Ideal Free Distribution Research Articles

Central place foragers, prey depletion halos, and how behavioral niche partitioning promotes consumer coexistence

Many seabirds congregate in large colonies for breeding, a time when they are central place foragers. An influential idea in seabird ecology posits that competition during breeding results in an area of reduced prey availability around colonies, a phenomenon known as Ashmole's halo, and that this limits colony size. This idea has gained empirical support, including the finding that species coexisting within a colony might be able to do so by foraging on a single prey species but at different distances. Here, we provide a comprehensive mathematical model for central place foragers exploiting a single prey in a two-dimensional environment, where the prey distribution is the result of intrinsic birth and death, movement in space, and mortality due to foraging birds (we also consider a variant tailored toward colonial social insects). Bird predation at different distances occurs according to an ideal free foraging distribution that maximizes prey delivery under flight and search costs. We fully characterize the birds' ideal free distribution and the prey distribution it generates. Our results show that prey depletion halos around breeding colonies are a robust phenomenon and that the birds' ideal free distribution is sensitive to prey movement. Furthermore, coexistence of several seabird species on a single prey easily emerges through behavioral niche partitioning whenever trait differences between species entail trade-offs between efficiently exploiting a scarce prey close to the colony and a more abundant prey far away. Such behavioral-based coexistence-inducing mechanism should generalize to other habitat and diet choice scenarios.

Multiscale spatial analysis of two plant–insect interactions: effects of landscape, resource distribution, and other insects

ContextBiotic resource exploitation is a critical determinant of species’ distributions. However, quantifying resource exploitation patterns through space and time can be difficult, complicating their incorporation in spatial ecology studies. Therefore, understanding the local drivers of spatial patterns of resource exploitation may contribute to better large-scale species distribution models.ObjectivesWe investigated (1) how the resource exploitation patterns of two trophic interactions (plant–insect) are explained by insect behaviour, resource aggregation, and potential insect-insect interactions. We also analyzed how (2) resource patch size and (3) resource accessibility in a heterogeneous landscape affected host exploitation patterns.MethodsWe quantified nectar robbing by insects in the genus Bombus (bumblebees) and seed predation by Brachypterolus vestitus larvae (Antirrhinum beetle) on Antirrhinum majus L. (wild snapdragons) in the Pyrenees Mountains, Catalonia, Spain. We tested hypotheses about resource exploitation by integrating spatial analyses at multiple scales.ResultsBoth trophic interactions were aggregated, explained by the aggregation of their resource. At some scales, nectar robbing is more aggregated than the resource. Trophic interaction abundance is proportional to resource patch size, following the ideal free distribution model. Landscape features do not explain the locations exploited. Nectar robbing and seed predation occur together more often than expected.ConclusionsOur findings suggest that multiple biotic and ecological spatial factors may simultaneously affect resource exploitation at a local scale. These findings should be considered when developing agricultural projects, management plans and conservation policies.

Patterns of spawning and settlement of reef fishes as strategic responses to post-settlement competition

Settlement is a critical transition in the life history of reef fish, and the timing of this event can have a strong effect on fitness. Key factors that influence settlement timing are predictable lunar cyclic variation in tidal currents, moonlight, and nocturnal predation risk as larvae transition from pelagic to benthic environments. However, populations typically display wide variation in the arrival of settlers over the lunar cycle. This variation is often hypothesized to result from unpredictable conditions in the pelagic environment and bet-hedging by spawning adults. Here, we consider the hypothesis that the timing of spawning and settlement is a strategic response to post-settlement competition. We use a game theoretic model to predict spawning and settlement distributions when fish face a tradeoff between minimizing density-independent predation risk while crossing the reef crest vs. avoiding high competitor density on settlement habitat. In general, we expect competition to spread spawning over time such that settlement is distributed around the lunar phase with the lowest predation risk, similar to an ideal free distribution in which competition spreads competitors across space. We examine the effects of overcompensating density dependence, age-dependent competition, and competition among daily settler cohorts. Our model predicts that even in the absence of stochastic variation in the larval environment, competition can result in qualitative divergence between spawning and settlement distributions. Furthermore, we show that if competitive strength increases with settler age, competition results in covariation between settler age and settlement date, with older larvae settling when predation risk is minimal. We predict that competition between daily cohorts delays peak settlement, with priority effects potentially selecting for a multimodal settlement distribution.

