Perturbation analysis of transient population dynamics using matrix projection models

How Spatial Heterogeneity Affects Transient Behavior in Reaction-Diffusion Systems for Ecological Interactions?

Most studies of ecological interactions study asymptotic behavior, such as steady states and limit cycles. The transient behavior, i.e., qualitative aspects of solutions as and before they approach their asymptotic state, may differ significantly from asymptotic behavior. Understanding transient dynamics is crucial to predicting ecosystem responses to perturbations on short timescales. Several quantities have been proposed to measure transient dynamics in systems of ordinary differential equations. Here, we generalize these measures to reaction-diffusion systems in a rigorous way and prove various relations between the non-spatial and spatial effects, as well as an upper bound for transients. This extension of existing theory is crucial for studying how spatially heterogeneous perturbations and the movement of biological species involved affect transient behaviors. We illustrate several such effects with numerical simulations.

How can we augment the few that remain? Using stable population dynamics to aid reintroduction planning of an iteroparous species

Restoration of depleted populations is an important method in biological conservation. Reintroduction strategies frequently aim to restore stable, increasing, self-sustaining populations. Knowledge of asymptotic system dynamics may provide advantage in selecting reintroduction strategies. We introduce interactive software that is designed to identify strategies for release of females that are immediately aligned with stable population dynamics from species represented by 2-, 3-, 4-, and 5-stage life history strategies. The software allows managers to input a matrix of interest, the desired number of breeding females, and the desired management timeline, and calls upon stable population theory to give release strategies that are in concert with both stable population status and the management goals. We demonstrate how the software can aid in assessing various strategies ahead of a hypothetical restoration. For the purpose of demonstration of the tool only, we use published vital rates of an ungulate species, but remark that the selection of species for demonstration is not central to the use of this tool. Adaption of this tool to real-life restorations of any 2-, 3-, 4-, or 5-stage iteroparous species may aid in understanding how to minimize undesirable recovery complications that may naturally arise from transient population dynamics. The software is freely available at: https//cwhl.vet.cornell.edu/tools/stapopd.