Slide 18: Mammal dynamics
The population dynamics of herbivores and carnivores basically follows logistic growth functions: there is a maximum intrinsic population growth rate (which scales with body size), and it is reduced linearly as the population approaches its 'carrying capacity', which is in turn determined by the abundance of its food.
Thus the change in mammalian population numbers is equivalent to the current population multiplied by the growth rate, less the offtake (through predation or other mortality).
The growth rate is calculated in this second equation. The value rmax is the maximum growth rate for a population, and is a logarithmic function as described in the third equation. The f value in the second term of the growth rate calculation is the food requirement per head per day, and the C in the same term is the fraction of prey biomass that can be consumed in a year.