Search

In this paper, we develop a stochastic predator–prey model driven by demographic stochasticity, where prey are subject to predation by both generalist and specialist predators. We begin by analyzing the asymptotic dynamics of the system in a stable environment using a deterministic framework, focusing on boundary dynamics and coexistence equilibria. With the introduction of demographic noise, we demonstrate that population extinction occurs within finite time. To capture the transient dynamics prior to extinction, we employ quasi-stationary distributions. By studying the stability of the sub-Markov semi-group of the stochastic system, we establish key conditions for the existence, uniqueness, and convergence of the quasi-stationary distribution. The quasi-stationary distribution serves as a bridge between the eventual extinction and the transient, time-dependent behavior of the species. [ABSTRACT FROM AUTHOR]

Theoretical studies from diverse areas of population biology have shown that demographic stochasticity can substantially impact evolutionary dynamics in finite populations, including scenarios where traits that are disfavored by natural selection can nevertheless increase in frequency through the course of evolution. Here, we analytically describe the eco-evolutionary dynamics of finite populations from demographic first principles. We investigate how noise-induced effects can alter the evolutionary fate of populations in which total population size may vary stochastically over time. Starting from a generic birth-death process, we derive a set of stochastic differential equations (SDEs) that describe the eco-evolutionary dynamics of a finite population of individuals bearing discrete traits. Our equations recover well-known descriptions of evolutionary dynamics, such as the replicator-mutator equation, the Price equation, and Fisher's fundamental theorem in the infinite population limit. For finite populations, our SDEs reveal how stochasticity can predictably bias evolutionary trajectories to favor certain traits, a phenomenon we call "noise-induced biasing." We show that noise-induced biasing acts through two distinct mechanisms, which we call the "direct" and "indirect" mechanisms. While the direct mechanism can be identified with classic bet-hedging theory, the indirect mechanism is a more subtle consequence of frequency- and density-dependent demographic stochasticity. Our equations reveal that noise-induced biasing may lead to evolution proceeding in a direction opposite to that predicted by natural selection in the infinite population limit. By extending and generalizing some standard equations of population genetics, we thus describe how demographic stochasticity appears alongside, and interacts with, the more well-understood forces of natural selection and neutral drift to determine the eco-evolutionary dynamics of finite populations of nonconstant size. [ABSTRACT FROM AUTHOR]

Incorporating stochasticity into ecological modeling is vital for understanding the structure and function of ecological systems, but stochasticity has been challenging to consistently introduce into foundational ecological theory. The Gillespie stochastic simulation algorithm (herein SSA) provides a key method to represent demographic stochasticity, but due to its foundational assumptions is inadequate for problems involving intra‐population variation and extrinsically/environmentally‐driven rapid changes in demographic rates. Two recent extensions to the SSA address these limitations: one augments the SSA with individual‐linked trait distributions that let us track trait changes across individuals and populations and the other introduces a methodological innovation to allow demographic rates to change between events; in four case studies we demonstrate the utility of these advances and highlight that simultaneously integrating both extensions into a single framework allows us to tackle a new class of ecological and evolutionary questions that have typically not been explored in continuous time modeling. [ABSTRACT FROM AUTHOR]

We study the stochastic hydrodynamics of colonies of flagellated swimming cells, typified by multicellular choanoflagellates, which can form both rosette and chainlike shapes. The objective is to link cell-scale dynamics to colony-scale dynamics for various colonial morphologies. Via autoregressive stochastic models for the cycle-averaged flagellar force dynamics and statistical models for demographic cell-to-cell variability in flagellar properties and placement, we derive effective transport properties of the colonies, including cell-to-cell variability. We provide the most quantitative detail on disclike geometries to model rosettes, but also present formulas for the dynamics of general planar colony morphologies, which includes planar chain-like configurations. [ABSTRACT FROM AUTHOR]

An individual's access to mates (i.e., its "mating potential") can constrain its reproduction but may also influence its fitness through effects on offspring survival. For instance, mate proximity may correspond with relatedness and lead to inbreeding depression in offspring. While offspring production and survival might respond differently to mating potential, previous studies have not considered the simultaneous effects of mating potential on these fitness components. We investigated the relationship of mating potential with both production and survival of offspring in populations of a long-lived herbaceous perennial, Echinacea angustifolia. Across 7 years and 14 sites, we quantified the mating potential of maternal plants in 1,278 mating bouts and followed the offspring from these bouts over 8 years. We used aster models to evaluate the relationship of mating potential with the number of offspring that emerged and that were alive after 8 years. Seedling emergence increased with mating potential. Despite this, the number of offspring surviving after 8 years showed no relationship to mating potential. Our results support the broader conclusion that the effect of mating potential on fitness erodes over time because of demographic stochasticity at the maternal level. [ABSTRACT FROM AUTHOR]

Despite the importance of population structures throughout ecology, relatively little theoretical attention has been paid to understanding the implications of social groups for population dynamics. The dynamics of socially structured populations differ substantially from those of unstructured or metapopulation‐structured populations, because social groups themselves may split, fuse, and compete. These "between‐group processes" remain understudied as drivers of the dynamics of socially structured populations. Here, we explore the role of various between‐group processes in the dynamics of socially structured populations. To do so, we analyze a model that includes births, deaths, migration, fissions, fusions, and between‐group competition and flexibly allows for density dependence in each process. Both logistic growth and an Allee effect are considered for within‐group density dependence. We show that the effect of various between‐group processes is mediated by their influence on the stable distribution of group sizes, with the ultimate impact on the population determined by the interaction between within‐group density dependence and the process's effect on the group size distribution. Between‐group interactions that change the number of groups can lead to both negative and positive density dependence at the global population level (even if birth and death rates depend only on group size and not population size). We conclude with a series of case studies that illustrates different ways that age, sex, and class structure impact the dynamics of social populations. These case studies demonstrate the importance of group‐formation mechanisms, the cost of having excess males in a group, and the potential drawbacks of generating too many reproductive individuals. In sum, our results make clear the importance of within‐group density dependence, between‐group dynamics, and the interactions between them for the population dynamics of social species and provide a flexible framework for modeling social populations. [ABSTRACT FROM AUTHOR]

