We develop a model for the population dynamics of the Florida scrub lizards. Two parts compose the model: inner patch growth and migration effect. We construct a new model for inner patch system based on Leslie Matrix model and Logistic model. We use Leslie Matrix to depict the age structure. We consult Logistic Model and introduce density dependent factor into our Matrix model. We determine the parameters in our model by calculating the intrinsic increase rate and predicting carrying capacity. We estimate the migrant between patches based on probability of surviving the migration between any two patches. We assume the probability obeys exponential distribution and use MLE to estimate the density function based on given histogram. We employ two simulations for the given landscape: one considers stochastic factor and one not. We start the simulation from different beginning values and show good stability. We vary the parameters and test the change in result, in which the model appears good.
As a result, our model shows that in steady environment the overall population size will converge to equilibrium population size and the equilibrium value is noticeably higher than without considering the migration. The advantage of migration is shown. We classify the patches suitable or not for living based on the predicted carrying capacity and fluctuation property. We analyze the result of simulation and find more biological meaning in it.