Jan A. van Gils, Bernard Spaans, Anne Dekinga, and Theunis Piersma. 2006. Foraging in a tidally structured environment by red knots (Calidris canutus): ideal, but not free. Ecology 87:1189–1202.

Appendix A. On the calculation of ∆x.

The change ∆x in energy store x per 50-min time step equals gross energy gain B minus energy cost C, or formally:

(A.1)

We assume that storing 1-g of fat costs 40/0.75 = 53.3 kJ and burning yields 40 kJ (Ricklefs 1974).

Gross energy gain B is the product of gross energy gain rate (predicted from the observed prey densities in a block as described in the main text) and time spent feeding in the 50-min time interval (which is determined by whether it decided to feed or to rest and the travel time to the patch in the next time interval; see below). It therefore depends on respectively the current location s, the current action i, and the location k in the next time step.

Energy cost C is determined by current action i (foraging is more costly than resting), the time lost to traveling which is a function of current patch s and patch k chosen in the next time interval (traveling is more costly than foraging), and by energy store x (metabolic rates during traveling and during foraging are mass-dependent). More specifically, metabolic rate while resting is set to 1.63 W (Piersma et al. 2003 taking into account a gizzard mass of 6-g). On top of this comes a thermoregulatory cost of 0.69 W, which is typical for knots living in the western Dutch Wadden Sea in late summer (Wiersma and Piersma 1994). When foraging, a constant component of 0.47 W is added due to probing (Piersma et al. 2003), and a mass-dependent component is added due to walking (Bruinzeel et al. 1999; expressed in W):

(A.2)

which assumes a walking speed of 0.072 m/s as observed by Piersma et al. (2003). As an energetic saving, 30% of the heat produced during walking substitutes for thermostatic heat (Bruinzeel and Piersma 1998). In addition, a variable digestion cost is added, which amounts to 5,195 J/g AFDM_flesh digested (Piersma et al. 2003), where we assume that 100% of this heat increment of feeding (HIF) substitutes for thermostatic heat (cf. Van Gils et al. 2003). When traveling between current patch s and future patch k, the following mass-dependent flight cost is added (Kvist et al. 2001; expressed in W):

(A.3)

Time devoted to traveling is calculated by assuming a flight speed of 15 m/s (cf. Kvist et al. 2001; truncated at a maximum of 50 min) and is subtracted from the foraging or resting time in the current patch s.

LITERATURE CITED

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Bruinzeel, L. W., T. Piersma, and M. Kersten. 1999. Low costs of terrestrial locomotion in waders. Ardea 87:199–205.

Kvist, A., Å. Lindström, M. Green, T. Piersma, and G. H. Visser. 2001. Carrying large fuel loads during sustained bird flight is cheaper than expected. Nature 413:730–731.

Piersma, T., A. Dekinga, J. A. van Gils, B. Achterkamp, and G. H. Visser. 2003. Cost-benefit analysis of mollusc-eating in a shorebird. I. Foraging and processing costs estimated by the doubly labelled water method. Journal of Experimental Biology 206:3361–3368.

Ricklefs, R. E. 1974. Energetics of reproduction in birds. Pages 152–292 in R. A. Paynter, Jr., editor. Avian Energetics. Nuttall Ornithological Club, Cambridge, Massachusetts, USA.

Van Gils, J. A., T. Piersma, A. Dekinga, and M. W. Dietz. 2003. Cost-benefit analysis of mollusc-eating in a shorebird. II. Optimizing gizzard size in the face of seasonal demands. Journal of Experimental Biology 206:3369–3380.

Wiersma, P., and T. Piersma. 1994. Effects of microhabitat, flocking, climate and migratory goal on energy expenditure in the annual cycle of red knots. Condor 96:257–279.