Effects of growth rates in models of size distribution formation in plants and animals

Size is critical in the life cycles of many organisms. In organisms like plants, fish, and numerous invertebrates, where growth rates are highly variable, even-aged cohorts may develop broad size distributions. A description of such distributions is provided by the Von Foerster equation (also called the Sinko and Streifer equation). Using mathematical methods developed for solving analogous equations in physics, one can obtain analytical results for a variety of assumptions concerning organism growth rates. Two general properties of growth rates are considered: (a) the functional form of the dependence of the individual organism's growth rate on time and organism size, and (b) the variation in growth rate magnitude across members of the cohort. Special cases of each of these properties are considered and applied to different phenomena related to the development of size distributions in animal and plant population cohorts.