By fixing the postural costs (the y-intercept) based on this equation rather than allowing the postural costs to be estimated based on model fit, we improve the biological realism of our models outside the range of our data (i.e. when speed is zero), while only slightly sacrificing goodness of fit within the range of our data (speeds of 1.8–7.92 km/h). We note, however, that results were qualitatively similar whether postural costs were fixed based on Equation 4 or estimated based on our data. We evaluated relative support for the models using Akaike's information criterion (AICc; Akaike, 1973) and found that the exponential and double-exponential models received similar support (Table 1; ΔAICc = 0 and 0.5, respectively), and greatly outperformed the linear model (ΔAICc = 24). Table 1:Model selection results incorporating effects of mass on the relationship between speed and oxygen consumption.ModellogLikAICcΔLogLikΔAICcparametersWeightPebS 10.1−15.512020.288PebSc 11.3−1513.20.530.223Pe(b+m1*mass)S(c+m2*mass) 14.9−14.716.70.750.199PebS(c+m2*mass) 12.3−13.614.21.940.113Pe(b+m1*mass)Sc 12.2−13.414.12.140.101Pe(b+m1*mass)S 10.3−12.812.12.730.076P+bS −1.88.50242<0.001Model parameters are as follows: b and c, single and double exponents, respectively; e, the natural logarithm (2.718…); m1 and m2, scaling parameters that relate the single exponent and the double exponent, respectively, to polar bear mass; mass, polar bear mass (in kilograms); P, postural costs; and S, polar bear movement speed. In all models, postural costs are described by Equation 4 and thus depend on polar bear mass.