Genetic Diversity in Introduced Populations with an Allee Effect

A phenomenon that strongly influences the demography of small introduced populations and thereby potentially their genetic diversity is the demographic Allee effect, a reduction in population growth rates at small population sizes. We take a stochastic modeling approach to investigate levels of genetic diversity in populations that successfully overcame either a strong Allee effect, in which populations smaller than a certain critical size are expected to decline, or a weak Allee effect, in which the population growth rate is reduced at small sizes but not negative. Our results indicate that compared to successful populations without an Allee effect, successful populations with a strong Allee effect tend to (1) derive from larger founder population sizes and thus have a higher initial amount of genetic variation, (2) spend fewer generations at small population sizes where genetic drift is particularly strong, and (3) spend more time around the critical population size and thus experience more genetic drift there. In the case of multiple introduction events, there is an additional increase in diversity because Allee-effect populations tend to derive from a larger number of introduction events than other populations. Altogether, a strong Allee effect can either increase or decrease genetic diversity, depending on the average founder population size. By contrast, a weak Allee effect tends to decrease genetic diversity across the entire range of founder population sizes. Finally, we show that it is possible in principle to infer critical population sizes from genetic data, although this would require information from many independently introduced populations.     

Allee effects in stochastic populations

The Allee effect, or inverse density dependence at low population sizes, could seriously impact preservation and management of biological populations. The mounting evidence for widespread Allee effects has lately inspired theoretical studies of how Allee effects alter population dynamics. However, the recent mathematical models of Allee effects have been missing another important force prevalent at low population sizes: stochasticity. In this paper, the combination of Allee effects and stochasticity is studied using diffusion processes, a type of general stochastic population model that accommodates both demographic and environmental stochastic fluctuations. Including an Allee effect in a conventional deterministic population model typically produces an unstable equilibrium at a low population size, a critical population level below which extinction is certain. In a stochastic version of such a model, the probability of reaching a lower size a before reaching an upper size b , when considered as a function of initial population size, has an inflection point at the underlying deterministic unstable equilibrium. The inflection point represents a threshold in the probabilistic prospects for the population and is independent of the type of stochastic fluctuations in the model. In particular, models containing demographic noise alone (absent Allee effects) do not display this threshold behavior, even though demographic noise is considered an "extinction vortex". The results in this paper provide a new understanding of the interplay of stochastic and deterministic forces in ecological populations.     

Variation in Allee effects: evidence,unknowns, and directions forward

Allee effects, positive effects of population size or density on per-capita fitness, are of broad interest in ecology and conservation due to their importance to the persistence of small populations and to range boundary dynamics. A number of recent studies have highlighted the importance of spatiotemporal variation in Allee effects and the resulting impacts on population dynamics. These advances challenge conventional understanding of Allee effects by reframing them as a dynamic factor affecting populations instead of a static condition. First, we synthesize evidence for variation in Allee effects and highlight potential mechanisms. Second, we emphasize the “Allee slope,” i.e., the magnitude of the positive effect of density on the per-capita growth rate, as a metric for demographic Allee effects. The more commonly used quantitative metric, the Allee threshold, provides only a partial picture of the underlying forces acting on population growth despite its implications for population extinction. Third, we identify remaining unknowns and strategies for addressing them. Outstanding questions about variation in Allee effects fall broadly under three categories: (1) characterizing patterns of natural variability; (2) understanding mechanisms of variation; and (3) implications for populations, including applications to conservation and management. Future insights are best achieved through robust interactions between theory and empiricism, especially through mechanistic models. Understanding spatiotemporal variation in the demographic processes contributing to the dynamics of small populations is a critical step in the advancement of population ecology.     

