An efficient method for stochastic simulation of biological populations in continuous time

We present an efficient algorithm for individual-based, stochastic simulation of biological populations in continuous time. A simple method for its implementation is given and it is compared to Gillespie's commonly used Direct Method. These two methods are proven to be exactly equivalent and, using a basic evolutionary model, it is demonstrated that the new algorithm can run thousands of times faster. Furthermore, while computational cost per event increases linearly with population size under the Direct Method, this cost is independent of population size under the new algorithm. We argue that this gain in efficiency opens up the possibility to explore a new class of models in population biology.