  We propose a faster algorithm for individual based simulations for adaptive
dynamics based on a simple modification to the standard Gillespie Algorithm for
simulating stochastic birth-death processes. We provide an analytical
explanation that shows that simulations based on the modified algorithm, in the
deterministic limit, lead to the same equations of adaptive dynamics as well as
same conditions for evolutionary branching as those obtained from the standard
Gillespie algorithm. Based on this algorithm, we provide an intuitive and
simple interpretation of the canonical equation of adaptive dynamics. With the
help of examples we compare the performance of this algorithm to the standard
Gillespie algorithm and demonstrate its efficiency. We also study an example
using this algorithm to study evolutionary dynamics in a multi-dimensional
phenotypic space and study the question of predictability of evolution.
