Can a species keep pace with a shifting climate?

Consider a patch of favorable habitat surrounded by unfavorable habitat and assume that due to a shifting climate, the patch moves with a fixed speed in a one-dimensional universe. Let the patch be inhabited by a population of individuals that reproduce, disperse, and die. Will the population persist? How does the answer depend on the length of the patch, the speed of movement of the patch, the net population growth rate under constant conditions, and the mobility of the individuals? We will answer these questions in the context of a simple dynamic profile model that incorporates climate shift, population dynamics, and migration. The model takes the form of a growth-diffusion equation. We first consider a special case and derive an explicit condition by glueing phase portraits. Then we establish a strict qualitative dichotomy for a large class of models by way of rigorous PDE methods, in particular the maximum principle. The results show that mobility can both reduce and enhance the ability to track climate change that a narrow range can severely reduce this ability and that population range and total population size can both increase and decrease under a moving climate. It is also shown that range shift may be easier to detect at the expanding front, simply because it is considerably steeper than the retreating back.

Non-equilibria in small metapopulations: comparing the deterministic Levins model with its stochastic counterpart.

In this paper, we examine, for small metapopulations, the stochastic analog of the classical Levins metapopulation model. We study its basic model output, the expected time to metapopulation extinction, for systems which are brought out of equilibrium by imposing sudden changes in patch number and the colonization and extinction parameters. We find that the expected metapopulation extinction time shows different behavior from the relaxation time of the original, deterministic, Levins model. This relaxation time is therefore limited in value for predicting the behavior of the stochastic model. However, predictions about the extinction time for deterministically unviable cases remain qualitatively the same. Our results further suggest that, if we want to counteract the effects of habitat loss or increased dispersal resistance, the optimal conservation strategy is not to restore the original situation, that is, to create habitat or decrease resistance against dispersal. As long as the costs for different management options are not too dissimilar, it is better to improve the quality of the remaining habitat in order to decrease the local extinction rate.

Discrete clutch sizes, local mate competition, and the evolution of precise sex allocation.

Optimal sex allocation under a population structure with local mate competition has been studied mainly in deterministic models that are based on the assumption of continuous clutch sizes; Hamilton's (1967) model is the classic example. When clutch sizes are small, however, this assumption is not appropriate. When taking the discrete nature of eggs into account it becomes critically important whether females control only the mean sex ratio ("binomial" females) or the variance as well ("precise" females). As both types of sex ratio control have been found, it is of interest to investigate their evolutionary stability. In particular, it may be questioned whether perfect control of the sex ratio is always favoured by natural selection when mating groups are small. Models based on discrete clutch sizes are developed to determine evolutionarily stable (ES) sex ratios. It is predicted that when all females are of the binomial type they should produce a lower proportion of daughters than predicted by Hamilton's model, especially when clutch size and foundress number are small. When all females are of the precise type, the ES number of sons should generally be either a stable mixed strategy or a pure strategy, but there are special cases (for two foundresses and particular clutch sizes) where the ES number of sons lies in a trajectory of neutrally stable mixed strategies; the predicted mean sex ratios can be either higher or lower than predicted by Hamilton's model. The existence of ES mixed strategies implies that individual females do not necessarily have to produce sex ratios with perfect precision; some level of imperfection can be tolerated (i.e., will not be selected against). When the population consists of both binomial and precise females, the latter always have a selective advantage. This advantage of precision does not disappear when precision approaches fixation in the population. The latter result contradicts the conclusions of Taylor and Sauer (1980) which is due to their way of expressing selective advantage; they define selective advantage as the between-generation increase per allele, which will always become vanishingly small when an allele reaches fixation, irrespective of fitness differences.

Formation and ecological significance of aggregations in collembola : An experimental study.

Spatial distribution in the two collembolan species Tomocerus minor and Orchesella cincta is greatly influenced by the distribution of the environmental factors water and food. T. minor is totally restricted in distribution to water-saturated places, where it forms spaced-out aggregations. O. cincta assembles in water-saturated places during ecdysis and subsequent reproduction. This leads to dense contact-aggregations. 'Dispersal' follows during the feeding period, probably caused by food shortage, presence of other species and/or saturated conditions in the aggregation site. After feeding, orientation toward water-saturated places occurs by means of orthokinetic reactions and the aggregations are reestablished. The effect of this 'periodical aggregation" for the population is discussed.