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.     

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.     

滨海湿地植物种群Allee效应驱动机制研究进展

Allee效应是指生物个体适应度与种群规模或密度之间呈正向关联的现象,因与植物种群动态和种群灭绝密切相关而受到生态学家的普遍重视。阐释多重胁迫下滨海湿地植物种群响应机制,从保护生物多样性和维持生态系统稳定性层面发展系统性生态修复措施成为相关研究关注的重点。本研究分别从遗传过程、花粉扩散过程和生物互作关系不同层面,总结分析了植物种群Allee效应驱动机制的研究进展。一方面,植物因遗传过程中近交衰退、遗传变异丧失、有害突变累积等遗传结构改变造成繁殖失败而引发Allee效应;另一方面,植物花粉扩散过程和动植物互作关系影响下的花粉限制也通过影响植物种群繁殖力成为驱动Allee效应的关键因素。滨海湿地水盐梯度变异及格局破碎化影响下,植物种群遭受Allee效应的风险需引起关注,维持滨海湿地植物种群适宜分布格局和生物连通过程成为缓解Allee效应的重要手段。结合生理学与化学生态学研究手段和长时间尺度动态监测技术,有助于进一步阐释环境及生物等多重胁迫下Allee效应的非线性驱动机制。     

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.     

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效应对具有生境恢复的集合种群的影响

Allee效应与种群的灭绝密切相关,其研究对生态保护和管理至关重要。Allee效应对物种续存是潜在的干扰因素,濒危物种更容易受其影响,可能会增加生存于生境破碎化斑块的濒危物种的死亡风险,因此研究Allee效应对种群的动态和续存的影响是必要的。从包含由生物有机体对环境的修复产生的Allee效应的集合种群模型出发,引入由其他机制形成的Allee效应,建立了常微分动力系统模型和基于网格模型的元胞自动机模型。通过理论分析和计算机模拟表明:(1)强Allee效应不利于具有生境恢复的集合种群的续存;(2)生境恢复有利于种群续存;(3)局部扩散影响了集合种群的空间结构、动态行为和稳定性,生境斑块之间的局部作用将会减缓或消除集合种群的Allee效应,有利于集合种群的续存。     

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.     

Generalizing Levins metapopulation model in explicit space: models of intermediate complexity

A recent study [Harding and McNamara, 2002. A unifying framework for metapopulation dynamics. Am. Nat. 160, 173-185] presented a unifying framework for the classic Levins metapopulation model by incorporating several realistic biological processes, such as the Allee effect, the Rescue effect and the Anti-rescue effect, via appropriate modifications of the two basic functions of colonization and extinction rates. Here we embed these model extensions on a spatially explicit framework. We consider population dynamics on a regular grid, each site of which represents a patch that is either occupied or empty, and with spatial coupling by neighborhood dispersal. While broad qualitative similarities exist between the spatially explicit models and their spatially implicit (mean-field) counterparts, there are also important differences that result from the details of local processes. Because of localized dispersal, spatial correlation develops among the dynamics of neighboring populations that decays with distance between patches. The extent of this correlation at equilibrium differs among the metapopulation types, depending on which processes prevail in the colonization and extinction dynamics. These differences among dynamical processes become manifest in the spatial pattern and distribution of “clusters” of occupied patches. Moreover, metapopulation dynamics along a smooth gradient of habitat availability show significant differences in the spatial pattern at the range limit. The relevance of these results to the dynamics of disease spread in metapopulations is discussed.     

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-like effects in metapopulation dynamics

The existences of the Allee effect at the local population level and of the Allee-like effect at the metapopulation level are important for both ecology and conservation. Although there have been a great many papers on the Allee effect, they have mainly referred to only local populations and have not dealt with the relationship between the two. In this paper, we begin with local population dynamics and then construct a model including both local population and metapopulation dynamics. Then we simulate with computer at these two levels. The results indicate that the Allee-like effect in a metapopulation may emerge from the imposed Allee effect at the local population level. This threshold fraction of occupied patches below which the metapopulation goes extinct is seriously affected by the per capita migration rate, the survival rate during migration and the initial population size on the occupied patches. We also find that severe demographic stochasticity may compound the metapopulation extinction risk posed by the Allee effect. These conclusions are helpful for nature conservation, especially for the preservation of rare species.     

Dangerously few liaisons: a review of mate-finding Allee effects

In this paper, we review mate-finding Allee effects from ecological and evolutionary points of view. We define ‘mate-finding’ as mate searching in mobile animals, and also as the meeting of gametes for sessile animals and plants (pollination). We consider related issues such as mate quality and choice, sperm limitation and physiological stimulation of reproduction by conspecifics, as well as discussing the role of demographic stochasticity in generating mate-finding Allee effects. We consider the role of component Allee effects due to mate-finding in generating demographic Allee effects (at the population level). Compelling evidence for demographic Allee effects due to mate-finding (as well as via other mechanisms) is still limited, due to difficulties in censusing rare populations or a failure to identify underlying mechanisms, but also because of fitness trade-offs, population spatial structure and metapopulation dynamics, and because the strength of component Allee effects may vary in time and space. Mate-finding Allee effects act on individual fitness and are thus susceptible to change via natural selection. We believe it is useful to distinguish two routes by which evolution can act to mitigate mate-finding Allee effects. The first is evolution of characteristics such as calls, pheromones, hermaphroditism, etc. which make mate-finding more efficient at low density, thus eliminating the Allee effect. Such adaptations are very abundant in the natural world, and may have arisen to avoid Allee effects, although other hypotheses are also possible. The second route is to avoid low density via adaptations such as permanent or periodic aggregation. In this case, the Allee effect is still present, but its effects are avoided. These two strategies may have different consequences in a world where many populations are being artificially reduced to low density: in the first case, population growth rate can be maintained, while in the second case, the mechanism to avoid Allee effects has been destroyed. It is therefore in these latter populations that we predict the greatest evidence for mate-finding Allee effects and associated demographic consequences. This idea is supported by the existing empirical evidence for demographic Allee effects. Given a strong effect that mate-finding appears to have on individual fitness, we support the continuing quest to find connections between component mate-finding Allee effects (individual reproductive fitness) and the demographic consequences. There are many reasons why such studies are difficult, but it is important, particularly given the increasing number of populations and species of conservation concern, that the ecological community understands more about how widespread demographic Allee effects really are, and why.     

