Modeling shrimp
protein and energy
requirements for
growth
Submitted to Swansea University
in fulfillment of the requirements
for the Degree of MSc
Environmental Biology 2012
Martin Richardson 578168
Martin Richardson 578168
Summary
In addition to presenting a basic individual, factorial growth model for shrimp, this dissertation
provides an overview of some of the ways that modeling and simulation have developed from single
equation mathematical models to modern dynamic systems capable of integrating data from
multiple experiments. A model may use results or data from several sources, and where necessary
make assumptions. The model can then be tested by comparing the results to empirical data.
Models attempt to analyze entire ecosystems and therefore seek to use the principle of conservation
of energy, or stoichiometry as a means of integrating as many elements as possible in a consistent
manner. This new paradigm allows for rapid evaluation of environmental problems at both large and
small scale. Models can be used to analyze behavior of complex ecosystems and their interactions
with a changing environment in a general way. Eventually they will be integrated with global climate
models, abiotic resources and anthropogenic factors to develop a comprehensive model of the
Biosphere. A model that can be played backwards or forwards, to predict the future or remember
the past, as things were.
Dynamic modeling provides a means of synthesizing disparate fields associated with global issues,
particularly economics, ecology and biodiversity, and developing holistic analysis. However, modeling
is inherently descriptive as opposed to analytically deterministic. There has been a shift away from
deterministic thinking, towards a more open analysis of environmental and ecological issues.
Whereas mathematics was viewed as playing an important role in ecological thought, analysis of the
issues themselves has now taken centre stage and the role of mathematics somewhat subsumed.
The next paradigm will see implementation of artificial neural networks (ANNs) and the use of
machine learning to incorporate very large data sets and further distance modeling from constricted,
analytical thinking. In some engineering applications it is the pattern itself that is the information,
and the changes in the patterns reveal changes in the system. Similarly, ecology is moving toward
analysis of patterns as a means of identifying change.
Figure 1: Penaeid shrimp. Illustration by Jo Taylor, Museum Victoria.
2
Martin Richardson 578168
Declarations and Statements
Declaration
This work has not previously been accepted in substance for any degree and is not being concurrently
submitted in candidature for any degree.
Signed .........................................................
Date...............................................
Statement 1
This dissertation is the result of my own independent work/investigation, except where otherwise stated.
Other sources are acknowledged by footnotes giving explicit references. A bibliography is appended.
Signed .........................................................
Date ...............................................
Statement 2
I hereby give my consent for my dissertation, if relevant and accepted, to be available for photocopying and for
inter-library loan, and for the title and summary to be made available to outside organizations.
Signed .........................................................
Date ...............................................
3
Martin Richardson 578168
Contents
Summary ....................................................................................................................................................... 2
Declarations and Statements ........................................................................................................................ 3
Acknowledgements....................................................................................................................................... 5
Abbreviations ................................................................................................................................................ 6
Abstract ......................................................................................................................................................... 7
Introduction .................................................................................................................................................. 8
Methods ...................................................................................................................................................... 16
Results ......................................................................................................................................................... 21
Discussion ................................................................................................................................................... 24
Appendix ..................................................................................................................................................... 30
References .................................................................................................................................................. 30
4
Martin Richardson 578168
Acknowledgements
Data and formulae for the shrimp growth model were developed by Dr. Ingrid Lupatsch and
colleagues at the Swansea University centre for sustainable aquatic research (CSAR). With thanks to
Dr. Ingrid Lupatsch and Prof. Kevin Flynn for their guidance.
