ABSTRACT
This chapter deals with the Leslie matrix model for the dynamics of a population with discrete age structure. The model is based upon several simplifying assumptions, whose oversimplicity has long been invoking widespread theoretical discussions, while narrowing the area of practical applications of the model in its "pure" Leslie form. To study population dynamics of an individual species it is necessary, as a rule, to account for the biology of various age groups or stages of development in the life cycle of organisms. Since the classic Leslie model does not account for effects of this kind, constraint is acceptable as long as we take into account only the reproductive groups. Invertibility of a Leslie matrix is equivalent to its being indecomposable, which is certainly not true for a general matrix. However, the Leslie operator has a simple structure if and only if its eigenvalues are all different.
