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Using a nonparametric Bayesian approach Palacios and Minin (2013) dramatically improved the accuracy, precision of Bayesian inference of population size trajectories from gene genealogies. These authors proposed an extension of a Gaussian Process (GP) nonparametric inferential method for the intensity function of non-homogeneous Poisson processes. They found that not only the statistical properties of the estimators were improved with their method, but also, that key aspects of the demographic histories were recovered. The authors’ work represents the first Bayesian nonparametric solution to this inferential problem because they specify a convenient prior belief without a particular functional form on the population trajectory. Their approach works so well and provides such a profound understanding of the biological process, that the question arises as to how truly “biology-free” their approach really is. Using well-known concepts of stochastic population dynamics, here I demonstrate that in fact, Palacios and Minin’s GP model can be cast as a parametric population growth model with density dependence and environmental stochasticity. Making this link between population genetics and stochastic population dynamics modeling provides novel insights into eliciting biologically meaningful priors for the trajectory of the effective population size. The results presented here also bring novel understanding of GP as models for the evolution of a trait. Thus, the ecological principles foundation of Palacios and Minin (2013)’s prior adds to the conceptual and scientific value of these authors’ inferential approach. I conclude this note by listing a series of insights brought about by this connection with Ecology. [ABSTRACT FROM AUTHOR]

A fundamental problem in the fields of population genetics, evolution, and community ecology, is the fate of a single mutant, or invader, introduced in a finite population of wild types. For a fixed-size community of N individuals, with Markovian, zero-sum dynamics driven by stochastic birth-death events, the mutant population eventually reaches either fixation or extinction. The classical analysis, provided by Kimura and his coworkers, is focused on the neutral case, [where the dynamics is only due to demographic stochasticity (drift)], and on time-independent selective forces (deleterious/beneficial mutation). However, both theoretical arguments and empirical analyses suggest that in many cases the selective forces fluctuate in time (temporal environmental stochasticity). Here we consider a generic model for a system with demographic noise and fluctuating selection. Our system is characterized by the time-averaged (log)-fitness s 0 and zero-mean fitness fluctuations. These fluctuations, in turn, are parameterized by their amplitude γ and their correlation time δ . We provide asymptotic (large N ) formulas for the chance of fixation, the mean time to fixation and the mean time to absorption. Our expressions interpolate correctly between the constant selection limit γ  → 0 and the time-averaged neutral case s 0 = 0 . [ABSTRACT FROM AUTHOR]

The dynamics of two competing species in a finite size community is one of the most studied problems in population genetics and community ecology. Stochastic fluctuations lead, inevitably, to the extinction of one of the species, but the relevant timescale depends on the underlying dynamics. The persistence time of the community has been calculated both for neutral models, where the only driving force of the system is drift (demographic stochasticity), and for models with strong selection. Following recent analyses that stress the importance of environmental stochasticity in empirical systems, we present here a general theory of the persistence time of a two-species community where drift, environmental variations and time independent selective advantage are all taken into account. [ABSTRACT FROM AUTHOR]

Dynamic models – often deterministic in nature – were used to estimate the basic reproductive number, R 0 , of the 2014-5 Ebola virus disease (EVD) epidemic outbreak in West Africa. Estimates of R 0 were then used to project the likelihood for large outbreak sizes, e.g., exceeding hundreds of thousands of cases. Yet fitting deterministic models can lead to over-confidence in the confidence intervals of the fitted R 0 , and, in turn, the type and scope of necessary interventions. In this manuscript we propose a hybrid stochastic-deterministic method to estimate R 0 and associated confidence intervals (CIs). The core idea is that stochastic realizations of an underlying deterministic model can be used to evaluate the compatibility of candidate values of R 0 with observed epidemic curves. The compatibility is based on comparing the distribution of expected epidemic growth rates with the observed epidemic growth rate given “process noise”, i.e., arising due to stochastic transmission, recovery and death events. By applying our method to reported EVD case counts from Guinea, Liberia and Sierra Leone, we show that prior estimates of R 0 based on deterministic fits appear to be more confident than analysis of stochastic trajectories suggests should be possible. Moving forward, we recommend including process noise among other sources of noise when estimating R 0 CIs of emerging epidemics. Our hybrid procedure represents an adaptable and easy-to-implement approach for such estimation. [ABSTRACT FROM AUTHOR]

