Predator-Prey Interaction in Structured Models

1. Predator-Prey Interaction in Structured Models Glenn Ledder J. David Logan University of Nebraska-Lincoln gledder@math.unl.edu

2. Simple Holling type II dynamics

3. Simple Holling Type II Dynamics • Time is split between searching and feeding U – prey density R(U) – overall predation rate s – search speed h – handling time food total t search t total t space search t food space search t total t feed t total t ------- = --------- · --------- · ------- --------- = 1 – -------

4. Simple Holling Type III Dynamics • Time is split between searching and feeding • Searching is density-dependent U – prey density R(U) – overall predation rate s – maximum search speed h – handling time

5. Simple Holling Type II Dynamics • Time is split between searching and feeding U – prey density R(U) – overall predation rate s – search speed h – handling time

6. Holling type II—Multiple Prey • Time is split between searching and feeding Ui – prey densities Ri(Ui) – overall predation rates si – search speeds hi – handling times

7. Full Model – 1 Predator Class Ui – prey densities Ri(Ui) – overall predation rates si – search speeds hi – handling times ci -- conversion G– per capita growth M – per capita mortality

8. Multiple Prey and Predators Ui – prey densities Pk – predator densities sik – search speeds hik – handling times cik – conversion efficiencies

9. Continuous Structure x – prey class y – predator class u(x, t) – prey density p(y, t) – predator density s(x, y)– search speed h(x, y)– handling time I(y) – set of prey consumed by predators of size y K(x) – set of predators capable of consuming prey of size x dF(x, y, t) – predation of (y, y+dy) on (x, x+dx)