A timing histogram relating the timing of electromyogram (EMG) activity, muscle length change, muscle force production and kinematic data for an individual bird flying at 7 m s^-1. The zero time is set to the time at which maximum force occurred, which corresponds to mid-downstroke. The bars on each rectangle indicate standard deviation. Additional data on the variation across speeds in the relationship between EMG onset time, muscle shortening and force production are given in Table 2.

Whole wingbeat in vivo work loops obtained from an individual cockatiel flying at (A) 1 m s^-1, (B) 7 m s^-1 and (C) 13 m s^-1. The direction of each loop is counter-clockwise, resulting in positive work. Pectoralis mass-specific power output, wingbeat duration and work `shape factor' are noted in the upper left for each loop. The shape factor quantifies work loop shape by dividing the actual loop area by the theoretical maximum area for the observed peak force and length change.

(A) The relationship between mechanical power output and flight speed expressed as inter-individual means ± S.D. (N=5 for each speed; mean and minimum wingbeat sample sizes were 46 and 17, respectively, across all individuals). Pectoralis force recordings were calibrated using an aerodynamic power analysis at two intermediate flight speeds (7 m s^-1 and 9 m s^-1). The broken lines indicate the possible range of variation in muscle power output given varying aerodynamic assumptions. (B) A power curve for an individual cockatiel showing within-individual means ± S.D. (mean and minimum sample sizes were 50 and 19 wingbeats, respectively, per animal for each speed). The cockatiels tended to repeatedly gain and lose potential energy while flying in the wind tunnel, leading to large variation in per-wingbeat power output at all but the fastest speeds. We restricted our analysis to sequences of wingbeats with no net change in potential energy but allowed individual wingbeats that resulted in a change in potential energy.

Variation in pectoralis power, pectoralis work and wingbeat frequency across flight speeds. All values are inter-individual means (N=5 for each speed) normalized as a percentage of the overall mean for each parameter. Standard deviations are not shown to improve clarity (these are presented in Table 2). These data show that pectoralis power is determined mainly by changes in muscle work per wingbeat and not by wingbeat frequency.

(A) Variation in whole wingbeat, upstroke and downstroke durations across flight speeds (inter-individual means ± S.D.; N=5 for each speed) as measured via muscle lengthening and shortening. Consistent with the modest change in wingbeat frequency versus speed (Fig. 5), wingbeat duration varies slightly but significantly (P<0.05; Table 2) with speed. Changes in wingbeat duration across speeds is due entirely to changes in upstroke duration, as downstroke duration does not vary significantly with speed (P>0.1; Table 2). (B) Variation in wingbeat duration measured via a 125 Hz, three-dimensional kinematic reconstruction. Although the general pattern is similar to that shown in A, the relative durations of upstroke and downstroke have shifted such that downstroke is shorter than or equal to, rather than longer than or equal to, upstroke.

(A) Variation in peak muscle force and muscle strain rate as a function of flight speed. (B) Changes in the amplitude of muscle strain with speed (P<0.01; Table 2). Values represent interindividual means ± S.D. (N=5 for each speed). Pectoralis force, strain rate and strain amplitude vary similarly with speed, and the pattern of variation matches that found for muscle power output versus speed (Fig. 5).

A partial regression component model of the factors underlying pectoralis power output among individual birds as a function of flight speed with a least-squares multiple linear regression of power against selected factors. The arrows indicate the proposed relationships between variables, together with their partial regression coefficients, which indicate the relative strength of the relationship. Pectoralis power output as a function of flight speed is determined by the combination of work per wingbeat and wingbeat frequency, but work per wingbeat exerts the strongest effect. Pectoralis work per wingbeat is influenced by several factors, but the two most important are muscle force (r²=0.77) and muscle length change (r²=0.45; also see Fig. 6). The double-headed arrow between muscle length change and work loop shape factor indicates that increases in length change are correlated with decreases in the shape factor, and vice versa. The correlation also influences the total effect of the variables; for example, the total effect of muscle length change is 0.80-(0.63×0.40), or 0.55. There were no significant correlations between model variables aside from those indicated in the model via arrows. Statistical tests were conducted based on a set of individual means across speeds (5 individuals × 7 speeds: N=35).

(A) A least-squares regression of muscle force versus electromyogram (EMG) amplitude within one individual across speeds. (B) A least-squares regression of muscle shortening velocity during downstroke versus EMG amplitude within the same individual across speeds. EMG amplitude was quantified as the integrated rectified EMG signal, divided by its duration. We performed the regression against mean values for amplitude, force and shortening velocity at each speed to give a balanced data set. However, we plotted all points included in the mean values as small `x' symbols to show the full range of variation; the mean values used in the regression analyses are shown as large diamonds. Table 4 reports additional analyses of EMG amplitude with respect to muscle force.