11. Growth trajectories as a function of degree-days modeled for temperature regimes 2°C warmer than current
conditions. Because the warmer temperature would result in an earlier onset of sexual maturity, thus at a smaller size, growth
was modeled for two scenarios, one with (a) no change in size-at-maturity, and (b) smaller sizes-at-maturity estimated from the
linear function in Fig. 2.10. Horizontal lines labeled “m” and “r” indicate size at which sexual maturity is reached. Note
different sizes for “m” in (a) and (b). Harvestable size was 82.5 mm in each region.
81
Figure 2.12. Predicted size-at-age curves for temperature regimes 2°C warmer than current conditions. Growth was modeled
for two scenarios, one where (a) there was no difference in size-at-maturity, and (b) where smaller sizes-at-maturity were
estimated for the new temperature regimes. Horizontal lines labeled “m” and “r” indicate size at which sexual maturity is
reached. Note the different sizes in (a) and (b)) and harvestable size (82.5 mm) in each region. Sizes-at-age determined by
length frequency analysis are shown by black points.
As expected, in each region, growth was faster under warmer temperatures
resulting in smaller size-at-age and therefore younger age at harvestable size (Table 2.5).
Between the two size-at-maturity scenarios modeled (Figures 2.12a and b), females in the
Bay of Fundy, and both sexes in southern New England, not surprisingly grew slower
under the earlier maturity scenario. In contrast, there was almost no difference in growth
trajectories for Gulf of Maine lobsters under the two scenarios.
Between model comparisons of the distribution of growing degree-days for male
lobsters to reach 50 mm and 82.5 mm were done by KS-test (Table 2.7). There was no
significant difference at either size in any region between the original growing degreeday model and the scenario with warmer temperatures and no change in size-at-maturity.
However, when comparing the scenario with warmer temperature and associated
decrease in size of maturity (Figure 2.11b) to the original model (Figure 2.8) or the
scenario with only warmer temperature (Figure 2.11a), there was a significant increase in
the number of degree days required to reach both sizes in the southern New England
region (p<0.001, for both comparisons at both sizes) (Table 2.7). This suggests that with
warmer temperature and a subsequent decrease in size-at maturity a noticeable difference
in growth rate will only occur in the warmest region.
82
Table 2.7. Results of Kolmogorov-Smirnov test to compare growing degree-day
distributions required for male lobsters to reach 50 mm and harvestable size (82.5 mm)
within regions by three models; original growing degree-day model (Original GDD),
scenario with increased temperature (Predicted), and scenario with increased temperature
and decreased size-at-maturity (Predicted w/SOM) .
Harvestable
D
Prob
Original GDD Original GDD vs vs Predicted Predicted w/ SOM
50 mm
D
Prob
BOF
0.0921
0.4594
0.0815
0.8896
GOM 10 m
0.069
0.7514
0.1175
0.4536
GOM 20 m
0.0564
0.902
0.1485
0.2165
SNE
0.0668
0.8329
0.0792
0.9153
BOF
0.0645
0.6524
0.0768
0.6976
GOM 10 m
0.1462
0.003173
0.0941
0.4763
GOM 20 m
0.0618
0.5631
0.0875
0.6287
SNE
0.3337
8.33E‐13
0.3299
< 0.001 *
Predicted vs Predicted w/SOM
Models compared Region
BOF
0.0719
0.78
0.1017
0.6849
GOM 10 m
0.1144
0.1532
0.1666
0.1082
GOM 20 m
0.0798
0.5148
0.1152
0.5464
SNE
0.3575
5.28E‐10
0.3013
< 0.001 *
Discussion
This is the first time the growing degree-day metric has been incorporated into
growth modeling using empirical field data for the American lobster. By using this
metric, the growth curves incorporate the effect of temperature on the molting process.
