Ideal Free Distribution Research Articles

The role of density-dependent and -independent processes in spawning habitat selection by salmon in an Arctic riverscape.

Density-dependent (DD) and density-independent (DI) habitat selection is strongly linked to a species’ evolutionary history. Determining the relative importance of each is necessary because declining populations are not always the result of altered DI mechanisms but can often be the result of DD via a reduced carrying capacity. We developed spatially and temporally explicit models throughout the Chena River, Alaska to predict important DI mechanisms that influence Chinook salmon spawning success. We used resource-selection functions to predict suitable spawning habitat based on geomorphic characteristics, a semi-distributed water-and-energy balance hydrologic model to generate stream flow metrics, and modeled stream temperature as a function of climatic variables. Spawner counts were predicted throughout the core and periphery spawning sections of the Chena River from escapement estimates (DD) and DI variables. Additionally, we used isodar analysis to identify whether spawners actively defend spawning habitat or follow an ideal free distribution along the riverscape. Aerial counts were best explained by escapement and reference to the core or periphery, while no models with DI variables were supported in the candidate set. Furthermore, isodar plots indicated habitat selection was best explained by ideal free distributions, although there was strong evidence for active defense of core spawning habitat. Our results are surprising, given salmon commonly defend spawning resources, and are likely due to competition occurring at finer spatial scales than addressed in this study.

Phylogenetic patterns of tragedy of commons in intraspecific root competition

Aims For some plant species, intraspecific belowground competition takes a form of the tragedy of the commons (TOC), where competing neighbours invest more in root systems than would be appropriate for optimal nutrient uptake for the group. However, there are also species not involved in TOC, optimizing their root investment according to the ideal free distribution (IFD). Important and yet unresolved question is which ecological and evolutionary forces determine whether a species follows the strategy yielding TOC or IFD.

The redistribution of non-breeding dunlins in response to the post-DDT recovery of falcons.

Large-scale changes in predator populations are occurring worldwide due to (re-)introductions, over-exploitation, or recovery after decimation by pesticides and persecution. These widespread changes may affect the distribution of their prey. We studied the continental-scale distributions of non-breeding Calidris alpina pacifica and C. a. hudsonia (Pacific and Atlantic dunlins, respectively), as numbers of their major predators-peregrines (Falco peregrinus) and merlins (F. columbarius; together 'falcons')-increased after DDT was banned in 1973. For the period 1975-2010 we compiled the number of dunlins and falcons in each of 244 Christmas Bird Count circles, which cover most of the dunlins' non-breeding ranges. Over the study period, falcons increased by 6.5- (Pacific) and 3.1- (Atlantic) fold, spread to more count circles, and the number of dunlins per falcon fell. The annual total count of the two dunlin sub-species fluctuated strongly and independently. We measuredannual aggregation as the expected proportion of a subspecies total found on the same count circle as a randomly selected dunlin. The average aggregation of Pacific dunlins (0.117) was about double that of Atlantic dunlins (0.059), with annual variation largely attributable to changes in a few large count circles. The slope of the aggregative response to year-on-year changes in dunlin numbers was identical on the two coasts. The response to the ongoing falcon increase was positive and significant on the Pacific and slightly negative on the Atlantic. We interpret these results using a version of the ideal free distribution that includes predation danger.

Drivers of redistribution of fishing and non-fishing effort after the implementation of a marine protected area network.

