We estimate the parameters present in several differential equation models of population growth, specifically logistic growth models and two-species competition models. We discuss student-evolved strategies and offer "Mathematica" code for a gradient search approach. We use historical (1930s) data from microbial studies of the Russian biologist, G. F. Gause, and estimate growth rates, carrying capacities, and "coefficients for the struggle for existence." (Contains 9 figures and 5 tables.)