PARENT SESSION
Contributed Oral Session 112: Evolutionary Ecology: Invasion Dynamics; Populations; Communities
Thursday, August 11, 8:00 AM - 11:30 AM, Meeting Room 514 A, Level 5, Palais des congrès de Montréal

Density-dependent matrix population models: sensitivity, elasticity, and evolution.

Caswell, Hal¹, ¹ Woods Hole Oceanographic Institution, Woods Hole, MA, USA

ABSTRACT- Sensitivity analysis of matrix population models links the demographic and evolutionary consequences of changes in life history parameters. The evolutionary consequences depend on the effects on the invasion exponent, which measures the rate at which a modified phenotype can invade a population composed of another. The demographic consequences depend on effects on future population size. In linear matrix population models, the invasion exponent is the dominant eigenvalue . The sensitivity of to a parameter measures both the selection gradient on that parameter and the effect of a change in that parameter on future population size. In nonlinear models, the population typically converges to an attractor (equilibrium, cycle, quasicycle, or stange attractor). The invasion exponent is still given by the dominant eigenvalue (of an appropriate matrix), but the relation between the sensitivity of the invasion exponent and the sensitivity of population size is more complicated. Here, I present a new approach that clarifies this relation. The results show that, in general, the sensitivity of the invasion exponent is equal to the sensitivity of an effective population size, averaged over the attractor. The effective population is a weighted average of the stage densities; the weights are determined by the details of stage-specific density-dependence. The effective population is not in general equal to the total population size. If density-dependence is 'negative' in an appropriate sense, then evolutionary stable strategies (ESSs) maximize this effective population size. These results have implications for the use of sensitivity analysis in conservation biology and life history evolution.

Key words: matrix population models, sensitivity, elasticity, ESS