Metapopulation extinction risk: Dispersal’s duplicity

Metapopulation extinction risk is the probability that all local populations are simultaneously extinct during a fixed time frame. Dispersal may reduce a metapopulation’s extinction risk by raising its average per-capita growth rate. By contrast, dispersal may raise a metapopulation’s extinction risk by reducing its average population density. Which effect prevails is controlled by habitat fragmentation. Dispersal in mildly fragmented habitat reduces a metapopulation’s extinction risk by raising its average per-capita growth rate without causing any appreciable drop in its average population density. By contrast, dispersal in severely fragmented habitat raises a metapopulation’s extinction risk because the rise in its average per-capita growth rate is more than offset by the decline in its average population density. The metapopulation model used here shows several other interesting phenomena. Dispersal in sufficiently fragmented habitat reduces a metapopulation’s extinction risk to that of a constant environment. Dispersal between habitat fragments reduces a metapopulation’s extinction risk insofar as local environments are asynchronous. Grouped dispersal raises the effective habitat fragmentation level. Dispersal search barriers raise metapopulation extinction risk. Nonuniform dispersal may reduce the effective fraction of suitable habitat fragments below the extinction threshold. Nonuniform dispersal may make demographic stochasticity a more potent metapopulation extinction force than environmental stochasticity.     

Effects on population persistence: the interaction between environmental noise colour,intraspecific competition and space

It is accepted that accurate estimation of risk of population extinction, or persistence time, requires prediction of the effect of fluctuations in the environment on population dynamics. Generally, the greater the magnitude, or variance, of environmental stochasticity, the greater the risk of population extinction. Another characteristic of environmental stochasticity, its colour, has been found to affect population persistence. This is important because real environmental variables, such as temperature, are reddened or positively temporally autocorrelated. However, recent work has disagreed about the effect of reddening environmental stochasticity. Ripa and Lundberg (1996) found increasing temporal autocorrelation (reddening) decreased the risk of extinction, whereas a simple and powerful intuitive argument (Lawton 1988) predicts increased risk of extinction with reddening. This study resolves the apparent contradiction, in two ways, first, by altering the dynamic behaviour of the population models. Overcompensatory dynamics result in persistence times increasing with increased temporal autocorrelation; undercompensatory dynamics result in persistence times decreasing with increased temporal autocorrelation. Secondly, in a spatially subdivided population, with a reasonable degree of spatial heterogeneity in patch quality, increasing temporal autocorrelation in the environment results in decreasing persistence time for both types of competition. Thus, the inclusion of coloured noise into ecological models can have subtle interactions with population dynamics.     

Approximating persistence in a general class of population processes

We provide a general framework for estimating persistence in populations which may be affected by catastrophic events, and which are either unbounded or have very large ceilings. We model the population using a birth-death process modified to allow for downward jumps of arbitrary size. For such processes, it is typically necessary to truncate the process in order to make the evaluation of expected extinction times (and higher-order moments) computationally feasible. Hence, we give particular attention to the selection of a cut-off point at which to truncate the process, and we present a simple method for obtaining quantitative indicators of the suitability of a chosen cut-off.     

The extinction context enables extinction performance after a change in context

One experiment with human participants determined the extent to which recovery of extinguished responding with a context switch was due to a failure to retrieve contextually controlled learning, or some other process such as participants learning that context changes signal reversals in the meaning of stimulus-outcome relationships. In a video game, participants learned to suppress mouse clicking in the presence of a stimulus that predicted an attack. Then, that stimulus underwent extinction in a different context (environment within the game). Following extinction, suppression was recovered and then extinguished again during testing in the conditioning context. In a final test, participants that were tested in the context where extinction first took place showed less of a recovery than those tested in a neutral context, but they showed a recovery of suppression nevertheless. A change in context tended to cause a change in the meaning of the stimulus, leading to recovery in both the neutral and extinction contexts. The extinction context attenuated that recovery, perhaps by enabling retrieval of the learning that took place in extinction. Recovery outside an extinction context is due to a failure of the context to enable the learning acquired during extinction, but only in part.     

Issues in the extinction of specific stimulus-outcome associations in Pavlovian conditioning

This paper reviews a variety of studies designed to examine the effects of extinction upon control by specific stimulus-outcome (S-O) associations in Pavlovian conditioning. Studies conducted with rats in a magazine approach conditioning paradigm have shown that control by specific S-O associations is normally unaffected by extinction treatments, although other aspects of conditioned responding seem affected in a more enduring way. However, recent work suggests that extinction can undermine control by such associations if it is administered after the conditioned stimulus is weakly encoded. The results from these studies suggest that it may be important to consider multiple response systems in assessing the impact of extinction. Studies conducted with the flavor preference learning paradigm in rats also show that specific S-O associations can be undermined by procedures that involve presenting a flavor cue in the absence of its associated nutrient. These findings provide no support for the view that flavor preference learning necessarily entails some unique learning process that differs from more conventional processes. As in other situations, some of these effects likely involve a masking process, but the extent to which masking or true associative weakening occurs in extinction more generally is a topic that is not well understood. Finally, we present some data to suggest that extinction also involves conditional "occasion-setting" control by contextual cues. Special procedures are recommended in assessing such learning when the goal is to distinguish this form of learning from other more conventional mechanisms of extinction.     

