Effects of heterogeneity and spatial pattern in multi-patch consumer-resource systems with asymmetric diffusion

This paper considers consumer-resource systems, in which the consumer moves between multiple patches with heterogeneous distributions of environmental stressors. Using dynamical systems theory, we show global dynamics of the model, which demonstrate how stressor’s heterogeneity, consumer’s diffusion and spatial pattern of patches influence total population abundance of the consumer. Further analysis on the dynamics shows that, total abundance with stressor’s homogeneity is less than that with stressor’s heterogeneity, which was observed in laboratory experiments. Moreover, our study provides new insights: (i) Total abundance with consumer’s asymmetric diffusion and stressor’s homogeneity is always less than that with homogeneity; (ii) Total abundance with no-diffusion and heterogeneity can also be less than it; (iii) Total abundance with asymmetric diffusion and heterogeneity can reach the minimum among all others. These results have potential implications for investigating both human risk posed by pollutants and pest control by toxicant.