Theorems on the invasion process in stage-structured populations with density-dependent dynamics

Several theoretical results on evolution in stage-structured models with density-dependent dynamics are obtained. The first one concerns the invadable condition of mutant types when 'density' is considered as the weighted sum of the population densities at each stage. In the second and third results, it is shown that the invadability is equivalent to the increase of the weighted sum at equilibrium when certain conditions are satisfied. It is also shown that the sensitivity for the dominant eigenvalue is proportional to that for the weighted sum at equilibrium. Finally, a theorem on the coexistence of a wild and the mutant types is obtained and the condition for coexistence is discussed. A part of these results are the extended theorems of what Charlesworth (1971, 1980, 1994) has already obtained.