.,'\.

"

This paper not to be cited without prior reference to the authors

International Commission forthe Exploration of the Sea

Shellfish CornmitteeCommunication C.M. 1985/K:29

Please substitute pages 17 1819, 22, 23. New pages are' sti~hedon the back.

Errata: .. '.- .

Functional maturity of the Americanlobster Homarus americanus

by

Gerard Y. Conan, Michel Comeau andMikio MoriyasuDepartment of Fisheries and OCeansFisheries Research Branch, Gulf RegionMarine Bio1ogy Research Centerat Universite de MonctonMoncton, N.B. E1A 3E9CANADA

,II'

---- -- --- -- -----1I

------------------ ---- ---

- 1 -,.

Summary . " .::

'" .." {,~::~~~::.::~ ,• '.. ,,-",,".1' : .. ,., ......_~ .....

Morphometry.has beerr::frequentlY~~~,,~;g: for defining size at,I' ~ l ~ ,...~ :;".'~ ,;. ,.:

maturity of lobsters • A.-jinear relati"öns.hip is fitted to some.:-~'~;~,~.; ,~~:\!\;.~:~:)

measure of chela sizevs:'~15ody size to'::diflne maturity of males. It

is assumed that a sharp change in slope occurs at onset of maturity.

Similarily some measure of abdomen width is plotted against carapace

or body size to define maturity of females. An inflection point is

believed to occur at onset of maturity. We have analyzed such

sexual dimorphisms in males and in females by standard log linear

transformations and bivariate allometric plots as well as multiva-

riate Principal Components Analysis. We conclude that onset of

maturity cannot be detected efficiently by morphometry of the claw

-of male lobsters or of the abdomen of fema1e lobsters. The diffe-

renciation of these secondary sexual characters is initiated

gradually from early juvenile stages.

Resume

La morphometrie a frequemment ete utilisee pour tenter de

definir la taille a maturite des homards. Chez les males il est

•d'usage d'ajuster une relation lin'~ireauxdonn'esde mesure

standard de la pince en fonction de la mesure standard du corps. On

admet qu1une modification importante de 1a pente de cette droite

apparait a 1a maturite. Chez les femelles il est d'usage de porter

une mesure de la largeur de 1 1abdomen en fonction d'une rnesure

standard du corps. Dn point d'inflexion apparaitrait dans la courbe

a 1a taille de maturit'. Nous avons analys' ces dimorphismes

sexuels chez les males et les feme1les apres transformation

, .

•

"

- 2 -

INTRODUCTION

Size at onset of sexual maturity is often used as a reference

for defining legal minimal size at capture of male and female

lobsters. This goal is set intuitively or after calculations of

spawning biomass and fecundity per recruit (Campbell 1985). Size at

onset of maturity of male and female has been reported to vary geo­

graphically (Aiken and Waddy, 1980) and a general assumption is tllat

lobsters become mature at larger sizes towards high latitudes.

Maturity of females can be easily identified by external examination

when they carry their brood (ovigerous females) or b~fore spawning

by reading the,stages of the cementary glands on the pleopods (Aiken

and Waddy, 1982; Campbell and Robinson, 1983). There is no known

way of defining maturity of males by direct observation of presence/

absence of external secondary sexual characters.

Maturity of the females can also be defined by observations of

ova size and ovary color. The stages of development of the ovocytes

have been defined (Squires 1970; Krouse 1973; Aiken & Waddy, 1980),

by observation of these stages it can be known whether a female is

ready to spawn. Histological preparations of the male testis can

also efficiently show whether spermatozoa are present, or more

- 3 J

.'

simply a squash of the vasa deferentia observeu under microscope

will show whether spermatozoa are ready to be released.

Histological techniques although accurate are difficult to use on

large numbers for population studies. Further, they have the

disadvantage of being destructive.

Several authors (Skud and Perkins, 1969; Squires, 1970: Krouse,

1973: Aiken and Waddy, 1980; Ennis, 1980) after Templeman (1935,

1939, 1944) have attempted to define "functional maturity" of male

or female lobsters by morphometry of external secondary sexual

characters. It is widely believed that morphometry may allow to

define the size at which male and females are "functionally mature"

i.e. able to mate or spawn efficiently (Aiken & Ivaddy, 1980). This

"functional" maturity is often contras ted with si.ze at IIphysiologi­

cal" maturity i.e. size at which males and females start producing

spermatozoa or mature ovocytes (Aiken & Waddy, 1980).

Templeman (1935) reported that the males have larger claws than

the females and that abdomen width of tlle females is wider than for

the males. Hany authors (Templeman 1935, 1939, 1944; Squires, 1970;

Aiken & Waddy, 1980; Ennis, 1980) have attempted thereafter to

define functional maturity by changes of relative size, weight or

vo1ume of these parts of the body compared to total size or weight

or to carapace size. Severa1 "maturity inuices" have been deve10ped

(Templeman 1935: Squires, 1970: Aiken & Waddy, 1980). For the

males, it is generally assumed that when these indices are

calculated within aseries of intervals of the variable of reference

(total size or weight, carapace size) and averaged within each of

these intervals (Skud and Perkins, 1969), and then plotted against

•

.. ,.- 4 -

------- ----------

•

the variable of referenee, two different eurves will appear, one for

the immatures another one for the mature animals. The two eurves

are said to be separated by an "infleetion point"(Aiken and Waddy,

1980). This "infleetion point" is believed to reveal the onset of

"funetional" sexual maturity. Ennis (1980), however, tried this

teehnique on H. amerieanus in Newfoundland. He notes that "in many

graphs of abdomen width/earapaee length ratios that have been

__ presented by other authors infleetions and asymptote are not very

distinet ll• He eoneludes that for females eonsiderable eaution must

be exereised when interpreting such data. Aiken and Waddy (1980)

mention that the relationship to funetional maturity of their elaw

volume index has yet to be demonstrated.

The teehnique of using ratios of measurements of body parts

expressing seeondary sexual charaeters to standard parts expressing

only of the size of the animal is rather unusual. Rieker (1984)

mentions that "within eaeh stanza of an organism's growth the almost

universally applieable deseriptive expression relating the lengths

x,y of two body parts is y = axb , when b = 1 growth is isometrie,

with the two parts growing proportionally y/x = a. The relationship

y = axb is the allometrie equation for relative growth it was first

suggested by Huxley (1926) and fully doeumented by Teissier (1931)

and by Hux1ey (1932). From the above it is elear that the ratio

method used for H. amerieanus will eomform to the allometrie

relationship only if the growth is isometrie.

Tbe a110metrie relationship has been wide1y used for studying

the relative growth of body parts expressing secondary sexual

eharaeters in erustaeean speeies (Hartnoll, 1978, 1982). Aeeording

----------

- 5 -

to White and Gould (1965) the b value undergoes a sudden change at

the molt before maturity. Teissier showed that in the particular

case of majid crabs, their was first a change in the b value at a

prepuberty molt and later a change in the a value at the pUberty

molt.

The allometric relationship has been used by Saila and Flowers

(1969) for comparing relative growth in different populations of

H. americanus. Teissier (1936b) was apparently the only one to date

to use it for attempting to define sexual maturity in H. americanus,

the data was provided by Templernan.

