Metapopulation capacity determines food chain length in fragmented landscapes

Abstract

Metapopulation capacity provides an analytic tool to quantify the impact of landscape configuration on metapopulation persistence, which has proven powerful in biological conservation. Yet surprisingly few efforts have been made to apply this approach to multispecies systems. Here, we extend metapopulation capacity theory to predict the persistence of trophically interacting species. Our results demonstrate that metapopulation capacity could be used to predict the persistence of trophic systems such as prey-predator pairs and food chains in fragmented landscapes. In particular, we derive explicit predictions for food chain length as a function of metapopulation capacity, top-down control, and population dynamical parameters. Under certain assumptions, we show that the fraction of empty patches for the basal species provides a useful indicator to predict the length of food chains that a fragmented landscape can support and confirm this prediction for a host-parasitoid interaction. We further show that the impact of habitat changes on biodiversity can be predicted from changes in metapopulation capacity or approximately by changes in the fraction of empty patches. Our study provides an important step toward a spatially explicit theory of trophic metacommunities and a useful tool for predicting their responses to habitat changes.

Keywords: fragmentation; habitat changes; heterogeneous landscapes; trophic interactions.

Fig. 1.

The equilibrium average occupancies of prey and predator species along a gradient of local extinction parameter, on a landscape with 20 patches. For simplicity, we assume that prey and predator have same extinction parameter (e). Solid and dashed lines show results from simulation and analytic approximation, respectively. The three upper panels exhibit the distribution of habitat patches and species occupancy corresponding to three values of extinction parameters (e), indicated by the dashed gray lines. The habitat patch is indicated by green points, with size proportional to patch area. The size of blue and red points (relative to green points) indicates the occupancy probability of prey and predator, respectively. See SI Appendix, Table S1 for parameter values.

Fig. 2.

(A) The maximum food chain length as a function of metapopulation capacity (λ) and strength of top-down control (f), as predicted by Eq. 6. (B and C) The realized food chain length (points) as functions of the theoretical expectation on the maximum food chain length ($\widehat{L}$, Eq. 6) (B) and the average fraction of empty patches (U₁) (C). The red lines show the theoretical expected food chain length by Eq. 6 in B and Eq. 7 in C. The blue and green points indicate, respectively, simulated food chains whose realized food chain are higher and lower than the theoretical expectation. The inserted panels in B and C show the relationship of deviation between predicted and realized food chain length with the strength of top-down effects. See SI Appendix, Table S1 for parameter values.

Fig. 3.

The effect of habitat changes on food chain length: habitat deterioration (A and D), habitat loss (B and E), and habitat fragmentation (C and F). A–C illustrate the three types of habitat changes. In A and B, green and gray points represent the remaining and destroyed habitats, respectively. In C, habitats are not reduced, but the distance between patches increases. D–F show results in food chains with different strengths of top-down control: f = 0.5 (red), 1 (black), and 2 (blue). Solid lines represent simulated results, and dashed and dotted lines show the theoretical expectations by Eqs. 8 and 9, respectively. See SI Appendix, Table S1 for parameter values.

Fig. 4.

Average occupancy of the parasitoid C. melitaearum as a function of the average fraction of empty patches for the host butterfly (i.e., one minus the average occupancy) across 102 patch networks in the Åland archipelago. Black points represent patch networks consisting of more than 10 patches and circles with no more than 10 patches. The gray area indicates the region where the parasitoid is predicted to persist (i.e., U₁ < 1/3). The red line shows the predicted occupancy (SI Appendix, Eq. S4).