Using a lattice model based on Monte Carlo simulations, we study the role of the reproduction pattern on the fate of an evolving population. Each individual is under the selection pressure from the environment and random mutations. The habitat ("climate") is changing periodically. Evolutions of populations following two reproduction patterns are compared, asexual and sexual. We show, via Monte Carlo simulations, that sexual reproduction by keeping more diversified populations gives them better chances to adapt themselves to the changing environment. However, in order to obtain a greater chance to mate, the birth rate should be high. In the case of low birth rate and high mutation probability there is a preference for the asexual reproduction.