Polyvariant Ontogeny in Plants: When the Second Eigenvalue Plays a Primary Role

Abstract

In a local population of a plant species, individual plants may follow various pathways through successive stages in their ontogenesis or/and different schedules in the succession of stages. This feature is called polyvariant ontogeny and considered to be the major mechanism of adaptation at the population level. While the field study reveals this phenomenon in nature, its quantitative characteristics are gained from what is called a matrix model of stage-structured population dynamics. The classical Perron–Frobenius theorem for nonnegative matrices provides for the existence and uniqueness of the dominant eigenvalue, λ1(L), of the model matrix L, the asymptotic growth rate, which is considered to be the quantitative measure of adaptation. This chapter reports on a recently developed theory of rank-1 corrections of nonnegative matrices, a strong extension of the classics in what concerns λ2(L), the second positive eigenvalue, why λ2(L) is always less than 1, and what it means for the matrix population model.