Natal habitat effects drive density—dependent scaling of dispersal decisions

The dispersal behavior of a species is critical for the stability and persistence of its populations across a landscape. How population density affects dispersal decisions is important for predicting these dynamics, as the form of density‐dependent dispersal influences the stability and persistence of populations. Natal habitat experience often has strong impacts on individual dispersal behavior as well, but its influence on density‐dependent dispersal behaviors remains unexplored. Here we address this conceptual gap in two experiments separately examining habitat selection and emigration from recently colonized patches for two species of flour beetle Tribolium sp. We found that interactions between the quality of habitat experienced during natal development and current habitat for dispersal capable adults can strongly affect the form of density dependence, including reversing the direction of nonlinearities (accelerating to decelerating), or even negating the influence of population density for individual dispersal decisions. Across heterogeneous landscapes, where individuals from different populations may experience different natal habitats, this altering of density‐dependent relationships is predicted by theory to fundamentally influence regional population dynamics. Our results indicate that species which occur across heterogeneous environments, such as during conservation reintroductions, or as invasive species spread, have much potential for natal experience to interact with density dependence and influence local and regional population dynamics.     

Individual-based modeling of the spread of pine wilt disease: vector beetle dispersal and the Allee effect

Pine wilt disease is caused by the pinewood nematode Bursaphelenchus xylophilus, which is vectored by the Japanese pine sawyer beetle Monochamus alternatus. Due to their mutualistic relationship, according to which the nematode weakens and makes trees available for beetle reproduction and the beetle in turn carries and transmits the nematode to healthy pine trees, this disease has resulted in severe damage to pine trees in Japan in recent decades. Previous studies have worked on modeling of population dynamics of the vector beetle and the pine tree to explore spatial expansion of the disease using an integro-difference equation with a dispersal kernel that describes beetle mobility over space. In this paper, I revisit these previous models but retaining individuality: by considering mechanistic interactions at the individual level it is shown that the Allee effect, an increasing per-capita growth rate as population abundance increases, can arise in the beetle dynamics because of the necessity for beetles to contact pine trees at least twice to reproduce successfully. The incubation period after which a tree contacted by a first beetle becomes ready for beetle oviposition by later beetles is crucial for the emergence of this Allee effect. It is also shown, however, that the strength of this Allee effect depends strongly on biological mechanistic properties, especially on beetle mobility. Realistic individual-based modeling highlights the importance of how spatial scales are dealt with in mathematical models. The link between mechanistic individual-based modeling and conventional analytical approaches is also discussed.     

Competition,facilitation and the Allee effect

Individuals of different species may interact in many different ways, such as competition, mutualism, or predation, to name but a few. Recent theory and experiments reveal that whether an interaction is beneficial or detrimental to the dynamics of a population often depends on species densities and other environmental factors. Here, we explore how, for suitable densities, facilitation may arise between two competing species with an Allee effect. We consider two different mechanisms for the Allee effect: 1) plant species with obligate insect pollination, and 2) generalist predation. In the first case, a second plant species, competing for nutrients, may have a facilitative effect by attracting more pollinators. In the second case, another potentially competing species may serve to satiate the same generalist predator and thereby have a facilitative effect. We explore three aspects of facilitation in each of the two systems. The focal species may benefit from the presence of a ‘competitor’ if it experiences 1) the removal of the Allee threshold, 2) a lowering of the Allee threshold, or 3) an increase in carrying capacity. We find that the latter two effects occur in both study systems whereas the first only occurs for the generalist predation system but not for the plant‐pollination system. We give precise conditions on when such a facilitative effect can be expected. We also demonstrate several unexpected outcomes of these two‐species interactions with multiple steady states, such as obligate co‐occurence; we draw parallels to the dynamics of species known as ‘ecosystem engineers’, and we discuss implications for conservation and management.     

Generalized Allee effect model

The Allee effect consists of a positive correlation between very small population size and fitness. Offering a new view point on the weak and strong demographic Allee effect, we propose to combine them with the Richards growth model. In particular, a peculiar manifestation of the Allee effect is analytically predicted and still not validated by experiments. Model validation with ecological data is presented for some special situations.     

Age dependent dispersal is not a simple process: Density dependence, stability, and chaos

I present both discrete and continuous models for a single species with overlapping generations, density dependence, and movement rates that vary with age. In the discrete time and space model, I show that if the strongly density dependent age class(es) are stationary, the spatially structured model may exhibit instabilities or even chaos which are not present in the corresponding model without spatial structure. I argue that the conditions which lead to these diffusive instabilities are likely to be met in natural populations. Thus it is important to consider the interaction between age structure and spatial structure in both experimental and theoretical work. In particular, the conditions leading to chaos are more common than would be predicted in models which ignore structure.     

