Habitat selection reduces extinction of populations subject to Allee effects

Theoretical studies indicate that a single population under an Allee effect will decline to extinction if reduced below a particular threshold, but the existence of multiple local populations connected by random dispersal improves persistence of the global population. An additional process that can facilitate persistence is the existence of habitat selection by dispersers. Using analytic and simulation models of population change, I found that when habitat patches exhibiting Allee effects are connected by dispersing individuals, habitat selection by these dispersers increases the likelihood that patches persist at high densities, relative to results expected by random settlement. Populations exhibiting habitat selection also attain equilibrium more quickly than randomly dispersing populations. These effects are particularly important when Allee effects are large and more than two patches exist. Integrating habitat selection into population dynamics may help address why some studies have failed to find extinction thresholds in populations, despite well-known Allee effects in many species.     

Allee effects within small populations of Aconitum napellus ssp. lusitanicum, a protected subspecies in northern France

Plants growing at low density can suffer from Allee effects as a result of pollen limitation. Previous studies of Allee effects have focused on the effects of variation among populations in size or density on reproduction. Here, the effects of plant distribution within populations on fitness components are explored in a rare plant, Aconitum napellus ssp. lusitanicum, and ecological and genetic mechanisms underlying these effects are identified. To detect pollen limitation, seed production was compared under natural versus hand-supplemented pollinations on inflorescences of different sizes in natural patches differing both in flower density and in isolation from other patches. Germination rate and juvenile survival of seeds produced in low- and high-density patches were also compared. Pollen-supplemented flowers always produced more seeds than open-pollinated flowers, especially among small plants and plants growing at low density. Offspring produced in low-density patches exhibited lower fitness that those produced in high-density patches. This could have been caused by post-fertilization mechanisms, including inbreeding depression or differential maternal resource allocation. These results show that Allee effects on fitness components (ecological and genetic Allee effects) occur within A. napellus populations at different spatial scales. The spatial distribution of plants seems to be a crucial factor affecting reproductive output and fitness.     

Variable reproductive success in fragmented populations

Marine habitats are naturally patchy and anthropogenic disturbance can further fragment them. Many marine animals are sessile as adults or obligate inhabitants of particular habitats, so populations living in isolated patches of habitat are linked largely by dispersal of planktonic larvae. Theoretically, larvae are more likely to find and settle into large patches of habitat than small patches, thus small habitat patches may experience a more discontinuous supply of recruits resulting in small populations with unusual size- or age-structures or odd sex ratios — conditions where Allee effects on reproductive success are likely. We tested this hypothesis for the Caribbean spotted spiny lobster (Panulirus guttatus), an obligate inhabitant of coral patch reefs whose mating dynamics are size-dependent. We found that P. guttatus were less abundant on small reefs where their size structure and per capita reproductive success were significantly more variable, particularly among large females that are susceptible to sperm limitation that diminishes fertilization rates. These results are indicative of Allee effects and provide a mechanistic understanding of how size-dependent mating dynamics influence reproductive success in ways that alter population dynamics in patchy habitats.     

Expansion or extinction: deterministic and stochastic two-patch models with Allee effects

We investigate the impact of Allee effect and dispersal on the long-term evolution of a population in a patchy environment. Our main focus is on whether a population already established in one patch either successfully invades an adjacent empty patch or undergoes a global extinction. Our study is based on the combination of analytical and numerical results for both a deterministic two-patch model and a stochastic counterpart. The deterministic model has either two, three or four attractors. The existence of a regime with exactly three attractors only appears when patches have distinct Allee thresholds. In the presence of weak dispersal, the analysis of the deterministic model shows that a high-density and a low-density populations can coexist at equilibrium in nearby patches, whereas the analysis of the stochastic model indicates that this equilibrium is metastable, thus leading after a large random time to either a global expansion or a global extinction. Up to some critical dispersal, increasing the intensity of the interactions leads to an increase of both the basin of attraction of the global extinction and the basin of attraction of the global expansion. Above this threshold, for both the deterministic and the stochastic models, the patches tend to synchronize as the intensity of the dispersal increases. This results in either a global expansion or a global extinction. For the deterministic model, there are only two attractors, while the stochastic model no longer exhibits a metastable behavior. In the presence of strong dispersal, the limiting behavior is entirely determined by the value of the Allee thresholds as the global population size in the deterministic and the stochastic models evolves as dictated by their single-patch counterparts. For all values of the dispersal parameter, Allee effects promote global extinction in terms of an expansion of the basin of attraction of the extinction equilibrium for the deterministic model and an increase of the probability of extinction for the stochastic model.     

