Optimal sampling regimes for estimating predator-prey dynamics

Abstract

Predator-prey models are often used in ecology to represent realistic encounters between species. Lotka-Volterra differential equations are famously used by ecologists to model the relationship between a predator and prey. Given ecological data collection is known to be time consuming and difficult, the purpose of this paper is to optimize the process and improve sampling efficiency. The method of sequential optimality is applied to a more complex population model with multiple basins of attraction, the Lotka-Volterra differential equations. In this application, various theoretical scenarios are simulated using varying sample sizes and timeframes to determine optimal designs. The first scenario uses a standard sample size and design window to represent a realistic budget for ecological data collection. The second scenario decreases the budget and extends the design window as a representation of a limited budget. The third scenario represents ample resources available for sampling. The three scenarios are used to then compare the optimal designs and help ecologists evaluate the method of sequential optimality. I, A and D optimal designs are compared in the simulation results. The I-optimality criterion tends to outperform the A and D criteria and is recommended as a primary selection when using the sequential optimality algorithm. This simulation study has further developed sequential optimality by predicting optimal sampling regimes according to the dynamics associated with the Lotka-Volterra differential equations.