I am now trying to take my linear model and make it nonlinear by determining which of my paramters should depend on the environment, population size, etc. I am creating a couple different models with different assumptions. My first model at the moment only has birth rate dependent on the environment, and my second model has both birth and death rate depending on the environment. I am at the moment wondering weather I should some how add a carrying capacity that would decrease birth rate and increase death rate when the population becomes too large. An example of this is represented in the equation below, where the change in population size is dependent on the population size N, the growth rate r, and the carrying capacity K (if N=K, then the population size will remain unchanged).

I also read about the Ricker function today (another function that could help incorporate density dependence). I am trying to decide what would be a better fit for the model.

dN/dt = B(N)N − dN where B(N) is a birth rate function and d is the death rate (not dependent on anything). B(N) can be written as a Ricker function, where B(N) = b*e^(−N), with b > d, where b is the birth rate. Here also when N, the population size becomes very large the birth function gets close to zero.