Marine spatial planning (MSP) is increasingly utilized to sustainably manage ocean uses. Marine protected areas (MPAs), a form of spatial management in which parts of the ocean are regulated to fishing, are now a common tool in MSP for conserving marine biodiversity and managing fisheries. However, the use of MPAs in MSP often neglects, or simplifies, the redistribution of fishing and non-fishing activities inside and outside of MPAs following their implementation. This redistribution of effort can have important implications for effective MSP. Using long-term (14yr) aerial surveys of boats at the California Channel Islands, we examined the spatial redistribution of fishing and non-fishing activities and their drivers following MPA establishment. Our data represent 6yr of information before the implementation of an MPA network and 8yr after implementation. Different types of boats responded in different ways to the closures, ranging from behaviors by commercial dive boats that support the hypothesis of fishing-the-line, to behaviors by urchin, sport fishing, and recreational boats that support the theory of ideal free distribution. Additionally, we found that boats engaged in recreational activities targeted areas that are sheltered from large waves and located near their home ports, while boats engaged in fishing activities also avoided high wave areas but were not constrained by the distance to their home ports. We did not observe the expected pattern of effort concentration near MPA borders for some boat types; this can be explained by the habitat preference of certain activities (for some activities, the desired habitat attributes are not inside the MPAs), species' biology (species such as urchins where the MPA benefit would likely come from larval export rather than adult spillover), or policy-infraction avoidance. The diversity of boat responses reveals variance from the usual simplified assumption that all extractive boats respond similarly to MPA establishment. Our work is the first empirical study to analyze the response of both commercial and recreational boats to closure. Our results will inform MSP in better accounting for effort redistribution by ocean users in response to the implementation of MPAs and other closures.

Settlement ecology in Bronze Age Messenia

In this paper, we model patterns of expansion and contraction of settlement in Bronze Age Messenia (ca. 3100–1050 BCE) using the ideal free distribution (IFD). We rank potential settlement locations on the landscape using environmental and cultural variables, including watershed size, which is a proxy for fresh water availability, net primary productivity, and the distance to the location of the Palace of Nestor at Pylos, a central site of political importance throughout most of the Bronze Age. The settlement chronology for the region is derived from an existing database of survey data and conforms to the predictions of the IFD. The highest-ranked habitats were settled first and the population expanded to lower-ranked habitats as population density increased. The data also conforms to the IFD prediction that important political centers should follow the same pattern, expanding from higher- to lower-ranked habitats. This model helps to provide an understanding of the effects of the unique environmental and cultural landscape of the region on settlement prior to the rise of the major Mycenaean centers in mainland Greece. The application of the IFD to a sociopolitically complex case demonstrates its broad potential for understanding historical trajectories in settlement patterns throughout the world.

Large mammal biomass predicts the changing distribution of hunter-gatherer settlements in mid-late Holocene Alaska

This study provides an ecological explanation for the distribution of Arctic Small Tool tradition (ASTt) settlements in Alaska and the origin of their arctic maritime adaptation. Theoretically grounded in the ideal free distribution (IFD) model, which predicts that higher ranked habitats will be occupied first and most continuously, we contend that the location of large mammals was a major factor influencing human dispersal and settlement decisions in the arctic and subarctic ecosystems of Alaska. We rank habitat suitability based on historic mammal population densities from wildlife ecology reports across predefined ecological zones in Alaska; we multiply densities by average animal weights per species to determine suitability rankings. Coastal habitats in Alaska are higher ranked than adjacent tundra habitats, but the interior boreal forest may have been the highest ranked, considering technological constraints of hunting aquatic species. The ASTt migration into Alaska created population pressure that promoted the colonization of the unoccupied Arctic coast and development of the dual, terrestrial-maritime economy. When pan-Alaska human populations declined around 3200–2500years ago low ranked tundra ecoregions were abandoned. As human populations recovered Alaska coasts became the most densely populated habitats. The adaptive logic entailed in the IFD provides a consistent evolutionary interpretation for settlement patterns documented in this region.

Geospatial modelling for predicting the ideal free settlement of Rapa

ABSTRACTThis paper describes a geospatial model that was developed to be the basis for applying models from human behavioural ecology (HBE). Specifically, the logic of the ideal free distribution (IFD) is narrowed and applied to the post‐colonisation spread of intensive agriculture in order to predict the order and locations of its expansion. The island of Rapa, Austral Islands, is used to highlight the utility of this method. Rapa is an ideal location due to the prominent use of intensive irrigated taro agriculture and its role in explanations of the social development of territoriality on the island. The use of similar geospatial models has wider implications for island archaeology in furthering the understanding of diachronic settlement patterns.

