Death-birth adaptive dynamics: modeling trait evolution.

Here, we derive stochastic adaptive dynamics from the microscopic death-birth process by explicitly modeling the trait variation from offspring to parent in each reproductive event, thereby accounting for a highly polymorphic population. This generalization enables the construction of a quantitative model that can be subjected to empirical validation. Our mathematical analysis furnishes a formula for estimating the trait variation in the reproductive step by exclusively observing the current trait variation in the population. In addition, we provide a straightforward approach to obtain the fitness function associated with a particular trait by examining its actual evolutionary trajectory, which can be employed to forecast the continued evolution of the trait.