Genetic analysis of risk in clonal populations of forest trees.

A major concern arising from the culture of clonally propagated crops of forest trees is risk of catastrophic loss due to an agent or event not anticipated at the time of population establishment. Since danger of such a catastrophe depends to some degree on the genetic variability within clonal mixtures, attention has been focused on the number of clones needed to keep the risk of catastrophic loss below specified levels. In this paper, we describe a genetical analysis of susceptibility to a destructive agent and the effect that frequency of genes for susceptibility have on the number of clones needed to effectively manage this risk. As a part of the analysis, parameters representing the minimum unacceptable mortality rates in plantations (β) and acceptable levels of risk (α) are defined, and their effects on the number of single-pair matings needed for the production of clonal stock are evaluated. Dominance and recessive gene action models for a single two-allele genetic locus are investigated. Probabilities for plantation failure are functions of the gene frequency for the allele conferring susceptibility. These functions converge to zero for allele frequencies less than β but to one for frequencies greater than or equal to β. This convergence is periodic rather than monotonie, since probabilities for plantation failure increase rather than decrease over restricted ranges of increasing numbers of clones. Recessive and dominance gene actions are found to have different effects on the minimum number of clones needed to attain acceptable risk levels. For conditions in which substantial numbers of clones are required, selecting multiple clones per mating is an effective method for reducing the number of matings necessary to achieve acceptable risks.