A trade-off-invariant life-history rule for optimal offspring size.

Optimization models have been widely and successfully used in evolutionary ecology to predict the attributes of organisms. Most such models maximize darwinian fitness (or a component of fitness) in the face of trade-offs and constraints; the numerical results usually depend on the exact form of the trade-offs/constraints. Here we report the first (to our knowledge) numerical optimum for life-history evolution which is independent of the details of the underlying trade-off, for a large 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 set the value of the proportionality constant, but the -1 exponent, the inverse proportionality itself, is universal. Studies of life histories have yielded many empirical examples of universality for various scaling exponents (for example, adult lifespan scales as approximately 0.25 with adult body mass within many taxa); this is an example 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.