Density dependent neurodynamics

The dynamics of a neural network depends on density parameters at (at least) two different levels: the subcellular density of ion channels in single neurons, and the density of cells and synapses at a network level. For the Frankenhaeuser-Huxley (FH) neural model, the density of sodium (Na) and potassium (K) channels determines the behaviour of a single neuron when exposed to an external stimulus. The features of the onset of single neuron oscillations vary qualitatively among different regions in the channel density plane. At a network level, the density of neurons is reflected in the global connectivity. We study the relation between the two density levels in a network of oscillatory FH neurons, by qualitatively distinguishing between three regions, where the mean network activity is (1) spiking, (2) oscillating with enveloped frequencies, and (3) bursting, respectively. We demonstrate that the global activity can be shifted between regions by changing either the density of ion channels at the subcellular level, or the connectivity at the network level, suggesting that different underlying mechanisms can explain similar global phenomena. Finally, we model a possible effect of anaesthesia by blocking specific inhibitory ion channels.     

Allee effect in exotic and introduced blowflies

We combined two models to investigate the theoretical dynamics of five exotic and native blowfly species in response to the Allee effect by using demographic parameters estimated from experimental populations. Most of the results suggest stabilization of dynamic behavior in response to the Allee effect. However, the results depended on the magnitude of the demographic parameters of each species, and also indicated chaotic fluctuations and limit cycles. The results are discussed in the context of larval aggregation, an important biological process for blowflies, which naturally incorporates the Allee effect.     

Invasion dynamics of epidemic with the Allee effect

Investigating the likely success of epidemic invasion is important in the epidemic management and control. In the present study, the invasion of epidemic is initially introduced to a predator-prey system, both species of which are considered to be subject to the Allee effect. Mathematically, the invasion dynamics is described by three nonlinear diffusion-reaction equations and the spatial implicit and explicit models are designed. By means of extensive numerical simulations, the results of spatial implicit model show that the Allee effect has an opposite impact on the invasion criteria and local dynamics when that on the different species. As the intensity of the Allee effect increases, the domain of epidemic invasion reduces and the system dynamics is changed from the stable state to the limit cycle and finally becomes the chaotic state when the susceptible prey with the Allee effect, but the domain expands and the system dynamics is changed from limit cycle to a table point when the predator is subject to the Allee effect. Results from the spatial explicit model show that the strong intensity of the Allee effect can lead to the catastrophic global extinction of all species in the case of that on the susceptible prey. While the predator with the Allee effect, the increased intensity of which makes spatial species reach a stable state. Furthermore, numerical simulations reveal a certain relationship between the invasion speed and spatial patterns.     

Rarity value and species extinction: the anthropogenic Allee effect

Standard economic theory predicts that exploitation alone is unlikely to result in species extinction because of the escalating costs of finding the last individuals of a declining species. We argue that the human predisposition to place exaggerated value on rarity fuels disproportionate exploitation of rare species, rendering them even rarer and thus more desirable, ultimately leading them into an extinction vortex. Here we present a simple mathematical model and various empirical examples to show how the value attributed to rarity in some human activities could precipitate the extinction of rare species—a concept that we term the anthropogenic Allee effect. The alarming finding that human perception of rarity can precipitate species extinction has serious implications for the conservation of species that are rare or that may become so, be they charismatic and emblematic or simply likely to become fashionable for certain activities.     

Allee effect,spatial structure and species coexistence

Both positive and negative interactions among species are common in communities. Until recently, attention has focused on negative interactions such as competition. However, the importance of positive interactions such as the Allee effect has recently been recognized. We construct a single-patch model that incorporates both an Allee effect and competition between two species. A species that experiences an Allee effect cannot establish in a patch which is already occupied by a competitor unless its density is over a critical value. This effect, when translated into a metapopulation, makes migrants of a species unable to colonize patches where another species has established. This interaction between the Allee effect and inter-specific competition creates and stabilizes spatial segregation of species. Therefore, under circumstances in which competition would preclude local coexistence, the presence of an Allee effect can allow coexistence at a metapopulation scale. Furthermore, we found that a species can resist displacement if stronger competitors experience an Allee effect.     

Allee effect, sexual selection and demographic stochasticity

The negative frequency-dependent effect of reproductive success in animals on population growth refers to a category of phenomena termed the Allee effect. The mechanistic basis for this effect and hence an understanding of its consequences has been obscure. We suggest that sexual selection, in particular female mate preferences, is a previously neglected component giving rise to the Allee effect. Lack of breeding and reduced reproductive success of females at low population densities are commonly described in situations where females have little or no opportunity to choose a mate, consistent with this suggestion. We developed a demographic model that incorporated the effects of lack of female choice on rates of reproduction. Using either a mating system with incompatibility or a system with a directional mate preference, we show that commonly encountered levels of reproductive suppression in the absence of suitable mates in a population, where sexual selection still operates, may increase the effects of demographic stochasticity considerably.     

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.     

