Presence Of Allee Effect Research Articles

DYNAMIC STUDY OF A RATIO-DEPENDENT PREDATOR–PREY MODEL WITH STRONG ALLEE EFFECT AND NONLINEAR HARVESTING

The harvesting of species occurs in terrestrial and aquatic habitats across the world. It not only causes alteration in the population structure of the species subjected to harvesting but also of the species in interaction with the harvested species. The present work investigates the effect of nonlinear prey harvesting on the dynamics of a ratio-dependent predator–prey system with a strong Allee effect in prey population. It is found that the system exhibits a rich spectrum of dynamics including saddle-node bifurcation, Hopf bifurcation and homoclinic bifurcation with respect to the parameters that shape the nonlinear harvesting rate, namely, the maximum harvesting rate and a half-saturation constant that represents the prey density at which half of the maximum harvesting rate is reached. It is found that the basin of attraction of the stable coexistence state shrinks as the harvesting rate increases and if the harvesting rate is above a threshold value at which saddle-node bifurcation occurs, the stable coexistence of predator and prey populations is not possible for any initial start. It is also found that the harvesting policies in which the harvesting rate increases less rapidly at low prey population size are more favorable for the stable coexistence of species. The presence of Allee effect in the prey population is found to increase the chances of extinction of both species by reducing the threshold value of the harvesting rate at which the unconditional extinction occurs. Numerical simulations are carried out to support the analytical findings.

Allee effect in a diffusive predator–prey system with nonlocal prey competition

Nonlocal competition and Allee effect have extensively been considered in modeling population dynamics of species independently. This paper introduces two aspects, which prey has nonlocal competition and predator is subject to Allee effect, in a predator–prey system to investigate the effects of predation on the spatial distribution of prey. The conditions for the coexistence equilibrium point to remain stable and to undergo spatially inhomogeneous Hopf bifurcation and Turing bifurcation have been studied. In the absence of Allee effect, we find that the coexistence equilibrium point of the system is locally asymptotically stable independent of the nonlocal competition. In the presence of Allee effect, nonlocal prey competition can destabilize the coexistence equilibrium point. Numerical simulations are carried out to illustrate the theoretical results. The amplitude of oscillation solution for nonlocal prey competition system is larger than local prey competition system until oscillation solution evolves to periodic solution. Also, nonlocal prey competition term can drive a spatially inhomogeneous Hopf bifurcation, and the spatially inhomogeneous periodic solution emerges. Moreover, it is showed that when the habitat domain is larger, comparing with local prey competition system, the prey diffusion coefficient of system with nonlocal prey competition needs to be larger for two species coexistence in the spatially homogeneous form.

Dynamical bifurcation and explicit stationary density of a stochastic population model with Allee effects

This article is concerned with a stochastic different equation which describes the evolution of a species in the presence of Allee effects. By utilizing the Feller boundary classification criteria, it is testified that the model has a unique dynamical bifurcation point Δ with the following properties: if Δ<0, then the zero solution of the equation is stable; if Δ>0, then the equation possesses a unique invariant measure with an explicit density form. Some previous studies are improved and extended. This article also utilizes the theoretical findings to probe the living situation of Painted Hunting Dogs in Africa.

Impact of Allee effect on an eco-epidemiological system

In this paper, we propose a general ratio-dependent prey-predator model with disease in predator subject to the strong Allee effect in prey. We obtain the complete dynamics of both models: (a) full model with Allee effect; (b) full model without Allee effect. Model (a) may have more than one interior equilibrium point, but model (b) has only one interior equilibrium point. Numerical results reveal that the coexistence of all the populations at the endemic state is possible for both the models. But for the model with Allee effect, the coexistence can be destroyed by an increased supply of alternative food for the predators. It can also be proved that for the full model with Allee effect, the disease can be suppressed under certain parametric conditions. Also by comparing models (a) and (b), we conclude that Allee effect can create or destroy the interior attractor. Finally, we have studied the disease free-submodel (prey and susceptible predator model) with and without Allee effect. The comparative study between these two submodels leads to the following conclusions: 1) In the presence of Allee effect, the number of interior equilibrium points can change from zero to two whereas the submodel without Allee effect has unique interior equilibrium point; 2) Both with and without Allee effect, initial conditions play an important role on the survival and extinction of prey as well as its corresponding predator; 3) In the presence of Allee effect, bi-stability occurs with stable or periodic coexistence of prey and susceptible predator and the extinction of prey and susceptible predator; 4) Allee effect can generate or destroy the interior equilibrium points.

