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In addition, the following measurements were taken with digital calipers (Fisherbrand, 0.01 mm accuracy): bill length, bill depth, bill width, tarsus length, and length of the outermost primary feather from where it emerged from the skin to its distal tip.
We measured several ecologically important traits including bill length (measured to skull), bill depth, bill width (both measured at frontal margin of nostrils), tarsus length (excluding heel joint), wing length, and body mass.
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In the case of crossbills, the optimal bill depth is the bill depth that minimizes the time necessary to meet daily energy demands.
In almost all cases, we have found a curvilinear relationship between time per seed and bill depth with an intermediate bill depth requiring the least amount of time to extract a seed.
Consequently, the optimal bill depth, which minimizes the product between time per seed and estimated daily energy requirements, is smaller than the time minimizing bill depth.
Because body size increases allometrically with increases in bill depth in crossbills as in most seed-eating finches and sparrows (Benkman 1993; Benkman et al. 2001), daily energy requirements increase with increases in bill depth.
I then solved for the optimal bill depth for foraging on each of the conifers (Fig. 3).
First, we need to consider the relationship between bill depth and the time to remove seeds from the cones.
However, the optimal bill depth is not simply the one that requires the least amount of time to extract a seed.
If each call type was adapted for foraging on a particular conifer, then the average bill depth of a given call type should match the predicted optimum.
An example is shown for 27 Red Crossbills timed foraging on Douglas-fir cones (Benkman 1993), where the bill depth minimizing the time to extract a seed is approximately 9.4 millimeters (Fig. 3a).
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