We have developed the allometric approach for describing the

relative growths of the chela of male lobsters and of the abdomen

width of female lobsters compared to carapace length. We have com­

pared the allometric and the ratio techniques for modelling rela­

tive growth and defining onset of "functional maturity". We have

compared "functional maturity" with "physiological maturity" by

simultaneously taking morphometric measurements and observing color

of gonads and size of ova as weIl as cementary glands on pleopods

for individuals within a subsampIe. We endeavoured the "raison

d'etre" of the peculiar relative growth of the claw and tbe width of

the abdomen as secondary sexual characters.

MATERIAL AND METHODS

Sampling

Male and female lobsters were caught by trapping and diving in

six locations of the Gulf of St. Lawrence (Fig. l): Richibucto

•

•

"

- 6 -

Cape, Petit Rocher, Val Comeau in New Brunswick, Port-au-Choix in

Newfoundland, and Ellerslie in Prince Edward Island•. Individuals

ranging from the smaller sizes encountered to the largest were

selected for morphometric measurements, sexing and maturity reading.

Morphometric measurements

Measurements were made with a caliper to the nearest

millimeter. Six standard measures were made on each individual

(Fig. 2): 1) Carapace length from the posterior part of the eye

socket to the back of the carapace, parallel to the medio dorsal

linei 2) width of the carapace between the third and the fourth pair

of pereiopodsi 3) width of the abdomen, externally at the level of

the second segment: 4) Length of the crusher, from the tip of the

claw to its rear end close to the articulation of the carpopoditei

5) width of the "crusher" claw, from the cavity anterior to the

dactylopodite to the curvature of the external margini 6) Height of

the crusher, maximum distance between the dorsal and the ventral

margins.

Staging of cement glands on the pleopods of females

Maturity of females was estimated by examining development

stages of cement.glands (Aiken and \vaddy, 1982) under a dissecting

microscope with magnification of x64. Females with weIl developed

cement glands (stages 3 and 4), indicating imminent egg extrusion

during the current spawning season, were considered as mature. (Fig.

3, A, B)

..

- 7 -

Staging of ovocytes in female gonads

Preparations of freshly dissected gonads were observed undera

compound microscope at magnifications x 100. The females were con­

sidered potentially mature when the ova were dark green in color and

when a sample of 10 ova averaged a diameter greater than 1 mm. (Fig.

3, E, F) (Squire, 1970: Aiken and Waddy, 1980)

Presence of spermatozoa in the vasa deferentia

Sexual maturity of males was determined from observation of the

presence or absence of spermatozoa in the~ deferentia (Krouse,

1973) smeared on a glass slide under a compound microscope with

magnifications of xlOO - x400. (Fig. 3, E" F)

Statistical analysis

Linear functional and predictive regressions (Ricker, 1973)

were fitted to the data of log transforms of secondary sexual

character measurements or indices of maturity vs log transform of

reference size (carapace length). Functional regressions allow for

random error on the two variables and are convenient for the allo­

metric log transform model. Predictive regressions allow further

statistical comparision of regression parameters between sets of

data, 'they provide estimates very similar to the functional regres­

sion when the correlation coefficient is high, usually when the

range of observations is wide. For the males, we used plots of the

"Anderson" index (Aiken and Waddy, 1980) against carapace size to

visually identify "inflection" points.

•

..

- 8 -

'.

We further plotted log transforms of the "Anderson" index

against carapace size. We fitted functional and predictive regres­

sions to each set of data in order to allow for geographic compari­

sons available. The "Anderson Cheliped Index" is described by'Aiken

and Waddy (1980) as

I = Lp • W. D. 10

Lc '

where Lp is the crusher propodite length, W is the width across the

palm, D is the maximum thickness' or depth. The rational for the log

trans form was to linearize the relationship in the event that the

variables were interrelated by simple allometric relationships. The

'relationship between the products or ratios of several allometric

measures and a constant is also allometric:

For the females an equivalent approach was used substituting the

"maturity index" of Simpson (1961) to the "Anderson index". The

"maturity index is defined as the ratio V'lALc in percentage and is

plotted versus Lc where WA is the abdomen width' and Lc is the

carapace length.

A multivariate generalization of the bivariate regressions was

used by running a Principal Components Analysis (PCA) on the log

transfonns of the measurements. The log transform for the variates

is a current procedure for tlle multivariate in morphometrics

approach (Teissier, 1938, 1955,1960: Jolicoeur, 1963: Saila and

Flowers, 1969). The log transform allows to linearize the relation­

ships between variates and to stabilize the residual variances, two

conditions impl'icitely required for the PCA. We used the

- 9 -

corre1ation matrix as recommended by Teissier (1960) rather than on

the covariance matrix as advocated by Jolicoeur (1963) because the

former provides better output for a graphie analysis as described in

Lebart et ~ (1979).

The purpose of the PCA is to identify uncorrelated (orthogonal)

theoretical variables (the principa1 components) against which each

individual defined by the set of its morphometric measures (each

observation) can be plotted. By using the principa1 components as

axes in the graphica1 representations one can often: 1) identify

discrete groups of individua1s sharing common morphometric charac­

teristics, in this instance secondary sexual charaeters. 2) identify

the contribution of the variables (measurements) which differenciate

(discriminate) most efficiently the discrete groups and eliminate

redundant variables carrying identica1 information. 3) eventua1ly

identify the principa1 components to some independent underlying

faetors, in this instance one principal component may represent a

size factor, another one a geographie variation factor.

We used the graphica1 representation of the PCA described by

Lebart et ~ (1979) in order to visualize a) discrete groups of

individuals among the observations, and b) the contribution of the

lneasurements to the principal components. ~le observations and the

variables are projected into bivariate planes defined by prineipal

components taken two at a time. In this representation the

variables are centered (the mean is substracted) and reduced

(divided by their standard deviations) in order to standardize the

scale for all variables in the projections. The variables are

represented by a vector of unit'length equal to one standard

.'

,

•

, .- 10 -

deviation, projected on the plane. The observations are represented

by a point projected on the plane.

S shaped curves representing the proportion of mature

individuals within each size class were modelied by the logistic

equation: P = 1/(1 + exp (a + bL» where P is the proportion, L the

carapace length, a and b are parameters. Logistic equations were

fitted using Marquadt's iterative non linear least square algorithm.

The initial estimates were obtained from a linear ajustment of the

equation:

Y = a + bL

where Y = Log(l - l/P)

All software was custom made and programmed in Basic on a HP

9845 desk top computer.

Results

The number of individuals sampled in each site and their size

range is presented in Table 1. The size ranges cover the sizes of

onset of maturity defined by other authors. The dispersion diagrams

of the Anderson index vs carapace length are presented in figures 4

(Val Comeau) and 5 (Ellerslie).The dispersion diagrams of the log

transforms are presented for the same locations in figures 6 and 7

with functional regression lines. The horn like shape of the

clusters of points in figures 4 and 5 are characteristic of an allo-

metric relation: the variance of any of the two variables arbitra-

rily taken as dependent varies as a function of the other variable

(the spreading of the points increases with size). There is a

general curvature within the cluster. The log transformation

- 11 -

perfectly linearizes the clusters in figures 6 and 7. There is no

indication of inflection points in any of the sets of data. Tbe

slopes of the predictive linear regressions differ significantly

from 1 (Table 2) indicating allometry rather than isometry.