5
Martin Richardson 578168
Abbreviations
SGR
Specific growth rate
DE
Digestible energy
DP
Digestible protein
DP/DE Ratio of DP to DE
BW
Individual body weight
TGC
Thermal unit growth coefficient
AGR
Absolute growth rate
Mass balance equation
IBW
Initial body weight
FBW
Final body weight
t
Time
D
Number of days
DGC
Daily growth coefficient
Predicted final Body Weight
GE
Gross energy
HeE
Basal metabolism
HEf
Fasting heat production
HxE
Molting energy loss
MBW Metabolic body weight
a
Constant
Metabolic rate
T
Water temperature
RE
Energy gain
FCR
Feed conversion ratio
Feed efficiency
CL
Carapace length
BW, CL conversion
GIS
Geographic Information systems
100x(lnFBW-lnIBW)/D
Dependent on BW
DP/DE
(FBW1/3-IBW1/3))/(TxD)x100
[1]
dW/dt=( C-(MR+ S)-( F+U)-G)xCal xW [2]
Days
100x(FBW1/3-IBW1/3)/D
(IBW1/3 +(TGC/100 x T x D))3
kJ
~ HeE
0.25xRE
BWb (kg)b
Related to species and T
aBWb, with 0.7<b<0.9
[1]
[1]
[1]
[1]
[1]
[1]
[3]
[4]
[1]
Feed/ weight gain
Weight gain/feed
mm
Log10BW = 2.8xLog10CL -2.9
[5]
6
Martin Richardson 578168
Abstract
“We left him at the seaside and returned to our ship where, in five or six hours absence, we had
pestered our ship so with codfish that we threw numbers of them overboard again; and surely, I am
persuaded that in the months of March, April, and May, there is upon this coast (Cape Cod) better
fishing, and in as great plenty, as in Newfoundland. For the schools of mackerel, herrings, cod, and
other fish that we daily saw as we went and came from shore, were wonderful...” John Brereton,
1602
Many fish stocks are now managed; wild salmon in several countries, Georges Bank cod in Canada;
and fishing is regulated in many countries. Rapid oscillations and even decimation of wild stocks and
a growing world population has made this a necessity. Predicting the effects of anthropogenic forcing
is becoming increasingly urgent as global food security concerns develop. Some individual species are
adapting and changing their range and diet, producing major modifications to ecosystems in certain
instances; but overall there is a steadily increasing decline. An understanding of the ways ecosystems
impact climate is needed to improve climate models. In many cases ecological studies lasting years or
even decades are no longer possible as sea level rise, ocean acidification, pollution, and other factors
are changing environmental conditions at an increasing rate. Ecological models offer the means to
analyze these issues quickly. Simulations that cover years or even decades can be run within a few
minutes or even hours providing insight pertaining to the problems in question. Accurate individual
based models, such as the individual growth model discussed here do more, they provide the
building blocks for assimilation into a future grand model of the entire Biosphere incorporating both
climate and ecological effects. Such a model will permit improved prediction for the future and
empower governmental policy making so that efforts to mitigate against climate change and other
anthropogenic factors can be made as part of an overall strategy to regulate the Biosphere rather
than discrete initiatives with unpredictable effects on other elements. This work utilizes the results of
careful growth studies carried out by Dr. Ingrid Lupatsch at the Centre for Sustainable Aquatic
Research (CSAR) at Swansea University. The model produced reproduces the equations and results of
Dr. Lupatsch’s work. In particular, the primary growth equation is a simple power function that may
be easily adapted to a variety of fish and shrimp species by changing the coefficient and exponent of
the body weight (BW) to values associated with a particular species. It appears that the main factors
affecting growth of shrimp are temperature (T) and the molting cycle. Apart from salinity, the myriad
other considerations associated with growth have not been the subject of comparable studies and
7
Martin Richardson 578168
therefore do not warrant inclusion at the current time. Too detailed an approach may introduce
instability and create larger errors and thereby reduce the usefulness of an individual growth model
to other potential applications.
Introduction
“Remember that all models are wrong; the practical question is how wrong do they have to be to not
be useful.”
George E. P. Box
There are inevitably, limitations to our ability to understand nature. Mathematics has found
application to ecology, but analytical solutions to ecological problems are few and far between. It is
also extremely difficult, if not impossible, to combine analytical processes so as to build complete
ecosystem models. The mathematics becomes intractable. In some ways this parallels the application
of models to economics and other fields such as sociology that now rely on extensive modeling to
analyze problems and even predict possible outcomes[6]. The advantage of course is that modeling
inherently unites all these fields. This is important in aquaculture, where profit is a fundamental
driver, but it is also true of ecology and the struggle to protect biodiversity. The essential feedback
from ecosystems services, the value of their production, which has been largely taken for granted.
Now, the time is fast approaching when ecosystem services will be limiting factors to human
population growth, and indeed, economic growth. Obviously continued growth is unsustainable, but
in order to successfully divine a new economics, an incorporation of ecosystem services and
environmental costs will be required.
Ecology, as with many other areas of science, has sought a more rigorous foundation through the
application of mathematics as well as physical and chemical laws. In-depth ecological studies are
painstaking work, and can take decades to yield meaningful results. Models do not replece field
research, but they can compliment or guide fields of study. Mathematical ecology has not been able
to provide a global set of ecological laws. The species-area concept for example is a reductionist view
of a system, and the relationship does not hold for many situations like tropical rainforests or
polluted environments. Results overall have been mixed with some success in areas such as species
interactions but applications involving fisheries management are frequently problematic. Solutions to
management problems involve social, economic and cultural factors which are not easily modeled
using mathematics. In this regard therefore, mathematics is a subdiscipline of modeling. The current
8
Martin Richardson 578168
trend is to ever more ad hoc systems and machine learning, moving away from analytical solutions
and deterministic models. Here the application software selects the best mathematics, and ‘learns’
from prior analysis without human intervention. In this manner it is the patterns themselves that can
be compared over time. The question has shifted to ‘what has changed’ from ‘what are the causes’.
