Trophic cascades have been demonstrated in food webs of different length and complexity. Recent experimental work has also demonstrated evidence for cross-system cascades where spatial subsidies facilitate strong food web interactions that transcend ecosystem boundaries. The focus of subsidy research has been on investigating the effects of constant flows on the ecosystem that receives subsidies (i.e. recipient system). However, spatial subsidies are often temporally variable and recipient system traits may feedback to affect the system that provides the subsidy (i.e. donor system). The objective of this research is to theoretically investigate the effects of temporally variable spatial subsidies on the strength of trophic cascades in donor and recipient ecosystems. We derive a model of two ecosystems each composed of three biotic compartments (primary producers, primary consumers, and predators), two abiotic compartments (inorganic nutrients, detritus) and explicit nutrient recycling. The ecosystems are linked by flows of producers (e.g. litterfall) and primary consumers (e.g. insects). We investigate the effects of subsidy location, frequency and magnitude on the strength of trophic cascades in donor and recipient ecosystems. 
Results/Conclusions

Our meta-ecosystem model predicts that producer and primary consumer subsidies increase the strength of trophic cascades in recipient ecosystems but weaken the strength of cascades in donor ecosystems. Primary consumer subsidies have a larger effect on the strength of trophic cascades than producer subsidies. Top predators in donor ecosystems are unable to persist when their local ecosystem experiences high frequency or large magnitude flows because the minimum energy requirements of the predators are not satisfied under these conditions. Infrequent subsidies enable predators in donor ecosystems to persist during interpulse periods, which leads to temporally variable cascade strength. Our model demonstrates that temporally variable subsidies may be a mechanism for variable trophic cascade strength. This may help to reconcile contrasting experimental results on the strength of cross-system cascades. Human activities are interrupting natural flows of energy, material, and organisms across ecotones. Therefore, a better understanding of the mechanisms responsible for variation in the strength of predator regulation may be crucial for predicting the effects of, and managing, current and future human activities in open ecosystems.