The Ideal Free Distribution with travel costs.

This article studies the effect of travel costs on population distribution in a patchy environment. The Ideal Free Distribution with travel costs is defined in the article as the distribution under which it is not profitable for individuals to move, i.e., the movement between patches ceases. It is shown that depending on the travel costs between patches, the Ideal Free Distribution may be unique, there may be infinitely many possible IFDs, or no Ideal Free Distribution exists. In the latter case, animal distribution can converge to an equilibrium of distributional dynamics at which individuals do disperse, but the net movement between patches ceases. Such distributional equilibrium corresponds to balanced dispersal.

Intraguild processes drive space-use patterns in a large-bodied marine predator community.

Interspecific interactions, including predator-prey, intraguild predation (IGP) and competition, may drive distribution and habitat use of predator communities. However, elucidating the relative importance of these interactions in shaping predator distributions is challenging, especially in marine communities comprising highly mobile species. We used individual-based models (IBMs) to predict the habitat distributions of apex predators, intraguild (IG) prey and prey. We then used passive acoustic telemetry to test these predictions in a subtropical marine predator community consisting of eight elasmobranch (i.e. shark and ray) species in Bimini, The Bahamas. IBMs predicted that prey and IG prey will preferentially select habitats based on safety over resources (food), with stronger selection for safe habitat by smaller prey. Elasmobranch space-use patterns matched these predictions. Species with predator-prey and asymmetrical IGP (between apex and small mesopredators) interactions showed the clearest spatial separation, followed by asymmetrical IGP among apex and large mesopredators. Competitors showed greater spatial overlap although with finer-scale differences in microhabitat use. Our study suggests space-use patterns in elasmobranchs are at least partially driven by interspecific interactions, with stronger spatial separation occurring where interactions include predator-prey relationships or IGP.

Density-dependent habitat selection alters drivers of population distribution in northern Yellowstone elk.

Although it is well established that density dependence drives changes in organismal abundance over time, relatively little is known about how density dependence affects variation in abundance over space. We tested the hypothesis that spatial trade-offs between food and safety can change the drivers of population distribution, caused by opposing patterns of density-dependent habitat selection (DDHS) that are predicted by the multidimensional ideal free distribution. We addressed this using winter aerial survey data of northern Yellowstone elk (Cervus canadensis) spanning four decades. Supporting our hypothesis, we found positive DDHS for food (herbaceous biomass) and negative DDHS for safety (openness and roughness), such that the primary driver of habitat selection switched from food to safety as elk density decreased from 9.3 to 2.0 elk/km2 . Our results demonstrate how population density can drive landscape-level shifts in population distribution, confounding habitat selection inference and prediction and potentially affecting community-level interactions.

The Joint Evolution of Animal Movement and Competition Strategies.

AbstractCompetition typically takes place in a spatial context, but eco-evolutionary models rarely address the joint evolution of movement and competition strategies. Here we investigate a spatially explicit forager-kleptoparasite model where consumers can either forage on a heterogeneous resource landscape or steal resource items from conspecifics (kleptoparasitism). We consider three scenarios: (1) foragers without kleptoparasites, (2) consumers specializing as foragers or as kleptoparasites, and (3) consumers that can switch between foraging and kleptoparasitism depending on local conditions. We model movement strategies as individual-specific combinations of preferences for environmental cues, similar to step-selection coefficients. Using mechanistic, individual-based simulations, we study the joint evolution of movement and competition strategies, and we investigate the implications for the distribution of consumers over this landscape. Movement and competition strategies evolve rapidly and consistently across scenarios, with marked differences among scenarios, leading to differences in resource exploitation patterns. In scenario 1, foragers evolve considerable individual variation in movement strategies, while in scenario 2, movement strategies show a swift divergence between foragers and kleptoparasites. In scenario 3, where individuals' competition strategies are conditional on local cues, movement strategies facilitate kleptoparasitism, and individual consistency in competition strategy also emerges. Even in the absence of kleptoparasitism (scenario 1), the distribution of consumers deviates considerably from predictions of ideal free distribution models because of the intrinsic difficulty of moving effectively on a depleted resource landscape with few reliable cues. Our study emphasizes the advantages of a mechanistic approach when studying competition in a spatial context and suggests how evolutionary modeling can be integrated with current work in animal movement ecology.

