Size-selectivity of lobster pots with escape-gaps: application of the SELECT method to the southern rock lobster (Jasus edwardsii) fishery in Victoria, Australia

Fisheries Research 34 Ž1998. 289–305

Size-selectivity of lobster pots with escape-gaps: application of the SELECT method to the southern rock lobster žJasus edwardsii / fishery in Victoria, Australia Rodney J. Treble b

a,)

, Russell B. Millar b, Terence I. Walker

c

a Department of Zoology, The UniÕersity of Melbourne, ParkÕille, Victoria 3052, Australia Department of Statistics, School of Mathematical and Information Sciences, UniÕersity of Auckland, PriÕate Bag 92019, Auckland, New Zealand c Marine and Freshwater Resources Institute, P.O. Box 114, Queenscliff, Victoria 3225, Australia

Accepted 1 August 1997

Abstract We have utilised a relatively new modelling method, SELECT, to calculate size-selectivity curves for data from two escape-gap field experiments on southern rock lobster Ž Jasus edwardsii . in Victoria, Australia. Size-selectivity curves based on an asymmetric Richards model fitted the data better than the commonly used logistic model, possibly because of higher than expected retention of small lobsters. Theoretical size-selectivity curves, calculated from morphometric data, were remarkably close to size-selectivity curves obtained from one experiment. In a second experiment, we showed that retention probabilities for lobsters close to the legal minimum length were lower than that predicted by the theoretical size-selectivity curves. Size-selectivity curves confirm that the current escape-gap size of 60 mm is close to optimum for the legal minimum lengths used in the Victorian southern rock lobster fishery. Our analyses failed to support the common assertion that escape-gaps increase the fishing power of lobster pots. q 1998 Published by Elsevier Science B.V. Keywords: Catchability; Escape-gap; Fishing power; Jasus edwardsii; Lobster; SELECT model; Size-selectivity

1. Introduction Most commercial lobster fisheries use baited traps and have legal minimum length regulations. Nevertheless, many undersize lobsters are caught. Even if undersize lobsters are discarded in heavily exploited

)

Corresponding author. Tel.: q61 3 9344 4844; fax: q61 3 9344 7909; e-mail: [email protected]

fisheries, they suffer exposure, displacement and appendage loss, which can reduce their growth and increase their mortality. This leads to lower yields ŽBrown and Caputi, 1986., and lower population egg production levels ŽLyons, 1986.. These problems can be rectified to a degree by using escape-gaps that reduce the retention of undersize lobsters in traps Že.g., Bowen, 1963; Ritchie, 1966; Krouse and Thomas, 1975; Nulk, 1978; Fogarty and Borden, 1980; Brown, 1982; Brown and Caputi, 1986.. For reviews see Elner Ž1980., Krouse Ž1989. and Miller

0165-7836r98r$19.00 q 1998 Published by Elsevier Science B.V. All rights reserved. PII S 0 1 6 5 - 7 8 3 6 Ž 9 7 . 0 0 0 7 2 - 6

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Ž1990.. Most lobster fisheries around the world have regulations requiring traps to have escape-gaps or wide lath spacing. Carapace depth determines whether a lobster can pass through an escape-gap, although in Homarus, the width of the carapace can sometimes be a limiting factor ŽBowen, 1963; Nulk, 1978; Brown, 1982; Winstanley, R.H., 1971. Southern rock lobster carapace length–depth relationship. Fish. Div., Dep. Agric., Hobart, Tasmania, 3 pp., unpublished report.. Except during ecdysis, lobsters have hard exoskeletons and are dexterous in their movements, so the size of escape-gaps must be set accurately. Morphometric data, physically passing lobsters of various sizes through escape-gaps, and monitoring the movement of lobsters of known size in partitioned tanks or from traps with escape-gaps, have all been used to investigate the retention properties of traps fitted with escape-gaps, Že.g., Bowen, 1963; Krouse and Thomas, 1975; Nulk, 1978; Brown, 1982.. In a novel experiment, Crous Ž1976. attached mesh bags just outside the escape-gap to measure the size of lobsters Ž Jasus lalandii . that managed to pass through. The above experiments do not recreate true commercial conditions, although the study by Crous Ž1976. is close. Some studies have used field experiments where traps with escape-gaps of different sizes or configurations have been fished with control traps without escape-gaps Že.g., Bowen, 1963; Walker, 1977; Krouse, 1978; Fogarty and Borden, 1980; Brown and Caputi, 1986.. These escape-gap experiments are usually conducted after some of the above analyses are undertaken Že.g., Krouse and Thomas, 1975; Nulk, 1978; Brown, 1982; Everson et al., 1992.. The optimal escape-gap size is that which provides the best compromise between low catches of undersize lobsters while maintaining the CPUE of legal-size lobsters. Instead of using catch rates of legal-size and undersize lobsters, calculation of a size-selectivity curve will provide a universal summary of trap performance. There are few published reports of size-selectivity curves for lobsters caught in traps with escape-gaps, calculated from field experiment data. Exceptions are Bowen Ž1963. and Brown and Caputi Ž1986. who used the observed ratio of escape-gap to control trap CPUE for various carapace length classes as size-selectivity curves, and

