Children's competition in a natural setting: evidence for the ideal free distribution

Little is known of the foraging abilities of children in modern cultures, especially when children forage in groups. Here we present a test of optimal foraging theory in groups of street children working for money. The children we observed were selling bottles of water to drivers distributed in two lanes at a crossroad of Istanbul, Turkey. As predicted by the ideal free distribution (a model of optimal group foraging), the ratio of children working in the two lanes was sensitive to the ratio of cars (and therefore the ratio of potential buyers) present in each lane. Deviations from the ideal free model arose largely from numerical restrictions on the set of possible ratios compatible with a small group size. When these constraints were taken into account, optimal behavior emerged as a robust aspect of the children's group distribution. Our results extend to human children aspects of group foraging that were previously tested in human adults or other animal species.     

Putting competition strategies into ideal free distribution models: habitat selection as a tug of war

When resources are patchily distributed in an environment, behavioral ecologists frequently turn to ideal free distribution (IFD) models to predict the spatial distribution of organisms. In these models, predictions about distributions depend upon two key factors: the quality of habitat patches and the nature of competition between consumers. Surprisingly, however, no IFD models have explored the possibility that consumers modulate their competitive efforts in an evolutionarily stable manner. Instead, previous models assume that resource acquisition ability and competition are fixed within species or within phenotypes. We explored the consequences of adaptive modulation of competitive effort by incorporating tug-of-war theory into payoff equations from the two main classes of IFD models (continuous input (CI) and interference). In the models we develop, individuals can increase their share of the resources available in a patch, but do so at the costs of increased resource expenditures and increased negative interactions with conspecifics. We show how such models can provide new hypotheses to explain what are thought to be deviations from IFDs (e.g., the frequent observation of fewer animals than predicted in good patches of habitat). We also detail straightforward predictions made uniquely by the models we develop, and we outline experimental tests that will distinguish among alternatives.     

Tracking prey or tracking the prey's resource? Mechanisms of movement and optimal habitat selection by predators

We synthesize previous theory on ideal free habitat selection to develop a model of predator movement mechanisms, when both predators and prey are mobile. We consider a continuous environment with an arbitrary distribution of resources, randomly diffusing prey that consume the resources, and predators that consume the prey. Our model introduces a very general class of movement rules in which the overall direction of a predator's movement is determined by a variable combination of (i) random diffusion, (ii) movement in the direction of higher prey density, and/or (iii) movement in the direction of higher density of the prey's resource. With this model, we apply an adaptive dynamics approach to two main questions. First, can it be adaptive for predators to base their movement solely on the density of the prey's resource (which the predators do not consume)? Second, should predator movements be exclusively biased toward higher densities of prey/resources, or is there an optimal balance between random and biased movements? We find that, for some resource distributions, predators that track the gradient of the prey's resource have an advantage compared to predators that track the gradient of prey directly. Additionally, we show that matching (consumers distributed in proportion to resources), overmatching (consumers strongly aggregated in areas of high resource density), and undermatching (consumers distributed more uniformly than resources) distributions can all be explained by the same general habitat selection mechanism. Our results provide important groundwork for future investigations of predator-prey dynamics.     

Details of local dispersion improve the fit of neighborhood competition models

I performed a series of greenhouse experiments to explore how patterns in the dispersion of local competitors affect the reproductive performance of Capsella bursa-pastoris, Poa annua and Senecio vulgaris. I manipulated the density and relative frequency of competitors in each of three concentric rings surrounding a central plant, thereby creating a variety patterns by which local competitors were distributed. Neighborhood competition models were used to predict the seed output of these central plants. For both Senecio vulgaris and Capsella bursa-pastoris, I found that models which incorporated the dispersion of competitors, as well as the relative emergence date of plants, performed substantially better than those that considered only the distance between the central plant and each of its competitors. I was unable to measure the seed output of Poa annua but neither emergence data nor the dispersion of competitors were important in determining its final dry-weight.Present address: Department of Biology, Box 1137, Washington University, 1 Brookings Drive, St. Louis, MO 63130, USA     

A master equation for a spatial population model with pair interactions

We derive a closed master equation for an individual-based population model in continuous space and time. The model and master equation include Brownian motion, reproduction via binary fission, and an interaction-dependent death rate moderated by a competition kernel. Using simulations we compare this individual-based model with the simplest approximation, the spatial logistic equation. In the limit of strong diffusion the spatial logistic equation is a good approximation to the model. However, in the limit of weak diffusion the spatial logistic equation is inaccurate because of spontaneous clustering driven by reproduction. The weak-diffusion limit can be partially analyzed using an exact solution of the master equation applicable to a competition kernel with infinite range. This analysis shows that in the case of a top-hat kernel, reducing the diffusion can increase the total population. For a Gaussian kernel, reduced diffusion invariably reduces the total population. These theoretical results are confirmed by simulation.     