The Classic Period Maya transition from an ideal free to an ideal despotic settlement system at the polity of Uxbenká

Journal of Anthropological Archaeology 45 (2017) 53–68 Contents lists available at ScienceDirect Journal of Anthropological Archaeology journal homepage: www.elsevier.com/locate/jaa The Classic Period Maya transition from an ideal free to an ideal despotic settlement system at the polity of Uxbenka Keith M. Prufer a, ⇑ , Amy E. Thompson a , Clayton R. Meredith a , Brendan J. Culleton b , Jillian M. Jordan a , Claire E. Ebert b , Bruce Winterhalder c , Douglas J. Kennett b a b c Department of Anthropology, University of New Mexico, United States Department of Anthropology, The Pennsylvania State University, United States Department of Anthropology, University of California-Davis, United States 1. Introduction More than eleven hundred years of settlement history at Uxbenka, a Classic Period Maya polity (ca. 300 BC to AD 900) located in southern Belize (Fig. 1), conform to a patterned shift from an ideal free to a despotic distribution, coincident with a change toward habitat suitability increasingly dependent on anthropogenic features of the landscape. To demonstrate this claim, we document the development and geospatial organization of the settlement systems at Uxbenka using differential GPS and LiDAR data associated with extensive survey and excavations (Prufer et al., 2015). We also chronicle the development of the built landscape; a major trade corridor, neighborhoods, districts, and the ceremonial center being the prime features under consideration. Finally, we assess the relationships between the spatial patterns as populations in-fill to political developments within the frame- work of two population ecology models: the Ideal Free Distribution (IFD) and Ideal Despotic Distribution (IDD). 1.1. Setting, objectives and questions Uxbenka (Fig. 1) was a moderately sized Maya center during the Classic Period (AD 250–900), comparable to nearby sites such as Pusilha and Lubaantun but small when compared to the major cen- ters of Tikal and Caracol to the northwest. Since 2005 the Uxbenka Archaeological Project (UAP) has conducted extensive survey and excavations in the settlement zone surrounding Uxbenka, with a focus on building a precise absolute chronology for the develop- ment of the community and its environmental context (Culleton et al., 2012; Prufer et al., 2011, 2015; Prufer and Thompson, 2016). Cultural ecological studies conducted in parallel are docu- menting the agro-ecology of contemporary subsistence tactics in the nearby community of Santa Cruz (Baines, 2015; Culleton, 2012). We draw on both sources of information in our analysis. In agrarian communities, residential settlements are the pri- mary social unit and location of human interactions that articulate with broader economic and political processes (Ashmore, 1981; ⇑ Corresponding author. E-mail address: kmp@unm.edu (K.M. Prufer). http://dx.doi.org/10.1016/j.jaa.2016.11.003 0278-4165/Published by Elsevier Inc. Willey, 1968). Despite their importance they remain understudied and poorly dated in the Maya area (See Supplement S-1). For instance, little research has examined the precise chronological histories of settlements surrounding Classic Period Maya centers. This leaves us unable to answer basic anthropological questions: Why were people more successful in some locations compared to others on a landscape? How did population growth, the natural environment, and the built environment influence status dispari- ties of settlements through time? What are the relationships between settlements, which generate agricultural and other resources, and the consolidation and differential control of those resources by emerging political elites? We explore fundamental questions in the development of set- tlement systems in the Maya Lowlands and beyond: What organiz- ing principles and socio-environmental factors guide residential settlement decisions in agricultural societies when the environ- ment is an open access frontier? How do these initial choices change with the growth and development of low-density urban environments? And, what are the long-term consequences of these initially open but increasingly constrained settlement options? We identify and assess the relative importance of social and environ- mental variables that may have been important to human decision-making in a bounded, community-centered landscape. Furthermore, we examine how those decisions were reflected in the relative success of residential compounds over centuries of growth. In pursuit of answers to these and related questions, we (a) pre- sent a high precision AMS 14 C chronology for the development of the Uxbenka settlement system; (b) identify and describe neigh- borhoods (loci of daily household interactions) and districts (local seats of power and authority) as organizing principles for the dis- tribution of households and local economic and political control across the landscape; (c) develop population estimates and a model of demographic growth; (d) analyze factors affecting deci- sions about household location; and (e) offer an evolutionary anthropology model, drawing on behavioral ecology, to help explain why some households and neighborhoods were larger, longer-occupied, and apparently more successful over the 1150 year occupation of the polity. Our evidence and interpreta- tion together document an increasingly stratified relationship

