Red-tailed hawks (C) in southern California mainly feed on rabbits (R) and squirrels (S). They tend to focus their hunting efforts on the most abundant prey species. Use the assumptions below to write a model of interactions among these species, Rabbits have a per-capita birth rate of 6 and a per-capita death rate of 1.5. Squirrels have a per-capita birth rate of 3 and a per-capita death rate of 0.8. Hawks eat only rabbits and squirrels. There are no other prey. The fraction of a hawk's diet made up of squirrels is a sigmoid function of the squirrel population. The number of squirrels eaten by each hawk is proportional to the fraction of the hawks' diet made up of squirrels, with a proportionality constant of 0.9. The number of rabbits eaten by each hawk is proportional to the fraction of the hawks' diet made up of rabbits, with a proportionality constant of 1.3. . The hawk total birth rate is proportional to the total number of squirrels and rabbits eaten, with a proportionality constant of 0.4. Hawks have a per-capita death rate of 0.1.