,
,
LC.E.S C~M.J 995 "
C.M.1995/K:39
-
'
'.
' . ' ' ' '
,
1
AGE DETERMINATION OF HOMARUS AMERICANUS USING
AN INDEX OF L1POFUSCIN A8UNDANCE
by
Ä.de Kerios (1)
G.Conan (2)
M.R.J. Sheehy (3)
(1) Universlte de Moneton, Departement de ehimie-biöchimie,
Marieton, N.8., E1 A 3E9, Canada
,
,
(2) Dep~utmerit of Fisheries and Oeeans, Gulf Region, Moneten, N.8.,
E1C 986, Canada
,,'
.
,
(3) University of Queenslarid; Zoology Departmerit, Australia arid
University of Leicester, Zoology DeparÜnent, England
•
~<"
ABSTRACT
A lipofusein abundanee index is used for age determiriations
(Sheehy, M.R.i, 1989) of Homaius americanus. LipofusCins' are
identified on histological preparatiens of. the brain by fluorescence
microscopy, arid histochemic~1 staining. Lipofuscin. abundance is
quaritified by semi:autornated measurerri.ents of its yellowautofluörescence under U.V. excitation. The f1uofescence is. measüred
either by digital, image analysis of the preparatioris or by analogue
phetometry of fluorescence intensity. The between-age-groups ,
vadability is much greaÜJr than the between-individuals variability,
allowing precise age discriminaticiris.
•
..
A preliminary calibration on preparations fram cuitured lobsters of
known age (Couftesy Bodega Bay; U.C. Davis team) is coridLicted.
Lipofuscin provides apreeise age index (R2=.95). No significant
differences are found between lipofusein aecumulations in
individuals of a same age group. A 100% disei-imination of
individuals into cor'rect 'age groups could be achieved. Over the range
of ages studied, a positive exponeritial, cir an allometrie model
adequately represent Iipefuscin accumulationvs age.Th~
Lipofuscin/age relatioriship should not be ealibrated on 19bsters
reared at constarit temperature for age determimitions of wild
lobsters· beeause the lipofusein contents can differ considenibly.
.Calibrations are attempted on wild lobsters uslng age
.
"
..... determinations based on modal analysis of younQ individuäls and life
1
••
cycle information. The he~erogeneity of Iipofuscin abundance reveals
that ages in sinall size modal groups may, already be quite variable.
The life history arid genetic charactedstics of each individual
might also affsct Iipofuscin metabolism. The waters of the Gulf' of
5t Lawrence are strongly stratified in summer (~1 oe to 22°C) and
provide a yery heterogeneous habitat Individuals Iife historiE~s may
widely differ.
Notwithstanding the difficulties encountered for calibration, our
best working hypothesis suggested an age of 5 years for a 63 mm
carapace length (minimal legal size) males arid 8 years for one
female of the same size.
_.
INTRODUCTION
~
After the recerit decline of the cod fishery, the lobster fishery now
provides the most important catch in vfllue withiri the Gulf of 5t
Lawrence. The forecasting of lobster recruitment to the fishery
several years in advance is of growing importance for management
as weil as economic planning; Unfortunately, the estimatiori of the
abundance of un-recruited age groups is hindered by the present
difficulty to estimate the aga of lobsters.
For age determinatioris one must rely exclusively on sizes. The molt
and growth schedules may vary considerably between individuals and
between locations. Only the very first mcidesin the size-frequency
distributions of the youngest benthic stages may be attributad to
age groups. Large modal sizes are. artefacts created by a
combination of harVesting regulations, and molt groups. Lobsters
having molted the same nuinber of times may belong t6 very
different age groups. This is partially due to the fact that lobsters
may molt less than once· a year as they grow older. Females foi'
instance will alternate molling arid spawning in such a way that
they will· normally skip a molt while incubating eggs.
Attempts to age lobster by other means than size have not been
fully successful. For instance, the number of antennular segments 0 r
the number of cirrimaHdia have proved to be beuer correlated w i t h
size than with aga (Henocque, 1987; 5h.elton,1991).
