Density dependent populations require density dependent elasticity analysis: An illustration using the LPA model of Tribolium.

Alastair Grant and Tim G. Benton, 2003

Journal of Animal Ecology 72: 94-105

1. Elasticity and sensitivity analyses are widely used in evolutionary biology, ecology and population management. However, almost all applications ignore density dependence, despite the widespread assumption that density dependence is ubiquitous. We assess whether this matters by comparing density dependent and density independent elasticity analyses for the LPA model of Tribolium.

2. Density independent elasticities of lambda are a poor indicator of the effects of changes in demographic parameters on population size, even for populations at stable equilibrium. With non-equilibrium dynamics, the divergence can be particularly large. In the extreme, a change in a demographic parameter with a positive effect on individual fitness can reduce mean population size, so even the sign of a density independent elasticity may be wrong. Elasticities of larval, pupal and adult numbers are not proportional to each other, neither are they proportional to elasticities of total population size.

3. A full density dependent analysis is therefore vital when concerned with effects on population numbers, as in population management, pest control and prediction of population effects of toxins.

4. When examining the consequences for individual fitness of changes in demographic parameters, density independent elasticities provide a more useful approximation to the density dependent values. However, they fail to detect cases where non-equilibrium dynamics means that particular life histories gain an advantage by exploiting predictable periods when density dependence is relaxed.

5. This phenomenon can produce a marked change in the pattern of elasticities as a bifurcation is crossed. The corresponding changes in selection pressures may act to stabilise dynamics in some circumstances and destabilise them in others. There is no single answer to the question of whether selection should favour equilibrium or non-equilibrium dynamics.

Alastair Grant

Centre for Ecology, Evolution and Conservation
School of Environmental Sciences
University of East Anglia

If you are interested in undergraduate study in ecology, environmental sciences or related fields, please look at the web pages describing the University of East Anglia's degree programmes in Ecology and Environmental Sciences.

If you would like a reprint of this paper, or are interested in opportunities for postgraduate research in this field, then please email