Reconstructing Local Population Dynamics in Noisy Metapopulations—The Role of Random Catastrophes and Allee Effects

Reconstructing the dynamics of populations is complicated by the different types of stochasticity experienced by populations, in particular if some forms of stochasticity introduce bias in parameter estimation in addition to error. Identification of systematic biases is critical when determining whether the intrinsic dynamics of populations are stable or unstable and whether or not populations exhibit an Allee effect, i.e., a minimum size below which deterministic extinction should follow. Using a simulation model that allows for Allee effects and a range of intrinsic dynamics, we investigated how three types of stochasticity—demographic, environmental, and random catastrophes— affect our ability to reconstruct the intrinsic dynamics of populations. Demographic stochasticity aside, which is only problematic in small populations, we find that environmental stochasticity—positive and negative environmental fluctuations—caused increased error in parameter estimation, but bias was rarely problematic, except at the highest levels of noise. Random catastrophes, events causing large-scale mortality and likely to be more common than usually recognized, caused immediate bias in parameter estimates, in particular when Allee effects were large. In the latter case, population stability was predicted when endogenous dynamics were actually unstable and the minimum viable population size was overestimated in populations with small or non-existent Allee effects. Catastrophes also generally increased extinction risk, in particular when endogenous Allee effects were large. We propose a method for identifying data points likely resulting from catastrophic events when such events have not been recorded. Using social spider colonies (Anelosimus spp.) as models for populations, we show that after known or suspected catastrophes are accounted for, reconstructed growth parameters are consistent with intrinsic dynamical instability and substantial Allee effects. Our results are applicable to metapopulation or time series data and are relevant for predicting extinction in conservation applications or the management of invasive species.     

Neglecting uncertainty behind Allee effect estimation may generate false predictions of population extinction risk

Estimation of extinction thresholds arising from Allee effects (Allee thresholds) and related probabilities of population extinction is notoriously difficult. One way is to analyze adequately parameterized population models. Traditionally, a point estimate is substituted for the Allee effect strength in such models. However, each point estimate entails an underlying uncertainty. We explore how accounting for this uncertainty affects the probability of population extinction, and show that this probability decreases sigmoidally with increasing population density, even in the absence of any stochasticity. Deviations from when only a point estimate of the Allee effect strength is used can be significant, unless stochasticity is added and the stochastic noise intensity is high. Significant deviations from when only a point estimate is used also occur when the Allee threshold and the environmental carrying capacity of the species are close enough one to another. We also show that the impact of the uncertainty in the Allee effect strength estimate increases as the Allee effect strength itself increases and decreases as the species recovery potential increases. This is not a good news, since we would like to preferentially and efficiently manage slowly recovering populations prone to strong Allee effects. Still, there is a way to come up with relatively good Allee threshold estimates. Besides an obvious option of collecting as many data as possible, the impact of the uncertainty can be mitigated by diversifying Allee effect experiments such that we put more emphasis on larger size groups. This is somewhat surprising, given that frequent complaints on the (im)possibility of detecting Allee effects concern difficulties in locating, observing and experimenting on rare populations. Our results extend current theory surrounding Allee effects and have broad ramifications for applied ecology.     

When bigger is not better: intraspecific competition for pollination increases with population size in invasive milkweeds

One of the essential requirements for an introduced plant species to become invasive is an ability to reproduce outside the native range, particularly when initial populations are small. If a reproductive Allee effect is operating, plants in small populations will have reduced reproductive success relative to plants in larger populations. Alternatively, if plants in small populations experience less competition for pollination than those in large populations, they may actually have higher levels of reproductive success than plants in large populations. To resolve this uncertainty, we investigated how the per capita fecundity of plants was affected by population size in three invasive milkweed species. Field surveys of seed production in natural populations of different sizes but similar densities were conducted for three pollinator-dependent invasive species, namely Asclepias curassavica, Gomphocarpus fruticosus and G. physocarpus. Additionally, supplemental hand-pollinations were performed in small and large populations in order to determine whether reproductive output was limited by pollinator activity in these populations. Reproductive Allee effects were not detected in any of the study species. Instead, plants in small populations exhibited remarkably high levels of reproductive output compared to those in large populations. Increased fruit production following supplemental hand-pollinations suggested that the lower reproductive output of naturally pollinated plants in large populations is a consequence of pollen limitation rather than limitation due to abiotic resources. This is consistent with increased intraspecific competition for pollination amongst plants in large populations. It is likely that the invasion of these milkweed species in Australia has been enhanced because plants in small founding populations experience less intraspecific competition for pollinators than those in large populations, and thus have the ability to produce copious amounts of seeds.     

