As a wildlife biologist for the Channel Islands Preserve in California, you are

Question

As a wildlife biologist for the Channel Islands Preserve in California, you are tasked with managing two populations: (1) a population of the endangered Channel Island fox that has a spring breeding period and competes strongly with skunks for food and (2) a population of non-native, feral pigs that can breed any season of the year in the mild climate and are growing rapidly because they have no competitors. As your first step to get a handle on these populations, you decide to build single species population growth models. Write down the equation you would use to model the population growth for each species. Then, list the assumptions of the model you chose for each species.

SO this quesiton has been confusing to me and I beleive that we use the lotka-volterra models and another one. Someone prior had answered it but added a large amount of information that was unecessary. I am just looking wha tmodel would I use for each species and the assumptions for each model.

Explanation / Answer

According to me this case study depicts the continuous and discrete population growth in single species, lotka – volterra model is used for the interspecific competition which cannot be apply in both the cases.

Continuous population growth

In the first case, population of the endangered channel island fox that has a spring breeding period and competes strongly with the shunks for food.

Continuous population growth model for population growth is used in the possible population, with its impact on the food supply etc. Simple model derived was

                                           dP/ dt= aP- bP2

This model explains the exponential growth when the population is small, but it tends towards the finite level. This level corresponds to the steady solution

                                                     P= a/b

Discrete population growth

In the second case , population of non-native, feral pigs that can breed any season of the year in the mild climate and are growing rapidly because they have no competitors.

If the population only breeds once a year, more realistic model may be given by

                                    Pn+1 - Pn = a Pn - b Pn2

By rescaling of P, and by defining a new constant r (which depends on a and b) the Discrete Logistic Equation can be derived:

With the help of this equation possible steady state solutions can be derived

                                                  Xn+1 = Xn = x

and can find the possible solutions.

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