We attempt to adapt a technique developed by 5heehy (1989) for age
determinations of ci crayfish; Cherax cuspidatus. The. accumulation
of lipofuscins in tissues during aging is foimd in a wide range of
.animals, from arthropods to mammals. The biochemistry of the
. > accumulation in the human eye has been described (Eldred and Lasky,
2
e
1993). It appears thai IlpofusCin accurriulatian is actually the
consequence of an incomplete destruction of metabölites during the
process,of rejuvenaticin of the cells. The rejuvenation results from a
destructiön(lysis) and rebuilding of cellular structures, tiut,the
process "of .Iysiswould become incomplete with, seriescence. Tissues
in wh ich thecells are thought t6 have stopped dividing (postmitotic
tissues) should, contain an arrlOunt of lipofuscin wh ich is a funCtiöri
of age. By callbrating the lipofuscin/age relationship arid fitting' an
adequate model, it should be possible to read age as a function of
amount öf lipofusCin deposited.
o.
•
•
MATERIAL AND METHODS
•
Bioiogical
material
Thirty four löbsters from early berithic to commercial sizes were
collected from the wild in Malpeque Bay (Prince Edward Islarid) by
trawling (Conan
eil., ,1994). The Jobsters were selected fra'm modal
groups ranging in size. from 30 to 80 mm. The iridividuals were
measured, weighed and sexed. Caution was taken. not to chose
lobsters with missing legs.er sigris of regeneration that might· have
hindered growth. The sampling had been designed to be
,
simultarieously used for surveying and mapping the aburidarice of all
slze caiegories of lobsters (Conari et al., this meeting). It is feit
that the lobsters selected weil represerit average characteristics of
the Malpeque Bay stock.
et
EighteEm lobsters of known, age were obtained from an aquaculture
facility (Courtesy Bodega, Baylaboratory; University of California
Davis). Three sets öf six iridividLials were. provided ,each fram three
hatc~ing. everits which hild occurred on 11, August, 1991, 19 February .
1992, and 6 August 1992. At the time of the tissue sampling these
lobsh3rs, were respectively 42; 37 and 31 month old.
on
After tdals
the heart and ether· tissues, the oifactory lobe of the
brain was seiectedas im expected post-mitotic .tissue for
measurement of. Iipofuscin abundance. Prior to dissection the .
lobsters were ariesthetized at, cold, temperature. The brains, of the
animals from the wild were dissected in, vivo. The cephalothöraxes
of the. a,nimals from t~e aquaculture, facility were fixed in toto
immediately after sacrifice. The fixations were made for 24 hours
in 10% formalin in seawater. The lobsters ,from the aquaculture"
facility 'ware shipped arid remained in the fixative rrieqiurri for 3
.daYs.
3
Lipofuscin
abundance
index
LipofusCin .deposits were identified arid. quantified .on histological
serial histological sections of the ol!actory lobe byselective
histochemical staining (Pearse, 1985) and by U.V. induced ,autofluorescence. We had initially considered extraction arid titration by
standard biochemicai mettlods, out we were aeterredfrom this
procedure hy the fact that "Iipofuscins" a complex mixture of
products which; so hir, cannot be easily detected in solution.
Lipofuscin grariules conversely have adefinite structure and can be
identified in histological preparations oy auto-fluorescence or
staining.
The Iipofuscin deposits were located by comparing sections stained
by reactants specific to different biochemical characteristics of
lipofuscin, and by obserVation under U.V; light within a range of
wavelengths specific for. Iipofuscin autö-fluorescence. Histological
preparations were made from 6Jlm serial sections in. paraffin wax
using standard mounting procedures. Lipofuscin-specific staining
was achieved using either Sudan, black periodic acid-Schiff, or
haematoxylin-eosin (Pearse, 1985). Unstained preparations were
observed under a f1uorescerice microscope, using 330 to 380 nm UV
excitation light.