Growth has traditionally been measured using a mass balance approach[2], or in terms of absolute
growth rate (AGR), specific growth rate (SGR), thermal growth coefficient (TGC), weight gain, or
length. Many of these methods originated in the field of animal nutrition and their derivation is
related more to system isomorphisms than rigorous analysis[7]. SGR, for example, has found
extensive application despite being weight dependent and therefore not useful in comparing growth
rates in animals of different weights[1]. In turn, mathematics has failed to embrace metabolic
processes and falls short in providing analytical foundations for terms involving weights to a noninteger power[8]. Linear, polynomial, von Bertalanffy, Gompertz, exponential and more recently,
artifical neural network models have been developed for growth[9]. Best practice[10] iincludes using
multiple models, and although they are not always completely accurate, nevertheless formal models
have been demonstrated to be the best means of making predictions[10].
Formal systems models are developed using application software such as PowerSim®, VenSim®, or
STELLA®. These packages use a so-called systems approach which is more adaptable, easier to use
and utilizes charateristics of natural systems in a similar way that analytical models are derived from
system isomorphisms. The application of system dynamics means that resulting models vary
considerably in their precision and character. Detailed models of of an algal population maintained in
a controlled environment are mechanistic and can achieve a high degree of accuracy and produce
good representation, particularly of well understood processes. It should be noted however that the
model inevitably reflects the experiment within the range of empirical data. From an epistemological
perspective the model forms a repository of knowledge concerning a system rather than knowledge
in itself. Descriptive models using broad assumptions, and gross simplification involving a fishery over
a large geographic area are necessarily less precise. But at the same time they can offer broader
analysis of the commercial fishery operation, market price, employment and the like[11,12], and
thereby aid policy and management decisions[13]. And, finally, individual growth models may be
incorporated into a fluid dynamics model of an estuary or bay being used for aquaculture of a
9
Martin Richardson 578168
particular species. This can involve input from other commonly used software including mapping
(GIS), and EcoSim[14].
Figure 2: Yu, R et al. Predicting shrimp growth. Artificial neural network versus single equation, nonlinear regression
models. The artificial neural network, ANN, approach does not require specification of the numerous individual nonlinear factors in order to predict growth and results in the best growth predictions but does not illuminate the relative
contribution of the many factors that affect growth. The other functions indicate the relative importance of contributing
factors by the values of their coefficients.
The schematic diagram below is taken from a paper by A. R. Franco et al [5], and shows a conceptual
diagram of the shrimp growth model developed using PowerSim®. This model uses a von Bertalanffy
equation parameterized for Panaeus indicus. It includes waste and egg production with consideration
of physiological processes using formulae derived from several different sources. Originally it was
developed with the intention of making it available for inclusion into broader ecological models. It
was
Figure 3: Franco, A R et al, 2006. Here two forcing functions are considered: food availability and water temperature.
Temperature affects both the feeding rate and metabolism.
10
Martin Richardson 578168
subsequently updated to include additional factors and incorporated into a commercial software
package called POND for use by shrimp farmers. It can be seen that the POND model incorporates
effects due to temperature, salinity, and dissolved oxygen as well as natural food (zooplankton and
bacteria) which feed on phytoplankton occurring in the water. The model also includes business
planning as well as a cost and profit analysis.
Figure 4: POND® shrimp aquaculture software console.
An additional model derived from fish was produced by Mishra et al. in 2002[15] in attempt to try
and better understand shrimp bioenergetics in order to consider fluctuations in wild populations.
This model details several physiological functions especially relating to metabolism and molting.
Feeding patterns are simulated (nocturnal with cessation during molting) and the discontinuous
growth pattern of shrimp detailed.
11
Martin Richardson 578168
Figure 5: From Mishra et al. 2002. This model uses results from fish experiments and several assumptions when
experimental data is unavailable.
On a larger scale, models that integrate geographic information from GIS, and hydrodynamic models
to model currents are becoming available. A good example of this is the SMILE project[14][16].
These can be used to evaluate carrying capacity of a coastal area for mariculture of shellfish by
employing an individual species model; in this case it is called SHELLSIM®.
12
Martin Richardson 578168
Figure 6: Combined modelling framework used in SMILE, the Sustainable Mariculture in Irish Lough Ecosystems project.
The composite framework uses 3 systems: Delft3D for hydrology, EcoWin2000 for carrying capacity, and an individual
bespoke shellfish growth model, ShellSim.
Results from a simple model analyzing the global shrimp market[11], which includes fishery and
aquaculture production as well as environmental impacts[17] are shown below. Such a model is
necessarily highly descriptive as characteristics of the global market are greatly simplified.