Shared space and resource use within a building environment: An indoor geography

AbstractIndoor spaces are essential to most humans' lives. Furthermore, in many cases, buildings are shared indoor environments that contain diverse people and resources. Spatial patterns of use are important but under‐examined aspects of human‐building interactions. This study leverages perspectives from human‐environment geography and mechanical engineering to examine spatial patterns of use within a network of shared indoor spaces in an academic building at a research university in the United States. Here we ask: (1) What spaces and resources do building users value? and (2) How are values associated with observed measures of use? We hypothesise that spatial patterns of use follow an ideal free distribution (IFD), a common ecological model of resource use. To test this, we define measures of value and use derived from mixed qualitative (n = 50) and survey‐based social data (n = 196) and data from a building‐based system of accelerometers. Our analyses provide some support for the IFD hypothesis. We discuss the implications of this finding and potential new avenues for geographic research in shared indoor environments.

The adaptive value of density-dependent habitat specialization and social network centrality

Density dependence is a fundamental ecological process. In particular, animal habitat selection and social behavior often affect fitness in a density-dependent manner. The Ideal Free Distribution (IFD) and niche variation hypothesis (NVH) present distinct predictions associated with Optimal Foraging Theory about how the effect of habitat selection on fitness varies with population density. Using caribou (Rangifer tarandus) in Canada as a model system, we test competing hypotheses about how habitat specialization, social behavior, and annual reproductive success (co)vary across a population density gradient. Within a behavioral reaction norm framework, we estimate repeatability, behavioral plasticity, and covariance among social behavior and habitat selection to investigate the adaptive value of sociality and habitat selection. In support of NVH, but not the IFD, we find that at high density habitat specialists had higher annual reproductive success than generalists, but were also less social than generalists, suggesting the possibility that specialists were less social to avoid competition. Our study supports niche variation as a mechanism for density-dependent habitat specialization.

The evolutionary stability of partial migration with Allee effects

An Allee effect is a density-dependent phenomenon in which population growth or individual components of fitness increase as population density increases. Understanding the density-dependent effects is vital to elucidate how populations evolve and to investigate evolutionary stability. Partial migration, where a proportion of a population migrates while other individuals remain resident, is widespread across most migratory lineages. However, the mechanism still needs to be better understood in most taxa, especially those experiencing positive density-dependent effects. Here we investigate the evolutionary stability of a partial migration population with only the migrant population experiencing Allee effects. Using the Evolutionary Game Theoretic (EGT) approach, we prove the existence and uniqueness of an evolutionary stable strategy (ESS). EGT provides a mathematical framework for understanding and modelling Darwinian evolution by natural selection. We also show that the ESS is the only Ideal Free Distribution (IFD) that arises in the context of a partially migrating population in a two-habitat environment.

Predator–Prey Dynamics and Ideal Free Distribution in a Heterogeneous Environment

The concept of an ideal free distribution (IFD) is extended to a predator–prey system in a heterogeneous environment. We consider reaction–diffusion–advection equations which describe the evolution of spatial distributions of predators and prey under directed migration. Modification of local interaction terms is introduced, if some coefficients depend on resource. Depending on coefficients of local interaction, the different scenarios of predator distribution are possible. We pick out three cases: proportionality to prey (and respectively to resource), indifferent distribution and inversely proportional to the prey. These scenarios apply in the case of nonzero diffusion and taxis under additional conditions on diffusion and migration rates. We examine migration functions for which there are explicit stationary solutions with nonzero densities of both species. To analyze solutions with violation of the IFD conditions, we apply asymptotic expansions and a numerical approach with staggered grids. The results for a two-dimensional domain with no-flux boundary conditions are presented.

Ideal free distributions form across a regulatory boundary in the Northwest Atlantic Fisheries Organization (NAFO) Division 4X and 5Z groundfish fisheries

We used isodars, developed from the ideal free distribution (IFD), to predict the distribution of fishing effort across regulatory boundaries in the south-western Scotian Shelf’s haddock fishery. Our analysis was focused around the boundary between Northwest Atlantic Fisheries Organization’s Divisions 4X and 5Z. While effort within 4X was related to the standardized catch value and effort experienced along the 4X–5Z boundary, most effort predictions across the boundary were also accurate. Accuracy of these cross-boundary isodars suggests that a high degree of movement across the boundary meets the IFD assumption of free movement and thus, effort on one side of the boundary is related to fishing success on the other side of the boundary. Fisheries management strategies should adopt a broad view that encompasses adjacent regulatory regions to understand where vessels may choose to fish when multiple regulatory regions are accessible. In fisheries where isodars describe effort distributions across a regulatory boundary, the relative abundance of the underlying fish population could be better indicated by effort distribution among regulatory regions than by catch rates.

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.

