The intrinsic mean time to extinction: a unifying approach to analysing persistence and viability of populations

Competition for resources can reshape the evolutionary properties of spatial structure

Many evolving ecosystems have spatial structures that can be conceptualized as networks, with nodes representing individuals or homogeneous subpopulations and links the patterns of interaction and replacement between them. Prior models of evolution on networks do not take ecological niche differences and eco-evolutionary interplay into account. Here, we combine a resource competition model with evolutionary graph theory to study how heterogeneous topological structure shapes evolutionary dynamics under global frequency-dependent ecological interactions. We find that the addition of ecological competition for resources can produce a reversal of roles between amplifier and suppressor networks for deleterious mutants entering the population. Moreover, we show that this effect is a non-linear function of ecological niche overlap and discuss intuition for the observed dynamics using simulations and analytical approximations.

Does deterministic coexistence theory matter in a finite world?

Contemporary studies of species coexistence are underpinned by deterministic models that assume that competing species have continuous (i.e., noninteger) densities, live in infinitely large landscapes, and coexist over infinite time horizons. By contrast, in nature, species are composed of discrete individuals subject to demographic stochasticity and occur in habitats of finite size where extinctions occur in finite time. One consequence of these discrepancies is that metrics of species' coexistence derived from deterministic theory may be unreliable predictors of the duration of species coexistence in nature. These coexistence metrics include invasion growth rates and niche and fitness differences, which are now commonly applied in theoretical and empirical studies of species coexistence. In this study, we tested the efficacy of deterministic coexistence metrics on the duration of species coexistence in a finite world. We introduce new theoretical and computational methods to estimate coexistence times in stochastic counterparts of classic deterministic models of competition. Importantly, we parameterized this model using experimental field data for 90 pairwise combinations of 18 species of annual plants, allowing us to derive biologically informed estimates of coexistence times for a natural system. Strikingly, we found that for species expected to deterministically coexist, community sizes containing only 10 individuals had predicted coexistence times of more than 1000 years. We also found that invasion growth rates explained 60% of the variation in intrinsic coexistence times, reinforcing their general usefulness in studies of coexistence. However, only by integrating information on both invasion growth rates and species' equilibrium population sizes could most (>99%) of the variation in species coexistence times be explained. This integration was achieved with demographically uncoupled single-species models solely determined by the invasion growth rates and equilibrium population sizes. Moreover, because of a complex relationship between niche overlap/fitness differences and equilibrium population sizes, increasing niche overlap and increasing fitness differences did not always result in decreasing coexistence times, as deterministic theory would predict. Nevertheless, our results tend to support the informed use of deterministic theory for understanding the duration of species' coexistence while highlighting the need to incorporate information on species' equilibrium population sizes in addition to invasion growth rates.

Resist or perish: Fate of a microbial population subjected to a periodic presence of antimicrobial

The evolution of antimicrobial resistance can be strongly affected by variations of antimicrobial concentration. Here, we study the impact of periodic alternations of absence and presence of antimicrobial on resistance evolution in a microbial population, using a stochastic model that includes variations of both population composition and size, and fully incorporates stochastic population extinctions. We show that fast alternations of presence and absence of antimicrobial are inefficient to eradicate the microbial population and strongly favor the establishment of resistance, unless the antimicrobial increases enough the death rate. We further demonstrate that if the period of alternations is longer than a threshold value, the microbial population goes extinct upon the first addition of antimicrobial, if it is not rescued by resistance. We express the probability that the population is eradicated upon the first addition of antimicrobial, assuming rare mutations. Rescue by resistance can happen either if resistant mutants preexist, or if they appear after antimicrobial is added to the environment. Importantly, the latter case is fully prevented by perfect biostatic antimicrobials that completely stop division of sensitive microorganisms. By contrast, we show that the parameter regime where treatment is efficient is larger for biocidal drugs than for biostatic drugs. This sheds light on the respective merits of different antimicrobial modes of action.