Modeling epidemics dynamics on heterogenous networks

The dynamics of the SIS process on heterogenous networks, where different local communities are connected by airlines, is studied. We suggest a new modeling technique for travelers movement, in which the movement does not affect the demographic parameters characterizing the metapopulation. A solution to the deterministic reaction-diffusion equations that emerges from this model on a general network is presented. A typical example of a heterogenous network, the star structure, is studied in detail both analytically and using agent-based simulations. The interplay between demographic stochasticity, spatial heterogeneity and the infection dynamics is shown to produce some counterintuitive effects. In particular it was found that, while movement always increases the chance of an outbreak, it may decrease the steady-state fraction of sick individuals. The importance of the modeling technique in estimating the outcomes of a vaccination campaign is demonstrated.     

The ideal free distribution and bacterial growth on two substrates

A population dynamical model describing growth of bacteria on two substrates is analyzed. The model assumes that bacteria choose substrates in order to maximize their per capita population growth rate. For batch bacterial growth, the model predicts that as the concentration of the preferred substrate decreases there will be a time at which both substrates provide bacteria with the same fitness and both substrates will be used simultaneously thereafter. Preferences for either substrate are computed as a function of substrate concentrations. The predicted time of switching is calculated for some experimental data given in the literature and it is shown that the fit between predicted and observed values is good. For bacterial growth in the chemostat, the model predicts that at low dilution rates bacteria should feed on both substrates while at higher dilution rates bacteria should feed on the preferred substrate only. Adaptive use of substrates permits bacteria to survive in the chemostat at higher dilution rates when compared with non-adaptive bacteria.     

A spatially explicit model for tropical tree diversity patterns

A simple two-parameter model resembling the classical voter model is introduced to describe macroecological properties of tropical tree communities. The parameters of the model characterize the speciation- and global-dispersion rates. Monte Carlo type computer simulations are performed on the model, investigating species abundances and the spatial distribution of individuals and species. Simulation results are critically compared with the experimental data obtained from a tree census on a 50 hectare area of the Barro Colorado Island (BCI), Panama. Fitting to only two observable quantities from the BCI data (total species number and the slope of the log-log species-area curve at the maximal area), it is possible to reproduce the full species-area curve, the relative species abundance distribution, and a more realistic spatial distribution of species.     

The ideal free distribution: a review and synthesis of the game-theoretic perspective

The Ideal Free Distribution (IFD), introduced by Fretwell and Lucas in [Fretwell, D.S., Lucas, H.L., 1970. On territorial behavior and other factors influencing habitat distribution in birds. Acta Biotheoretica 19, 16-32] to predict how a single species will distribute itself among several patches, is often cited as an example of an evolutionarily stable strategy (ESS). By defining the strategies and payoffs for habitat selection, this article puts the IFD concept in a more general game-theoretic setting of the “habitat selection game”. Within this game-theoretic framework, the article focuses on recent progress in the following directions: (1) studying evolutionarily stable dispersal rates and corresponding dispersal dynamics; (2) extending the concept when population numbers are not fixed but undergo population dynamics; (3) generalizing the IFD to multiple species.For a single species, the article briefly reviews existing results. It also develops a new perspective for Parker’s matching principle, showing that this can be viewed as the IFD of the habitat selection game that models consumer behavior in several resource patches and analyzing complications involved when the model includes resource dynamics as well. For two species, the article first demonstrates that the connection between IFD and ESS is now more delicate by pointing out pitfalls that arise when applying several existing game-theoretic approaches to these habitat selection games. However, by providing a new detailed analysis of dispersal dynamics for predator-prey or competitive interactions in two habitats, it also pinpoints one approach that shows much promise in this general setting, the so-called “two-species ESS”. The consequences of this concept are shown to be related to recent studies of population dynamics combined with individual dispersal and are explored for more species or more patches.     

Transition from a random to an ideal free to an ideal despotic distribution: the effect of individual difference in growth

Individual differences in growth can lead to a monopolistic form of food competition. We studied the long-term transition in the mode of competition and the distribution of individuals between food patches of the cloned salmonid fish, Oncorhynchus masou ishikawae, in the laboratory. This transition was accompanied by growth depensation, i.e., the increase over time in the variance of size between individuals resulting from the differences in individual growth rates. The 120-cm experimental tanks were divided into two compartments (patches) between which an opaque partition was placed. Fish were able to move freely between the patches and therefore were able to assess the patch quality using long-term memory, but they were not able to see the food input in the other patch directly. The distribution between the two food patches, the amount of food gained, and the growth and the agonistic behavior of four groups of six individuals were observed over 4 weeks. We found that (1) within-group variation in body weight increased with time; (2) on average, the better patch was used by more individuals than predicted by a random distribution but fewer individuals than predicted by an ideal free distribution, and (3) the distribution and pattern of resource use by the fish changed over the 4-week experimental period from a random distribution to an ideal free distribution and finally to an ideal despotic distribution. We suggest that growth depensation causes the long-term change in the spatial distribution and pattern of resource use by competitors. Received: December 19, 2000 / Accepted: March 19, 2001     