For female lobsters the dispersion diagrams of maturity index

vs carapace lengths are presented on an arithmetic scale in figures

8 and 9 for Val Comeau and Ellerslie. The equivalent dispersion

diagrams of log transforms are presented in figures 10 and 11. The

points in the dispersion diagrams are much more scattered than for

the males, there is no clcar effect of change in the variance around

a regression line as a function of size. Tbe correlation coeffi­

eients are poor Witll or without Log transformation. R = 0.68,

N = 235iR = 0.69, N = 235. There is no indication that thc means

of the maturity indices calculated within each size class would be

modelled by a curve with a distinct asymptote towards larger sizes

and an inflection point.

The % variance explained by the different principal components

of the PCA for Val Comeau data are shown in Table 3. The graphics

output of the PCA are prcscnted in Figures 12 to 14 for Val Comeau

data. Due to thc abundance of data points and in order to obtain a

better definition we provided distinct graphie outputs for the

observations of the males (Fig. 12), the f~males (Fig. 13) and for

tlle variables (Fig. 14). The analysis was made on all data

combined. From Table 3 it can be seen that Principal components 1

and 2 explain 94.57% of the variance, we therefore neglected thc

other components for further analysis and projected observations and

•

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variables only on the plane defined by the first and second

principal components (Fig. 12 to 14).

Observations for the males (Fig. l2) and for the females (Fig.

13) define two distinct ellipsoids discriminated on each side of the

first axis. Tbe discrimination is more pronounced towards larger

sizes along the positive direction of the 1st axis, this results in

a V shape of the overall cluster. Small male and female individuals

are not weIl discriminated. There is no indication of a discrete

change in allometry at maturity which would result in a Y shape of

the overall cluster rather than a V shape, and possibly three

ellipsoids rather than two.

The correlations between variables and principal components is

presented in Table 4. Variable 1 representing the cephalothorax

length (Fig. 14) is highly correlated with the first principal com­

ponent (R2 = .98). Variables 2 (width of cephalothorax) and 3

(width of abdomen) are positively correlated with the second princi­

pal component, on the same side of the first component as the

tt ellipsoid of female points. Variable 3, the width of the abdomen,

is more correlated (R2 = .46) with tlle second principal component

than variable 2 (R2 = .15). Therefore, the most discriminant

variable for the females is the width of the abdomen.

Variables 4, 5 and 6, the length of the crusher cheliped, its

width and thickness (or depth) are negatively correlated with the

second principal component. Variables 4 and 5 are highly correlated

between themselves and represent redundant information. Variable 6,

the thickness of the crusher, is the most negatively correlated with

the second principal component (R2 = .26). These variables are on

.'

- 13 -

the same side of the first component as the ellipsoid of male

points. The most discriminant variable for the males is therefore

the thickness of the crusher.

All variables almost reach the circumference of the circle of

radius one and are therefore almost at a 0 angle with the plane

defined by the first and the second component (they bring very

little, if any information which is not explained by prineipal

eomponents 1 and 2).

The eomparisons by ANOVA of the predietive r~gressions of Log

transforms of the Anderson index vs earapaee 1ength are presented in

Table 5. The ellipses of joint eonfidenee limit for slopes and

elevations (Y intereept) of these regressions are presented in

figure 15. Both approaehes show that the sampie from Port-au-Choix

(Newfoundland), wide1y differs from New Brunswiek sampies. The

differenee originates from the slopes of the lines but also from the

Y intereepts. The five sets of data were further regrouped into

three entities on the basis of greatest similarities deteeted on

figures 15, 16 (interseetion or proximity of e11ipses of joint

confidence limits) and in Tab1e 5. Port au Choix, Nortll East New.,

Brunswiek (Petit Roeher and Val Comeau), Southern Gulf (Ellerslie

and Richibueto Cape). This grouping results in three very distinet

sets of data (Fig. 17). It is interesting to note that the

eentroids of the ellipses whieh represent the aetual eentral

estimates for the e1evations und the s10pes of the 10g transformed

allometric relationships elosely fit onto a linear regression 1ine

on figures 15 to 17. The equa~~on of this line in figure 17 is

a = 4.9106 - 4.3490b.

,

•

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Geographie eomparisons of dispersion diagram are not presented

for the "maturity index" of the fema1es. The dispersion of the

points is wide, the eorrelation weak, and the data do not fo11ow a

simple allometrie model. No e1ear regional pattern eould be

deteeted.

Maturity eurves in the form of % mature individuals in eaeh

size elass modelled by a logistie eurve fitted by Marquadtls

'algorithm are presented in figures 18 for the males and 19 for the

females. The data was collected at Ellerslie. The maturity for the

males was defined by the presenee of spermatozoa in the vasa

deferentia (Fig. 3, E, F), for the females by the presence of well

developed eement glands (Fig. 3, A, B) or the maturity stages of the

ovocytes (Fig. 3, C, D). Using these direct methods the sizes at

50%maturity were identified as 49.9 mm for males and 70.9 to 71.7

mm for females (Fig. 18, 19). Nothing partieu1ar ean be deteeted in

the dispersion diagrams of Anderson or maturity indices at the sizes

of 50% maturity of males or females (Fig. 4 to 11) whatever the

4t method used for defining maturity.

Diseussion

The simple allometrie model and maturityb

The al10metrie relationship Ll = a.L2 or its Log transform

form

Log Ll = k + b.LogL2 (1)I

is the most eommon~y used and widely accepted relationship for

- 15 -

within each " s tanza" the coefficients a and b remain constant. This

b• C = a.Li

measurements by a constant when plotted against another measurement

with isometry.

.'

modelling relative growth of body parts (Huxley, 1932: Teissier,

modelied by an allometric relationship.

does not imply however that the ratios of body parts remain constant

view, crustaceans ~o through different "s tanza" in their life span,

1960: Hartnoll, 1982 for reviews). In the most generally accepted

It can be easily shown that the ratio, or product of various

within each " s tanza" unless b is equal to 1 in which case we deal

like any simple bivariate allometric relationship. The practice of ttmUltiplying several measurements would have the advantage of using

or one of the measurements included in the ratio/product, is also

Therefore the "Anderson" index of maturity for the males (the -

product of several measurements Ll ••• Ln , LI ••• L'n and an arbitrary

constant C) when plotted against another measurements should behave

the information drawn from several variables instead of a single

one. The practice of multiplying by a constant only changes the

scale in the arithmetic plot and allows for a translation along the

Y axis in the logarithmic plot, it does not add to the definition.

Several models can be considered for differenciation of

secondary sexual characters:

1) Differenciation of the secondary sexual characters may take place

progressively from the smallest. sizes (onwards ) over all the series

....