Extinction and colonization processes in subpopulations of five neotropical small mammal species

We report the extinction and colonization rates of five sympatric small mammal species at a semiarid locality in north central Chile. We provide information based on 6 years of monitoring on how colonization and extinction rates change according to landscape features (slope aspect) and on their relationship to populations size, population variability, and body size. We found that: (1) for all species in the assemblage, extinction rates of subpopulations from equatorial-facing slopes were significantly lower than those in polar-facing slopes, (2) population size was the most important factor determining extinction rates, (3) colonization rates did not vary between slopes, and were affected by population size only in equatorial-facing slopes, and (4) most species had higher extinction than colonization rates. Persistence of the metapopulation system for all five small mammal species appears to be fueled by repeated colonization events.     

Sur l’extinction des populations avec plusieurs types dans un environnement aléatoire

This study focuses on the extinction rate of a population that follows a continuous-time multi-type branching process in a random environment. Numerical computations in a particular example inspired by an epidemic model suggest an explicit formula for this extinction rate, but only for certain parameter values.     

A branching process, its application in biology: influence of demographic parameters on the social structure in mammal groups

Branching processes are widely used in biology. This theoretical tool is used in cell dynamics, epidemics and population dynamics. In population dynamics, branching processes are mainly used to access extinction probabilities of populations, groups or families, with the Galton-Watson branching process. Many mammal species live in socially-structured groups, and the smallest units of these groups are lineages (or families) of kin-related individuals. In many primate species, these lineages are matrilines, as females remain in their natal groups most of the time, whereas males generally disperse. Lineage parameters, such as numbers of matrilines, size of each matriline and average degree of relatedness, could strongly influence the genetic composition of groups. Evidence indicates that division along matrilines could induce substantial differentiation among fission groups. Here, we develop a novel mathematical model based on the branching process theory describing demographic dynamics of groups. The main result of this model is an explicit analytical expression of the joint distribution of numbers of lineages and sizes of socially-structured groups. We investigated the influence of parameters such as natality and mortality on the outcome of the process, including extinction probability. Finally, we discuss this theoretical result with respect to biological significance.     

BIODIVERSITY RESEARCH: When is a species really extinct? Testing extinction inference from a sighting record to inform conservation assessment

Aim The global extinction of a species typically represents the end point in a series of population extinctions, during which unique evolutionary history is lost at every stage. Insight into the process of extinction can provide the means to identify species at high risk, but the number of extinctions being identified languishes far behind true totals. More proactive ways of inferring extinction from limited data are required. Location Historic sightings, collections and specimen data from Australia and Asia. Method We used a technique called optimal linear estimation to analyse the sightings record of mammal and bird species of varying ecology, life history and population demography. The mammal species chosen were all considered regionally extinct in the literature, while the bird species chosen had all been highlighted as candidates for the new IUCN Red List category flag: Critically Endangered (Possibly Extinct). Results Nine of the ten mammal species were predicted to be probably extinct, but only two with 95% certainty. Seven of the ten bird species were predicted to be probably extinct, four with 95% certainty. Main conclusions Superficially, determining whether a species is extinct might seem a simple task, whereby we either find a species extant, or it is extinct. In reality, however, the task is much more complex. Techniques such as optimal linear estimation, in combination with other data sources, and knowledge of recording effort, may prove useful in inferring extinction across a variety of taxa but should not be used in isolation.     

Parasite evolution and extinctions

We examine the evolution of diseases that show the frequency‐dependent transmission process that is commonly applied to sexually and vector‐transmitted infections. As is commonly found, the basic reproductive ratio (R₀) of the parasite is maximized by evolution. This has important implications, as it implies that for a wide range of circumstances diseases that show frequency‐dependent transmission may be selected to evolve towards driving their hosts to extinction. This contrasts with the results obtained in spatially explicit models where although parasite‐driven host extinction may occur, it is unlikely to evolve. We further show that an evolutionary constraint between transmission and virulence is required for evolution to lead to an endemic coexistence of both the host and the disease. Furthermore, this constraint needs to be saturating, such that transmission is ‘bought’ at an increasing cost in terms of virulence, to avoid evolution to extinction.     

