An analysis of life history evolution in terms of the density-dependent Lefkovitch matrix model

The evolution of demographic characteristics is considered in terms of the density-dependent Lefkovitch matrix model, which describes a species' population dynamics with a stage-specific pattern of reproduction and mortality. We obtain the invadability condition of a mutant-type into the wild-type population at the equilibrium state. The condition depends on the left and right eigenvectors at the equilibrium state. The condition depends on the left and right eigenvectors at the equilibrium state and the difference, between wild-type and mutant-type populations, of the values of elements in the Lefkovitch matrix at the equilibrium state. It is also shown that if elements of the density-dependent Lefkovitch matrix are decreasing functions of population density, then the equilibrium population density increases in the process of natural selection; that is, K-selection acts even on the stage-structured population. The evolution of life history in perennial plants is discussed through two models as an application of the above results. The evolution of perennial plants with no vegetative reproduction is analyzed in the first example. It is shown that whether monocarpic perennials (which reproduce once and die) or polycarpic perennial plants (which reproduce more than once) are favored depends on the cost of a produced seed. The second example concerns perennial plants that reproduce vegetatively. It is shown that whether monocarpic or polycarpic perennial plants are favored depends on the cost of a seed and that where vegetative reproduction is common, polycarpic perennials with no seed reproduction are favored.