Stability and Hopf Bifurcation of Three-Species Prey-Predator System with Time Delays and Allee Effect

Allee effect is one of the important factors in ecology, and taking it into account can cause significant impacts in the system dynamics. In this paper, we study the dynamics of a two-prey one-predator system, where the growth of both prey populations is subject to Allee effects, and there is a direct competition between the two-prey species having a common predator. Two discrete time delays τ1 and τ2 are incorporated into the model to represent reaction time of predators. Sufficient conditions for local stability of positive interior equilibrium and existence of Hopf bifurcations in terms of threshold parameters τ1∗ and τ2∗ are obtained. A Lyapunov functional is deducted to investigate the global stability of positive interior equilibrium. Sensitivity analysis to evaluate the uncertainty of the state variables to small changes in the Allee parameters is also investigated. Presence of Allee effect and time delays in the model increases the complexity of the model and enriches the dynamics of the system. Some numerical simulations are provided to illustrate the effectiveness of the theoretical results. The model is highly sensitive to small changes in Allee parameters at the early stages and with low population densities, and this sensitivity decreases with time.

Influence of the components of propagule pressure, Allee effects, and stochasticity on the time to establish introduced populations

Forecasting whether individuals of an introduced population will succeed to establish is a challenge in invasion and conservation biology. The present work aims to decouple the impact of the components of propagule pressure on the time for population establishment in the presence of Allee effects and stochasticity in propagule sizes. The mean first passage time (MFPT) for a population to reach a viable size is used as a measure of the establishment success for the introduction processes involving periodic introductions. By fixing the introduction rate (mean number of introduced individuals per unit time) and varying the period of introduction from small ranges (small and frequent introductions) to large ones (infrequent and large releases), we study the influence of introduction distribution over time. These patterns of introduction are compared in a semi-stochastic model by observing which factors minimize the MFPT from an initially absent population, and hence, ensure the fastest population establishment. We investigate the influence on these minima of the introduction rate, variability in the introduction sizes, and occurrence of catastrophes that temporarily wipe out the population. Whereas most investigated cases show that infrequent and large introductions favor population establishment as expected, small and frequent introductions are preferred when the introduction rate is large and/or the variability in the introduction size is strong. Moreover, we observed counterintuitively that catastrophes strongly increase MFPT at small periods of introduction. In addition, we showed that stochasticity in introduction tends to increase the MFPT except when the introduction rate is small and introductions are evenly spread out in time.

Qualitative Analysis of an Additional Food Provided Predator–Prey Model in the Presence of Allee Effect

The present paper analyzes a predator–prey model in which the predator is provided with additional food and subjected to Allee effect. The conditions for the existence of equilibrium points and their local stability have been investigated. Under certain conditions, it is found that the solutions depend highly on the initial values. The existence of the bifurcations such as Bogdanov–Takens, Hopf–Andronov, Transcritical and Saddle-node, for the system have been shown. Further, the appearance of homoclinic loop, emerging through Hopf-bifurcation has been shown through numerical simulation. Numerical simulations have been proposed to confirm the analytical results.

Algae-herbivore interactions with Allee effect and chemical defense

Macroalgae exhibit a variety of characteristics that provide a degree of protection from herbivores. One characteristic is the production of chemicals that are toxic to herbivores. The toxic effect of macroalgae on herbivorous reef fish is studied by means of a spatiotemporal model of population dynamics with a nonmonotonic toxin-determined functional response of herbivores. It is assumed that the growth rate of macroalgae is mediated by Allee effect. We see that under certain conditions the system is uniformly persistent. Conditions for local stability of the system is obtained with weak and strong Allee effects. We observe that in presence of Allee effect on macroalgae, the system exhibits complex dynamics including Hopf bifurcation and saddle-node bifurcation. The obtained results show that the spatiotemporal system does not exhibit diffusion-driven instability. Computer simulations have been carried out to illustrate different analytical results.