Conan Ž1987. who fitted a logistic size-selectivity model to such catch ratio data. Our paper describes the production of size-selectivity curves for lobsters Ž J. edwardsii . in traps Ž‘pots’. with escape-gaps, from an experiment conducted over 20 years ago ŽWalker, 1977., and from an experiment conducted more recently ŽTreble, 1996.. These size-selectivity curves have been used to investigate the effects of escape-gap size on the retention properties of J. edwardsii in lobster pots, and to determine if escape-gaps increase the catchability of legal-size lobsters in pots in the Victorian southern rock lobster Ž J. edwardsii . fishery. Size-selectivity curves are not only useful for the selection of an appropriate escape-gap size. They can be incorporated into length based spatial models Že.g., Walters et al., 1993. and thus, be used to evaluate the effect of changing escape-gap regulations on the future state of the fishery, but only if a non-zero discard mortality parameter is included. In addition, size-selectivity curves can show at what length lobsters become fully recruited to the fishery, information that is required for yield- and egg-perrecruit analyses Že.g., Annala and Breen, 1989., and to estimate total mortality rates from size-frequency data Že.g., Annala, 1979.. Determination of growth matrices for such length based models, and estimation of size-specific molting probabilities, are also dependent on knowledge of the size-selectivity characteristics of the gear used to sample the population ŽMohr and Hankin, 1989; Legault, 1996.. We have used the SELECT ŽShare Each LEngthclass’s Catch Total. modelling method, in its first application to lobster escape-gap experiments, to calculate our size-selectivity curves. The SELECT method can be used to analyse data where two Žor more. types of fishing gear are fished at the same time. Data needed are fishing effort for each gear type, and the size of individuals in the catch. Xu and Millar Ž1993. provide a description of how the method can be applied to trap fisheries. A more detailed statistical description of the SELECT method is given in Millar Ž1992.. The SAS code for a simple logistic SELECT model as fitted to a two-gear experiment is given in Millar Ž1993a.. Cadigan and Millar Ž1992. have shown that unlike methods used in the past, SELECT produces asymptotically unbiased and statistically well behaved results, can fit different

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models to the data, and can be used in situations where the experimental and control fishing gears are fished with different effort Žas was the case in the experiments presented here., or when the different types of gear used are suspected of having unequal fishing power.

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2. Methods We utilised data collected from two separate experiments conducted in the southern rock lobster fishery in Victoria, Australia. The southern rock lobster Ž J. edwardsii . fishery in Victoria, has legal

Fig. 1. Map of Ža. Australia, and Žb. coastal Victoria, showing the two sites, Apollo Bay and Portland, where escape-gap experiments were conducted.

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minimum lengths of 105 mm carapace length for female and 110 mm carapace length for male lobsters. One escape-gap 60 mm high by 250 mm wide must be fitted to all traps Ž‘pots’. used in the fishery. One recent experiment was conducted near Apollo Bay, Victoria ŽFig. 1., using standard commercial pots, some of which have their escape-gaps covered to serve as control pots ŽTreble, 1996.. A much earlier experiment was undertaken off Portland, Victoria ŽFig. 1., where pots with many different escape-gap configurations were deployed simultaneously with pots without escape-gaps Žcontrol pots. ŽWalker, 1977.. 2.1. Apollo bay experiment This experiment was conducted on board the commercial fishing vessels, on two separate fishing trips during August 1992. Most pots were of traditional ‘beehive’ construction, i.e., using tea tree, cane, steel rod and cable. All pots had standard Victorian escape-gaps with openings 60 mm high by 250 mm wide. On the first day of each fishing trip, about one third of the pots were selected at random and had their escape-gaps closed with metal plates or rope. Data on the sex and carapace length of each lobster caught Žmeasured to the nearest 0.1 mm., whether it was caught in a pot with an open or closed escape-gap, and the soak time, were recorded for all potlifts Žtrap hauls. during these fishing trips. 2.2. Portland experiment This experiment was designed to find the optimum escape-gap configuration for the Victorian southern rock lobster fishery ŽWalker, 1977.. Data were collected over 13 days of fishing off Portland during December 1972. Pots were of welded steel construction with woven cane necks, and were covered in 50 mm square galvanised wire mesh ŽFig. 2a.. A total of 104 pots was used, 84 with escape-gaps and 20 with no escape-gaps Žcontrols.. Escape-gaps were constructed from marine plywood panels that could be exchanged between pots. Six different escape-gap ‘sizes’ Ždefined as the distance between the top and bottom edges of the escape-gap opening, see Fig. 2b. were used: 50.8, 54.0, 57.2, 60.3, 63.5 and 66.7 mm. All escape-gap openings were 250 mm

Fig. 2. Ža. Typical pot used in the escape-gap experiment at Portland. Part Žb. an escape-gap showing definitions of escape-gap size and escape-gap elevation.

wide. In addition, Ž7. escape-gap ‘elevations’ Ždefined as the distance between the floor of the pot and the lower edge of the escape-gap opening, see Fig. 2b. of 12.7, 25.4, 38.1, 50.8, 63.5, 76.2, and 88.9 mm were used for each escape-gap size. Two pots were used for each of the 42 escape-gap size and escape-gap elevation combinations Ži.e., 6 escape-gap sizes by 7 escape-gap elevations., one pot with the escape-gap on the same side as the hauling rope, the other pot with the escape-gap on the opposite side of the hauling rope Žtermed the escape-gap ‘side’ treatment.. During fishing, data on the sex and carapace length of each lobster caught, the escape-gap configuration of the pot, and the soak time, were recorded for each potlift. 2.3. Theoretical size-selectiÕity curÕes Carapace length and carapace depth data for J. edwardsii from a Tasmanian population ŽWinstan-