Neutral mechanisms and niche differentiation in steady-state insular microbial communities revealed by single cell analysis

In completely insular microbial communities, evolution of community structure cannot be shaped by the immigration of new members. In addition, when those communities are run in steady state, the influence of environmental factors on their assembly is reduced. Therefore, one would expect similar community structures under steady‐state conditions. Yet, in parallel setups, variability does occur. To reveal ecological mechanisms behind this phenomenon, five parallel reactors were studied at the single‐cell level for about 100 generations and community structure variations were quantified by ecological measures. Whether community variability can be controlled was tested by implementing soft temperature stressors as potential synchronizers. The low slope of the lognormal rank‐order abundance curves indicated a predominance of neutral mechanisms, i.e., where species identity plays no role. Variations in abundance ranks of subcommunities and increase in inter‐community pairwise β‐diversity over time support this. Niche differentiation was also observed, as indicated by steeper geometric‐like rank‐order abundance curves and increased numbers of correlations between abiotic and biotic parameters during initial adaptation and after disturbances. Still, neutral forces dominated community assembly. Our findings suggest that complex microbial communities in insular steady‐state environments can be difficult to synchronize and maintained in their original or desired structure, as they are non‐equilibrium systems.

Evaluation of Two Approaches to Defining Extinction Risk under the U.S. Endangered Species Act

The predominant definition of extinction risk in conservation biology involves evaluating the cumulative distribution function (CDF) of extinction time at a particular point (the "time horizon"). Using the principles of decision theory, this article develops an alternative definition of extinction risk as the expected loss (EL) to society resulting from eventual extinction of a species. Distinct roles are identified for time preference and risk aversion. Ranges of tentative values for the parameters of the two approaches are proposed, and the performances of the two approaches are compared and contrasted for a small set of real-world species with published extinction time distributions and a large set of hypothetical extinction time distributions. Potential issues with each approach are evaluated, and the EL approach is recommended as the better of the two. The CDF approach suffers from the fact that extinctions that occur at any time before the specified time horizon are weighted equally, while extinctions that occur beyond the specified time horizon receive no weight at all. It also suffers from the fact that the time horizon does not correspond to any natural phenomenon, and so is impossible to specify nonarbitrarily; yet the results can depend critically on the specified value. In contrast, the EL approach has the advantage of weighting extinction time continuously, with no artificial time horizon, and the parameters of the approach (the rates of time preference and risk aversion) do correspond to natural phenomena, and so can be specified nonarbitrarily.

Viability of cyclic populations

Theory on viability of small populations is well developed and has led to the standard methodology of population viability analysis (PVA) to assess vulnerability of single species. However, more complex situations involving community dynamics or environmental change violate theoretical assumptions. Synthesizing concepts from population, community, and conservation ecology, we develop a generic theory on the viability of cyclic populations. The interplay of periodic population decline and demography causes varying risk patterns that aggregate during cycles and modify the temporal structure of viability. This variability is visualized and quantitatively assessed. For two standard viability metrics that summarize immediate extinction risk and the general long-term conditions of populations, we mathematically describe the impact of population cycles. Finally, we suggest and demonstrate PVA for cyclic populations that respond to, e.g., seasonality, interannual variation, or trophic interactions. Our theoretical and methodological advancement opens a route to viability analysis in food webs and trophic meta-communities and equips biodiversity conservation with a long-missing tool.

A discrete Markov metapopulation model for persistence and extinction of species

A simple discrete generation Markov metapopulation model is formulated for studying the persistence and extinction dynamics of a species in a given region which is divided into a large number of sites or patches. Assuming a linear site occupancy probability from one generation to the next we obtain exact expressions for the time evolution of the expected number of occupied sites and the mean-time to extinction (MTE). Under quite general conditions we show that the MTE, to leading order, is proportional to the logarithm of the initial number of occupied sites and in precise agreement with similar expressions for continuous time-dependent stochastic models. Our key contribution is a novel application of generating function techniques and simple asymptotic methods to obtain a second order asymptotic expression for the MTE which is extremely accurate over the entire range of model parameter values.

Extinction dynamics of a discrete population in an oasis

Understanding the conditions ensuring the persistence of a population is an issue of primary importance in population biology. The first theoretical approach to the problem dates back to the 1950s with the Kierstead, Slobodkin, and Skellam (KiSS) model, namely a continuous reaction-diffusion equation for a population growing on a patch of finite size L surrounded by a deadly environment with infinite mortality, i.e., an oasis in a desert. The main outcome of the model is that only patches above a critical size allow for population persistence. Here we introduce an individual-based analog of the KiSS model to investigate the effects of discreteness and demographic stochasticity. In particular, we study the average time to extinction both above and below the critical patch size of the continuous model and investigate the quasistationary distribution of the number of individuals for patch sizes above the critical threshold.