To understand the success of invasive alien species, it is necessary to evaluate the site-specific eco-evolutionary challenges they face in their new environments. We explored whether the rearrangement of genetic diversity is linked to the invasiveness of Prosopis juliflora by (i) comparing different stages of invasion (founding vs invasive populations) in two invaded areas (Afar Region, Ethiopia and Baringo County, Kenya) to evaluate whether different stages are dominated by different genetic attributes (e.g., characteristic genotypes or levels of genetic diversity) and by (ii) evaluating if landscape features affected dispersal between invasive populations in the two invaded areas. We hypothesised that different invasion stages would have unique genetic characteristics due to either site-specific demographic and/or dispersal dynamics. We also compared the genetic characteristics at an 'invasive–non-invasive congener' level by studying the non-invasive P. pallida, introduced to Baringo County, and assessed whether it hybridises with P. juliflora. In the Afar Region, the establishment and spread of P. juliflora were characterised by extensive gene flow that homogenised genetic diversity across all populations. In contrast, in Baringo County, invasive populations had lower genetic diversity than founders, and genetic differentiation was lower between invasive populations than between invasive and founder populations. In both invaded areas, we found no evidence that dispersal was hampered by geographic distance, bioclimatic conditions, or distance to roads, rivers and villages, at least at the spatial scales of our study; indicating frequent long-distance dispersal. Allelic richness was higher in P. juliflora than P. pallida founders and hybrids were mainly planted trees probably resulting from the sympatric cultivation of the two species following their introduction. Thus, management actions on Prosopis invasion in eastern Africa should consider site-specific dynamics occurring during the invasion. [ABSTRACT FROM AUTHOR]

Exponential model for population growth (exponential model) is a foundation to evaluate population dynamics in Population Ecology field. Here, we used a didactic experiment to teach exponential model for an undergraduate course of Population Ecology. We built nine populations of weevils with three different initial population sizes: eight, 16, and 32 individuals with three replicates each. We provided equal food resource availability, and counted their population sizes weekly for 12 weeks. We estimated the intrinsic growth rate (i.e., r parameter), by trials and errors with an exponential model build in an Excel spreadsheet. The population growth rate (i.e., dN/dt parameter) was estimated using r values. Replicates with eight and 16 individuals reached the highest values of r and dN/dt, while replicates with 32 individuals reached the lowest values. Beyond of exponential model, two density dependency issues acting in populations were observed. First, in the lowest initial population sizes we observed the effect of demographic stochasticity acting in both r and dN/dt in one of the three populations. Second, we observed the intraspecific competition reducing r values in largest initial populations. Therefore, we highlight the importance of didactic experiment into learning exponential model in Population Ecology course, both for teaching and learning practices.

Mutations allowing pathogens to escape host immunity promote the spread of infectious diseases in heterogeneous host populations and can lead to major epidemics. Understanding the conditions that slow down this evolution is key for the development of durable control strategies against pathogens. Here, we use theory and experiments to compare the efficacy of three strategies for the deployment of resistance: (i) a mixing strategy where the host population contains two single-resistant genotypes, (ii) a pyramiding strategy where the host carries a double-resistant genotype, (iii) a combining strategy where the host population is a mix of a single-resistant genotype and a double-resistant genotype. First, we use evolutionary epidemiology theory to clarify the interplay between demographic stochasticity and evolutionary dynamics to show that the pyramiding strategy always yields lower probability of evolutionary emergence. Second, we test experimentally these predictions with the introduction of bacteriophages into bacterial populations where we manipulated the diversity and the depth of immunity using a Clustered Regularly Interspaced Short Palindromic Repeats-CRISPR associated (CRISPR-Cas) system. These biological assays confirm that pyramiding multiple defences into the same host genotype and avoiding combination with single-defence genotypes is a robust way to reduce pathogen evolutionary emergence. The experimental validation of these theoretical recommendations has practical implications in various areas, including for the optimal deployment of resistance varieties in agriculture and for the design of durable vaccination strategies. [ABSTRACT FROM AUTHOR]

Species coexistence in ecological communities is a central feature of biodiversity. Different concepts, i.e., contemporary niche theory, modern coexistence theory, and the unified neutral theory, have identified many building blocks of such ecological assemblies. However, other factors, such as phenotypic plasticity and stochastic inter‐individual variation, have received little attention, in particular in animals. For example, how resource polyphenisms resulting in predator–prey interactions affect coexistence is currently unknown. Here, we present an integrative theoretical–experimental framework using the nematode plasticity model Pristionchus pacificus with its well‐studied mouth‐form dimorphism resulting in cannibalism. We develop an individual‐based model that relies upon synthetic data based on our empirical measurements of fecundity and polyphenism to preserve demographic heterogeneity. We demonstrate how the interplay between plasticity and individual stochasticity result in all‐or‐nothing outcomes at the local level. Coexistence is made possible when spatial structure is introduced. [ABSTRACT FROM AUTHOR]