13
Martin Richardson 578168
Figure 7: Scenario incorporating environmental impacts of aquaculture with effluent from farms limiting production.
Price rises as supply is limited. In turn the fishery grows and wild shrimp are reduced. Johnston et al. 2002.
Figure 8: As wild populations are reduced in the previous scenario, wild populations are reduced, thereby increasing the
cost per unit effort of the fishery. This scenario demonstrates the effect of a one-time government subsidy to commercial
fisherman at month 200 leading to a brief upturn in wild catches, limitation of aquaculture production and steady
increase in price. Johnston et al. 2002.
Key to model outputs
Actual price
Global shrimp price
14
Martin Richardson 578168
Harvesting
Aquaculture production
Catching
Fishery production
Wild shrimp biomass
Production of P. Vannamei has undergone a complete shift from wild fishery to aquaculture starting
around the turn of the millennium[18], due in part to development of disease resistant strains[19].
One scenario considered using the model, termed ‘Unbounded Aquaculture’ was closest to the mark
but was not considered a likely outcome. Illustrating how bias can influence the use of a model.
Analysis was skewed towards maintenance of a commercial fishery.
Shrimp characteristics
Penaid shrimp are marine but may spend part of their lifecycle in brackish estuaries[20]. Shrimp live
for 1.5 to 6 years with multiple cohorts in wild populations. In aquaculture there may be more than
one cohort in a pond. As with all crustaceans growth is discontinuous with periods of rapid growth,
no growth, and even negative growth particularly related to water temperature[21]. Growth can be
measured in terms of carapace length, total length or weight. The molt cycle is dependent on the
species in question as well as the age and size of the individual animal. Wild populations synchronize
molting with lunar cycles and bury themselves in the substrate to minimize predation and
cannibalism while the carapace hardens. The molting interval is affected by food availability and
environmental conditions, particular temperature[22]. Molting duration increases as the
temperature drops. Water is taken up during molting, with rapid gain in the wet weight of
replacement exuvia. However, the majority of somatic growth occurs during intermolt periods.
Feeding is nocturnal in many species, and there is a break of several days in feeding while molting
occurs. Feed intake increases with temperature. Light sensitivity to feeding varies widely, with some
species only active for 1 to 2 hours a night[23].
Shrimp show sexual dimorphism with females being larger, and growing faster than males. Females
achieve maturity at approximately 30-40 mm, after some 6 months, and produce from 100,000 to
over 250,000 eggs[23][24]. They usually spawn twice annually, although some species spawn only
once each year. Survivability is related to both temperature and salinity with increased salinity
mitigating against critical low thermal limit associated with mortality. Mortality due to cannibalism,
particularly during molting, is a factor in aquaculture. Aquaculture studies have shown significant
15
Martin Richardson 578168
increased production potential through the use of a ‘substrate’ made of plastic mesh that permits
vertical separation of the shrimp[25], thereby greatly reducing the effective stocking density.
Methods
Shrimp bioenergetics research by Ingrid Lupatsch et al. at Swansea University’s’ centre for
sustainable aquatic research (CSAR) assessed protein and energy requirements for optimal growth of
shrimp under controlled conditions. Knowing daily protein and energy requirements for provides for
improved aquaculture practice in reducing waste and optimizing feed. Waste from aquaculture
facilities is an important problem[17] and results in contributions to dissolved organic matter as well
as benthic deposits[26]. Feed may account for as much as 50%[27] of all costs. Various protein and
energy sources can be used to formulate a feed to known composition. Until quite recently feed
composition in aquaculture was determined by comparison with dietary requirements of
domesticated animals (e.g. chickens). Since shrimp aquaculture is now a large industrial enterprise
around the World such calculations are of economic importance. For pacific white shrimp (L.
vanneamei) growth was measured by increase in wet weight, the body weight (BW) in grammes at
28°C with 32 ppt (parts per thousand) water salinity. pH and dissolved oxygen (DO) were not
specified. The equation for growth rate applies to post larval juvenile and adult stages over the range
of 1 g to 35 g.
This is an individual growth model so all quantities are per shrimp.
Growth rate is measured as incremental body weight per day, weight gain (g day-1).