Density-dependent regulation of population size in colonial breeders: Allee and buffer effects in the migratory Montagu’s harrier

Expanding populations offer an opportunity to uncover the processes driving spatial variation in distribution and abundance. Individual settlement decisions will be influenced by the availability and relative quality of patches, and by how these respond to changes in conspecific density. For example, conspecific presence can alter patch suitability through reductions in resource availability or territorial exclusion, leading to buffer effect patterns of disproportionate population expansion into poorer quality areas. However, conspecific presence can also enhance patch suitability through Allee effect processes, such as transmission of information about resources or improved predator detection and deterrence. Here, we explore the factors underlying the settlement pattern of a growing population of Montagu’s harriers (Circus pygargus) in Spain. The population increased exponentially between 1981 and 2001, but stabilised between 2001 and 2004. This population increase occurred alongside a remarkable spatial expansion, with novel site use occurring prior to maximum densities in occupied sites being reached. However, no temporal trends in fecundity were observed and, within sites, average fecundity did not decline with increasing density. Across the population, variance in productivity did increase with population size, suggesting a complex pattern of density-dependent costs and benefits. We suggest that both Allee and buffer effects are operating in this system, with the benefits of conspecific presence counteracting density-dependent declines in resource availability or quality.     

Density-dependent habitat selection in muskrats: a test of the ideal free distribution model

Summary Two predictions of the ideal free distribution model, a null hypothesis of habitat selection, were examined using free-ranging muskrats. We rejected the prediction that the proportion of the animals found in each of five habitats was independent of population size. Data on over-winter occupancy of muskrat dwellings tend also to refute the prediction of equal fitness reward among habitats. Habitat type and water-level had a profound effect on the suitability of a site for settlement. We concluded that the observed pattern of muskrat distribution followed more closely an ideal despotic distribution where some individuals benefited from a higher fitness because of resource monopolization. Current theories of density-dependent habitat selection, which assume an ideal free distribution, would not apply to muskrats and possibly to many other mammal species.     

Distribution pattern of an expanding Osprey ( Pandion haliaetus) population in a changing environment

We studied the nest site selection and distribution pattern at landscape level of the German Osprey population, and demonstrated how to test the predictions of the ideal free distribution theory and its derivatives on such an expanding population. Information about the location and breeding success of each Osprey nest site between 1995 and 2005 was collected through a long-term monitoring programme. Data of land cover types were acquired from the administrations of each federal state and the CORINE Land Cover database. The results showed that Ospreys preferred landscapes with more water bodies and forests. Such sites were also occupied earlier and had higher local population density. However, in the study period of 11 years, there was a gradual shift from forest-dominated landscapes to agricultural land-dominated landscapes. The breeding success increased over time, with no difference in the breeding success between pairs nesting on trees and poles, whereas there was higher breeding success at nest sites surrounded by more agricultural land and less forest. The more efficient foraging in eutrophic lakes in agricultural landscapes was the most likely cause for the higher breeding success. The distribution pattern of the Ospreys did not match the resource allocation, which deviated from the models tested. We suggested that the proximate cues used for nest site selection mismatched site quality due to anthropogenic environmental changes.     

Architecture,seasonal growth and interference in three grass species with different flowering phenologies in a tropical savanna

In a field experiment we studied the relationships between architecture, seasonal aerial biomass growth and interference from neighbours in three savanna grass species differing in time of flowering: a precocious species (Elyonurus adustus), an early species (Leptocoryphium lanatum) and a late species (Andropogon semiberbis). To detect the neighbour interference upon architecture and seasonal regrowth, we measured the leaf interception of a plane at different heights, when the species grew alone, in pairs and in groups of three. Although the three species differed widely in the spatial and temporal patterns of occupation of above-ground space, important levels of interference among neighbouring plants were detected. The species differ in: a) the pattern of space occupation when growing alone; b) the magnitude of the interference effect by the companion species; c) the change in pattern as a consequence of interference; d) their reaction to fire.The interference is not symmetric and it is not related to phenological similarities based on flowering season.L. lanatum was both the most impaired and the least impairing of the three species and the opposite is valid forA. semiberbis. The basal species (E. adustus andL. lanatum) showed a higher potential to produce leaf surface during the growth season than the tall species (A. semiberbis), but the stronger interference from the latter tended to equate their growth when the species grew in mixtures.In all three species interference led to a reduction of the growing period. Based on the analysis of growth at the various heights and the architectural peculiarities of the species we concluded that neighbour interference is probably reducing both tillering and leafing in the basal species but only culm elongation and leafing in the erect species.The species also differed in their reaction to fire.A. semiberbis andE. adustus showed a pulse of regrowth after the passing of fire which is missing inL. lanatum. In all cases the neighbour interference affected both the intensity of growth and the length of the growing period, but it did not affect either the height of the plants nor the reproductive phenology of these three grass species.