James H. Roberds

Dynamic gene conservation for uncertain futures

Abstract Programs for conserving genes in forest trees should be based on evolutionary concepts. Our recommendations for gene conservation are appropriate for conditions of rapid environmental change such as might occur under accumulation of greenhouse gases. We describe the impact that the evolutionary forces of selection, migration and genetic drift have on the genetic architecture of tree species and emphasize that maximum fitness for all traits will never be obtained in any plant population. Genetic variation is a prerequisite for future evolution and we stress that gene conservation programs should provide opportunities for future evolution. Two methods have been developed to manage populations for this purpose. One is hierarchical; in it useful genes are intended to be gradually transferred by crossing from lower to higher levels of improvement. The second, the multiple population breeding system, generates the sizeable genetic variance that is necessary to cope with future uncertainties regarding environmental conditions and trait values. We recommend this latter system whenever financing allows. Existing adaptations should be used when populations are appointed as gene resource populations. The multiple breeding population system was developed to incorporate ex situ gene conservation as an integral part of breeding. However, its basic premise of broadening among-population variance can also be accomplished in in situ programs by choosing widely varying stands as gene resource populations and diversifying them further through selection.

Lumped-density population models of pioneer-climax type and stability analysis of Hopf bifurcations

The effects of population density on the survival and growth of an individual species are modeled by assuming that the species per capita growth rate (i.e., fitness) is a function of a weighted total density. A species is called a pioneer population if it thrives at low density but its fitness decreases monotonically with increasing density. A species is called a climax population if its fitness increases up to a maximum value and then decreases as a function of its total density. Hopf bifurcations for deterministic models of the interaction of pioneer and climax populations are discussed. Stability properties for the Hopf invariant curves in the discrete models are compared to the stability properties of the Hopf periodic orbits in the corresponding continuous models. Examples illustrate that stability may be more common in the discrete models.

Analysis of failure time in clonally propagated plant populations

A problem originating in forest tree breeding concerns the number of clones needed in clonally propagated plantings to manage risk of failure due to an unforeseen catastrophic event. In this paper, we present a model for and analysis of time to failure for clonally propagated populations, assuming that in each year there is a chance for attack by an insect or pathogen. We develop the probability distribution of the number of years until population failure, T. A surprising finding is that in some circumstances increasing the number of clones can increase, rather than decrease, the chance of population failure. This suggests that laws, such as those current in the European Community, mandating minimum numbers of clones to be used in reforestation, may not achieve their intended effects, and that further investigation is needed to clarify the situation.

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.

Evolutionary effects of density-dependent selection in plants

The evolution of traits that affect genotypic responses to density regulated resources can be strongly affected by population dynamics in ways that are unpredictable from individual viability or reproduction potentials. Genotypes that are most efficient in utilizing energy may not always displace less efficient ones, and the evolution of energy allocation strategies may not always favour reproductive fitness because of their effects on destabilizing population growth rates. Furthermore, genetic polymorphisms in single loci that affect such traits can be maintained in populations with stable, periodic changes in population size and gene frequencies in the absence of heterozygote superiority. In fact, in the models investigated in this paper, the polymorphism is maintained, even in the absence of equilibrium genotypic frequencies.