MUTATIONAL MELTDOWNS IN SEXUAL POPULATIONS

Although it is widely acknowledged that the gradual accumulation of mildly deleterious mutations is an important source of extinction for asexual populations, it is generally assumed that this process is of little relevance to sexual species. Here we present results, based on computer simulations and supported by analytical approximations, that indicate that mutation accumulation in small, random-mating monoecious populations can lead to mean extinction times less than a few hundred to a few thousand generations. Unlike the situation in obligate asexuals in which the mean time to extinction (t?_e) increases more slowly than linearly with the population carrying capacity (K), t?_e increases approximately exponentially with K in outcrossing sexual populations. The mean time to extinction for obligately selfing populations is shown to be equivalent to that for asexual populations of the same size, but with half the mutation rate and twice the mutational effect; this suggests that obligate selfing, like obligate asexuality, is inviable as a long-term reproductive strategy. Under all mating systems, the mean time to extinction increases relatively slowly with the logarithm of fecundity, and mutations with intermediate effects (similar to those observed empirically) cause the greatest risk of extinction. Because our analyses ignore sources of demographic and environmental stochasticity, which have synergistic effects that exacerbate the accumulation of deleterious mutations, our results should yield liberal upper bounds to the mean time to extinction caused by mutational degradation. Thus, deleterious mutation accumulation cannot be ruled out generally as a significant source of extinction vulnerability in small sexual populations or as a selective force influencing mating-system evolution.     

Population extinction risks of three Neotropical small mammal species

The population persistence and extinction probabilities of three small mammal species were analyzed by estimating growth and extinction properties obtained from 10 years of live-trapping data at two different habitat types in semiarid Chile. We used a stochastic formulation with an exponential growth model known as a Wiener-drift process, out of which growth and extinction quantities were estimated. The rodent Phyllotis darwini showed the lowest rates of growth, and the lowest infinitesimal variances, whereas the opposite trend was found for the rodent Akodonolivaceus. The marsupial Thylamys elegans showed intermediate values for growth rates and infinitesimal variances. The rodent P. darwini showed the lowest extinction risk in the study site. We also detected spatial differences between mesic and xeric habitats in the growth rates of P. darwini and T. elegans, and in the extinction risks of the three species studied. Although the population growth of these three species can be approximated by purely stochastic processes, the introduction of density dependence through autoregressive log-linear models reduced the extinction times of all species analyzed. Received: 16 May 1997 / Accepted: 22 January 1998     

Inbreeding,inbreeding depression and extinction

Inbreeding is unavoidable in small, isolated populations and can cause substantial fitness reductions compared to outbred populations. This loss of fitness has been predicted to elevate extinction risk giving it substantial conservation significance. Inbreeding may result in reduced fitness for two reasons: an increased expression of deleterious recessive alleles (partial dominance hypothesis) or the loss of favourable heterozygote combinations (overdominance hypothesis). Because both these sources of inbreeding depression are dependent upon dominance variance, inbreeding depression is predicted to be greater in life history traits than in morphological traits. In this study we used replicate inbred and control lines of Drosophila simulans to address three questions:1) is inbreeding depression greater in life history than morphological traits? 2) which of the two hypotheses is the major underlying cause of inbreeding depression? 3) does inbreeding elevate population extinction risk? We found that inbreeding depression was significantly greater in life history traits compared to morphological traits, but were unable to find unequivocal support for either the overdominance or partial dominance hypotheses as the genetic basis of inbreeding depression. As predicted, inbred lines had a significantly greater extinction risk.     

Synchronous dynamics and rates of extinction in spatially structured populations

We explore extinction rates using a spatially arranged set of subpopulations obeying Ricker dynamics. The population system is subjected to dispersal of individuals among the subpopulations as well as to local and global disturbances. We observe a tight positive correlation between global extinction rate and the level of synchrony in dynamics among thesubpopulations. Global disturbances and to a lesser extent, migration, are capable of synchronizing the temporal dynamics of the subpopulations over a rather wide span of the population growth rate r. Local noise decreases synchrony, as does increasing distance among the subpopulations. Synchrony also levels off with increasing r: in the chaotic region, subpopulations almost invariably behave asynchronously. We conclude that it is asynchrony that reduces the probability of global extinctions, not chaos as such: chaos is a special case only. The relationship between global extinction rate, synchronous dynamics and population growth rate is robust to changes in dispersal rates and ranges.     