Life history traits are used to predict asymptotic odds of extinction from dynamic conditions. Less is known about how life history traits interact with stochasticity and population structure of finite populations to predict near‐term odds of extinction. Through empirically parameterized matrix population models, we study the impact of life history (reproduction, pace), stochasticity (environmental, demographic), and population history (existing, novel) on the transient population dynamics of finite populations of plant species. Among fast and slow pace and either a uniform or increasing reproductive intensity or short or long reproductive lifespan, slow, semelparous species are at the greatest risk of extinction. Long reproductive lifespans buffer existing populations from extinction while the odds of extinction of novel populations decrease when the reproductive effort is uniformly spread across the reproductive lifespan. Our study highlights the importance of population structure, pace, and two distinct aspects of parity for predicting near‐term odds of extinction. [ABSTRACT FROM AUTHOR]

Exponential model for population growth (exponential model) is a foundation to evaluate population dynamics in Population Ecology field. Here, we used a didactic experiment to teach exponential model for an undergraduate course of Population Ecology. We built nine populations of weevils with three different initial population sizes: eight, 16, and 32 individuals with three replicates each. We provided equal food resource availability, and counted their population sizes weekly for 12 weeks. We estimated the intrinsic growth rate (i.e., r parameter), by trials and errors with an exponential model build in an Excel spreadsheet. The population growth rate (i.e., dN/dt parameter) was estimated using r values. Replicates with eight and 16 individuals reached the highest values of r and dN/dt, while replicates with 32 individuals reached the lowest values. Beyond of exponential model, two density dependency issues acting in populations were observed. First, in the lowest initial population sizes we observed the effect of demographic stochasticity acting in both r and dN/dt in one of the three populations. Second, we observed the intraspecific competition reducing r values in largest initial populations. Therefore, we highlight the importance of didactic experiment into learning exponential model in Population Ecology course, both for teaching and learning practices. [ABSTRACT FROM AUTHOR]

Populations suffer two types of stochasticity: demographic stochasticity, from sampling error in offspring number, and environmental stochasticity, from temporal variation in the growth rate. By modelling evolution through phenotypic selection following an abrupt environmental change, we investigate how genetic and demographic dynamics, as well as effects on population survival of the genetic variance and of the strength of stabilizing selection, differ under the two types of stochasticity. We show that population survival probability declines sharply with stronger stabilizing selection under demographic stochasticity, but declines more continuously when environmental stochasticity is strengthened. However, the genetic variance that confers the highest population survival probability differs little under demographic and environmental stochasticity. Since the influence of demographic stochasticity is stronger when population size is smaller, a slow initial decline of genetic variance, which allows quicker evolution, is important for population persistence. In contrast, the influence of environmental stochasticity is population‐size‐independent, so higher initial fitness becomes important for survival under strong environmental stochasticity. The two types of stochasticity interact in a more than multiplicative way in reducing the population survival probability. Our work suggests the importance of explicitly distinguishing and measuring the forms of stochasticity during evolutionary rescue. [ABSTRACT FROM AUTHOR]

How demographic factors lead to variation or change in growth rates can be investigated using life table response experiments (LTRE) based on structured population models. Traditionally, LTREs focused on decomposing the asymptotic growth rate, but more recently decompositions of annual 'realized' growth rates using 'transient' LTREs have gained in popularity.Transient LTREs have been used particularly to understand how variation in vital rates translate into variation in growth for populations under long‐term study. For these, complete population models may be constructed to investigate how temporal variation in environmental drivers affect vital rates. Such investigations have usually come down to estimating covariate coefficients for the effects of environmental variables on vital rates, but formal ways of assessing how they lead to variation in growth rates have been lacking.We extend transient LTREs to further partition the contributions from vital rates into contributions from temporally varying factors that affect them. The decomposition allows one to compare the resultant effect on the growth rate of different environmental factors, as well as density dependence, which may each act via multiple vital rates. We also show how realized growth rates can be decomposed into separate components from environmental and demographic stochasticity. The latter is typically omitted in LTRE analyses.We illustrate these extensions with an integrated population model (IPM) for data from a 26 years study on northern wheatears (Oenanthe oenanthe), a migratory passerine bird breeding in an agricultural landscape. For this population, consisting of around 50–120 breeding pairs per year, we partition variation in realized growth rates into environmental contributions from temperature, rainfall, population density and unexplained random variation via multiple vital rates, and from demographic stochasticity.The case study suggests that variation in first year survival via the unexplained random component, and adult survival via temperature are two main factors behind environmental variation in growth rates. More than half of the variation in growth rates is suggested to come from demographic stochasticity, demonstrating the importance of this factor for populations of moderate size. [ABSTRACT FROM AUTHOR]

Evolutionary dynamics are subject to constraints ranging from limitations on what is physically possible to limitations on the pathways that evolution can take. One set of evolutionary constraints, known as 'demographic constraints', constrain what can occur evolutionarily due to the demographic or dynamical consequences of evolution leading to conditions that make populations susceptible to extinction. These demographic constraints can limit the strength of selection or the rates of environmental change populations can experience while remaining extant and the trait values a population can express. Here we further hypothesize that the population demographic and dynamic consequences of evolution also can constrain the eco‐evolutionary pathways that populations can traverse by defining ecological boundaries represented by areas of likely extinction. We illustrate this process using a model of predator evolution. Our results show that the populations that persist over time tend to be those whose eco‐evolutionary dynamics have avoided ecological boundaries representing areas of likely extinction due to stochastic deviations from a deterministic eco‐evolutionary expectation. We term this subset of persisting pathways viable eco‐evolutionary pathways. The potential existence of ecological boundaries constraining evolutionary pathways has important implications for predicting evolutionary dynamics, interpreting past evolution, and understanding the role of stochasticity and ecological constraints on eco‐evolutionary dynamics. [ABSTRACT FROM AUTHOR]

Stochasticity is a core component of ecology, as it underlies key processes that structure and create variability in nature. Despite its fundamental importance in ecological systems, the concept is often treated as synonymous with unpredictability in community ecology, and studies tend to focus on single forms of stochasticity rather than taking a more holistic view. This has led to multiple narratives for how stochasticity mediates community dynamics. Here, we present a framework that describes how different forms of stochasticity (notably demographic and environmental stochasticity) combine to provide underlying and predictable structure in diverse communities. This framework builds on the deep ecological understanding of stochastic processes acting at individual and population levels and in modules of a few interacting species. We support our framework with a mathematical model that we use to synthesize key literature, demonstrating that stochasticity is more than simple uncertainty. Rather, stochasticity has profound and predictable effects on community dynamics that are critical for understanding how diversity is maintained. We propose next steps that ecologists might use to explore the role of stochasticity for structuring communities in theoretical and empirical systems, and thereby enhance our understanding of community dynamics.

