Spatiotemporal complexity of patchy invasion in a predator-prey system with the Allee effect

Invasion of an exotic species initiated by its local introduction is considered subject to predator-prey interactions and the Allee effect when the prey growth becomes negative for small values of the prey density. Mathematically, the system dynamics is described by two nonlinear diffusion-reaction equations in two spatial dimensions. Regimes of invasion are studied by means of extensive numerical simulations. We show that, in this system, along with well-known scenarios of species spread via propagation of continuous population fronts, there exists an essentially different invasion regime which we call a patchy invasion. In this regime, the species spreads over space via irregular motion and interaction of separate population patches without formation of any continuous front, the population density between the patches being nearly zero. We show that this type of the system dynamics corresponds to spatiotemporal chaos and calculate the dominant Lyapunov exponent. We then show that, surprisingly, in the regime of patchy invasion the spatially average prey density appears to be below the survival threshold. We also show that a variation of parameters can destroy this regime and either restore the usual invasion scenario via propagation of continuous fronts or brings the species to extinction; thus, the patchy spread can be qualified as the invasion at the edge of extinction. Finally, we discuss the implications of this phenomenon for invasive species management and control.     

Connectivity of Caribbean coral populations: complementary insights from empirical and modelled gene flow

Understanding patterns of connectivity among populations of marine organisms is essential for the development of realistic, spatially explicit models of population dynamics. Two approaches, empirical genetic patterns and oceanographic dispersal modelling, have been used to estimate levels of evolutionary connectivity among marine populations but rarely have their potentially complementary insights been combined. Here, a spatially realistic Lagrangian model of larval dispersal and a theoretical genetic model are integrated with the most extensive study of gene flow in a Caribbean marine organism. The 871 genets collected from 26 sites spread over the wider Caribbean subsampled 45.8% of the 1900 potential unique genets in the model. At a coarse scale, significant consensus between modelled estimates of genetic structure and empirical genetic data for populations of the reef-building coral Montastraea annularis is observed. However, modelled and empirical data differ in their estimates of connectivity among northern Mesoamerican reefs indicating that processes other than dispersal may dominate here. Further, the geographic location and porosity of the previously described east-west barrier to gene flow in the Caribbean is refined. A multi-prong approach, integrating genetic data and spatially realistic models of larval dispersal and genetic projection, provides complementary insights into the processes underpinning population connectivity in marine invertebrates on evolutionary timescales.     

Exploiting Allee effects for managing biological invasions

Biological invasions are a global and increasing threat to the function and diversity of ecosystems. Allee effects (positive density dependence) have been shown to play an important role in the establishment and spread of non-native species. Although Allee effects can be considered a bane in conservation efforts, they can be a benefit in attempts to manage non-native species. Many biological invaders are subject to some form of an Allee effect, whether due to a need to locate mates, cooperatively feed or reproduce or avoid becoming a meal, yet attempts to highlight the specific exploitation of Allee effects in biological invasions are surprisingly unprecedented. In this review, we highlight current strategies that effectively exploit an Allee effect, and propose novel means by which Allee effects can be manipulated to the detriment of biological invaders. We also illustrate how the concept of Allee effects can be integral in risk assessments and in the prioritization of resources allocated to manage non-native species, as some species beset by strong Allee effects could be less successful as invaders. We describe how tactics that strengthen an existing Allee effect or create new ones could be used to manage biological invasions more effectively.     

Establishing a beachhead: a stochastic population model with an Allee effect applied to species invasion

We formulated a spatially explicit stochastic population model with an Allee effect in order to explore how invasive species may become established. In our model, we varied the degree of migration between local populations and used an Allee effect with variable birth and death rates. Because of the stochastic component, population sizes below the Allee effect threshold may still have a positive probability for successful invasion. The larger the network of populations, the greater the probability of an invasion occurring when initial population sizes are close to or above the Allee threshold. Furthermore, if migration rates are low, one or more than one patch may be successfully invaded, while if migration rates are high all patches are invaded.     