• 1

- 16 -

of molts (since size is correlated with age) additional term M f(L2)

should be added to relationship Cl) Log Ll = b.Log L2 + k + M ~~L2)

if f(L2) = Log L2 the additional term will be indissociable from b

and the relationship will remain allometric. This is what is.._-

observed in figures 6 and 7 for male lobsters. There is no indica-

tion of an Ilinflectionll point or an angular point (model 2) reveal-

ling onset of maturity. 2) Or it may start over a small range of

individual sizes and progressover several molts 3) Or it may start

over a wide range of individual sizes and by achieved after a single

final molt. The second and third model coexist in majid crabs. In

plots of log transforms of abdomen or chela size as a function of

log trans form of carapace size, there is an angular point (a change

in.the value of the allometric coefficient Ilb ll in relation (1»

characteristic of a type 2, a prepuberal differenciation, and a type

3 distinct shiftin ordinate at onset of maturity (an increment in _

the j coefficient of relation 1). In majid crabs onset of maturity

.-,f<

occurs over avery wide range of sizes, this results in two linear

.. clusters of points oriented in a parallel fashion. Type 2 model is

known for Nephrops norvegicus (Farmer, 1974: Morizur, 1980) and

various species of crab (Hartnoll, 1974). Type 1 model has been-

reported for -the cfab Carcinus maenas (Demeusy, 1958). In modell

there is only one growth "stanzall, in models 2 and 3 there are two

growth Il s tanzas ll •

The multivariate allometriC-model and maturity

A more adequate way of dealing with several measurements at a

time consists in using a multivariate tool. The Principal

•

- 17,.

Components Analysis is quite adequate. As many measurements as

required can be used at atime and it is possible to test for the

relative contribution of information brought be each of the measure­

ments. Redundant variables can be discarded. The basic assumptions

of the PCA constant residual variance of any of the variables along

linear functional regression lines are not violated as long as a' log

transform is used. The PCA allows for reg;essions of all variables

against principal components. The principal components are under­

lying factors for which a biological meaning can be eventually

identified. The PCA has the advantage over a multivariate linear

regression to avoid the arbitrary use of an "a priori" independent

variable. It also allows to visualize graphically the data in sets

of planes defined by the principal components taken two at a time.

The plane defined by the first and second components usually

summarize most of the information. The PCA seems a more logical

approach than apriori index set by arbitarily chosing significant

variables eventually by trial and error.

The practice of taking the average of individual values of the

index within each size class of the independent variable (cephalo­

thorax length) is an alternative to the log transformation for

dealing with the fact that the variance of the index increases with

the cephalothorax size. However, this minimizes the unstable

variance effect, it does not suppress it, because cr 2 (i) = cr 2 (x)/n.

The new variance is now going to be dependent on the number of

observations within each size class as weIl as cr 2 (x), it is cer­

tainly not constant. This practice may normalize the distribution

- 18 -

of the dependent variable within each size class however (Central

limit theorem). Since we cannot study allometric relationships for.

each individual in a population but have to assess the relationship

as averaged for a population of individuals sampled at various

stages, we shall model the central tendency and then the individual

• deviations from this central tendency •

For the central tendency a better understanding of the

underlying allometric relationship can be obtained by comparing the

instantaneous intrinsic rates of relative growth in size of two body

parts LI' L2 rather than the direct relationship between the

observed sizes of these body parts.

61.dLl ... ~.dL2.·ti. dt L2 dt

or

or we may compare the instantaneous intrinsic rate of relative

growth of one body part Li with the "size factor" L that we may

identify with the first component extracted

by integrating with respect to dL and dLi:

Log L ... k.Log Li + ki

by the PCA.

S.l;t~nC\ bi:.io 'fi.

dLL

or.!.dL ... "i. dLjL dt ti dt

ki is an integration constant. The ordinate intercept of the

regression line (the value of Log Li when Log L ... 0) is equal to

ki' The "offset" characteristic of any given individual x from the

central tendency (represented by the regression line) is represented

as a random error term ai(X).

If we assume that the variance of the Log L(x)'s for each

individual is constant around the regression line for any given Log

L, the usual additive error assumption in fitting allometric lines,

we cannot allow for a random error term in (2) for the relative rate

of increase. We implicitely assume that the offset for a given

individual results from its initial position relative to the mean at

the beginning of the "stanza", not from an

~ .- lS -

individual departure from rule (1) representing the relative rates

of increase.

Similar results are obtained when Li is expressed in terms of

Another way of writing (3) is:

L~x) = L b 1 • exp ki. exp 0i(X)

setting ai = exp ki and 8i (X) = exp 0i(X)

Li~)= ai· L bi·€i(X)

the error term 8i(x) is now mUltiplicative

eanother measurement Lj instead of the growth factor L. The error is

additive for the log transforms, it is mUltiplicative for the

untransformed measurements. However for any given individual, there

is a random error term both along the abscissa and along the ordi-

nate associated to each average value in the population estimated by

the functional regression line in a bavariate plot Li vs Lj. The

coordinates of one individual point are:

(ai. Lr~ •C i (x) : aj. L~:i • € j (x)

8i (X) and 8j (X) are assumed to be independent, i.e. the departure

from the average of the size of a body part relative to the size

factor is independent_from the departure from the average of another

body part.

In figure 14 there is only one variable which is almost

completely defined by the first principal component: Variable 1,

the cephalothorax length. The correlation is very high (0.98). The

other variables are highly correlated with_the first principal

component, but also with the second principal component. The second

principal component discriminates the males from the females (Figs.

12, 13). The variables (cephalothorax width) and 3 (abdomen width

•

, .- 20 -

are positively correlated) with axis 2 in the direction of the

females (Fig. 13) while the variables 4 to 6 (measurements of the

chela) are negatively correlated with this axis in direction of the

males (Fig. 12).

We may therefore identify the first axis to the "size factor"

and axis 2 to a "sexual maturity factor". Variable 1, the

cephalothorax length is almost entirely defined by the size factor

and can therefore be conveniently used as an approximation to the

size factor for practical purposes.

By representing any combination (product or ratio) of the

variables 1, 2, and 3 (maturity index of the females) or 4, 5, and 6

(Anderson index of the males) as a function of the variable one

(cephalothorax length) we actually model measurements of body parts

believed to represent secondary sexual characters as a function of

the size factor, neglecting the effect of the sexual "maturity

factor". Ideally the logarithm of the "Indices" or more simply of

the variables correlated with the "maturity factor" should be

modelled as a function of both the size factor and the maturity

factor. This could be achieved by the technique of regression on

the principal components but it has little practical interest. We

have identified no variable entirely defined by the "maturity

factor" independently of the "size factor". We cannot plot the

observations representing secondary sexual characters as a function

of two directly measurable variables one approximating the size

factor the other one the maturit~ factor.

In a bivariate allometric model differenciation of

secondary sexual characters will be explained by the effects of the

, '

- 21 -

"maturity factor". In type 1 model the effects of the "maturity

factor" are expressed over all sizes, on the PCA projection in the

plane defined by the size factor and the maturity factor the points

will be organized as an elongated cluster: the small sizes will be

distributed around axis 1 (0 values for axis 2), the large sizes

progressively be shifted towards positive values ofaxis 2 for one

sex, towards the negative values for the other sex. If the effect

is linearly correlated with the size factor the cluster will be V

shaped with two ellipsoids one for the males, the other for the

females overlaping towards small sizes and their main axes forming

an angle towards large sizes. This is exactly what is observed in

figures 11 and 12 for male and female lobsters.