The highs and lows of dispersal: how connectivity and initial population size jointly shape establishment dynamics in discrete landscapes

Identifying the main factors driving introduced populations to establishment is a major challenge of invasion biology. Due to their small initial size, introduced populations are most vulnerable to extinction because of demographic stochasticity or Allee effects. While an increase in initial population size is known to increase establishment success, much remains to be understood regarding its interplay with connectivity in spatially structured environments. In order to better understand how demographic mechanisms interact at such spatial scale, we developed a stochastic model of population dynamics in discrete space to investigate the effect of connectivity and initial population size on establishment. The predictions derived from the model were then tested using experimental introductions of an insect parasitoid (Trichogramma chilonis) in spatially structured laboratory microcosms. Both theoretical and experimental results demonstrated that the connectivity of the introduction site had 1) a deleterious effect in the first generation when the introduced population was small and 2) a beneficial impact brought about by metapopulation effects in the subsequent generations. Interestingly, populations displayed a weakly pushed invasion pattern promoting early establishment, which was mainly underpinned by dispersal stochasticity and the discrete nature of the landscape. These results shed light on the critical influence of landscape connectivity on establishment dynamics.     

Establishing a beachhead: a stochastic population model with an Allee effect applied to species invasion

We formulated a spatially explicit stochastic population model with an Allee effect in order to explore how invasive species may become established. In our model, we varied the degree of migration between local populations and used an Allee effect with variable birth and death rates. Because of the stochastic component, population sizes below the Allee effect threshold may still have a positive probability for successful invasion. The larger the network of populations, the greater the probability of an invasion occurring when initial population sizes are close to or above the Allee threshold. Furthermore, if migration rates are low, one or more than one patch may be successfully invaded, while if migration rates are high all patches are invaded.     

Allee effects, aggregation, and invasion success

Understanding the factors that influence successful colonization can help inform ecological theory and aid in the management of invasive species. When founder populations are small, individual fitness may be negatively impacted by component Allee effects through positive density dependence (e.g., mate limitation). Reproductive and survival mechanisms that suffer due to a shortage of conspecifics may scale up to be manifest in a decreased per-capita population growth rate (i.e., a demographic Allee effect). Mean-field population level models are limited in representing how component Allee effects scale up to demographic Allee effects when heterogeneous spatial structure influences conspecific availability. Thus, such models may not adequately characterize the probability of establishment. In order to better assess how individual level processes influence population establishment and spread, we developed a spatially explicit individual-based stochastic simulation of a small founder population. We found that increased aggregation can affect individual fitness and subsequently impact population growth; however, relatively slow dispersal—in addition to initial spatial structure—is required for establishment, ultimately creating a tradeoff between probability of initial establishment and rate of subsequent spread. Since this result is sensitive to the scaling up of component Allee effects, details of individual dispersal and interaction kernels are key factors influencing population level processes. Overall, we demonstrate the importance of considering both spatial structure and individual level traits in assessing the consequences of Allee effects in biological invasions.     

Demographic and genetic effects on reproduction as related to population size in a rare, perennial herb, Senecio integrifolius (Asteraceae)

Seed-set of the rare and threatened plant Senecio integrifolius increased significantly with population size. Experimental studies as well as field observations showed this to be due to density-dependent seed-set (Allee effect). Hand-pollination revealed lower seed-set, and a lower germination rate of inbred progeny than of outbred progeny, with great differences among populations. Contrary to general predictions in models of minimum viable population sizes, the present study indicates little negative effects of inbreeding in small populations. A genetic load model was invoked to explain the results, hypothesizing that purging of deleterious alleles in small populations has reduced inbreeding depression. However, no clear correlation between population size and genetic load was found. The results in this paper suggest that demographic and environmental factors are of greater immediate importance than population genetics in determining extinction probabilities of small plant populations.     

Experimental island invasion of house mice

The ability of invasive species to recurrently establish populations from small numbers of founders, while threatened species struggle at the same low population sizes, is a paradox in conservation biology. Little is known about the mechanisms contributing to the post-arrival success of low density invasive populations as most invasive species research focuses on established, high density populations. Experimental studies are powerful, but generally limited to laboratory or invertebrate experiments. Here, we experimentally demonstrate that vertebrate mammal invasion from a very small (n = 2) number of founders follows relatively simple deterministic predictions. An intentional island invasion of introduced house mice (Mus musculus Linnaeus) from one founding pair closely tracked the density dependent logistic growth curve and reached the seasonal carrying capacity of a previously extant population in only 5 months. Carrying capacity reflected both density dependent and independent processes. In contrast to the previously incumbent population, the invading population retained a marked genetic signal of its recent founder event, but the populations were otherwise demographically indistinguishable. Stochastic events such as individual variability, supplemental immigration and ecological release, but not Allee effects, played important roles during colonisation, but following establishment dynamics rapidly became deterministic, with little demographic impact of reduced genetic diversity. The small population paradigm appears to have little influence on the population dynamics of highly successful invasive species.     

