Urban R. et al.: Megaptera novaeangliae in waters off the Pacific coast of Mexico 



1021 



abundance was also estimated for the 

 coastal stock by using the model that only 

 allows relaxation of the requirement for 

 constant capture probability in time 

 (Darroch, 1958; model M^ in Otis et al., 

 1978). Model M,[, provides the estimator 

 of population size for a situation where 

 capture probabilities vary in time and 

 among individuals. Model Mj provides the 

 estimate of population size when capture 

 probabilities are the same among individu- 

 als but vary in time (Otis et al., 1978). 



Outputs from CAPTURE were used only 

 as a "screening technique," as suggested by 

 Menkins and Anderson ( 1988) to investigate 

 departures from the assumption of equal catchability. 

 The test for population closure within CAPTURE was 

 ignoi-ed because its power is low (Otis et al., 1978). 



Open population estimation was done through the 

 software program RECAP^ This program provides 

 estimates of parameters under the basic Jolly-Seber 

 model where all individuals have equal capture prob- 

 abilities and survivorship, but these were allowed to 

 vary between sampling occasions. Also, it incorpo- 

 rates a modification of the Jolly-Seber model (modi- 

 fied J-S model) that constrains estimates to feasible 

 values, stabilizing them and providing more reliable 

 confidence intervals (Buckland, 1980). Open popu- 

 lation estimates were also obtained by using the soft- 

 ware program JOLLY described by Pollock et al. 

 (1990). Of particular interest is the goodness-of-fit 

 tests performed for this program to investigate how 

 well our data are explained by the Jolly-Seber model 

 or any of the variants included in the program. The 

 results obtained under such variants were also very 

 useful because they allowed for the estimation of 

 more precise parameters when either capture prob- 

 abilities or survivorship ( or both ) were kept constant. 

 Even in the case when the more general Jolly-Seber 

 model was chosen (model A), observation of survi- 

 vorship estimates under model 2 (temporary trap 

 response model ) were useful to look for the amount 

 of transit within the areas occupied by each stock. 



Results and discussion 



Photo identification 



A total of 1184 humpback whales were identified in 

 Mexican waters between 1986 and 1993. Of the to- 



■■^ Contact Stephen Buckland. Mathematical Institute. North 

 Haugh, University of St Andrews, St. Andrews, Fife KY169SS, 

 U.K. 



tal, 733 individuals were observed in the area occu- 

 pied by the coastal stock, 412 in Revillagigedo, and 39 

 in both areas (a summary of the number of individuals 

 identified in each area is provided in Table 3). 



Abundance estimation 



The closed population estimators showed that het- 

 erogeneity and variations in capture probabilities in 

 time are present in both stocks. However, the confi- 

 dence intervals built for models M, and M,,^ overlap 

 to a gi-eater extent in the coastal estimates than in 

 the Revillagigedo estimates, indicating that both 

 models M^^ and M, are equally good for the coastal 

 stock (Table 4). These relatively small capture prob- 

 abilities estimated with the closed models are consis- 

 tent with a positive bias in the population size esti- 

 mates because, as will be discussed, the populations 

 were open through the period of study. Therefore, the 

 closed population models were useful in showing that 

 the assumption of equal catchability is not met. 