Determining when to change course in management actions

Time is of the essence in conservation biology. To secure the persistence of a species, we need to understand how to balance time spent among different management actions. A new and simple method to test the efficacy of a range of conservation actions is required. Thus, we devised a general theoretical framework to help determine whether to test a new action and when to cease a trial and revert to an existing action if the new action did not perform well. The framework involves constructing a general population model under the different management actions and specifying a management objective. By maximizing the management objective, we could generate an analytical solution that identifies the optimal timing of when to change management action. We applied the analytical solution to the case of the Christmas Island pipistrelle bat (Pipistrelle murrayi), a species for which captive breeding might have prevented its extinction. For this case, we used our model to determine whether to start a captive breeding program and when to stop a captive breeding program and revert to managing the species in the wild, given that the management goal is to maximize the chance of reaching a target wild population size. For the pipistrelle bat, captive breeding was to start immediately and it was desirable to place the species in captivity for the entire management period. The optimal time to revert to managing the species in the wild was driven by several key parameters, including the management goal, management time frame, and the growth rates of the population under different management actions. Knowing when to change management actions can help conservation managers' act in a timely fashion to avoid species extinction.

A comparison of six methods for stabilizing population dynamics

Over the last two decades, several methods have been proposed for stabilizing the dynamics of biological populations. However, these methods have typically been evaluated using different population dynamics models and in the context of very different concepts of stability, which makes it difficult to compare their relative efficiencies. Moreover, since the dynamics of populations are dependent on the life-history of the species and its environment, it is conceivable that the stabilizing effects of control methods would also be affected by such factors, a complication that has typically not been investigated. In this study, we compare six different control methods with respect to their efficiency at inducing a common level of enhancement (defined as 50% increase) for two kinds of stability (constancy and persistence) under four different life-history/environment combinations. Since these methods have been analytically studied elsewhere, we concentrate on an intuitive understanding of realistic simulations incorporating noise, extinction probability and lattice effect. We show that for these six methods, even when the magnitude of stabilization attained is the same, other aspects of the dynamics like population size distribution can be very different. Consequently, correlated aspects of stability, like the amount of persistence for a given degree of constancy stability (and vice versa) or the corresponding effective population size (a measure of resistance to genetic drift) vary widely among the methods. Moreover, the number of organisms needed to be added or removed to attain similar levels of stabilization also varies for these methods, a fact that has economic implications. Finally, we compare the relative efficiencies of these methods through a composite index of various stability related measures. Our results suggest that Lower Limiter Control (LLC) seems to be the optimal method under most conditions, with the recently proposed Adaptive Limiter Control (ALC) being a close second.

Tail probabilities of extinction time in a large number of experimental populations

Determining the distribution of population extinction times is a fundamental problem in theoretical population biology. In particular, the tail properties, patterns in the probability of long-term persistence, have not been studied. Further, until now there have been no experimental or observational data sets with which to empirically test the "rare event" predictions of the standard stochastic theory of extinction, which holds that extinction times should be exponentially distributed. I performed an experimental study of extinction in a large number of replicate (n = 1076) laboratory populations of the waterflea Daphnia pulicaria. Observed extinction time ranged from 1 to 1239 days. Statistical models supported the hypothesis of a power-law distribution over the exponential distribution and other alternatives. This pattern contradicts the notion that population extinction time has an exponential tail, questioning its ubiquitous use in theoretical ecology. It is also a rare instance of a data set that exhibits power-law scaling under appropriate statistical criteria.

A protocol for better design, application, and communication of population viability analyses

Population viability analyses (PVAs) contribute to conservation theory, policy, and management. Most PVAs focus on single species within a given landscape and address a specific problem. This specificity often is reflected in the organization of published PVA descriptions. Many lack structure, making them difficult to understand, assess, repeat, or use for drawing generalizations across PVA studies. In an assessment comparing published PVAs and existing guidelines, we found that model selection was rarely justified; important parameters remained neglected or their implementation was described vaguely; limited details were given on parameter ranges, sensitivity analysis, and scenarios; and results were often reported too inconsistently to enable repeatability and comparability. Although many guidelines exist on how to design and implement reliable PVAs and standards exist for documenting and communicating ecological models in general, there is a lack of organized guidelines for designing, applying, and communicating PVAs that account for their diversity of structures and contents. To fill this gap, we integrated published guidelines and recommendations for PVA design and application, protocols for documenting ecological models in general and individual-based models in particular, and our collective experience in developing, applying, and reviewing PVAs. We devised a comprehensive protocol for the design, application, and communication of PVAs (DAC-PVA), which has 3 primary elements. The first defines what a useful PVA is; the second element provides a workflow for the design and application of a useful PVA and highlights important aspects that need to be considered during these processes; and the third element focuses on communication of PVAs to ensure clarity, comprehensiveness, repeatability, and comparability. Thereby, DAC-PVA should strengthen the credibility and relevance of PVAs for policy and management, and improve the capacity to generalize PVA findings across studies.