Population size,habitat fragmentation,and the nature of adaptive variation in a stream fish

Whether and how habitat fragmentation and population size jointly affect adaptive genetic variation and adaptive population differentiation are largely unexplored. Owing to pronounced genetic drift, small, fragmented populations are thought to exhibit reduced adaptive genetic variation relative to large populations. Yet fragmentation is known to increase variability within and among habitats as population size decreases. Such variability might instead favour the maintenance of adaptive polymorphisms and/or generate more variability in adaptive differentiation at smaller population size. We investigated these alternative hypotheses by analysing coding-gene, single-nucleotide polymorphisms associated with different biological functions in fragmented brook trout populations of variable sizes. Putative adaptive differentiation was greater between small and large populations or among small populations than among large populations. These trends were stronger for genetic population size measures than demographic ones and were present despite pronounced drift in small populations. Our results suggest that fragmentation affects natural selection and that the changes elicited in the adaptive genetic composition and differentiation of fragmented populations vary with population size. By generating more variable evolutionary responses, the alteration of selective pressures during habitat fragmentation may affect future population persistence independently of, and perhaps long before, the effects of demographic and genetic stochasticity are manifest.     

French wasps in the New World: experimental biological control introductions reveal a demographic Allee effect

Many populations introduced into a novel environment fail to establish. One underlying process is the Allee effect, i.e., the difficulty of individuals to survive and reproduce when rare, and the consequently low or negative population growth. Although observations showing a positive relation between initial population size and establishment probability suggest that the Allee effect could be widespread in biological invasions, experimental tests are scarce. Here, we used a biological control program against Diuraphis noxia (Mordvilko) (Hemiptera: Aphididae) in the United States to manipulate initial population size of the introduced parasitoid Aphelinus asychis Walker (Hymenoptera: Aphelinidae) originating from France. For eight populations and three generations after introduction, we studied spatial distribution and spread, density, mate-finding, and population growth. Dispersal was lower in small populations during the first generation. Smaller initial population size nonetheless resulted in lower density during the three generations studied. The proportion of mated females and the population sex ratio were not affected by initial population size or population density. Net reproductive rate decreased with density within each generation, suggesting negative density-dependence. But for a given density, net reproductive rate was smaller in populations initiated with few individuals than in populations initiated with many individuals. Hence, our results demonstrate a demographic Allee effect. Mate-finding is excluded as an underlying mechanism, and other component Allee effects may have been overwhelmed by negative density-dependence in reproduction. Impact of generalist predators could provide one potential explanation for the relationship between initial population size and net reproductive rate. However, the continuing effect of initial population size on population growth suggests genetic processes may have been involved in the observed demographic Allee effect.     

Demographic response of plant populations to habitat fragmentation and temporal environmental variability

Many plant species currently exist in fragmented populations of different sizes, while they also experience unpredictable climatic fluctuation over time. However, we still understand little about how plant demography responds to such spatial and temporal environmental variability. We studied population dynamics of an understory perennial herb Trillium camschatcense in the Tokachi plain of Hokkaido, Japan, where a significant effect of forest fragmentation on seedling recruitment was previously reported. Four populations across a range of fragment sizes were studied for 6 years, and the data were analyzed using matrix population models. Per capita fecundity (the number of recruits per plant) varied greatly among populations, but the variation in population growth rates (λ) was mainly driven by the variation in stasis and growth rates, suggesting that the general trend of reduced fecundity in fragmented populations may not be readily translated into subsequent dynamics. Temporal variation in λ among years was more than 2 times larger than spatial variation among populations, and this result was likely attributable to the contrasting response of correlation structures among demographic rates. The among-population variation in λ was dampened by negative covariation between matrix elements possibly due to density-dependent regulation as well as an inherent constraint that some elements are not independent, whereas positive covariation between matrix elements resulted in large temporal variation in λ. Our results show that population dynamics responded differently to habitat fragmentation and temporal variability of the environment, emphasizing the need to discriminate these spatial and temporal variations in demographic models. Although no populations were projected to be declining in stochastic simulations, correlation between current habitat size and plant density implies historical λ is positively related to habitat size.     