Evolution of natal dispersal in spatially heterogenous environments

Understanding the evolution of dispersal is an important issue in evolutionary ecology. For continuous time models in which individuals disperse throughout their lifetime, it has been shown that a balanced dispersal strategy, which results in an ideal free distribution, is evolutionary stable in spatially varying but temporally constant environments. Many species, however, primarily disperse prior to reproduction (natal dispersal) and less commonly between reproductive events (breeding dispersal). These species include territorial species such as birds and reef fish, and sessile species such as plants, and mollusks. As demographic and dispersal terms combine in a multiplicative way for models of natal dispersal, rather than the additive way for the previously studied models, we develop new mathematical methods to study the evolution of natal dispersal for continuous-time and discrete-time models. A fundamental ecological dichotomy is identified for the non-trivial equilibrium of these models: (i) the per-capita growth rates for individuals in all patches are equal to zero, or (ii) individuals in some patches experience negative per-capita growth rates, while individuals in other patches experience positive per-capita growth rates. The first possibility corresponds to an ideal-free distribution, while the second possibility corresponds to a “source-sink” spatial structure. We prove that populations with a dispersal strategy leading to an ideal-free distribution displace populations with dispersal strategy leading to a source-sink spatial structure. When there are patches which cannot sustain a population, ideal-free strategies can be achieved by sedentary populations, and we show that these populations can displace populations with any irreducible dispersal strategy. Collectively, these results support that evolution selects for natal or breeding dispersal strategies which lead to ideal-free distributions in spatially heterogenous, but temporally homogenous, environments.

A continuous ideal free distribution approach to the dynamics of selfish, cooperative and kleptoparasitic populations.

Population distributions depend upon the aggregate behavioural responses of individuals to a range of environmental factors. We extend a model of ideally motivated populations to describe the local and regional consequences of interactions between three populations distinguished by their levels of cooperation and exploitation. Inspired by the classic prisoner's dilemma game, stereotypical fitness functions describe a baseline non-cooperative population whose per capita fitness decreases with density, obligate co-operators who initially benefit from the presence of conspecifics, and kleptoparasites who require heterospecifics to extract resources from the environment. We examine these populations in multiple combinations, determine where both local and regional coexistence is permitted, and investigate conditions under which one population will invade another. When they invade co-operators in resource-rich areas, kleptoparasites initiate a dynamic instability that leads to the loss of both populations; however, selfish hosts, who can persist at low densities, are immune to this risk. Furthermore, adaptive movement may delay the onset of instability as dispersal relieves dynamic stress. Selfish and cooperative populations default to mutual exclusion, but asymmetric variations in interference strength may relax this condition and permit limited sympatry within the environment. Distinct sub-communities characterize the overall spatial structure.

Density-dependent changes in effective area occupied for sea-bottom-associated marine fishes.