With species increasingly imperiled due to anthropogenic activities, conservation practitioners are tasked with determining conservation priorities to make the best use of limited resources. One way of setting priorities is to categorize species based on risk of extinction. The United States' Endangered Species Act (ESA) has two listing statuses into which imperiled species are placed to receive protections: threatened or endangered. Our objective was to identify differences between threatened and endangered (T&E) species beyond what is outlined in their ESA definitions. For 6 broad‐resolution threats (habitat modification, overutilization, pollution, species‐species interactions, environmental stochasticity, and demographic stochasticity), we investigated whether there is a difference in the number and types of threats which impacted T&E species at the time of their listing. We found that threatened (x̄ = 2.9, SD = 1.4) and endangered (x̄ = 3.0, SD = 1.1) species faced a similar number of threats at time of their listing. The only broad‐resolution threat that impacted endangered species more than threatened species was demographic stochasticity, with endangered species being 2.1 times (95% CI = 1.5–2.8) more likely to be impacted than threatened species. We examined demographic stochasticity by breaking it down into finer‐resolution threats to identify additional differences between T&E species. We found 4 finer‐resolution demographic stochasticity threats (few individuals in one population, few individuals in multiple populations, lack of reproduction, and genetic loss) to be strong predictors of endangered status. The similarities in the number and types of broad‐resolution threats faced by T&E species indicated that they are equally conservation reliant. [ABSTRACT FROM AUTHOR]

Heterogeneity among individuals in fitness components is what selection acts upon. Evolutionary theories predict that selection in constant environments acts against such heterogeneity. But observations reveal substantial non‐genetic and also non‐environmental variability in phenotypes. Here, we examine whether there is a relationship between selection pressure and phenotypic variability by analysing structured population models based on data from a large and diverse set of species. Our findings suggest that non‐genetic, non‐environmental variation is in general neither truly neutral, selected for, nor selected against. We find much variations among species and populations within species, with mean patterns suggesting nearly neutral evolution of life‐course variability. Populations that show greater diversity of life courses do not show, in general, increased or decreased population growth rates. Our analysis suggests we are only at the beginning of understanding the evolution and maintenance of non‐genetic non‐environmental variation. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Species interaction networks are subject to natural and anthropogenic disturbances that lead to their disassembly, while natural regeneration or restoration efforts facilitate their reassembly. Previous models for assembling ecological networks did not include stochasticity at the level of population dynamics (e.g., demographic noise, environmental noise) and focused mainly on food webs. Here, we present a model for the assembly of mutualistic bipartite networks, such as plant-pollinator networks, and examine the influence of demographic noise on the trajectory of species and strategy diversity, that is, the range of present strategies from specialism to generalism. We find that assembled communities show at intermediate assembly stages a maximum of species diversity and of average generalization. Our model thus provides a mechanism for nonlinear, hump-shaped diversity trajectories at intermediate succession, consistent with the intermediate disturbance hypothesis. Long-term coexistence of specialists and generalists emerges only in the presence of demographic noise and is due to a persistent species turnover. These findings highlight the importance of stochasticity for maintaining long-term diversity. [ABSTRACT FROM AUTHOR]

Invasibility, the chance of a population to grow from rarity and become established, plays a fundamental role in population genetics, ecology, epidemiology and evolution. For many decades, the mean growth rate of a species when it is rare has been employed as an invasion criterion. Recent studies show that the mean growth rate fails as a quantitative metric for invasibility, with its magnitude sometimes even increasing while the invasibility decreases. Here we provide two novel formulae, based on the diffusion approximation and a large‐deviations (Wentzel–Kramers–Brillouin) approach, for the chance of invasion given the mean growth and its variance. The first formula has the virtue of simplicity, while the second one holds over a wider parameter range. The efficacy of the formulae, including their accompanying data analysis technique, is demonstrated using synthetic time series generated from canonical models and parameterised with empirical data. [ABSTRACT FROM AUTHOR]

Abstract Training in Population Ecology asks for scalable applications capable of embarking students on a trip from basic concepts to the projection of populations under the various effects of density dependence and stochasticity. Demography_Lab is an educational tool for teaching Population Ecology aspiring to cover such a wide range of objectives. The application uses stochastic models to evaluate the future of populations. Demography_Lab may accommodate a wide range of life cycles and can construct models for populations with and without an age or stage structure. Difference equations are used for unstructured populations and matrix models for structured populations. Both types of models operate in discrete time. Models can be very simple, constructed with very limited demographic information or parameter‐rich, with a complex density‐dependence structure and detailed effects of the different sources of stochasticity. Demography_Lab allows for deterministic projections, asymptotic analysis, the extraction of confidence intervals for demographic parameters, and stochastic projections. Stochastic population growth is evaluated using up to three sources of stochasticity: environmental and demographic stochasticity and sampling error in obtaining the projection matrix. The user has full control on the effect of stochasticity on vital rates. The effect of the three sources of stochasticity may be evaluated independently for each vital rate. The user has also full control on density dependence. It may be included as a ceiling population size controlling the number of individuals in the population or it may be evaluated independently for each vital rate. Sensitivity analysis can be done for the asymptotic population growth rate or for the probability of extinction. Elasticity of the probability of extinction may be evaluated in response to changes in vital rates, and in response to changes in the intensity of density dependence and environmental stochasticity.

