Efficient Simulations of Individual Based Models for Adaptive Dynamics and the Canonical Equation

TL;DR

This paper introduces a faster algorithm for individual-based adaptive dynamics simulations that maintains accuracy in the deterministic limit and offers new insights into the canonical equation of adaptive dynamics.

Contribution

A novel, efficient simulation algorithm for adaptive dynamics that preserves key theoretical properties and enhances computational performance.

Findings

The modified algorithm produces the same adaptive dynamics equations as the standard Gillespie algorithm.

It offers improved efficiency over the standard Gillespie algorithm.

The algorithm enables analysis of evolutionary predictability in multi-dimensional phenotypic spaces.

Abstract

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.