A Cladistic Analysis of Phenotypic Associations With ...Cladistic Analysis of Phenotypes 345 our analysis. It is important, however, to keep in mind that this cladogram is constructed

Copyright 0 1987 by the Genetics Society of America

A Cladistic Analysis of Phenotypic Associations With Haplotypes Inferred From Restriction Endonuclease Mapping.

I. Basic Theory and an Analysis of Alcohol Dehydrogenase Activity in Drosophila

Alan R. Templeton,’ Eric Boerwinkle* and Charles F. Sing Department of Human Genetics, University of Michigan, Ann Arbor, Michigan 48109-0618

Manuscript received March 2, 1987 Revised copy accepted June 24, 1987

ABSTRACT 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.

ENETIC studies of quantitative phenotypes have G traditionally been carried out using phenotypic correlations between related and unrelated individuals. These biometrical genetic studies estimate the contribution of genetic variation to phenotypic variability, but they do not provide information about the effects of specific gene loci that are contributing to phenotypic variability. However, if the phenotype of interest can be related to biochemical or physiological functions controlled by known loci, then markers at or near the loci of known function (candidate loci) have the potential for either directly or indirectly (through linkage disequilibrium) affecting the phenotype. This “measured genotype” approach enables one to assign phenotypic effects to specific alleles or haplotypes at the candidate loci and has been success- fully applied to protein polymorphisms at enzyme (HOPKINSON, SPENCER and HARRIS 1964) and apolipoprotein gene loci (SING and DAVIGNON 1985; BOER-

’ Permanent address: Department of Biology, Washington University, St.

* Current address: Center for Demographic and Population Genetics, Louis, Missouri 63130.

University of Texas Health Center, Houston, Texas 77025.

Genetics 117: 343-351 (October, 1987)

WINKLE et al. 1987) in human populations. As more genes of known function are cloned, the

ability to implement the measured genotype approach is being enhanced. It is therefore important to exam- ine some of the biological and statistical problems that are associated with this type of analysis. The purpose of this paper is to raise some of the problems encountered with the measured genotype approach as applied to molecular data and to propose solutions for some of them.

PROBLEMS T O BE ADDRESSED

Linkage disequilibrium commonly exists between sites in small DNA regions. Consequently, phenotypic associations with polymorphic sites are not statistically independent between sites. The problem of depend- ence between sites is avoided by investigating the associations with the haplotypes as defined by all avail- able polymorphic sites considered simultaneously. We defer the problem of estimating haplotype states until our next paper. This paper deals only with a data set for which the haplotypes have been determined in an

344 A. R. Templeton, E. Boerwinkle and C. F. Sing

unambiguous manner by breeding homozygous lines. A second problem is also related to linkage disequi-

librium. It is quite probable that the phenotypic associations observed with present day restriction fragment length polymorphisms (RFLPs) are due to their linkage disequilibrium with phenotypically important mutations. For example, many restriction site markers are associated with sickle-cell anemia, but these associations are caused by linkage disequilibrium between the RFLPs and the hemoglobin S mutation (ORKIN and KAZAZIAN 1984). Consequently, the second problem is to develop an analytical technique that is efficient at finding indirect phenotypic associations that are caused by disequilibrium at the population level.

Because phenotypic associations are often caused by disequilibrium, phenotypic heterogeneity can exist within some of the haplotype classes if the disequilibrium is not absolute. For example, KAN and DOZY (1 980) discovered that every individual in their sample that had the C allele at the hemoglobin /3 chain locus also had an HpaI site causing a 13.0-kb fragment. However, some individuals with this 13.0-kb fragment did not have hemoglobin C. KAN and DOZY (1980) explain this pattern of heterogeneity by arguing that the HpaI site mutation that caused the 13.0-kb RFLP evolutionarily preceded the phenotypically important hemoglobin C mutation, and that when the hemoglobin C mutation did occur, it happened to be on a chromosome with the HpaI site. In contrast, ANTON- ARAKIS et al. (1984) found that every individual with a restriction haplotype pattern denoted by “B” had the sickle-cell (S) allele, but that not all individuals with the S allele had the B haplotype. This pattern is explained by having the mutations causing the B haplotype occurring after the S mutation occurred and upon a chromosome bearing the S allele. Given that a very large number of haplotype classes are commonly encountered, a third problem is to have an algorithm that will identify which haplotype classes are the most likely ones to display phenotypic heterogeneity. Once identified, a fourth problem is how to statistically detect heterogeneity within the candidate haplotypes.