In a type 2 model, the effects of maturity are revealed only

after a certain size, they are then expressed over a large number of

molts. On the PCA projection the overall cluster of juveniles,

males and females will appear Y shaped.

The juveniles will form a cluster evenly distributed along the

first axis, at onset of maturity two clusters will diverge towards

the positive direction of the second axis for one sex, towards the

negative direction for the other sex. Lobster data does not behave

this way (Figs. 12, 13).

In a type 3 model, the effects of rnaturity are revealed over a

wide range of sizes for different individuals. Some achieve the

maturity mo~t and stop growing, others keep on growing to larger

sizes without being affected by maturity. One can expect on the PCA

projection three non overlaping ellipsoids with parallel major axes.

One for the juveniles with its major axis along axis 1 of the PCA.

•

. . ..- 22 -

\.

One for the mature males shifted in towards one direction of the 2nd

axis of the PCA. One for the- females shifted towards the opposite

direction. The ellipsoids of the mature sets will be shifted

towards larger sizes than the juveniles but not necessarily by the

same arnount if one sex starts to reach rnaturity at smaller sizes

than the other.

Measurements made on the seeondary sexual character eould be

expressed as a funetion of the first and second principal components

(size factor Land sexual maturity factor M) as:

Log Li(X) = bi,L + k i,L + Ji,L(X) +

bi,M Log M + k i,M +di,M(X).

The fact whether M will be expressed at all sizes or only after a

eertain size or after a certain size as a function of size, or after

a certain size independently from size or over a wide range of sizes

for different individuals will determine the shape of the cluster of

points in the PCA projection and the shape of the cluster of points

in the simple bivariate plot of maturity or Anderson index against

cephalothorax length.

Geographie variations of the allometrie model

We noticed in figures 15 that when the elevations of the log

transforms of the bivariate allometric model are plotted against the

slopes (the allometric coeffieient) for various geographie locali-

ties, the relationship appears to be closely approximated by a

straight line. This type of relationship has been observed for very

different organisms by other authors (White and Gould, 1965 for

review). White and Gould suggest it is a eomputation artifaet

''-'-=.<--=''''-=--' ;"--~-resültTngo.-·fforn'-the-'size"--öf~the-'o-rganl~sWü3-ret'aEivE(-'t0-the units of

·.- 23

.1

measurement chosen because the slope is independent of the units

while the elevation is not. However, it is interesting to note that

the curvature of the allometric relationships varies between the

different geographic locations. From north to south the curvature

seems to increase. The linear model between elevations and slopes,

although disputed by White and Gould (1965) would imply that the

family of curves y = axb would intersect at two points 1) at the

origin: when x = 0, y = 0: 2) if we write the log transform as

Log y = Log a + b.Log x

Y = k + b.X

then let us define the family of curves such that

k = c + d.b (4)

for two different allometric relationships pertaining to the family

Y = (e + d.bi) + bi'X

Y'= (e + d.b2) + b2'X'

all relationships intersect at:

X=X',y=y'

d.bl + bl'X = d.b2 + b2'X

X.(bl - b2) = -d.(bl - b2)

X = -d

the log transforms intersect at X = -d

the allometric eurves at x = exp(-d)

In our case the linear relationship k = c + d.b was c = 4.9106,

d = -4.3490. All allometric curves modelling ehela size vs carapaee

length should be elose to interseet at a earapace length of 77.5 mm.

This prediction fits quite aceurately the allometric relationships

ealeulated for the sets of data regrouped in three regions defined

,

•

- 24

as Southern Gulf, Northeast New Brunswiek and Western Newfoundland

(Fig. 20). This would imply that.on the average, below 77.5 mm

earapaee length male lobsters tend to have smaller elaws towards the

north of their distribution in the Gulf (or in eolder waters), the

effeet would be reversed above 77.5 mm earapaee length. There is no

demonstrated relationship between these geographie differenees in

the eurvature of the eurves and onset of maturity.

Conelusions

The Anderson index and the maturity index plotted against

eephalothorax length do not provide adequate means of deteeting

maturity of male or female American lobsters by morphometry whether

this maturity is "physiologieal" or "funetional". Log transforms of

these indices do not provide better means of defining sexual

maturity. More generally onset of maturity eannot be deteeted by

morphometry of the elaw of male· lobsters or of the abdomen of female

lobsters. The differeneiation of these secondary sexual eharaeters

is initiated gradually from early juvenile stages. The size at

maturity defined by the intersection (the "infleetion") of two

predietive linear regression lines fitting average chela size,

surfaee, volume or index vs body size is an illusion resulting from

modelling a curve with two segments of straight lines. The geogra­

phie "differenees" mentioned for size at onset of morphometrie

"functional" maturity of male lobsters are actually explained by

slight differenees in morphometry (shape) of lobsters in different

geographie areas (Tab1e 4, Fig. 15). Such differenees are modelled

by differenees in ehe eurvature of the relationships between

- 25 -

bivariate morphometric measurements, Le. the "b" coefficients in

the allometric model.

The sexual dimorphism in chela size may have behavioral

function in ritualized encounters of male lobsters. Scrivener

(1971) describes a "Meral spread" posture for male American lobsters

in which the claws are displayed by aggressive individuals during

agonistic encounters. There is no mechanical need related to

maturity for a sharp change of size or shape of the claw at maturity

rather, large powerfull animals will have claws proportionally ,

larger than smaller ones according to a simple positive allornetric

relationship with body size. As shown by the PCA, the ratio of the

width of the abdomen to body size or to a lesser extent the ratio of

the cephalothorax to body size are related to maturity and may be

considered as secondary sexual characters. These widths are

generally larger in females, possibly to provide more space for the

gonads in the cephalothorax and for the brood on the abdomen.

However the sexual differenciation of these characters appears to be

initiated gradually from early juvenile stages. The shape of the

cluster of points in the simple bivariate diagrams (Fig. 8, 9) or

the log transform diagrams (Fig. 10, 11) indicate that the relation­

ship between maturity index and body size does not obey to a simple

logarithmic relationship. Some unidentified source of variation

unrelated to size or maturity is likely to exist. Egg carrying and

growth phases alternate in the life history of adult fernales, as a

possible interpretation we suggest that the allometric relationship

between the width of the abdomen and the cephalothorax length is

different during egg carrying intermolt phases and non egg carrying

•

·.- 26 -

intermolt phases. There is no indieation of an "asymtotie" value

oran "infleetion point" in the data.

Maturity ean be easily deteeted in males on squash preparations

of the~ deferentia observed under mieroseope and by observation

of the eementary glands on the pleopods of the females. Logistie

eurves adequately model the proportion of mature individuals as a

funetion of eephalothorax length. For eomparison of sizes at matu­

rity in different geographie regions the infleetion points (50%

maturity points) as well as the range of these eurves should be

used. Existing information on geographie variations of size at

maturity of the size at whieh a male or a female lobster may be

funetionally able to mate, independently from their physiologieal

maturity eannot be aehieved by morphometry, experimentation would be

required. There is no morphologieal impediment for a small physio­

logieally mature lobster to mate although small males may be

prevented from mating by large males through ritualized agonistie

behavior.

·'

- 27 -

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biology and management of lobsters, J.S. Cobb and B.F.

