Dataset for: Persistence and stability analysis of discrete-time predator–prey models: a study of population and evolutionary dynamics

The datasets illustrate the effect of prey evolution on the predator-prey dynamics through numerical simulation. These numerical examples help us understand how toxicant exposure and the prey evolution to resist toxicants may have a significant impact on the dynamical outcomes of a predator-prey system. In particular, the datasets for example 4.1 in the manuscript illustrates what happens to the populations when the initial toxicant effect is fixed at a low, intermediate, and high level. This example shows the time-series population densities of prey and predator values and gives the measure of the amount of toxicant resistance that the prey population evolves. In addition, example 4.2 provides long-time dynamics of the population equilibrium values of prey, predator, and the mean trait value of prey evolution (toxicant resistance) for different prey growth rate independent of the environment (i.e. r_0) when the initial toxicant level varies over the range 0≤ϵ_0≤1 instead of fixing ϵ_0 at a low, intermediate, or high level. This example provides the equilibrium densities of prey and predator populations as a function of the initial level of toxicant ϵ_0 with a step size of 0.01 ranging from 0 to 1. Combined, these two examples show that both prey and predator populations may survive in higher initial toxicant levels with evolution compared to when there is no evolution. Also, both species may go extinct for lower toxicant levels when, prior to evolving toxicant resistance, the prey’s inherent growth rate is small. This dataset supports the publication: Ackleh, A. S., Hossain, M. I., Veprauskas, A., & Zhang, A. (2019). Persistence and stability analysis of discrete-time predator–prey models: a study of population and evolutionary dynamics. Journal of Difference Equations and Applications, 25(11), 1568–1603. doi:10.1080/10236198.2019.1669579.