Avoiding bias in calculations of relative growth rate

In classical growth analysis, relative growth rate (RGR) is calculated as RGR = (ln W-2 - ln W-1)/(t(2)-t(1)), where W-1 and W-2 are plant dry weights at times t(1) and t(2). Since RGR is usually calculated using destructive harvests of several individuals, an obvious approach is to substitute W-1 and W-2 with sample means (W) over bar (1) and (W) over bar (2). Here we demonstrate that this approach yields a biased estimate of RGR whenever the variance of the natural logarithm-transformed plant weight changes through time. This bias increases with an increase in the variance in RGR, in the length of the interval between harvests, or in sample size. The bias can be avoided by using the formula RGR = ((ln W-2) over bar-(ln W-1) over bar)/(t(2) - t(1)), where (ln W-1) over bar and (ln W-2) over bar are the means of the natural logarithm-transformed plant weights. (C) 2002 Annals of Botany Company.