Carrying capacity in overwintering birds: when are spatial models needed?
We sometimes need to predict the maximum number of bird-days that can be supported by the food supply in a site used by migratory birds outside the breeding season. So defined, carrying capacity is often estimated using the daily ration model (DRM). In this, the total biomass of accessible food, aggregated across all patches of differing food density, is divided by an individual's daily requirement. Carrying capacity can also be estimated using spatial depletion models (SDM), in which patches of differing food density are treated separately. We identify here some of the features of the food supply that enable patches to be amalgamated so that the very simple DRM can be used instead of a more complex SDM. We show by theoretical modelling that the predictions of the DRM and SDM are often the same even though initial food density varies between patches. The wide range of conditions over which this is so are specified. A DRM and a SDM of wildfowl eating seagrass Zostera spp. in a nature reserve produced similar predictions for the number of bird-days supported intertidally before the birds switched to farmland. We conclude that a DRM can often be used instead of a SDM to predict bird-day carrying capacity. We identified two conditions in which the DRM cannot be used: (i) when the rate of additional food loss due to factors other than depletion by the birds themselves differs between patches; and (ii) when the relative profitabilities of patches, and thus the number of birds using each patch, change through the depletion period in non-simple ways that cannot be predicted without a SDM. Examples of such exceptions are described. Synthesis and applications. By showing when a DRM can be used instead of a SDM, this study should help nature managers to predict the bird-day carrying capacity of a site in the simplest way yet available. However, predicting the maximum number of bird-days supported is not equivalent to predicting demographic rates and should not be confused with predictions for population size. Rather, it is probably best regarded as a measure of site quality.