Overcoming Allee effects through evolutionary,genetic, and demographic rescue

Despite the amplified threats of extinction facing small founder populations, successful colonization sometimes occurs, bringing devastating ecological and economic consequences. One explanation may be rapid evolution, which can increase mean fitness in populations declining towards extinction, permitting persistence and subsequent expansion. Such evolutionary rescue may be particularly important, given Allee effects. When a population is introduced at low density, individuals often experience a reduction in one or more components of fitness due to novel selection pressures that arise from diminished intraspecific interactions and positive density dependence (i.e. component Allee effects). A population can avoid extinction if it can adapt and recover on its own (i.e. evolutionary rescue), or if additional immigration sustains the population (i.e. demographic rescue) or boosts its genetic variation that facilitates adaptation (i.e. genetic rescue). These various forms of rescue have often been invoked as possible mechanisms for specific invasions, but their relative importance to invasion is not generally understood. Within a spatially explicit modelling framework, we consider the relative impact of each type of rescue on the probability of successful colonization, when there is evolution of a multi-locus quantitative trait that influences the strength of component Allee effects. We demonstrate that when Allee effects are important, the effect of demographic rescue via recurrent immigration overall provides the greatest opportunity for success. While highlighting the role of evolution in the invasion process, we underscore the importance of the ecological context influencing the persistence of small founder populations.     

Determinants of extinction in fragmented plant populations: Crepis sancta (asteraceae) in urban environments

Local populations are subject to recurrent extinctions, and small populations are particularly prone to extinction. Both demographic (stochasticity and the Allee effect) and genetic factors (drift load and inbreeding depression) potentially affect extinction. In fragmented populations, regular dispersal may boost population sizes (demographic rescue effect) or/and reduce the local inbreeding level and genetic drift (genetic rescue effect), which can affect extinction risks. We studied extinction processes in highly fragmented populations of the common species Crepis sancta (Asteraceae) in urban habitats exhibiting a rapid turnover of patches. A four-year demographic monitoring survey and microsatellite genotyping of individuals allowed us to study the determinants of extinction. We documented a low genetic structure and an absence of inbreeding (estimated by multilocus heterozygosity), which suggest that genetic factors were not a major cause of patch extinction. On the contrary, local population size was the main factor in extinction, whereas connectivity was shown to decrease patch extinction, which we interpreted as a demographic rescue effect that was likely due to better pollination services for reproduction. This coupling of demographic and genetic tools highlighted the importance of dispersal in local patch extinctions of small fragmented populations connected by gene flow.     

Allee effects and resilience in stochastic populations

Allee effects, or positive functional relationships between a population’s density (or size) and its per unit abundance growth rate, are now considered to be a widespread if not common influence on the growth of ecological populations. Here we analyze how stochasticity and Allee effects combine to impact population persistence. We compare the deterministic and stochastic properties of four models: a logistic model (without Allee effects), and three versions of the original model of Allee effects proposed by Vito Volterra representing a weak Allee effect, a strong Allee effect, and a strong Allee effect with immigration. We employ the diffusion process approach for modeling single-species populations, and we focus on the properties of stationary distributions and of the mean first passage times. We show that stochasticity amplifies the risks arising from Allee effects, mainly by prolonging the amount of time a population spends at low abundance levels. Even weak Allee effects become consequential when the ubiquitous stochastic forces affecting natural populations are accounted for in population models. Although current concepts of ecological resilience are bound up in the properties of deterministic basins of attraction, a complete understanding of alternative stable states in ecological systems must include stochasticity.     

