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This study combines data on changes in cardiovascular variables with body mass (Mb) and with exercise intensity to model the oxygen supply available to birds during flight. Its main purpose is to provide a framework for identifying the factors involved in limiting aerobic power input to birds during flight and to suggest which cardiovascular variables are the most likely to have been influenced by natural selection when considering both allometric and adaptive variation. It is argued that natural selection has acted on heart rate (fh) and cardiac stroke volume (Vs), so that the difference in the arteriovenous oxygen content (CaO2-Cv¯O2) in birds, both at rest and during flight, is independent of Mb. Therefore, the Mb exponent for oxygen consumption (V(dot)O2) during flight can be estimated from measurements of heart rate and stroke volume. Stroke volume is likely to be directly proportional to heart mass (Mh) and, using empirical data, values for the Mb coefficients and exponents of various cardiovascular variables are estimated. It is concluded that, as found for mammals, fh is the main adaptive variable when considering allometric variation, although Mh also shows a slight scaling effect. Relative Mh is likely to be the most important when considering adaptive specialisations. The Fick equation may be represented as: (V(dot)O2)Mbz = (fh)Mbw x (Vs)Mbx x (CaO2 - Cv¯O2)Mby , where w, x, y, z are the body mass exponents for each variable and the terms in parentheses represent the Mb coefficients. Utilising this formula and data from the literature, the scaling of minimum V(dot)O2 during flight for bird species with a 'high aerobic capacity' (excluding hummingbirds) is calculated to be: 166Mb0.77&amp;plusmn;0.09 = 574Mb-0.19&amp;plusmn;0.02 x 3.48Mb0.96&amp;plusmn;0.02 x 0.083Mb0.00&amp;plusmn;0.05 , and for hummingbirds (considered separately owing to their unique wing kinematics) it is: 314Mb0.90&amp;plusmn;0.22 = 617Mb-0.10&amp;plusmn;0.06 x 6.13Mb1.00&amp;plusmn;0.11 x 0.083Mb0.00&amp;plusmn;0.05 . These results are largely dependent on the cardiovascular values obtained from pigeons flying near to the minimum power speed of 10 m s-1, but would appear to provide realistic values. Both the measured and the estimated V(dot)O2 for hummingbirds appear to scale with a larger Mb exponent than that for all other birds, and it is suggested that this is as a result of the larger Mb exponent for flight muscle mass as the larger species of hummingbirds try to maintain hovering performance. It is proposed that estimated V(dot)O2 for birds during flight, which is based on Mh in combination with estimates of fh and CaO2-Cv¯O2, gives an indirect measure of relative aerobic power input and, when corrected for the estimated scaling influences of the mechano-chemical conversion efficiency and lift generation with respect to Mb, may be a useful indicator of the relative capacity of the muscle to sustain power output and lift production during flight.

Physiological Modelling of Oxygen Consumption In Birds During Flight