INDIVIDUAL OPTIMIZATION - MECHANISMS SHAPING THE OPTIMAL REACTION NORM

In general, optimal reaction norms in heterogeneous populations can be obtained only by iterative numerical procedures (McNamara, 1991; Kawe cki and Stearns, 1993). We consider two particular, but biologically p lausible and analytically tractable cases of individual optimization t o gain insight into the mechanisms which shape the optimal reaction no rm of fecundity in relation to an environmental variable or an individ ual trait. In the first case, we assume that the quality of the enviro nment (e.g. food abundance) or the quality of the individual (e.g. bod y size) is fixed during its entire life; it may also be a heritable in dividual trait. In the second case, individual quality is assumed to c hange randomly such that the probability distribution of quality in th e next year is the same for the parent and for her offspring. For thes e two cases, we obtain analytical expressions for the shape of the opt imal reaction norm, which are heuristically interpretable in terms of underlying selective mechanisms. It is shown that better quality may r educe the optimal fecundity. This outcome is particularly likely if be tter quality increases a fecundity-independent factor of parental surv ival in a long-lived species with fixed quality.