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 Ue (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.
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 .
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 Ue 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 Ue for these species in our analyses.
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 (Ue) 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  for the scaling relationships between Ue and m and Q, respectively, were performed in Matlab, with calculations of confidence intervals by bootstrapping . 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 Ue
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 Ue
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)  were calculated with Ue as dependent variable. Logarithmic values were used for Ue, 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 .