= 0.050 × BW 0.582 , for 1g ≤ BW ≤35g
(1) Growth rate (g day-1)
(2) Voluntary feed intake rate (g day-1) = 0.086 × BW 0.720
Energy requirements in kJ per day
Digestible energy required for maintenance, DEmaint (kJ day-1)
DEmaint=0.345xBW (kJ day-1)
(3)
(4) Expected energy gain (kJ day-1)
=(growth rate)x(energy content of gain)
Energy content of gain =4.844 kJ g-1
Energy gain
= 0.050 × BW 0.582x4.844 (kJ day-1)
Digestible energy requirement for growth, DEgrowth (kJ day-1)
(5) DEgrowth
=(growth rate)x3.23x(cost in DE to deposit a unit of energy as growth)
16
Martin Richardson 578168
 DEgrowth =0.050 × BW 0.582x3.23 x4.844 (kJ day-1)
(6) Digestible energy for maintenance and growth DEmaint+growth= DEmaint+DEgrowth (kJ day-1)
Protein requirements in grammes per day
= 0.75xBW(g day-1)
(7) Digestible protein required for maintenance (DPmaint)
(8) Expected protein gain
Protein content of gain
=(growth rate)x(protein content of gain)
= 17.2%
Protein gain = 0.050 × BW 0.582x0.172 (g day-1)
(9) Digestible protein required for growth (DPgrowth)
= (protein gain)x(cost in DP to deposit a unit of protein as growth)
DPgrowth
= 0.050 × BW 0.582x0.172x2.270
(10)Total DP required for maintenance and growth (DPmaint+growth) = DPmaint+DPgrowth
Feed related calculations
Let DE content of feed
= 14 kJ g-1 .Then the …
(11)required feed intake to meet DE requirements (g)
= DEmaint+growth/(DE content of feed)
=DEmaint+growth/14
(12)Required DP content of feed to meet DP requirement (%)=(DPmaint+growthx100)/Feed intake
=(DPmaint+growthx100)/(DEmaint+growth/14)
=14x100xDPmaint+growth/DEmaint+growth
=1400xDPmaint+growth/ DEmaint+growth
(13)Feed conversion ratio (FCR) =(feed intake)/(weight gain)
(14)DP/DE ratio
=DP content of feed (mg)/DE content of feed(kJ)
17
Martin Richardson 578168
Energy
Energy content of
body
Growth Rate
Energy gain
Total energy
component
DEefficiency
DEgrowth
DEmaint
DEcost
Body Weight
DEmaint&growth
Figure 9: Energy component of model. The diamonds are constants. Circles and oblongs are variable quantities that are
calculated using inputs from incoming arrows. The bracketed variables reference the same quantities at different
locations within the model without using connecting arrows and thereby reduce clutter.
Model object name
Quantity
Value/ Equation number
Energy content of body
Constant
4.844 kJ g-1[28]
Total energy component (Energy content of body)x(body weight)
DEmaint
DEmaint
(3)
DEgrowth
DEgrowth
(5)
DEmaint&growth
DEmaint+growth
(6)
Energy gain
(4)
DEefficiency
Constant
0.31
DEcost
1/DEefficiency
3.23
18
Martin Richardson 578168
Protein
protein content of
body
Growth Rate
Protein gain
Total protein
component
DPefficiency
DPmaint
DPgrowth
DPcost
Body Weight
DPmaint&growth
Figure 10: Protein related calculations of the model.
Model object name
Quantity
Value/ Equation number
Protein content of body
Constant
0.172 [28]
Total protein component (protein content of body)x(body weight)
DPmaint
DPmaint
(7)
DPgrowth
DPgrowth
(9)
DPmaint&growth
DPmaint+growth
(10)
Protein gain
(8)
DPefficiency
Constant
0.44
DPcost
1/DPefficiency
2.27
19
Martin Richardson 578168
Body Weight
Growth Rate
b
a
Voluntary Feed
Intake
Figure 11: PowerSim model of energy, protein and feed calculations applied to growth of L. Vannamei
Model object name
Quantity
Value/ Equation number
a
Coefficient of MBW
0.05
b
Exponent of BW
0.582
Growth rate
Body weight
(1)
BW g
Voluntary feed intake
(2)
20
Martin Richardson 578168
Results
Allometric weight gain
Weight gain (g per day)
0.4
0.3
0.2
0.1
0
5
10
15
20
Body weight (g)
Non-commercial use only!
Feed intake (g per day)
Feed intake vs. body weight
1.0
0.5
0
5
10
15
20
Body weight (g)
Non-commercial use only!
Figure 12: Model results for allometric weight gain and feed intake against body weight.
These results match the calculations given in Lupatsch et al. 2008 as listed below.
21
Martin Richardson 578168
Figure 13: Lupatsch et al. 2008. Studies on Energy and Protein Requirements to Improve Feed Management of the Pacific
White Shrimp, Litopenaeus vannamei. The calculations have been completed for shrimp at 2 different weights: 2g and
10g. Feed calculations follow from specified digestible energy (DE) content which was set at 14 kJ g -1.
22
Martin Richardson 578168
Growth in L. vannamei at 28 C with 32 ppt salinity and
optimal feeding
Body Weight (g)
30
20
10
0
0
20
40
60
80
100
120
140
Time in days
Non-commercial use only!
