The ecology of animal species’ behaviors in a Solow-type model

In light of the rapidly expanding body of literature examining the adverse effects of human-induced changes in animal behavior on ecological dynamics, biodiversity conservation, and human well-being, this study investigates a bio-economic dynamic model characterized by a system of three ordinary differential equations. The model incorporates three state variables: K , x , and y . The variable K represents the stock of productive capital in the economy. The variable x denotes the size of the population of animals (from a representative species) exhibiting “typical” behavior; that is, the one that animals would adopt in the absence of human interference (e.g., hunting prey). The variable y denotes the size of the population displaying “non-typical” behavior, adopted either to mitigate the harmful impacts of human activities or to opportunistically exploit anthropogenic resources, such as food by-products. The dynamics of x and y are modelled starting from a system of Lotka-Volterra equations and augmenting it with a component depending on the difference in the payoffs (fitness) of the two behaviors. The stock of capital follows a Solow-type dynamics incorporating defensive expenditure aimed at protecting animals that adopt typical behavior. Our study reveals that the interaction between the dynamics of animal behavior adoption and economic growth can lead to a wide range of equilibrium outcomes. In some equilibria, the animal population fully specializes by adopting either the typical or the non-typical behavior, while in others, a coexistence is observed. We derive policy recommendations to minimize the adoption of non-typical behavior, finding that the optimal ecological outcome is not achieved by maximizing expenditure, but rather by striking a precise balance between ecological defense and economic viability.