Calculating molt probability as a function of growing degree-days allows temperature to
dictate the probability that an individual will molt. While the molt probability curves for
the three regions did not converge as much as expected under the growing degree-day
model, or as has been observed in other studies (Smith 1997; Neuheimer and Taggart
2007), the persisting differences may be due to factors unrelated to temperature. The
83
estimated sizes-at-age from this model were very consistent with those estimated for each
region in the original stepwise model without temperature as a variable. Furthermore,
there was some convergence between regional growth curves in terms of the average
number of degree-days to reach 50 mm or 82.5 mm. The residual regional differences
detected in the number of degree-days to grow to a certain size may be due to factors
unrelated to temperature.
In previous studies, the growing degree-day approach has explained temperature
specific differences in molt probability and intermolt period. With the spiny lobster
Panulirus cygnus, for example, Smith (1997) demonstrated that when expressed as a
function of degree-days intermolt periods converged for lobsters reared at three different
temperatures. Similarly, in case studies of several fish and crab species grown in the
laboratory at differing temperatures, the growing degree-day metric reduced the variation
between growth trajectories (Neuheimer and Taggart 2007). It is important to note that
both of these studies were conducted under controlled environments in the laboratory.
In the present study I considered the added complexity that the onset of sexual
maturity not only influences growth, but is also temperature dependent. By modeling
temperature influences on somatic growth and onset of maturity independently, I show
the extent of the influence of maturity on growth. Sexual maturity occurs sooner and at a
smaller size in warmer regions (Aiken and Waddy 1980, Little and Watson 2005), and
thus growth comes under the influence of reproductive maturation at an earlier age. By
decreasing the size of maturity growth slows down sooner resulting in decreased size-atage. Because of the regional differences in the size at which lobsters become mature, it is
difficult to make fair comparisons of growth curves at sizes beyond maturity.
84
Differences in temperature, however, did not completely explain differences in
growth, even when the effects of the onset of sexual maturity were considered. Plotting
growth curves by degree-day reduced regional differences, but not completely. It is
important to note that the present study used growth data generated in situ, and not in the
laboratory. Other environmental factors, as well as heritable differences among the
lobster populations, therefore may be important components of regional differences in
growth that still remain unexplained.
Because it was impossible to know the individual histories of each lobster in the
study, I made reasonable assumptions about the range of temperature and depths they
experienced. The temperature time series employed were likely appropriate estimates of
the actual temperature experienced by most lobsters within a region since lobsters
movements are minimal during their first few years, but widen as they reach sexual
maturity (Wilder 1963, Cooper 1970, Cooper and Uzmann 1971, Krouse 1980). As
movements increase, changes in the depth encountered may alter thermal regime lobsters
experience, depending on the degree of stratification. In the Gulf of Maine, lobsters do
not have to move very far or very deep to cross the thermocline, and therefore may
encounter a wide range of temperatures. For this reason, two thermal regimes were
modeled for this region. In the Bay of Fundy, temperature differences were likely not
large due to strong tidal mixing. In southern New England, the nearshore shelf area has a
gradual slope, the stratified layer is deeper and lobsters nearshore are also not likely to
experience as wide a temperature change with changes in depth.
Temperature was likely not the only environmental factor affecting growth. Food
availability, photoperiod, shelter limitation, population density, and predation, may also
85
contribute to the regional differences in growth rates (Bordner and Conklin 1981, Wahle
and Fogarty 2006). We may gain a better understanding of the relative contribution of
other environmental factors if parallel time series of these variables were available.
Furthermore, a bioenergetic model of growth that includes variability due to temperature
as well as metabolic rates and nutrition would provide a clearer picture of growth
(Brylawski and Miller 2003).
While they must be used with caution, predictions were made for increasing
bottom water temperature in each region. To make these predictions, I assumed that
temperature had a dominant and non-interactive effect. Thus the molt probability curves
developed under the current conditions were applied to a projected 2°C warmer regime.
Furthermore, changes in size-at-maturity are expected with temperature increase. The
size-at-maturity-to-temperature relationship that was predicted in this study in order to
simulate growth in the warmer scenarios corresponds well to observations from other
studies (Little and Watson 2005). However, a better understanding of this process is
needed to make further predictions.