Figure 14: Early stage growth. The curve has not yet reached the asymptotic weight as the equation is only valid for
shrimp below 35g. Lupatsh et al. 2008.
Feed
DEmaint&growth
Required feed
intake rate
FCR
DPmaint&growth
DEcontent
Growth Rate
DPcontent
DP DE ratio
Figure 15: Feed calculations
Model object name
Quantity
Value/ Equation number
DEmaint&growth
DEmaint+growth
(5)
23
Martin Richardson 578168
DPmaint&growth
DPmaint+growth
(9)
Required feed intake rate
Required feed intake for growth (10)
DEcontent
DE content of feed (constant)
14 kJ g-1
DPcontent
Required DP content of feed
(11)
(%)
DP DE ratio
DP/DE
(13)
FCR
Feed conversion ratio (FCR)
(12)
Required feed intake rate
Voluntary feed intake
Feed intake in grammes
1.0
0.5
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
Time in days
Non-commercial use only!
Figure 16: Model results showing voluntary feed intake against actual feed intake.
Discussion
Experimental results for shrimp growth, as well as growth models[5,15,29] all show generally
monotonic, asymptotic curves from juvenile through to adult stage. While there are numerous
factors that affect growth at the individual level, temperature and the molting cycle appear to be
most important. Growth has also been found to be affected by stocking density and biomass as well
24
Martin Richardson 578168
as water salinity, pH, naturally occurring food[30][31] and photoperiod. There are numerous studies
in the literature addressing one or more of these environmental factors; however no clear picture
emerges as to how they interact to affect growth in combination. The mode developed by Franco et
al. [5] indicates sensitivity to temperature as shown below and this is also evident from experiments
and aquaculture.
Figure 17: Franco, A. R. et al, 2006. The model developed by Franco et al. is not sensitive to a ±10% variation in food
availability, but shows susceptibility to a ±10% change in water temperature indicating that temperature has a major
effect on growth.
Temperature considerations
Wild shrimp populations and pond shrimp are subjected to diurnal and seasonal temperature
variation. The characteristics of these temperature changes are well understood[32]. Seasonal
temperature effects upon growth can be added to the model. Temperature curves are generally
sinusoidal with a winter minimum and summer maximum as shown below.
25
Martin Richardson 578168
Figure 18: Adamack et al. 2012. Seasonal temperature curve for wild shrimp population.
Figure 19: Weekly pond water temperature in Australian aquaculture. Seasonal variation is clearly evident. The shaded
area shows weekly maxima and minima. Jackson, C. J. et al. 1998.
These temperature changes can then be combined with the variation in growth at different
temperature in order to model the effect. The expected results are accelerating or decelerating
26
Martin Richardson 578168
growth with periodic negative growth dependent upon response for the species in question and
environmental temperature range.
Figure 20: Growth in length at various temperatures. Species not identified. Source: Northern Gulf Institute, data derived
from the literature. Growth ceases at 0°C and increases to a maximum rate at around 25°C. As temperature increases,
growth declines and stops at approximately 35°C. Continuing temperature increases result in mortality. This is a problem
in shallow aquaculture ponds in the tropics. Low temperatures can decimate overwintering stocks in wild shrimp.
Food intake and growth increase with water temperature but decline beyond the optimal point.
Franco et al. [5] used a quadratic equation as a temperature function ,𝑓(𝑇), to model the effect of
temperature on shrimp feeding rate.
(15)𝑓(𝑇) =
−0.02𝑇 2 +1.44𝑇−17.41
𝑅32
[5]
Where R32 is the maximum feeding rate at the optimum temperature of 32°C for P. japonicus. If we
assume that the behavior is similar for P. vannemei, and that the maximum feeding rate is achieved
at, say 27°C then the general form of the graph of this function is as follows:
27
Martin Richardson 578168
Figure 21: General form of the temperature function with temperature in °C on the x-axis. The y-axis value represents a
growth coefficient, as yet not defined.
Using the graph in figure (18) above taken from Adamack et al. 2012 , the annual temperature
variation in this location (Mississippi, USA) is approximately 22°C over 365 days (1 year). We can
approximate this without considering the actual date using the following equation:
(16)Water temperature=11sin( 360𝐷 /365) + 24, where D is the time in days.
Water temperature
40
30
20
10
0
0
20
40
60
80
100
120
140
Time in days
Non-commercial use only!
Figure 22: Natural fluctuation in water temperature associated with seasonal change over time.
Equation (16) can then be adjusted to match particular dates as required. Further studies, possibly
combined with salinity variation[33], are needed in order to better understand temperature effect. A
study by Rothlisberg, 1998 [34]considered larval growth as illustrated below
28
Martin Richardson 578168
Figure 23: Rothlisberg, 1998. Effects of salinity and temperature on growth of shrimp protozoae.
