The recent study gave a sufficient condition for population survival in matrix population models. This sufficient condition ensures that if the matrix at the origin is both irreducible and unstable, then population survives in the sense that the total population density is eventually greater than some positive constant. But this sufficient condition does not ensure that all cohorts coexist. For example, it is known that competitive exclusion of cohorts occurs in some specific matrix population models without primitive life cycle graphs. In this talk, we focus on matrix population models with primitive life cycle graphs and obtain a sufficient condition which ensures cohort coexistence.