Flight speed is expected to increase with mass and wing loading among …

• Abstract
• Author Summary
• Introduction
• Results
• Discussion
• Materials and Methods
• References

Tracking radar measurements.

Our main dataset, based on tracking radar measurements in Sweden and the Arctic 1979–1999, consists of 1,399 tracks of 102 identified species, with a mean track time of 369 s (range 20–2,220 s). Altitudes ranged from sea level to 3,600 m. Number of tracks for each species ranged between one and 240, and mean U_e (with SD), vertical speed as well as information about number of tracks, track time, and biometry data are given for each species in Protocol S1.

An extensive additional dataset of equivalent airspeeds of identified birds, obtained by similar tracking radar techniques, has been published from the work of Bruno Bruderer and his research group in Switzerland, Germany, Israel, and Spain [15]. Flight speed data from tracks of birds in natural migratory flight (excluding released birds and soaring flight) were incorporated into our analysis. This additional dataset comprised 64 species, and with 28 species shared between the two sets of data, the combined data added up to a total of 138 species (Protocol S1). Mean U_e for the shared species were not significantly different between the two sets (paired sample t-test, t = 1.28, and p = 0.21), and we used weighted (according to the number of tracks) overall mean U_e for these species in our analyses.

The bulk of flight speed data were measured 1979–1999 by tracking radar studies at five sites in southern Sweden and on two expeditions by icebreaker to the Arctic (for detailed methods see [19,32]). Targets were identified to species and flock sizes through telescopes simultaneously with radar registrations providing computer readings of range, elevation, and bearing to the target usually every 10 s with the radar in automatic tracking mode. All flight speeds have been corrected for the influence of wind by subtraction of the wind vector at the altitude where the birds were flying from the ground speed vector of the birds. Winds were measured by releasing and tracking hydrogen/helium-filled balloons carrying a radar reflector. Mean airspeed, altitude, and vertical flight speed were calculated for each track, excluding segments with a convoluted flight path. Altitudes were corrected in relation to sea level by adding the altitude of the radar antenna (10–185 m above sea level at the different sites), and true airspeeds were reduced to equivalent airspeeds (U_e) referring to sea level air density, according to the standard atmosphere change in air density with altitude [14,15].

Scaling calculations and statistical analyses.

Reduced major axis regressions [16] for the scaling relationships between U_e and m and Q, respectively, were performed in Matlab, with calculations of confidence intervals by bootstrapping [33]. Calculations of reduced major axis regressions based on phylogenetic independent contrasts are further described in Protocol S2. We checked for possible bias arising as a consequence of including species with only one or a few tracks, by restricting the calculations to species with at least five or ten tracks. The results remained the same, as exemplified for the sample of 56 species with ≥10 tracks in Table 1. For 39 of the species with ≥10 tracks, we could account for the within-species variation of U_e in relation to vertical flight speed, head- and side-wind components, and flock size by multivariate regression (statistically significant influences were found in 26 of these 39 species; unpublished data). Restricting the analysis to intercept values of U_e for these 39 species (corrected to zero vertical speed, zero wind, and a flock size of one from the multiple regression equations of significant variables for each species) still gave the same scaling result (Table 1). General Linear Models (Figure 2) [34] were calculated with U_e as dependent variable. Logarithmic values were used for U_e, m, and Q. Phylogenetic group and flight mode (limited analysis of this provisionally estimated variable) were treated as fixed factors. Complex models (different combinations or interactions of mass, aspect ratio, and phylogenetic group or of wing loading, aspect ratio, and phylogenetic group) were presented in Figure 2 only if AIC improved from that of models with single independent variables [19].