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Fishery Bulletin 97(4), 1999 



to the population were occurring in the form of ani- 

 mals born in previous years that became identifiable 

 as they gi'ew. Also, some individuals died. Because 

 we would therefore expect to be studying an open 

 population, we chose the Jolly-Seber mark and re- 

 capture model. One of the critical assumptions of this 

 method is the highly unlikely condition that all ani- 

 mals have the same capture probabilities at the mo- 

 ment of the sample (Seber, 1982). If heterogeneity in 

 capture probabilities is present, the open population 

 models will underestimate population size to a 

 greater extent than closed population models (Car- 

 others, 1973; Pollock et al., 1990). Given that there 

 was no way to account for such problems with open 

 population models (Hammond, 1986), we decided to 

 use closed population models to test for variations 

 in capture probabilities. 



Closed population estimates were obtained and 

 assumptions were tested by using the software pro- 

 gram CAPTURE developed by Otis et al. (1978i, 

 which included an algorithm to select the appropri- 

 ate model after the hypothesis'testing procedure. The 

 conceptual basis for this selection procedure is a 

 tradeoff between precision and bias. If a simple 

 model, such as the null model M^ in Otis et al. ( 1978), 

 is used to estimate parameters from data that vio- 



lates in any way the assumption of equal capture 

 probability, then significant biases are introduced in 

 parameter estimates and sampling variances will be 

 artificially small. On the other hand, if a more com- 

 plex model is used, such as M,,^ of Otis et al.. ( 1978), 

 that allows capture probabilities to vary with time 

 and among individuals, biases may be reduced but 

 the sampling variance will be greater than it should 

 be. The selection procedure takes into account the 

 individual goodness-of-fit tests performed for specific 

 models on the data and the confrontation of related 

 models (i.e. where one model is a particular case of a 

 general one). The significance levels for all these tests 

 are combined in a standard discriminant analysis 

 and the resulting statistic is standardized so that its 

 value ranges from to 1, 1 being the score that indi- 

 cates the appropriate model (Otis et al., 1978). 



The basic or null model M^^ can be applied to the 

 general case of multiple recaptures in a closed popu- 

 lation, where all animals have equal capture prob- 

 abilities, and where this probability remains constant 

 in time. The model that allows the capture probabil- 

 ity to vary in time, simultaneously permitting indi- 

 viduals to have unequal capture probability (Chao 

 et al., 1991: model M,^ in Otis et al., 1978) was se- 

 lected for estimation of both stock sizes. In addition. 



