A TRADE-OFF-INVARIANT LIFE-HISTORY RULE FOR OPTIMAL OFFSPRING SIZE

OPTIMIZATION models have been widely and successfully used in evolutio nary ecology to predict the attributes of organisms(1-6) Most such mod els maximize darwinian fitness (or a component of fitness) in the face of trade-offs and constraints; the numerical results usually depend o n the exact form of the trade-offs/constraints. Here we report the fir st (to our knowledge) numerical optimum for life-history evolution whi ch is independent of the details of the underlying trade-off, for a la rge array for trade-off forms. The rule is that at small litter sizes, the range in offspring size is inversely proportional to the size of the litter. Details of the offspring-survival/offspring-size trade-off (7-10) set the value of the proportionality constant, but the -1 expon ent, the inverse proportionality itself, is universal. Studies of life histories have yielded many empirical examples of universality for va rious scaling exponents (for example, adult lifespan scales as approxi mate to 0.25 with adult body mass within many taxa); this is an exampl e of the numerical value of an exponent (here -1) emerging from a life -history model as independent of all but a few general features of the underlying economic structure.