Consequences of environmental fluctuations on Taylor's power law and implications for the dynamics and persistence of populations

Conservation Biologists have found that demographic stochasticity causes the mean time to extinction to increase exponentially with population size. This has proved helpful in analyses determining extinction times and characterizing the pathway to extinction. The aim of this investigation is to explore the possible interactions between environmental/demographic noises and the scaling effect of the mean population size with its variance, which is expected to follow Taylor's power law relationship. We showed that the combined effects of environmental/demographic noises and the scaling of population size variability interact with the population dynamics and affect the mean time to extinction.

Effects of constant immigration on the dynamics and persistence of stable and unstable Drosophila populations

Constant immigration can stabilize population size fluctuations but its effects on extinction remain unexplored. We show that constant immigration significantly reduced extinction in fruitfly populations with relatively stable or unstable dynamics. In unstable populations with oscillations of amplitude around 1.5 times the mean population size, persistence and constancy were unrelated. Low immigration enhanced persistence without affecting constancy whereas high immigration increased constancy without enhancing persistence. In relatively stable populations with erratic fluctuations of amplitude close to the mean population size, both low and high immigration enhanced persistence. In these populations, the amplitude of fluctuations relative to mean population size went down due to immigration, and their dynamics were altered to low-period cycles. The effects of immigration on the population size distribution and intrinsic dynamics of stable versus unstable populations differed considerably, suggesting that the mechanisms by which immigration reduced extinction risk depended on underlying dynamics in complex ways.

Establishment probability in newly founded populations

BACKGROUND

Establishment success in newly founded populations relies on reaching the established phase, which is defined by characteristic fluctuations of the population's state variables. Stochastic population models can be used to quantify the establishment probability of newly founded populations; however, so far no simple but robust method for doing so existed. To determine a critical initial number of individuals that need to be released to reach the established phase, we used a novel application of the "Wissel plot", where -ln(1 - P0(t)) is plotted against time t. This plot is based on the equation P(0)t=1-c(1)e(-ω(1t)), which relates the probability of extinction by time t, P(0)(t), to two constants: c(1) describes the probability of a newly founded population to reach the established phase, whereas ω(1) describes the population's probability of extinction per short time interval once established.

RESULTS

For illustration, we applied the method to a previously developed stochastic population model of the endangered African wild dog (Lycaon pictus). A newly founded population reaches the established phase if the intercept of the (extrapolated) linear parts of the "Wissel plot" with the y-axis, which is -ln(c(1)), is negative. For wild dogs in our model, this is the case if a critical initial number of four packs, consisting of eight individuals each, are released.

CONCLUSIONS

The method we present to quantify the establishment probability of newly founded populations is generic and inferences thus are transferable to other systems across the field of conservation biology. In contrast to other methods, our approach disaggregates the components of a population's viability by distinguishing establishment from persistence.

The influence of agroforestry and other land-use types on the persistence of a Sumatran tiger (Panthera tigris sumatrae) population: an individual-based model approach

The importance of preserving both protected areas and their surrounding landscapes as one of the major conservation strategies for tigers has received attention over recent decades. However, the mechanism of how land-use surrounding protected areas affects the dynamics of tiger populations is poorly understood. We developed Panthera Population Persistence (PPP)--an individual-based model--to investigate the potential mechanism of the Sumatran tiger population dynamics in a protected area and under different land-use scenarios surrounding the reserve. We tested three main landscape compositions (single, combined and real land-uses of Tesso-Nilo National Park and its surrounding area) on the probability of and time to extinction of the Sumatran tiger over 20 years in Central Sumatra. The model successfully explains the mechanisms behind the population response of tigers under different habitat landscape compositions. Feeding and mating behaviours of tigers are key factors, which determined population persistence in a heterogeneous landscape. All single land-use scenarios resulted in tiger extinction but had a different probability of extinction within 20 years. If tropical forest was combined with other land-use types, the probability of extinction was smaller. The presence of agroforesty and logging concessions adjacent to protected areas encouraged the survival of tiger populations. However, with the real land-use scenario of Tesso-Nilo National Park, tigers could not survive for more than 10 years. Promoting the practice of agroforestry systems surrounding the park is probably the most reasonable way to steer land-use surrounding the Tesso-Nilo National Park to support tiger conservation.