Community dynamics is influenced by multiple ecological processes such as environmental spatiotemporal variation, competition between individuals and demographic stochasticity. Quantifying the respective influence of these various processes and making predictions on community dynamics require the use of a dynamical framework encompassing these various components. We here demonstrate how to adapt the framework of stochastic community dynamics to the peculiarities of herbaceous communities, by using a short temporal resolution adapted to the time scale of competition between herbaceous plants, and by taking into account the seasonal drops in plant aerial biomass following winter, harvesting or consumption by herbivores. We develop a hybrid inference method for this novel modelling framework that both uses numerical simulations and likelihood computations. Applying this methodology to empirical data from the Jena biodiversity experiment, we find that environmental stochasticity has a larger effect on community dynamics than demographic stochasticity, and that both effects are generally smaller than observation errors at the plot scale. We further evidence that plant intrinsic growth rates and carrying capacities are moderately predictable from plant vegetative height, specific leaf area and leaf dry matter content. We do not find any trade-off between demographical components, since species with larger intrinsic growth rates tend to also have lower demographic and environmental variances. Finally, we find that our model is able to make relatively good predictions of multi-specific community dynamics based on the assumption of competitive symmetry. [ABSTRACT FROM AUTHOR]

Abstract: Simple models of density-dependent population growth such as the discrete logistic map provide powerful demonstrations of complex population dynamics. Yet it is unclear whether the dynamics observed in such idealized systems would be present, under realistic conditions, in the context of demographic stochasticity, which is well known to exist in finite natural populations. Here, using a set of simple, individual-based models (IBM's) and their population-level iterative map counterparts, we computationally investigate the contribution of demographic stochasticity to density-dependent population dynamics in a simple model of seed production and recruitment. Notably, for a sufficiently large lattice, even in the presence of demographic stochasticity, many of the qualitative features of these idealized maps – including bifurcations – are still present. Demographic stochasticity and the constraints imposed by a finite lattice size appear to produce mixed dynamics that are partially stochastic, yet qualitatively similar to the deterministic models. The mechanistic assumptions and lattice sizes required to generate these dynamics cast doubt on whether they might be observable in annual plant populations. Nevertheless, we cannot rule out the theoretical possibility that such dynamics might be observable in ecological communities having similar mechanistic properties. [Copyright &y& Elsevier]

Mating theory (Hubbell & Johnson 1987, American Naturalist, 130, 91–112; Gowaty & Hubbell 2009, Proceedings of the National Academy of Sciences, U.S.A., 106, 10017–10024) says that reproductive decisions of individuals are flexibly expressed and adaptive. It also makes the following five predictions about polyandry. (1) Demography determines within-population, between-female variation in mating rates. That is, (a) an individual's encounters with potential mates, (b) an individual's risk of death, (c) the number of potential mates in the population, (d) the distribution of fitness under random mating, and (e) for nonvirgins, the duration of any postcopulation period of nonreceptivity together determine within-population, between-female variation in mating rate. (2) When demography is dynamic, there is unlikely to be an optimal female mating rate. That is, when potential mates enter or leave the pool of potential mates or when decision makers face survival risks from conspecifics, predators, parasites or pathogens, females who adaptively adjust their reproductive decisions in real-time outcompete females whose behaviour is fixed. (3) Female multiple mating often increases production of adult offspring through enhanced offspring viability (indirect fitness) and between-generation lineage success. (4) Polyandry will increase female exposure to pathogens and thus decrease female survival (direct fitness cost) unless females use environmental or intrinsic resources or opportunities to reduce survival risks. (5) Under many circumstances, female remating may enhance female survival (direct fitness benefit). Future research attention will focus on how intrinsic, ecological and social opportunities/constraints affect the likelihood of polyandry and its fitness effects for particular females. Future researchers may also consider that polyandrous mating is sometimes sexually collaborative and cooperative, rather than always sexually antagonistic. [Copyright &y& Elsevier]

Abstract: We derive the frequency-dependent selection coefficient caused by “demographic” stochasticity resulting from the random sampling of opponents an individual faces during behavioral “contests” with other individuals. The mean, variance, and higher moments of fitness all influence the direction and strength of selection. A frequency-dependent trait can be stable when an individual’s fitness depends upon an infinite number of contests with other individuals and unstable when it depends upon a finite number of contests. Conversely, unstable equilibria for an infinite number of contests can be stable when there is a finite number of contests. At stable equilibria for a finite number of contests, higher moments of fitness can outweigh the joint influence of the first two moments so that natural selection favors “within-generation” or developmental-trait variation (also known as phenotypic plasticity) contrary to the claim that natural selection always acts against such variation. We use second-moment estimates of the fitness functions in a diffusion approximation to compute fixation probabilities of competing strategies. These estimates are shown to be qualitatively consistent with those derived from simulations when population sizes are sufficiently large to ignore the contribution of higher-moment terms. We also show that explicit solutions to the diffusion approximation only exist for pair-wise interactions that lead to positive frequency-dependent selection. [Copyright &y& Elsevier]