We analyse how migration from a large mainland influences genetic load and population numbers on an island, in a scenario where fitness-affecting variants are unconditionally deleterious, and where numbers decline with increasing load. Our analysis shows that migration can have qualitatively different effects, depending on the total mutation target and fitness effects of deleterious variants. In particular, we find that populations exhibit a genetic Allee effect across a wide range of parameter combinations, when variants are partially recessive, cycling between low-load (large-population) and high-load (sink) states. Increased migration reduces load in the sink state (by increasing heterozygosity) but further inflates load in the large-population state (by hindering purging). We identify various critical parameter thresholds at which one or other stable state collapses, and discuss how these thresholds are influenced by the genetic versus demographic effects of migration. Our analysis is based on a 'semi-deterministic' analysis, which accounts for genetic drift but neglects demographic stochasticity. We also compare against simulations which account for both demographic stochasticity and drift. Our results clarify the importance of gene flow as a key determinant of extinction risk in peripheral populations, even in the absence of ecological gradients. This article is part of the theme issue 'Species' ranges in the face of changing environments (part I)'. [ABSTRACT FROM AUTHOR]

Many wild populations are suffering from the loss of genetic diversity caused by habitat fragmentation, while the degree of diversity loss differs among species and populations based on their life history characteristics. Trillium camschatcense, an understory perennial plant, has undergone intensive habitat fragmentation in the Tokachi region, Hokkaido, Japan. Although demographic deteriorations, such as reduced seed production, were already reported, genetic consequences of fragmentation have not been studied with reference to its life history. Here, we examined how life history events (e.g., growth and reproduction) and the stochasticity therein influence genetic diversity in two (each large and small) fragmented T. camschatcense populations. Genetic diversity was evaluated using genome‐wide 2,008 single nucleotide polymorphisms (SNPs). In the small population, genetic diversity of newly germinated seedlings was significantly lower than that of matured life history stages, and effective number of breeders (Nb) was smaller than that of the large population. Simulations using a matrix population model showed that the diversity loss at seedlings is caused by genetic drift during reproduction, which was intensified by smaller Nb. Besides, simulations using randomly perturbed transition matrices suggested that stasis at juvenile stages, which is a common characteristics of T. camschatcense, maintains genetic diversity by buffering stochastic decrease, possibly contributing to population viability. While previous studies showed the importance to facilitate reproduction and recruitment for demographic recovery, this study highlighted the crucial roles of juvenile survival in terms of genetic diversity for the conservation of fragmented T. camschatcense populations in the Tokachi region. [ABSTRACT FROM AUTHOR]

Aim: The influence of niche and neutral mechanisms on the assembly of ecological communities have long been debated. However, we still have a limited knowledge on their relative importance to explain patterns of diversity across latitudinal gradients (LDG). Here, we investigate the extent to which these ecological mechanisms contribute to the LDG of reef fishes. Location: Eastern Atlantic Ocean. Taxon: Reef‐associated ray‐finned fishes. Methods: We combined abundance data across ~60° of latitude with functional trait data and phylogenetic trees. A null model approach was used to decouple the influence of taxonomic diversity (TD) on functional (FD) and phylogenetic (PD) diversity. Standardized effect sizes (SES FD and SES PD) were used to explore patterns of overdispersion, clustering and randomness. Information theoretic approaches were used to investigate the role of large‐ (temperature, geographic isolation, nitrate and net primary productivity) and local‐scale (human population and depth) drivers. We further assessed the role of demographic stochasticity and its interaction with species trophic identity and dispersal capacity. Results: Taxonomic diversity peaked at ~15°–20°N, with a second mode of lower magnitude at ~45°N; a pattern that was predicted by temperature, geographic isolation and productivity. Tropical regions displayed a higher proportion of overdispersed assemblages, whilst clustering increased towards temperate regions. Phylogenetic and functional overdispersion were associated with warmer, productive and isolated regions. Demographic stochasticity also contributed largely to community assembly, independently of ecoregions, although variation was dependent on the trophic identity and body size of species. Main conclusions: Niche‐based processes linking thermal and resource constraints to local coexistence mechanisms have contributed to the LDG in reef fishes. These processes do not act in isolation, stressing the importance of understanding interactions between deterministic and stochastic factors driving community structure in the face of rapid biodiversity change. [ABSTRACT FROM AUTHOR]

In this paper, we utilize an absorbed diffusion process to model the dynamics of a single species under the influence of demographic stochasticity and component Allee effects. The trajectories of stochastic solutions exhibits multi-scale dynamics distinct from those of the corresponding mean-field model. The primary focus is on analyzing transient dynamics before extinction, which is described by the quasi-stationary distribution. The paper provides results on the existence, uniqueness, and exponential convergence to the quasi-stationary distribution for initial distributions with compact support. Due to the singularity of the noise at 0, we employ the idea of changing variables to transfer the model into one-dimensional Kolmogorov diffusions with a drift possibly exploding at 0, to prove the main results. [ABSTRACT FROM AUTHOR]

