Mid-domain effect for food chain length in a colonization–extinction model

Abstract

The mid-domain effect states that in a spatially bounded domain species richness tends to decrease from the center towards the boundary, thus producing a peak or plateau of species richness in the middle of the domain even in the absence of any environmental gradient. This effect has been frequently used to describe geographic richness gradients of trophically similar species, but how it scales across different trophic levels is poorly understood. Here, we study the role of geometric constraints for the formation of spatial gradients in trophically structured metacommunities. We model colonization–extinction dynamics of a simple food chain on a network of habitat patches embedded in a one- or two-dimensional domain. In a spatially homogeneous or well-mixed system, we find that the food chain length increases with the square root of the ratio of colonization and extinction rates. In a spatially bounded domain, we find that the patch occupancy decreases towards the edge of the domain for all species of the food web, but this spatial gradient varies with the trophic level. As a consequence, the average food chain length peaks in the center and declines towards the boundaries of the domain, thereby extending the notion of a mid-domain effect from species richness to food chain length. This trophic mid-domain effect already arises in a one-dimensional domain, but it is most pronounced at the headlands in a two-dimensional domain. As the mid-domain effect for food chain length is caused solely by spatial boundaries and requires no other environmental heterogeneity, it can be considered a null expectation for geographic patterns in spatially extended food webs.