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Fig. 3. Theoretical size-selectivity curves for the escape-gap sizes used in the Portland and Apollo Bay Experiments, calculated using carapace depth vs. carapace length regression data for Jasus edwardsii from Tasmania ŽWinstanley, 1971.. Theoretical proportion retaineds proportion of lobsters at each carapace length that have a carapace depth greater than the escape-gap size. Also shown are the legal minimum lengths for J. edwardsii in Victoria.

ley, 1971. were used to create theoretical size-selectivity curves for the escape-gap sizes used in the two field experiments examined here. Raw data were unavailable so the regression parameters from Winstanley’s study were used to calculate the mean and standard error of carapace depth for 2.5 mm carapace length intervals between 0 and 200 mm. For this analysis, we assumed that the error around the regression line was constant for all carapace lengths. Winstanley Ž1971. found that the carapace depth vs. carapace length regressions were slightly different for male and female J. edwardsii Žfemales being slightly deeper in carapace depth.. However, regression data where males and females were pooled are shown here, because the SELECT analyses were also done with pooled data Žsee below.. The carapace length at which 50% of lobsters that enter the pot are 50 When captured, is defined in the literature as ‘l’. separate theoretical size-selectivity curves for males and females were calculated, l50 for females was only 3 mm carapace length lower than the male estimate. The parameters of the carapace depth ŽCD. vs. carapace length ŽCL. regression ŽCD s a q b P CL. used to calculate the theoretical size-selectivity curves are: n s 1592, a s 0.1684 ŽSE s 0.1447., b s 0.6123, ŽSE s 0.0015., and r s 0.9950 ŽWinstanley, 1971.. l

l

We assumed that all lobsters with a carapace depth greater than the escape-gap size in question would be retained in a pot, and that all lobsters with a carapace depth less than the escape-gap size escaped. Thus, the proportion of lobsters at a particular carapace length that had a carapace depth greater than the particular escape-gap size Žcalculated using normal distribution theory. were plotted directly as probabilities of retention Ži.e., size-selectivity curves.. 2.4. SELECT modelling of the escape-gap experiment data The SELECT method uses data from experiments where fishing gear with unknown size-selectivity Table 1 Mean number of undersize and legal-size lobsters Ž Jasus edwardsii . per potlift caught in pots with 60 mm escape-gaps Ž ns 242 potlifts. and in control pots Ž ns130 potlifts. in the Apollo Bay Experiment. Data for male and female lobsters have been pooled Size-class

Undersize Legal-size

Mean number of lobsters per potlift ŽSE. Escape-gap pots

Control pots

1.01 Ž0.10. 1.50 Ž0.11.

2.90 Ž0.27. 1.78 Ž0.15.

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Fig. 4. Apollo Bay Experiment. Fit of the four SELECT models to the proportion of the total number of lobsters Žescape-gap plus control pots. caught in pots with 60 mm escape-gaps, for 5 mm carapace length-classes. Data for male and female lobsters have been pooled. Graph Ža. shows the fit of the Richards and logistic SELECT models with estimated p, and graph Žb. is for models where p s 0.65. Approximate 95% confidence intervals for the observed proportion in escape-gap pots are also shown, calculated using the method in Millar Ž1995..

characteristics is fished with control gear that is assumed to retain all length classes of fish that encounter the gear. Unlike traditional methods, the SELECT method models the proportion of the total catch in various length classes Žexperimental and control combined. that is caught in the experimental fishing gear, to produce a size-selectivity curve for the experimental gear. For a given length of individ-

ual, l, the proportion of the total catch caught in the experimental gear, f Ž l ., is given by the SELECT Eq. Ž1..

fŽ l. s

pPr Ž l.

Ž 1.

p P r Ž l . q Ž1 yp.

The size-selectivity function r Ž l . describes the probability of retention of animals of length l in the

Table 2 Results of the SELECT modelling of the data from the Apollo Bay Experiment Žsee Fig. 4., including results of using the Akaike’s Information Criterion method ŽAIC. to rank the different models in order of the most parsimonious fit Select Model

Parameter estimates

Curve

p

a

b

d

p

Likelihood

Richards Richards Logistic Logistic

estimated 0.65 estimated 0.65

y207.3 y49.0 y14.4 y15.2

1.90 0.44 0.14 0.15

17.0 4.2 y y

0.61 y 0.68 y

y787 y788 y791 y792

df

16 17 17 18

AIC Value

Rank

1591 1590 1595 1592

2 1 4 3

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Fig. 5. Size-selectivity curves for the 60 mm escape-gap size, obtained from the SELECT modeling of the Apollo Bay Experiment data, calculated using the parameters shown in Table 2 and Eq. Ž2. or Eq. Ž3.. Also shown is the theoretical size-selectivity curve for 60 mm escape-gaps Žfrom Fig. 3., and the legal minimum lengths for J. edwardsii in Victoria.