Molting
Figure 24: Simulated oxygen consumption during 3 stages of moulting, pre-moult, moult, and post-moult. Mishra et al
2002. In actuality the cycle increases with size and age of the individual.
P. vannamei, molt every 5 days at 1-5g and every 14 days at 15g[23][35]. Information regarding the
molting cycle permits derivation of a scalar quantity that can be used to stretch the timeline, thereby
increasing both the inter-moult period and the length of the molt itself to better match observed
behavior. However, molting is also affected by temperature as shown below. Molting interval
increases inversely with temperature[36][22], tripling as temperature drops from 18°C to 14°C.
29
Martin Richardson 578168
Figure 25: Molting period at 3 different temperatures. Kumlu et al 2005.
Conclusion
In order to improve the model additional experiments are needed to better understand the effects of
salinity and temperature, molting and spawning. There is little available data in the literature
concerning shrimp bioenergetics in general and environmental effects in particular. There is need to
standardize nomenclature, notation and formulae so as to provide a more rigorous foundation for
this field of research and to avoid errors of interpretation. A standardized metadata and verification
algorithm would also permit easier combination and exchange of models. The primary value is in the
data, as well as associated costs so best practice might involve the sharing of ‘open’ models through
the use of an industry ‘ecosystem’ of stakeholders. This would ensure improved scrutiny of the
methods used and enable the facilitation of popularity ratings and error calculation to indicate
stability as an indication of descriptive vs. quantitative purpose.
Appendix
Body weight to carapace length conversion
A body weight to carapace length conversion formula[5] was developed by Franco et al. in their
paper ‘Development of a growth model for penaeid shrimp’. Shrimp were measured and weighed to
determine the relationship. The species used was Penaeus indicus.
Log10BW
= 2.8xLog10CL -2.9
References
30
Martin Richardson 578168
1
Bureau, D. & Azevedo, P. 2000 Pattern and cost of growth and nutrient deposition in
fish and shrimp: Potential implications and applications. , 111-140.
2
Adamack, A., Stow, C., Mason, D., Rozas, L. & Minello, T. 2012 Predicting the effects
of freshwater diversions on juvenile brown shrimp growth and production: a Bayesianbased approach. Marine Ecology Progress Series 444, 155-173.
(doi:10.3354/meps09431)
3
Lupatsch, I. 2009 Quantifying nutritional requirements in aquaculture: the factorial
approach. New Technologies in Aquaculture. Woodhead Publishing Limited,
Cambridge, UK , 417–439.
4
Lupatsch, I. In press. Aquatic Animal Nutrition Feed formulation. Growth (Lakeland)
5
Franco, a, Ferreira, J. & Nobre, a 2006 Development of a growth model for penaeid
shrimp. Aquaculture 259, 268-277. (doi:10.1016/j.aquaculture.2006.05.051)
6
Daviddottir, B. 2002 Management of the Commons: Social Behavior and Resource
Extraction. In Dynamic Modeling for Marine Conservation (eds M. Ruth & J.
Lindholm), pp. 356-373. Springer.
7
Kleiber, M. 1932 Body size and metabolism. Hilgardia 6, 37.
8
Green, D. 1976 The historical development of complex numbers. The Mathematical
Gazette 60, 99-107.
9
Yu, R., Leung, P. & Bienfang, P. 2006 Predicting shrimp growth: Artificial neural
network versus nonlinear regression models. Aquacultural Engineering 34, 26-32.
(doi:10.1016/j.aquaeng.2005.03.003)
10
Tetlock, P. 2006 Expert Political Judgment: How Good Is It? How Can We Know?
Princeton University Press; New Ed edition (31 July 2006).
11
Johnston, D., Soderquist, C. & Meadows, D. 2002 The Global Shrimp Market. In
Dynamic Modeling for Marine Conservation (eds M. Ruth & J. Lindholm), pp. 394417. Springer New York.
12
Christensen, V. 2009 Ecopath with Ecosim: linking fisheries and ecology. In Handbook
of ecological modelling and informatics (eds S. E. Jorgensen T. S. Chon & F.
Recknagel), pp. 55-70. WITpress.
13
France, B. 2002 Policy Research for Sustainable Shrimp Farming in Asia Centre for the
Law and Economics of the Sea CEDEM University of Shrimp Farming in Thailand : A
Review of Issues Shrimp Farming in Thailand : A Review of Issues.
31
Martin Richardson 578168
14
Ferreira, J. et al. In press. SMILE Sustainable Mariculture in northern Irish Lough
Ecosystems.
