In order to explain the process of biological evolution based on some conditions, the differential equation deduced from directional selection describes the evolutionary process of two populations (species) which share the same resource without amalgamation. Although it is generally held that the larger population obtains better chances of survival, such view is not complete. By using differential equations and computer simulations, we found that, when a population gains beneficial mutation, the other population will go extinct regardless of its initial conditions. The larger population is superior since it is more likely to obtain advantageous mutation if the rate of advantageous mutation remains constant between the two populations. On the other hand, if both populations have favorable mutation, the chance of the survival for the smaller population will be apparently better.