Phillips eds. Vol l, 463 pp., Academic Press, New York:215-276

AlKEN, D.E •. and S.L. WADDY, 1982. Cement gland development, ovary

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CAMPBELL, A., 1985. Application of a yield and egg-per-recruit model

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CAMPBELL, A., and D.G. ROBINSON, 1983. Reproductive potential of

three American lobster (Homarus americanus) stocks in the

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CONAN, G.Y., 1978. Life history, growth, produetion and biomass

modelling of Emerita analoga, Nephrops norvegicus, and Homarus

vulgaris (Crustaeea, deeapoda). Ph. D. Univ. Calif. San Diego.

349 pp.

•

- 28 -

ELNER, R.W. and A. CAMPBELL, 1981. Force, function and mechanica1

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americanus (Decapoda: Crustacea). J. Zooi., Landon.

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ENNIS, G.P., 1980. Size-maturity re1ationships and re1ated

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37:945-956

FARMER, A.S.D., 1974. Relative growth in Nephrops norvegicus (L.)

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JOLICOEUR, P., 1963. The mu1tivariate genera1ization of tlle

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HARTNOLL, R.G., 1974. Variation in growth pattern between some

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HARTNOLL, R.G., 1978. The determination of relative growth in

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HARTNOLL, R.G., 1982. Growth - The Biology of crustacea, Vol. 2,

D.E. B1iss Ed., Academic Press, New York, 111-196.

- 29 -

HUXLEY, J.S., 1924. The variation in the width of the abdomen in

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grwoth-rate. Amer. Nat., 58:468-475.

HUXLEY, J.S., 1932. Problems of relative growth. Methven, London.

276pp.

HUXLEY, J.S. and O.W. RICHARDS, 1931. Relative growth of the abdomen ttand the carapace of the shore crab Carcinus maenas. J. Mar.

bio1. assoc. V.K. (17)3:1001-1015.

KROUSE, J.S., 1973. Maturity, sex-ratio, and size composition of the

natural population of American lobster, Homarus americanus

along the Maine Coast, Fish. Bull. 71:165-173.

LEBART, L., A. MORINEAU and J.P. FENELON, 1979. Traitement des

donnees statistiques, methodes et programmes. Dunod, Paris.

513pp.

MORIZUR, Y., 1980. Reproduction de la langoustine, Nephrops

norvegicus, dans 1a region Sud-Bretagne. These de specialite

Oceanographie, Biologie, Universite Pierre et Marie Curie,

Paris 6:115pp.

PERKINS, H.C., and B.E. SKUD, 1966. Body proportions and maturity of

female lobsters, Amer. Zool. 6:615.

·., - 30 -

RICKER, W.E., 1973. Linear regressions in fishery research. J. Fish.

Res. Bd. Canada. 30:409-434.

RICKER, W.E., 1984. Computation and uses of centra1 trend 1ines.

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SAlLA, S.B. and J.M. FLOWERS, 1969. Geographie morphometric

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SCRIVENER, J.C.E., 1971. Agonistic behavior of the Arnerican 10bster

Homarus americanus (Mi1ne-Edwards). Fish. Res. Bd Canada.

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SIMPSON, A.C., 1961. A contribution to the bionomics of the lobster

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SKUD, B.E. and H.C. PERKINS, 1969. Size composition, sex ratio and

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- 31 -

SQUIRES, H.J., 1970. Lobster (Homarus amerieanus) fishery and

r

..

eeo1ogy in Port au Port Bay, Newfound1and, 1960-65. Proe. Nat1.

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..- 32 -

•

TEISSIER, G., 1955. A110metrie de taille et variabi1ite chez MaYa

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6:281-290.

,---- ~-------~

Table 1 - Numbers in sampIe, geographie loeation, size range.

Geographie Number in sampIe Size range (nun)

Iloeation Male female male female

Val Comeau 235 235 50-114 52-123

Petit Roeher 135 176 50-106 45-104

Riehibueto Cape 89 188 45- 94 48- 98

Ellerslie 306 299 26-108 27- 96

Port aux Choix 152 166 68-102 65-100

.'

•

, ...

Table 2 - Summary of functional predictive linear regressions.

PC VC RC PR Ellerslie

a. -9.482493995 -6.32645 -5.6915 -5.77944 -4.934688

b 3.31005685187 2.58358641 2.45085217807 2.44979980753 2.263738

N 152 235 89 135 306

ELI 678.033236502 1003.55043203 367.704517083 564.241891527 1258.69365308

ELf 3025.18950123 4290.40985124 1520.73780736 2360.57357384 5196.82046745

LLIL2 3584.10314322 4735.7295745 1633.03080285 2521. 93077413 5552.97848873

24253.61244869 5243.08643497 1758.3527166 2701. 50444318 5965.8713655EL2

EL2 802.989473037 1106.0427165 394.335496136 602.055335844 1339.33787801

R 0.79 0.93 0.92 0.91 0.98

Res. var. 0.0291 0.0225 0.0203 . 0.0212 0.0151

t test for~ #:1 ~ t:;Rvl0-21 2 14xlO-62 1 ShxlO-21 1. 67xlO-30 0fY

N = Sample size

R = Corre1ation coefficient

Res. var = Residual variance

PC = Port-au-choix

VC = Val Comeau

RC = Richibucto Cape

PR = Petit Rocher

L2. = a + bLl

L2 = InY

a ::: Ina

LI = InX

Table 3 - contribution of the principal components (% variance).

·.

,

Axis Percentage of variances

1 88.42

2 6.15

3 1.8

4 1. 69 -5 1. 24

6 0.69

Table 4 - Correlation between variables and principal components.

Carapace Abdomen Claw

AXES Length Width Width Length Width Heigth

1 .982316 .949095 .870861 .946873 .952799 .936406

2 .026707 .154118 .463813 -.15952 -.19086 -.26007

3 -.01189 -.20236 .095578 .228319 -.04048 -.06101

4 -.01952 -.17544 .126577 -.15376 .077433 .157263

5 .003945 .025920 .001689 .027125 -.21701 .161398

6 -.18386 .055390 .036281 .038444 .031909 .031650

Table 5 - Comparison of regression equations of male lobsters by ANOVA.

Ccnp:ired Region All Regions (1) PAC vs PR EL VS RC (2) VC vs PR RCvs\C PR vs R::

>;2 or 2 - F = 1,37 F = F '" F = 1,06 F = 1,11 F = 1,04x- = 24,19 x- = 11,91 1,34 20,61Ul t.ai.led F

.... llJ

" LI4 3 150/133 87/304 2 233/133 87/233 133/87" " Degrees of

"C " Freedan-.-t ....

