Showing papers on "Allee effect published in 2008"

Allee Effects in Ecology and Conservation

Abstract: 1. What are Allee effects? 2. Mechanisms for Allee effects 3. Population dynamics: modelling demographic Allee effects 4. Genetics and evolution 5. Conservation and management 6. Conclusions and perspectives

Population ecology of insect invasions and their management

Abstract: During the establishment phase of a biological invasion, population dynamics are strongly influenced by Allee effects and stochastic dynamics, both of which may lead to extinction of low-density populations. Allee effects refer to a decline in population growth rate with a decline in abundance and can arise from various mechanisms. Strategies to eradicate newly established populations should focus on either enhancing Allee effects or suppressing populations below Allee thresholds, such that extinction proceeds without further intervention. The spread phase of invasions results from the coupling of population growth with dispersal. Reaction-diffusion is the simplest form of spread, resulting in continuous expansion and asymptotically constant radial rates of spread. However, spread of most nonindigenous insects is characterized by occasional long-distance dispersal, which results in the formation of isolated colonies that grow, coalesce, and greatly increase spread. Allee effects also affect spread, generally in a negative fashion. Efforts to slow, stop, or reverse spread should incorporate the spread dynamics unique to the target species.

Population Viability Analysis

Abstract: Population viability analysis (PVA) refers to the set of ideas, theoretical models, and conceptual and computational tools ecologists use to understand extinction risk and to forecast future scenarios of population growth and decline. PVA focuses on four phenomena that affect extinction risk of small populations: demographic stochasticity, environmental stochasticity, Allee effects, and inbreeding depression. PVAs fall into two categories. Analytical models are idealized mathematical models of population dynamics and are used to understand general principles of extinction risk. Computational models are more complex and are used to perform risk assessment for endangered populations. The cost of this complexity is relinquishing intuitive understanding of the drivers of population fluctuations. Simple examples of each class of models are illustrated with data on grizzly bear population fluctuations in Yellowstone National Park. Advances in PVA methodology have been rapid and continued progress promises to improve population management for threatened and endangered populations.

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

Abstract: 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.

Evolution of phenotypic clusters through competition and local adaptation along an environmental gradient

Abstract: We have analyzed the evolution of a quantitative trait in populations that are spatially extended along an environmental gradient, with gene flow between nearby locations. In the absence of competition, there is stabilizing selection toward a locally best-adapted trait that changes gradually along the gradient. According to traditional ideas, gradual spatial variation in environmental conditions is expected to lead to gradual variation in the evolved trait. A contrasting possibility is that the trait distribution instead breaks up into discrete clusters. Doebeli and Dieckmann (2003) argued that competition acting locally in trait space and geographical space can promote such clustering. We have investigated this possibility using deterministic population dynamics for asexual populations, analyzing our model numerically and through an analytical approximation. We examined how the evolution of clusters is affected by the shape of competition kernels, by the presence of Allee effects, and by the strength of gene flow along the gradient. For certain parameter ranges clustering was a robust outcome, and for other ranges there was no clustering. Our analysis shows that the shape of competition kernels is important for clustering: the sign structure of the Fourier transform of a competition kernel determines whether the kernel promotes clustering. Also, we found that Allee effects promote clustering, whereas gene flow can have a counteracting influence. In line with earlier findings, we could demonstrate that phenotypic clustering was favored by gradients of intermediate slope.

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

Abstract: 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.

Dispersion in time and space affect mating success and Allee effects in invading gypsy moth populations.

Abstract: 1. Understanding why invading populations sometimes fail to establish is of considerable relevance to the development of strategies for managing biological invasions. 2. Newly arriving populations tend to be sparse and are often influenced by Allee effects. Mating failure is a typical cause of Allee effects in low-density insect populations, and dispersion of individuals in space and time can exacerbate mate-location failure in invading populations. 3. Here we evaluate the relative importance of dispersal and sexual asynchrony as contributors to Allee effects in invading populations by adopting as a case study the gypsy moth (Lymantria dispar L.), an important insect defoliator for which considerable demographic information is available. 4. We used release-recapture experiments to parameterize a model that describes probabilities that males locate females along various spatial and temporal offsets between male and female adult emergence. 5. Based on these experimental results, we developed a generalized model of mating success that demonstrates the existence of an Allee threshold, below which introduced gypsy moth populations are likely to go extinct without any management intervention.