Copuling population dynamics and diel migration patterns.

The diel vertical migration is one of the main drivers of population dynamics in the ocean. Population dynamical models of the ocean typically do not incorporate the behavioral aspects of the migration. We demonstrate a model with coupled population dynamics and behavior with the diel vertical migration emerging. We study the population dynamics and behavioral dynamics of a predator-prey system. We impose a cost of motion for both consumers and prey, and model each individual as following an Itô stochastic differential equation. We study the fixed-points of the ecosystem. Our modeling shows that as we increase the basal resource load, the strength of the diel vertical migration increases, as well as maximal velocity. In addition, a bimodal pattern emerges both for predators and consumers. The increase in the magnitude of the diel vertical migration causes a change in the allocation of copepod resources.

Density-dependent changes in elk resource selection over successional time scales following forest disturbance.

There is an increasing need to understand how animals respond to modifications of their habitat following landscape-scale disturbances such as wildfire or timber harvest. Such disturbances can promote increased use by herbivores due to changes in plant community structure that improve forage conditions, but can also cause avoidance if other habitat functions provided by cover are substantially reduced or eliminated. Quantifying the total effects of these disturbances, however, is challenging because they may not fully be apparent unless observed at successional timescales. Further, the effects of disturbances that improve habitat quality may be density dependent, such that the benefits are (1) less valuable to high-density populations because the per-capita benefits are reduced when shared among more users or, alternatively, (2) more valuable to animals living in high densities because resources may be more depleted from the greater intraspecific competition. We used 30 years of telemetry data on elk occurring at two distinct population densities to quantify changes in space use at diel, monthly, and successional timescales following timber harvest. Elk selected logged areas at night only, with selection strongest during midsummer, and peak selection occurring 14 years post harvest, but persisting for 26-33 years. This pattern of increased selection at night following a reduction in overhead canopy cover is consistent with elk exploiting improved nutritional conditions for foraging. The magnitude of selection for logged areas was 73% higher for elk at low population density, consistent with predictions from the ideal free distribution. Yet elk avoided these same areas during daytime for up to 28 years post logging and instead selected untreated forest, suggesting a role for cover to meet other life history requirements. Our results demonstrate that while landscape-scale disturbances can lead to increased selection by large herbivores and suggest that the improvement in foraging conditions can persist over short-term successional timescales, the magnitude of the benefits may not be equal across population densities. Further, the enduring avoidance of logging treatments during the daytime indicates a need for structurally intact forests and suggests that a mosaic of forest patches of varying successional stages and structural completeness is likely to be the most beneficial to large herbivores.

Fire mosaics and habitat choice in nomadic foragers.

In the mid-1950s Western Desert of Australia, Aboriginal populations were in decline as families left for ration depots, cattle stations, and mission settlements. In the context of reduced population density, an ideal free-distribution model predicts landscape use should contract to the most productive habitats, and people should avoid areas that show more signs of extensive prior use. However, ecological or social facilitation due to Allee effects (positive density dependence) would predict that the intensity of past habitat use should correlate positively with habitat use. We analyzed fire footprints and fire mosaics from the accumulation of several years of landscape use visible on a 35,300-km2 mosaic of aerial photographs covering much of contemporary Indigenous Martu Native Title Lands imaged between May and August 1953. Structural equation modeling revealed that, consistent with an Allee ideal free distribution, there was a positive relationship between the extent of fire mosaics and the intensity of recent use, and this was consistent across habitats regardless of their quality. Fire mosaics build up in regions with low cost of access to water, high intrinsic food availability, and good access to trade opportunities; these mosaics (constrained by water access during the winter) then draw people back in subsequent years or seasons, largely independent of intrinsic habitat quality. Our results suggest that the positive feedback effects of landscape burning can substantially change the way people value landscapes, affecting mobility and settlement by increasing sedentism and local population density.