experimental gear given that they encountered this gear Žfor a derivation of Eq. Ž1., see Xu and Millar, 1993., and p is the ‘relative fishing intensity’ of the experimental and control fishing gear in the experiment. The SELECT model is fitted to the observed data using a maximum likelihood estimation procedure. Two different size-selectivity functions were used in the SELECT modelling of the Apollo Bay data: a symmetrical logistic function and an asymmetrical Richards function. The logistic model was tried first as it is commonly used in trawl size-selectivity studies ŽCadigan and Millar, 1992., and has also been used in studies modelling the selectivity of lobster and crab fishing gear Že.g., Conan, 1987; Sarda` et al., 1993; Xu and Millar, 1993.. The Richards model was tried as the logistic model tended to produce unrealistic size-selectivity curves, especially for the Apollo Bay Experiment data Žsee Section 3.. The logistic size-selectivity function is given by Eq. Ž2.:

around l 50 Žlength of 50% retention.. The asymmetrical Richards function ŽRichards, 1959. is a generalization of the logistic model, and is given by Eq. Ž3.: rŽ l. s

ž

e Ž aqbP l . 1 q e Ž aqbP1.

1d

/

Ž 3.

The extra parameter d defines the amount and direction of asymmetry that the size-selectivity curve will have, d ) 1 giving a longer tail to the left of l 50 , 0 - d - 1 giving a longer tail to the right of l 50 . Therefore, the logistic model is a special case of the Richards function, where d s 1.

Table 3 Mean number of undersize and legal-size lobsters Ž J. edwardsii . caught per potlift, for pots with the escape-gap on the same side or opposite side of the hauling rope in the Portland Experiment. Data have been pooled with respect to lobster sex, escape-gap size and escape-gap elevation Mean number of lobsters per potlift ŽSE.

rŽ l. s

e Ž aqbP l . 1qe

Ž aqbP l .

Ž 2.

where a - 0, b ) 0. This function is symmetrical

Same side

Opposite side

Undersize

1.07 Ž0.08.

1.03 Ž0.08.

Legal-size

1.39 Ž0.10.

1.43 Ž0.10.

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Fig. 6. Plot of the mean number of undersize and legal-size lobsters caught in control pots and pots with different escape-gap sizes in the Portland Experiment. Data have been pooled with respect to lobster sex, escape-gap side and escape-gap elevation. Error bars are standard errors. Linear regression lines through the mean CPUE values for legal-size and undersize lobsters are also shown on this graph.

power. For a sigmoid size-selectivity function Že.g., as in pots with escape-gaps., the parameter p can be thought of as the proportion of the total catch above the point of maximum retention that is caught in the experimental gear. If the experimental and control fishing gears are assumed to have the same fishing power, then p is equal to the proportion of the total fishing effort allotted to the experimental gear. However, if the two gear types are suspected of having unequal fishing power, p will have some other value, which can be estimated by the SELECT procedure. The model that best fits the data Ž p estimated or p s proportion of total fishing effort with experimental gear. can then be used to determine whether the fishing power of the experimental and control fishing gears are equal.

3. Results 3.1. Theoretical size-selectiÕity curÕes

Because p is a parameter in the SELECT model, experimental and control fishing gears do not have to be fished with equal effort or have the same fishing

The theoretical size-selectivity curves show that there is a marked change in size-selectivity for only

Table 4 Results of Mann–Whitney U-tests comparing CPUE Žlobsters per potlift. of undersize and legal-size lobsters Ž J. edwardsii . between control pots and pots with different escape-gap sizes in the Portland Experiment. Data have been pooled with respect to lobster sex, escape-gap side and escape-gap elevation. Threshold significance level s 0.0083 ŽBonferroni p-value for 6 individual tests at 5% level. Escape-gapsize Žmm.

Potlifts

Mean CPUE Žwith SE.

% of control

Mann–Whitney U-tests U statistic

p-value

Undersize lobsters Control 50.8 54.0 57.2 60.3 63.5 66.7

259 177 175 166 170 172 166

1.70 Ž0.16. 1.41 Ž0.17. 1.46 Ž0.18. 1.24 Ž0.16. 0.99 Ž0.12. 0.54 Ž0.08. 0.64 Ž0.09.

y 83% 86% 73% 58% 32% 38%

y 25 244 24 332 23 883 25 856 29 467 27 558

y 0.055 0.167 0.040 0.001 - 0.001 - 0.001

Legal-size lobsters Control 50.8 54.0 57.2 60.3 63.5 66.7

259 177 175 166 170 172 166

1.26 Ž0.11. 1.49 Ž0.17. 1.26 Ž0.14. 1.49 Ž0.17. 1.38 Ž0.16. 1.58 Ž0.20. 1.26 Ž0.14.

y 118% 100% 118% 110% 125% 100%

y 22 829 23 646 21 071 22 628 22 289 22 187

y 0.940 0.413 0.714 0.603 0.990 0.552

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a small change Ži.e., a few mm. in escape-gap size ŽFig. 3.. For the current escape-gap size of 60 mm used in the Victorian southern rock lobster fishery, full retention of lobsters occurs at about 105 mm carapace length, suggesting that the current escapegap size is optimal for the present legal minimum lengths Ž105 and 110 mm carapace length.. An escape-gap larger than 60 mm would theoretically let legal-size lobsters escape, whereas an escape-gap smaller than 60 mm would not maximise the escapement of undersize lobsters. 3.2. Apollo bay experiment CPUE analysis