The Goldilocks Zone for maize agriculture and the settlement and abandonment of the West Tavaputs Plateau

Between 2100 and 500 BP, maize farming spread throughout the American Southwest, driving changes in land use patterns and relative increases in the number of archaeological sites, which is commonly interpreted as increases in population. In the context of the Southwest, with its variable topography and limited water sources, the locations suitable for productive maize agriculture are limited. Higher elevation locations often have a greater abundance of water, both in the form of precipitation and perennial water sources but lack the growing season lengths required for maize farming. Lower elevation locations have the long growing seasons required for maize, but often have higher evaporation rates corresponding with higher temperatures, and thus decreased soil moisture retention. The relationship between elevation and maize agriculture is well recognized, and locations where both growing season length and moisture requirements can be met serve as a Goldilocks Zone in which maize farming is possible. Here, we use a regional approach to model the Goldilocks Zone for maize farming in Utah, and then contextualize patterns of settlement and abandonment on the West Tavaputs Plateau (WTP) in east-central Utah. We use archaeological sites with direct evidence of maize cultivation, modern growing degree days estimates, and modern estimates of moisture abundance to bracket the prehistoric maize farming niche in Utah. Then, we apply the model to archaeological data from the WTP to test hypotheses derived from the Ideal Free Distribution model about the effects population and precipitation changes had on prehistoric land use patterns of settlement and abandonment, and whether the patterns of settlement and abandonment differ from one another. We find that a) population drives land use patterns in the WTP, but not in the way we originally hypothesized, suggesting there is an important decision variable missing from our model, which may pertain to the specific topographic setting of the WTP and the distribution of its water sources, b) precipitation has no effect on land use patterns suggesting that maize agriculture on the WTP was dependent on irrigation, and c) that patterns of settlement and abandonment seem to mirror each other.

Applying the ideal free distribution to the movement of a highly mobile gillnet fishery for Pacific salmon

Ecological models are used to understand where fishing vessels operate, improving fisheries management success. The ideal free distribution (IFD) predicts equalization of catch across locations in response to distributions of fish and competing vessels. We applied the IFD as a null model to investigate the movement and catch per vessel (CPUE) of the sockeye salmon drift gillnet fleet in Bristol Bay, AK, from 1980 to 2019. The IFD prediction of equal CPUE across areas was not supported, so we explored violations of two assumptions of the theory. We categorized each vessel according to its mobility, highlighting the “free to move” assumption, and found that when we removed nonmobile vessels, some districts had fewer vessels than predicted from their high CPUE. We examined the “equal competitive ability” assumption by calculating the average CPUE, relative to success of other vessels. The underutilization of profitable districts persisted. Overall, the fleet underused high CPUE areas when considering differences in mobility and relative fishing success, indicating that unmeasured safety concerns, travel costs, knowledge of fishing grounds, or other factors could be preventing an IFD.

Maximum sustainable yield as a reference point in the presence of fishing effort that follows an ideal free distribution

AbstractThe concept of maximum sustainable yield (MSY), and the underlying Schaefer model, remain relevant in fisheries management today in spite of past difficulties. However, this model is often applied without the consideration of the spatial structure or dynamics of fishing activities. We expand the Schaefer model to account for multiple fishing sites and fishing activities (effort) that follow an ideal free distribution (IFD, a form of Nash equilibrium) driven by exploitation. We explore this conceptual model using both analytical and numerical solutions. MSY across the fishery is unaffected by the spatial structure when fishing is allocated independently within sites. However, in other cases IFD effort dynamics depress MSY and modify the values of associated reference points. The game theoretic aspect of fleet dynamics should be considered in the use of MSY as a management reference point or during the application of the Schaefer model to data‐limited fisheries.

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.

Mathematical model of ideal free distribution in the predator-prey system

We consider a system of reaction-diffusion-advection equations which describes the evolution of spatial distributions of antagonistic populations under directed migration. The concept of an ideal free distribution (IFD) for a predator-prey system is introduced. We find conditions on parameters under which there exist explicit stationary solutions with nonzero densities of both species. The numerical approach with staggered grids is used to analyze solutions in case of violation of the conditions on the coefficients that provide the IFD. We construct asymptotic expansions for an inhomogeneous one-dimensional area and present the results of a computational experiment in the case of violation of the IFD conditions.

Coevolution of Patch Selection in Stochastic Environments.

AbstractSpecies interact in landscapes where environmental conditions vary in time and space. This variability impacts how species select habitat patches. Under equilibrium conditions, evolution of this patch selection can result in ideal free distributions where per capita growth rates are zero in occupied patches and negative in unoccupied patches. These ideal free distributions, however, do not explain why species occupy sink patches, why competitors have overlapping spatial ranges, or why predators avoid highly productive patches. To understand these patterns, we solve for coevolutionarily stable strategies (coESSs) of patch selection for multispecies stochastic Lotka-Volterra models accounting for spatial and temporal heterogeneity. In occupied patches at the coESS, we show that the differences between the local contributions to the mean and the variance of the long-term population growth rate are equalized. Applying this characterization to models of antagonistic interactions reveals that environmental stochasticity can partially exorcize the ghost of competition past, select for new forms of enemy-free and victimless space, and generate hydra effects over evolutionary timescales. Viewing our results through the economic lens of modern portfolio theory highlights why the coESS for patch selection is often a bet-hedging strategy coupling stochastic sink populations. Our results highlight how environmental stochasticity can reverse or amplify evolutionary outcomes as a result of species interactions or spatial heterogeneity.

