Body size dependent dispersal influences stability in heterogeneous metacommunities

Abstract

Body size affects key biological processes across the tree of life, with particular importance for food web dynamics and stability. Traits influencing movement capabilities depend strongly on body size, yet the effects of allometrically-structured dispersal on food web stability are less well understood than other demographic processes. Here we study the stability properties of spatially-arranged model food webs in which larger bodied species occupy higher trophic positions, while species' body sizes also determine the rates at which they traverse spatial networks of heterogeneous habitat patches. Our analysis shows an apparent stabilizing effect of positive dispersal rate scaling with body size compared to negative scaling relationships or uniform dispersal. However, as the global coupling strength among patches increases, the benefits of positive body size-dispersal scaling disappear. A permutational analysis shows that breaking allometric dispersal hierarchies while preserving dispersal rate distributions rarely alters qualitative aspects of metacommunity stability. Taken together, these results suggest that the oft-predicted stabilizing effects of large mobile predators may, for some dimensions of ecological stability, be attributed to increased patch coupling per se, and not necessarily coupling by top trophic levels in particular.

Figure 1

Model metacommunities are composed of local food webs connected to one another by dispersal. (A) Each local web inhabits a habitat patch that is part of a spatial network, generated as a random geometric graph. Species in each web have a body size that is larger at higher trophic levels. Food webs have the same number of species and topology in all patches, but interaction rates and other ecological parameters vary among habitats mimicking spatial environmental heterogeneity. (B) Dispersal varies as either an increasing or decreasing function of body size.

Figure 2

The relationship between local and metacommunity stability as influenced by dispersal. The baseline dispersal rate d and the body size scaling coefficient z determine the species-specific dispersal rate ${\delta }_i=d{M}_i^z$, where $M_i$ is the mass of species i. All species have the same dispersal rate d when z = 0. When z is positive, larger bodied species have faster dispersal rates, whereas when z is negative, it is smaller bodied species that have faster dispersal rates. Other parameters vary across all simulations as indicated by Table 1. Error bars denote ± 2 S.E.M., and are too small to see.

Figure 3

The effects of key parameters on metacommunity stability. Stability is as defined in Fig. 2 and parameters are defined in Table 1. Correlations given are coefficients from the best-fitting generalized linear model $\pm 2$ SEM. Positive correlations indicate that larger values of a parameter correspond to a higher probability that a randomly-assembled metacommunity will be stable.

Figure 4

The effect of dispersal variation on metacommunity stability for spatial link strength $d=0.1$. The metacommunity is stable when the real part of the leading eigenvalue of the metacommunity Jacobian ${\lambda }_1<0$. Allometric dispersal is defined Eq. (3). Permuted dispersal refers to the metacommunity where the allometric dispersal rates for all species were randomly reassigned to new species. Each data point represents a unique metacommunity with allometric dispersal compared to 100 counterparts with dispersal rates randomly rearranged among species, and are shown with 1:1 lines. Points that lie above the 1:1 line represent cases where the median value of ${\lambda }_1$ for the permuted dispersal metacommunities are greater than the corresponding original metacommunity, indicating that the permuted metacommunities are typically less stable. Points that lie below the 1:1 line represent cases where the permuted metacommunities are typically more stable. Grey regions mark portions of the plot representing qualitative changes in stability where the real part of the leading eigenvalue ${\lambda }_1$ of the original metacommunity has a different sign than the median value of the eigenvalues of the comparable metacommunities with permuted dispersal.

Figure 5

Eigenvalues ${\lambda }_1$ from Fig. 4 categorized by qualitative effects on stability. Categories Stability is gained and Stability is lost correspond to cases where the median effect of randomly reassigning species’ dispersal rates is a change in the sign of ${\lambda }_1$. Stability is unaffected indicates no sign change.