Avoiding bias in calculations of relative growth rate

In classical growth analysis, relative growth rate (RGR) is calculated as RGR = (ln W2 - ln W1)/(t2 - t1), where W1 and W2 are plant dry weights at times t1 and t2. Since RGR is usually calculated using destructive harvests of several individuals, an obvious approach is to substitute W1 and W2 with sample means W1 and W2. 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 W2 - ln W1)/(t2 - t1),where ln W1 and ln W2 are the means of the natural logarithm-transformed plant weights.