'
The abundance of Iipofuscins in the deposits within a section was
quantified by measuring the auto-fluorescence they produce either
by image analysis of a digitized colour picture (IADCP) of the
section, or by direct analogue ,measurement of the light emitted
(DAMLE) by a specific area of the section. ,Initial trials for directly
digitizing the image of the slide' under microscope, using a digital
camera; and feeding the data direCtly into a computer did not provide
high enough a resolution in coiours and a sufficiEnlt pixel definition.
A higher definition, both in colour resqlution and iri definition was
obtained by taking a ,colour photographic arid digitizing it using a
standard page scariner. In DAMLE, the amourit of light emitted by the
Iipofuscin was measured oya photometer mourited on a Leitz
fluorescence microscope. Ttle power of resolution ,of the photometer
was enhariced tiy a monochromator arid a photomultiplier. The
position and size· of llle field measured was adjusted manually. We
proceeded by measuririg the 'light emitted bcith by llle preparation in
toto, and by 3 conspicuous lipofuscin graiiules.
lri the IADCP, the scanned digital data was processed using the
software "Adobe Photoshop". Colours, were scanried into three
.components red, green, and. blue (RGB) for display on three colour
'._. plane monitors. Tne intensities of the red, green, and blue
4
•
.\
components for each pixel were classified into frequency
histograms which were analyzed ,separately. Since aach, pieture was
a different photographie framewith its own. scale of colours, each
picture needed to be calibrated separately. For calibratio,n; the range
of intensities in red, green,' and blue is measured on histograms
. Ülken fram fields on the digitized photograph which appear to
'contain Iipofuscin exclusively. The modal sub-components
. charactt3ristic of lipofuscins were theri identified. and estimated on
the digitized. in toto, photograph; In ttlis, process the frequencies of
the ,intensities within, the range identified .. as characteristic of
Iipofuscin ware simply summed. After initial trials, for si~plicity,
the cinalyses were conducted only on the green component which
contained most of the· information on the characteristic yellow .
. fluorescence oflipofuscin. The index of Iipofuscin is rf3presanted by
the number of fluorescent pixels or by the ratio of the number of
fluorescent pixels rapresenting· the 'organ., '
In the DAMLE, the measures of light emitted we automatically
processed by the MPV-STAT software provided by Leitz. Direct
measurements of lightintensity. emitted within the selected range
of wavelengths either by the lobe in toto or by the seleeted field,
were provided as output.
.......
RESULTS
Location
•
arid' aspect
of
Iipofusciri
concenthitions.
Lipofuscin appeared to be rarido~ly distributed wlthin the olfactory
lobe in the form of structured granules of sizes rariging' from 2 to 6
. Jl., Jhe gr~nules fluoiesced in bright yellow (560 to 620 nm) unaer
330 to 380 nm UV light. The. granules are conspicuously revealed by
Sudan Black, periodic acia-Schiff reaction, and Haematoxyliri-eosin.
The distribution Of lipofuscins along a sequence series of serial
sections is presented in figiües. 1. and 2. The data is proviaea both as
counts of f1uorescent pixels (1) and as the. rätios of fluorescerit
pixels. to the total number. 6f pixels within the se6tio~ of the. lobe
(2). Figure 1. shows a quadrati6. relcitionship between counts. eif .'. ,
fluorescent pixels arid theirserial (Spearman' rank correlatiein P=.47)
locationwhi6h was satisfactor,ily cOrrected .by taking the, ratio
index (Flg 2). SUbsequently cill further stätistics' were calculated for
ra.tio indices.
.A ~istogram of the frequencies ..of counts or ratios of fluorescent
...-. pixels on a complete series of 74,serial sections eif an olfactory
5
lobe (figure 3) showed a symetrical distribution which was
approximated by anormal curve. A Student test shows that a random
selection of 12 sectiens weuld prövide. an estimate of mean ratio
within +/- 10% of the true mean in 950/0 ef cases. For practical
purposes only 12 sections were fully analyzed for each lobster in
further werk.
