Multilocus structure in the Pinus contorta – Pinus banksiana complex

Natural hybridization between lodgepole pine ( Pinus contorta Dougl. ex Loud.) and jack pine ( Pinus banksiana Lamb.) in western Canada provides a distinct opportunity to infer evolutionary and demographic determinants of nonrandom associations of the alleles at different loci occurring in this Pinus contorta – Pinus banksiana complex (PCBC). Here, we investigated multilocus associations among and within 40 PCBC populations sampled from central and northwestern Alberta, using 39 random amplified polymorphic DNA (RAPD) markers. For each of the 40 PCBC populations, we examined distributions of 741 pairs of linkage (gametic) disequilibria (LD) between the 39 RAPDs and measured the “average” multilocus associations using the summary statistics that allow for packaging of individual LD in each population. We then partitioned the variance of LD in the total population to assess the causes of multilocus population structure. The results showed that (i) LD were more prominent in hybrid populations than in parental populations; (ii) multilocus Wahlund effect was a much more important determinant of population structure than its single-locus counterpart, particularly in hybrid populations; and (iii) considerable mutlilocus associations across the populations within each taxa group was due to the presence of different multilocus haplotypes in different populations. Such results are best explained by the fact that PCBC populations are geographically and ecologically marginal and are produced at the balance between mixing of two distinct gene pools creating new recombinants and selection in favor of parental gametes, but against the recombinants.

Analysis of Multilocus Zygotic Associations

While nonrandom associations between zygotes at different loci (zygotic associations) frequently occur in Hardy-Weinberg disequilibrium populations, statistical analysis of such associations has received little attention. In this article, we describe the joint distributions of zygotes at multiple loci, which are completely characterized by heterozygosities at individual loci and various multilocus zygotic associations. These zygotic associations are defined in the same fashion as the usual multilocus linkage (gametic) disequilibria on the basis of gametic and allelic frequencies. The estimation and test procedures are described with details being given for three loci. The sampling properties of the estimates are examined through Monte Carlo simulation. The estimates of three-locus associations are not free of bias due to the presence of two-locus associations and vice versa. The power of detecting the zygotic associations is small unless different loci are strongly associated and/or sample sizes are large (>100). The analysis of zygotic associations not only offers an effective means of packaging numerous genic disequilibria required for a complete characterization of multilocus structure, but also provides opportunities for making inference about evolutionary and demographic processes through a comparative assessment of zygotic association vs. gametic disequilibrium for the same set of loci in nonequilibrium populations.

Dynamics of gametic disequilibria between loci linked to chromosome inversions: the recombination-redistributing effect of inversions

SummaryThe total gametic disequilibrium between two loci linked to polymorphic inversions can be partitioned into two types of components: within and between chromosome arrangements. The within components depend on the gametic disequilibrium within each chromosome arrangement. The between components depend on the locus-inversion disequilibria. This partitioning has practical applications and is indispensable for studying the dynamics of these systems because inversions greatly reduce recombination in the heterokaryotypes while allowing free, and sometimes different, recombination in each of the homokaryotypes. We provide equations for the per generation change of the various disequilibria for systems with two and three chromosome arrangements, and the general recursive equations predicting the disequilibria after any number of generations for the case of two arrangements. Simulation studies were carried out using different values of the recombination parameters and all possible initial conditions. The results show a complex convergence to linkage equilibrium in inversion systems. The various disequilibria can have local maxima and minima while approaching equilibrium and, moreover, their dynamics cannot be described, in general, using a single parameter, i.e. an effective recombination rate. We conclude that the effects of inversions on gametic disequilibria must be carefully considered when dealing with disequilibriain inversion systems. The formulae provided in this paper can be used for such purpose.

The Genetical Response to Natural Selection by Varied Environments. IV. Gametic Disequilibrium in Spatially Varied Environments

ABSTRACT Gametic disequilibria between allozyme loci were related to spatial variation of the environment in caged populations of Drosophila melanogaster . Two experiments, one with flies collected at "Chateau Tahbilk," South Australia, and the other with flies from "Groningen," The Netherlands, were sampled at generations 16 and 32. Spatial variation of the environment was stimulated using three food media. Eight polymorphic allozyme loci were used to estimate gametic disequilibria from digenic combinations of allotypes. All populations were duplicated within an environment and maintained at about 2500 adults. Standardized gametic disequilibria were compared by a weighted least squares analysis of the z-transformed statistical correlation of allele frequencies. Gametic disequilibria were strongly dependent upon food niche and food-niche interactions. The effects also varied with sampling time and were similar in duplicate populations. Gametic disequilibria were most often detected in the "Groningen"-derived populations and their strength was not strongly associated with recombination fraction. Many of the disequilibria concerned unlinked loci. The strength of selection was probably considerable and populations were evolving genetic architectures which reflected niche selection by the different foods without marked genetic isolation between foods; gene frequencies did not vary between niches within a population cage.

MULTIVARIATE ANALYSIS OF GAMETIC DISEQUILIBRIUM IN THE YANOMAMA

ABSTRACT The gametic disequilibria between all possible pairs of loci were examined for a set of eight codominant loci in each of fifty Yanomama villages, using a multivariate correlation analysis which reduces the results to a single measure of departure from multiple-locus-gametic equilibrium. Thirty-two of the fifty villages departed significantly from multiple-locus gametic equilibrium. The largest contributions to the departure from multiple-locus equilibrium were due to the disequilibria between MN and Ss and between Rh(Cc) and Rh(Ee), indicating the effects of tight linkage. After removing the effects of these obvious sources of disequilibrium, sixteen of the fifty villages still remained significantly out of equilibrium. The disequilibrium between any particular pair of loci was highly erratic from village to village, and (with the exception of the MN-Ss and Cc-Ee disequilibria) averaged out very close to zero overall, suggesting a lack of systematic forces (epistatic selection). The departure from equilibrium in any one village is in excess of that expected from random sampling alone, and is attributed primarily to the fission-fusion mode of village formation operative in the Yanomama and the fact that a single village consists of a few extended lineages. Village allele frequencies are highly correlated across loci, and most of the non-independence is accounted for by large correlations in the average allelic frequencies of different loci for related villages. It is suggested that these correlations also are due to territorial expansion and population growth. For the tribe as a whole, all but the tightly linked markers of the MNSs and Rh complexes are approximately uncorrelated, and large departures from multiple-locus Hardy-Weinberg expectation are primarily due to substantial Wahlund variance within the tribe. There is no need to postulate a role for selection in these disequilibria.