Experimental demonstration of a two-phase population extinction hazard

Population extinction is a fundamental biological process with applications to ecology, epidemiology, immunology, conservation biology and genetics. Although a monotonic relationship between initial population size and mean extinction time is predicted by virtually all theoretical models, attempts at empirical demonstration have been equivocal. We suggest that this anomaly is best explained with reference to the transient properties of ensembles of populations. Specifically, we submit that under experimental conditions, many populations escape their initially vulnerable state to reach quasi-stationarity, where effects of initial conditions are erased. Thus, extinction of populations initialized far from quasi-stationarity may be exposed to a two-phase extinction hazard. An empirical prediction of this theory is that the fit Cox proportional hazards regression model for the observed survival time distribution of a group of populations will be shown to violate the proportional hazards assumption early in the experiment, but not at later times. We report results of two experiments with the cladoceran zooplankton Daphnia magna designed to exhibit this phenomenon. In one experiment, habitat size was also varied. Statistical analysis showed that in one of these experiments a transformation occurred so that very early in the experiment there existed a transient phase during which the extinction hazard was primarily owing to the initial population size, and that this was gradually replaced by a more stable quasi-stationary phase. In the second experiment, only habitat size unambiguously displayed an effect. Analysis of data pooled from both experiments suggests that the overall extinction time distribution in this system results from the mixture of extinctions during the initial rapid phase, during which the effects of initial population size can be considerable, and a longer quasi-stationary phase, during which only habitat size has an effect. These are the first results, to our knowledge, of a two-phase population extinction process.

Rapid viability analysis for metapopulations in dynamic habitat networks

For land-use planning, numerically fast and easily applicable tools are urgently needed that allow us to assess how landscape structure and dynamics affect biodiversity. To date, such tools exist only for static landscapes. We provide an analytical formula for the mean lifetime of species in fragmented and dynamic habitat networks where habitat patches may be destroyed and created elsewhere. The formula is able to consider both patch size heterogeneity and dynamics additionally to patch number and connectivity. It is validated through comparison with a dynamic and spatially explicit simulation model. It can be used for the optimization of spatio-temporal land-use patterns in real landscapes and for advancing our general understanding of key processes affecting the survival of species in fragmented heterogeneous dynamic landscapes.

Population models in pesticide risk assessment: lessons for assessing population-level effects, recovery, and alternative exposure scenarios from modeling a small mammal

In the last few years, the interest in using ecological population models as a tool for pesticide risk assessment has increased rapidly. Practical guidance, however, on how to perform a risk assessment with a population model is still lacking. It is still unclear which endpoint (population density, population growth, etc.) is the most sensitive indicator of population-level effects and how risk can be evaluated at the population level. Moreover, a main added value of model-based risk assessments, which is an understanding of the mechanisms involved in alternative exposure scenarios, so far has received little attention. We therefore used an example model to compare commonly used endpoints and alternative exposure scenarios. The model is a structurally realistic, but relatively simple, individual-based, spatially explicit model for the common shrew (Sorex araneus), which was selected because it has been tested and validated extensively. We show that population density is more sensitive for detecting population-level effects in the short term (months) than population growth rate. Population viability measured by extinction risk can also be a relevant endpoint, because it is especially sensitive for small populations. We show that landscape structure and the timing of pesticide application (population structure at the time of application) can have a great impact on population recovery, and we analyze statistical tests for use in population-level risk assessments. Our results demonstrate which factors and insights should be taken into account in population-level risk assessments.

