Population dynamics of shrews on small islands accord with the equilibrium model

Three of the six species of shrew in Finland, Sorex araneus, S. caecutiens, and S. minutus , are common on the mainland and widespread on islands in lakes. The islands range from 0.01 to 500 ha in area, and from 10 to 3000 m in isolation (distance from the mainland). The species-area relationship, the lack of importance of habitat diversity, the increasing frequency of unoccupied small islands with isolation, and direct observations of small populations, all suggest that populations on small islands have a high extinction rate. Demographic stochasticity is the main cause of extinctions in the superior competitor, S. araneus , which occurs consistently on islands greater than 2 ha. The small species, S. caecutiens and S. minutus , are more sensitive to environmental stochasticity than is S. araneus , and are inferior to it in interspecific competition; these factors probably contribute to the absence of the small species from many islands tens of hectares in area. Frequent colonization of islands less than 500 m from the mainland is indicated by large numbers of shrews trapped from tiny islets where breeding is not possible, by increasing epigenetic divergence of island populations with isolation, and by observations of dispersal to and colonization of islands. Dispersal ability decreases with decreasing individual size, which may partly explain the absence of the small shrews from many relatively large islands. The shrew populations persist in a dynamic equilibrium on the islands. Epigenetic morphological variation is a useful tool in ecological studies of island populations.     

Late pleistocene population dynamics: An alternative view

An attempt is made to argue for a more dynamic view of huntergatherer population behavior in place of the largely static one that has been widely accepted. Following a review of how the concept of carrying capacity has been used in both huntergatherer and ecological studies, attention is drawn to the role of stochastic factors in producing fluctuations over time among populations that are small in size. Some of the implications of this alternative view are briefly discussed.Research supported in part by NIH Grant GM 20467-03.This is a revised version of a paper presented at the symposium, Systems and Their Environments, at the Annual Meeting of the American Anthropological Association, 1973, New Orleans.     

Public avoidance and epidemics: insights from an economic model

In this paper, we present a mathematical model of infectious disease transmission in which people can engage in public avoidance behavior to minimize the likelihood of acquiring an infection. The framework employs the economist's theory of utility maximization to model people's decision regarding their level of public avoidance. We derive the reproductive number of a disease which determines whether an endemic equilibrium exists or not. We show that when the contact function exhibits saturation, an endemic equilibrium must be unique. Otherwise, multiple endemic equilibria that differ in disease prevalence can coexist, and which one the population gets to depends on initial conditions. Even when a unique endemic equilibrium exists, people's preferences and the initial conditions may determine whether the disease will eventually die out or become endemic. Public health policies that increase the recovery rate or encourage self-quarantine by infected people can be beneficial to the community by lowering disease prevalence. However, it is also possible for these policies to worsen the situation and cause prevalence to rise since these measures give people less incentive to engage in public avoidance behavior. We also show that implementing policies that result in a higher level of public avoidance behavior in equilibrium does not necessarily lower prevalence and can result in more infections.     

The effect of superspreading on epidemic outbreak size distributions

Recently, evidence has been presented to suggest that there are significant heterogeneities in the transmission of communicable diseases. Here, a stochastic simulation model of an epidemic process that allows for these heterogeneities is used to demonstrate the potentially considerable effect that heterogeneity of transmission will have on epidemic outbreak size distributions. Our simulation results agree well with approximations gained from the theory of branching processes. Outbreak size distributions have previously been used to infer basic epidemiological parameters. We show that if superspreading does occur then such distributions must be interpreted with care. The simulation results are discussed in relation to measles epidemics in isolated populations and in predominantly urban scenarios. The effect of three different disease control policies on outbreak size distributions are shown for varying levels of heterogeneity and disease control effort.     

On the survival probability of a slightly advantageous mutant gene in a multitype population: A multidimensional branching process model

The estimated survival probability of a slightly supercritical Galton-Watson process is generalized to a multitype branching process. The result is used to estimate the probability of initial success of a mutant gene whose effect on the individual carrier depends on the carrier's sex, class, etc. The probability of initial success is also estimated in a case where the effect of the mutation is manifested in terms of the distribution of types within one's progeny, e.g. in a case of a change in the sex ratio.     