Size-at-maturity was most affected by increased temperature in BOF therefore the
decreased size-at-maturity had the greatest effect on growth in this region. In southern
New England maturity already occurred at a small size and influenced growth thus the
subsequent estimated decrease in growth further slowed growth after maturity. One factor
that was not accounted for in these estimated growth rates was non–linear effects of
temperature on growth for example high temperatures that approach stressful or lethal
levels.
86
In addition to a better understanding of the effects of environmental factors, this
model would benefit from more information of other aspects of lobster physiology.
Although the temperature time series used here do not exceed the estimated physiological
thermal maximum temperature of 20°C, the projected 2°C warmer thermal regimes did
exceed it. In the degree-day formula [Eq. 2.6], growth remained the same above the
thermal maximum. However, this may not be biologically realistic as temperatures may
become physiologically stressful even below the thermal maximum resulting in reduced
growth rates and survival. These conditions are referred to as “pejus” - or turning worse temperatures (Pörtner 2001). Under pejus temperatures an organism’s physiology cannot
keep up with oxygen requirements; thus growth and survival are affected. Evaluating
responses to pejus conditions will be important to our understanding of the American
lobster’s ability to persist in the southern part of its geographic range where temperatures
are likely approach the upper limits more frequently.
Model parameterization in this study was also limited by the available data. While
the size range of lobsters available in the data sets spanned the most abundant size
classes, the smallest and the largest lobsters were under-represented. Inferences about
growth beyond the domain of existing data should therefore be made with caution. In
both southern New England and the Gulf of Maine this model would benefit from
additional data for lobsters less than 40 mm and larger than 80 mm. Information for the
larger, sexually mature size classes was especially lacking. In the Bay of Fundy data for
the smallest sizes were lacking.
Although I have incorporated temperature as a predictive variable in these
regional growth models, we have yet to produce a generalized model of growth that
87
predicts regional differences in growth simply on the basis of temperature. To model
growth of American lobster in thermally contrasting regions, we need to better describe
the temperature dependent relationships of molt probability, molt increment, and
maturity. The models I developed are regionally specified, but I have yet to describe a
single generalized function for the relationship of temperature to lobster growth
processes. Further studies investigating the intrinsic and extrinsic determinants of growth,
such as metabolic processes, nutrition, maturity, phenotypic plasticity, and genetics
would also shed light on how to go about modeling American lobster growth across this
species’ environmentally variable range.
88
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99
APPENDIX
Size transition matrices by sex and region
100
Table A1. Size transition matrix for (a) male and (b) female lobsters in SNE.
(a)
2.5
7.5
12.5
17.5
22.5
27.5
32.5
37.5
42.5
47.5
52.5
57.5
62.5
67.5
72.5
77.5
82.5
87.5
92.5
97.5
102.5
107.5
112.5
117.5
122.5
127.5
2.5
NA
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7.5
NA
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
12.5 17.5 22.5 27.5 32.5 37.5 42.5 47.5 52.5 57.5 62.5 67.5 72.5 77.5 82.5 87.5 92.5 97.5 102.5 107.5 112.5 117.5 122.5
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
0.071 0.321 0.357 0.179 0.071
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.022 0.142 0.24 0.222 0.187 0.138 0.031 0.009 0.004 0.004
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.011 0.058 0.166 0.261 0.306 0.132 0.037 0.016 0.011 0.003
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.004 0.033 0.21 0.355 0.246 0.087 0.036 0.011 0.007 0.007
0
0
0.004
0
0
0
0
0
0
0
0
0
0
0
0
0.101 0.207 0.254 0.219 0.095 0.071 0.041 0.012
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.158 0.061 0.255 0.182 0.188 0.085 0.048 0.018
0
0
0
0
0.006
0
0
0
0
0
0
0
0
0
0