Predicting metapopulation lifetime from macroscopic network properties

This paper presents a comparatively simple approximation formula for the mean life time of a metapopulation in a habitat network where habitat patch arrangement may be irregular and patch sizes differ. It is based on previous work on the development of an analytical approximation formula by Frank and Wissel [K. Frank, C. Wissel, A formula for the mean lifetime of metapopulations in heterogeneous landscapes, Am. Nat. 159 (2002) 530] and extends it by abstracting from individual patch locations. The mean metapopulation lifetime is expressed as a function of four macroscopic network properties: the ratio of dispersal range and network size, the ratio of range of environmental correlation and network size, and the total number and (geometric mean) size of the patches. The analysis takes into account that (ceteris paribus) patches close to the boundary of the habitat network contribute less to metapopulation survival than patches close to the centre of the network. Ignoring this fact can lead to a substantial overestimation of the mean metapopulation lifetime. Due to its numerical simplicity, the formula can be used as a conservation objective function even in complex network design problems where the number of patches to be allocated is very large. Numerical tests of the formula show that it performs very well within a wide range of network structures.

Use of the Abundance Spectrum and Relative‐Abundance Distributions to Analyze Assemblage Change in Massively Altered Landscapes

Fragmentation of natural landscapes is a pervasive process in the world. Common models predict coherent change in assemblages, with less numerous species becoming locally extinct first, then species of intermediate abundance, and so forth. Relative-abundance distributions should change systematically in landscapes characterized by greater change. Such a predictable sequence of change is not evident in the avifaunas of landscapes of central Victoria, Australia, where relative-abundance patterns in more affected landscapes bear little resemblance to reference distributions. I provide two sets of analyses of relative-abundance distributions: (1) analyses that do not depend on the identity of individual species and (2) abundance spectra, which use ordered lists of species ranked by species' commonness in reference systems. While abundance spectra change dramatically in smaller remnants, relative-abundance distributions change little, suggesting that the "reorganization" of abundances occurs over ecological time frames. The dispersal-limited multinomial is a flexible distribution that may fit many data sets yet be unrelated to assumptions (species neutrality) and processes (fixed total numbers of individuals) of the unified neutral theory. A more complete understanding of human impacts at landscape scales must include capacities to predict those species that will be advantaged by change, as well as those that will be disadvantaged.

Metapopulation extinction risk is increased by environmental stochasticity and assemblage complexity

Extinction risk is a key area of investigation for contemporary ecologists and conservation biologists. Practical conservation efforts for vulnerable species can be considerably enhanced by thoroughly understanding the ecological processes that interact to determine species persistence or extinction. Theory has highlighted the importance of both extrinsic environmental factors and intrinsic demographic processes. In laboratory microcosms, single-species single-habitat patch experimental designs have been widely used to validate the theoretical prediction that environmental heterogeneity can increase extinction risk. Here, we develop on this theme by testing the effects of fluctuating resource levels in experimental multispecies metapopulations. We compare a three-species host-parasitoid assemblage that exhibits apparent competition to the individual pairwise, host-parasitoid interactions. Existing theory is broadly supported for two-species assemblages: environmental stochasticity reduces trophic interaction persistence time, while metapopulation structure increases persistence time. However, with increasing assemblage complexity, the effects of trophic interactions mask environmental impacts and persistence time is further reduced, regardless of resource renewal regime. We relate our findings to recent theory, highlighting the importance of taking into account both intrinsic and extrinsic factors, over a range of spatial scales, in order to understand resource-consumer dynamics.

Making conservation decisions under uncertainty for the persistence of multiple species

Population models for multiple species provide one of the few means of assessing the impact of alternative management options on the persistence of biodiversity, but they are inevitably uncertain. Is it possible to use population models in multiple-species conservation planning given the associated uncertainties? We use information-gap decision theory to explore the impact of parameter uncertainty on the conservation decision when planning for the persistence of multiple species. An information-gap approach seeks robust outcomes that are most immune from error. We assess the impact of uncertainty in key model parameters for three species, whose extinction risks under four alternative management scenarios are estimated using a metapopulation model. Three methods are described for making conservation decisions across the species, taking into account uncertainty. We find that decisions based on single species are relatively robust to uncertainty in parameters, although the estimates of extinction risk increase rapidly with uncertainty. When identifying the best conservation decision for the persistence of all species, the methods that rely on the rankings of the management options by each species result in decisions that are similarly robust to uncertainty. Methods that depend on absolute values of extinction risk are sensitive to uncertainty, as small changes in extinction risk can alter the ranking of the alternative scenarios. We discover that it is possible to make robust conservation decisions even when the uncertainties of the multiple-species problem appear overwhelming. However, the decision most robust to uncertainty is likely to differ from the best decision when uncertainty is ignored, illustrating the importance of incorporating uncertainty into the decision-making process.

