Inferences involving individual coefficients of relatedness and inbreeding in natural populations of Abies

Individual coefficients of relatedness and inbreeding, as estimated from genetic markers, are increasingly used for fine-scale studies of natural populations. We describe three approaches based upon these coefficients, two of which involve novel statistics, and illustrate their use with a study of four populations of two Abies species (A. amabilis and A. lasiocarpa) in British Columbia, Canada. Prior to their use, we recommend that an estimator be chosen via an evaluation of their properties via Monte-Carlo simulation. First, we examined isolation-by-distance, via both pairwise relatedness and actual variance of relatedness. Significant declines of relatedness with distance were found in two of four populations, and actual variance of relatedness increased with distance. As an alternative to regression, a new statistic, the "spatial variance of gene identity" is introduced, of utility for among-population comparisons, but it displays a high estimation variance. Second, we estimated of "heritability in the field" for relative growth rate. While estimates were significantly positive for A. amabilis (the first demonstration of heritable variation in the field for a conifer), estimates of the actual variance of relatedness were too uncertain to give absolute levels of heritability. Third, the relative depression of fitness due to inbreeding, characterized with a new measure termed the "inbreeding genetic load", was estimated with individual inbreeding coefficients. Levels of load for relative growth rates were positive but non-significant in all four populations. The latter two methods are particularly for long-lived species such as forest trees, where experimental manipulation is difficult. The relevance of these inferences to breeding and gene conservation in natural forest populations is also discussed.