Evolution and population dynamics in stochastic environments

Abstract

Inter-generational temporal variability of the environment is important in the evolution and adaptation of phenotypic traits. We discuss a population-dynamic approach which plays a central role in the analysis of evolutionary processes. The basic principle is that the phenotypes with the greatest long-term average growth rate will dominate the entire population. The calculation of longterm average growth rates for populations under temporal stochasticity can be highly cumbersome. However, for a discrete non-overlapping population, it is identical to the geometric mean of the growth rates (geometric mean fitness), which is usually different from the simple arithmetic mean of growth rates. Evolutionary outcomes based on geometric mean fitness are often very different from the predictions based on the usual arithmetic mean fitness. In this paper we illustrate the concept of geometric mean fitness in a few simple models. We discuss its implications for the adaptive evolution of phenotypes, e.g. foraging under predation risks and clutch size. Next, we present an application: the risk-spreading egg-laying behaviour of the cabbage white butterfly, and develop a two-patch population dynamic model to show how the optimal solution diverges from the usual arithmetic mean approach. The dynamics of these stochastic models cannot be predicted from the dynamics of simple deterministic models. Thus the inclusion of stochastic factors in the analyses of populations is essential to the understanding of not only population dynamics, but also their evolutionary dynamics.

Mark-Recapture and Stochastic Population Models for Polar Bears of the High Arctic

“…In extreme environments, like the High Arctic, female bears are expected to allocate resources for reproduction in a safer, though less productive, manner (Ferguson and McLoughlin, 2000). Changes in life history that affect timing of reproduction (e.g., later age at maturity, longer inter-birth intervals, greater longevity; Cohen, 1970;Philippi and Seger, 1989;Sajah and Perrin, 1990) reduce the effects of extreme or stochastic environments, so that the geometric mean fitness of individuals is increased (Yoshimura and Jansen, 1996). For example, increased age at first reproduction has been observed for grizzly bear populations in response to reduced productivity and increased seasonality of the environment (Ferguson and McLoughlin, 2000).…”

Bet-hedging for variability in life cycle duration: bigger and later-emerging chestnut weevils have increased probability of a prolonged diapause

“…In fact, there is no parent-offspring conflict because what counts is how many copies of a gene survive, not numbers of direct descendants." From such considerations, adaptive coin-flipping strategies and diversified bet-hedging can be considered as a kind of kin selection (Yoshimura and Jansen 1996) or more generally as an example of Dawkins' (1976) selfish gene.…”

Bet hedging based cooperation can limit kin selection and form a basis for mutualism

“…We'll call this the maximum offspring condition. Proofs for this can be found in the evolution literature (Yoshimura and Jansen, 1996), and in statistical mechanics. A total, N t therefore maximizes with zero variation, and any variation will reduce the amount of offspring.…”

“…The exact reduction in offspring, due to variations in the offspring, can be quantified for the case of G i << l i (small variation) (Lewontin and Cohen, 1969;Yoshimura and Jansen, 1996). If the variance in the dataset {l 1 , …, l t } is defined as…”