Information thresholds,habitat loss and population persistence in breeding birds

The combination of spatial structure and non‐linear population dynamics can promote the persistence of coupled populations, even when the average population growth rate of the patches seen in isolation would predict otherwise. This phenomenon has generally been conceptualized and investigated through the movement of individuals among patches that each holds many individuals, as in metapopulation models. However, population persistence can likewise increase as the result of individuals moving among sites (e.g. breeding territories) within in a single patch. Here I examine the latter: individuals making small‐scale informed decisions with respect to where to breed can promote population persistence in poor environments. Based on a simple algebraic model, I demonstrate information thresholds, and predict that greater information use is required for population persistence under lower spatial heterogeneity in habitat quality, all else equal. Second, I implement an individual‐based model to explore prior experience and prospecting on conspecific success within a more complex, and spatially heterogeneous environment. Uniquely, I jointly examine the effects of simulated habitat loss, spatial heterogeneity prior to habitat, and variation in information gathering on population persistence. I find that habitat loss accelerates population quasi‐extinction risk; however, information use reduces extinction probabilities in proportion to the level of information gathering. Per capita reproductive success declines with number of breeding sites, suggesting that information‐mediated Allee effects may contribute to extinction risk. In conclusion, my study suggests that populations in a changing world may be increasingly vulnerable to extinction where patch size and spatial heterogeneity constrain the effectiveness of information‐use strategies.     

局域种群的Allee效应和集合种群的同步性

从包含Allee效应的局域种群出发,建立了耦合映像格子模型,即集合种群模型.通过分析和计算机模拟表明:(1)当局域种群受到Allee效应强度较大时,集合种群同步灭绝;(2)而当Allee效应强度相对较弱时,通过稳定局域种群动态(减少混沌)使得集合种群发生同步波动,而这种同步波动能够增加集合种群的灭绝风险;(3)斑块间的连接程度对集合种群同步波动的发生有很大的影响,适当的破碎化有利于集合种群的续存.全局迁移和Allee效应结合起来增加了集合种群同步波动的可能,从而增加集合种群的灭绝风险.这些结果对理解同步性的机理、利用同步机理来制定物种保护策略和害虫防治都有重要的意义.     

Allee effects, mating systems and the extinction risk in populations with two sexes

The Allee effect is one of the population consequences of sexual reproduction that has received increased attention in recent years. Due to its impact on small population dynamics, it is commonly accepted that Allee effects should render populations more extinction prone. In particular, monogamous species are considered more susceptible to the Allee effect and hence, more extinction prone, than polygamous species. Although this hypothesis has received theoretical support, there is little empirical evidence. In this study, we investigate (1) how variation in tertiary sex ratio affects the presence and intensity of the Allee effect induced by mating system, as well as (2) how this effect contributes to extinction risk. In contrast with previous predictions, we show that all mating systems are likely to experience a strong Allee effect when the operational sex ratio (OSR) is balanced. This strong Allee effect does not imply being exceptionally extinction prone because it is associated with an OSR that result in a relatively small extinction risk. As a consequence, the impact of Allee effects on overall extinction risk is buffered. Moreover, the OSR of natural populations appears to be often male biased, thus making it unlikely that they will suffer from an Allee effect induced by mating system.     

Interplay between Allee effects and collective movement in metapopulations

Population growth can be positively or negatively dependent on density. Therefore, the distribution pattern of individuals in a patchy environment can greatly affect the growth of each subpopulation and thereby of the metapopulation. When population growth presents positive density‐dependence (Allee effect), the distribution pattern becomes crucial, as small populations have an increased extinction risk. The way in which individuals move between patches largely determines the distribution pattern and thereby the population dynamics. Collective movement, in particular, should be expected to increase the potential number of colonisers and therefore the probability of colonising success. Here, we use mathematical modelling (differential equations and stochastic simulations) to study how collective movement can influence metapopulation dynamics when Allee effects are at stake. The models are inspired by the two‐spotted spider mite, a phytophagous pest of recognised agricultural importance. This sub‐social mite displays trail laying/following behaviour that can provoke collective movement. Moreover, experimental evidence suggests that it is subject to Allee effects. In the first part of this study we present a single‐species population growth model incorporating Allee effects, and study its properties. In the second part, this growth model is integrated into a larger simulation model consisting of a set of interconnected patches, in which the individuals move from one patch to the other either independently or collectively. Our results show that collective movement is more advantageous than independent dispersal only when Allee effects are present and strong enough. Furthermore they provide a theoretical framework that allows the quantification of the interplay between Allee effects and collective movement.     

