Consider a density$-$dependent animal population model, in which birth fraction $bf=0\mathrm{.}05$ per

month, and death fraction df is a joint function of Crowding, and Water Availability:

a$.$ First, the death fraction should be a realistic non$-$linear function of Crowding, which is

defined as the ratio of the current population to the carrying capacity of the ecosystem;

b$.$ Death fraction also depends on Water Availability relative to the population size.

$($Assume that there is a stock of water that replenishes by rainfall and is consumed by the

animals$).$

c$.$ You must thus formulate death fraction as a joint function of both Crowding and Water

Availability.

You should give all related equations, define your parameters, and the plots of any graphical

functions necessary. Also give the complete stock$-$flow diagram of the model. $($You are NOT

asked to give any equations for rainfall and water consumption, and not expected to upload a

running model$).$