Ul ...

llJ " 0,99 0,99 0,06 0,071 0,99 0,71 0,59 0,84a: > Cl

1 tailed F F =12,57 F = 7,77 F = 14,85 F = 3,11 F = 24,71 F = 1,26 F '" 0,95 F=4,92xl0-5Ul

~ Degrees of 4/907 3/757 1/283 1/391 2/911 1/366 1/320 1/2200 Freedan....'" *** **. *** ***

5,89xl0- 1O -5 1,44 x 10-4 0,079 3,5xl0- 11 0,26 0,33 0,99Ci 4,08xl0

Ul 1 tailed F F = 22,85 F = 10,63 F = 5.93 F = 0,66 F '" 43,46 F = 0,91 F = 15,20 F=19,73c0.... Degrees of 4/911 3/760 1/284 1/392 2/913 1/367 1/321 1/220.," Freedan;>

*** ***llJ -18 -7 -1(;;; Ci 5,19xl0 7,45xl0 0,0155 0,418 9,37xl0 0,34 1,18 X 10-4 1,41 x 10-5

* 0,05 > P > 0,01 PAC = Fbrt-au-Q1Oix (1) VC vs PR vs RC vs EL

** 0,01 > P > 0,001 VC '"' Val Coneau (2) EIrRC vs VC-PR vs PAC

*** P ( 0,001 PR = Petit-Rocher

R:: = cap de Richiboucto

EL = E11erslie

Quebee

New

Gulf of St Lawrenee

~agdalen Islands

..

..-

N

+Fig.l Geographie loeation of sampling sites in the Gulf of St Lawrenee.

·.

"" CL : carapace length"'1~~6 CW : width of carapace

D

W

L

maximum thickness

maximum width

total length

W width of the second segmentof abdomen

Fig. 2. Morphometric measurements used as variables

~--------------------------------------------------------------,

Fig. 3 Determination of physiological maturity of female lobster ( A-D ) and male lobster ( E,F ).

A : pleopod with undeveloped cement glands ( x25 ) ; ß : pleopod with well-developedcement glands ( arrows ) ; C : histological section of ovary of immature female ( xl00,Hematoxylin-eosin stain ) ; D histological section of ovary'of mature female ( x 100,Hematoxylin-eosin stain ) ; Evas deferens containing no spermatozoa ( xl00,Hematoxylin-eosin stain ) ; F vas deferens containing spermatozoa ( SP ; x250,Hematoxylin-eosin stain ).

CARAPACE LENGTH (MM)

1 113113090813713613513

13 L-.......................l-..................~-'-'.........~I.......o-~'-'-...L-l'-'-...........-.l..--.l-'..................-l-..................~..................-"I

413

11313 f-

' ..: .

..2013 I-

31313 f-

. .

xWt:l 51313zH

zocn~Wt:lZa:. 41313 I-

Fig.4 Relationship between Anderson index and carapace

length for male lobsters from Val-Comeau ( N = 235 ).

No conspicuous inflection point or angular point can

be observed.

, .

. '

xWQ

~ 400 I-

ZoUltk:WQZCI:

300 f-

'. •..200 I- ..

100

o -

..,.. . -.

.. .. ... .. .. "".!-.. .. ... .. ...-

.. .. "I •.. ..li: I:.' .... ...:': .:.

:1-::1:.._, ... -.11:·':1 .." ... .. : I: I'·'

•. Ii ll • t".. : ....'Ii I." Size at 50% rnaturity

1008060

- 10 0 L->-.>-.>-.>-..1...-................~...a...-...L-...0.-..0.-..0.-..0.-...1-........................___.-1---'---'-----1

20

CARAPACE LENGTH (MM)

Fig. 5 Relationship between Anderson index and carapacelength for male lobsters from Ellerslie ( N = 306 ).No conspicuous inflection point or angular pointcan be observed around the size at 50% maturitydefined by observation of spermatozoa in the vasadeferentia.

..

.. \ .

•

,...CIlmo-'..; 6.0IdZ...,

XLJQZH 5.5zo(J)e::LJQZa:

5.0' .

4.5

....... ,: •..... :.- : ... ..: ...

I. .' :...: ::.. ... . ... '.'.-:.1 .:~ fl.. .: .. : ....: ..

4.64.44.24.03 . 5 L---<'---4_o.__'_......I-..........-'---...-..o...-.L----o....-o-o.--'-......I-..........-'---...-..o...-~'--'-o.--'-_l

3.8

4.0

CARAPACE LENGTH (MM) (Nat.Logs)

Fig. 6 Relationship between Anderson index and carapacelength for male lobsters from Val-Comeau ( Logarithmicscales, N = 235 ).

No discontonuity, inflectin point or angular point mayallow to define a size at functional maturity.

..

•

.·tSize at 50% maturity3.S

3.21

4.21

4.S

x S •sWt:l.ZH

zo(/)s.e0:wt:lzer.

'"'•0)6.21o

...J.

4.64.44.21 4.23.83.63.42 • 5 L...-......A.-......J..-o-.a....-.......L...ol-l-..........L-o....................-....--......L-................J....&.....................JI.....o-...........&-.l

3.2

CARAPACE LENGTH (MH) (Nat.Logs)

Fig. 7 Relationship between Anderson index and carapacelength for male lobsters from Ellerslie ( Logarithmicscales, N = 306 ).

No discontinuity, inflection point or angular pointcoincides with the size at 50% physiological maturitydefined by the presence of spermatozoa in the vasadeferentia •

.....

X4JQZH

>­t­HCl:: .7S I--::lt-a:1:. .. . ..

.....70 I-

•. ... ..'.... .. . .. . .. .. . . ..... ... .. .... . .

• 65 -

.. .. . . .. .. .. .. . '.. .. .'. ... 60 !'-

~ .• 55 I-

12011010090807060

•5 0 L-a.-'-'.......~__~..J.__~....a...J.L-a-~--.L-&-.-'-'.......~.~~..J.~~~.L-a-~~

50

CARAPACE LENGTH (MM)

Fig. 8 Relationship between maturity index ( width of thesecond segment of abdomen / carapace length ) andcarapace length for female lobsters from Val-Comeau( N = 235 ).

No conspicuous inflection point or asymptote representingstages in differenciation of functional maturity canbe observed.

. '

.. .. ..

• •

. 65 I-

.60 I-•

•

•

•

.. . .. .... .

. .... .. ... ...

. . •

• .. ... 55 I-• • ..

. 50 -

.. ..

Size at 50% maturity

CARAPACE LENGTH (MM)

Fig. 9 Relationship between maturity index ( width of thesecond segment of abdomen / carapace length ) andcarapace length for female lobsters from Ellerslie( N = 229 ).

No conspicuous inflection point or asymptote representingstages in differenciation of maturity is observedaround the sizes of 50% physiological maturitydefined by observations on size of ova, color of gonador stages of the cementary glands.

..

•

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.. .. . . .• •. .

.· .. . .

. . .

.. . . . . .'. .. .. . . . ... . .. . . . ... ... .. ..

){"350 I­WQZH

>-400 •t-HEr:;:)t-~450 I-

.~IGZ...,-300 l-

MI<(g...

-500•

-550 I-

-60e i..

4.84.64.24.0

-65 0 ,-,~.......-..._L--l'.......-..._...J'.............-...__-l':"""'-..._..........'--&o ..........-'--I

3.8

CARAPACE LENGTH (MM) (Nat.Logs)

Fig. 10 Relationship between maturity index ( width of thesecond segment of abdomen / carapace length ) andcarapace length for female lobsters from Val-Comeau( Logarithmic scales, N = 235 ).

No conspicuous inflection point or asymptote representingstages in differenciation of functional maturity can beobserved.

..

•

..

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..

•

• • •.........

•.