Probability of fixation under weak selection: a branching process unifying approach

We link two-allele population models by Haldane and Fisher with Kimura's diffusion approximations of the Wright-Fisher model, by considering continuous-state branching (CB) processes which are either independent (model I) or conditioned to have constant sum (model II). Recent works by the author allow us to further include logistic density-dependence (model III), which is ubiquitous in ecology. In all models, each allele (mutant or resident) is then characterized by a triple demographic trait: intrinsic growth rate r, reproduction variance sigma and competition sensitivity c. Generally, the fixation probability u of the mutant depends on its initial proportion p, the total initial population size z, and the six demographic traits. Under weak selection, we can linearize u in all models thanks to the same master formula u = p + p(1 - p)[g(r)s(r) + g(sigma)s(sigma) + g(c)s(c)] + o(s(r),s(sigma),s(c), where s(r) = r' - r, s(sigma) = sigma-sigma' and s(c) = c - c' are selection coefficients, and g(r), g(sigma), g(c) are invasibility coefficients (' refers to the mutant traits), which are positive and do not depend on p. In particular, increased reproduction variance is always deleterious. We prove that in all three models g(sigma) = 1/sigma and g(r) = z/sigma for small initial population sizes z. In model II, g(r) = z/sigma for all z, and we display invasion isoclines of the 'mean vs variance' type. A slight departure from the isocline is shown to be more beneficial to alleles with low sigma than with high r. In model III, g(c) increases with z like ln(z)/c, and g(r)(z) converges to a finite limit L > K/sigma, where K = r/c is the carrying capacity. For r > 0 the growth invasibility is above z/sigma when z < K, and below z/sigma when z > K, showing that classical models I and II underestimate the fixation probabilities in growing populations, and overestimate them in declining populations.     

Evolution of dispersal in metapopulations with local density dependence and demographic stochasticity

In this paper, we predict the outcome of dispersal evolution in metapopulations based on the following assumptions: (i) population dynamics within patches are density-regulated by realistic growth functions; (ii) demographic stochasticity resulting from finite population sizes within patches is accounted for; and (iii) the transition of individuals between patches is explicitly modelled by a disperser pool. We show, first, that evolutionarily stable dispersal rates do not necessarily increase with rates for the local extinction of populations due to external disturbances in habitable patches. Second, we describe how demographic stochasticity affects the evolution of dispersal rates: evolutionarily stable dispersal rates remain high even when disturbance-related rates of local extinction are low, and a variety of qualitatively different responses of adapted dispersal rates to varied levels of disturbance become possible. This paper shows, for the first time, that evolution of dispersal rates may give rise to monotonically increasing or decreasing responses, as well as to intermediate maxima or minima.     

A stochastic model of a cell population with quiescence

A cell population in which cells are allowed to enter a quiescent (nonproliferating) phase is analyzed using a stochastic approach. A general branching process is used to model the population which, under very mild conditions, exhibits balanced exponential growth. A formula is given for the asymptotic fraction of quiescent cells, and a numerical example illustrates how convergence toward the asymptotic fraction exhibits a typical oscillatory pattern. The model is compared with deterministic models based on semigroup analysis of systems of differential equations.     

Cultivation Fosters Plant Naturalization by Reducing Environmental Stochasticity

A large fraction of the immigrant (or founder) populations of terrestrial plants are small (< 10⁴) and are acutely sensitive to environmental stochasticity. As a result, they undergo radical size fluctuations during a prolonged lag phase that almost always result in their extirpation. Naturalizations are those rare examples in which an immigrant population increases above a threshold size such that the consequences of environmental stochasticity are markedly lower. The likelihood that a non-indigenous population will reach this threshold size would be enhanced substantially through either deliberate or inadvertent cultivation. Cultivation (e.g. protection from predators, parasites, drought, frost) shields small immigrant populations from the extreme expressions of environmental stochasticity. In addition, cultivation can preserve through seed storage a residual non-indigenous population from which new populations can be established. As disseminules are spread locally, and even regionally, immigrant populations sample a wide variety of micro-habitats, thus increasing the likelihood that some plants will survive even without cultivation. Origins of naturalized floras in Australia and the US reveal a strong circumstantial link between cultivation and subsequent naturalization: the single largest group of naturalized species was deliberately introduced as either crops, forage spp., or ornamentals. Another group was introduced inadvertently as contaminants in crop seeds. This correspondence between cultivation and subsequent naturalization provides a common demographic explanation for non-indigenous plant persistence that largely transcends species’ attributes and the commonly ascribed features of communities that are vulnerable to the entry of non-indigenous plants. Humans have played a more profound role in fostering plant naturalizations than by acting simply as plant dispersers; their post-immigration cultivation fosters much naturalization. This revised version was published online in July 2006 with corrections to the Cover Date.     

