Aline Magdalena Lee

Demographic Stochasticity, Allee Effects, and Extinction : The Influence of Mating System and Sex Ratio

Demographic stochasticity has a substantial influence on the growth of small populations and consequently on their extinction risk. Mating system is one of several population characteristics that may affect this. We use a stochastic pair-formation model to investigate the combined effects of mating system, sex ratio, and population size on demographic stochasticity and thus on extinction risk. Our model is designed to accommodate a continuous range of mating systems and sex ratios as well as several levels of stochasticity. We show that it is not mating system alone but combinations of mating system and sex ratio that are important in shaping the stochastic dynamics of populations. Specifically, polygyny has the potential to give a high demographic variance and to lower the stochastic population growth rate substantially, thus also shortening the time to extinction, but the outcome is highly dependent on the sex ratio. In addition, population size is shown to be important. We find a stochastic Allee effect that is amplified by polygyny. Our results demonstrate that both mating system and sex ratio must be considered in conservation planning and that appreciating the role of stochasticity is key to understanding their effects.

Evidence of inbreeding depression but not inbreeding avoidance in a natural house sparrow population.

Inbreeding is common in small and threatened populations and often has a negative effect on individual fitness and genetic diversity. Thus, inbreeding can be an important factor affecting the persistence of small populations. In this study, we investigated the effects of inbreeding on fitness in a small, wild population of house sparrows (Passer domesticus) on the island of Aldra, Norway. The population was founded in 1998 by four individuals (one female and three males). After the founder event, the adult population rapidly increased to about 30 individuals in 2001. At the same time, the mean inbreeding coefficient among adults increased from 0 to 0.04 by 2001 and thereafter fluctuated between 0.06 and 0.10, indicating a highly inbred population. We found a negative effect of inbreeding on lifetime reproductive success, which seemed to be mainly due to an effect of inbreeding on annual reproductive success. This resulted in selection against inbred females. However, the negative effect of inbreeding was less strong in males, suggesting that selection against inbred individuals is at least partly sex specific. To examine whether individuals avoided breeding with close relatives, we compared observed inbreeding and kinship coefficients in the population with those obtained from simulations of random mating. We found no significant differences between the two, indicating weak or absent inbreeding avoidance. We conclude that there was inbreeding depression in our population. Despite this, birds did not seem to actively avoid mating with close relatives, perhaps as a consequence of constraints on mating possibilities in such a small population.

The influence of persistent individual differences and age at maturity on effective population size

Ratios of effective populations size, Ne, to census population size, N, are used as a measure of genetic drift in populations. Several life-history parameters have been shown to affect these ratios, including mating system and age at sexual maturation. Using a stochastic matrix model, we examine how different levels of persistent individual differences in mating success among males may affect Ne/N, and how this relates to generation time. Individual differences of this type are shown to cause a lower Ne/N ratio than would be expected when mating is independent among seasons. Examining the way in which age at maturity affects Ne/N, we find that both the direction and magnitude of the effect depends on the survival rate of juveniles in the population. In particular, when maturation is delayed, lowered juvenile survival causes higher levels of genetic drift. In addition, predicted shifts in Ne/N with changing age at maturity are shown to be dependent on which of the commonly used definitions of census population size, N, is employed. Our results demonstrate that patterns of mating success, as well as juvenile survival probabilities, have substantial effects on rates of genetic drift.

FIXATION OF SLIGHTLY BENEFICIAL MUTATIONS: EFFECTS OF LIFE HISTORY

Recent studies of rates of evolution have revealed large systematic differences among organisms with different life histories, both within and among taxa. Here, we consider how life history may affect the rate of evolution via its influence on the fixation probability of slightly beneficial mutations. Our approach is based on diffusion modeling for a finite, stage‐structured population with stochastic population dynamics. The results, which are verified by computer simulations, demonstrate that even with complex population structure just two demographic parameters are sufficient to give an accurate approximation of the fixation probability of a slightly beneficial mutation. These are the reproductive value of the stage in which the mutation first occurs and the demographic variance of the population. The demographic variance also determines what influence population size has on the fixation probability. This model represents a substantial generalization of earlier models, covering a large range of life histories.

Spatial distribution and optimal harvesting of an age-structured population in a fluctuating environment

We analyze a spatial age-structured model with density regulation, age specific dispersal, stochasticity in vital rates and proportional harvesting. We include two age classes, juveniles and adults, where juveniles are subject to logistic density dependence. There are environmental stochastic effects with arbitrary spatial scales on all birth and death rates, and individuals of both age classes are subject to density independent dispersal with given rates and specified distributions of dispersal distances. We show how to simulate the joint density fields of the age classes and derive results for the spatial scales of all spatial autocovariance functions for densities. A general result is that the squared scale has an additive term equal to the squared scale of the environmental noise, corresponding to the Moran effect, as well as additive terms proportional to the dispersal rate and variance of dispersal distance for the age classes and approximately inversely proportional to the strength of density regulation. We show that the optimal harvesting strategy in the deterministic case is to harvest only juveniles when their relative value (e.g. financial) is large, and otherwise only adults. With increasing environmental stochasticity there is an interval of increasing length of values of juveniles relative to adults where both age classes should be harvested. Harvesting generally tends to increase all spatial scales of the autocovariances of densities.

Modelling time to population extinction when individual reproduction is autocorrelated

In nature, individual reproductive success is seldom independent from year to year, due to factors such as reproductive costs and individual heterogeneity. However, population projection models that incorporate temporal autocorrelations in individual reproduction can be difficult to parameterise, particularly when data are sparse. We therefore examine whether such models are necessary to avoid biased estimates of stochastic population growth and extinction risk, by comparing output from a matrix population model that incorporates reproductive autocorrelations to output from a standard age-structured matrix model that does not. We use a range of parameterisations, including a case study using moose data, treating probabilities of switching reproductive class as either fixed or fluctuating. Expected time to extinction from the two models is found to differ by only small amounts (under 10%) for most parameterisations, indicating that explicitly accounting for individual reproductive autocorrelations is in most cases not necessary to avoid bias in extinction estimates.