Evolution of dispersal in metapopulations with local density dependence and demographic stochasticity

In this paper, we predict the outcome of dispersal evolution in metapopulations based on the following assumptions: (i) population dynamics within patches are density-regulated by realistic growth functions; (ii) demographic stochasticity resulting from finite population sizes within patches is accounted for; and (iii) the transition of individuals between patches is explicitly modelled by a disperser pool. We show, first, that evolutionarily stable dispersal rates do not necessarily increase with rates for the local extinction of populations due to external disturbances in habitable patches. Second, we describe how demographic stochasticity affects the evolution of dispersal rates: evolutionarily stable dispersal rates remain high even when disturbance-related rates of local extinction are low, and a variety of qualitatively different responses of adapted dispersal rates to varied levels of disturbance become possible. This paper shows, for the first time, that evolution of dispersal rates may give rise to monotonically increasing or decreasing responses, as well as to intermediate maxima or minima.     

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.     

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.     

Evolutionary suicide and evolution of dispersal in structured metapopulations

 We study the evolution of dispersal in a structured metapopulation model. The metapopulation consists of a large (infinite) number of local populations living in patches of habitable environment. Dispersal between patches is modelled by a disperser pool and individuals in transit between patches are exposed to a risk of mortality. Occasionally, local catastrophes eradicate a local population: all individuals in the affected patch die, yet the patch remains habitable. We prove that, in the absence of catastrophes, the strategy not to migrate is evolutionarily stable. Under a given set of environmental conditions, a metapopulation may be viable and yet selection may favor dispersal rates that drive the metapopulation to extinction. This phenomenon is known as evolutionary suicide. We show that in our model evolutionary suicide can occur for catastrophe rates that increase with decreasing local population size. Evolutionary suicide can also happen for constant catastrophe rates, if local growth within patches shows an Allee effect. We study the evolutionary bifurcation towards evolutionary suicide and show that a discontinuous transition to extinction is a necessary condition for evolutionary suicide to occur. In other words, if population size smoothly approaches zero at a boundary of viability in parameter space, this boundary is evolutionarily repelling and no suicide can occur. Received: 10 November 2000 / Revised version: 13 February 2002 / Published online: 17 July 2002     

Determinism in a transient assemblage: the roles of dispersal and local competition

Both dispersal and local competitive ability may determine the outcome of competition among species that cannot coexist locally. I develop a spatially implicit model of two-species competition at a small spatial scale. The model predicts the relative fitness of two competitors based on local reproductive rates and regional dispersal rates in the context of the number, size, and extinction probability of habitat patches in the landscape. I test the predictions of this model experimentally using two genotypes of the bacteriophagous soil nematode Caenorhabditis elegans in patchy microcosms. One genotype has higher fecundity while the other is a better disperser. With such a fecundity-dispersal trade-off between competitors, the model predicts that relative fitness will be affected most by local population size when patches do not go extinct and by the number of patches when there is a high probability of patch extinction. The microcosm experiments support the model predictions. Both approaches suggest that competitive dominance in a patchily distributed transient assemblage will depend upon the architecture and predictability of the environment. These mechanisms, operating at a small scale with high spatial admixture, may be embedded in a larger metacommunity process.     

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.     

Regional and local scale metapopulation dynamics in the interaction between Callosobruchus maculatus and Anisopteromalus calandrae

Habitat structure increases the persistence of many extinction‐prone resource–consumer interactions. Metapopulation theory is one of the leading approaches currently used to explain why local, ephemeral populations persist at a regional scale. Central to the metapopulation concept is the amount of dispersal occurring between patches, too much or too little can result in regional extinction. In this study, the role of dispersal on the metapopulation dynamics of an over‐exploitative host–parasitoid interaction is assessed. In the absence of the parasitoid the highly vagile bruchid, Callosobruchus maculatus, can maintain a similar population size regardless of the permeability of the inter‐patch matrix and exhibits strong negative density‐dependence. After the introduction of the parasitoid the size of the bruchid population decreases with a corresponding increase in the occurrence of empty patches. In this case, limiting the dispersal of both species decouples the interaction to a greater extent and results in larger regional bruchid populations. Given the disparity between the dispersal rates of the two species, it is proposed that the more dispersive host benefits from the reduction in landscape permeability by increasing the opportunity to colonise empty patches and rescue extinction prone populations. Associated with the introduction of the parasitoid is a shift in the strength of density‐dependence as the population moves from bottom–up towards top–down regulation. The importance of local and regional scale measurements is apparent when the role of individual patches on regional dynamics is considered. By only taking regional dynamics into account the importance of dispersal regime on local dynamics is overlooked. Similarly, when local dynamics were examined, patches were found to have different influences on regional dynamics depending on dispersal regime and patch location.