.•.' .... .'

.... .. ...•

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-.6 ,..

-.7 ,..

••• • •• • •

• • •••

• • •• • • •• • ..• •

• . • ..

t+Size at 50% maturity

3.83.6-. 8 .......--......-I--......&--...~~ .......~......~.............&-...........01-...0..__.-_.~~......-l.~

3.2

CARAPACE LENGTH CMM) (Nat.Log~)

Fig. 11 Relationship between maturity index ( width of thesecond segment of abdomen / carapace length ) andcarapace length for female lobsters from Ellerslie( Logarithmic scales, N = 229 ).

No conspicuous inflection point or asymptote representingstages in differenciation of maturity is observedaround the size at 50% physiological maturity definedby observations on size of ova, color of gonad orstages of the cementary glands.

•

..

(\J

(J)HXer:

5

4

3

e 2

1

"' "' III

0"'"' ~"'"'RI"In "'

"'ltt :'III\m... '\, m ...

"' "' 111 "' "" "'-1

-2-3 -2 -1 o 2 3

AXIS 1

Fig. 12 Graphie output of the Prineipal Component Analysisof logarisms of morphometrie measurements.Analysis for all sexes eombined ( Val-Comeau data ).

Plot of male observation in the plane defined bythe first and seeond Prineipal Components.One eonspieuous ellipsoid below axis 1.No indieation of a diseontinuity between juvenilesand adults.

3

2

..

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o

-1

(r

fr

-2-3 -2 -1 o 2 3

AXIS 1

Fig. 13 Graphie output of the Prineipal Component Analysisof logarithms of morphometrie measurements.Analysis for all sexes eombined ( Val-Comeau data ).

Plot of female observations in the plane defined bythe first and second Principal Components.One eonspieuous ellipsoid above axis 2.No indieation of diseontinuity between juveniles andadults.

..

..

N

(J)t-IXCI:

5

4

3

2

o

-1

..

-2-3 -2 -1 o 2 3

AXIS 1

Fig. 14 Graphie output of the Prineipal Component Analysisof logarithms of morphometrie measurements.Analysis for all sexes eombined ( Val-Comeau da ta ).

1- Carapaee length, 2- Carapaee width, 3- Abdomen width,4- Length of erusher elaw, 5- Width of erusher elaw,6- Height of erusher elaw.All variables are almost entirely defined within the plane.Variable 1 defines very weIl the first axis ( the sizefaetor ). Variable 3 diseriminates most effieiently thefemales. Variable 6 diseriminates effieiently the males.Variables 4 and 5 are redundant.

- -----------------------------------,

(I)zoJ-f....a:>4J

cl

-5

-6

-7

-8

-9

-le

-11

-12

~N.B. COAST + ELLERSLIE

3.83.63.43.23.e2.82.62.2-1 3 .........__-.,..-I-o~~I-.-.I-~L.._+_..._...lI_a_..........__..J_.I__~_J__....._a__.J,_a_...__._e__........._e__~_J_~......'_l__...................,

2.e

SLOPES

Fig. 15 Ellipses of joint 95% confidence region for slopes and elevationsindex vs carapace length linear regressions on log transforms.Alllocations sampled in the Gulf of St Lawrence. Port au Choix (appears as a sepattte entity. __

of Anderson

Newfoundland )1)..

lJ) -4.5zoHI-CI:>~ -5.0w

-5.5

-6. 0 ~

-6.5

-7.0 I-

-7.52. 1

.2.2

.2.3 2.4

! I ! ! I

2.5 2.6

,2.7

SLOPES

Fig. 16 Ellipses of joint 95% confidence region for slopes and elevationsof Anderson index vs carapace length linear regression on logtransforms for locations in the Southeastern Gulf of St Lawrence( window on figure 15 ).

Two separate entities may he identified : Richibucto Cape and Ellerslie( Southwestern Gulf of St Lawrence'), Val-Comeau and Petit Rocher ( North­eastern New Brunswick ).

'-K ~RINCE: E:DWARD ISLAND AND NORTHERN NORTHUMBE:RLAND STRAIT(J)z -50Ht-a:> -6w.Jw

-7

-8

-12

"~NORTHEAST NEW BRUNSWICK

"

PORT AU CHOIX (WEST NEWfOUNDLAND)

•- 13 L.....~.........--l....-L-l'-l-...&--l.-I..~ .........-l--L-l'-l-_.,-l-I......, -1-'_~.--L..1-J'e.-1..J-1'-I-........·e.-1..1-1'-1-""""''-.-1..1-1'_..a-..........'-.-1.....&--l--L.-'!

2.0 2.2 2.~ 2.6 2.8 3.0 3.2 3.~ 3.6 3.8

SLOPES

Fig. 17 Ellipses of joint 95% confidence region for slopes and elevationsof Anderson index vs carapace length linear regressions on logtransforms.

Three major regions have been used for regrouping the data fromdifferent sets.

f •

..

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1.0

.8

.6

.1

.2

p = 1 / (l+exp(-(15.2369+0.3052 CL )

9080'706050100. 0 L-_=::::ö:::....-J._.........----........L.-_.--.o--L-.............'"'--&_-J.--a- .....-L-__.--.o--L-.............'"'--&_--L.~

30

CARAPACE: LE:NCTH CIIIID)

Fig. 18 Physiological rnaturity curve for male lobsters from Ellerslie definedby presence of sperrnatozoa in the vasa deferentia.

90

•+

p= 1 111+exPI-/-12.1907+0.1719 CL!

80

.... -- ....-­--~~.",'"

'"'"'"/\I Ov.ry Condltlon,

,~,/

~ e

10

IIIIIIIII:,....-71.7mmIIIII

70.9mm I'1:60

P =1 I1 1+expl-I-17.9816 + 0.2484 CL I

5040

.8

.6

.4

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1.0

50% m.turlty--------------------------------------------I

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I

I,I

II

//

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.,'" e;/

.... '"--tf­0. 0 L-.a.---.............~=-.-~-......-FC~-.L-....-.-~-a...-LltL. .......----I--JL.-_.a._.a._...._._L__A__a..._......_J,__l

30

CARAPACE: LE:NCTHCIllIIl]

Fig. 19 Physiological maturity curves for female lobsters from Ellerslie definedby development stages of the cemantary glands and by ovary conditionstages.

..t •

Port .u Chol" (Nowfoundl.nd~·

xQ)

"'0C

co1/1L.,

"'0Ca:

100 I-

300 -

200 '-

100 I-

GEOGRAPHIC VARIATIONS IN CHELA GROWTH RELATIVE TO CEPHALOTHORAX

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/ /'"

///:" /,(

North••et Now Irun.wlok -----------:7.: - Southern Culf

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4t:<' I...::'r oe.':;'- .'~ .. ,

~~.."., I':::::-- .'~,--;::: • ", •• , Intereeotlon predlohd .\ 77.5 _

~.:::::,".~., ..[:"....

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-'.

.....

Cephalothorax length (mm)

Fig. 20 Geographie variation in the relationship between Anderson indexand earapaee length.

The three albometrie eurves Y = aXb belong to a same family definedby the relationship Log a = 4.91 - 4.349b. The model prediets thatall eurves interseet at x = 77.5 mm.