Relationship between lipofu·scin abundance
IADCP and age in reared lobsters
measured
by
The best fit was obtained for an exponential or allometric models
(R2 = .95) rather than a simple linear (figure 4, 5, and table 1). ,
There were no significant difference ( P:>.05) between lipofuscin
abundance indices of different iridividuals within the same age group
(ANOVA and Kruskall-Wallis). The average lipofuscin abundance
indices for individuals to different age groups did not overlap. The
between-age-group difference was significant (P<.0001) when
tested by ANOVA.
Within each age group there was lihle correiation between the
lipofuscin abundance and the weight of the individuals (Fig. 6; R2 <
.25). It was the age independently from the weight of the individual
which appeared to determine its Iipofuscin conterit.
Relationship between lipöfuscin abundance
IADCP and age of wild lebsters
measured
by
The lipofuscin contentsof lobsters .taken from the wild in Malpeque
Bay were much lower than those of reared lobsters of comparable
size. However, the wild individuals were thought to be much older
than the reared lobsters, based on previous, tagging arid modal
analyses of size frequency distributions.. The lipofuscin content vs
age relatioriship of wilo indiviauals could not be calibrated from
data on reared iridividuals.
Alternatively age were estimated from modal analysis and previous
knowledge on the molting seasons arid molting frequencies of
lobsters iri Malpeque Bay' (Moriyasu, 1984). Figure 7 and table 2
illustrate the relationship between lipofuscin abundance and age as
defined from the size of the individuals studied and 'the position of
the first 6 modes in the size frequency distributions. Ttiere was a
definite relationship between Iipofuscin coriterit and presumed age,
and a discrimination betWeen presumed, äges was achievablE3 for
most individuals on the basis of their lipofuscin content However,
there were significarit differences between the Iipofuscin contents
. 'of individuals within .any of the modal groups at the 5% level; when
6
tested by ANOVA. The maan lipofuscin eontents of ihe different ,
modal groups did not diffe,r significantly wl1en compared by ANOVA
(Table 3).
Measuremerits
of
Iipofuscin abundance by' DAMLE and age
The DAMLE results were eomparable to the IADCP results; but the
disci'imination .between .age groups was not as good, and there were
signifieant differenees (P <:.05) between individui:lIs within' the same
groups. Mecisurements on individual granules did not provide a beUer
resolution than measurements on the lobe in toto. The DAMLE was a
faster but lass selective pracedure than the IADCP. Photometrie
measures were possibly corrupted by light emissions fram sources
other than Iipofusein.
DISCUSSION
.'
e
Our experimenÜll results ean be explained in the eontext of the '
current interpreÜltions of Iipofuscinmetabolism. Within an age
graup; the lobsters of knöwn age obtained trom ci rearing. experiment
all came trom " the same brciöd; and their indices of Iipofuscin ",.' .
accumulation did not' differ significantly. This may l1ave resulted
trom the fact that they all ware genetically similar,' that they häd
been reared under similar conditiöns, but also that tl1ey had
precisely the same age. Conversely lobsters ,taken from the wild, and
attributed to the saine age group had significantly different indices
of lipofuscin accurTlUlation. Their actual bii1.h dates must have been
spread over ä whole sp'awning season of about montl1 since they
most Iikely oi'iginated trom distind broöds. They had experienced
different Iife conditions in an environment which is hlghly
seasomilly arid spatially variable, 'ranging in temperatures trom -1
to 20 2C; and in saliriity fram.20 to 33 per mil.
a
The ciriinials obtained from a rearing experiment provide simplified
information which is usetuifor tasting models öf lipotusein
accumulaÜon vs age. The relationship appeared t6 ba curvilinear arid
monotonie with a slope iricreäsing with age (over· the, age interval
studied). An exponential or an allometi'ic model provided ci good fit.
This is similar to observ.ations o~, Cherax for the earty part of the
Iifespan only (sheehy, et ,al., 1994).
