Lozano-Alvarez et al.: Fishery, growth, and movements of Panultrus argus 



81 



Detailed data on monthly production (in boxes) of the 

 cooperative during the 1985-86 fishing season were 

 obtained from the processing plant. The relationship 

 between tail weight (TW, in g) and carapace length 

 (CL, in mm) was estimated by linear regression ex- 

 pressed as a power equation, 



TW (g) = 0.00203 CL (mm) 2 - 5503 



where N = 98, r 2 = 0.98, CL range = 44.7-137.9mm. 



Data on catch in kg/tail weight of each fishing team 

 were available since 1981 and converted to catch-per- 

 unit-effort (CPUE, catch/boat -day). A Leslie analysis 

 (Leslie and Davis 1939) was applied to the CPUE data 

 to estimate the fishing mortality (F). 



Tagging 



Lobsters were tagged in Bahia de la Ascension during 

 16 April-14 May 1985, and 18 May-30 June 1986, i.e., 

 during the closed season. The area of the bay where 

 casitas are distributed was divided into six sampling 

 zones (Fig. lb). Lobsters were tagged in all zones dur- 

 ing 1985, and in zones II- VI in 1986. Chittleborough's 

 (1974) western rock lobster tags were used. Only 

 animals > 44 mm CL were tagged in order to reduce 

 incidental mortality which might occur on smaller 

 animals (Chittleborough 1974). Tags were inserted in- 

 to the dorsolateral extensor muscle between the 

 cephalothorax and first abdominal segment. After tag- 

 ging, the lobsters were immediately released where 

 they had been caught. Underwater observations re- 

 vealed that after a few minutes, the tagged lobsters 

 returned under the same casita. 



Tag number, date, release location, sex, reproduc- 

 tive state, and CL (± 0.1mm measured from between 

 the rostral horns to the posterior dorsal edge of the 

 carapace) were recorded. Fishermen were requested 

 to keep the head of a recaptured lobster with its tag 

 so the CL could be measured, and to provide the recap- 

 ture date and location. The tagging program was 

 advertised widely, and a reward was offered in the 

 form of a lottery to encourage tag returns. 



Analyses of growth data 



The analysis of growth using capture-recapture data 

 was performed using Fabens' method (1965), and a 

 technique developed by M. Palmer (CSIRO Div. Math. 

 Stat., Floreat Park, W.A. 6014, Australia). This tech- 

 nique assumes an individual lobster grows exponential- 

 ly with time: 



y = a (1 - e bt ) + E 



where y = CL (mm), a = asymptotic CL (mm), b = a 

 growth coefficient, t = time, and E = residuals. A mean 

 value of 6mm CL obtained from 50 settling pueruli was 

 introduced as a starting size (zero age) into the model. 



Parameters for the model, including variability of in- 

 dividual growth, were estimated using a multivariate 

 Gaussian distribution. The residuals around an in- 

 dividual's curve (E) were assumed to be independent 

 Gaussian normal with constant variance. The likelihood 

 estimate, assuming that individual coefficients are 

 known for an individual, was 



Lj = p (y | a,b) p (a,b) 



where L ; = initial length, and p(.|.) denotes a probabil- 

 ity distribution. 



Since the individual animal's coefficients were 

 unknown, we consider them as "nuisance" parameters 

 and integrate them out of the likelihood, giving 



oo 



/ 



p (y | a,b) p(a,b) dadb 



where lj is the likelihood for the i th individual. Then 

 the product of the individual likelihood must be max- 

 imized to find the estimates of the population param- 

 eters. A convenient algorithm to use in this case is the 

 EM algorithm (Dempster et al. 1977). Details of its ap- 

 plication in this context are in Laird et al. (1987), 

 Palmer (1986), and Palmer et al. (1988). 



Although the time between subsequent captures was 

 known, the age at first capture was unknown. A prob- 

 ability distribution for this unknown parameter was 

 also assumed, but now the initial time is treated as 

 "missing" and is removed from the likelihood by in- 

 tegrating it out. The likelihood for the i th animal is 

 now of the form 



OO CO 



;; 



p(y | a,b,tx) p(a,b) dadbdti. 



Maximum likelihood is used to estimate both the 

 growth parameters and the distribution of initial ages. 

 The method of constructing and maximizing the likeli- 

 hood is described in Palmer et al. (1988). 



Mean weekly growth rates (Hunt and Lyons 1986) 

 of recaptured lobsters were analysed to determine if 

 there were significant changes in growth rate along 

 their size range. 