0.167 0.106 0.241 0.203 0.1
0.09 0.045 0.032 0.003
0
0.01 0.003
0
0
0
0
0
0
0
0
0
0
0
0
0.018 0.121 0.183 0.216 0.148 0.157 0.095 0.041 0.015 0.003 0.003
0
0
0
0
0
0
0
0
0
0
0
0
0
0.015 0.073 0.133 0.196 0.272 0.157 0.057 0.039 0.033 0.012 0.012
0
0
0
0
0
0
0
0
0
0
0
0
0
0.004 0.058 0.117 0.304 0.226 0.121 0.097 0.062 0.012
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.022 0.339 0.15 0.225 0.132 0.093 0.031 0.004 0.004
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.014 0.093 0.34 0.13 0.256 0.14 0.014
0
0.005 0.009
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.103 0.082 0.323 0.221 0.144 0.097 0.023 0.005 0.003
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.051 0.067 0.411 0.322 0.073 0.061 0.016
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.118 0.024 0.394 0.285 0.073 0.082 0.018 0.006
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.248 0.064 0.398 0.171 0.077 0.036 0.002 0.002
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.267 0.101 0.377 0.198 0.04 0.016
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.244 0.137 0.45 0.155 0.007 0.005
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.265 0.198 0.395 0.118 0.021 0.002
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.409 0.218 0.284 0.076 0.012
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.001 0.424 0.19 0.292 0.086
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.409 0.207 0.295
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.001 0.421 0.231
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
9E‐04 0.461
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.007
(b)
2.5
7.5
12.5
17.5
22.5
27.5
32.5
37.5
42.5
47.5
52.5
57.5
62.5
67.5
72.5
77.5
82.5
87.5
92.5
97.5
102.5
107.5
112.5
117.5
122.5
127.5
2.5
NA
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7.5
12.5 17.5 22.5 27.5 32.5 37.5 42.5 47.5 52.5 57.5 62.5 67.5 72.5 77.5 82.5 87.5 92.5 97.5 102.5 107.5 112.5 117.5 122.5
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
0.012 0.224 0.541 0.188 0.012 0.024
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.003 0.178 0.307 0.274 0.134 0.065 0.036
0
0
0.003
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.002 0.052 0.159 0.244 0.276 0.177 0.063 0.013 0.006 0.006 0.002
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.01 0.072 0.235 0.42 0.153 0.052 0.033 0.013 0.007 0.007
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.005 0.189 0.35 0.24 0.138 0.032 0.014 0.023
0
0.005 0.005
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.117 0.146 0.296 0.214 0.131 0.053 0.019 0.015 0.005
0
0.005
0
0
0
0
0
0
0
0
0
0
0
0
0
0.213 0.124 0.224 0.208 0.124 0.043 0.022 0.022 0.013 0.005 0.003
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.023 0.165 0.201 0.265 0.149 0.113 0.031 0.028 0.021 0.003
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.009 0.106 0.189 0.183 0.224 0.124 0.088 0.053 0.021 0.003
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.017 0.062 0.202 0.243 0.219 0.127 0.106 0.017 0.007
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.007 0.057 0.313 0.153 0.246 0.149 0.071 0.004
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.118 0.042 0.221 0.164 0.321 0.107 0.027
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.16 0.07 0.352 0.225 0.136 0.041 0.014 0.003
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.044 0.141 0.607 0.174 0.022 0.007 0.004
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.161 0.313 0.432 0.071 0.023
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.367 0.283 0.283 0.047 0.018 0.003
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.385 0.331 0.233 0.047 0.004
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.382 0.355 0.225 0.035 0.003
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.428 0.387 0.169 0.016 9E‐04
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6E‐04 0.574 0.279 0.132 0.013 0.002
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.003 0.615 0.26 0.114 0.006
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.001 0.651 0.246 0.098
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.005 0.702 0.221
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.005 0.744
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.006
101
Table A2. Size transition matrix for (a) male and (b) female lobsters in GOM.
