A method for estimating mortality rate and divers' sighting rate for tagged abalones.

This paper proposes a method for estimating the mortality rate and divers' sighting rate by taking the effect of movement of abalones into consideration, from the data of the number of alive and dead abalones counted by divers at survey day and the initial number of tagged abalones. The abalones are classified into four states by the combination from the elements as alive or dead and observable or unobservale. The probabilities for the states at survey day t are presented by a stationary Markov chain. The probabilities which an abalone is sighted alive or dead at t are given by the products of the probabilities of the divers' sighting and the probabilities for the alive or dead states in the observable. The log-likelihood function L is obtained from the multinominal distribution. The unknown parameters are estimated. by maximizing L. The variance-covariance matrix of the estimates is approximately given by the inverse of the information matrix. The values of the parameters for maximizing L are found by Davidon's variable metric method. Furthermore, the method is applied to the data of Japanese black abalone Haliotis discus discus in the coast off Chiba Prefecture. The estimates of the mortality rate per day are about 3.2% for group 1 (10-24mm) and 0.64% for group 2 (22-30mm). The true values of the sighting rate for alive abalones are 41% at one day after releare, 23% at six, 20% at fourty five for group 1, and 37%, 15% and 13% for group 2, respectively. The limitations of the application and the modification of the method are discussed.