Allee effects may slow the spread of parasites in a coastal marine ecosystem

Allee effects are thought to mediate the dynamics of population colonization, particularly for invasive species. However, Allee effects acting on parasites have rarely been considered in the analogous process of infectious disease establishment and spread. We studied the colonization of uninfected wild juvenile Pacific salmon populations by ectoparasitic salmon lice (Lepeophtheirus salmonis) over a 4-year period. In a data set of 68,376 fish, we observed 85 occurrences of precopular pair formation among 1,259 preadult female and 613 adult male lice. The probability of pair formation was dependent on the local abundance of lice, but this mate limitation is likely offset somewhat by mate-searching dispersal of males among host fish. A mathematical model of macroparasite population dynamics that incorporates the empirical results suggests a high likelihood of a demographic Allee effect, which can cause the colonizing parasite populations to die out. These results may provide the first empirical evidence for Allee effects in a macroparasite. Furthermore, the data give a rare detailed view of Allee effects in colonization dynamics and suggest that Allee effects may dampen the spread of parasites in a coastal marine ecosystem.     

Allee effects limit population viability of an annual plant

ABSTRACT Allee effects may be experienced by plants when populations are too small or isolated to receive sufficient pollinator services to replace themselves. This article reports experimental data from an annual herb, Clarkia concinna, documenting that small patches suffered reproductive failure due to lack of effective pollination when critical thresholds of isolation were exceeded. In contrast, sufficiently large patches attracted pollinators regardless of their degree of isolation. These data accord with data on patch extinctions showing that small and isolated patches have a higher extinction rate than do large patches and with observations showing chronically low reproductive success in such patches prior to extinction. While not conclusively demonstrating that Allee effects cause extinction in small and isolated patches, the data are suggestive. Although threshold effects have been postulated in several mathematical models of population viability, this is the first report of data from natural populations that display the occurrence of such thresholds. These results have implications for the management of endangered plants, which often are restricted to isolated, small populations, as well as suggesting a potential limit to spatial spread in plant populations dependent on animal vectors for reproduction.     

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.     

Allee effects in biological invasions

Understanding the dynamics of small populations is obviously important for declining or rare species but is also particularly important for invading species. The Allee effect, where fitness is reduced when conspecific density is low, can dramatically affect the dynamics of biological invasions. Here, we summarize the literature of Allee effects in biological invasions, revealing an extensive theory of the consequences of the Allee effect in invading species and some empirical support for the theory. Allee effects cause longer lag times, slower spread and decreased establishment likelihood of invasive species. Expected spatial ranges, distributions and patterns of species may be altered when an Allee effect is present. We examine how the theory can and has been used to detect Allee effects in invasive species and we discuss how the presence of an Allee effect and its successful or unsuccessful detection may affect management of invasives. The Allee effect has been shown to change optimal control decisions, costs of control and the estimation of the risk posed by potentially invasive species. Numerous ways in which the Allee effect can influence the efficacy of biological control are discussed.     

Dose-dependent infection rates of parasites produce the Allee effect in epidemiology

In many epidemiological models of microparasitic infections it is assumed that the infection process is governed by the mass-action principle, i.e. that the infection rate per host and per parasite is a constant. Furthermore, the parasite-induced host mortality (parasite virulence) and the reproduction rate of the parasite are often assumed to be independent of the infecting parasite dose. However, there is empirical evidence against those three assumptions: the infection rate per host is often found to be a sigmoidal rather than a linear function of the parasite dose to which it is exposed; and the lifespan of infected hosts as well as the reproduction rate of the parasite are often negatively correlated with the parasite dose. Here, we incorporate dose dependences into the standard modelling framework for microparasitic infections, and draw conclusions on the resulting dynamics. Our model displays an Allee effect that is characterized by an invasion threshold for the parasite. Furthermore, in contrast to standard epidemiological models a parasite strain needs to have a basic reproductive rate that is substantially greater than 1 to establish an infection. Thus, the conditions for successful invasion of the parasite are more restrictive than in mass-action infection models. The analysis further suggests that negative correlations of the parasite dose with host lifespan and the parasite reproduction rate helps the parasite to overcome the invasion constraints of the Allee-type dynamics.     

Genetic Allee effects on performance, plasticity and developmental stability in a clonal plant

Negative effects of small population size on fitness, so-called Allee effects, may threaten population persistence even in intact habitat remnants. We studied genotypes of 14 isolated populations of the clonal plant Ranunculus reptans, for which molecular genetic (RAPD-) variability is higher for large than for small populations. In a competition-free greenhouse environment vegetative offspring of genotypes from large populations produced more rosettes and flowers, indicating higher fitness. Within-genotype coefficients of variation in performance traits, indicating developmental instability, were lower for genotypes from populations with higher RAPD-variability. In competition with a taller grass, we found relative reduction in leaf length less pronounced for plants from large populations, suggesting higher adaptive plasticity. Our experimental study of a plant with predominantly vegetative reproduction suggests, that negative genetic effects of recent habitat fragmentation, which so far rather were expected in plants with frequent sexual reproduction, are more severe and more common than previously acknowledged.     

