| I present general conceptual framework for understanding mean-variance scaling of abundance in ecological populations. I derive the mean-variance scaling relationship known as Taylor's power law for common population growth models and discuss the effect of deterministic dynamics on power law slope. Then I make a case for viewing populations as aggregates of random variables and I explore the mean-variance scaling for such populations. This perspective yields results that agree with the empirical range of power law exponents and has an intuitive basis. Correlation among individuals in populations determines the slope of Taylor's power law. Completely correlated individuals produce a scaling exponent of two, and independent individuals produce a scaling exponent of one, the respective upper and lower limits of empirical scaling exponents. Intermediate degrees of correlation generate intermediate slopes of Taylor's power law. The relationship between correlation and power law slope is supported by a model of tree reproduction in forests. Finally, I calculate Taylor's power law for seed production data and relate these data to the forest model. |