Past environmental changes have shaped the evolutionary and ecological diversity of extant organisms. Specifically, climatic fluctuations have made environmental conditions alternatively common or rare over time. Accordingly, most taxa have undergone restriction of their distribution to local refugia during habitat contraction, from which they could expand when suitable habitat became more common. Assessing how past restrictions in refugia have shaped species distributions and genetic diversity has motivated much research in evolutionary biology and biogeography. But there is still lack of clear synthesis on whether and how the taxonomic, functional and phylogenetic composition of extant multispecies assemblages retains the imprint of past restriction in refugia. We devised an original eco-evolutionary model to investigate the temporal dynamics of a regional species pool inhabiting a given habitat today, and which have experienced habitat reduction in the past. The model includes three components: (i) a demographic component driving stochastic changes in population sizes and extinctions due to habitat availability, (ii) a mutation and speciation component representing how divergent genotypes emerge and define new species over time, and (iii) a trait evolution component representing how trait values have changed across descendants over time. We used this model to simulate dynamics of multispecies assemblages that occupied a restricted refugia in the past and could expand their distribution subsequently. We characterized the past restriction in refugia in terms of two parameters representing the ending time of past refugia, and the extent of habitat restriction in the refugia. We characterized extant patterns of taxonomic, functional and phylogenetic diversity depending on these parameters. We found that extant relative abundances reflect the lasting influence of more recent refugia on demographic dynamics, while phylogenetic composition reflects the influence of more ancient habitat change. Extant functional diversity depends on the interplay between diversification dynamics and trait evolution, offering new options to jointly infer current trait adaptation and past trait evolution dynamics.

This article analyzes the conditions for local adaptation in a metapopulation with infinitely many islands under a model of hard selection, where population size depends on local fitness. Each island belongs to one of two distinct ecological niches or habitats. Fitness is influenced by an additive trait which is under habitat‐dependent directional selection. Our analysis is based on the diffusion approximation and accounts for both genetic drift and demographic stochasticity. By neglecting linkage disequilibria, it yields the joint distribution of allele frequencies and population size on each island. We find that under hard selection, the conditions for local adaptation in a rare habitat are more restrictive for more polygenic traits: even moderate migration load per locus at very many loci is sufficient for population sizes to decline. This further reduces the efficacy of selection at individual loci due to increased drift and because smaller populations are more prone to swamping due to migration, causing a positive feedback between increasing maladaptation and declining population sizes. Our analysis also highlights the importance of demographic stochasticity, which exacerbates the decline in numbers of maladapted populations, leading to population collapse in the rare habitat at significantly lower migration than predicted by deterministic arguments. [ABSTRACT FROM AUTHOR]

Introduction: Despite extensive science-based conservation policy recommendations, with fewer than 20 individuals remaining, the vaquita (Phocoena sinus) -endemic to the Gulf of California- is the world's most endangered marine mammal due to incidental catch in fishing nets and whether it can recover is unclear. Objective: Assess expectations for vaquita over the next two decades. Methods: We identified factors affecting the vaquita, constructed life tables, derived demographic parameters for different scenarios and conducted a population viability analysis using stochastic age-structured matrix Leslie models. Results: Analytical results indicate that the vaquita net growth rate is particularly sensitive to juvenile survival. We find that intensive, ongoing bycatch in gillnets used to poach totoaba (Totoaba macdonaldi) over the past decade brought the vaquita population to its current critically low size. Currently this seems to be exacerbated by demographic stochasticity and a potential Allee effect. Conclusions: If totoaba poaching is eliminated immediately, demographically, vaquita can recover; its long-term survival will depend on its uncertain genetic status, although a recent study found encouraging results in this regard. [ABSTRACT FROM AUTHOR]

Rapid evolution on ecological time scales can play a key role in species responses to environmental change. One dynamic that has the potential to generate the diversity necessary for evolution rapid enough to allow response to sudden environmental shifts is introgressive hybridization. However, if distinct sub-species exist before an environmental shift, mechanisms that impede hybridization, such as assortative mating and hybrid inferiority, are likely to be present. Here we explore the theoretical potential for introgressive hybridization to play a role in response to environmental change. In particular, we incorporate assortative mating, hybrid inferiority, and demographic stochasticity into a two-locus, two-allele population genetic model of two interacting species where one locus identifies the species and the other determines how fitness depends on the changing environment. Simulation results indicate that moderately high values for the strength of assortative mating will allow enough hybridization events to outweigh demographic stochasticity but not so many that continued hybridization outweighs backcrossing and introgression. Successful introgressive hybridization also requires intermediate relative fitness at the allele negatively affected by environmental change such that hybrid survivorship outweighs demographic stochasticity but selection remains strong enough to affect the genetic dynamics. The potential for successful introgression instead of extinction with greater environmental change is larger with monogamous rather than promiscuous mating due to lower stochasticity in mating events. These results suggest species characteristics (e.g., intermediate assortative mating and mating systems with low variation in mating likelihood) which indicate a potential for rapid evolution in response to environmental change via introgressive hybridization. © 2011 The Author(s).

Many populations live and disperse in advective media. A fundamental question, known as the “drift paradox” in stream ecology, is how a closed population can survive when it is constantly being transported downstream by the flow. Recent population-level models have focused on the role of diffusive movement in balancing the effects of advection, predicting critical conditions for persistence. Here, we formulate an individual-based stochastic analog of the model described in (Lutscher et al., SIAM Rev. 47(4):749–772, 2005) to quantify the effects of demographic stochasticity on persistence. Population dynamics are modeled as a logistic growth process and dispersal as a position-jump process on a finite domain divided into patches. When there is no correlation in the interpatch movement of residents, stochasticity simply smooths the persistence-extinction boundary. However, when individuals disperse in “packets” from one patch to another and the flow field is memoryless on the timescale of packet transport, the probability of persistence is greatly enhanced. The latter transport mechanism may be characteristic of larval dispersal in the coastal ocean or wind-dispersed seed pods.

