Persistence Time Of Populations Research Articles

On the establishment, persistence, and inevitable extinction of populations.

Comprehensive models of stochastic, clonally reproducing populations are defined in terms of general branching processes, allowing birth during maternal life, as for higher organisms, or by splitting, as in cell division. The populations are assumed to start small, by mutation or immigration, reproduce supercritically while smaller than the habitat carrying capacity but subcritically above it. Such populations establish themselves with a probability wellknown from branching process theory. Once established, they grow up to a band around the carrying capacity in a time that is logarithmic in the latter, assumed large. There they prevail during a time period whose duration is exponential in the carrying capacity. Even populations whose life style is sustainble in the sense that the habitat carrying capacity is not eroded but remains the same, ultimately enter an extinction phase, which again lasts for a time logarithmic in the carrying capacity. However, if the habitat can carry a population which is large, say millions of individuals, and it manages to avoid early extinction, time in generations to extinction will be exorbitantly long, and during it, population composition over ages, types, lineage etc. will have time to stabilise. This paper aims at an exhaustive description of the life cycle of such populations, from inception to extinction, extending and overviewing earlier results. We shall also say some words on persistence times of populations with smaller carrying capacities and short life cycles, where the population may indeed be in danger in spite of not eroding its environment.

Inbreeding–environment interactions increase extinction risk

AbstractBeing able to accurately estimate the persistence time of populations of endangered plants and animals is central to conservation biology and is of considerable importance in informing land‐use decisions. Genetic deterioration (due to inbreeding and random genetic drift) and environmental deterioration (e.g. climate change, pollution and introduced species) clearly contribute to population extinction, however, considerable recent evidence suggests that interactions between genetic deterioration and environmental stress are ubiquitous. The importance of these interactions for potentially reducing persistence times has not been quantified and has not been taken into account by major conservation organizations. Using a computer simulation, we determined that including reasonable estimates of the inbreeding–environment interaction reduces persistence times by 17.5–28.5% (mean=23%) for a wide range of carrying capacities, assumptions concerning the number of lethal equivalents and different regimes for the frequency and magnitude of the stressful environment. We note that the proportional decrease in persistence time with inclusion of the interactions becomes larger (i.e. the interaction becomes more important) as absolute time to extinction gets larger. Thus, inclusion of the interaction is important and surprisingly may be most needed when populations are of intermediate size and are considered relatively safe from environmental and genetic stresses acting independently.

Extinction in Fragmented Habitats Predicted from Stochastic Birth–death Processes with Density Dependence

Habitat loss, the reduction of the habitat area available, is known to greatly reduce resident species' expected time to extinction. This process is widely recognized, if not adequately understood or quantified except in very simple models. However, it is not well understood how the time to extinction will change if the remaining habitat is distributed across a set of smaller, isolated patches, instead of being left in one single, continuous tract. The effect of habitat fragmentation on population persistence under demographic stochasticity has not been resolved. Specifically, it is not known whether a single large population will persist longer than an aggregate set of several smaller populations (with the same total size). Analytical studies of birth–death processes typically report the mean time to extinction for a single population as a function of the maximum population size, but omit higher moments. To estimate the overall persistence time, or the probability of extinction as a function of time, for a set of small populations, the entire distribution of extinction times must be known for a single population of each size. Knowing all the moments of the distribution of extinction times is not adequate, unless one can reconstruct the distribution from them. Here I analyse stochastic birth–death processes with linear density dependence in per capita birth and death rates, and obtain analytical expressions and numerical solutions for the distribution of extinction times in both subdivided and continuous populations. This is a single-species model that deals with demographic stochasticity only, and assumes independence of extinction events in different patches. These assumptions are relaxed elsewhere. Habitat fragmentation, even without any loss of overall area, has a great and detrimental effect on the persistence time of populations across all temporal and spatial scales. The effect is similar across spatial scales, but shifted in time—larger populations take longer to go extinct but the extinction risk relative to that of a smaller or more fragmented population is the same across spatial scales for the available habitat.

A simple direct method for finding persistence times of populations and application to conservation problems.

The computation of persistence times of populations has become a central focus in conservation biology. We describe a simple, direct method for finding the statistics of persistence times by assuming that there is a maximum population size. Thus, even though the population dynamics may be very complex for population sizes below the maximum, it is possible to write a finite set of equations from which the mean and second moment of the persistence time can be found by using simple, algebraic methods. We apply the method to compute the mean and coefficient of variation of persistence times of populations that suffer large decrements (catastrophes). Our results show that in the presence of catastrophes, the increase in mean persistence time with large populations is not nearly as rapid as other theories suggest and that catastrophes occurring at even modest rates can considerably increase the risk of extinction.

Persistence times of populations with large random fluctuations

The growth of populations which undergo large random fluctuations can be modelled with stochastic differential equations involving Poisson processes. The problem of determining the persistence time is that of finding the time of first passage to some small critical population size. We consider in detail a simple model of logistic growth with additive Poisson disasters of fixed magnitude. The expectation and variability of the persistence time are obtained as solutions of singular differential-difference equations. The dependence of the persistence time of a colonizing species on the parameters of the model is discussed. The model may also be viewed as random harvesting with fixed quotas and a comparison is made between the mean extinction time and those for deterministic models.