Limit theorems and a general framework for risk analysis in clonal forestry

Use of clonally propagated plantings in reforestation offers management advantages of phenotypic uniformity and high yields. Disadvantages include low genetic diversity and the possibility that the clone or clones chosen are particularly susceptible to attack by an insect or pathogen unforeseen as a problem at the time of clonal selection. In this paper, we continue consideration of the problem of choosing an optimal number of clones to minimize the risk of plantation failure. We present an analysis in which risk of failure for a plantation is represented by the probability that the proportion, S, of ramets that survive until harvest is less than or equal to a prescribed value. Our approach includes most earlier treatments as special cases. We show that the proportion S converges in distribution and, furthermore, that, under general conditions, a moderate number of clones, usually no more than 20 to 40 and often fewer, provides equivalent or better protection against catastrophic loss than does a large number of clones.