The spatial distribution of marine fishes can change for many reasons, including density-dependent distributional shifts. Previous studies show mixed support for either the proportional-density model (PDM; no relationship between abundance and area occupied, supported by ideal-free distribution theory) or the basin model (BM; positive abundance-area relationship, supported by density-dependent habitat selection theory). The BM implies that fishes move towards preferred habitat as the population declines. We estimate the average relationship using bottom trawl data for 92 fish species from six marine regions, to determine whether the BM or PDM provides a better description for sea-bottom-associated fishes. We fit a spatio-temporal model and estimate changes in effective area occupied and abundance, and combine results to estimate the average abundance-area relationship as well as variability among taxa and regions. The average relationship is weak but significant (0.6% increase in area for a 10% increase in abundance), whereas only a small proportion of species-region combinations show a negative relationship (i.e. shrinking area when abundance increases). Approximately one-third of combinations (34.6%) are predicted to increase in area more than 1% for every 10% increase in abundance. We therefore infer that population density generally changes faster than effective area occupied during abundance changes. Gadiformes have the strongest estimated relationship (average 1.0% area increase for every 10% abundance increase) followed by Pleuronectiformes and Scorpaeniformes, and the Eastern Bering Sea shows a strong relationship between abundance and area occupied relative to other regions. We conclude that the BM explains a small but important portion of spatial dynamics for sea-bottom-associated fishes, and that many individual populations merit cautious management during population declines, because a compressed range may increase the efficiency of harvest.

Density‐Dependent Foraging and Interference Competition by Common Gartersnakes are Temperature Dependent

AbstractThe ideal free distribution (IFD) predicts that optimal foragers will select foraging patches to maximize food rewards and that groups of foragers should thus be distributed between food patches in proportion to the availability of food in those patches. Because many of the underlying mechanisms of foraging are temperature dependent in ectotherms, the distribution of ectothermic foragers between food patches may similarly depend on temperature because the difference in fitness rewards between these patches may change with temperature. We tested the hypothesis that the distribution of Common Gartersnakes (Thamnophis sirtalis) between food patches can be explained by an IFD, but that conformance to an IFD weakens as temperature departs from the optimal temperature because fitness rewards, interference competition and the number of individuals foraging are highest at the optimal temperature. First, we determined the optimal temperature for foraging. Second, we examined group foraging at three temperatures and three density treatments. Search time was optimized at 27°C, handling time at 29°C and digestion time at 32°C. Gartersnakes did not match an IFD at any temperature, but their distribution did change with temperature: snakes at 20°C and at 30°C selected both food patches equally, while snakes at 25°C selected the low food patch more at low density and the high food patch more at high density. Food consumption and competition increased with temperature, and handling time decreased with temperature. Temperature therefore had a strong impact on foraging, but did not affect the IFD. Future work should examine temperature‐dependent foraging in ectotherms that are known to match an IFD.

Ideal Cost-Free Distributions in Structured Populations for General Payoff Functions

The important biological problem of how groups of animals should allocate themselves between different habitats has been modelled extensively. Such habitat selection models have usually involved infinite well-mixed populations. In particular, the model of allocation over a number of food patches when movement is not costly, the ideal free distribution (IFD) model, is well developed. Here we generalize (and solve) a habitat selection game for a finite structured population. We show that habitat selection in such a structured population can have multiple stable solutions (in contrast to the equivalent IFD model where the solution is unique). We also define and study a “predator dilution game” where unlike in the habitat selection game, individuals prefer to aggregate (to avoid being caught by predators due to the dilution effect) and show that this model has a unique solution when movement is unrestricted.

Traumatic injury risk and agricultural transitions: A view from the American Southeast and beyond.