Impact of Prey Refuge on a Discrete Time Predator–Prey System with Allee Effect

We study the impact of the Allee effect and prey refuge on the stability of a discrete time predator–prey system. We focus on the stability behavior of the system with the Allee effect in predator, prey and both populations. Based on the combination of analytical and numerical results, we observe that: (1) the Allee effect stabilizes the systems dynamics in a moderate value of prey refuge. (2) For a large fraction of prey refuge no significant improvement in stability is observed due to Allee effect. (3) Refuge may play an important role in managing the populations which are subject to the Allee effect. The population remains stable at an intermediate level of refuge parameter, whereas at relatively low and high refuge effect, prey exhibits chaotic oscillation. Such chaotic behavior is suppressed in the presence of Allee effect. The Allee mechanism and refuge are considered simultaneously on the populations and is shown to have a significant impact on the predator–prey dynamics that may be helpful in the conservation of endangered species.

Dynamics of a predator-prey system with prey subject to Allee effects and disease

In this article, we propose a general predator-prey system where prey is subject to Allee effects and disease with the following unique features: (i) Allee effects built in the reproduction process of prey where infected prey (I-class) has no contribution; (ii) Consuming infected prey would contribute less or negatively to the growth rate of predator (P-class) in comparison to the consumption of susceptible prey (S-class). We provide basic dynamical properties for this general model and perform the detailed analysis on a concrete model (SIP-Allee Model) as well as its corresponding model in the absence of Allee effects (SIP-no-Allee Model); we obtain the complete dynamics of both models: (a) SIP-Allee Model may have only one attractor (extinction of all species), two attractors (bi-stability either induced by small values of reproduction number of both disease and predator or induced by competition exclusion), or three attractors (tri-stability); (b) SIP-no-Allee Model may have either one attractor (only S-class survives or the persistence of S and I-class or the persistence of S and P-class) or two attractors (bi-stability with the persistence of S and I-class or the persistence of S and P-class). One of the most interesting findings is that neither models can support the coexistence of all three S, I, P-class. This is caused by the assumption (ii), whose biological implications are that I and P-class are at exploitative competition for S-class whereas I-class cannot be superior and P-class cannot gain significantly from its consumption of I-class. In addition, the comparison study between the dynamics of SIP-Allee Model and SIP-no-Allee Model lead to the following conclusions: 1) In the presence of Allee effects, species are prone to extinction and initial condition plays an important role on the surviving of prey as well as its corresponding predator; 2) In the presence of Allee effects, disease may be able to save prey from the predation-driven extinction and leads to the coexistence of S and I-class while predator can not save the disease-driven extinction. All these findings may have potential applications in conservation biology.

Allee effects in ants

1. Allee effects occur when the aggregation of individuals result in mutually beneficial intraspecific interactions whereby individual fitness, or per capita growth rate, increases with the number of individuals. Allee effects are common in social species due to their cooperative behaviours, such as breeding, feeding or defence. Allee effects have important implications for many aspects of basic and applied ecology. Over the past decades, the study of Allee effects has influenced population dynamics, community ecology, endangered species management and invasion biology. 2. Despite the fact that cooperation is the basis of their social structure, Allee effects have received little attention among eusocial insects. Extreme cooperation is common, and reproductive specialization of individuals occurs due to division of labour. These life-history traits suggest that the potential contribution of each caste to reproduction and survival may be differential and nonadditive. 3. We studied Allee effects in the invasive Argentine ant (Linepithema humile). In this species, many queens and workers are present in colonies, which allowed us to explore the differential effects of castes on the presence of Allee effects. In the laboratory, we measured brood production and individual survival in experimental colonies that differed in the initial numbers of queens and workers.4. Our results highlight the differential effect of queens and workers on survival and productivity. We found three positive density-dependent relationships indicative of component Allee effects at the colony level: both workers and queens had a positive effect on the productivity of the other caste, and queens had a positive effect on worker survivorship. 5. Our experimental results suggest a potential positive feedback between worker and queen abundance, which may have contributed to the evolution of large colony sizes. Our study provides the first evidence of Allee effects in eusocial insects and highlights the need to consider castes separately in population dynamics. Division of labour and differential reproductive rates are factors that should be integrated into the study of Allee effects.

