Difficulties in summing log-normal distributions.

(a) The mean of the log-normal distribution is pulled right by the long right tail as compared to the median. (b) The distribution of sums of log-normally distributed abundance samples across 1,000 populations each distributed according to (a). The median of this distribution of sums is much larger than the sum of the medians of each individual population, since samples from log-normal distributions will include extreme values from the right-hand tails (circled pink in (c)). (c) This situation is illustrated with 4 populations and 11 samples from the distribution for each population.