Spatial resource heterogeneity stabilizes local and regional predator-prey dynamics in ecologically realistic networks.

Spatial resource heterogeneity (SRH; the variable spatial distribution of resources) is a surprisingly understudied component of oscillatory predator-prey dynamics. SRH may be particularly important in large, ecologically realistic networks where different patterns of resource distribution can manifest, which have important implications for spatial synchrony. Here, we explore how SRH in large spatial networks influences both local and regional predator-prey stability. To do so, we employ a spatially explicit Rosenzweig-MacArthur model and vary resource distribution accordingly: homogeneously distributed resources of low, medium, and high productivity and heterogeneously distributed resources. The latter includes networks with SRH of random variability in productivity ("random networks") or a spatial productivity gradient ("gradient networks"). We analyze the effects of local patch factors (i.e., productivity and connectivity) and regional factors (i.e., productivity distribution and structure) as components of SRH. First, we find that SRH, regardless of productivity distribution type, stabilizes regional dynamics via statistical stabilization of asynchronous oscillations and local dynamics by reducing the amplitude of oscillations and bounding them further from zero. Local stabilization, in particular, is enhanced in networks with SRH compared to those with homogeneously distributed resources. Second, the local-level stabilizing effect in networks with SRH increases with patch productivity and connectivity. Lower productivity patches are subsequently destabilized in return, albeit minimally. Lastly, random variability in productivity provides the greatest effects observed at the local level, because high-productivity patches are often highly connected to lower ones in a way not possible in gradient networks. We conclude that SRH is a particularly strong driver of predator-prey stability in that it provides local-level stability in a way that other forms of heterogeneity do not. To promote predator-prey stability in managed systems, stability in oscillatory predator-prey systems is likely to arise from (1) variable resource distribution patterns in large spatial networks and (2) high connectivity between patches of different productivity levels.