Role Of Allee Effect Research Articles

The role of Allee effect in cannibalistic species: An action plan to sustain the declining cod population

Atlantic cod collapsed in the late 20th century after being harvested heavily for 50 years. This paper aims to design conservation guidelines for the cod population, which is diminishing due to predation by grey seals and cannibalism. For this purpose, we first designed a continuous time ecological model (with and without the Allee effect) using a system of differential equations consisting of juvenile Atlantic cod, adult Atlantic cod, and grey seals. The developed model has set forth global existence, non-negativity, and long-term behavior. Subsequently, to handle the extinction problem cost-effectively, Pontryagin’s principle is employed to construct the optimal control, which is then numerically solved using an iterative forward–backward method. We numerically explored the impact of the Allee effect on cod survival within the original model and its two extended versions (i) stochastic and (ii) reaction–diffusion, to thoroughly understand the possible consequences wherein a population has cannibalistic tendencies. The numerical comparison between the non-Allee and Allee models (Ordinary, Stochastic, Reaction–Diffusion) reveals that the Allee effect may significantly promote recovery and benefit the cannibalistic population. We adopted a partial rank correlation coefficient (PRCC) to conduct a global sensitivity analysis to estimate the most sensitive parameters responsible for cod prevalence.

The role of propagule pressure in experimental bark beetle invasions

Abstract Although many non‐native species arrive in novel environments, only a fraction successfully establish. A crucial factor affecting the colonization process of invading species is propagule pressure. The positive association between propagule pressure and colonization probability is driven both by stochastic dynamics and the ‘Allee effect’. Although the role of Allee effects in invading populations is theoretically compelling, they are difficult to quantify in the field because the earliest phases of biological invasions are typically not observed. We conducted parallel studies using two species of bark beetles, Hylurgus ligniperda in New Zealand and Ips pini in North America, to (i) assess the role of propagule pressure on colonization success, (ii) empirically test for Allee effects and (iii) estimate Allee thresholds. We evaluated each of these factors by experimentally testing the effect of propagule pressure (numbers released) on simulated tree colonization success in two different settings: (1) field conditions where beetles could disperse freely and (2) enclosed cages where dispersal loss was prevented. Colonization success was positively associated with numbers released (i.e. propagule pressure) for both species, though colonization occurred at lower numbers for H. ligniperda than for I. pini. A demographic Allee effect was only detected in H. ligniperda and the Allee threshold was smaller when beetles were released 1 m from host billets than when they were released 10 m away. Greater colonization success at lower release densities may explain the invasion success of H. ligniperda worldwide. Higher release densities required for successful colonization may explain why I. pini is a poor establisher. Synthesis and applications. Our results linking invasion failure to small founding population densities generally support the theoretical literature on the role of propagule pressure and Allee effects in biological invasions. Agencies such as the International Plant Protection Committee (IPPC) setting phytosanitary measures such as the International Standards for Phytosanitary Measures No. 15 (ISPM 15) should consider using the colonization thresholds estimated here to limit numbers of colonizing individuals below invasion thresholds. Additionally, agencies conducting trapping efforts at ports‐of‐entry should be aware of these thresholds and widely report when trapping numbers exceed these thresholds.

Role of Allee effect on prey–predator model with component Allee effect for predator reproduction

In the context of prey–predator interaction, Allee effect can have a significant impact and capture the complex dynamics in ecology. In this work, we modify the predator–prey model with component Allee effect for predator reproduction by incorporating the strong Allee effect in prey growth function. We explore the system dynamics in two aspects. Firstly, we study the system dynamics of the model without Allee effect through a comprehensive bifurcation structure and perform the sensitivity analysis of model parameters for fixed coexistence extensively; ii) we analyze the impact of Allee effect on the system dynamics. We determine the number of fixed coexistence points through graphical representation of non-trivial prey and predator nullclines. We study the stability analysis of the fixed coexistence point with the help of the graphical Jacobian method. Interestingly, we observe that initially, a low concentration of prey drives the system toward total extinction and the system will be settled to predator extinction for initially high prey concentration. This system behavior supplements the existence of bi-stability involving trivial and predator extinction equilibria independent of parametric conditions. The inclusion of the Allee effect enhances the stability behavior of the proposed model i.e. tetra stable equilibrium points are deduced. We demonstrate the system dynamics through co-dimension one and two bifurcations structure and also show possible phase portraits. Model with Allee effect generates all possible local and global bifurcations namely Hopf bifurcation, saddle–node bifurcation, B-T bifurcation, Bautin bifurcation and homoclinic bifurcation respectively. We observe that low predator reproduction growth rate provides oscillations with low prey densities and high predator reproduction growth rate results in oscillations with high prey densities. We investigate that the low impact of Allee always promotes the persistence of the coexistence. For a model with the Allee effect, we perform sensitivity analysis of model parameters for fixed coexistence points. We demonstrate results analytically and make them more comprehensive, we perform numerical simulation. Moreover, to show the vast applicability of our results, we compare it with the model without Allee effect.

