# A novel length-based empirical estimation method of spawning potential ratio (SPR), and tests of its performance, for small-scale, data-poor fisheries

### Abstract

The spawning potential ratio (SPR) is a well-established biological reference point, and estimates of SPR could be used to inform management decisions for data-poor fisheries. Simulations were used to investigate the utility of the length-based model (LB-SPR) developed in Hordyk et al. (2015. Some explorations of the life history ratios to describe length composition, spawning-per-recruit, and the spawning potential ratio. ICES Journal of Marine Science, 72: 204–216.) to estimate the SPR of a stock directly from the size composition of the catch. This was done by (i) testing some of the main assumptions of the LB-SPR model, including recruitment variability and dome-shaped selectivity, (ii) examining the sensitivity of the model to error in the input parameters, and (iii) completing an initial empirical test for the LB-SPR model by applying it to data from a well-studied species. The method uses maximum likelihood methods to find the values of relative fishing mortality (F/M) and selectivity-at-length that minimize the difference between the observed and the expected length composition of the catch, and calculates the resulting SPR. When parameterized with the correct input parameters, the LB-SPR model returned accurate estimates of F/M and SPR. With high variability in annual recruitment, the estimates of SPR became increasingly unreliable. The usefulness of the LB-SPR method was tested empirically by comparing the results predicted by the method with those for a well-described species with known length and age composition data. The results from this comparison suggest that the LB-SPR method has potential to provide a tool for the cost-effective assessment of data-poor fisheries. However, the model is sensitive to non-equilibrium dynamics, and requires accurate estimates of the three parameters (M/k, $L_\infty$, and $CV_{L_\infty}$). Care must be taken to evaluate the validity of the assumptions and the biological parameters when the model is applied to data-poor fisheries.

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Publication
In ICES Journal of Marine Science
Date