Linkage Disequilibrium And Multilocus Associations

As shown in Chapter 2, both past history as well as recurrent evolutionary forces influence the genetic parameter of linkage disequilibrium, D. The creation of disequilibrium is influenced by historical factors such as the exact haplotype background upon which a new mutation originated or historical admixture between two previously genetically differentiated subpopulations (Chapter 2). Recurrent processes such as the system of mating and the amount of recombination then influence the decay of linkage disequilibrium over time—a decay that can be quite slow for closely linked genes or sites. This slow decay means that the signature of the historical events that initially created linkage disequilibrium is often apparent for many generations.

For example, in Chapters 3 and 6 we saw that the current African American gene pool has been greatly shaped by historical admixture between previously differentiated European and African populations (see Figure 6.2). In human populations without evidence of historical admixture, most of the significant linkage disequilibrium disappears between marker pairs greater than 2 cM (Wilson and Goldstein 2000). However, in African Americans, significant linkage disequilibrium extends up to 30 cM (Lautenberger et al. 2000), a result consistent with their known population history of admixture. An even more dramatic example of ancient admixture affecting current linkage disequilibrium is provided by the Lemba, a southern African group who speak a variety of Bantu languages but claim Jewish ancestry (Wilson and Goldstein 2000). According to their oral traditions, the Lemba are descended from a group of Jewish males who centuries ago came down the eastern coast of Africa by boat. Many were lost at sea, but the remainder interbred with local Bantu women, thereby establishing the ancestors of the current Lemba, who are now found mostly in South Africa and Zimbabwe (Thomas et al. 2000). Consistent with this oral tradition of historical admixture, the modern-day Lemba have significant linkage disequilibrium over intervals up to 19-24 cM. In contrast, modern-day populations of Bantus and Jews with no evidence of historical admixture have significant linkage disequilibrium only up to 1-6 cM.

Identifying specific populations that have high levels of linkage disequilibrium due to historical admixture has practical importance in human genetics because the linkage disequilibrium allows one to localize disease-associated genes with a bank of genetic markers scattered throughout the genome (Lautenberger et al. 2000). However, the history that makes these populations so valuable in disease association studies means that any detected associations between a marker and a disease are specific to the population being studied and cannot be generalized to all of humanity. Other human populations that had different histories will not show the same marker associations, as already illustrated by the example of using color blindness as a marker for G6PD deficiency in the Italian population west of the Apennines versus the population on the island of Sardinia (Chapter 4). Associations detected through linkage disequilibrium are due to history, not cause and effect, and therefore cannot be generalized across populations with different histories.

The fact that linkage disequilibrium is often population specific can also be a serious limitation to using linkage disequilibrium as a tool for investigating the general influence of historical events upon a species' population structure. Often, we are interested in the history of the entire species, or at least that of many different subpopulations living in a certain geographical area. Many interesting historical events (such as past fragmentation or colonization events) are expected to influence primarily the amount of genetic differentiation between subpopulations rather than the amount of linkage disequilibrium within any one subpopulation. Linkage disequilibrium can also be created by pooling genetically distinct subpopulations, as shown in Chapter 3. Hence, disequilibrium within and among subpopulations detects different aspects of evolutionary history. This in turn leads to the problem of how to interpret linkage disequilibrium; is it due to historical admixture or current pooling of differentiated demes?

Another limitation of using linkage disequilibrium to investigate population structure and history is that disequilibrium is inherently a two-locus (or two-site) statistic, whereas most genetic surveys assay multiple polymorphic loci or sites. You can always calculate all the pairwise disequilibrium between the multiple markers, but the resulting large matrix of correlated numbers is a very cumbersome investigative tool. Consequently, other methods of multilocus association are often used, particularly when the desired inference concerns not a single deme but a collection of many demes.

One method used to measure multilocus associations between demes is principal-component analysis, a statistical procedure used to simplify multivariate data with a minimal loss of information that has many uses in data analysis. Multivariate data can always be plotted in a multidimensional space, with each dimension corresponding to one of the variables being measured. A principal-component analysis rotates the axes of the original coordinate system through this multidimensional space such that one rotated axis, called the first principal component, captures the maximum amount of variation possible in a single dimension. The second principal component is the rotated axis constrained to be perpendicular (and thereby statistically independent) to the first principal component that captures the maximum amount of the remaining variation, and so on until an entire new set of perpendicular rotated axes has been defined.

To illustrate how principal-component analysis is specifically applied as a measure of multilocus association, consider the data set given in Table 7.1 on the frequencies of the D— allele at the human Rh blood group locus and the frequencies of the O allele at the human ABO blood group locus in five human populations (data from Cavalli-Sforza et al. 1994). No linkage disequilibrium exists between these unlinked loci within these populations. However, if we amalgamate these five human populations into a single pooled population (weighting each population equally), the D— allele has a frequency of 0.146, the O allele of 0.720, and the combination of D— and O has a gamete frequency of 0.096. The linkage disequilibrium in the amalgamated population is given by the difference

Table 7.1. Allele Frequency Data on Five Human Populations for O Allele at ABO Blood Group Locus and D— Allele at Rh Blood Group Locus

Population

Frequency of O

Frequency of D-

Africa

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