Density dependent dispersal decisions and the Allee effect

The decision to move between patches in the environment is among the most important life history choices an organism can make. I derive a new density dependent dispersal rule, and examine how dispersal decisions based on avoiding fitness loss associated with an Allee effect or competitive effects impact upon population dynamics in spatially structured populations with qualitatively different dynamics. I also investigate the effects of the number of patches in the system and a limit to the patch sampling time available to dispersers. Dispersing to avoid competitive pressures can destabilise otherwise stable population dynamics, and stabilise chaotic dynamics. Dispersing to avoid an Allee effect does not qualitatively change local population dynamics until eventually driving unstable populations to global extinction with a sufficiently high fitness threshold. A time limit for sampling can stabilise dynamics if dispersal is based on escaping the Allee effect, and rescue populations from global extinction. The results are sensitive to the number of patches available in the environment and suggest that dispersal to avoid an Allee effect will only arise under biologically plausible conditions, i.e. where there is a limit to the number of dispersal attempts that can be made between generations.     

Modelling the mating system of polar bears: a mechanistic approach to the Allee effect

Allee effects may render exploited animal populations extinction prone, but empirical data are often lacking to describe the circumstances leading to an Allee effect. Arbitrary assumptions regarding Allee effects could lead to erroneous management decisions so that predictive modelling approaches are needed that identify the circumstances leading to an Allee effect before such a scenario occurs. We present a predictive approach of Allee effects for polar bears where low population densities, an unpredictable habitat and harvest-depleted male populations result in infrequent mating encounters. We develop a mechanistic model for the polar bear mating system that predicts the proportion of fertilized females at the end of the mating season given population density and operational sex ratio. The model is parametrized using pairing data from Lancaster Sound, Canada, and describes the observed pairing dynamics well. Female mating success is shown to be a nonlinear function of the operational sex ratio, so that a sudden and rapid reproductive collapse could occur if males are severely depleted. The operational sex ratio where an Allee effect is expected is dependent on population density. We focus on the prediction of Allee effects in polar bears but our approach is also applicable to other species.     

Density-dependent seed set in the Haleakala silversword: evidence for an Allee effect

Plant species may be subject to Allee effects if individuals experience a reduction in pollination services when populations are small or sparse. I examined temporal variation in reproductive success of the monocarpic Haleakala silversword (Argyroxiphium sandwicense subsp. macrocephalum) over five years, to determine if plants flowering out of synchrony with most of the population (i.e., in low flowering years) exhibited lower percent seed set than synchronously-flowering plants (i.e., those flowering in high flowering years). Through two pollination experiments conducted over multiple years, I also measured pollen limitation and self-incompatibility in this species. The number of flowering plants varied greatly among years, as did reproductive success. Percent seed set was significantly correlated with the number of plants flowering annually, such that plants flowering in high flowering years (1997 and 2001) exhibited significantly higher percent seed set than did plants flowering in low flowering years (1998-2000). In the 3-year pollen limitation study, plants flowering asynchronously were pollen-limited, whereas plants flowering synchronously were not. This species is strongly self-incompatible. Results of this study demonstrate that the Haleakala silversword experiences reduced reproductive success in low flowering years, and suggest that this Allee effect is pollinator-mediated. Allee effects in plants are an understudied yet potentially important force with implications for the population dynamics and conservation of rare species.     

Reproductive assurance through self-fertilization does not vary with population size in the alien invasive plant Datura stramonium

Autonomous self-fertilization is suggested to be associated with invasiveness in plants because it offers reproductive assurance when there is a shortage of suitable mates or pollinators. Given that shortages of mates and pollinators are a common cause of Allee effects in small plant populations, we predict that the benefits of self-fertilization in terms of reproductive assurance should be greatest in small populations. We tested this idea for the invasive herb Datura stramonium , a self-fertilizing species which is also cross-pollinated to some extent by insects (mainly hawkmoths and honeybees). During two consecutive years, we studied 20 and 55 populations, respectively, of different sizes. Untreated flowers of D. stramonium showed high levels of fruit and seed set in all populations studied. Although, fruit and seed set were generally reduced by about 90% in flowers in which self-fertilization was prevented through emasculation, this effect did not vary according to population size. By using a natural color (anthocyanin) dimorphism in 12 populations, we showed that the average outcrossing rate was low (1.3%) and that there was no relationship between outcrossing rate and population size. Pollen removal from flowers also did not vary according to population size, suggesting that the pollinator visitation rate is not lower in small populations. However, decreasing deviations of observed from expected fruit set with population size imply that small populations may have an increased chance of extinction due to demographic stochasticity. Overall, our results suggest that reproductive assurance through self-fertilization in invasive plants may be important for all stages of population establishment, and not just in the founder population.     