Bioarchaeological research has documented a general decline in health with the transition from foraging to farming, primarily with respect to changing patterns of morbidity. Less is known about changes in injury risk, an aspect of health more obviously tied to particular landscapes and behaviors associated with different subsistence regimes. The purpose of this research is to evaluate several hypotheses emerging from the ideal free distribution model (Fretwell & Lucas, ) that predict injury risk based on subsistence-specific practices and land use patterns. Postcranial fracture frequencies for long bones and clavicles in human skeletal remains from three Southeast U.S. regions permit examination of variability in injury risk among low-intensity (floodplain) farmers. Published data on six hunter-gatherer samples, four low-intensity agriculturalist samples, and six high-intensity agriculturalist samples comprise a comparative sample for examining variability in injury risk across three distinct subsistence traditions. Differences are evaluated using Z scores and the Fisher Exact test, Chi-Square test, and Mann-Whitney U test. While statistically significant differences are apparent among low-intensity farming groups in the Southeast sample, in the global comparison postcranial fractures are significantly less common in low-intensity agriculturalists than in hunter-gatherers or high-intensity agriculturalists. The results of this study support the hypothesis that, with respect to traumatic injury risk, low-intensity farming is a risk-averse subsistence strategy in comparison with full-time foraging or high-intensity agriculture. These data suggest that it is not agriculture per se that predicts an increase in this health risk, but rather the mode and intensity of agricultural production, findings that have important ramifications for our understanding of the health consequences of major subsistence transitions.

Competitive–cooperative models with various diffusion strategies

The paper is concerned with different types of dispersal chosen by competing species. We introduce a model with the diffusion-type term ∇⋅[a∇(u/P)] which includes some previously studied systems as special cases, where a positive space-dependent function P can be interpreted as a chosen dispersal strategy. The well-known result that if the first species chooses P proportional to the carrying capacity while the second does not then the first species will bring the second one to extinction, is also valid for this type of dispersal. However, we focus on the case when the ideal free distribution is attained as a combination of the two strategies adopted by the two species. Then there is a globally stable coexistence equilibrium, its uniqueness is justified. If both species choose the same dispersal strategy, non-proportional to the carrying capacity, then the influence of higher diffusion rates is negative, while of higher intrinsic growth rates is positive for survival in a competition. This extends the result of Dockery et al. (1998) for the regular diffusion to a more general type of dispersal.

Male Aggregation Pheromones Inhibit Ideal Free Habitat Selection in Red Flour Beetles (Tribolium castaneum)

The ideal free distribution (IFD) predicts that individuals should be distributed between habitats in proportion to habitat suitability such that mean fitness is equal in each habitat. The IFD is useful in studies examining habitat selection, yet its key assumptions are often violated and the expected IFDs are not consistently detected. While the use of aggregation pheromones by insects is expected to evolve in systems that experience positive density dependence (Allee effect), through a series of experiments we test the hypothesis that aggregation pheromones may limit the ability of individuals to achieve an IFD. Using red flour beetles (Tribolium castaneum), we specifically test the prediction that beetles in groups with an equal sex ratio or in the presence of an artificial aggregation pheromone will deviate from an IFD, whereas female-only groups will achieve an IFD. We also test the hypothesis that aggregation pheromones evolved to promote Allee effects by testing the prediction that beetle fitness will show positive density dependence at low densities. Consistent with our first hypothesis, female groups achieved an IFD, while mixed sex groups and females in the presence of an aggregation pheromone in the low food habitat under-matched the IFD. We found no evidence of Allee effects at low density, but we did find evidence of strong negative density dependence. We demonstrate that the use of aggregation pheromones may negatively impact a population’s ability to achieve an IFD and cast doubt on the hypothesis that male aggregation pheromones evolve to promote Allee effects.

Supply-demand equilibria and the size-number trade-off in spatially structured recreational fisheries.

