| Yhteenveto: | Allochthonous resources can be found in many foodwebs, and can influence both the structure and stability of an ecosystem. In order to better understand the role of how allochthonous resources are transferred as quarry from one predator-prey system to another, we propose a predator-prey-quarry-resource-scavenger (PPQRS) model, which is an extension of an existing model for quarry-resource-scavenger (a predator-prey-subsidy (PPS) model). Instead of taking the allochthonous resource input rate as a constant, as has been done in previous theoretical work, we explicitly incorporated the underlying predator-prey relation responsible for the input of quarry. The most profound diggerences between PPS and PPQRS system are found when the predator-prey system has limit cycles, resulting in a periodic rather than constant influx of quarry (the allochthonous resource) into the scavenger-resource interactions. This suggest that the way in which allochthonous resources are input into a predator-prey system can have a strong influence over the population dynamics. In order to understand the role of seasonality, we incorporated non-autonomous terms, and show that these terms can either stabilize or destabilize the dynamics, depending on the parameter regime. We also considered the influence of spatial motion (via diffusion) by constructing a continuum PDE model over space. We determine when such spatial dynamics essentially give the same information as the ODE system, versus other cases where there are strong spatial differences (such as spatial pattern formation) in the populations. In situations where increasing the carrying capacity in the ODE model drives the amplitude of the oscillations up, we found that a large carrying capacity in the PDE model results in a very small variation in average population size, showing that spatial diffusion is stabilizing for the PPQRS model.
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