A fifth problem is to localize the physical site of the actual genetic cause of any detected phenotypic effects. This is a difficult task when the phenotypic associations are due to linkage disequilibrium. When dealing with small regions of DNA, the magnitude of the disequilibrium is not necessarily a good indicator of the physical location of the sites; i . e . , sites with small magnitudes of disequilibrium can be physically closer to one another than sites with greater amounts of disequilibrium (CROSS and BIRLEY 1986). Hence, the sites with the strongest phenotypic associations may actually be farther away from the phenotypically important mutational site than other RFLP sites that show little or no phenotypic associations.

In addition to the above problems that relate spe- cifically to restriction site and/or sequence data in relatively small DNA regions, there are more general problems that need to be addressed in order to implement the measured genotype approach. When the phenotype is discontinuous, one can use the phenotypic discontinuity to subdivide the population prior to the genotypic analysis. This allows a contingency table approach. This approach is inapplicable to continuously distributed phenotypes unless one makes artificial categories. Hence, a sixth problem is to develop a general algorithm that is applicable to both continuously and discontinuously distributed phenotypic data without resorting to artificial categories.

A seventh problem is that of assigning and testing a phenotypic measure applicable to alleles or haplotypes when the actual phenotype is expressed only in diploid individuals. This is primarily a problem when studying natural populations with no control over genotypic states and will be deferred to our next paper. We now present a strategy for dealing with problems 1, 2, 3, 5 and 6.

CLADES AND CLADOGRAMS

As noted above, there is often a poor correlation between physical distance and magnitude of linkage disequilibrium between polymorphic sites in small DNA regions. The reason for this is that the magnitude and extent of disequilibrium is greatly influenced by historical events in addition to the amount of recombination between sites. As shown by the example given in KAN and DOZY (1 980), the relative place- ment of mutations in evolutionary time determines the patterns of present-day associations and types of phenotypic heterogeneity. Once mutations have occurred, genetic drift, selection, and hitchhiking influence the amount of linkage disequilibrium in addition to recombination rates. If recombination and gene conversion are rare throughout the DNA region being examined, these historical factors are more important than physical location as a determinant of linkage disequilibrium. History can therefore explain the poor correlation between physical location and magnitude of disequilibrium found in such DNA regions as the 13-kb region surrounding the alcohol dehydrogenase (Adh) locus in Drosophila melanogaster (Cross and BIR- LEY 1986).

In this paper, inference is restricted to DNA regions in which recombination and gene conversion are rare. Under these conditions, it is possible to construct a cladogram of the observed haplotypes. The cladogram represents the mutational steps that interrelate the observed haplotypes to one another. I f the root of the cladogram can be determined o r estimated, the cladogram represents a phylogenetic tree of the region in question. Rooting the tree is not important to

Cladistic Analysis of Phenotypes 345

our analysis. It is important, however, to keep in mind that this cladogram is constructed by examining all the restriction sites simultaneously as multisite haplotypes. Hence, disequilibrium is directly incorporated into the cladogram.