The evidence for Allee effects

Allee effects are an important dynamic phenomenon believed to be manifested in several population processes, notably extinction and invasion. Though widely cited in these contexts, the evidence for their strength and prevalence has not been critically evaluated. We review results from 91 studies on Allee effects in natural animal populations. We focus on empirical signatures that are used or might be used to detect Allee effects, the types of data in which Allee effects are evident, the empirical support for the occurrence of critical densities in natural populations, and differences among taxa both in the presence of Allee effects and primary causal mechanisms. We find that conclusive examples are known from Mollusca, Arthropoda, and Chordata, including three classes of vertebrates, and are most commonly documented to result from mate limitation in invertebrates and from predator–prey interactions in vertebrates. More than half of studies failed to distinguish component and demographic Allee effects in data, although the distinction is crucial to most of the population-level dynamic implications associated with Allee effects (e.g., the existence of an unstable critical density associated with strong Allee effects). Thus, although we find conclusive evidence for Allee effects due to a variety of mechanisms in natural populations of 59 animal species, we also find that existing data addressing the strength and commonness of Allee effects across species and populations is limited; evidence for a critical density for most populations is lacking. We suggest that current studies, mainly observational in nature, should be supplemented by population-scale experiments and approaches connecting component and demographic effects. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Allee effects under climate change

Understanding how climate change affects population dynamics is crucial for assessing future of biodiversity. Here I ask how can Allee effects, occurring when mean individual fitness is reduced in rare populations, respond to increasing temperature. Despite the role Allee effects play in ecology of invasive, threatened and harvested populations, impacts of climate change on Allee effects are practically unknown. Analysis of two population models reveals that whereas the Allee effect driven by predation generally weakens as temperature increases, the Allee effect due to need of finding mates is predicted to become stronger when warming occurs. For the former model, the metabolic theory suggests that with increasing temperature prey growth rate should increase faster than predator attack rate. Increasing temperature thus weakens the Allee effect. In the latter, gypsy moth population model, mating rate increases with warming due to enhanced female?male encounter rate and temperature‐induced modifications in female and male adult emergence distributions. However, male and female mortality rates increase, too and the net effect is strengthening of the Allee effect. These results have repercussions also for pest control, indicating that augmentation of biocontrol agents may perhaps be not as effective as using pesticides or disrupting mating.     

The maintenance of sex in parasites

The maintenance of sex is an unresolved paradox in evolutionary biology, given the inherent twofold fitness advantage for asexuals. Parasitic helminths offer a unique opportunity to address this enigma. Parasites that can create novel antigenic strains are able to escape pre-existing host immunity. Viruses produce diversity through mutation with rapid clonal proliferation. The long generation times of helminth parasites prevent them from adopting this strategy. Instead, we argue that sexual reproduction enables parasitic helminths to rapidly generate strain diversity. We use both a stochastic, individual-based model and a simple analytical model to assess the selective value of sexual versus asexual reproduction in helminth parasites. We demonstrate that sexual reproduction can more easily produce and maintain strain diversity than asexual reproduction for long-lived parasites. We also show that sexual parasite populations are resistant to invasion by rare asexual mutants. These results are robust to high levels of cross-immunity between strains. We suggest that the enhancement of strain diversity, despite stochastic extinction of strains, may be critical to the evolutionary success of sex in long-lived parasites.     

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.     

集合种群的Allee效应研究进展

随着全球环境破坏的加剧,物种丧失的速度加快,人们日益关注生物多样性的保护。种群生物学和自然保护生物学的一些研究表明,如果一个局域种群受到Allee效应的影响,最终可能走向灭绝。从物种保护的角度考虑,分别介绍了集合种群水平上的Allee效应的和似Allee效应,比较了集合种群的Allee效应和似Allee效应产生的原因,以及集合种群的Allee效应和局域种群的Allee效应之间的关系、集合种群的似Allee效应和局域种群的Allee效应之间的关系,并提出集合种群的Allee效应还需要进一步的研究。     

Multiple Allee effects and population management

Allee effects, strongly related to the extinction vulnerability of populations and gradually becoming acknowledged by both theoretically oriented and applied ecologists, have already been shown to have important roles in the dynamics of many populations. Although not yet widely recognized, two or more Allee effects can occur simultaneously in the same population. Here, we review the evidence for multiple Allee effects and show that their interactions can take several forms, many of which are far from inconsequential. We suggest that more research is needed to assess the prevalence and interactions of multiple Allee effects, as failing to take them into account could have adverse consequences for the management of threatened or exploited populations.     

Evolutionary dynamics and strong Allee effects

We describe the dynamics of an evolutionary model for a population subject to a strong Allee effect. The model assumes that the carrying capacity k(u), inherent growth rate r(u), and Allee threshold a(u) are functions of a mean phenotypic trait u subject to evolution. The model is a plane autonomous system that describes the coupled population and mean trait dynamics. We show bounded orbits equilibrate and that the Allee basin shrinks (and can even disappear) as a result of evolution. We also show that stable non-extinction equilibria occur at the local maxima of k(u) and that stable extinction equilibria occur at local minima of r(u). We give examples that illustrate these results and demonstrate other consequences of an Allee threshold in an evolutionary setting. These include the existence of multiple evolutionarily stable, non-extinction equilibria, and the possibility of evolving to a non-evolutionary stable strategy (ESS) trait from an initial trait near an ESS.     