Spatially Explicit Habitat Selection: Testing Contagion and the Ideal Free Distribution with Culex Mosquitoes.

AbstractSince its inception, attempts have been made to improve ideal free distribution (IFD) theory to make it better fit real-world data. Spatial contagion is a newer ecological concept that suggests that the perceived quality of a patch can be affected by the quality of its neighbor patches. Here, we present a series of experiments testing for potential contagion effects, examining how contagion can interact with the IFD and determining whether spatial context affects assessment of habitat quality. First, we tested whether the presence of conspecific competitors negatively impacts oviposition habitat selection by female mosquitoes (Culex restuans). We then used a more complex spatial landscape to determine whether competition can create a spatial contagion effect. Finally, we examined whether the density of conspecifics can adjust the contagion effect of nutrient availability. While females avoided patches containing conspecifics, there was no effect of competition/density on neighboring patches. Additionally, we found that resource availability was a significant predictor of where egg rafts were laid, but resource availability did not have a contagion effect. These results provide further support for the utility of the IFD, as individuals were able to accurately assess patch-level habitat quality.

Total biomass of a single population in two-patch environments.

For the two-patch logistic model, we study the effect of dispersal intensity and dispersal asymmetry on the total population abundance and its distribution. Two complete classifications of the model parameter space are given: one concerning when dispersal causes smaller or larger total biomass than no dispersal, and the other addressing how the total biomass changes with dispersal intensity and dispersal asymmetry. The dependencies of the population abundance of each individual patch on dispersal intensity and dispersal asymmetry are also fully characterized. In addition, the maximal and minimal total population sizes induced by dispersal are determined for the logistic model with an arbitrary number of patches, and a weak order-preserving result correlated the local population abundances with and without dispersal is established.

Ideal free dispersal in integrodifference models.

In this paper, we use an integrodifference equation model and pairwise invasion analysis to find what dispersal strategies are evolutionarily stable strategies (also known as evolutionarily steady or ESS) when there is spatial heterogeneity and possibly seasonal variation in habitat suitability. In that case there are both advantages and disadvantages of dispersing. We begin with the case where all spatial locations can support a viable population, and then consider the case where there are non-viable regions in the habitat. If the viable regions vary seasonally, and the viable regions in summer and winter do not overlap, dispersal may really be necessary for sustaining a population. Our findings generally align with previous findings in the literature that were based on other modeling frameworks, namely that dispersal strategies associated with ideal free distributions are evolutionarily stable. In the case where only part of the habitat can sustain a population, we show that a partial occupation ideal free distribution that occupies only the viable region is associated with a dispersal strategy that is evolutionarily stable. As in some previous works, the proofs of these results make use of properties of line sum symmetric functions, which are analogous to those of line sum symmetric matrices but applied to integral operators.

A general theory of avian migratory connectivity.

Birds exhibit a remarkable array of seasonal migrations. Despite much research describing migratory behaviour, the underlying forces driving how a species' breeding and wintering populations redistribute each year, that is, migratory connectivity, remain largely unknown. Here, we test the hypothesis that birds migrate in a way that minimises energy expenditure while considering intraspecific competition for energy acquisition, by developing a modelling framework that simulates an optimal redistribution of individuals between breeding and wintering areas. Using 25 species across the Americas, we find that the model accurately predicts empirical migration patterns, and thus offers a general explanation for migratory connectivity based on first ecological and energetic principles. Our model provides a strong basis for exploring additional processes underlying the ecology and evolution of migration, but also a framework for predicting how migration impacts local adaptation across seasons and how environmental change may affect population dynamics in migratory species.