Demographic stochasticity can have large effects on the dynamics of small populations as well as on the persistence of rare genotypes and lineages. Survival is sensibly modeled as a binomial process, but annual reproductive success (ARS) is more complex and general models for demographic stochasticity do not exist. Here we introduce a stochastic model framework for ARS and illustrate some of its properties. We model a sequence of stochastic events: nest completion, the number of eggs or neonates produced, nest predation, and the survival of individual offspring to independence. We also allow multiple nesting attempts within a breeding season. Most of these components can be described by Bernoulli or binomial processes; the exception is the distribution of offspring number. Using clutch and litter size distributions from 53 vertebrate species, we demonstrate that among-individual variability in offspring number can usually be described by the generalized Poisson distribution. Our model framework allows the demographic variance to be calculated from underlying biological processes and can easily be linked to models of environmental stochasticity or selection because of its parametric structure. In addition, it reveals that the distributions of ARS are often multimodal and skewed, with implications for extinction risk and evolution in small populations.

Training in Population Ecology asks for scalable applications capable of embarking students on a trip from basic concepts to the projection of populations under the various effects of density dependence and stochasticity. Demography_Lab is an educational tool for teaching Population Ecology aspiring to cover such a wide range of objectives. The application uses stochastic models to evaluate the future of populations. Demography_Lab may accommodate a wide range of life cycles and can construct models for populations with and without an age or stage structure. Difference equations are used for unstructured populations and matrix models for structured populations. Both types of models operate in discrete time. Models can be very simple, constructed with very limited demographic information or parameter‐rich, with a complex density‐dependence structure and detailed effects of the different sources of stochasticity. Demography_Lab allows for deterministic projections, asymptotic analysis, the extraction of confidence intervals for demographic parameters, and stochastic projections. Stochastic population growth is evaluated using up to three sources of stochasticity: environmental and demographic stochasticity and sampling error in obtaining the projection matrix. The user has full control on the effect of stochasticity on vital rates. The effect of the three sources of stochasticity may be evaluated independently for each vital rate. The user has also full control on density dependence. It may be included as a ceiling population size controlling the number of individuals in the population or it may be evaluated independently for each vital rate. Sensitivity analysis can be done for the asymptotic population growth rate or for the probability of extinction. Elasticity of the probability of extinction may be evaluated in response to changes in vital rates, and in response to changes in the intensity of density dependence and environmental stochasticity. [ABSTRACT FROM AUTHOR]

Although metacommunity ecology has been a major field of research in the last decades, with both conceptual and empirical outputs, the analysis of the temporal dynamics of metacommunities has only emerged recently and consists mostly of repeated static analyses. Here we propose a novel analytical framework to assess metacommunity processes using path analyses of spatial and temporal diversity turnovers. We detail the principles and practical aspects of this framework and apply it to simulated datasets to illustrate its ability to decipher the respective contributions of entangled drivers of metacommunity dynamics. We then apply it to four empirical datasets. Empirical results support the view that metacommunity dynamics may be generally shaped by multiple ecological processes acting in concert, with environmental filtering being variable across both space and time. These results reinforce our call to go beyond static analyses of metacommunities that are blind to the temporal part of environmental variability. [ABSTRACT FROM AUTHOR]

Spatial variation in phenology can occur at small spatial scales over which individuals can disperse or forage within one generation. Previous studies have assumed that variations in phenological peaks are caused by differences in abiotic environmental characteristics. However, environments should generally be similar among local habitats over small spatial scales. When the local population size is small, the phenological peak of the local population should be strongly affected by the variation in timing expressed by individuals. If a regional population consists of small local subpopulations (e.g., a metapopulation), the stochastic processes regulated by population sizes may explain the spatial variation in phenology. In this study, we quantitatively evaluated the extent of the spatial and annual variations in the breeding phenology of the forest green tree frog, Rhacophorus arboreus habiting a small area (<10 km2). The spatial variation in phenological peaks among 25 breeding sites was large over 6 years. This spatial variation was not explained by differences in air temperature or water depth. Randomization tests revealed that a large portion of the spatial variation could be explained by differences in population size, without considering site‐specific factors. Annual variations in phenological peaks tended to be greater for smaller populations. These results imply that the stochastic process might have caused the spatial and annual variations in the phenological peaks of R. arboreus observed in the study region. Understanding spatiotemporal variation in phenology determined by stochastic process would be important to better predict interspecific interactions and (meta)population dynamics at small spatial scales. [ABSTRACT FROM AUTHOR]

Ecological drift can override the effects of deterministic niche selection on small populations and drive the assembly of some ecological communities. We tested this hypothesis with a unique data set sampled identically in 200 streams in two regions (tropical Brazil and boreal Finland) that differ in macroinvertebrate community size by fivefold. Null models allowed us to estimate the magnitude to which β‐diversity deviates from the expectation under a random assembly process while taking differences in richness and relative abundance into account, i.e., β‐deviation. We found that both abundance‐ and incidence‐based β‐diversity was negatively related to community size only in Brazil. Also, β‐diversity of small tropical communities was closer to stochastic expectations compared with β‐diversity of large communities. We suggest that ecological drift may drive variation in some small communities by changing the expected outcome of niche selection, increasing the chances of species with low abundance and narrow distribution to occur in some communities. Habitat destruction, overexploitation, pollution, and reductions in connectivity have been reducing the size of biological communities. These environmental pressures might make smaller communities more vulnerable to novel conditions and render community dynamics more unpredictable. Incorporation of community size into ecological models should provide conceptual and applied insights into a better understanding of the processes driving biodiversity. [ABSTRACT FROM AUTHOR]