(a)
2.5
7.5
12.5
17.5
22.5
27.5
32.5
37.5
42.5
47.5
52.5
57.5
62.5
67.5
72.5
77.5
82.5
87.5
92.5
97.5
102.5
107.5
112.5
117.5
122.5
127.5
2.5
NA
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7.5
12.5 17.5 22.5 27.5 32.5 37.5 42.5 47.5 52.5 57.5 62.5 67.5 72.5 77.5
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
0.155 0.732 0.103 0.01
0
0
0
0
0
0
0
0
0
0
0
0.003 0.253 0.551 0.155 0.033 0.003 0.002
0
0
0
0
0
0
0
0
0.001 0.006 0.135 0.445 0.28 0.098 0.023 0.01
0
0.001
0
0
0
0
0
0
0
0
0.066 0.334 0.296 0.187 0.07 0.022 0.019 0.002
0
0.002 0.002
0
0
0
0
0
0.046 0.226 0.351 0.201 0.092 0.04 0.015 0.015 0.004 0.01
0
0
0
0
0
0
0.015 0.325 0.194 0.181 0.112 0.057 0.06 0.032 0.02 0.002
0
0
0
0
0
0
0.159 0.096 0.196 0.135 0.144 0.085 0.093 0.048 0.019
0
0
0
0
0
0
0
0.003 0.021 0.1 0.197 0.163 0.218 0.125 0.066
0
0
0
0
0
0
0
0
0
0.036 0.061 0.142 0.271 0.186 0.101
0
0
0
0
0
0
0
0
0
0
0.037 0.058 0.195 0.153 0.132
0
0
0
0
0
0
0
0
0
0
0
0.037 0.169 0.111 0.259
0
0
0
0
0
0
0
0
0
0
0
0
0.011 0.051 0.096
0
0
0
0
0
0
0
0
0
0
0
0
0.155 0.047 0.161
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.02
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.095
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
82.5
NA
0
0
0
0
0
0
0.013
0.08
0.121
0.279
0.19
0.421
0.168
0.607
0.014
0.43
0
0
0
0
0
0
0
0
0
87.5
NA
0
0
0
0
0
0.002
0.009
0.024
0.077
0.121
0.18
0.343
0.288
0.342
0.338
0.006
0.411
0
0
0
0
0
0
0
0
92.5
NA
0
0
0
0
0
0
0.002
0.003
0.004
0.026
0.048
0.073
0.171
0.031
0.473
0.159
0.002
0.41
0
0
0
0
0
0
0
97.5
NA
0
0
0
0
0
0
0
0
0
0
0
0.006
0.006
0
0.068
0.33
0.107
0
0.433
0
0
0
0
0
0
102.5
NA
0
0
0
0
0
0
0
0
0
0
0
0
0.003
0
0.009
0.071
0.352
0.048
0
0.428
0
0
0
0
0
107.5
NA
0
0
0
0
0
0
0
0
0
0
0.005
0
0
0
0.005
0
0.123
0.29
0.091
0
0.412
0
0
0
0
112.5
NA
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.003
0.003
0.235
0.412
0.078
0
0.431
0
0
0
117.5
NA
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.001
0.003
0.013
0.059
0.404
0.039
0
0.414
0
0
122.5
NA
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.089
0.375
0.027
0
0.457
0
2.5
NA
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7.5
NA
0.115
0.004
0
0.002
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
82.5
NA
0
0
0
0
0.002
0.002
0.014
0.046
0.084
0.173
0.193
0.391
0.172
0.603
0.05
0.448
0
0
0
0
0
0
0
0
0
87.5
NA
0
0
0
0
0
0
0.003
0.013
0.017
0.039
0.117
0.268
0.243
0.312
0.456
0.007
0.453
0
0
0
0
0
0
0
0
92.5
NA
0
0
0
0
0
0
0.002
0
0.008
0.009
0.025
0.022
0.129
0.013
0.383
0.269
0.011
0.441
0
0
0
0
0
0
0
97.5
NA
0
0
0
0
0
0
0
0
0
0
0
0.006
0.008
0
0.023
0.266
0.273
0.01
0.446
0
0
0
0
0
0
102.5
NA
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.008
0.255
0.211
0.009
0.449
0
0
0
0
0
107.5
NA