Allee effect limits colonization success of sexually reproducing zooplankton

Abstract: Understanding the dynamics of populations at low density and the role of Allee effects is a priority due to concern about the decline of rare species and interest in colonization/invasion dynamics. Despite well-developed theory and observational support, experimental examinations of the Allee effect in natural systems are rare, partly because of logistical difficulties associated with experiments at low population density. We took advantage of fish introduction and removal in alpine lakes to experimentally test for the Allee effect at the whole-ecosystem scale. The large copepod Hesperodiaptomus shoshone is often extirpated from the water column by fish and sometimes fails to recover following fish disappearance, despite the presence of a long-lived egg bank. Population growth rate of this dioecious species may be limited by mate encounter rate, such that below some critical density a colonizing population will fail to establish. We conducted a multi-lake experiment in which H. shoshone was stocked at densities that bracketed our hypothesized critical density of 0.5-5 copoepods/m3. Successful recovery by the copepod was observed only in the lake with the highest initial density (3 copepods/m3). Copepods stocked into small cages at 3000 copepods/m3 survived and reproduced at rates comparable to natural populations, confirming that the lakes were suitable habitat for this species. In support of mate limitation as the mechanism underlying recovery failure, we found a significant positive relationship between mating success and density across experimental and natural H. shoshone populations. Furthermore, a mesocosm experiment provided evidence of increased per capita population growth rate with increasing population density in another diaptomid species, Skistodiaptomus pallidus. Together, these lines of evidence support the importance of the Allee effect to population recovery of H. shoshone in the Sierra Nevada, and to diaptomid copepods in general.

Reproductive asynchrony in natural butterfly populations and its consequences for female matelessness

Abstract: Summary 1. Reproductive asynchrony, where individuals in a population are short-lived relative to the population-level reproductive period, has been identified recently as a theoretical mechanism of the Allee effect that could operate in diverse plant and insect species. The degree to which this effect impinges on the growth potential of natural populations is not yet well understood. 2. Building on previous models of reproductive timing, we develop a general framework that allows a detailed, quantitative examination of the reproductive potential lost to asynchrony in small natural populations. 3. Our framework includes a range of biologically plausible submodels that allow details of mating biology of different species to be incorporated into the basic reproductive timing model. 4. We tailor the parameter estimation methods of the full model (basic model plus mating biology submodels) to take full advantage of data from detailed field studies of two species of Parnassius butterflies whose mating status may be assessed easily in the field. 5. We demonstrate that for both species, a substantial portion of the female population (6·5‐ 18·6%) is expected to die unmated. These analyses provide the first direct, quantitative evidence of female reproductive failure due to asynchrony in small natural populations, and suggest that reproductive asynchrony exerts a strong and largely unappreciated influence on the population dynamics of these butterflies and other species with similarly asynchronous reproductive phenology.

Allee Effect and Self-Fertilization in Hermaphrodites: Reproductive Assurance in a Structured Metapopulation

Abstract: Reproductive assurance through selfing during colonization events or when population densities are low has often been put forward as a mechanism selecting for the evolution of self-fertilization. Such arguments emphasize on the role of both local demography and metapopulation processes. We developed a model for the evolution of self-fertilization in a structured metapopulation in which local densities are not steady because of population growth. Reproduction by selfing is density-independent (reproductive assurance) but selfed seeds endure inbreeding depression, whereas reproduction by outcrossing is density-dependent (Allee effect). First, we derived an analytical criterion for metapopulation viability as a function of the selfing rate and metapopulation parameters. We show that outcrossers can develop a viable metapopulation when they produce a high amount of dispersal seeds that counterbalances their incapacity to found new populations from low densities. Second, the model shows there is a positive feedback between demography and outcrossing rates, leading to either complete outcrossing or selfing. Specifically, we illustrate that inbreeding depression can paradoxically favor the evolution of selfing because of its negative effect on density. Also, complete outcrossing can be selected despite pollen limitation, although it does not provide a full seed set. This model underlines the influence of the mating system both on demography and gene dynamics in a metapopulation context.

A population facing climate change : joint influences of Allee effects and environmental boundary geometry

Abstract: As a result of climate change, many populations have to modify their range to follow the suitable areas—their “climate envelope”—often risking extinction. During this migration process, they may face absolute boundaries to dispersal because of external environmental factors. Consequently, not only the position, but also the shape of the climate envelope can be modified. We use a reaction-diffusion model to analyse the effects on population persistence of simultaneous changes in the position and shape of the climate envelope. When the growth term is of logistic type, we show that extinction and persistence are principally conditioned by the species mobility and the speed of climate change, but not by the shape of the climate envelope. However, with a growth term taking an Allee effect into account, we find a high sensitivity to variations in the shape of the climate envelope. In this case, the species which have a high mobility, although they could more easily follow the migration of the climate envelope, would be at risk of extinction when encountering a local narrowing of the boundary geometry. This effect can be attenuated by a progressive opening at the exit of the narrowing into the available space, even though this leads temporarily to a diminished area of the climate envelope.

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

Abstract: Summary • 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.

Control of invasive hosts by generalist parasitoids.

Abstract: This article was motivated by the invasion of leaf-mining microlepidopteron attacking horse chestnut trees in Europe and the need for a biological control. Following Owen & Lewis (2001, Bull. Math. Biol., 63, 655-684), we consider predation of leafminers by a generalist parasitoid with a Holling Type II functional response. We first identified six equilibrium points and discussed their stabilities in the non-spatial model. The model always predicts persistence of the parasitoid. Depending on the parameter values, the model may predict that the host persists and goes extinct or there is something like an Allee effect where the outcome depends on the initial host density. Special cases were also studied for small carrying capacities leading to complex dynamical behaviours. Then, numerical simulations of the spatial reaction--diffusion model enabled us to identify the conditions for which the leafminer's advance can be stopped and reversed by parasitoids. Compared to the ordinary differential equation model, the incorporation of space, combined with the polyphagy of the parasitoid, leads to a decrease of the parameter domain of coexistence. This is in stark to several other models in which space promotes coexistence by enabling hosts to escape.