Landscape structure and the genetic effects of a population collapse

Both landscape structure and population size fluctuations influence population genetics. While independent effects of these factors on genetic patterns and processes are well studied, a key challenge is to understand their interaction, as populations are simultaneously exposed to habitat fragmentation and climatic changes that increase variability in population size. In a population network of an alpine butterfly, abundance declined 60–100% in 2003 because of low over-winter survival. Across the network, mean microsatellite genetic diversity did not change. However, patch connectivity and local severity of the collapse interacted to determine allelic richness change within populations, indicating that patch connectivity can mediate genetic response to a demographic collapse. The collapse strongly affected spatial genetic structure, leading to a breakdown of isolation-by-distance and loss of landscape genetic pattern. Our study reveals important interactions between landscape structure and temporal demographic variability on the genetic diversity and genetic differentiation of populations. Projected future changes to both landscape and climate may lead to loss of genetic variability from the studied populations, and selection acting on adaptive variation will likely occur within the context of an increasing influence of genetic drift.     

Genetic rescue in interconnected populations of small and large size of the self-incompatible Ranunculus reptans

Small populations of our study species Ranunculus reptans have reduced fitness because of inbreeding, genetic load, and reduced mate availability; that is, they suffer from a three-fold genetic Allee effect. Here, we investigate how the effect of interpopulation outbreeding on offspring fitness depends on population size. We performed within- and between-population crosses with plants originating from 15 populations, and measured offspring performance in a common environment. Interpopulation outbreeding led to an increase in population means of clonal performance, which was defined as the number of rooted offspring rosettes produced per maternal ovule. This fitness gain mainly occurred at the life stage of seed set. It was especially pronounced for populations with a long-term history of small size inferred from their low genetic diversity, estimated from eight allozyme loci. We conclude that in a self-incompatible plant such as R. reptans, interpopulation outbreeding can lead to an immediate genetic rescue effect due to increased cross-compatibility and heterosis, and that this rescue effect is increased as population size decreases.     

Population size,center–periphery,and seed dispersers’ effects on the genetic diversity and population structure of the Mediterranean relict shrub Cneorum tricoccon

The effect of population size on population genetic diversity and structure has rarely been studied jointly with other factors such as the position of a population within the species’ distribution range or the presence of mutualistic partners influencing dispersal. Understanding these determining factors for genetic variation is critical for conservation of relict plants that are generally suffering from genetic deterioration. Working with 16 populations of the vulnerable relict shrub Cneorum tricoccon throughout the majority of its western Mediterranean distribution range, and using nine polymorphic microsatellite markers, we examined the effects of periphery (peripheral vs. central), population size (large vs. small), and seed disperser (introduced carnivores vs. endemic lizards) on the genetic diversity and population structure of the species. Contrasting genetic variation (H_E: 0.04–0.476) was found across populations. Peripheral populations showed lower genetic diversity, but this was dependent on population size. Large peripheral populations showed high levels of genetic diversity, whereas small central populations were less diverse. Significant isolation by distance was detected, indicating that the effect of long‐distance gene flow is limited relative to that of genetic drift, probably due to high selfing rates (F_IS = 0.155–0.887), restricted pollen flow, and ineffective seed dispersal. Bayesian clustering also supported the strong population differentiation and highly fragmented structure. Contrary to expectations, the type of disperser showed no significant effect on either population genetic diversity or structure. Our results challenge the idea of an effect of periphery per se that can be mainly explained by population size, drawing attention to the need of integrative approaches considering different determinants of genetic variation. Furthermore, the very low genetic diversity observed in several small populations and the strong among‐population differentiation highlight the conservation value of large populations throughout the species’ range, particularly in light of climate change and direct human threats.     