Role of Allee effect in prey and hunting cooperation in a generalist predator

Cooperation is a very common phenomenon in the predator population. It can also be considered as one kind of Allee effect. By cooperation, we mean that the consumption rate per predator is dependent on the density of the predator. Despite a few recent studies the study of such systems is rare in the literature. It is well known from previous studies that incorporation of Allee effect in prey population enables the models to address many complex dynamical features. On the other hand, the dynamics of a generalist predator in a prey–predator system is also a very important area of research on populations. In this work, we concentrate on a model where Allee effect is incorporated in the prey growth in the presence of hunting cooperation in a generalist predator to observe how the Allee effect and the hunting cooperation affect the dynamics. Here we mainly study the stability and bifurcation of the system and hence describe the global dynamics to see how the Allee effect in prey and hunting cooperation affect the system dynamics.

The role of Allee effect in modelling post resection recurrence of glioblastoma.

Resection of the bulk of a tumour often cannot eliminate all cancer cells, due to their infiltration into the surrounding healthy tissue. This may lead to recurrence of the tumour at a later time. We use a reaction-diffusion equation based model of tumour growth to investigate how the invasion front is delayed by resection, and how this depends on the density and behaviour of the remaining cancer cells. We show that the delay time is highly sensitive to qualitative details of the proliferation dynamics of the cancer cell population. The typically assumed logistic type proliferation leads to unrealistic results, predicting immediate recurrence. We find that in glioblastoma cell cultures the cell proliferation rate is an increasing function of the density at small cell densities. Our analysis suggests that cooperative behaviour of cancer cells, analogous to the Allee effect in ecology, can play a critical role in determining the time until tumour recurrence.

On the role of Allee effect and mass migration in survival and extinction of a species

We use interacting particle systems to investigate survival and extinction of a species with colonies located on each site of ℤd. In each of the four models studied, an individual in a local population can reproduce, die or migrate to neighboring sites. We prove that an increase of the death rate when the local population density is small (the Allee effect) may be critical for survival, and that the migration of large flocks of individuals is a possible solution to avoid extinction when the Allee effect is strong. We use attractiveness and comparison with oriented percolation, either to prove the extinction of the species, or to construct nontrivial invariant measures for each model.

Wave phenomena and edge of chaos in a diffusive predator-prey system under Allee effect

We investigate a spatial predator-prey system; predator under Allee effect. The predator-prey community dynamics is assumed to be of Holling-Tanner type. When community’s local dynamics displays sustained periodic oscillations, the system’s spatio-temporal dynamics supports periodic traveling waves. Dispersal of species is assumed to be a random process in one-dimension only. Two dimensional (2D) parameter scan studies reveal that the system dynamics is self-organized at Edges of Chaos (EOC). This is a vital result as existence of EOC has not been demonstrated in a reaction-diffusion system yet. As population dynamics of all animals are governed by two basic processes: a) growth and b) dispersal, existence of EOC puts a recent theory of ecological chaos (Upadhyay, 2009; Rai and Upadhyay, 2006) on robust footing. Role of Allee effect in enhancing chaos presents an opportunity for its application in control of biological invasions and conservation of small populations. Extinction-persistence transitions were also explored.

ALLEE EFFECT LIMITS COLONIZATION SUCCESS OF SEXUALLY REPRODUCING ZOOPLANKTON

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.