Abstract by Tyler Mansfield
Modeling Taylor’s Law with Exponential Growth and Migration
Taylor’s Law is an empirically observed phenomena that relates the mean size of n populations to the respective variance by a power law relationship. This empirical formula has been observed in hundreds of species, as well as in non-ecological systems such as cancer metastasis, spread of disease, gene structures, and the distribution of prime numbers. In modeling population dynamics, previous mathematical research has shown that exponential growth is a contributing factor to this law holding. We build upon this by introducing migration between these populations and discuss the factors that predict whether Taylor’s Law will hold for a given pattern (network) of migration within our model.