利用元胞自动机研究一类捕食食饵模型中的斑块扩散现象

利用概率元胞自动机模型对空间隐式的、食饵具Allee效应的一类捕食食饵模型进行模拟,发现随着相关参数的变化,种群的空间扩散前沿由连续的扩散波逐渐转变为一种相互隔离的斑块向外扩散,这种斑块扩散现象与以往的扩散模式有所不同。研究结果表明：(1)在斑块扩散的情况下,相关参数的微小变化会导致种群灭绝或者形成连续的扩散波,即斑块扩散发生在种群趋于灭绝和连续扩散之间;(2)当种群的空间扩散方式为斑块扩散时,种群的扩散速度会变慢,与其他扩散方式下的速度有着明显的区别。该研究结果对生物入侵控制和外来物种监测有重要的启发和指导作用。     

A diffusive SI model with Allee effect and application to FIV

A minimal reaction-diffusion model for the spatiotemporal spread of an infectious disease is considered. The model is motivated by the Feline Immunodeficiency Virus (FIV) which causes AIDS in cat populations. Because the infected period is long compared with the lifespan, the model incorporates the host population growth. Two different types are considered: logistic growth and growth with a strong Allee effect. In the model with logistic growth, the introduced disease propagates in form of a travelling infection wave with a constant asymptotic rate of spread. In the model with Allee effect the spatiotemporal dynamics are more complicated and the disease has considerable impact on the host population spread. Most importantly, there are waves of extinction, which arise when the disease is introduced in the wake of the invading host population. These waves of extinction destabilize locally stable endemic coexistence states. Moreover, spatially restricted epidemics are possible as well as travelling infection pulses that correspond either to fatal epidemics with succeeding host population extinction or to epidemics with recovery of the host population. Generally, the Allee effect induces minimum viable population sizes and critical spatial lengths of the initial distribution. The local stability analysis yields bistability and the phenomenon of transient epidemics within the regime of disease-induced extinction. Sustained oscillations do not exist.     

Overcoming Allee effects through evolutionary,genetic, and demographic rescue

Despite the amplified threats of extinction facing small founder populations, successful colonization sometimes occurs, bringing devastating ecological and economic consequences. One explanation may be rapid evolution, which can increase mean fitness in populations declining towards extinction, permitting persistence and subsequent expansion. Such evolutionary rescue may be particularly important, given Allee effects. When a population is introduced at low density, individuals often experience a reduction in one or more components of fitness due to novel selection pressures that arise from diminished intraspecific interactions and positive density dependence (i.e. component Allee effects). A population can avoid extinction if it can adapt and recover on its own (i.e. evolutionary rescue), or if additional immigration sustains the population (i.e. demographic rescue) or boosts its genetic variation that facilitates adaptation (i.e. genetic rescue). These various forms of rescue have often been invoked as possible mechanisms for specific invasions, but their relative importance to invasion is not generally understood. Within a spatially explicit modelling framework, we consider the relative impact of each type of rescue on the probability of successful colonization, when there is evolution of a multi-locus quantitative trait that influences the strength of component Allee effects. We demonstrate that when Allee effects are important, the effect of demographic rescue via recurrent immigration overall provides the greatest opportunity for success. While highlighting the role of evolution in the invasion process, we underscore the importance of the ecological context influencing the persistence of small founder populations.     

kernelpop,a spatially explicit population genetic simulation engine

Individual‐based, spatially explicit models provide a mechanism to understand distributions of individuals on the landscape; however, few models have been coupled with population genetics. The primary benefits of such a combination is to assess performance of population‐genetic estimators in realistic situations. kernelpop represents a flexible framework to implement almost any arbitrary population‐genetic and demographic model in a spatially explicit context using a variety of dispersal kernels. Estimates of type I error associated with genome scans in metapopulations are provided as an illustration of this software's utility.     

Inferring landscape effects on dispersal from genetic distances: how far can we go?

Functional connectivity affects demography and gene dynamics in fragmented populations. Besides species-specific dispersal ability, the connectivity between local populations is affected by the landscape elements encountered during dispersal. Documenting these effects is thus a central issue for the conservation and management of fragmented populations. In this study, we compare the power and accuracy of three methods (partial correlations, regressions and Approximate Bayesian Computations) that use genetic distances to infer the effect of landscape upon dispersal. We use stochastic individual-based simulations of fragmented populations surrounded by landscape elements that differ in their permeability to dispersal. The power and accuracy of all three methods are good when there is a strong contrast between the permeability of different landscape elements. The power and accuracy can be further improved by restricting analyses to adjacent pairs of populations. Landscape elements that strongly impede dispersal are the easiest to identify. However, power and accuracy decrease drastically when landscape complexity increases and the contrast between the permeability of landscape elements decreases. We provide guidelines for future studies and underline the needs to evaluate or develop approaches that are more powerful.