Food dispersion and foraging energetics : A mechanistic synthesis for field studies of avian benthivores

Much effort has focused on modeling and measuring the energy costs of free existence and the foraging strategies of animals. However, few studies have quantitatively linked these approaches to the patch structure of foods in the field. We developed an individual-based model that relates field measurements of the dispersion of benthic foods to search costs and foraging profitability of diving ducks. On Lake Mattamuskeet, North Carolina, Canvasback ducks (Aythya valisineria) eat only the belowground winter buds of the submerged plant Vallisneria americana. We measured and modeled the patch structure of winter buds at the level of potential foraging loci, defined as contiguous circles 1 m in diameter. In the field and in the model, Canvasbacks make repeated vertical dives in such loci, foraging in the sediments by touch, before surface-swimming to another locus. We quantified first-order patchiness by fitting a negative binomial distribution to core samples taken at 50-m intervals along transects, to yield the frequencies of loci with different bud densities. Second-order patchiness was measured by taking cores at 1-m increments radiating from each sampling point, and regressing bud density at each sampling point on densities at these increments. No significant correlations were found, indicating that Canvasbacks could not predict food densities based on densities in nearby foraging loci. For the model, we generated food grids from the negative binomial distributions of core samples. Energy costs of diving were calculated by applying aerobic efficiencies (mechanical power output + aerobic power input) to biomechanical models. Unlike respirometry alone, this method accounts for effects on dive costs of varying water depth and dive duration. We used measurements of Canvasback intake rates at different bud densities to calculate profitability (energy intake minus expenditure) for each dive. Multivariate uncertainty analyses (Latin hypercube) indicated that profitability for Canvasbacks foraging on Vallisneria buds is determined mainly by food-item size and locomotor costs of descent. Bud metabolizable energy, water temperature, bud dispersion, and search and handling time coefficients of the functional response for intake rate have relatively minor influence. Individual-parameter perturbations indicated that to maintain the same foraging benefits, the total area of Vallisneria habitat would have to increase by 1.4-fold if dry mass per bud decreased from 0.10 to 0.03 g, and by 2.1-fold if water depth increased from 0.5 to 2 m. Our method allows study of interactions between patch structure and foraging energetics without detailed spatial mapping of foods, which is not feasible at appropriate scales for highly mobile benthivores. The model yields estimates of energy balance, contaminant intake, and amount and quality of foraging habitat required to sustain diving duck populations under varying environmental conditions. More accurate prediction of giving-up times and giving-up food densities will require better understanding of the time scale over which ducks balance their energy budgets.