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.     

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     

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.     

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.     

The ideal free distribution of clonal plant's ramets among patches in a heterogeneous environment

The plastic response of clonal plant to different patch quality is not always the same and the degree is different too. So the result of this kind of foraging behaviour is different. In order to make clear whether the ramtes stay in favourable patches and get the quantitative relationship between the ramets distribution among patches and the available resource amount in heterogeneous environment, we develop a theoretical work under ideal free distribution (IFD) theory framework by neglecting some morphological plasticity of the spacer in this article. The results of our general model show that the ramet distribution should obey input matching rule at equilibrium. That means the ratio of ramet number in different patches should be equal to the ratio of available resource amount in these patches. We also use the simulation to predict the distribution pattern under history mattering. The results show that the initial ramets number has significant influence on the final distribution: over matching and under matching both can occur. More initial ramets in favourable patch result in over matching and more initial ramets in unfavourable patch result in under matching. The degree of the deviation from input matching rule is great when the difference of patches is small. These results prove that ideal free distribution theory works the same with animals. The ramets can stay in favourable patches sometimes in spite of the plasticity of the spacer, and the distribution depends on both patch quality and the history factors. But these results are true only when the functional response is type II.     

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.     

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.     

The energetic equivalence of cover to juvenile coho salmon (Oncorhynchus kisutch): ideal free distribution theroy applied

Cover is often thought to be an important habitat characteristicfor juvenile stream salmonida. In addition to providing protectionfrom predators, cover may be associated with reduced food availability.Thus, an individual's use of cover is likely to reflect a trade-offbetween the conflicting demands of growth and survival. We measuredthe influence of cover on foraging-site selection in groupsof eight juvenile coho salmon (Oncorhynchus kisutch) by examiningtheir distribution across two stream channel patches, one providingaccess to cover but little food (the "poor" patch), the otherproviding more food but no cover (the "good" patch). Becausefish distributions in the absence of cover conformed to an idealfree distribution (IFD) for unequal competitors (i.e., the distributionof competitive abilities matched the distribution of food),we used IFD theory to quantify the energetic equivalence ofcover to the fish. In the presence of cover and a model avianpredator, use of the poor patch increased relative to the predictionsof the IFD model. Using this observed deviation from an IFD,we calculated how much extra food must be added to the goodpatch to return the distribution of fish to the previously observedIFD of unequal competitors. As predicted, adding this amountof food caused the fish to return to their previous distribution,demonstrating that IFD theory can be used to relate energy intakeand risk of predation in a common currency     

Foraging behaviour in tadpoles of the bronze frog<Emphasis Type="Italic">Rana temporalis</Emphasis>: Experimental evidence for the ideal free distribution

The ability of bronze frogRana temporalis tadpoles (pure or mixed parental lines) to assess the profitability of food habitats and distribute themselves accordingly was tested experimentally using a rectangular choice tank with a non-continuous input design. Food (boiled spinach) was placed at two opposite ends of the choice tank in a desired ratio (1:1, 1:2 or 1:4) to create habitat A and B. The tadpoles in Gosner stage 28–33, pre-starved for 24 h, were introduced in an open ended mesh cylinder placed in the center of the choice tank, held for 4 min (for acclimation) and then released to allow free movement and habitat selection. The number of tadpoles foraging at each habitat was recorded at 10, 15, 20, 25 and 30 min time intervals. The actual suitability,S _i (the food available in a habitat after colonization of tadpoles) of each habitat was obtained from the equationS _i =B _i−f _i (d _i) whereB _i is basic suitability (amount of food provided at each habitat before release of tadpoles),f _i is the rate of depletion of food (lowering effect) with introduction of each tadpole, andd _i is the density of tadpoles in habitati. The expected number of tadpoles at each habitat was derived from the actual suitability. With no food in the choice tank, movement of the tadpoles in the test arena was random indicating no bias towards any end of the choice tank or the procedure. In tests with a 1:1 food ratio, the observed ratio of tadpoles (11.71: 12.28) was comparable with the expected 12:12 ratio. The observed number of tadpoles in the habitats with a 1:2 food ratio was 8.71:15.29 and 7.87:16.13 for pure and mixed parental lines respectively. In both cases, the observed ratios were close to the expected values (7:17). Likewise, in experiments with a 1:4 food ratio, the observed number of tadpoles in the two habitats (10.78:37.22) did not differ significantly from the expected ratio of 7:41. In all tests, the number ofR. temporalis tadpoles matched ideally with habitat profitability (undermatching indexK ≜ 1. The study shows that tadpoles of the bronze frog exhibit an ideal free distribution while foraging regardless of whether they are siblings or non-siblings in a group, which correlates well with their group living strategy in nature.     

Spatial relationships between mate acquisition probability and aggregation size in a gregarious coreid bug, (Colpula lativentris): A case of the ideal free distribution under perceptual constraints

Spatial relationships of mate acquisition probability for individuals of both sexes of a gregariously-mating coreid bug, Colpula lativentris, were studied in relation to aggregation size. Operational sex ratio was always strongly male biased. Mate acquisition probability of females was rather constant and independent of aggregation size, as predicted by an ideal free distribution. Moreover laboratory experiments showed that both multiple mating and rearing density little affected female fecundity, suggesting ideal free distribution of females in terms of reproductive success. On the other hand, mate acquisition probability of males was higher in larger aggregations, where more receptive females were available. This male discrepancy from an ideal free distribution was similar to the patterns predicted by an ideal free distribution under perceptual constraints (Abrahams, 1986), but not by that under unequal competitive ability.     

Two gerbils of the Negev: A long-term investigation of optimal habitat selection and its consequences

Optimal foraging theory has entered a new phase. It is not so much tested as used. It helps behavioural ecologists discover the nature of the information in an animals brain. It helps population ecologists reveal coefficients of interaction and their patterns of density-dependent variation. And it helps community ecologists examine niche relationships. In our studies on two species of Negev desert gerbil, we have taken advantage of the second and third of these functions. Both these gerbils prefer semi-stabilized dune habitat, and both altered their selective use of this habitat and stabilized sand according to experimental changes we made in their populations. Their changes in selectivity agree with a type of optimal foraging theory called isoleg theory. Isoleg theories provide examples of dipswitch theories – bundles of articulated qualitative predictions – that are easier to falsify than single qualitative predictions. By linking behaviour to population dynamics through isoleg theory, we were able to use the behaviour of the gerbils to reveal the shapes of their competitive isoclines. These have the peculiar non-linear shapes predicted by optimal foraging theory. Finally, when owl predation threatens, the behaviour of Gerbillus allenbyi reveals the shape of their victim isocline. As has long been predicted by predation theory and laboratory experiments, it is unimodal.