Individual optimization:
Mechanisms shaping the optimal reaction norm

E. Kisdi, G. Meszena and L. Pasztor
 
Summary

Optimal reaction norms in heterogeneous populations, in general,
can be obtained only by iterative numerical procedures (McNamara,
1991; Kawecki and Stearns, 1993). We consider two particular, but
biologically plausible and analytically tractable cases of
individual optimization to get insight into the mechanisms which
shape the optimal reaction norm of fecundity in relation to an
environmental variable or an individual trait. In the first case,
we assume that the quality of the environment (e.g. food
abundance) or the quality of the individual (e.g. body size) is
fixed during the whole life; it may also be a heritable
individual trait. In the second case, individual quality is
assumed to change randomly such that the probability distribution
of quality in the next year is the same for the parent and for
her offspring. In these two cases we obtain analytical
expressions for the shape of the optimal reaction norm, which are
heuristically interpretable in terms of underlying selective
mechanisms. It is shown that better quality may reduce the
optimal fecundity. This outcome is particularly likely if better
quality increases a fecundity-independent factor of parental
survival in a long-lived species with fixed quality.