Allee effects on population dynamics with delay

Abstract: In this paper, we study the stability analysis of equilibrium points of population dynamics with delay when the Allee effect occurs at low population density. Mainly, our mathematical results and numerical simulations point to the stabilizing effect of the Allee effects on population dynamics with delay.

Allee effect in a prey-predator system

Abstract: We construct a model of a specialist predator and its prey species for the case of non-overlapping generations and we assume that the prey obeys to the Allee effect. We observe that, for small values of the minimal viable population of the prey, there are stable dynamical configurations corresponding either to stable fixed points or to a stable limit cycle which supports quasiperiodic orbits. In this last case we observe the paradox of enrichment, where an initial increase of the population of the prey may lead to cycles of very fast increase and subsequent decrease of the predator population. This behavior increases the probability of extinction due to unpredictable external factors. We consider also non-zero dispersal probability of the prey to neighboring sites and observe that predation causes the disappearance of a rescue effect, even when the Allee threshold is small.

Differential equations models for interacting wild and transgenic mosquito populations.

Abstract: We formulate and study continuous-time models, based on systems of ordinary differential equations, for interacting wild and transgenic mosquito populations. We assume that the mosquito mating rate is either constant, proportional to total mosquito population size, or has a Holling-II-type functional form. The focus is on the model with the Holling-II-type functional mating rate that incorporates Allee effects, in order to account for mating difficulty when the size of the total mosquito populations is small. We investigate the existence and stability of both boundary and positive equilibria. We show that the Holling-II-type model is the more realistic and, by means of numerical simulations, that it exhibits richer dynamics.

Limits to genetic bottlenecks and founder events imposed by the Allee effect

Abstract: The Allee effect can result in a negative population growth rate at low population density. Consequently, populations below a minimum (critical) density are unlikely to persist. A lower limit on population size should constrain the loss of genetic variability due to genetic drift during population bottlenecks or founder events. We explored this phenomenon by modeling changes in genetic variability and differentiation during simulated bottlenecks of the alpine copepod, Hesperodiaptomus shoshone. Lake surveys, whole-lake re-introduction experiments and model calculations all indicate that H. shoshone should be unlikely to establish or persist at densities less than 0.5–5 individuals m−3. We estimated the corresponding range in minimum effective population size using the distribution of habitat (lake) sizes in nature and used these values to model the expected heterozygosity, allelic richness and genetic differentiation resulting from population bottlenecks. We found that during realistic bottlenecks or founder events, >90% of H. shoshone populations in the Sierra Nevada may be resistant to significant changes in heterozygosity or genetic distance, and 70–75% of populations may lose <10% of allelic richness. We suggest that ecological constraints on minimum population size be considered when using genetic markers to estimate historical population dynamics.

Mate limitation in an estuarine population of copepods

Abstract: We determined the probability of mating as a function of population density in the estuarine copepod Acartia hudsonica by combining experimental measurements with a simple model. Pairs of unmated copepods were confined in containers of various volumes to simulate variable population density, and experiments were run for 8, 16, and 24 h. Mating frequencies indicated that males search for females at an effective search volume rate of 0.34 6 0.15 L h21 or 8.2 6 3.5 L d21 and that males become ready to mate only after ,15 h exposure to the females. We applied these parameters in a simple population model to determine the critical density for zero population growth. With high egg production, zero mortality, and residence time of 60 d, the critical density for A. hudsonica was 0.01 m23, at the low end of the range of observed population densities. Critical densities for less favorable conditions were well within the range of observed population densities, even allowing for the effects of aggregation. Thus, mate limitation in sexually reproducing organisms, or Allee effects, can cause negative density dependence in growth rate of these populations at low but realistic population densities. We applied these results to the introduction of exotic zooplankton via ships’ ballast water under various scenarios of initial dilution in harbors and subsequent conditions for reproduction and survival. Inocula resulting from the discharge of postexchange ballast water were often high enough to establish new resident populations.

A simple method to account for natural selection when predicting inbreeding depression.

Abstract: It has been widely appreciated that natural selection opposes the progress of inbreeding in small populations, thus limiting the actual inbreeding depression for fitness traits. However, no method to account for the consequences of this process has been given so far. I give a simple and intuitive method to predict inbreeding depression, taking into account the increase in selection efficiency against recessive alleles during inbreeding. It is based on the use of a “purged inbreeding coefficient” gt that accounts for the reduction of the probability of the deleterious homozygotes caused by the excess d of detrimental effect for deleterious alleles in the homozygous condition over its additive expectation. It is shown that the effect of purging can be important even for relatively small populations. For between-loci variable deleterious effects, accurate predictions can be obtained using the effective homozygous deleterious excess de, which can be estimated experimentally and is robust against variation of the ancestral effective population size. The method can be extended to any trait and it is used to predict the evolution of the mean viability or fecundity in a conservation program with equal or random family contributions.