Althöugh the inadequaey of using reared animals to caiibrate ihe
age/lipofuscin abundance relationship is understandable, it is not
.fullY explained. We have' no information on the ,influanee of geneties
or on environmerital tactors on the procass of lipofuscin
7
accumulation in lobsters. The variability of lipofuscin contents in
animals taken trom the wild arid atii-ibuted to the same age group
increases considerably with presumed aga. This may reveals an
artetact due to imprecise age determination by modal analysis
starting trom the' smallest modal sizes, and increasing to the
largest. The number of molts and the time interval between molts is
known to diverge between individuals mostly after onset of maturity
which is reached at a size varying considerably between individuals.
Although very provisional, the age/lipoh.iscin content model, we
produced can be temtatively used for estimating the age of lobsters
captured in Malpeque Bay. We recorTunend however, cautious
interpretations since we do not have information on the year to year
variability in Iipofusciri accumulations, or on environmerital effects..
The most efficient way of calihraÜng the age/lipofusciri content for
lobster in their natural, environment would involve in tagging and
recapture of early benthic stages .of the lobster. It would then be
possible to analyze the between-brood, the between-Iocation and
between-year variability. The experiment should be run over a
minimum of, teri years to allow for a comprehensive coverage of the
presumed life span of commercially harvested lobsters. This may
seem a tedious task, but in the present context of total lack of
,
precise information on the age structure of naturallobster
populations, and of tlle commercial catch; tlle investment would be
highly profitable.
.
•
,
ACKNOLEDGMENTS
The authors wish to thank br. Sharon Me Gladery and Pierre Mallet
for the histological advices, Eimer Wade for collecting and
processing the data, Dr. Mikio Moryasu for the use of the facilities in
Moncton and Guy Robichaud for his assistance on the field.
8
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e
REFERENCES
Conan, G.Y., M. Comeau, C. Gosset, G. Robichaud, and C. GaraTcoechea.
1994. The Bigouden Nephrops trawl, and the Devismes trawl, two
otter trawls efficiently catching benthic stages of Snow Crab
(Chionoecetes opilio),. and American lobster (Homarus americanus).
Can. tech. rep. Fish Aqual. Sei. 1992, 27 pp.
Eldred, G.E. and M.R. Lasky, 1993. Retinal age pigments generated by
seit-assembling Iysosomotropic detergents, Nature, 361,p 724-726
Henocque, Y., 1987. Observations des antennules et determination de
I'äge chez le homard, Homanis gammarus, La Mer, 25, p 1,12.
Moryasu, M., 1984, Molting season and growth at molt of lobsters in
Malpeque Bay, P.E.L, Canada. , LC.E.S., Shelfish Commitee, 17 p.
Pearse, A., 1985, Histochemistry, Theoretical and Applied, Churchill
Eds, London, 245 pp.
Sheehy, M.R.J., 1989. Crustacean brain lipofuscin: an examination
the morphological pigment in the treshwater crayfish Cherax
cuspidatus (Parastacidae), J. Crust. BioL, 9(3), p 387-391.
ot
Sheehy, M.R.J., Greenwood, J.R, Zielder, D.R, 1994, More acurate age
-determination of crustaceans trom field situations using the
physiological age marker, lipofuscin, Mar. BioL, 121 (2), p-237-245
Shelton, P.M.J., RG.J Shelton and P.R. Richards, 1991. Eye
.
development in relation to moult stage in European lobster Homarus
gammarus (L.), ICES CM 1991/K:33, 9 pp.
9 .
~
4000 -f-'
~ 3800
~ 3600
~ 3400
V)
~ 3200
3000
~ 2800
~ 2600
~ 2400
~ 2200
L.....&..
&......L..
....L.....<
-t-
I....I...
