The offspring-development-time/offspring-number trade-off.

The metabolic theory of ecology (MTE) states that metabolic rate, ruled mainly by individual mass and temperature, determines many other biological rates. This view of ecology as ruled by the laws of physics and thermodynamics contrasts with life-history-optimization (LHO) theories, where traits are shaped by evolutionary processes. Integrating the MTE and LHO can lead, however, to a synthetic theory of ecology. In this work, we link the two theories to show that offspring development time is the result of both maternal investment in offspring and the metabolic constraints on offspring growth. We formulate a model that captures how offspring development time is the consequence of both offspring growth rate, determined by temperature and allometric scaling in accordance with the MTE, and the size reached by offspring at the end of the developmental period, determined mainly by LHO and reproductive strategies. We first extend the trade-off between offspring size and offspring number to ectotherms, showing that increased body temperatures result in increased resources available for reproduction. We then combine this trade-off with the general ontogenetic growth model to show that there is a trade-off between the number of offspring produced and offspring development time. The model predicts a shorter developmental time in organisms producing larger numbers of offspring.