Since the introduction of the ideal free distribution in the 1970s, amendments have attempted to explain observations that deviate from the prediction of input matching. We consider a perceptual limit model that relaxes the assumption that animals are ideal. Under the model, individuals move to the location with the highest potential intake rate, unless the potential intake rates differ by less than some fixed amount, in which case the animals move at random. The random movements of the animals mean that there are often many feasible distributions. Here we present a new method of implementing the model in which we treat movements between the feasible distributions as a Markov chain. Analysis of this model shows that the range of feasible distributions is determined by the limits on the random movements of the animals. This new method allows us to compute the equilibrium probability of observing each feasible distribution, to compute the expected long-term rate of intake overall and on each site, and to compute differences in the expected total intake of individual animals depending on their initial site and the initial number on that site. We show that observed Emits from feeding trials could be used to provide a more robust test of the perceptual Emit model than comparing predicted average distributions.

The functional response and variation in foraging efficiency of captive Barnacle Geese was measured on pasture sward. Intake rates were calculated for a range of grass sward heights using direct measurements of peck rate, bite height and number of leaves removed with each bite. The functional response was found to be curved reaching a maximum at 85 mm and then declining. Each of the three components of intake rate responded differently to sward height. Peck rate declined steadily with increasing sward height whereas bite height increased throughout the sward heights used. The number of leaves per bite showed a curved response to sward height, increasing to a maximum at sward height of 90 mm then declining. There were significant differences between individuals for bite height and leaves taken per bite. Multiple regression analysis using age, sex, body size and bill size found that 73% of the variation in leaves taken per bite could be explained by the age of the goose, where more leaves were taken per bite by older geese. The results are discussed in relation to other studies on geese foraging on salt-marsh sward and other grazers foraging on pasture.

1. Behaviour‐based models of animal population dynamics provide ecologists with a powerful tool for predicting the response of such populations to both natural and human‐induced environmental changes.2. We developed this approach by addressing two outstanding issues in the application of such models: the need to adopt a large‐scale spatially explicit approach, and the need to consider the year‐round dynamics of animal populations.3. Spatially explicit, year‐round, behaviour‐based models of two populations of arctic‐breeding geese, the Svalbard population of the barnacle gooseBranta leucopsisand the dark‐bellied race of the brent gooseBranta bernicla, were developed. Both populations have been the subject of serious conservation concern and are currently a source of increasing conflict with agricultural interests.4. There was generally good agreement between empirically derived and model‐generated density‐dependent functions, and of seasonal patterns of the distribution and movement of populations within and between sites, and of energy reserve levels within a population.5. Sensitivity analyses, however, highlighted the importance of accurate parameter estimation with respect to the predictions of such models, and the potential flaws in the predictions of existing models that have not adopted a spatially explicit approach when dealing with wide‐ranging migratory populations.6. The effect of the removal of a given area of habitat on both populations was predicted to vary depending upon the spatial configuration of the change. This further emphasizes the need for a spatially explicit approach.7. Both barnacle goose and brent goose populations were predicted to decline following habitat loss in their winter or spring‐staging sites. Simulations suggested that barnacle geese might be less vulnerable to winter habitat loss than brent geese. This reflected the relative strengths of the density‐dependence of productivity and winter mortality in the two models and provided a clear illustration of the need for a year‐round approach to animal population dynamics.8. We believe that these models, and this approach to understanding the population dynamics of long‐distance migrants, will be beneficial in attempting to answer the increasingly urgent and frequent requests to predict the response of such populations to environmental change.

We present an individuals-based simulation model that predicts changes in energetic reserve levels for barnacle geese Branta leucopsis during spring staging on the archipelago of Helgeland, Norway. We assume a despotic distribution of geese foraging on small patches of vegetation with the best competitors foraging on the patches that offer the highest daily intake rate and biomass. Competitive ability in the model increases with age, past reproductive success and previous residency on an archipelago. Intake rates and energetic reserves are calculated on a daily basis. There are two traditional archipelago types included in the model (managed and unmanaged) and three classes of vegetation (Festuca, Herb and Hay meadows). The Hay meadow is a result of the application of fertilisers and grazing and is therefore only present on the managed archipelago. Our model explores the effect of food availability on an archipelago of each type at different population densities. At high goose densities there is a marked reduction in the intake rates of poor competitors. This effect is stronger on the unmanaged archipelago where there is no Hay meadow. We then consider how this basic model could be improved with further parameterisation.

We examine two methods of allocating animals between sites of different resource input rate in the context of the ideal free distribution. The basic models are of individuals of two classes of competitive weight distributing themselves between two sites. The importance of arrival sequence and the subsequent movements of animals between sites are investigated. When all the good competitors arrive before the poor competitors, the distribution of each class conforms to the input matching rule. When competitors arrive in a random sequence, poor competitors switch between patches. Resulting distributions are compared with predictions from the ideal free distribution with unequal competitors and from statistical mechanics. The comparisons show fewer animals using the site with the highest resource than predicted by the input matching rule, that is, undermatching is found. The effect of each animal having a unique competitive ability is then examined. We discuss the application of ideal free distribution models to areas of behavioural ecology other than foraging, together with alternative rules to the standard instantaneous intake rates rule.