3
-f--',1"""'T'"""T"'""r"""T'"""T"'""I"""T""""T"""'I"""'T'""'T"""'I"""'T'"........,I"""'T'"""T"""'I"""T'"""T"""'I"""'T'""'T"""I"""'T'"........,r-r-+-
0
Z
10
20
30
40
50
60
70
NUMBER OF THE SECTION IN THE SERIAL SERIES
Rgure 1- Lipofuscin deposits along 74 histological 6 Jlm serial sections of the'
olfactive lobe of lobster. The deposits appear' sm aller towards the extremities
due to the lobular shape of the organ.
7.5 -f-'.................L.....&..........&......L..~.............L.....<....................I....I...~.............L.....<............L...L....L............L....L.-+7
o 6.5
~
6
5.5
u
5
z
~ 4.5
~
4
c:::
3.5
Li 3
2.5
LU
g
-f--',1"""'T'"""T"'""1"""'T'"""T"'""r""'T'"""T"""'I"""'T'""'T"""'I"""'T'"-.-,I"""'T""""T"""'lr"""T"""T"""'lI"""'T'""'T"""'I"""'T'".......-,I'""""I"'"-+-
o
,0
20
30
40
SO
60
NUMBER OF THE SECTION IN THE SERIAL SERIES
70
Figure 2- Lipofuscin deposits along 74 histological. 6 Jlm serial sections of the
olfactive lobe of lobster. The fluorescence ratio is the ratio of the number of
fluorescent pixels to the total number of pixels representing the organ. This
type of index provides similar results independently of the position of the
section.
10
•
FREQUENCIES
16
14
12
10
8
6
4
2
o
2.5
3
3.5
4
4.5
5
5.5
6
6.5 7
7.5
FLUORESCENCE RATIO
Figure 3- Frequency distribution of the fluorescence ratios in 74 serial sections
of the olfacory lobe of a lobster. The distribution can be approximated by a
normal curve.Twelve random sampies would provide an estimate within· +/10% of the mean in 95% of cases.
11
45
_--------------=---r
40
0
f= 35
~30
~25
a:i 20
~ 15
~ 10
5
g
~O
......"T-------r-------r-----L.
31
37
42
AGE IN MONTHS
Y .. -75.388 + 2.483
* X;
RA 2 ...894
•
o
~ 3.5
3
u
a:i 2.5
~ 2
UJ
UJ
~ 1.5
::::>
Li
1
3
.5 -..,.-;~-----~-----~----'31
42
37
AGE IN MONTHS
Y = -5.21 + 0.207
o
4
* X;
RA 2 .. 0.951
_--------------=--r
~3.5
UJ
3
u
a:i 2.5
~ 2
UJ
~ 1.5
cx:
::::>
Li
3
1
.5 ........---,----------,------r'3.3
3.6
3.7
LN AGE IN MONTHS
Y - -24.516 + 7.481
Figure 4-Reared lobsters.
fluorescence
* X; RA2
Linear, exponential
- .955
and a1lometric
models
tor
ratio vs age data. A1llobsters within a group had identical ages
although the points were shifted in abscissa tor clarity ot the display.
12
Table 1- Fit of models to Fluorescence ratio vs age relationship for reared
lobsters. Residual variance for untransformed variables.
16.7 .
LI NEAR MOOEL
EXPONENTI AL MOOEL
9.0
ALLOMETRI C MOOEL
9.1
13
LINEAR MODEL
+ ......................
10
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...............
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6 4 -
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:
-
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1 .......~"T"""r--rI_""T"""-r+
o
10
15
AGE IN MONTHS
5
20
25
30
EXPONENTIAL MODEL
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1
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1_--'1
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-.2 •
-.3 -.4 -.5 -.6
1
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. .
1.25 1.5 1.75
""
rrr-
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2 2.25 2.5 2.75
LN AGE IN MONTHS
3
3.25 3.5 3.75
ALLOMETRIC MODEL
.5
+-_......_--'.__.......__"--._"""'.__.1....-._.. . . . _ _-'-'_......._-+
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-.4-
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•
II-
•
1
1
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1.25
1.5
1.75
1
1
1
I
2
2.25 2.5 2.75
LN AGE IN MONTHS
1
1
3
3.25
Figure 5-Residual plots for the linear, exponential and allometric models of
fluorescence ratio vs age for untransformed variables. The allometric model
provides the most balanced residuals and the exponential model is the next
best. The linear model is not satisfactory.
