Charles F. Sing

We previously developed a cladistic approach to identify subsets of haplotypes defined by restriction endonuclease mapping or DNA sequencing that are associated with significant phenotypic deviations. Our approach was limited to segments of DNA in which little recombination occurs. In such cases, a cladogram can be constructed from the restriction site or sequence data that represents the evolutionary steps that interrelate the observed haplotypes. The cladogram is used to define a nested statistical design to identify mutational steps associated with significant phenotypic deviations. The central assumption behind this strategy is that any undetected mutation causing a phenotypic effect is embedded within the same evolutionary history that is represented by the cladogram. The power of this approach depends upon the confidence one has in the particular cladogram used to draw inferences. In this paper, we present a strategy for estimating the set of cladograms that are consistent with a particular sample of either restriction site or nucleotide sequence data and that includes the possibility of recombination. We first evaluate the limits of parsimony in constructing cladograms. Once these limits have been determined, we construct the set of parsimonious and nonparsimonious cladograms that is consistent with these limits. Our estimation procedure also identifies haplotypes that are candidates for being products of recombination. If recombination is extensive, our algorithm subdivides the DNA region into two or more subsections, each having little or no internal recombination. We apply this estimation procedure to three data sets to illustrate varying degrees of cladogram ambiguity and recombination.

The apo E locus contributes to determining the variation in plasma cholesterol levels of healthy and diseased populations. It also influences the expression of hyperlipidemia and appears to modulate the susceptibility to atherosclerosis in a complex multifactorial interaction. There is evidence that the presence of apo E2 is protective, whereas that of apo E4 predisposes to coronary artery disease. The burden of proof, however, lies on future, well-designed clinical trials and prospective studies. The study of the biological significance of the apo E polymorphism in humans has emphasized the importance of gene-gene and gene-environment interactions in the pathogenesis of hyperlipidemia and atherosclerosis. The apo E polymorphism involves the coding region of the apo E gene and results in alterations of the gene product which, in turn, either directly or secondarily affect the metabolic fate of the lipoprotein particles. Rapid advances in knowledge over the last decade have provided a metabolic explanation for the observation of the opposite effects of the epsilon 4 and the epsilon 2 alleles on lipoprotein levels. Apo E2 has lower receptor binding affinity which results in delayed clearance of apo E2-bearing lipoprotein particles from plasma. Apo E4 is distributed differently from apo E3 between VLDL and HDL, is degraded more rapidly than apo E3, and may enhance the catabolism of E4-bearing particles, leading to other alterations in lipoprotein metabolism which result in elevated levels of LDL. In view of the significant opposite impacts of the epsilon 4 and the epsilon 2 alleles on plasma LDL cholesterol concentrations, it is evident that determination of the apo E phenotype will become a useful adjunct to the assessment of the cardiovascular risk profile of an individual. In addition, the relationship between the epsilon 2 allele and type III hyperlipoproteinemia provides a valuable model for the study of complex genetic interactions in the pathogenesis of hyperlipidemia. The further study of apo E and its interactions shows great promise for a deeper comprehension of the pathogenesis of atherosclerosis.

Because some genes have been cloned that have a known biochemical or physiological function, genetic variation can be measured in a population at loci that may directly influence a phenotype of interest. With this measured genotype approach, specific alleles or haplotypes in the probed DNA region can be assigned phenotypic effects. In this paper we address several problems encountered in implementing the measured genotype approach with restriction site data. A number of analytical problems arise in part as a consequence of the linkage disequilibrium that is commonly encountered when dealing with small DNA regions: 1) different restriction site polymorphisms are not statistically independent, 2) the sites being measured are not likely to be the direct cause of the associated phenotypic effects, 3) haplotype classes may be phenotypically heterogeneous, and 4) the sites that are most strongly associated with phenotypic effects are not necessarily the most closely linked to the actual genetic cause of the effects. When recombination and gene conversion are rare, the primary cause of linkage disequilibrium is history (mutational origin, genetic drift, hitchhiking, etc.). We deal with historical association directly by producing a cladogram that partially reconstructs the evolutionary history of the present-day haplotype variability. The cladogram defines a nested analysis of variance that simultaneously detects phenotypic effects, localizes the effects within the cladogram, and identifies haplotypes that are potentially heterogeneous in their phenotypic associations. The power of this approach is illustrated by an analysis of the associations between alcohol dehydrogenase (ADH) activity and restriction site variability in a 13-kb fragment surrounding the ADH locus in Drosophila melanogaster.

The structural gene locus for apolipoprotein E (apo E) is polymorphic. Three common alleles (epsilon 2, epsilon 3, epsilon 4) code for three major isoforms in plasma and determine six apo E phenotypes that may be identified by isoelectric focusing on polyacrylamide. To establish what fraction of the inherited variation in a normal plasma lipid and lipoprotein profile is attributable to the segregation of the common alleles at the apo E gene locus, we have estimated the average apo E allelic effects on plasma cholesterol (C), triglycerides, very low-density lipoprotein (VLDL)-C, VLDL-apo B, low-density lipoprotein (LDL)-C, LDL-apo B, and high-density lipoprotein (HDL)-C in a representative sample of normolipidemic individuals from Ottawa, Canada. Data from published studies were also analyzed by the same statistical procedures. As much as 16% of the genetic variance (8.3% of the total variance) for LDL-C could be accounted for by the apo E gene locus. After correction for differences in age, sex, height, and weight, it was found that the epsilon 2 allele lowered and the epsilon 4 allele raised total cholesterol, LDL-C, and LDL-apo B. No other gene has been identified that contributes as much to normal cholesterol variability. Analysis of these data and those of others also indicates that the apo E locus imparts a differential susceptibility to a variety of factors that promote hyperlipidemia. The hypothesis is proposed that the epsilon 2 allele protects against coronary heart disease (CHD) and, hence, gives a reproductive advantage that is balanced by a predisposition to CHD when the epsilon 2 is combined with a second, independent causative factor to give a reproductive disadvantage. A similar mechanism is proposed for the maintenance of the epsilon 4 allele in the population.

We previously developed an analytical strategy based on cladistic theory to identify subsets of haplotypes that are associated with significant phenotypic deviations. Our initial approach was limited to segments of DNA in which little recombination occurs. In such cases, a cladogram can be constructed from the restriction site data to estimate the evolutionary steps that interrelate the observed haplotypes to one another. The cladogram is then used to define a nested statistical design for identifying mutational steps associated with significant phenotypic deviations. The central assumption behind this strategy is that a mutation responsible for a particular phenotypic effect is embedded within the evolutionary history that is represented by the cladogram. The power of this approach depends on the accuracy of the cladogram in portraying the evolutionary history of the DNA region. This accuracy can be diminished both by recombination and by uncertainty in the estimated cladogram topology. In a previous paper, we presented an algorithm for estimating the set of likely claodgrams and recombination events. In this paper we present an algorithm for defining a nested statistical design under cladogram uncertainty and recombination. Given the nested design, phenotypic associations can be examined using either a nested analysis of variance (for haploids or homozygous strains) or permutation testing (for outcrossed, diploid gene regions). In this paper we also extend this analytical strategy to include categorical phenotypes in addition to quantitative phenotypes. Some worked examples are presented using Drosophila data sets. These examples illustrate that having some recombination may actually enhance the biological inferences that may derived from a cladistic analysis. In particular, recombination can be used to assign a physical localization to a given subregion for mutations responsible for significant phenotypic effects.