Using the EM algorithm to age fish eggs

Abstract

Abstract Murta, A. G., and Vendrell, C. 2009. Using the EM algorithm to age fish eggs. -- ICES Journal of Marine Science, 66: 607–616. We describe an application of the expectation-maximization (EM) algorithm to obtain maximum likelihood estimates of the distribution of ages in fish egg samples. To compare this method with another one based on a non-linear regression of age as a function of development stage and water temperature, which is also suitable for asynchronous spawners, we applied both to simulated and real datasets. The estimates of egg abundance-at-age obtained with the traditional method were biased upwards, compared with estimates obtained with the proposed EM algorithm. The EM method also provided the most accurate and precise estimates, in terms of fitting an exponential-decay, egg-mortality model and the back-calculation of the time of spawning for two datasets used as examples. Besides the ageing of fish eggs, the method described here can be used for any analysis involving the fitting of multinomial models to age and stage classified data, such as the ageing of post-ovulatory follicles.