A simple model of population dynamics with beneficial and harmful interaction networks for empirical applications

Population dynamic models can forecast changes in the abundances of multiple interconnected species, which makes them potentially powerful tools for managing ecological communities, yet they remain largely under-utilised in applied settings. High data requirements and the ability to only model a narrow range of ecological interactions and/or trophic levels together limits their usefulness when faced with complex and data-poor systems, where beneficial (e.g. mutualism) and harmful (e.g. competition) interactions may operate simultaneously within and between species.

We present a model of population dynamics that can describe a wide range of ecological interaction outcomes with a simple, unified structure. Species growth rates are constrained by a maximum growth rate parameter which prevents the risk of population explosions even in the case of mutualism. Species interactions are defined by two, not mutually-exclusive interactions matrices that describe the effects of beneficial and harmful interactions respectively, together providing the potential for the net effect of interactions between one species and another to switch from beneficial to harmful as population density increases.

This model recreates classic dynamics in two-species mutualistic, competitive, and predator-prey scenarios, allowing us to model a wide range of trophic levels and interaction types together within the same equation. The maximum growth rate parameter, theoretically based in intrinsic constraints on reproduction, can be parameterised from a wide range of sources including natural history, historical data, and breeding programs. We illustrate the potential of this model with a data-poor case study of a threatened species and two interacting predators.

This new model is generaliseable to a wide range of natural ecological communities. Its model structure lowers data requirements whilst remaining intuitive and biologically realistic, making it an accessible option for predicting community-wide population changes in applied contexts where data is sparse and/or uncertain.