PARENT SESSION

HP10 New Advances in Estimating Effects of Toxicants on Populations
D135-136
1:20 PM - 5:20 PM, Thursday

() The myth of lambda and other measures of instantaneous population growth.

Ferson, S.¹, Litzgus, J.¹, Akçakaya, H.R.¹, ¹ Applied Biomathematics, Setauket, New York, USA

ABSTRACT- Academic discussions of biological populations commonly introduce the idea that a population's health can be measured by its instantaneous rate of population growth. The dominant eigenvalue lambda (), of the Leslie matrix characterizing population growth for age-structured populations is one such instantaneous rate. A value of lambda greater than unity reflects a growing population and a lambda less than unity reflects a declining population. Many researchers have suggested using lambda or similar scalar measures of population growth to characterize the effects of an environmental contaminant on a biological population in terms of how the contaminant changes lambda. It is easy to show with simple and realistic examples, however, that lambda measures neither short-term population growth nor long-term population growth. Lambda is a poor summary of population growth because it totally ignores three of the most significant ecological features of population growth: the variability induced by environmental and demographic stochasticity, density dependence (i.e., feedback of population size on demographic parameters), and the influence of initial abundance distribution. A considerably more comprehensive summary of population growth would be any of a family of related risk-analytic measures such as extinction risk, risk of population decline, and time to extinction or decline. These measures can take account of stochasticity, density dependence, and initial abundance distribution as well as age- or stage-structure of a population. Moreover, because the risk-analytic summaries are compatible with basic ideas traditionally employed in a variety of engineering contexts, they are straightforward to use in planning and assessments needed for management of biological populations. Indeed, these measures are the standard in conservation biology around the world. Using quantitative examples that show how and when lambda can be misleading, and demonstrate how risk-based summaries are much better for routine use in population-level ecotoxicology.

Key words: stochasticity, lambda, risk