Population dynamics of marine fishes at low abundance

The recovery of depleted species depends on their population dynamics at low abundance. Classical population growth models, applied widely in fisheries science, assume that per capita offspring production increases as abundance declines (compensation). However, slow or absent recovery by many depleted fishes might reflect unexpectedly weak compensation or the presence of Allee effects (depensation). Using meta-analytical techniques to describe reproductive dynamics, we find considerable variability among 207 exploited marine fish stocks (104 species) in how standardized per capita population growth changes with abundance. Although many species exhibit strong compensatory dynamics (negative density dependence), others show much weaker compensation than expected, and some exhibit evidence of an Allee effect, such as Atlantic cod ( Gadus morhua ) and Alaskan walleye pollock ( Theragra chalcogramma ). As data at low levels of abundance become increasingly available, it appears that compensation, while strong in some species, is comparatively weak or nonexistent in others, thus providing an explanation for why the recovery of some depleted stocks, despite reductions in exploitation, has been considerably less than what classic models of population growth would otherwise suggest.

Competition, predation and coexistence in a three trophic system

Simple ecological models that mostly operate with population densities using continuous variables, explain quite well the behavior of real populations. In this work we propose and discuss the continuous dynamics of a system of three species, which belongs to the well-known family of Lotka–Volterra models. In particular, the proposed model includes direct effects such as predation and competition among species, and indirect effects such as refuge. The model is proposed to explain recent studies about a group of crustacean (amphipods of genus Hyallela) found in all the plain streams and shallow lakes of the American continent. The studied system includes three compartments: algae, a strictly herbivore amphipod and an omnivore (herbivore and carnivore) one. The analysis of the model shows that there are stable extinction equilibria throughout all the parameters’ space. There are also equilibria with stable coexistence of the three species and two interesting binary equilibria: one with stable coexistence of algae and herbivore and other with coexistence between algae and omnivore amphipods. The presence of Allee effect in the algae growth and the existence of refuge for the herbivore amphipod (prey) determine a bottom-up control.

The evidence for Allee effects

AbstractAllee 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.

EVOLUTION OF PHENOTYPIC CLUSTERS THROUGH COMPETITION AND LOCAL ADAPTATION ALONG AN ENVIRONMENTAL GRADIENT

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.

THIS ARTICLE HAS BEEN RETRACTED Modeling Responses of Leafy Spurge Dispersal to Control Strategies

Abstract Leafy spurge (Euphorbia esula L.) has substantial negative effects on grassland biodiversity, productivity, and economic benefit in North America. To predict these negative impacts, we need an appropriate plant‐spread model which can simulate the response of an invading population to different control strategies. In this study, using a stochastic map lattice approach we generated a spatially explicitly stochastic process‐based model to simulate dispersal trajectories of leafy spurge under various control scenarios. The model integrated dispersal curve, propagule pressure, and population growth of leafy spurge at local and short‐temporal scales to capture spread features of leafy spurge at large spatial and long‐temporal scales. Our results suggested that narrow‐, medium‐, and fat‐tailed kernels did not differ in their ability to predict spread, in contrast to previous works. For all kernels, Allee effects were significantly present and could explain the lag phase (three decades) before leafy spurge spread accelerated. When simulating from the initial stage of introduction, Allee effects were critical in predicting spread rate of leafy spurge, because the prediction could be seriously affected by the low density period of leafy spurge community. No Allee effects models were not able to simulate spread rate well in this circumstance. When applying control strategies to the current distribution, Allee effects could stop the spread of leafy spurge; no Allee effects models, however, were able to slow but not stop the spread. The presence of Allee effects had significant ramifications on the efficiencies of control strategies. For both Allee and no Allee effects models, the later that control strategies were implemented, the more effort had to be input to achieve similar control results.