The cladogram can be constructed by the same algorithms used for phylogeny reconstruction from restriction site or nucleotide sequence data, such as D. SWOFFORD’S PAUP (Phylogenetic Analysis Using Parsimony) or FELSENSTEIN’S (1 985) PHYLIP. When analyzing restriction sites with these programs, it is important to note that it is much more probable for parallelisms or convergences in haplotype state to arise from losses of restriction sites than by gains (TEMPLE- TON 1983a,b). As long as recombination and gene conversion are rare, the few (if any) recombinant haplotypes actually present may be detectable by these analyses by looking for haplotypes that are assigned an abnormally high number of convergent or parallel events (homoplasious events). Recombinants can be distinguished from multiple convergent or parallel mutations by noting that homoplasious events caused by recombination are physically clustered together in the DNA region, whereas homoplasious events due to mutations will not in general be physically adjacent to one another. The resulting cladogram is an estimate of the evolutionary relationships between the haplotypes. Algorithms exist for placing statistical confidence limits upon the cladogram (TEMPLETON 1983a,b, 1986; FELSENSTEIN 1985), but this problem will not be further discussed in this paper. Here we focus on the use of the cladogram as a tool for the study of associations between RFLPs and phenotypic variability.

To use the cladogram for this purpose, our approach depends on the central assumption that if an undetected mutation causing a phenotypic effect occurred at some point in the evolutionary history of the population, it would be embedded within the same historical structure represented by the cladogram. In other words, one ex- pects from basic evolutionary principles that certain portions of the cladogram would display the phenotypic effect while other portions would not. We now turn our attention to how the cladogram can be used in the statistical analysis of phenotypic data, as illustrated by a worked example.

A CLADISTIC ANALYSIS OF DROSOPHILA ADH ACTIVITY DATA

T o illustrate our approach, we analyze the data on alcohol dehydrogenase (ADH) activity given in AQUADRO et al. (1986). The locus coding for this enzyme is on chromosome 11 of D. melanogaster. The DNA region that includes this structural gene is char- acterized by much disequilibrium between restriction cleavage sites, but the intensity of the disequilibria is

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FIGURE 1.-A cladogram of the haplotypes found in the ADH DNA region of D. melanogaster as constructed by GOLDING, AQUADRO and LANGLEY ( 1 986). Twenty-five of the 29 haplotypes fit into this cladogram, with the remaining four most likely representing recombinants. Numbers 1 through 25 refer to the nonre- combinant haplotypes that can be placed in the cladogram, and Os refer to inferred intermediate haplotypes that were not actually present in the sample but that are needed to interconnect the existing haplotypes. Each double-headed arrow represents a single mutational change detectable by restriction mapping.

not related to physical distance (CROSS and BIRLEY 1986). AQUADRO et al. (1986) isolated 49 second chromosomes from natural populations, in each case placing a homozygous chromosome Z I on a genetic back- ground controlled for the other chromosomes. ADH activities were then measured for each line, and a restriction site map was constructed for a 13-kb region encompassing the Adh gene. Twenty-nine distinct haplotypes were observed among the 49 chromosomes. GOLDING, AQUADRO and LANGLEY (1 986) constructed a cladogram for these haplotypes using PHYLIP, with the results shown in Figure 1. Twenty-five of the haplotypes, representing 4 1 of the 49 observations, fit well into a single cladogram, with 4 haplotypes most likely representing recombination events (GOLD- ING, AQUADRO and LANGLEY 1986). For now, we will ignore the recombinant haplotypes and confine our analysis to the 25 haplotypes that fit into the cladogram shown in Figure 1.

A straightforward statistical procedure for detecting phenotypic associations in these data is to simply perform a standard analysis of variance (ANOVA) using the haplotype categories as treatment effects. Such an analysis is shown in Table 1, and as can be seen, a highly significant statistical result is obtained. Hence, the standard ANOVA detects statistically significant phenotypic differences between haplotype categories. Up to this point, information provided by the cladogram has not been used. Given that a significant treatment effect is detected in the ANOVA, the standard procedure is to use an exploratory multiple- comparison test to localize the effects more precisely


TABLE 1

One-way analysis of variance of alcohol dehydrogenase activities in D. melanogaster

