Spatial-temporal models of multi-species interaction to study impacts of catastrophic events

Population dynamics modeling have been use for more than one hundred years to represent population growth, interaction, and migration patters. These models consider a stable habitat with consistent resources to describe ideal living conditions. However, devastating, catastrophic events occur naturally in the wild, wreaking havoc and chaos around the regions they impact. The damage can be calculated in population depletion, destruction of resources, and involuntary relocation. We would like to understand the impacts of these potentially detrimental events on ecosystems by analyzing spatial-temporal models of species interactions through Monte Carlo simulations of a nonlinear system of partial differential equations and applications. We apply Principal Component Analysis and other statistical tools to the obtained results to try to elucidate patterns. Our goal is to strengthen our ability to predict, under different conditions, plausible aftermaths on these ecological systems from catastrophes of different magnitudes and long term effects with varying concomitants.