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We used Akaike’s Information Criterion ŽAIC. Že.g., Burnham and Anderson, 1992. to choose between SELECT models. Because there was a significant amount of overdispersion in the fit of each model, we modified the AIC method after McCullagh and Nelder Ž1989. to take account of this bias. A quasi-AIC value of the fit of each model was calculated using Eq. Ž4.: AIC s y2 P L q 2 P n P c

Ž 4.

where L is the log-likelihood of the model fit, n is the number parameters in the model, and c is a ‘ variance inflation factor’ that represents the amount

Over 8 days of experimental fishing Žexcluding potlifts with soak times longer than one day., a total of 1215 lobsters was measured from 372 potlifts in the Apollo Bay Experiment Ž65% with open escapegaps.. The distribution of the CPUE data was highly variable and skewed toward zero, and could not be adequately transformed to be normally distributed. Nevertheless, the CPUE data from escape-gap and control pots had similar distributions, so non-parametric analyses ŽMann–Whitney U-tests. were used to test hypotheses regarding CPUE. The CPUE of undersize lobsters was markedly lower in pots with escape-gaps compared to control pots ŽTable 1; U s 9.01 = 10 3 , p - 0.001., suggesting that about 65% of undersize lobsters managed to pass through the escape-gap in this experiment. CPUE of legal-size lobsters was slightly lower in escape-gap pots in comparison to the controls, but this difference was not significant at the a s 0.05 level ŽTable 1; U s 1.40 = 10 4 , p s 0.070.. 3.3. Apollo bay experiment SELECT analysis We initially fitted the SELECT models to male and female data separately, but there was no significant improvement in fit compared to a pooled analysis. Hence, data were pooled with respect to sex for subsequent analyses. Fig. 4 shows the fit of each SELECT model ŽLogistic and Richards with p s 0.65 or estimated p . to the observed proportion of lobsters in 5 mm carapace length classes caught in pots with escape-gaps in the Apollo Bay Experiment. Parameter estimates and likelihoods of the four SELECT models fitted are shown in Table 2.

Fig. 7. Portland Experiment data. Part Ža. shows the mean CPUE Žlobsters per potlift. of legal-size and undersize lobsters caught in pots with different escape-gap elevations. Part Žb. shows the mean proportion of lobsters that were of legal-size lobsters in pots with catch, for each escape-gap elevation. Data have been pooled with respect to lobster sex, escape-gap size and escape-gap side. Control pots not shown. Error bars are standard errors.

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Fig. 8. Fit of the SELECT model to Portland Experiment data for each escape-gap size and control pot combination. SELECT model fitted: Richards size-selectivity curve, equal fishing power, l 50 and b proportional to escape-gap size, a and d constant, only data for lobsters greater than 90 mm carapace length used Žsee Table 5.. Observed proportion of lobsters in 5 mm carapace length classes is from the equation: proportions n escape-gaprŽ n escape-gap q n control .. Confidence limits Ž95%. of the observed proportions are also shown Žcalculated as in Millar, 1995.. Data have been pooled with respect to lobster sex, escape-gap side and escape-gap elevation.

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of overdispersion in the model’s fit. The value of c is calculated by dividing the fitted model deviance of the model with the most parameters, i.e., Richards with estimated p, by its df. The Richards models have lower AIC values and thus, fit the data better than the logistic models, the Richards curve with p s 0.65 being the most parsimonious model with an AIC rank of 1 ŽTable 2.. Because the estimated p Žfishing power effect. Richards model did not fit better than the fixed p Žequal fishing power. Richards model Žsee AIC ranks in Table 2., we conclude that escape-gaps did not increase the fishing power of pots in this experiment. Between 70 and 100 mm carapace length, there was little difference between the size-selectivity curves obtained from the SELECT models. However, above 100 mm carapace length, the logistic size-selectivity curves, due to their symmetric nature, predict much lower retention of lobsters above 100 mm carapace length than the Richards size-selectivity curve ŽFig. 5.. With the logistic curve, with full retention does not occur until 125 to 130 mm carapace length ŽFig. 5., even though lobsters of this length are 20 to 25 mm larger in carapace depth than the escape-gap size of 60 mm. The probability of retention for lobsters above 100 mm carapace length rapidly increases with carapace length when using a Richards-based size-selectivity curve, with full retention occurring at about 115 mm carapace length, just above the male legal minimum length of 110 mm carapace length ŽFig. 5.. Nevertheless, even the preferred Richards model Žwith p s 0.65. is shifted to the right about 5 to 10 mm for lobsters above 100 mm carapace length compared to the theoretical size-selectivity curve for 60 mm escape-gaps ŽFig. 5.. Thus, in this experiment there was apparently considerable loss of lobsters just above the female legal minimum length of 105 mm carapace length, and some loss of male lobsters just above their legal minimum length of 110 mm carapace length ŽFig. 5.. This loss of just legal-size lobsters may account for the nominally lower legal-size CPUE for escape-gap pots compared to control pots in this experiment ŽTable 1.. In contrast, the SELECT-produced sizeselectivity curves predict that very small lobsters have retention probabilities higher than expected from the theoretical curves from Winstanley’s carapace depth vs. carapace length relationship ŽFig. 5..