Empirical tests of habitat selection theory reveal that conspecific density and patch quality, but not habitat amount, drive long-distance immigration in a wild bird.

Individuals that disperse long distances from their natal site must select breeding patches with no prior knowledge of patch suitability. Despite decades of theoretical studies examining which cues dispersing individuals should use to select breeding patches, few empirical studies have tested the predictions of these theories at spatial scales relevant to long-distance dispersal in wild animal populations. Here, we use a novel assignment model based on multiple intrinsic markers to quantify natal dispersal distances of Wood Thrush (Hylocichla mustelina) breeding in forest fragments. We show that long-distance natal dispersal in this species is more frequent than commonly assumed for songbirds and that habitat selection by these individuals is driven by density-dependence and patch quality but not the amount of habitat surrounding breeding patches. These results represent an important contribution to understanding habitat selection by dispersing individuals, especially with regards to long-distance dispersal.

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).

Emergent sustainability in open property regimes.

Current theoretical models of the commons assert that common-pool resources can only be managed sustainably with clearly defined boundaries around both communities and the resources that they use. In these theoretical models, open access inevitably leads to a tragedy of the commons. However, in many open-access systems, use of common-pool resources seems to be sustainable over the long term (i.e., current resource use does not threaten use of common-pool resources for future generations). Here, we outline the conditions that support sustainable resource use in open property regimes. We use the conceptual framework of complex adaptive systems to explain how processes within and couplings between human and natural systems can lead to the emergence of efficient, equitable, and sustainable resource use. We illustrate these dynamics in eight case studies of different social-ecological systems, including mobile pastoralism, marine and freshwater fisheries, swidden agriculture, and desert foraging. Our theoretical framework identifies eight conditions that are critical for the emergence of sustainable use of common-pool resources in open property regimes. In addition, we explain how changes in boundary conditions may push open property regimes to either common property regimes or a tragedy of the commons. Our theoretical model of emergent sustainability helps us to understand the diversity and dynamics of property regimes across a wide range of social-ecological systems and explains the enigma of open access without a tragedy. We recommend that policy interventions in such self-organizing systems should focus on managing the conditions that are critical for the emergence and persistence of sustainability.

Geometry of the ideal free distribution: individual behavioural variation and annual reproductive success in aggregations of a social ungulate.

Variation in social environment can mitigate risks and rewards associated with occupying a particular patch. We aim to integrate Ideal Free Distribution (IFD) and Geometry of the Selfish Herd (GSH) to address an apparent conflict in their predictions of equal mean fitness between patches (IFD) and declining fitness benefits within a patch (GSH). We tested these hypotheses in a socio-spatial context using individual caribou that were aggregated or disaggregated during calving and varied in their annual reproductive success (ARS). We then tested individual consistency of these spatial tactics. We reveal that two socio-spatial tactics accorded similar mean ARS (IFD); however, ARS for aggregated individuals declined near the periphery (GSH). Individuals near the aggregation periphery exhibited flexibility, whereas others were consistent. The integration of classical theories through a contemporary lens of consistent individual differences provides evidence for an integrated GSH and IFD strategy that may represent an evolutionary stable state.

Models and measures of animal aggregation and dispersal.

The dispersal of individuals within an animal population will depend upon local properties intrinsic to the environment that differentiate superior from inferior regions as well as properties of the population. Competing concerns can either draw conspecifics together in aggregation, such as collective defence against predators, or promote dispersal that minimizes local densities, for instance to reduce competition for food. In this paper we consider a range of models of non-independent movement. We include established models, such as the ideal free distribution, but also develop novel models, such as the wheel. We also develop several ways to combine different models to create a flexible model of addressing a variety of dispersal mechanisms. We further devise novel measures of movement coordination and show how to generate a population movement that achieves appropriate values of the measure specified. We find the value of these measures for each of the core models described, as well as discuss their use, and potential limitations, in discerning the underlying movement mechanisms. The movement framework that we develop is both of interest as a stand-alone process to explore movement, but also able to generate a variety of movement patterns that can be embedded into wider evolutionary models where movement is not the only consideration.

