Measuring differentiation among populations at different levels of genetic integration

Abstract

Background: Most genetic studies of population differentiation are based on gene-pool frequencies. Population differences for gene associations that show up as deviations from Hardy-Weinberg proportions (homologous association) or gametic disequilibria (non-homologous association) are disregarded. Thus little is known about patterns of population differentiation at higher levels of genetic integration nor the causal forces. Results: To fill this gap, a conceptual approach to the description and analysis of patterns of genetic differentiation at arbitrary levels of genetic integration (single or multiple loci, varying degrees of ploidy) is introduced. Measurement of differentiation is based on the measure Delta of genetic distance between populations, which is in turn based on an elementary genic difference between individuals at any given level of genetic integration. It is proven that Delta does not decrease when the level of genetic integration is increased, with equality if the gene associations at the higher level follow the same function in both populations (e.g. equal inbreeding coefficients, no association between loci). The pattern of differentiation is described using the matrix of pairwise genetic distances Delta and the differentiation snail based on the symmetric population differentiation Delta(SD). A measure of covariation compares patterns between levels. To show the significance of the observed differentiation among possible gene associations, a special permutation analysis is proposed. Applying this approach to published genetic data on oak, the differentiation is found to increase considerably from lower to higher levels of integration, revealing variation in the forms of gene association among populations. Conclusion: This new approach to the analysis of genetic differentiation among populations demonstrates that the consideration of gene associations within populations adds a new quality to studies on population differentiation that is overlooked when viewing only gene-pools.