Cross-talk between jasmonate and salicylate plant defense pathways: effects on several plant parasites

Plants are often attacked by many herbivorous insects and pathogens at the same time. Two important suites of responses to attack are mediated by plant hormones, jasmonate and salicylate, which independently provide resistance to herbivorous insects and pathogens, respectively. Several lines of evidence suggest that there is negative cross-talk between the jasmonate and salicylate response pathways. This biochemical link between general plant defense strategies means that deploying defenses against one attacker can positively or negatively affect other attackers. In this study, we tested for cross-talk in the jasmonate and salicylate signaling pathways in a wild tomato and examined the effects of cross-talk on an array of herbivores of cultivated tomato plants. In the wild cultivar, induction of defenses signaled by salicylate reduced biochemical expression of the jasmonate pathway but did not influence performance of S. exigua caterpillars. This indicates that the signal interaction is not a result of agricultural selection. In cultivated tomato, biochemical attenuation of the activity of a defense protein (polyphenol oxidase) in dual-elicited plants resulted in increased of performance of cabbage looper caterpillars, but not thrips, spider mites, hornworm caterpillars or the bacteria Pseudomonas syringae pv. tomato. In addition, we tested the effects of jasmonate-induced resistance on the ability of thrips to vector tomato spotted wilt virus. Although thrips fed less on induced plants, this did not affect the level of disease. Thus, the negative interaction between jasmonate and salicylate signaling had biological consequences for two lepidopteran larvae but not for several other herbivores tested or on the spread of a disease.     

Incorporating Allee effects into reintroduction strategies

Allee effects, the reduction of vital rates at low population densities, can occur through several mechanisms, all of which potentially apply to reintroduced populations. Reintroduced populations are initially at low densities, hence Allee effects can potentially lead to reintroduction failure despite habitat quality being sufficient to allow long-term persistence if the population survived the establishment phase. The probability of such failures can potentially be reduced by releasing large numbers of organisms, by reducing post-release dispersal or mortality through management, or by directly managing the Allee effects, e.g., by implementing predator control or food supplementation until population size increases. However, such measures incur costs, as large releases have a greater impact on source populations, and management actions require financial and other resources. It is therefore essential to compare the costs and benefits of attempting to reduce Allee effects in reintroduction programs. Here we advocate the use of structured decision-making frameworks whereby alternative strategies are nominated, probability distributions of outcomes obtained under different strategies, and utilities assigned to different outcomes. We illustrate the potential application of such decision frameworks using projections from a stochastic population model including Allee effects. As there will seldom be estimates of Allee effects available from the species or system involved, it will be necessary to predict these effects based on the biology of the species and data from other systems. In doing so, it is important to identify mechanisms for proposed Allee effects, and to avoid misleading inferences from correlations subject to confounds. In particular, naive interpretations of correlations between numbers released and reintroduction success may exaggerate the benefits of releasing large numbers.     

Evolutionary dynamics and strong Allee effects

We describe the dynamics of an evolutionary model for a population subject to a strong Allee effect. The model assumes that the carrying capacity k(u), inherent growth rate r(u), and Allee threshold a(u) are functions of a mean phenotypic trait u subject to evolution. The model is a plane autonomous system that describes the coupled population and mean trait dynamics. We show bounded orbits equilibrate and that the Allee basin shrinks (and can even disappear) as a result of evolution. We also show that stable non-extinction equilibria occur at the local maxima of k(u) and that stable extinction equilibria occur at local minima of r(u). We give examples that illustrate these results and demonstrate other consequences of an Allee threshold in an evolutionary setting. These include the existence of multiple evolutionarily stable, non-extinction equilibria, and the possibility of evolving to a non-evolutionary stable strategy (ESS) trait from an initial trait near an ESS.     

Allee effects and extinction in a lattice model

In the interest of conservation, the importance of having a large habitat available for a species is widely known. Here, we introduce a lattice-based model for a population and look at the importance of fluctuations as well as that of the population density, particularly with respect to Allee effects. We examine the model analytically and by Monte Carlo simulations and find that, while the size of the habitat is important, there exists a critical population density below which the probability of extinction is greatly increased. This has large consequences with respect to conservation, especially in the design of habitats and for populations whose density has become small. In particular, we find that the probability of survival for small populations can be increased by a reduction in the size of the habitat and show that there exists an optimal size reduction.     

Allee effects and extinction in a lattice model

In the interest of conservation, the importance of having a large habitat available for a species is widely known. Here, we introduce a lattice-based model for a population and look at the importance of fluctuations as well as that of the population density, particularly with respect to Allee effects. We examine the model analytically and by Monte Carlo simulations and find that, while the size of the habitat is important, there exists a critical population density below which the probability of extinction is greatly increased. This has large consequences with respect to conservation, especially in the design of habitats and for populations whose density has become small. In particular, we find that the probability of survival for small populations can be increased by a reduction in the size of the habitat and show that there exists an optimal size reduction.