PARENT SESSION
Oral Session 11: Predator - Prey Ecology I: Modeling.
Presiding: L Prugh
Monday, August 2, 8:00 AM to 11:30 AM, Meeting Room C 124.
Population fluctuations and the importance of variation in a generalized individual-based model of predator-prey interaction.
CHIVERS, William*,1, HERBERT, Ric1, GLADSTONE, William1, 1 University of Newcastle, Australia, Newcastle, NSW, Australia
ABSTRACT- We describe an individual-based model of a generalized predator-prey system. We suggest that the complex nonlinear dynamics exhibited can be compared with the nonlinear difference equations used by Robert May. We also examine the sensitivity of the model to individual variation and compare this with similar models in the literature. The model, implemented as a computer program, creates heterogeneous individuals which interact according to a simple set of rules. The primary output is the population of each species after each cycle. More detailed output allows an investigation of the mechanism of the population dynamics. Interactions between the individuals result in population levels which cycle in a similar way to those of the Lotka-Volterra model, although in contrast to Lotka-Volterra the stochastic nature of this model is apparent in the population peaks and troughs which tend to fluctuate about stable means. These population levels emerge from the rules being followed by the individuals; there are no system-level rules to govern population levels. Occasionally large fluctuations occur in the populations, which then return to the stable means or sometimes extinction. An examination of the individuals and their interactions immediately before these fluctuations suggests that the model exhibits chaotic behaviour. A second characteristic of the model discussed here is the importance of individual variation. If the individual variation across the populations is not sufficiently high, extinction of one of the species usually results. The behaviour of the model is similar to May's nonlinear difference equations if the r value is allowed to fluctuate. Similarities include the stable cycling populations with occasional chaotic fluctuations and the sensitivity of the model to initial parameter values. The model differs from that of May, however, in its stochastic element. Opinions of the importance of individual variation for population viability in the modelling literature are divided: we argue that the nature of the parameter which varies must be considered. Some parameters will be less important than others, such as the level of individual energy reserves which is important in this model.
Key words: predator-prey, individual variation, individual-based model, nonlinear dynamics