Sex-biased evolutionary forces shape genomic patterns of human diversity

Comparisons of levels of variability on the autosomes and X chromosome can be used to test hypotheses about factors influencing patterns of genomic variation. While a tremendous amount of nucleotide sequence data from across the genome is now available for multiple human populations, there has been no systematic effort to examine relative levels of neutral polymorphism on the X chromosome versus autosomes. We analyzed ~210 kb of DNA sequencing data representing 40 independent noncoding regions on the autosomes and X chromosome from each of 90 humans from six geographically diverse populations. We correct for differences in mutation rates between males and females by considering the ratio of within-human diversity to human-orangutan divergence. We find that relative levels of genetic variation are higher than expected on the X chromosome in all six human populations. We test a number of alternative hypotheses to explain the excess polymorphism on the X chromosome, including models of background selection, changes in population size, and sex-specific migration in a structured population. While each of these processes may have a small effect on the relative ratio of X-linked to autosomal diversity, our results point to a systematic difference between the sexes in the variance in reproductive success; namely, the widespread effects of polygyny in human populations. We conclude that factors leading to a lower male versus female effective population size must be considered as important demographic variables in efforts to construct models of human demographic history and for understanding the forces shaping patterns of human genomic variability.     

Using genetic data to advance stream fish reintroduction science: a case study in brook trout

Widespread extirpation of native fish populations has led to a rise in species reintroduction efforts worldwide. Most efforts have relied on demographic data alone to guide project design and evaluate success. However, the genetic characteristics of many imperiled fish populations including low diversity, local adaptation, and hatchery introgression emphasize the importance of genetic data in the design and monitoring of reintroduction efforts. Focusing on a case study of brook trout (Salvelinus fontinalis) in North Carolina, we show how the combined use of genetic and demographic data can support reintroduction efforts by improving source population selection and providing opportunities to evaluate genetic viability and adaptive potential in restored populations. Using this combined approach, we reintroduced brook trout into a restored stream from two source populations and monitored changes in genetic diversity and population size in source and recipient populations. Three years after the initial translocation, the reintroduced population had comparable density, but higher genetic diversity, than either source population. This study demonstrates the utility of genetic and demographic data for reintroduction efforts, particularly when extant populations are genetically depauperate and maintaining adaptive potential is a primary restoration goal. However, we emphasize the value of continued monitoring at longer temporal and spatial scales to determine the effects of stochastic process on the long-term adaptive capacity and persistence of reintroduced populations. Overall, inclusion of genetic data in reintroduction efforts offers increased ability to meet project goals while simultaneously conserving critical sources of adaptive variation that exist across the landscape.     

The genetic underpinnings of population cyclicity: establishing expectations for the genetic anatomy of cycling populations

Despite extensive research into the mechanisms underlying population cyclicity, we have little understanding of the impacts of numerical fluctuations on the genetic variation of cycling populations. Thus, the potential implications of natural and anthropogenically‐driven variation in population cycle dynamics on the diversity and evolutionary potential of cyclic populations is unclear. Here, we use Canada lynx Lynx canadensis matrix population models, set up in a linear stepping‐stone, to generate demographic replicates of biologically realistic cycling populations. Overall, increasing cycle amplitude predictably reduced genetic diversity and increased genetic differentiation, with cyclic effects increased by population synchrony. Modest dispersal rates (1–3% of the population) between high and low amplitude cyclic populations did not diminish these effects suggesting that spatial variation in cyclic amplitude should be reflected in patterns of genetic diversity and differentiation at these rates. At high dispersal rates (6%) groups containing only high amplitude cyclic populations had higher diversity and lower differentiation than those mixed with low amplitude cyclic populations. Negative density‐dependent dispersal did not impact genetic diversity, but did homogenize populations by reducing differentiation and patterns of isolation by distance. Surprisingly, temporal changes in diversity and differentiation throughout a cycle were not always consistent with population size. In particular, negative density‐dependent dispersal simultaneously decreased differences in genetic diversity while increasing differences in genetic differentiation between numerical peaks and nadirs. Combined, our findings suggest demographic changes at fine temporal scales can impact genetic variation of interacting populations and provide testable predictions relating population cyclicty to genetic variation. Further, our results suggest that including realistic demographic and dispersal parameters in population genetic models and using information from temporal changes in genetic variation could help to discern complex demographic scenarios and illuminate population dynamics at fine temporal scales.