Exploring the dynamics of Lotka–Volterra systems: Efficiency, extinction order, and predictive machine learning

For years, a main focus of ecological research has been to better understand the complex dynamical interactions between species that comprise food webs. Using the connectance properties of a widely explored synthetic food web called the cascade model, we explore the behavior of dynamics on Lotka-Volterra ecological systems. We show how trophic efficiency, a staple assumption in mathematical ecology, affects species extinction. With clustering analysis, we show how straightforward inequalities of the summed values of birth, death, self-regulation, and interaction strengths provide insight into which food webs are more enduring or stable. Through these simplified summed values, we develop a random forest model and a neural network model, both of which are able to predict the number of extinctions that would occur without the need to simulate the dynamics. To conclude, we highlight the death rate as the variable that plays the dominant role in determining the order in which species go extinct.