Carrying capacity models should not use fixed prey density thresholds: a plea for using more tools of behavioural ecology

Abstract

Earlier studies have developed models of carrying capacity to predict the number of animals a certain area can support. These models assume that resources are not renewed after consumption ('standing stock' models), and that the initial number of prey and the rate of prey consumption determine the time a population of foragers can live in an area. Within such areas, foragers give up feeding at a sub-site or patch when intake rates no longer cover energy expenditure. To improve the success rate of the models' predictions, we here change the existing rate-maximising models into fitness-maximising models, and include dynamics in the availability of patches. These new (conceptual) models show that the approaches used so far may over-as well as underestimate carrying capacity. We review empirical studies that have aimed to estimate carrying capacity, and discuss how concepts have been confused. We make explicit suggestions on how to proceed in predicting carrying capacities in future studies.A forager's intake rate depends on the density of its prey, and this dependency is called the 'functional response'. The most popular form, Holling's disc equation (after Holling 1959), needs just two parameters to calculate intake rates from prey densities: (1) the searching efficiency, and (2) the time it takes to handle one prey item. Traditional distribution models use these expected intake rates to predict whether a patch will be used. According to these models (Piersma et al. 1995), a patch should not be used when it yields an expected intake rate that is below the average intake rate necessary to keep the energy budget balanced over a certain period of time (usually a day). This critical intake rate i c is thus a function of the fraction of time available for foraging and of the rate of energy expenditure. The functional response equation can provide the critical prey density d c at which i c is achieved. In an attempt to make simple predictive models for carrying capacity, Sutherland and Anderson (1993) used this critical prey density to model the number of animal-days an area could support when prey populations are not renewed (Note that carrying capacity as used here is an energetic rather than a demographic concept, i.e. carrying capacity is expressed as the maximum number of animal-days rather than the maximum number of animals -the latter often being expressed as K in population models. See also discussion in Goss-Custard et al. 2003.) All prey that are living in densities \ d c will be consumed, after which all foragers die of starvation or leave the area in search of better alternatives (Fig. 1a). Several field studies have tested the predictions of this model, some with greater success (Vickery et al. 1995) than others (Percival et al. 1998). The good thing about the unsuccessful studies is that they shed light on factors other than prey density that constrain carrying capacity, and that they showed the necessity to include these factors in the model (Percival et al. 1998).This contribution has three aims. Firstly,...

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