Dynamics of a small re-introduced population of wild dogs over 25 years: Allee effects and the implications of sociality for endangered species’ recovery

We analysed 25 years (1980–2004) of demographic data on a small re-introduced population of endangered African wild dogs (Lycaon pictus) in Hluhluwe-iMfolozi Park (HiP), South Africa, to describe population and pack dynamics. As small populations of cooperative breeders may be particularly prone to Allee effects, this extensive data set was used to test the prediction that, if Allee effects occur, aspects of reproductive success, individual survival and population growth should increase with pack and population size. The results suggest that behavioural aspects of wild dogs rather than ecological factors (i.e. competitors, prey and rainfall) primarily have been limiting the HiP wild dog population, particularly a low probability of finding suitable mates upon dispersal at low pack number (i.e. a mate-finding Allee effect). Wild dogs in HiP were not subject to component Allee effects at the pack level, most likely due to low interspecific competition and high prey availability. This suggests that aspects of the environment can mediate the strength of Allee effects. There was also no demographic Allee effect in the HiP wild dog population, as the population growth rate was significantly negatively related to population size, despite no apparent ecological resource limitation. Such negative density dependence at low numbers indicates that behavioural studies of the causal mechanisms potentially generating Allee effects in small populations can provide a key to understanding their dynamics. This study demonstrates how aspects of a species’ social behaviour can influence the vulnerability of small populations to extinction and illustrates the profound implications of sociality for endangered species’ recovery. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Combined impacts of Allee effects and parasitism

Despite their individual importance for population dynamics and conservation biology, the combined impacts of Allee effects and parasitism have received little attention. We built a mathematical model to compare the dynamics of populations with or without Allee effects when infected by microparasites. We show that the influence of an Allee effect takes the form of a tradeoff. The presence of an Allee effect in host populations may protect them, by reducing the range of population sizes that allow parasite spread. Yet if infection spreads, the Allee effect weakens host populations by reducing their size and by widening the range of parasite species that lead them to extinction. These results have important implications for predicting the survival of threatened populations or the success of reintroductions, and may help define size ranges within which given populations should be maintained to prevent both epidemics and Allee effects driven extinctions.     

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.     

Testing for ecological and genetic Allee effects in the invasive shrub Senna didymobotrya (Fabaceae)

For an introduced plant species to become invasive, it must be able to reproduce even in initially small populations. We tested for Allee effects (reduced reproductive performance of individuals in small populations) in the nonclonal, buzz-pollinated shrub Senna didymobotrya in its invasive range in South Africa. The species is self-compatible, but we found that in its invasive range in South Africa it requires pollinators to set seed. Nearly all stigmas (90%) received pollen, but natural fruit set was very low (3-20%). Pollen receipt and fruit set were not significantly correlated with population size. We thus found no evidence for an ecological Allee effect arising from pollen limitation in small populations. Offspring seedling performance, measured in terms of stem volume and leaf area, was also not significantly correlated with the number of plants in the source population, indicating that genetic Allee effects, such as inbreeding depression, are either absent or of such a small magnitude that they would be unlikely to limit further spread of S. didymobotrya in South Africa.     

Thresholds for impaired species recovery

Studies on small and declining populations dominate research in conservation biology. This emphasis reflects two overarching frameworks: the small-population paradigm focuses on correlates of increased extinction probability; the declining-population paradigm directs attention to the causes and consequences of depletion. Neither, however, particularly informs research on the determinants, rate or uncertainty of population increase. By contrast, Allee effects (positive associations between population size and realized per capita population growth rate, r_realized, a metric of average individual fitness) offer a theoretical and empirical basis for identifying numerical and temporal thresholds at which recovery is unlikely or uncertain. Following a critique of studies on Allee effects, I quantify population-size minima and subsequent trajectories of marine fishes that have and have not recovered following threat mitigation. The data suggest that threat amelioration, albeit necessary, can be insufficient to effect recovery for populations depleted to less than 10% of maximum abundance (N_max), especially when they remain depleted for lengthy periods of time. Comparing terrestrial and aquatic vertebrates, life-history analyses suggest that population-size thresholds for impaired recovery are likely to be comparatively low for marine fishes but high for marine mammals. Articulation of a ‘recovering population paradigm’ would seem warranted. It might stimulate concerted efforts to identify generic impaired recovery thresholds across species. It might also serve to reduce the confusion of terminology, and the conflation of causes and consequences with patterns currently evident in the literature on Allee effects, thus strengthening communication among researchers and enhancing the practical utility of recovery-oriented research to conservation practitioners and resource managers.