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.003
0.007
0.301
0.193
0
0.442
0
0
0
0
112.5
NA
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.001
0.036
0.298
0.156
0.002
0.438
0
0
0
117.5
NA
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.048
0.329
0.12
0
0.44
0
0
122.5
NA
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.003
0.065
0.347
0.106
0.002
0.449
0
(b)
2.5
7.5
12.5
17.5
22.5
27.5
32.5
37.5
42.5
47.5
52.5
57.5
62.5
67.5
72.5
77.5
82.5
87.5
92.5
97.5
102.5
107.5
112.5
117.5
122.5
127.5
12.5
NA
0.736
0.229
0.005
0.002
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
17.5
NA
0.138
0.526
0.123
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
22.5
NA
0.007
0.177
0.436
0.052
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
27.5
NA
0.004
0.054
0.273
0.333
0.039
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
32.5
NA
0
0.008
0.103
0.355
0.219
0.023
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
37.5
NA
0
0.002
0.042
0.157
0.387
0.322
0.211
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
42.5
NA
0
0
0.01
0.062
0.144
0.168
0.081
0.008
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
47.5
NA
0
0
0.005
0.018
0.093
0.208
0.134
0.025
0.004
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
52.5
NA
0
0
0.004
0.008
0.059
0.105
0.177
0.142
0.042
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
57.5
NA
0
0
0
0.007
0.02
0.086
0.132
0.158
0.093
0.035
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
62.5
NA
0
0
0
0.003
0.02
0.044
0.105
0.179
0.139
0.026
0.02
0
0
0
0
0
0
0
0
0
0
0
0
0
0
102
67.5
NA
0
0
0
0.002
0.012
0.03
0.095
0.246
0.295
0.355
0.228
0.078
0.124
0
0
0
0
0
0
0
0
0
0
0
0
72.5
NA
0
0
0
0
0.004
0.007
0.029
0.129
0.211
0.221
0.127
0.123
0.081
0.004
0
0
0
0
0
0
0
0
0
0
0
77.5
NA
0
0
0
0
0.002
0.002
0.017
0.054
0.105
0.143
0.289
0.112
0.243
0.068
0.087
0
0
0
0
0
0
0
0
0
0
Table A3 Size transition matrix for (a) male and (b) female lobsters in BOF.
(a)
2.5
7.5
12.5 17.5
22.5
27.5
32.5
37.5
42.5
2.5 0.235 0.676 0.088
0
0
0
0
0
0
7.5 9E‐04 0.357 0.596 0.045 0.0009
0
0
0
0
12.5
0
0.023 0.351 0.516 0.095 0.014 0.0007
0
0
17.5
0
0
0.002 0.213 0.4859 0.234 0.0574 0.006 0.0009
22.5
0
0
0
0
0.1293 0.41 0.3127 0.099 0.033
27.5
0
0
0
0
0
0.096 0.3608 0.314 0.1353
32.5
0
0
0
0
0
0
0.0797 0.276 0.2825
37.5
0
0
0
0
0
0
0
0.045 0.2203
42.5
0
0
0
0
0
0
0
0
0.0406
47.5
0
0
0
0
0
0
0
0
0
52.5
0
0
0
0
0
0
0
0
0
57.5
0
0
0
0
0
0
0
0
0
62.5
0
0
0
0
0
0
0
0
0
67.5
0
0
0
0
0
0
0
0
0
72.5
0
0
0
0
0
0
0
0
0
77.5
0
0
0
0
0
0
0
0
0
82.5
0
0
0
0
0
0
0
0
0
87.5
0
0
0
0
0
0
0
0
0
92.5
0
0
0
0
0
0
0
0
0
97.5
0
0
0
0
0
0
0
0
0
102.5
0
0
0
0
0
0
0
0
0
107.5
0
0
0
0
0
0
0
0
0
112.5
0
0
0
0
0
0
0
0
0
117.5
0
0
0
0
0
0
0
0
0
122.5
0
0
0
0
0
0
0
0
0
127.5
0
