A graphical analysis of life history evolution in biennial plants

Graphical analysis was done on the lfie history evolution of biennials (or monocarpic perennials). The age of seed production (x), the probability of surviving to agex l(x)], and the number of seeds produced at agexb(x)] determine the ultimate rate of population increase (r). The ages whenr=max andr=0 define the optimal and critical age for seed production, respectively, which depend on the shape and combination of thel(x) andb(x) curves. The otpimal age of seed production appears only for the convex function of the natural logarithm of the net reproductive rate R ₀(x)], while the critical age appears irrespective of the shape of theR ₀(x) curves. The effects of environmental change on the optimal and critical ages are, analyzed, with the conclusion that in an environment imposing higher mortality or lower fecundity, delayed reproduction is favored. Age- and size-dependent productions of seeds have different effects on the variation ofr in a changing environment.