The genetical theory of social behaviour

We survey the population genetic basis of social evolution, using a logically consistent set of arguments to cover a wide range of biological scenarios. We start by reconsidering Hamilton''s (Hamilton 1964 J. Theoret. Biol. 7, 1–16 (doi:10.1016/0022-5193(64)90038-4)) results for selection on a social trait under the assumptions of additive gene action, weak selection and constant environment and demography. This yields a prediction for the direction of allele frequency change in terms of phenotypic costs and benefits and genealogical concepts of relatedness, which holds for any frequency of the trait in the population, and provides the foundation for further developments and extensions. We then allow for any type of gene interaction within and between individuals, strong selection and fluctuating environments and demography, which may depend on the evolving trait itself. We reach three conclusions pertaining to selection on social behaviours under broad conditions. (i) Selection can be understood by focusing on a one-generation change in mean allele frequency, a computation which underpins the utility of reproductive value weights; (ii) in large populations under the assumptions of additive gene action and weak selection, this change is of constant sign for any allele frequency and is predicted by a phenotypic selection gradient; (iii) under the assumptions of trait substitution sequences, such phenotypic selection gradients suffice to characterize long-term multi-dimensional stochastic evolution, with almost no knowledge about the genetic details underlying the coevolving traits. Having such simple results about the effect of selection regardless of population structure and type of social interactions can help to delineate the common features of distinct biological processes. Finally, we clarify some persistent divergences within social evolution theory, with respect to exactness, synergies, maximization, dynamic sufficiency and the role of genetic arguments.     

EVOLUTION AND EXTINCTION IN A CHANGING ENVIRONMENT: A QUANTITATIVE-GENETIC ANALYSIS

Because of the ubiquity of genetic variation for quantitative traits, virtually all populations have some capacity to respond evolutionarily to selective challenges. However, natural selection imposes demographic costs on a population, and if these costs are sufficiently large, the likelihood of extinction will be high. We consider how the mean time to extinction depends on selective pressures (rate and stochasticity of environmental change, and strength of selection), population parameters (carrying capacity, and reproductive capacity), and genetics (rate of polygenic mutation). We assume that in a randomly mating, finite population subject to density-dependent population growth, individual fitness is determined by a single quantitative-genetic character under Gaussian stabilizing selection with the optimum phenotype exhibiting directional change, or random fluctuations, or both. The quantitative trait is determined by a finite number of freely recombining, mutationally equivalent, additive loci. The dynamics of evolution and extinction are investigated, assuming that the population is initially under mutation-selection-drift balance. Under this model, in a directionally changing environment, the mean phenotype lags behind the optimum, but on the average evolves parallel to it. The magnitude of the lag determines the vulnerability to extinction. In finite populations, stochastic variation in the genetic variance can be quite pronounced, and bottlenecks in the genetic variance temporarily can impair the population's adaptive capacity enough to cause extinction when it would otherwise be unlikely in an effectively infinite population. We find that maximum sustainable rates of evolution or, equivalently, critical rates of environmental change, may be considerably less than 10% of a phenotypic standard deviation per generation.     

Effects of climate on population fluctuations of ibex

Predicting the effects of the expected changes in climate on the dynamics of populations require that critical periods for climate‐induced changes in population size are identified. Based on time series analyses of 26 Swiss ibex (Capra ibex) populations, we show that variation in winter climate affected the annual changes in population size of most of the populations after accounting for the effects of density dependence and demographic stochasticity. In addition, precipitation during early summer also influenced the population fluctuations. This suggests that the major influences of climate on ibex population dynamics operated either through loss of individuals during winter or early summer, or through an effect on fecundity. However, spatial covariation in these climate variables was not able to synchronize the population fluctuations of ibex over larger distances, probably due to large spatial heterogeneity in the effects of single climate variables on different populations. Such spatial variation in the influence of the same climate variable on the local population dynamics suggests that predictions of influences of climate change need to account for local differences in population dynamical responses to climatic conditions.     

Population persistence time under intermittent control in stochastic environments

If there exists a critical population size above which environmental degradation becomes serious, the population should be suppressed or reduced upon reaching that level. Since population size control is accompanied by costs, a reduction in control frequency may be preferable from an economic viewpoint. Although this can be realized by decreasing the population size drastically in each control, such management may result in increased population extinction probability according to environmental stochasticity. The effects of population management on both mean population persistence time and management cost were analyzed theoretically using a diffusion process. The model showed the functional forms of both mean persistence time and control frequency explicitly; these decreased with an increasing number of individuals removed from the population in each control operation. Based on the analysis, indices representing management costs are proposed. Mean persistence time is generally an increasing function of the cost indices. Nevertheless, if the cost of each control increases with the number of individuals removed, even the most conservative management practice (continuous control) may not be overly expensive.