15
Mishra, A. K., Verdegem, M. & Dam, A. V. 2002 A Dynamic Simulation Model for
Growth of Penaeid shrimps. Metabolism Clinical And Experimental
16
Franco, a, Ferreira, J. & Nobre, a 2006 Development of a growth model for penaeid
shrimp. Aquaculture 259, 268-277. (doi:10.1016/j.aquaculture.2006.05.051)
17
Cao, L., Wang, W., Yang, Y., Yang, C., Yuan, Z., Xiong, S. & Diana, J. 2007
Environmental impact of aquaculture and countermeasures to aquaculture pollution in
China. Environmental science and pollution research international 14, 452-62.
18
Holthius, L. B. 1980 FAO Species Catalogue Shrimps and Prawns of the World.
19
Wyban, J. 2007 Domestication of pacific white shrimp revolutionizes aquaculture.
Global Aquaculture Advocate , 3.
20
Padlan, P. G. 1987 Pond culture: Pond Culture of Penaeid Shrimp. UN FAO: Fisheries
& Aquaculture department.
21
Coman, G. J., Crocos, P. J., Preston, N. P. & Fielder, D. 2002 The effects of
temperature on the growth, survival and biomass of different families of juvenile
Penaeus japonicus Bate. Aquaculture 214, 185-199. (doi:10.1016/S00448486(02)00361-7)
22
Kumlu, M. & Kir, M. 2005 Food consumption, moulting and survival of Penaeus
semisulcatus during over-wintering. Aquaculture Research 36, 137-143.
(doi:10.1111/j.1365-2109.2004.01196.x)
23
Dall, W. 1990 The biology of the Penaeidae. Academic Press Limited.
24
2012 Cultured Aquatic Species Information Program Penaeus vannamei. pp. 1-15. UN
FAO: Fisheries & Aquaculture department.
25
Tidwell, J. & Coyle, S. 2008 Impact of Substrate Physical Characteristics on Grow Out
of Freshwater Prawn, Macrobrachium rosenbergii, in Ponds and Pond Microcosm
Tanks. Journal of the World Aquaculture Society 39, 406–413.
26
Jimenez-Montealegre, R., Verdegem, M. C. J., van Dam, A. a & Verreth, J. a 2005
Effect of organic nitrogen and carbon mineralization on sediment organic matter
accumulation in fish ponds. Aquaculture Research 36, 1001-1014. (doi:10.1111/j.13652109.2005.01307.x)
27
Lupatsch, I. In press. Aquatic Animal Nutrition Feed formulation. Growth (Lakeland)
32
Martin Richardson 578168
28
Lupatsch, I., Cuthbertson, L., Davies, S. & Shields, R. J. 2008 Studies on Energy and
Protein Requirements to Improve Feed Management of the Pacific White Shrimp ,
Litopenaeus vannamei. Management , 281-295.
29
Jackson, C. 1998 Modelling growth rate of Penaeus monodon Fabricius in intensively
managed ponds: effects of temperature, pond age and stocking density. Aquaculture
research , 27-36.
30
Wyban, J. A., Lee, C. S., Sato, V. T. & Ssveekey, J. N. 1987 Effect of Stocking
Density on Shrimp Growth Rates in Manure-Fertilized Ponds. Public Health 61.
31
Otoshi, C. A., Moss, D. R. & Moss, S. M. 2011 Growth-Enhancing Effect of Pond
Water on Four Size Classes of Pacific White Shrimp, Litopenaeus vannamei. Journal
of the World Aquaculture Society 42, 417–422.
32
Hoang, T., Lee, S. Y., Keenan, C. P. & Marsden, G. E. 2002 Cold tolerance of the
banana prawn Penaeus merguiensis de Man and its growth at different temperatures. ,
21-26.
33
Adamack, A. T., Stow, C. A., Mason, D. M., Rozas, L. P. & Minello, T. J. 2009
Temperature and Salinity Effects on the Growth and Survival of Juvenile Penaeid
Shrimps: Implications for the Influence of River Diversions on Production.
34
Rothlisberg, P. C. 1998 Aspects of penaeid biology and ecology of relevance to
aquaculture: a review. Aquaculture 164, 49-65. (doi:10.1016/S0044-8486(98)00176-8)
35
Nunes, a 2000 Size-related feeding and gastric evacuation measurements for the
Southern brown shrimp Penaeus subtilis. Aquaculture 187, 133-151.
(doi:10.1016/S0044-8486(99)00386-5)
36
Sarac, H. Z., McMeniman, N. P., Thaggard, H., Gravel, M., Tabrett, S. & Saunders, J.
1994 Relationships between the weight and chemical composition of exuvia and whole
body of the black tiger prawn, Penaeus monodon. Aquaculture 119, 249-258.
(doi:10.1016/0044-8486(94)90179-1)
33