Estimation of natural mortality using catch-at-age and aged mark-recapture data: a multi-cohort simulation study comparing estimation for a model based on the Baranov equations versus a new mortality equation.

摘要

An estimation strategy for natural mortality, M, using multiple cohorts and multiple years of catch-at-age and aged mark-recapture data was tested using simulation. Alternative fishing selectivity functions of age of dome-shaped versus sigmoidally shaped were applied. Two alternative estimation models were developed both using a Poisson likelihood for annual number of recaptures-at-age and model the population numbersat- age by annual difference equations obtained by integrating an ordinary differential equation (ODE) for within-year population dynamics. The 'fully parametric' BODE model is based on the Baranov ODE while the 'semi-parametric' constant catch ODE (CCODE) model uses a new total mortality ODE with constant within-year catch per unit time and does not estimate annual fishing mortality rates (i.e. the F’s) or fishing selectivity function parameters. It removes the actual, considered known, catch-at-age numbers directly from the population. Estimation for the BODE model requires an extra component to the log-likelihood which defines the process error in predicted catch-at-age numbers.Simulations assumed 1 000 releases per year over 12 years with recruitment average of 2 million with annual coefficient of variation (CV) of 0.3 and annual catch of 500 000. Simulations which passed catch-at-age numbers to the estimation algorithm after perturbation by observational error were also carried out for each model in order to investigate the effect on estimation of M. Simulations carried out without observational error showed that when all parameters were jointly estimated and selectivity was domeshaped, estimation of M was unreliable for both models but more so for the BODE model. The reason for this is explained by the confounding of selectivity parameter estimates with that for M. In contrast, when sigmoidally shaped selectivity was simulated, and the functional form of selectivity was correctly specified in the BODE model, both models gave close to unbiased and reasonably precise (CVs of 0.07 to 0.14) estimates of M, but the BODE model estimate was substantially more precise. However, when a minor misspecification of the functional form of selectivity was fitted by the BODE model, in comparison the CCODE model gave superior accuracy. When realistic observational error in catch-at-age numbers was included in simulations and combined with the sigmoidally shaped selectivity function, the bias and imprecision in estimates of M increased by no more than 2% for the CCODE model with no increase detectable for the BODE model. With these caveats, both models can be used to estimate this notoriously difficult parameter with the profile likelihood a useful indicator of the degree of success of estimation, even if some bias remains.