Scientia Marina, Vol 71, No 1 (2007)

Direct Survival Analysis: a new stock assessment method

Eduardo Ferrandis
Departamento de Ciencias del Mar y Biología Aplicada, Universidad de Alicante, Alicante, Spain

Pilar Hernández
Departamento de Ciencias del Mar y Biología Aplicada, Universidad de Alicante, Alicante, Spain


In this work, a new stock assessment method, Direct Survival Analysis, is proposed and described. The parameter estimation of the Weibull survival model proposed by Ferrandis (2007) is obtained using trawl survey data. This estimation is used to establish a baseline survival function, which is in turn used to estimate the specific survival functions in the different cohorts considered through an adaptation of the separable model of the fishing mortality rates introduced by Pope and Shepherd (1982). It is thus possible to test hypotheses on the evolution of survival during the period studied and to identify trends in recruitment. A link is established between the preceding analysis of trawl survey data and the commercial catch-at-age data that are generally obtained to evaluate the population using analytical models. The estimated baseline survival, with the proposed versions of the stock and catch equations and the adaptation of the Separable Model, may be applied to commercial catch-at-age data. This makes it possible to estimate the survival corresponding to the landing data, the initial size of the cohort and finally, an effective age of first capture, in order to complete the parameter model estimation and consequently the estimation of the whole survival and mortality, along with the reference parameters that are useful for management purposes. Alternatively, this estimation of an effective age of first capture may be obtained by adapting the demographic structure of trawl survey data to that of the commercial fleet through suitable selectivity models of the commercial gears. The complete model provides the evaluation of the stock at any age. The coherence (and hence the mutual “calibration”) between the two kinds of information may be analysed and compared with results obtained by other methods, such as virtual population analysis (VPA), in order to improve the diagnosis of the state of exploitation of the population. The model may be drawn up in a deterministic format, but the main concepts may be interpreted as expectations if stock and catch are considered as stochastic processes.


marine population dynamics; stock assessment; survival analysis; mortality models

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