The Price equation has found widespread application in many areas of evolutionary biology, including the evolutionary epidemiology of infectious diseases. In this paper, we illustrate the utility of this approach to modelling disease evolution by first deriving a version of Price's equation that can be applied in continuous time and to populations with overlapping generations. We then show how this version of Price's equation provides an alternative perspective on pathogen evolution by considering the epidemiological meaning of each of its terms. Finally, we extend these results to the case where population size is small and generates demographic stochasticity. We show that the particular partitioning of evolutionary change given by Price's equation is also a natural way to partition the evolutionary consequences of demographic stochasticity, and demonstrate how such stochasticity tends to weaken selection on birth rate (e.g. the transmission rate of an infectious disease) and enhance selection on mortality rate (e.g. factors, like virulence, that cause the end of an infection). In the long term, if there is a trade-off between virulence and transmission across parasite strains, the weaker selection on transmission and stronger selection on virulence that arises from demographic stochasticity will tend to drive the evolution of lower levels of virulence. This article is part of the theme issue 'Fifty years of the Price equation'. [ABSTRACT FROM AUTHOR]

Synergistic and antagonistic interactions in multi-species populations—such as resource sharing and competition—result in remarkably diverse behaviours in populations of interacting cells, such as in soil or human microbiomes, or clonal competition in cancer. The degree of inter- and intra-specific interaction can often be quantified through the notion of an ecological ‘niche’. Typically, weakly interacting species that occupy largely distinct niches result in stable mixed populations, while strong interactions and competition for the same niche result in rapid extinctions of some species and fixations of others. We investigate the transition of a deterministically stable mixed population to a stochasticity-induced fixation as a function of the niche overlap between the two species. We also investigate the effect of the niche overlap on the population stability with respect to external invasions. Our results have important implications for a number of experimental systems.

Theory has shown that the effects of demographic stochasticity on communities may depend on the magnitude of fitness differences between species. In particular, it has been suggested that demographic stochasticity has the potential to significantly alter competitive outcomes when fitness differences are small (nearly neutral), but that it has negligible effects when fitness differences are large (highly non‐neutral). Here we test such theory experimentally and extend it to examine how demographic stochasticity affects exclusion frequency and mean densities of consumers in simple, but non‐neutral, consumer–resource communities. We used experimental microcosms of protists and rotifers feeding on a bacterial resource to test how varying absolute population sizes (a driver of demographic stochasticity) affected the probability of competitive exclusion of the weakest competitor. To explore whether demographic stochasticity could explain our experimental results, and to generalize beyond our experiment, we paired the experiment with a continuous‐time stochastic model of resource competition, which we simulated for 11 different fitness inequalities between competiting consumers. Consistent with theory, in both our experiments and our simulations we found that demographic stochasticity altered competitive outcomes in communities where fitness differences were small. However, we also found that demographic stochasticity alone could affect communities in other ways, even when fitness differences between competitors were large. Specifically, demographic stochasticity altered mean densities of both weak and strong competitors in experimental and simulated communities. These findings highlight how demographic stochasticity can change both competitive outcomes in non‐neutral communities and the processes underlying overall community dynamics. [ABSTRACT FROM AUTHOR]

In large but finite populations, weak demographic stochasticity due to random birth and death events can lead to population extinction. The process is analogous to the escaping problem of trapped particles under random forces. Methods widely used in studying such physical systems, for instance, Wentzel–Kramers–Brillouin (WKB) and Fokker–Planck methods, can be applied to solve similar biological problems. In this article, we comparatively analyse applications of WKB and Fokker–Planck methods to some typical stochastic population dynamical models, including the logistic growth, endemic SIR, predator-prey, and competitive Lotka–Volterra models. The mean extinction time strongly depends on the nature of the corresponding deterministic fixed point(s). For different types of fixed points, the extinction can be driven either by rare events or typical Gaussian fluctuations. In the former case, the large deviation function that governs the distribution of rare events can be well-approximated by the WKB method in the weak noise limit. In the later case, the simpler Fokker–Planck approximation approach is also appropriate. [ABSTRACT FROM AUTHOR]

Empirical knowledge of diversity–stability relationships is mostly based on the analysis of temporal variability. Variability, however, often depends on external factors that act as disturbances, which makes comparisons across systems difficult to interpret. Here, we show how variability can reveal inherent stability properties of ecological communities. This requires that we abandon one‐dimensional representations, in which a single variability measurement is taken as a proxy for how stable a system is, and instead consider the whole set of variability values generated by all possible stochastic perturbations. Despite this complexity, in species‐rich systems, a generic pattern emerges from community assembly, relating variability to the abundance of perturbed species. Strikingly, the contrasting contributions of different species abundance classes to variability, driven by different types of perturbations, can lead to opposite diversity–stability patterns. We conclude that a multidimensional perspective on variability helps reveal the dynamical richness of ecological systems and the underlying meaning of their stability patterns. [ABSTRACT FROM AUTHOR]

One of the most important challenges in conservation biology is to predict the viability of populations of vulnerable and threatened species. This requires that the demographic stochasticity strongly affecting the ecological and evolutionary dynamics of especially small populations is correctly estimated and modelled. Here, we summarize theoretical evidence showing that the demographic variance in population dynamics is a key parameter determining the probability of extinction and also is directly linked to the magnitude of the genetic drift in the population. The demographic variance is dependent on the mating system, being larger in a polygynous than in monogamous populations. Understanding factors affecting intersexual differences in mating success is therefore essential in explaining variation in the demographic variance. We hypothesize that the strength of sexual selection, for example, quantified by the Bateman gradient, may be a useful predictor of the magnitude of the demographic stochasticity and hence the genetic drift in the population. We provide results from a field study of moose that support this claim. Thus, including central principles from behavioural ecology may increase the reliability of population viability analyses through an improvement of our understanding of factors affecting stochastic influences on population dynamics and evolutionary processes. This article is part of the theme issue 'Linking behaviour to dynamics of populations and communities: application of novel approaches in behavioural ecology to conservation'. [ABSTRACT FROM AUTHOR]