0
0
0
0
0
0
0
0
47.5
0
0
0
0.0009
0.0092
0.0653
0.2149
0.2894
0.2157
0.015
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
52.5
0
0
0
0
0.005
0.017
0.076
0.231
0.203
0.153
0.035
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
57.5
0
0
0
0
0.001
0.003
0.04
0.123
0.236
0.223
0.107
0.013
0
0
0
0
0
0
0
0
0
0
0
0
0
0
62.5
0
0
0
0
0
0.003
0.017
0.048
0.14
0.243
0.223
0.089
0.034
0
0
0
0
0
0
0
0
0
0
0
0
0
67.5
0
0
0
0
0
0.002
0.007
0.022
0.091
0.17
0.182
0.215
0.058
0.023
0
0
0
0
0
0
0
0
0
0
0
0
72.5
0
0
0
0
0
0.002
0.002
0.006
0.028
0.075
0.214
0.116
0.18
0.026
0.014
0
0
0
0
0
0
0
0
0
0
0
77.5
0
0
0
0
0
0
0.003
0.004
0.015
0.048
0.091
0.215
0.099
0.14
0.019
0.02
0
0
0
0
0
0
0
0
0
0
82.5
0
0
0
0
0
0
0.002
0.009
0.025
0.028
0.053
0.125
0.18
0.143
0.198
0.01
0.031
0
0
0
0
0
0
0
0
0
87.5
0
0
0
0
0
0
0
0.002
0.005
0.02
0.041
0.059
0.167
0.113
0.16
0.173
0
0.031
0
0
0
0
0
0
0
0
92.5
0
0
0
0
0
0
0
0
0
0.013
0.006
0.063
0.068
0.2
0.075
0.137
0.112
0.005
0.04
0
0
0
0
0
0
0
97.5
0
0
0
0
0
0.002
0
0
0
0.005
0.022
0.04
0.068
0.113
0.165
0.041
0.229
0.087
0.006
0.075
0
0
0
0
0
0
102.5
0
0
0
0
0
0
0
0
0
0.008
0.013
0.033
0.071
0.068
0.208
0.259
0.117
0.518
0.149
0.005
0.23
0
0
0
0
0
107.5
0
0
0
0
0
0
0
0
0
0
0.003
0.017
0.048
0.087
0.071
0.193
0.121
0.231
0.497
0.075
0
0.266
0
0
0
0
112.5
0
0
0
0
0
0
0
0
0
0
0.006
0.013
0.017
0.064
0.047
0.112
0.229
0.062
0.269
0.457
0.045
0.003
0.247
0
0
0
117.5
0
0
0
0
0
0
0
0
0
0
0
0.003
0.01
0.015
0.038
0.046
0.13
0.036
0.023
0.312
0.338
0.024
0
0.28
0
0
122.5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.005
0.005
0.018
0.021
0.011
0.045
0.323
0.228
0.022
0
0.256
0
92.5
0
0
0
0
0
0
0.002
0
0.005
0.027
0.038
0.102
0.075
0.197
0.071
0.128
0.065
0
0.006
0
0
0
0
0
0
0
97.5
0
0
0
0
0
0
0
0
0.005
0.009
0.021
0.039
0.088
0.066
0.224
0.064
0.2
0.17
0.006
0.101
0
0
0
0
0
0
102.5
0
0
0
0
0
0
0
0
0.008
0.003
0.024
0.039
0.057
0.075
0.194
0.266
0.149
0.503
0.222
0
0.323
0
0
0
0
0
107.5
0
0
0
0
0
0
0
0
0.005
0.009
0.01
0.039
0.075
0.105
0.066
0.245
0.223
0.152
0.551
0.159
0.009
0.3
0
0
0
0
112.5
0
0
0
0
0
0
0
0.003
0.003
0
0.003
0.014
0.04
0.039
0.148
0.122
0.237
0.105
0.204
0.556
0.255
0.028
0.305
0
0
0
117.5
0
0
0
0
0
0
0
0
0
0
0.007
0.007
0.009
0.009
0.02
0.021
0.074
0.035
0
0.155
0.362
0.32
0.033
0.296
0
0
122.5
0
0
0
0
0
0
0
0
0
0
0
0
0.004
0
0.005
0.005
0.005
0
0.006
0.019
0.032
0.289
0.363
0.061
0.31
0
(b)
2.5
7.5
12.5 17.5 22.5 27.5 32.5 37.5 42.5 47.5 52.5 57.5 62.5 67.5
2.5 0.346 0.5 0.077 0.077
0
0
0
0
0
0
0
0
0
0
7.5 0.001 0.312 0.616 0.067 0.004
0
0
0
0
0
0
0
0
0
12.5
0
0.016 0.304 0.513 0.133 0.028 0.007
0
0
0
0
0
0
0
17.5
0
0.002 0.003 0.166 0.479 0.252 0.07 0.018 0.006 0.002
0
0
0
0
22.5
0
0
0
0
0.113 0.429 0.305 0.094 0.042 0.011 0.004 0.001
0