Evolution of dispersal in spatial population models with multiple timescales.

We study the evolutionary stability of dispersal strategies, including but not limited to those that can produce ideal free population distributions (that is, distributions where all individuals have equal fitness and there is no net movement of individuals at equilibrium). The environment is assumed to be variable in space but constant in time. We assume that there is a separation of times scales, so that dispersal occurs on a fast timescale, evolution occurs on a slow timescale, and population dynamics and interactions occur on an intermediate timescale. Starting with advection-diffusion models for dispersal without population dynamics, we use the large time limits of profiles for population distributions together with the distribution of resources in the environment to calculate growth and interaction coefficients in logistic and Lotka-Volterra ordinary differential equations describing population dynamics. We then use a pairwise invasibility analysis approach motivated by adaptive dynamics to study the evolutionary and/or convergence stability of strategies determined by various assumptions about the advection and diffusion terms in the original advection-diffusion dispersal models. Among other results we find that those strategies which can produce an ideal free distribution are evolutionarily stable.

Predation risk and patch size jointly determine perceived patch quality in ovipositing treefrogs, Hyla chrysoscelis.

Two of the most important factors determining community structure and diversity within and among habitat patches are patch size and patch quality. Despite the importance of patch size in existing paradigms in island biogeography, metapopulation biology, landscape ecology, and metacommunity ecology, and growing conservation concerns with habitat fragmentation, there has been little investigation into how patch size interacts with patch quality. We crossed three levels of patch size (1.13 m2 , 2.54 m2 and 5.73 m2 ) with two levels of patch quality (fish presence/absence, green sunfish [Lepomis cyanellus] and golden shiners [Notemigonus crysoleucus]) in six replicate experimental landscapes (3 × 2 × 6 = 36 patches). Both fish predators have been previously shown to elicit avoidance in ovipositing treefrogs. We examined how patch size and patch quality, as well as the interaction between size and quality, affected female oviposition preference and male calling site choice in a natural population of treefrogs (Hyla chrysoscelis). Females almost exclusively oviposited in the largest fishless patches, indicating that females use both risk, in the form of fish predators, and size itself, as components of patch quality. Females routinely use much smaller natural and experimental patches, suggesting that the responses to patch size are highly context dependent. Responses to fish were unaffected by patch size. Male responses largely mimicked those of females, but did not drive female oviposition. We suggest that patch size itself functions as another aspect of patch quality for H. chrysoscelis, and serves as another niche dimension across which species may behaviorally sort in natural systems. Because of strong, shared avoidance of fish (as well as other predators), among many colonizing taxa, patch size may be a critical factor in species sorting and processes of community assembly in freshwater habitats, allowing species to behaviorally segregate along gradients of patch size in fishless ponds. Conversely, lack of variation in patch size may concentrate colonization activity, leading to intensification of species interactions and/or increased use of lesser quality patches.

Competition, trait-mediated facilitation, and the structure of plant-pollinator communities.

In plant-pollinator communities many pollinators are potential generalists and their preferences for certain plants can change quickly in response to changes in plant and pollinator densities. These changes in preferences affect coexistence within pollinator guilds as well as within plant guilds. Using a mathematical model, we study how adaptations of pollinator preferences influence population dynamics of a two-plant-two-pollinator community interaction module. Adaptation leads to coexistence between generalist and specialist pollinators, and produces complex plant population dynamics, involving alternative stable states and discrete transitions in the plant community. Pollinator adaptation also leads to plant-plant apparent facilitation that is mediated by changes in pollinator preferences. We show that adaptive pollinator behavior reduces niche overlap and leads to coexistence by specialization on different plants. Thus, this article documents how adaptive pollinator preferences for plants change the structure and coexistence of plant-pollinator communities.