In this paper, the mathematical modeling of a new bio-inspired evolutionary search algorithm called Ecological Systems Algorithm (ESA) is presented. ESA imitates ecological rules to find iteratively the optimum of a given function through interaction between predator and prey search species. ESA is then compared to the well-known Genetic Algorithm which is a powerful bio-inspired stochastic search/optimization algorithm used for decades. Simulation results of the two algorithms optimizing ten different benchmark functions are used to investigate and compare both algorithms based on their speed, performance, reliability, and efficiency.