Two-patch population models with adaptive dispersal: the effects of varying dispersal speeds

The effect of dispersal on asymptotic total population size in discrete- and continuous-time two-patch models

Many populations occupy spatially fragmented landscapes. How dispersal affects the asymptotic total population size is a key question for conservation management and the design of ecological corridors. Here, we provide a comprehensive overview of two-patch models with symmetric dispersal and two standard density-dependent population growth functions, one in discrete and one in continuous time. A complete analysis of the discrete-time model reveals four response scenarios of the asymptotic total population size to increasing dispersal rate: (1) monotonically beneficial, (2) unimodally beneficial, (3) beneficial turning detrimental, and (4) monotonically detrimental. The same response scenarios exist for the continuous-time model, and we show that the parameter conditions are analogous between the discrete- and continuous-time setting. A detailed biological interpretation offers insight into the mechanisms underlying the response scenarios that thus improve our general understanding how potential conservation efforts affect population size.

Model of two competing populations in two habitats with migration: Application to optimal marine protected area size

The standard model of a single population fragmented into two patches connected by migration, was first introduced in the 1970s by Freedman and Waltman, since generating long-term research interest, though its full analysis for arbitrary values of migration rate has only been completed relatively recently. Here, we present a model of two competing species in a two-patch habitat with migrations between patches. We derive equilibrium solutions of this model for three cases of migration rate resulting in isolated, well-mixed and semi-isolated habitats. We evaluate the full range of effects of habitat, life-history and migration parameters on population sizes. Finally, we add harvesting mortality and define conditions under which introduction of a no-harvesting (protected) area may lead to increased maximum sustainable yield. The results have applications in mixed fishery management and the design of wildlife protection zones, including marine protected areas (MPAs).

Testing hypotheses of habitat use and temporal activity in relation to body plan in a Mediterranean lizard community

A body plan (bauplan) is a suite of morphological characters shared by phylogenetically related animals at some point during their development. Despite its value, the bauplan concept is still rarely employed to characterize functional groups in community ecology. Here, we examine habitat use and spatio-temporal activity correlates of an entire seven-species community of lizards with different bauplans. The study was carried out in three locations in central Italy, encompassing a complex landscape with a patchy mosaic of a wide variety of habitats and microclimates. We tested four hypotheses regarding niche breadth, habitat use, and activity patterns. The first hypothesis, niche complementarity, in which species with similar body shapes should non-randomly partition available habitats, was not supported. By contrast, the hypotheses that larger bodied species should have a wider niche breadth, that slower species should inhabit habitat types of higher cover, and species inhabiting open sunny habitats should exhibit more seasonally variable activity patterns, were all supported by the data. Sympatric lizard communities in our study area were clearly organized by autecological constraints and eco-physiological attributes.

Behaviour, life history and persistence in novel environments

Understanding what affects population growth in novel environments is fundamental to forecast organisms' responses to global change, including biological invasions and land use intensification. Novel environments are challenging because they can cause maladaptation, increasing the risk of extinction by negative population growth. Animals can avoid extinction by improving the phenotype-environment match through behavioural responses, notably matching habitat choice and learning. However, the demographic consequences of these responses remain insufficiently understood in part because they have not been analysed within a life-history context. By means of an individual-based model, we show here that matching habitat choice and learning interact with life history to influence persistence in novel environments. In maladaptive contexts, the likelihood of persisting is higher for life-history strategies that increase the value of adults over the value of offspring, even at the cost of decreasing reproduction. Such a strategy facilitates persistence in novel environments by reducing the costs of a reproductive failure while increasing the benefits of behavioural responses. Our results reinforce the view that a more predictive theory for extinction risk under rapid environmental changes requires considering behavioural responses and life history as part of a common adaptive strategy to cope with environmental changes. This article is part of the theme issue 'Linking behaviour to dynamics of populations and communities: application of novel approaches in behavioural ecology to conservation'.

Interaction rates, vital rates, background fitness and replicator dynamics: how to embed evolutionary game structure into realistic population dynamics

In this paper we are concerned with how aggregated outcomes of individual behaviours, during interactions with other individuals (games) or with environmental factors, determine the vital rates constituting the growth rate of the population. This approach needs additional elements, namely the rates of event occurrence (interaction rates). Interaction rates describe the distribution of the interaction events in time, which seriously affects the population dynamics, as is shown in this paper. This leads to the model of a population of individuals playing different games, where focal game affected by the considered trait can be extracted from the general model, and the impact on the dynamics of other events (which is not neutral) can be described by an average background fertility and mortality. This leads to a distinction between two types of background fitness, strategically neutral elements of the focal games (correlated with the focal game events) and the aggregated outcomes of other interactions (independent of the focal game). The new approach is useful for clarification of the biological meaning of concepts such as weak selection. Results are illustrated by a Hawk-Dove example.