The role of the Allee effect in species packing

The species-packing model of May and MacArthur is modified to include a commonly-expected influence of sexual reproduction, namely a systematic diminishing of the rate of increase in a population when it becomes rare (called the “Allee effect”). This effect causes discreteness, i.e., a finiteness to the density of species found along a resource axis. The species separate in a manner that relates to their intrinsic capacities to utilize the resources. Also discussed is the issue of species diversity gradients, and how the question of species discreteness might apply to it. The model with the Allee effect is in reasonable accord with island diversity patterns, but is minimally applicable to longitudinal gradients. Environmental stochasticity is modelled with noise terms governed by widely varying timescales. However, the resulting stochastic extinction is found neither to generate discrete distributions by itself, nor to have substantive effects on the discrete distributions generated by the Allee effect.     

具有Allee效应的合作进化

Allee效应对物种的续存是潜在的干扰因素,在很大程度上将增加种群局部甚至全局灭绝的可能性。对许多物种,尤其是濒临物种更容易受其影响。将Allee效应引入囚徒困境博弈模型,通过理论分析与数值模拟相结合的方法分析讨论了Allee效应对合作进化的影响。研究结果表明:在恶劣的环境条件下,Allee效应极易使物种灭绝,不利于合作进化;在相对优越的环境条件下(死亡率较低),Allee效应促进合作进化,且Allee效应强度越强,更有利于合作进化,不过种群的空间斑块占有率也会随着Allee效应强度的增强而降低,使物种最终灭绝。     

General Allee effect in two-species population biology

The main objective of this work is to present a general framework for the notion of the strong Allee effect in population models, including competition, mutualistic, and predator–prey models. The study is restricted to the strong Allee effect caused by an inter-specific interaction. The main feature of the strong Allee effect is that the extinction equilibrium is an attractor. We show how a ‘phase space core’ of three or four equilibria is sufficient to describe the essential dynamics of the interaction between two species that are prone to the Allee effect. We will introduce the notion of semistability in planar systems. Finally, we show how the presence of semistable equilibria increases the number of possible Allee effect cores.     

General Allee effect in two-species population biology

The main objective of this work is to present a general framework for the notion of the strong Allee effect in population models, including competition, mutualistic, and predator-prey models. The study is restricted to the strong Allee effect caused by an inter-specific interaction. The main feature of the strong Allee effect is that the extinction equilibrium is an attractor. We show how a 'phase space core' of three or four equilibria is sufficient to describe the essential dynamics of the interaction between two species that are prone to the Allee effect. We will introduce the notion of semistability in planar systems. Finally, we show how the presence of semistable equilibria increases the number of possible Allee effect cores.     

Bifurcations and chaos in a predator-prey system with the Allee effect

It is known from many theoretical studies that ecological chaos may have numerous significant impacts on the population and community dynamics. Therefore, identification of the factors potentially enhancing or suppressing chaos is a challenging problem. In this paper, we show that chaos can be enhanced by the Allee effect. More specifically, we show by means of computer simulations that in a time-continuous predator-prey system with the Allee effect the temporal population oscillations can become chaotic even when the spatial distribution of the species remains regular. By contrast, in a similar system without the Allee effect, regular species distribution corresponds to periodic/quasi-periodic oscillations. We investigate the routes to chaos and show that in the spatially regular predator-prey system with the Allee effect, chaos appears as a result of series of period-doubling bifurcations. We also show that this system exhibits period-locking behaviour: a small variation of parameters can lead to alternating regular and chaotic dynamics.     

Bubbling and hydra effect in a population system with Allee effect

We present a continuous time predator-prey model and predator’s growth subjected to component Allee effect. The model also includes density dependent mortality of predator. We investigate our model both analytically and numerically, and highlighted the effect of density independent mortality and Allee effect. In our system, we find that a fixed point representing the extinction of predator is always a stable point. When coexistence equilibria exists our system is bistable. We have observed that tristability is possible for our model that includes two stable co-existence fixed point. The most important phenomena which we have observed are hydra effect and cascading effect. Due to component Allee effect in predator the system shows multiple hydra effect. We discuss the phenomenon of bubbling, which indicates increasing and decreasing of amplitudes of cycles. We have presented one-parametric as well as two-parametric bifurcation diagram and also all possible bifurcations that the system could go through.     

Evolution of the distribution of dispersal distance under distance‐dependent cost of dispersal

Abstract We analyse the evolution of the distribution of dispersal distances in a stable and homogeneous environment in one‐ and two‐dimensional habitats. In this model, dispersal evolves to avoid the competition between relatives although some cost might be associated with this behaviour. The evolutionarily stable dispersal distribution is characterized by an equilibration of the fitness gains among all the different dispersal distances. This cost‐benefit argument has heuristic value and facilitates the comprehension of results obtained numerically. In particular, it explains why some minimal or maximal probability of dispersal may evolve at intermediate distances when the cost of dispersal function is an increasing function of distance. We also show that kin selection may favour long range dispersal even if the survival cost of dispersal is very high, provided the survival probability does not vanish at long distances.