ON METAPOPULATION RESISTANCE TO DRIFT AND EXTINCTION

The spatial configuration of metapopulations (numbers, sizes, and localization of patches) affects their ability to resist demographic extinction and genetic drift, but sometimes with opposite effects. Small and isolated patches, for instance, contribute marginally to demography but may play a large role in genetics by maintaining a sizeable amount of genetic variance among demes. In source-sink systems, similarly, connectivity may be beneficial in terms of effective size, but detrimental in terms of survival, by lowering the reproductive value of source populations. How to reconcile these opposite effects? Here we propose an analytical framework that integrates fixation time (ability to resist genetic drift) and extinction time (ability to resist demographic extinction) into a single index of resistance, measuring the ability of a metapopulation to maintain its demo-genetic integrity. We then illustrate with numerical examples how conflicting demands may be resolved.

THE UNIFIED NEUTRAL THEORY OF BIODIVERSITY: DO THE NUMBERS ADD UP?

Hubbell's unified neutral theory is a zero-sum ecological drift model in which population sizes change at random in a process resembling genetic drift, eventually leading to extinction. Diversity is maintained within the community by speciation. Hubbell's model makes predictions about the distribution of species abundances within communities and the turnover of species from place to place (beta diversity). However, ecological drift cannot be tested adequately against these predictions without independent estimates of speciation rates, population sizes, and dispersal distances. A more practical prediction from ecological drift is that time to extinction of a population of size N is approximately 2N generations. I test this prediction here using data for passerine birds (Passeriformes). Waiting times to speciation and extinction were estimated from genetic divergence between sister populations and a lineage-through-time plot for endemic South American suboscine passerines. Population sizes were estimated from local counts of birds in two large forest plots extrapolated to the area of wet tropical forest in South America and from atlas data on European passerines. Waiting times to extinction (ca. 2 Ma) are much less than twice the product of average population size (4.0 and 14.4 x 10(6) individuals in South America and Europe) and generation length (five and three years) for songbirds, that is, 40 and 86 Ma, respectively. Thus, drift is too slow to account for turnover in regional avifaunas. Presumably, other processes, involving external drivers, such as climate and physiographic change, and internal drivers, such as evolutionary change in antagonistic interactions, predominate. Hubbell's model is historical and geographic, and his perspective importantly links local and regional process and pattern. Ecological reality can be added to the mix while retaining Hubbell's concept of continuity of communities in space and time.

Behavioural flexibility in the mating system buffers population extinction: lessons from the lesser spotted woodpecker Picoides minor

1. In most stochastic models addressing the persistence of small populations, environmental noise is included by imposing a synchronized effect of the environment on all individuals. However, buffer mechanisms are likely to exist that may counteract this synchronization to some degree. 2. We have studied whether the flexibility in the mating system, which has been observed in some bird species, is a potential mechanism counteracting the synchronization of environmental fluctuations. Our study organism is the lesser spotted woodpecker Picoides minor (Linnaeus), a generally monogamous species. However, facultative polyandry, where one female mates with two males with separate nests, was observed in years with male-biased sex ratio. 3. We constructed an individual-based model from data and observations of a population in Taunus, Germany. We tested the impact of three behavioural scenarios on population persistence: (1) strict monogamy; (2) polyandry without costs; and (3) polyandry assuming costs in terms of lower survival and reproductive success for secondary males. We assumed that polyandry occurs only in years with male-biased sex ratio and only for females with favourable breeding conditions. 4. Even low rates of polyandry had a strong positive effect on population persistence. The increase of persistence with carrying capacity was slower in the monogamous scenario, indicating strong environmental noise. In the polyandrous scenarios, the increase of persistence was stronger, indicating a buffer mechanism. In the polyandrous scenarios, populations had a higher mean population size, a lower variation in number of individuals, and recovered faster after a population breakdown. Presuming a realistic polyandry rate and costs for polyandry, there was still a strong effect of polyandry on persistence. 5. The results show that polyandry and in general flexibility in mating systems is a buffer mechanism that can significantly reduce the impact of environmental and demographic noise in small populations. Consequently, we suggest that even behaviour that seems to be exceptional should be considered explicitly when predicting the persistence of populations.