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3.4. Portland experiment CPUE analysis Only data from potlifts with 1 day soak times, and where the escape-gap configuration was noted, have been used in our analysis of the Portland Experiment data. In this truncated data set, a total of 3447 lobsters was caught and measured from 1285 potlifts during 13 days of fishing. Although a graphical analysis of the CPUE of legal-size and undersize lobsters from the first 12 days of this experiment was given in Walker Ž1977., we have used non-parametric statistical methods to test some of the hypotheses presented by Walker. Pots with escape-gaps on the same or opposite ‘side’ of the hauling rope caught virtually equal numbers of undersize and legal-size lobsters ŽTable 3; Mann–Whitney U-tests: undersize CPUE: U s 1.31 = 10 5, p s 0.963; legal-size: U s 1.30 = 10 5, p s 0.717.. This suggests that loss of lobsters through the escape-gap did not happen during hauling of the pot, i.e., lobsters that escaped did so while the pot was still on the seabed. CPUE of undersize lobsters decreased with increasing escape-gap size, although as expected, CPUE of legal-size lobsters did not vary with escape-gap size ŽFig. 6., as they were too large to fit through most of the escape-gap sizes used. Nevertheless, Mann–Whitney U-tests showed that CPUE’s of undersize lobsters caught in pots with smaller escape-gaps Ž50.8, 54.0 and 57.2 mm. were not significantly different from control pots, although significantly fewer undersize lobsters were caught in pots with larger escape-gaps Ž60.3, 63.5 and 66.7 mm. compared to control pots ŽTable 4.. Although mean CPUE for legal-size lobsters was higher in pots with escape-gaps for some escape-gap sizes compared to control pots, these differences were not significant ŽTable 4.. These results are surprising because the theoretical size-selectivity curves ŽFig. 3. suggest that all escape-gap sizes should let at least some undersize lobsters escape, and that a small proportion of legal-size lobsters should be able to pass through the larger escape-gaps. It may be that the power of these tests was low due to the high variation in catch between individual potlifts. It should also be noted that for small escape-gap sizes, a reduction in catch only occurred in the very small length classes that only make up a small proportion of the undersize catch even in control pots. Hence,

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only a very small reduction in the total catch of undersize lobsters would be expected with the smaller escape-gap sizes in comparison to control pots. The CPUE of undersize lobsters was significantly different between escape-gap elevations ŽFig. 7a. ŽKruskall–Wallis ANOVA: H s 15.6, df s 6, p s 0.016., but the CPUE of legal-size lobsters was not significantly different between escape-gap elevations ŽFig. 7a. ŽKruskall–Wallis ANOVA: H s 5.55, df s 6, p s 0.475.. When CPUE of legal-size lobsters is high, it is also high for undersize lobsters and vice versa, hence, it may be by chance the pots with similar escape-gap elevations landed on areas of high or low abundance, as lobster J. edwardsii density is very patchy ŽTreble, 1996.. Nevertheless, the proportion of legal-size lobsters in non-zero potlifts did not vary between escape-gap elevations ŽFig. 7b. ŽKruskall–Wallis ANOVA: H s 10.68, df s 6, p s 0.099., suggesting that there were no differences in retention rates for legal-size lobsters captured in pots with different escape-gap elevations.

3.5. Portland experiment SELECT analysis Data for male and female lobsters, and all escapegap elevations and escape-gap side configurations were pooled for the Portland Experiment SELECT analysis. For each 5 mm carapace length class, the observed proportion of lobsters caught in escape-gap pots when compared to control pots was calculated, i.e., f s n escape-gaprŽ n escape-gap q n control . Žsee Fig. 8.. Logistic and Richards SELECT models were fitted to these data, but as with the Apollo Bay Experiment, the Richards model produced more ‘believable’ size-selectivity curves, especially near the length at maximum retention. Therefore, only the results of the SELECT analysis using the Richards model are presented here. Due to limitations of the data, and as maximum likelihood estimation becomes difficult as the underlying model becomes more complex Že.g., Wilson, 1992., we were forced to simplify the SELECT model applied to the Portland data to reduce the number of parameters to be estimated. The SELECT model was fitted to the data for each escapegap size and control pot combination simultaneously ŽFig. 8., assuming that l 50 Ži.e., b . was proportional

to escape-gap size, and assuming that the parameters a and d were constants. We also used a SELECT model that assumed equal fishing power between escape-gap and control pots Ži.e., p escape-gap size s potlifts escape-gap sizerpotlifts control ., because previous SELECT and CPUE analyses of the Apollo Bay data, and the CPUE analysis of the Portland data, suggested that escape-gaps did not increase fishing power significantly. For each escape-gap size and control pot combination, p was approximately 0.4. Lobsters below 90 mm carapace length were problematic to model because their observed retention proportions did not decrease to zero for the smallest sizes ŽFig. 8.. More reasonable results near the point of maximum retention were obtained when data for lobsters less than 90 mm carapace length were excluded, which is acceptable in some situations ŽWileman et al., 1996.. The above SELECT model fits the Portland Experiment data well ŽFig. 8.. The parameters from the fit of this model are shown in Table 5. Corresponding size-selectivity curves calculated from this SELECT model parameters are very close to the theoretical curves ŽFig. 9., especially near the point of maximum retention, in contrast to the data obtained from the Apollo Bay Experiment. The SELECT analysis of the Portland data suggest that the 60 mm escape-gap is optimal for the legal minimum lengths in the Victorian fishery, with full retention occurring at the female legal minimum length of 105 mm

