Evaluation of geostatistical estimators and their applicability to characterise the spatial patterns of recreational fishing catch rates

Abstract

Western Australians are heavily engaged in recreational fishing activities with a participation rate of approximately 30%. An accurate estimation of the spatial distribution of recreational catch per unit effort (catch rates) is an integral component for monitoring fish population changes and to develop strategies for ecosystem-based marine management. Geostatistical techniques such as kriging can provide useful tools for characterising the spatial distributions of recreational catch rates. However, most recreational fishery data are highly skewed, zero-inflated and when expressed as ratios are impacted by the small number problem which can influence the estimates obtained from the traditional kriging. The applicability of ordinary, indicator and Poisson kriging to recreational catch rate data was evaluated for three aquatic species with different behaviours and distribution patterns. The prediction performance of each estimator was assessed based on cross-validation. For all three species, the accuracy plot of the indicator kriging (IK) showed a better agreement between expected and empirical proportions of catch rate data falling within probability intervals of increasing size, as measured by the goodness statistic. Also, indicator kriging was found to be better in predicting the latent catch rate for the three species compared to ordinary and Poisson kriging. For each species, the spatial maps from the three estimators displayed similar patterns but Poisson kriging produced smoother spatial distributions. We show that the IK estimator may be preferable for the spatial modelling of catch rate data exhibiting these characteristics, and has the best prediction performance regardless of the life history and distribution patterns of those three species.

Keywords: Catch rate estimation; Indicator kriging; Kriging estimators; Ordinary kriging; Poisson kriging.

Fig. 1

Location maps of catch rates (top panel) and effort (bottom panel) for snapper (left), baldchin groper (middle) and blue swimmer crab (right). Snapper and baldchin groper catch rates share the same colour scale.

Fig. 2

Omnidirectional experimental semivariogram (dots) for snapper (left), baldchin groper (middle) and blue swimmer crab (right) catch rate with the fitted isotropic model (solid line).

Fig. 3

Omnidirectional experimental indicator semivariogram (dots) with the fitted models (solid line) for snapper (left panel), baldchin groper (middle panel) and blue swimmer crab (right panel) computed for the five thresholds. For each panel, the semivariogram and the fitted model are presented for the various thresholds from top to bottom.

Fig. 4

Omnidirectional experimental weighted semivariogram (dots) for snapper (left), baldchin groper (right) and blue swimmer crab (bottom) catch rate with the fitted isotropic models (solid line).

Fig. 5

Maps of ordinary (left), indicator (middle) and Poisson (right) kriging estimates of catch rate. The top, middle and bottom panels present the estimates for snapper, baldchingroperand blue swimmer crab respectively. Snapper and baldchin groper share the same colour scale.

Fig. 6

Maps of ordinary (left), indicator (middle) and Poisson variance. The top, middle and bottom panels present the variance estimates for snapper, baldchin groper and blue swimmer crab respectively. Snapper and baldchin groper share the same colour scale.

Fig. 7

Accuracy plot and goodness statistic obtained from leave-one-out cross-validation for snapper (top), baldchin groper (middle) and blue swimmer crab (bottom). The left, middle and right panels present the results from ordinary, indicator and Poisson kriging estimation respectively.

Fig. 8

The MSE for OK, IK and PK for different classes of fishing effort (the decile). The left, middle and right panels present the results for snapper, baldchin groper and blue swimmer crab, respectively. The MSE has been standardised by the maximum MSE of 0.135, 0.215 and 9.881 for snapper, baldchin groper and blue swimmer crab respectively.