Nonnegative matrices as a tool to model population dynamics: classical models and contemporary expansions amg

Matrix models of age- or/and stage-stru­ctu­red popu­lati­ons rest upon the Perron–Frob­enius
theorem for nonn­egat­ive matr­ices, and the life cycle graph for indi­vidu­als of a given
biol­ogi­cal species plays a major role in model cons­truc­tion and anal­ysis. A summary of
clas­sical results in the theory of matrix models for popu­lat­ion dyna­mics is pres­ented,
and gene­rali­zati­ons are prop­osed, which have been moti­vated by a need to account for an
addi­tio­nal stru­cture, i. e., to clas­sify indi­vidu­als not only by age, but also by an addi­tio­nal
(disc­rete) char­acte­ris­tic: size, phys­iolo­gical status, stage of deve­lopm­ent, etc.