Abstract: The debate between niche-based and neutral community theories centers around the question of which forces shape predominantly ecological communities. Niche theory attributes a central role to niche differences between species, which generate a difference between the strength of intra- and interspecific interactions. Neutral theory attributes a central role to migration processes and demographic stochasticity. One possibility to bridge these two theories is to combine them in a common mathematical framework. Here we propose a mathematical model that integrates the two perspectives. From a niche-based perspective, our model can be interpreted as a Lotka–Volterra model with symmetric interactions in which we introduce immigration and demographic stochasticity. From a neutral perspective, it can be interpreted as Hubbell''s local community model in which we introduce a difference between intra- and interspecific interactions. We investigate the stationary species abundance distribution and other community properties as functions of the interaction coefficient, the immigration rate and the strength of demographic stochasticity. [Copyright &y& Elsevier]

Abstract: Inbreeding depression, asymmetries in costs or benefits of dispersal, and the mating system have been identified as potential factors underlying the evolution of sex-biased dispersal. We use individual-based simulations to explore how the mating system and demographic stochasticity influence the evolution of sex-specific dispersal in a metapopulation with females competing over breeding sites, and males over mating opportunities. Comparison of simulation results for random mating with those for a harem system (locally, a single male sires all offspring) reveal that even extreme variance in local male reproductive success (extreme male competition) does not induce male-biased dispersal. The latter evolves if the between-patch variance in reproductive success is larger for males than females. This can emerge due to demographic stochasticity if the habitat patches are small. More generally, members of a group of individuals experiencing higher spatio-temporal variance in fitness expectations may evolve to disperse with greater probability than others. [Copyright &y& Elsevier]

Abstract: We develop a stochastic, individual-based model for food web simulation which in the large-population limit reduces to the well-studied Webworld model, which has been used to successfully construct model food webs with several realistic features. We demonstrate that an almost exact match is found between the population dynamics in fixed food webs, and that the demographic fluctuations have systematic effects when the new model is used to construct food webs due to the presence of species with small populations. [Copyright &y& Elsevier]

Abstract: 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 , reproduction variance and competition sensitivity . Generally, the fixation probability of the mutant depends on its initial proportion , the total initial population size , and the six demographic traits. Under weak selection, we can linearize in all models thanks to the same master formulawhere , and are selection coefficients, and , , are invasibility coefficients ( refers to the mutant traits), which are positive and do not depend on . In particular, increased reproduction variance is always deleterious. We prove that in all three modelsand for small initial population sizes . In model II, for all , 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 than with high . In model III, increases with like , and converges to a finite limit , where is the carrying capacity. For the growth invasibility is above when , and below when , showing that classical models I and II underestimate the fixation probabilities in growing populations, and overestimate them in declining populations. [Copyright &y& Elsevier]

Abstract: Quasi-stationarity and time to extinction are studied for the classic endemic model. Attention is restricted to the transition region in parameter space where the quasi-stationary distribution is non-normal. A new approximation of the marginal distribution of infected individuals in quasi-stationarity is presented. It leads to a simple explicit expression for an approximation of the critical community size in terms of model parameters. [Copyright &y& Elsevier]

We investigate the statistics of extinction times for an isolated population, with an initially modest number M of individuals, whose dynamics are controlled by a stochastic logistic process (SLP). The coefficient of variation in the extinction time V is found to have a maximum value when the death and birth rates are close in value. For large habitat size K we find that Vmax is of order K1/4/M1/2, which is much larger than unity so long as M is small compared to K1/2. We also present a study of the SLP using the moment closure approximation (MCA), and discuss the successes and failures of this method. Regarding the former, the MCA yields a steady-state distribution for the population when the death rate is low. Although not correct for the SLP model, the first three moments of this distribution coincide with those calculated exactly for an adjusted SLP in which extinction is forbidden. These exact calculations also pinpoint the breakdown of the MCA as the death rate is increased. [Copyright &y& Elsevier]

