Ideal Free Model Research Articles

Uganda kob mating success does not increase on larger leks

One explanation for the movement of sexually receptive females to clusters of male territories in lek-breeding species is that larger clusters provide females with higher-quality mating partners, as would be the case if males were distributed between leks in an ideal free distribution for unequal competitors. This ideal free model of lek evolution predicts that male competitive ability and mating success will be greater on larger leks than smaller ones. I tested these predictions by comparing the mean number of males on 19 different Uganda kob leks with the sex ratio, the availability of oestrous females, mating rates, male fighting rates and male turnover rates. Contrary to the predictions of the model, numbers of females, receptive females and fights increased proportionally with lek size, but were no greater per male on larger leks. Multivariate analyses of male and female numbers on leks showed that male numbers were associated with female numbers, female numbers in the past, and a variety of habitat variables which may have related to the costs of holding a lek territory, but female numbers varied only with male numbers and female density in the area. These data do not provide evidence that females gain access to superior males by mating on larger leks, though they do support the possibility that lekking may be promoted by a tendency for larger leks to retain females longer.

Can Ecological Theory Predict the Distribution of Foraging Animals? A Critical Analysis of Experiments on the Ideal Free Distribution

Opinions differ on the empirical success of the Ideal Free Distribution. The Ideal Free model predicts that the distribution of organisms between resource sites should match the distribution of resources. Many studies report support for this prediction. We review tests of this model utilising a method of analysis derived from the psychological principle called the matching law. Our reanalysis revealed that the distribution of organisms is consistently less extreme than the distribution of resources. This systematic deviation from the Ideal Free Distribution means organisms underuse richer sites and overuse poorer sites. We examine how deviations from the Ideal Free Distribution may arise as a consequence of discrimination constraints, competitive interactions, competitive asymmetries and travel between sites, and recommend ways in which the design of future tests of the Ideal Free Distribution may be improved.

The relationship between continuous input and interference models of ideal free distributions with unequal competitors

Fretwell's (1972, Populations in a Seasonal Environment, Princeton University Press) ideal tree model predicts the ideal distribution when individuals in a habitat are free to move between patches. In this paper, the relationship between the ‘continuous input’ and ‘interference’ ideal free models of Sutherland & Parker (1985, In: Behavioural Ecology: Ecological Consequences of Adaptive Behaviour, ed. by R. M. Sibly & R. H. Smith, pp. 255–274, Blackwell) and Parker & Sutherland (1986, Anim. Behav., 34, 1222–1242) are examined. Continuous input describes cases where resource items arrive at patches containing groups of waiting competitors. Increasing their density in a patch reduces individual gain rates because the resource items arrive at a fixed rate, and are shared between competitors. Interference describes cases where foragers search for prey items hidden within the patches. Increasing competitor density in a patch can reduce individual gain rates due to interference between individuals. Both can be modelled using the form: individual gain rate = Q i n i − m , in which Q i is the input rate or prey density in patch i, n i is the number of competitors, and m is a constant which increases with the strength of interference. A previous formulation of the above model in which individuals have unequal competitive abilities is extended to cover the case where phenotypic differences are reflected by a scaling of Q i (rather than by a scaling of the level of m). Here, many different mixed distributions of phenotypes can exist as ideal free equilibria, provided that relative competitive abilities stay constant across patches. Many different phenotypes can occur across several patch types. However, where phenotypic differences are best reflected by a scaling of m, then these mixed distributions of phenotypes are not possible, and no more than one phenotype can play a mixed strategy across the same pair of patch types. Typically, a truncated distribution of phenotypes between the patches can be expected, with the best phenotypes in the best patches. Some general conditions are proposed for ideal free distributions of unequal competitors.

Group foraging in starlings: distributions of unequal competitors

Twelve individually marked starlings, Sturnus vulgaris, were video recorded feeding at either a single patch of food (to determine relative competitive abilities) or two patches of food (to observe distributions). The observed distributions differed significantly from the predicted distributions of the ideal free model, the competitive ideal free model and a model of random distribution. The difference in mean rank of birds in the good and poor patches was inversely proportional to the proportion of individuals in the good patch, indicating that relative competitive ability affects patch choice. Dominants were able to defend a food patch from subordinates when there were four or fewer subordinates present. Thus, if a dominant was present, subordinates were more successful when in groups of more than four individuals. This violates the competitive ideal free model's assumption of constant ratios of success among individuals.

Ideal free distributions when individuals differ in competitive ability: phenotype-limited ideal free models

A series of prospective models is developed to investigate ideal free distributions in populations where individuals differ in competitive ability. The models are of three types. In the continuous-input models, there is continuous arrival of food or mates into each habitat patch, and competitors scramble to obtain as large a share as possible. In the interference models, the prey density in a particular patch stays constant but the presence of competitors slows down the rate at which prey are captured. In the kleptoparasitism model, individuals have food or females stolen from them by competitors higher in the dominance hierarchy, and in turn steal items from subordinates. A general result of the continuous-input and interference models is that the population of competitors can be truncated between patches so that the individuals with the highest competitive ability occur in the best patches, or in the patches where competitive differences are greatest. Individuals of lowest competitive ability occur in the poorest patches or where competitive differences are least, and intermediate phenotypes are ranked between these two extremes. Thus the ideal free prediction that all individuals will achieve equal fitness will not apply. However, in continuous-input cases where competitive differences between phenotypes remain constant across patches, this solution is only neutrally stable, and forms only one element of a set of equilibrium distributions. The fact that many empirical studies of continuous-input have found approximately equal mean fitness across patches may relate to this finding. Most interference studies contradict the simple ideal free solution by having different mean intake rates across patches; this may relate to the predicted positive correlation of competitive ability with patch quality. The kleptoparasitism model usually generated continuous cycling of individuals between habitat patches, though some correlation could be found between competitive ability and patch quality.

Foraging on patchily distributed prey by a cichlid fish (Teleostei, Cichlidae): A test of the ideal free distribution theory

Cichlid fish ( Aequidens curviceps) distributed themselves and allocated their foraging time between two drift food patches in close approximation to the patch profitability ratio, as predicted by the ideal free distribution theory. The fish thereby achieved similar average feeding rates in the two patches, in two of three patch profitability ratio experiments. However, one major assumption of the ideal free model was violated, since individual fish differed in their competitive abilities for limited food resources, which resulted in unequal payoffs among individuals within each patch. Individual variation in feeding rates, and thus in competitive ability, was not related to despotism, but perhaps rather to individual differences in perceptual ability and in the ability to learn which patch was currently the more profitable. The strategy used by the fish to assess patch profitability included sampling available patches. However, individual fish switched (sampled) patches with varying frequency. Sampling had an associated cost, since high-frequency switchers had lower feeding rates on average than low-frequency switchers. Differences in foraging strategy among the fish therefore contributed to the observed in-equality in individual payoffs within patches.

Competitive foraging in mallards: “Ideal free’ ducks

Mallards ( Anas platyrhynchos L.) distribute themselves between two patches of food in a close approximation to the distribution predicted by the ideal free model. However an important assumption of this model is violated since the despotic behaviour of some individuals results in different birds receiving unequal payoffs. The distribution of the birds between the food patches is influenced by the distribution of these despots. Evidence is presented to suggest that the ducks initially use the frequency of supply of food items at a patch to assess its profitability, but they can, over a longer time scale, use other cues.