Table 5 Estimates of parameter b for the SELECT model fitted to the Portland Experiment data Žsee Fig. 8.. ModelsRichards sizeselectivity curve, l 50 Ži.e., b . proportional to escape-gap size, model parameters a and d constant between escape-gap sizes, equal fishing power between escape-gap pots and control pots, and only lobsters with carapace lengths greater than 90 mm used in the model fitting procedure. Estimates of the other parameters from the SELECT modelling are: asy123.9, d s14.05 Escape-gap size Žmm.

b

50.8 54.0 57.2 60.3 63.5 66.7

1.406 1.323 1.249 1.184 1.125 1.071

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carapace length ŽFig. 9.. As data below 90 mm carapace length were excluded from the SELECT analysis of the Portland Experiment data, the sizeselectivity curves shown here are only applicable to

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lobsters above 90 mm carapace length in size. Nevertheless, as in the Apollo Bay Experiment, smaller animals have retention probabilities Žcalculated using SELECT. that are much higher than those expected

Fig. 9. Size-selectivity curves for each escape-gap size, obtained from the SELECT modeling of the Portland Experiment data. Curves were calculated from Eq. Ž3. using the parameters shown in Table 5. Also shown for comparison are the theoretical size-selectivity curves for each escape-gap size Žfrom Fig. 3..

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from the theoretical size-selectivity curves, even when considering that not all lobsters that can leave the pot through the escape-gap actually do so.

4. Discussion 4.1. Richards Õs. logistic size-selectiÕity curÕes The Richards size-selectivity model fitted our data better than the commonly used logistic model. This could be because it could model the higher than expected retention of very small undersize J. edwardsii without compromising where maximum retention is reached, unlike the logistic model. Millar Ž1991, 1993b. and Sarda` et al. Ž1993. found that a Richards size-selectivity model provided better results than the logistic model. In contrast, Xu and Millar Ž1993. found that a Richards SELECT model did not fit better than the logistic model. Conan Ž1987. also found a good fit for the logistic curve to data obtained from escape-gap field trials, although alternative models were not tried. Hence, the Richards model is not always a better size-selectivity model. 4.2. Comparing predicted (SELECT) curÕes with theoretical size-selectiÕity curÕes The theoretical size-selectivity curves are based on the assumption that all lobsters smaller in carapace depth than the escape-gap size can pass through the escape-gap, no matter how close they are to the threshold size. Winstanley Ž1971. assumed that J. edwardsii with carapace depths close to or equal to the escape-gap size do not escape the pot, although in theory, they should be able to pass through the escape-gap. In contrast to Winstanley Ž1971., the similarity between the Portland SELECT and theoretical size-selectivity curves close to the point of maximum retention suggests that J. edwardsii very close to the threshold size do escape from pots with escape-gaps. Bowen Ž1963., Stasko Ž1975. and Nulk Ž1978. also found good agreement between theoretical size-selectivity curves and data measured in field escape-gap trials.

Even the preferred Portland SELECT curves suggest that very small J. edwardsii are retained in the pot, even though the theoretical curves suggest that they should easily be able to pass through the escape-gap. Juvenile J. edwardsii are more gregarious than adults ŽWinstanley, 1977; MacDiarmid, 1994; Edmunds, 1995., so small lobsters may not leave a pot containing other lobsters, in contrast to larger lobsters that may leave the pot if it is possible to do so. Another explanation is that the smaller lobsters may be using the pot as shelter Že.g., as in Miller and Addison, 1995., or could still be feeding on the bait when the trap is hauled. Data from potlifts with longer soak times suggest that these small lobsters do eventually escape from pots with escape-gaps. We believe that the size-selectivity curves produced from the SELECT modelling of the Portland Experiment data are probably more representative than those produced from the study at Apollo Bay. This is because even the preferred model for the Apollo Bay SELECT analysis ŽRichards model with p s 0.65. suggests that lobsters slightly larger in carapace depth than the threshold size managed to escape through the escape-gap. Possible explanations for this phenomenon could be that: Ž1. the escapegaps used in the Apollo Bay Experiment were actually larger than 60 mm; Ž2. lobsters at Apollo Bay were smaller in carapace depth than equivalent J. edwardsii measured by Winstanley Ž1971. in Tasmania; or Ž3. lobsters that were theoretically too large to escape given their carapace length were able to squeeze through the escape-gaps. Recent examination of the metal escape-gaps used in pots at Apollo Bay showed that they only had surface rust and were all very close to 60 mm in size. Thus, oversize escape-gaps were probably not a problem when the Apollo Bay Experiment was undertaken. Breen et al. Ž1988. found that there was geographic variation in carapace morphometric data in New Zealand populations of J. edwardsii. Nevertheless, the theoretical size-selectivity curves produced from measuring Tasmanian J. edwardsii are not different Žat least in the upper regions. when compared to the Portland Experiment size-selectivity curves. This second hypothesis needs to be tested by measuring the carapace length vs. carapace depth relationship for lobsters at Moonlight Head, Apollo Bay. Newly moulted, soft-shelled H. americanus