A two-patch prey-predator model with predator dispersal driven by the predation strength

Foraging movements of predator play an important role in population dynamics of prey-predator systems, which have been considered as mechanisms that contribute to spatial self-organization of prey and predator. In nature, there are many examples of prey-predator interactions where prey is immobile while predator disperses between patches non-randomly through different factors such as stimuli following the encounter of a prey. In this work, we formulate a Rosenzweig-MacArthur prey-predator two patch model with mobility only in predator and the assumption that predators move towards patches with more concentrated prey-predator interactions. We provide completed local and global analysis of our model. Our analytical results combined with bifurcation diagrams suggest that: (1) dispersal may stabilize or destabilize the coupled system; (2) dispersal may generate multiple interior equilibria that lead to rich bistable dynamics or may destroy interior equilibria that lead to the extinction of predator in one patch or both patches; (3) Under certain conditions, the large dispersal can promote the permanence of the system. In addition, we compare the dynamics of our model to the classic two patch model to obtain a better understanding how different dispersal strategies may have different impacts on the dynamics and spatial patterns.

Conspecific density modulates the effect of predation on dispersal rates

Dispersal decisions underlie the spatial dynamics of metacommunities. Prey individuals may disperse to reduce the risk of either predation or starvation, and both of these risks may depend on conspecific density. Surprisingly, there is little theory examining how dispersal rates should change in response to the combined effects of predation and changes in conspecific density. We develop such a model and show that, under certain conditions, predators may induce dispersal at low prey densities but not high prey densities. We then experimentally manipulate the density of the ciliate Paramecium aurelia and the perceived presence of its predator, the flatworm Stenostomum virginiamum, in a two-patch metacommunity to parameterise the model. Paramecium dispersed in response to Stenostomum at low densities, but they reduced their dispersal in response to predation risk at high predator densities. By applying our model to the empirical data, we show that this switch in dispersal strategy, linked to increases in prey density, occurred because predators increased the difficulty or risk of dispersal. Together, the model and experiment reveal that the effects of predators on dispersal are contingent on prey density. Previous studies have sometimes reported an increase in dispersal rate when predation risk is elevated, and other times a decrease in dispersal rate. Our demonstration of a switch point, with predation risk increasing dispersal at low prey densities but reducing dispersal above a threshold of prey density, may reconcile the diversity of prey dispersal behaviours reported in these previous investigations and observed in nature.

Demographic stochasticity and evolution of dispersion I. Spatially homogeneous environments

The selection of dispersion is a classical problem in ecology and evolutionary biology. Deterministic dynamical models of two competing species differing only in their passive dispersal rates suggest that the lower mobility species has a competitive advantage in inhomogeneous environments, and that dispersion is a neutral characteristic in homogeneous environments. Here we consider models including local population fluctuations due to both individual movements and random birth and death events to investigate the effect of demographic stochasticity on the competition between species with different dispersal rates. In this paper, the first of two, we focus on homogeneous environments where deterministic models predict degenerate dynamics in the sense that there are many (marginally) stable equilibria with the species' coexistence ratio depending only on initial data. When demographic stochasticity is included the situation changes. A novel large carrying capacity ([Formula: see text]) asymptotic analysis, confirmed by direct numerical simulations, shows that a preference for faster dispersers emerges on a precisely defined [Formula: see text] time scale. We conclude that while there is no evolutionarily stable rate for competitors to choose in these models, the selection mechanism quantified here is the essential counterbalance in spatially inhomogeneous models including demographic fluctuations which do display an evolutionarily stable dispersal rate.

The Allee-type ideal free distribution

The ideal free distribution (IFD) in a two-patch environment where individual fitness is positively density dependent at low population densities is studied. The IFD is defined as an evolutionarily stable strategy of the habitat selection game. It is shown that for low and high population densities only one IFD exists, but for intermediate population densities there are up to three IFDs. Population and distributional dynamics described by the replicator dynamics are studied. It is shown that distributional stability (i.e., IFD) does not imply local stability of a population equilibrium. Thus distributional stability is not sufficient for population stability. Results of this article demonstrate that the Allee effect can strongly influence not only population dynamics, but also population distribution in space.