0
27.5
0
0
0
0
0
0.066 0.318 0.314 0.173 0.083 0.023 0.013 0.006 0.002
32.5
0
0
0
0
0
0
0.047 0.22 0.296 0.204 0.135 0.059 0.01 0.012
37.5
0
0
0
0
0
0
0
0.025 0.21 0.243 0.23 0.13 0.068 0.045
42.5
0
0
0
0
0
0
0
0
0.026 0.178 0.162 0.242 0.121 0.108
47.5
0
0
0
0
0
0
0
0
0
0.015 0.134 0.188 0.199 0.152
52.5
0
0
0
0
0
0
0
0
0
0
0.017 0.093 0.199 0.155
57.5
0
0
0
0
0
0
0
0
0
0
0
0.028 0.046 0.184
62.5
0
0
0
0
0
0
0
0
0
0
0
0
0.026 0.031
67.5
0
0
0
0
0
0
0
0
0
0
0
0
0
0.026
72.5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
77.5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
82.5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
87.5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
92.5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
97.5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
102.5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
107.5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
112.5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
117.5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
122.5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
127.5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
103
72.5
0
0
0
0
0
0.002
0.008
0.02
0.072
0.089
0.179
0.106
0.154
0.035
0
0
0
0
0
0
0
0
0
0
0
0
77.5
0
0
0
0
0
0
0.004
0.013
0.031
0.083
0.065
0.198
0.093
0.162
0.01
0.032
0
0
0
0
0
0
0
0
0
0
82.5
0
0
0
0
0
0
0.004
0.013
0.031
0.048
0.113
0.106
0.207
0.145
0.158
0.005
0.023
0
0
0
0
0
0
0
0
0
87.5
0
0
0
0
0
0
0
0.003
0
0.045
0.076
0.092
0.141
0.14
0.097
0.106
0.005
0.018
0
0
0
0
0
0
0
0
BIOGRAPHY OF THE AUTHOR
Charlene Emma Bergeron was born in Worcester, Massachusetts on May 17th,
1976. She lived in Acton, Massachusetts during the school year while spending summers
in Camp Ellis Beach, Maine where she developed a deep appreciation for the ocean.
Charlene graduated from Acton Boxboro Regional high school in 1994 and promptly
moved to Santa Cruz, California to attend University of California, Santa Cruz. There she
learned to SCUBA dive and surf. Charlene graduated from UCSC in 1998 with a B.A. in
Marine Biology.
After various marine and non-marine field ecology jobs in locations including
Prince William Sound, Alaska, Santa Cruz, CA, and Hawaii, Charlene moved back to
Maine. Here she began work as a Research Associate for Dr. Richard Wahle at Bigelow
Laboratory for Ocean Sciences. In 2007, Charlene entered the University of Maine’s
Marine Biology program. Charlene continues to dive, surf, and work for Dr. Wahle, and
is now employed at UMaine’s Darling Marine Center. She is a candidate for the Master
of Science degree in Marine Biology from the University of Maine in December, 2011.
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