Growth models of complex allometries in holometabolous insects

Allometries among body parts of adult holometabolous insects differ from allometries among body parts of many other animals because adult structures (many of which are derived from imaginal disks) do not grow synchronously with the body. Imaginal structures grow little during larval life but experience most of their growth during the prepupal and pupal period, after food intake and somatic growth have ceased. Growth of imaginal tissues thus occurs in a closed system at the expense of nutrients accumulated during larval life. In a closed system, growing imaginal tissues compete for available nutrients, and the growth trajectory and final size of one tissue (or disk) are influenced by the growth of others. We use the Gompertz growth equation and a model of growth in a closed system in which imaginal disks compete for nutrients to model the growth of imaginal disks and the resulting allometric relations among them. By incorporating known features of ant caste development, such as reprogramming of the critical size for metamorphosis in major workers (soldiers) and reprogramming of developmental parameters in individuals larger than a critical size, we show that the nonlinear and discontinuous allometries of ants with polymorphic castes result from normal developmental processes during the metamorphosis of holometabolous insects. The imaginal disk competition model predicts that when one disk is reprogrammed, others will show a compensatory response. Such correlated developmental responses may play a role in the evolution of body proportions in ants, rhinoceros beetles, and other insects.