14
3.5
HATCHED 6 AUGUST 1991
,
I
•
,
,
,
T
1
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III~
~
I~
I
I
I
240
200
I
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,
~
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320
280
360
WEIGHT IN GRAMS
Y = 9467.044 + 16.421
* X; RA2 = .057
(J)
~
HATCHED 19 FEBRUARY 1992
Ci: 9000 -f-L..........................L.L..........J...L.........L..L..........L...L..a...&..J'-'-'l....oI..I-'-'"""-J-
I
§ 8000
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5000
o 4000
c:::
~ 3000
~ 2000 ooh""T"T""""''''''''''''T""T''T'T'''T'"T"T''T'"T""T"TT"r-T''"T'"r''''''''''I'"'T'"'1''::;''''r-r+
z
100 120 140 160 180 200 220 240 260
WEIGHT IN GRAMS
Y = 7719.206 - 14.548 * X; RA2 = .251
~
><
LU
HATCHED 11 AUGUST 1992
Ci:
!z
~
(J)
~
o
:3
LI..
LI..
o
c:::
LU
~
~
I
3500
3000
2500
2000
1500
1000
500
, I
·
~
~
1
·
·
~
~
~
I
0
95
100
105
~
•
110
' I
115
120
125
130
WEIGHT IN GRAMS
Y = 2032.828 + 1.825 * X; RA2 = 6.539E-4
Figure 6-There was no apparent relationship between f1uorescence ratio and
weight of lobsters within a same age group. It appeared to be the age and not
the weight of the lobsters which determined the tluorescence ratio. If the
number of fluorescent pixels is independet trom weight, the fluorescence ratio
'should be more independent from the weight of the individuals.
15
16 ...f-a.........w..........l..L.I................................"..I-I-.......&..I...I~~..................
I
14
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~ 12
~ 10
as
8
~
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u
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2
O+r"'l""T',.+,""""""....................,..,..,........."l'"T"1.................rT"'I'"'T"'I'.........I""'I""lr+
o
1
2
3
AGE ATTRIBUTED TO THE MODEL GROUP IN YEARS
Y = 1.123 + 1.1 17
* X; R"2 = .076
3+O-........a..I...I........~.........l..L.I.................J................L.L..&;..a....&....L.L.........~
I
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as
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o
1
2
3
AGE ATTRIBUTED TO THE MODAL GROUPS IN YEARS
Y = -.81 5 + .769
* X; R"2 = .308
34--.L---I---I--..L..-..L--L.---J.--L.-4-
I
2.5
o
~
0::
tj
z
LU
.5
~
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2
1.5
1
O+:!!:..---~:ooo"fII::::.--__r---+---+
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-.75 -.5 -.25
0
.25
.5
.75
1
1.25 1.5
LN AGE AlTRIBUTED TO THE MODAL GROUPS IN YEARS
Y = .063 :t 1.172 * X; R"2 = .336·
Figure 7-Lobsters
trom the wild. Linear, exponential and allometric models tor
f1uorescence ratio vs presumed age.
16
Table 2- Fitting models to Fluorescence ratio vs age of wild lobsters. Residual
variance for untransformed variables.
LI NEAR MOOEL
11.36
EXPONENTIAL MOOEL
12.99
ALLOMETRIC MOOEL
12.34
Table 3- Analysis of Variance in fluorescence ratio between individuals within the
first 6 modal groups presumed to be age groups. The differences are not
significant. Regressions on a linear exponential or allometric model do show
that a correlation exists, however.
51 GNI FI CANCE
FLUORE5CENCE RATIO
.29
LN FLUORESCENCE RATIO
.17
17