Red Queen Simulator

Scientific Preamble — Some notes on size scaling of population density and energy-use

by John Damuth

Ecological allometry

      The size-dependence of many biological variables can be well described by what are known in biology as allometric equations, usually expressed as simple power laws of the form:

where V is some variable of interest, M is a measure of body size (e.g., body mass) , and a and b are constants specific to the relationship. It is often more useful to consider this allometric relationship in its equivalent logarithmic form:

This expression describes a linear relationship between the log-transformed variable and the logarithm of body size. Specifically, by plotting log V versus log M we should observe a linear relationship with a V-intercept of log a and a slope of b. This is useful because in empirical work all that is necessary to estimate a value for the allometric exponent b is to fit a line to the log-transformed data and determine its slope. In practice when working with allometric relationships people often use the terms “slope” and “exponent” interchangeably.

Next Page