Recreational fishing effort varies across complex inland landscapes (e.g., lake-districts) and appears influenced by both angler preferences and qualities of the fishery resource, like fish size and abundance. However, fish size and abundance have an ecological trade-off within a population, thereby structuring equal-quality isopleths expressing this trade-off across the fishing landscape. Since expressed preferences of recreational anglers (i.e., site-selection of high-quality fishing opportunities among many lakes) can be analogous to optimal foraging strategies of natural predators, adopting such concepts can aid in understanding scale-dependence in fish-angler interactions and impacts of fishing across broad landscapes. Here, we assumed a fish supply-angler demand equilibria and adapted a novel bivariate measure of fishing quality based on fish size and catch rates to assess how recreational anglers influence fishing quality among a complex inland landscape. We then applied this metric to evaluate (1) angler preferences for caught and released fish compared to harvested fish, (2) the nonlinear size-numbers trade-off with uncertainty in both traits, and (3) the spatial-scale of the equilibria across 62 lakes and four independent management regions in British Columbia's (BC) rainbow trout Oncorhynchus mykiss fishery. We found anglers had low preference for caught and released fish (~10% of the value compared to harvested fish), which modified anglers' perception of fishing quality. Hence, fishing quality and angler effort was not influenced simply by total fish caught, but largely by harvested fish catch rates. Fishing quality varied from BC's northern regions (larger fish and more abundant) compared to southern regions (smaller fish and less abundant) directly associated with a 2.5 times increase in annual fishing effort in southern regions, suggesting that latent fishing pressure can structure the size-numbers trade-off in rainbow trout populations. The presence of two different equal-quality isopleths suggests at least two effective landscapes support co-occurring ideal free distributions of recreational fishing effort in BC's rainbow fishery. Anglers' expressed preferences among lakes interacted with density dependent growth and survival within lakes to structure a size-numbers trade-off influencing how anglers perceive fishing quality and, ultimately, distribute across complex inland landscapes.

Effects of diffusion on total biomass in heterogeneous continuous and discrete-patch systems

Theoretical models of populations on a system of two connected patches previously have shown that when the two patches differ in maximum growth rate and carrying capacity, and in the limit of high diffusion, conditions exist for which the total population size at equilibrium exceeds that of the ideal free distribution, which predicts that the total population would equal the total carrying capacity of the two patches. However, this result has only been shown for the Pearl-Verhulst growth function on two patches and for a single-parameter growth function in continuous space. Here, we provide a general criterion for total population size to exceed total carrying capacity for three commonly used population growth rates for both heterogeneous continuous and multi-patch heterogeneous landscapes with high population diffusion. We show that a sufficient condition for this situation is that there is a convex positive relationship between the maximum growth rate and the parameter that, by itself or together with the maximum growth rate, determines the carrying capacity, as both vary across a spatial region. This relationship occurs in some biological populations, though not in others, so the result has ecological implications.

A fitness-driven cross-diffusion system from population dynamics as a gradient flow

We consider a fitness-driven model of dispersal of N interacting populations, which was previously studied merely in the case N=1. Based on some optimal transport distance recently introduced, we identify the model as a gradient flow in the metric space of Radon measures. We prove existence of global non-negative weak solutions to the corresponding system of parabolic PDEs, which involves degenerate cross-diffusion. Under some additional hypotheses and using a new multicomponent Poincaré–Beckner functional inequality, we show that the solutions converge exponentially to an ideal free distribution in the long time regime.

Ideal free distribution of metabolic activity: Implications of seasonal metabolic-activity patterns on competitive coexistence

The seasonal distribution of metabolic activity determines how much individuals experience different aspects of a periodically changing environment. Seasonal metabolic-activity patterns of coexisting species may differ significantly despite their shared environmental conditions, suggesting that interspecific diversification of this trait has a major role in the coexistence of competing species. In the present study the effect of the seasonal distribution of metabolic activity on intra- and interspecific competition is investigated in a consumer–resource model. It is shown that, in a periodically changing environment, for each environmental preference pattern there is an ideal seasonal distribution of metabolic activity, which results in maximum resource utilisation efficiency and competitive superiority. Contrary to the common interpretation of temporal niche segregation, opposing species-specific seasonal preferences are not a sufficient condition for the coexistence of two species on a population dynamical time scale. A necessary and sufficient condition for coexistence is the temporal segregation of the species via different seasonal activity distributions. However, coexistence is evolutionarily stable only if seasonal metabolic activities and preferences are positively correlated.