Estimating selective advantage and related parameters of a model for two populations competing in a bounded environment

Martingale theory and a method of moments are used to derive a class of estimators for the selective advantage of two types of individuals competing in a bounded environment in continuous time. Explicit expressions are given for these estimators which involve only simple computations. Also, an optimal estimator in the sense of giving tightest asymptotic bounds is obtained. Asymptotic results are given and simulation was performed to assess the quality of the proposed estimators. Estimates for the cumulative mortality rate and mortality rate at a specific point in time are also given.