| This dissertation contains three chapters where we develop discrete juvenile-adult population models. In chapter one, a general discrete juvenile-adult population model with time-dependent birth rate and nonlinear survivorship rates is studied. In both the cases of continuous and seasonal breeding, conditions on the net reproductive number are given to establish when the population will persist or will go to extinction. Conditions are provided on the birth rate where the population with seasonal breeding survives while the population with continuous breeding becomes extinct. In chapter 2, we develop a general discrete juvenile-adult population model that describes two competing species. Assuming competition efficiencies of the two species are similar, we analyze the cases where reproduction is either continuous or seasonal. In both cases, we develop conditions on the invasion net reproductive numbers of the two species that will lead to competitive exclusion. We show using numerical simulations that coexistence and bistability are possible outcomes when competition efficiencies of the two species are different. In chapter 3, we developed a juvenile-adult discrete model that describes the dynamics of one species migrating between two locations, patch 1 and patch 2. In the case of continuous breeding, we provide conditions that will lead to the global asymptotic stability of the extinction equilibrium and the existence and global asymptotic stability of an interior steady state. |