The major role played by demographic stochasticity in determining the dynamics and persistence of childhood diseases, such as measles, chickenpox and pertussis, has long been realized. Techniques which can be used to estimate the magnitude of this stochastic effect are of clear importance. In this study, we assess and compare the use of two moment closure approximations to estimate the variability seen about the average behavior of stochastic models for the recurrent epidemics seen in childhood diseases. The performance of the approximations are assessed using analytic techniques available for the simplest epidemiological model and using numerical simulations in more complex settings. We also present epidemiologically important extensions of previous work, considering variability in the SEIR model and in situations for which there is seasonal variation in disease transmission. Important implications of stochastic effects for the dynamics of childhood diseases are highlighted, including serious deficiencies of deterministic descriptions of dynamical behavior. [Copyright &y& Elsevier]

The moment closure method was recently shown in Na˚sell (Theor. Popul. Biol. 63 (2) (2003a) 159) to give asymptotic approximations of the first few cumulants for the stochastic logistic model. A slight extension of the method is introduced. It is shown to be robust with regard to the specific distributional assumption that is used to achieve moment closure. The phenomenon of spurious solutions is shown to be related to the domain of attraction of the non-spurious critical point. [Copyright &y& Elsevier]

The quasi-stationary distribution of the stochastic logistic model is studied in the parameter region where its body is approximately normal. Improved asymptotic approximations of its first three cumulants are derived. It is shown that the same results can be derived with the aid of the moment closure method. This indicates that the moment closure method leads to expressions for the cumulants that are asymptotic approximations of the cumulants of the quasi-stationary distribution. [Copyright &y& Elsevier]

Simple conditions to evaluate the persistence of populations living in fragmented habitats are of primary importance in ecology. We address this need here using a spatially implicit approach that accounts for discrete individuals in a metapopulation. Demographic stochasticity is incorporated into a Markovian model in a natural way, as local extinction is characterized by the death or the dispersal of the last individual inhabiting a patch. The variables of the model are the probabilities pi (i=0, 1, 2…) that a patch be occupied by a finite, integer number i of individuals at a given time. We compare the stationary distributions predicted by the model with field data and discuss the role of dispersal in determining different distributions of local abundances. The analysis of the model leads to a persistence criterion which is equivalent to a condition formerly proved by Chesson (Z. Wahrscheinlichkeitstheor. 66, 97–107, 1984) namely that E0>1, where E0 is the expected number of successful dispersers from a patch begun with one individual and to which immigration is excluded. We provide an analytic way of computing E0 as a function of the main biological characteristics of the species (natality, mortality and dispersal rates, and colonizing ability). We can thus obtain persistence–extinction boundaries in the space of model parameters. [Copyright &y& Elsevier]

• Makes use of measure-valued branching processes to motivate SDE tracking eco-evolutionary dynamics. • Presents framework and heuristics to rigorously compute biologically mechanistic models from first principles. • Presents efficient theoretical tools based on a Gaussian populations approximation. • Extends classical evolutionary formulas to account for noise-induced selection. • Demonstrates the use of these theoretical tools by computing and analyzing a model of coevolving competing species. Although the evolutionary response to random genetic drift is classically modelled as a sampling process for populations with fixed abundance, the abundances of populations in the wild fluctuate over time. Furthermore, since wild populations exhibit demographic stochasticity and since random genetic drift is in part due to demographic stochasticity, theoretical approaches are needed to understand the role of demographic stochasticity in eco-evolutionary dynamics. Here we close this gap for quantitative characters evolving in continuously reproducing populations by providing a framework to track the stochastic dynamics of abundance density across phenotypic space using stochastic partial differential equations. In the process we develop a set of heuristics to operationalize the powerful, but abstract theory of white noise and diffusion-limits of individual-based models. Applying these heuristics, we obtain stochastic ordinary differential equations that generalize classical expressions of ecological quantitative genetics. In particular, by supplying growth rate and reproductive variance as functions of abundance densities and trait values, these equations track population size, mean trait and additive genetic variance responding to mutation, demographic stochasticity, random genetic drift, deterministic selection and noise-induced selection. We demonstrate the utility of our approach by formulating a model of diffuse coevolution mediated by exploitative competition for a continuum of resources. In addition to trait and abundance distributions, this model predicts interaction networks defined by niche-overlap, competition coefficients, or selection gradients. Using a high-richness approximation, we find linear selection gradients and competition coefficients are uncorrelated, but magnitudes of linear selection gradients and quadratic selection gradients are both positively correlated with competition coefficients. Hence, competing species that strongly affect each other's abundance tend to also impose selection on one another, but the directionality is not predicted. This approach contributes to the development of a synthetic theory of evolutionary ecology by formalizing first principle derivations of stochastic models tracking feedbacks of biological processes and the patterns of diversity they produce. [ABSTRACT FROM AUTHOR]