MUTATIONAL MELTDOWN IN LABORATORY YEAST POPULATIONS

Abstract.— In small or repeatedly bottlenecked populations, mutations are expected to accumulate by genetic drift, causing fitness declines. In mutational meltdown models, such fitness declines further reduce population size, thus accelerating additional mutation accumulation and leading to extinction. Because the rate of mutation accumulation is determined partly by the mutation rate, the risk and rate of meltdown are predicted to increase with increasing mutation rate. We established 12 replicate populations of Saccharomyces cerevisiae from each of two isogenic strains whose genomewide mutation rates differ by approximately two orders of magnitude. Each population was transferred daily by a fixed dilution that resulted in an effective population size near 250. Fitness declines that reduce growth rates were expected to reduce the numbers of cells transferred after dilution, thus reducing population size and leading to mutational meltdown. Through 175 daily transfers and approximately 2900 generations, two extinctions occurred, both in populations with elevated mutation rates. For one of these populations there is direct evidence that extinction resulted from mutational meltdown: Extinction immediately followed a major fitness decline, and it recurred consistently in replicate populations reestablished from a sample frozen after this fitness decline, but not in populations founded from a predecline sample. Wild‐type populations showed no trend to decrease in size and, on average, they increased in fitness.     

Persistence in population models with demographic fluctuations

A persistence and extinction theory is developed through analytical studies of deterministic population models. Under hypotheses that require demographic parameters to fluctuate temporally, the populations may or may not oscillaate. Extinction, when it occurs, is asymptotic. An hierarchy of persistence criteria, based upon fluctuations measured by time average means, is derived. In some situations a threshold value is found to separate persistent population models from those that tend to extinction. Application of the persistence-extinction theory is to the problem of assessing effects of a toxic substance on a population when toxicant inputs to the environment and to resources are oscillatory.     

The prey-dependent consumption two-prey one-predator models with stage structure for the predator and impulsive effects

In this paper, we consider the prey-dependent consumption two-prey one-predator models with stage structure for the predator and impulsive effects. By applying the Floquet theory of linear periodic impulsive equation, we show that there exists a globally asymptotically stable pest-eradication periodic solution when the impulsive period is less than some critical value, that is, the pest population can be eradicated totally. But from the point of ecological balance and saving resources, we only need to control the pest population under the economic threshold level instead of eradicating it totally, and thus, we further prove that the system is uniformly permanent if the impulsive period is larger than some critical value, and meanwhile we also give the conditions for the extinction of one of the two preys and permanence of the remaining species. Thus, we can use the stability of the positive periodic solution and its period to control insect pests at acceptably low levels. Considering population communities always are imbedded in periodically varying environments, and the parameters in ecosystem models may oscillate simultaneously with the periodically varying environments, we add a forcing term into the prey population's intrinsic growth rate. The resulting bifurcation diagrams show that with the varying of parameters, the system experiences process of cycles, periodic windows, periodic-doubling cascade, symmetry breaking bifurcation as well as chaos.     

On density and extinction in continuous population models

Survival analyses, investigations of extinction and persistence, are executed for populations represented by a nonautonomous differential equation model. The population is assumed governed by density dependent and time varying density independent demographic parameters. While traditional approaches to extinction postulate extinction on an infinite time horizon and at zero abundance level, survival analysis is developed not only for this traditional setting but also on a finite time horizon and at a nonzero threshold level. A main conclusion is that extinction of a temporally stressed population is determined by a totality of density independent and density dependent factors.     

Extinction of populations by inbreeding depression under stochastic environments

Inbreeding depression may induce rapid extinction due to positive feedbacks between inbreeding depression and reduction of population size, which is often referred to as extinction vortex by inbreeding depression. The present analysis has demonstrated that the extinction vortex is likely to happen with realistic parameter values of genomic mutation rate of lethals or semilethals, equilibrium population size, intrinsic rate of natural increase, and rate of population decline caused by nongenetic extrinsic factors. Simulation models incorporating stochastic fluctuations of population size further indicated that extinction by inbreeding depression is facilitated by environmental fluctuations in population size. The results suggest that there is a positive interaction between genetic stochasticity and environmental stochasticity for extinction of populations by inbreeding depression. Received: May 10, 1999 / Accepted: November 5, 1999     

Spatiotemporal complexity of patchy invasion in a predator-prey system with the Allee effect

Invasion of an exotic species initiated by its local introduction is considered subject to predator-prey interactions and the Allee effect when the prey growth becomes negative for small values of the prey density. Mathematically, the system dynamics is described by two nonlinear diffusion-reaction equations in two spatial dimensions. Regimes of invasion are studied by means of extensive numerical simulations. We show that, in this system, along with well-known scenarios of species spread via propagation of continuous population fronts, there exists an essentially different invasion regime which we call a patchy invasion. In this regime, the species spreads over space via irregular motion and interaction of separate population patches without formation of any continuous front, the population density between the patches being nearly zero. We show that this type of the system dynamics corresponds to spatiotemporal chaos and calculate the dominant Lyapunov exponent. We then show that, surprisingly, in the regime of patchy invasion the spatially average prey density appears to be below the survival threshold. We also show that a variation of parameters can destroy this regime and either restore the usual invasion scenario via propagation of continuous fronts or brings the species to extinction; thus, the patchy spread can be qualified as the invasion at the edge of extinction. Finally, we discuss the implications of this phenomenon for invasive species management and control.