An empirical equation is obtained by doing a linear regression fit to a log-log plot of observed wing-beat frequency (fw) compared to body mass (Mp) of many species of bats.

The data and corresponding relation are shown in the figure. 1(a). With reference to the above plot, explain what is meant by an allometric scaling law. The largest existing bats (Pteropus) have a body mass of about 2 kg. Fossil remains for an extinct bat species, Pteropus Gigantus, indicate that this bat species had a body mass of about 3.5 kg, but was incapable of flight. 1. The maximum wing-beat frequency (fw,max) which can be achieved within metabolic rate constraints is proportional to Mp 2. The minimum wing-beat frequency (fw,min) Which is required for flight is proportional to Mp-1/6