The economics of early inequality.

We examine three recent frameworks that attempt to explain early inequality. One explanation involves the emergence of dense and predictable resource patches in the Holocene, together with differential asset accumulation and inheritance by individuals or households. In this view, agriculture and pastoralism led to greater inequality because farmland and animal herds were readily inherited. Another explanation involves the distinction between ideal free and ideal despotic population distributions, together with factors that could trigger a transition from the former to the latter. We offer a third framework based on economic concepts. In our view, inequality initially arose across locations (insider-outsider inequality) and reflected geographical differences in resource endowments at those locations. As population densities increased, the barriers to individual migration across locations included fewer kinship linkages and the use of force by insiders to exclude outsiders. These barriers became important with the transition from mobile to sedentary foraging and predate agriculture. Insider-outsider inequality was followed by stratification within settlements (elite-commoner inequality), which arose at still higher population densities. We see these three theoretical approaches as distinct but complementary. While they overlap, each emphasizes some phenomena and processes ignored by the other two. This article is part of the theme issue 'Evolutionary ecology of inequality'.

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.

Grazing-induced cattle behaviour modulates the secondary production in a Eurasian steppe ecosystem

Livestock-grassland interactions are among the most important relationships in grazed grassland ecosystems, where herbivores play a crucial role in plant community and ecosystem functions. However, previous studies primarily have focused on the responses of grasslands to grazing, with few focussing on the effects of livestock behaviour that in turn would influence livestock intake and primary and secondary productivity. Through a 2-year grazing intensity experiment with cattle in Eurasian steppe ecosystem, global positioning system (GPS) collars were used to monitor animal movements, where animal locations were recorded at 10-min intervals during the growing season. We used a random forest model and the K-means method to classify animal behaviour and quantified the spatiotemporal movements of the animals. Grazing intensity appeared to be the predominant driver for cattle behaviour. Foraging time, distance travelled, and utilization area ratio (UAR) all increased with grazing intensity. The distance travelled was positively correlated with foraging time, yielding a decreased daily liveweight gain (LWG) except at light grazing. Cattle UAR showed a seasonal pattern and reached the maximum value in August. In addition, the canopy height, above-ground biomass, carbon content, crude protein, and energy content of plants all affected cattle behaviour. Grazing intensity and the resulting change in above-ground biomass and forage quality jointly determined the spatiotemporal characteristics of livestock behaviour. Increased grazing intensity limited forage resources and promoted intraspecific competition of livestock, which induced longer travelling distance and foraging time, and more even spatial distribution when seeking habitat, which ultimately led to a reduction in LWG. In contrast, under light grazing where there were sufficient forage resources, livestock exhibited higher LWG with less foraging time, shorter travelling distance, and more specialized habitat occupation. These findings support the Optimal Foraging Theory and the Ideal Free Distribution model, which may have important implications for grassland ecosystem management and sustainability.

Ideal free distribution of unequal competitors: spatial assortment and evolutionary diversification of competitive ability

Ideal free distribution of unequal competitors: spatial assortment and evolutionary diversification of competitive ability

From spawner habitat selection to stock-recruitment: Implications for assessment.

The relationship between the spawning stock size and subsequent number of recruits is a central concept in fisheries ecology. The influence of habitat selection of spawning individuals on the stock-recruitment relationship is poorly known. Here we explore how each of four different spawner behaviors might influence the stock-recruitment relationship and estimates of its parameters in the two most commonly used stock-recruitment functions (Beverton-Holt and Ricker). Using simulated stock-recruitment data generated by four different spawner behaviors applied to multiple discrete habitats, we show that when spawners were distributed proportionally to local carrying capacities, there was small or no bias in estimated recruitment and stock-recruitment parameters. For an ideal free distribution of spawners, larger bias in the estimates of recruitment and stock-recruitment parameters was obtained, whereas a random and a stepwise spawner behavior introduced the largest bias. Using stock-recruitment data corresponding to a "realistic" range of population densities and adding measurement error (20%-60%) to the simulated stock-recruitment data generated larger variation in the estimation bias than what was introduced by the spawner behavior. Thus, for exploited stocks at low population density and where spawning stock size and recruitment cannot be observed perfectly, partial observation of the possible spawner abundance range and measurement error might be of higher concern for management.