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close to the threshold size are more able to pass through an escape-gap than hard-shelled, intermoult individuals ŽKrouse and Thomas, 1975.. Subjective observations on carapace softness of J. edwardsii made at the time of the Apollo Bay Experiment ŽAugust, 1992. showed that a large proportion of lobsters around legal-size had soft branchiostegites from recent ecdyses ŽTreble, 1996.. This suggests that the third hypothesis is the most likely one from examination of the available data. However, later observations suggest that carapace softness was overestimated during the Apollo Bay Experiment ŽTreble, 1996., putting the third hypothesis under some doubt. 4.3. Optimum escape-gap size As expected, our analyses show that escape-gaps markedly reduce the retention of undersize lobsters, and that the magnitude of this effect depends on escape-gap size. In the Victorian J. edwardsii fishery, there are different legal minimum lengths for female and male lobsters Ž105 and 110 mm carapace length, respectively. so the correct escape-gap size needs to be a compromise between an optimum escape-gap size for the two legal minimum lengths. Because female J. edwardsii have deeper carapaces than males ŽWinstanley, 1971., a single escape-gap size should be close to optimum for each sex’s legal minimum length. As concluded by Walker Ž1977. and Harris Ž1981., the 60 mm escape-gap is probably optimal for the legal minimum lengths used in the Victorian southern rock lobster fishery. 4.4. Effect of escape-gaps on CPUE of legal-size lobsters Some authors have suggested that catch rates of legal-size lobsters are higher when using pots with escape-gaps Že.g., Walker, 1977; Brown, 1982; Everson et al., 1992.. This is presumably due to higher entry rates of legal-size lobsters into traps with escape-gaps because of the lower retention of undersize lobsters, either because of less competition for space or food in the pot, or from reduced aggressive interactions with other lobsters in the pot, e.g., as Miller Ž1979. observed for crabs. Nevertheless, the Apollo Bay SELECT analysis and the statistical analyses of CPUE from both experiments failed to

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show that escape-gaps increase the fishing power of pots in the Victorian J. edwardsii fishery. It is possible that the power of the statistical tests on the CPUE data was low. Non-significant differences in the CPUE of undersize lobsters between escape-gap treatments and control pots in the Portland Experiment are surprising, because the theoretical sizeselectivity curves suggest that all escape-gap sizes examined should let at least some undersize lobsters escape Žsee Fig. 3.. Likewise, there are no significant differences in legal-size CPUE between control pots and pots with larger escape-gaps in the Portland Experiment, even though a small proportion of legal-size lobsters should be able to pass through the larger escape-gaps. Hence, the power of the CPUE analyses to detect differences in CPUE between escape-gap treatments is probably low, probably due to the high variation in CPUE between pots. In addition, analysis of CPUE data from fishers’ logbooks for the Apollo Bay area shows that when escape-gaps were introduced in the late 1980’s, there was not an immediate increase in CPUE as would be expected if there was an increase in fishing power Žcatchability. ŽTreble, 1996.. However, they may have been confounding effects that masked any rise in CPUE. In only half of the escape-gap studies reviewed by Miller Ž1990. were there increases in catch rates of legal-size H. americanus with the use of escape-gaps or pots with wide spaced laths. The other studies showed either no increase or a slight decrease in the CPUE of legal-size H. americanus. Some authors that have suggested escape-gaps increase the catch rates of legal-size lobsters, based their conclusions on very small sample sizes Že.g., Bain, 1967; Brown, 1982., or did not use statistical tests to test their hypotheses Že.g., Street, 1965; Harris, 1980; Walker, 1977; Brown, 1982.. Miller Ž1990. also stated that the lack of evidence for higher CPUE with the use of escape-gaps in traps may have been because legalsize animals could pass through the escape-gaps in some treatments, Že.g., in this study; Walker, 1977; Harris, 1980; Lyons and Hunt, 1991.. In the Florida P. argus fishery, because legal-size lobsters are attracted to undersize conspecifics that are used as bait, escape-gaps markedly reduced catch rates of legal-size lobsters ŽHeatwole et al., 1988.. Therefore, it cannot be taken as a rule for lobster fisheries that escape-gaps increase legal-size CPUE.

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4.5. Conclusions Four conclusions emerge from our study. Ž1. SELECT models based on the asymmetrical Richards function fit escape-gap size-selectivity data for J. edwardsii better than the symmetrical logistic function. Ž2. The theoretical and SELECT size-selectivity curves are very close for the Portland Experiment, but the best SELECT size-selectivity curve was shifted to the right of the theoretical curve in the Apollo Bay Experiment. Ž3. The 60 mm escape-gap is optimal for the Victorian southern rock lobster fishery. Ž4. There is no statistically significant increase in CPUE of legal-size J. edwardsii in Victoria from the use of escape-gaps, from both experiments analysed.

Acknowledgements We wish to thank the professional rock lobster fishers Russell Frost, Gerhard Wilmink, and John Sealey for their help in collecting the data presented in this paper. The Apollo Bay Project was funded by the Fisheries Research and Development, the Marine and Freshwater Resources Institute, the Department of Natural Resources and Environment, and the Department of Zoology, The University of Melbourne. Dr. Rob Day, who reviewed an earlier manuscript, provided valuable editorial comments. We also wish to thank the fisheries officers from the Colac branch of the Department of Natural Resources and Environment for the research permit used during the Apollo Bay Project.

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