Maximum sustainable yields from a spatially-explicit harvest model

TL;DR

This study extends the classic non-spatial harvest model to include spatial heterogeneity, revealing that ignoring spatial effects can lead to overestimating sustainable yields and risking overharvesting.

Contribution

The paper introduces a spatially-explicit harvest model that incorporates environmental heterogeneity and species exchange, providing a more accurate tool for sustainable resource management.

Findings

Spatial heterogeneity causes the Schaefer model to overestimate MSY.

The overestimation of MSY increases with the degree of heterogeneity.

Analytical proof shows the Schaefer model overestimates MSY in well-mixed populations regardless of patches.

Abstract

Spatial heterogeneity plays an important role in complex ecosystem dynamics, and therefore is also an important consideration in sustainable resource management. However, little is known about how spatial effects can influence management targets derived from a non-spatial harvest model. Here, we extended the Schaefer model, a conventional non-spatial harvest model that is widely used in resource management, to a spatially-explicit harvest model by integrating environmental heterogeneities, as well as species exchange between patches. By comparing the maximum sustainable yields (MSY), one of the central management targets in resource management, obtained from the spatially extended model with that of the conventional model, we examined the effect of spatial heterogeneity. When spatial heterogeneity exists, we found that the Schaefer model tends to overestimate the MSY, implying potential for causing overharvesting. In addition, by assuming a well-mixed population in the heterogeneous environment, we showed analytically that the Schaefer model always overestimate the MSY, regardless of the number of patches existing. The degree of overestimation becomes significant when spatial heterogeneity is marked. Collectively, these results highlight the importance of integrating the spatial structure to conduct sustainable resource management.