Sum of Degrees of Mean Source squares freedom square F-Statistic

Treatment 209.28 24 8.72 23.10*** Error 6.04 16 0.38

*** Significant at the 0.1% level. The 25 distinct haplotypes are regarded as the treatment effects.

(NETER, WASSERMAN and KUTNER 1985). The question then arises as to what multiple comparisons ought to be made. The cladogram can serve as a useful tool in defining the relevant multiple contrasts, but even with the aid of the cladogram, the number of possible comparisons is large. Consequently, it would be necessary to use a multiple comparison procedure that allows simultaneous confidence statements about a large number of potential contrasts. These procedures, such as the Scheffe method, achieve this flexi- bility at the expense of considerable statistical power (NETER, WASSERMAN and KUTNER 1985). As a result, although the ANOVA might detect significant treatment effects, it might prove difficult to define the effects more precisely. As will be illustrated shortly, this is the case for the ADH data. Second, there is always the danger that certain phenotypically significant effects might be missed because the appropriate contrast was not performed. Consequently, a procedure is needed for performing an exhaustive search over the entire cladogram. For example, one might look at all binary partitions of the data defined by an arrow in the cladogram (e.g., haplotypes 1-1 4 us. 15- 25, 2-14 vs. 1 and 15-25, etc.). This procedure would work if there were only one phenotypically important mutation imbedded in the cladogram. However, if there is more than one phenotypically important mutation, binary partitionings may be misleading. Fi- nally, subtle biases can often enter into exploratory data analyses. The number of potential comparisons is so large, that frequently the investigator “previews” the data and chooses those contrasts that seem mosj likely to give a significant result. Hence, the comparisons actually performed are often a biased subset.

The cladogram can be utilized in a much more powerful and efficient manner than simply as an aid in defining multiple comparisons. Ideally, a statistical procedure is needed that will exhaustively cover the entire cladogram, that provides statistical tests with greater power than the standard multiple comparison procedures, and that avoids the subtle biases that may infect the multiple comparison procedure. If the procedure cannot entirely eliminate the need for multiple comparison statistics, it should at least reduce the number of relevant comparisons so that procedures that are much more powerful than the Scheffe method

can be used. These requirements can be met by car- rying out a nested analysis of variance (NANOVA) in which the cladogram completely defines a priori the nesting structure of the analysis.

Our nesting algorithm defines larger and larger branches (clades) of the cladogram by single transitional steps until all transitions between haplotypes are incorporated into the nested design. Alternative nesting algorithms are possible, but the one we now present has the virtues of being easy to implement, of exhaustively covering the cladogram with no overlap, and of being applicable to any cladogram. For con- venience, we will call the units defined by the various nested branches of the cladogram as “n-step clades” where n indicates the number of transitional steps used to define the clade. Haplotypes correspond to 0- step clades in this terminology, and the individual observations nested within haplotypes represent our bottom level of nesting. We also distinguish between “terminal” and “internal” n-step clades. Terminal n- step clades have only one arrow pointing at them in the cladogram. For example, haplotypes 4, 5, 7, 9, 10, 11, 12, 14, 16, 18, 19, 21, 23and25 inFigure 1 represent terminal 0-step clades. Internal n-step clades have two or more arrows pointing at them in the cladogram. Once again referring to Figure 1, haplotypes 2 ,3 ,6 ,8 , 13, 15, 17,20,22 and 24 are examples of internal 0-step clades.

The nesting algorithm is as follows. Given the n- step clades, the n+ 1 step clades are created by forming the union of all n-step clades that can be joined together by moving back one mutational step from the terminal n-step clades. Any internal n-step clades that are not incorporated into an n+l step clade by this operation are treated as follows. First, identify those remaining n-step clades that are adjacent (i.e., only 1 mutational step) to an n+ 1 step clade that was defined in the initial operation. These n-step clades are now regarded as “terminal,” and the operation is repeated. This procedure is reiterated as needed until all n-step clades are members of an n+l step clade. The algorithm is applied recursively until one reaches the level at which the next round of nesting would unite the entire cladogram into a single category.

For example, consider constructing the 1 -step clades from the 0-step clades (haplotypes) shown in Figure 1. One terminal 0-step clade is haplotype 4, and going back one mutational step joins 4 with 3. Another terminal 0-step clade is haplotype 5, which is also joined with haplotype 3 by going back one step. No other terminal 0-step clade is within one mutational step of the internal 0-step clade represented by haplotype 3. Hence, the union operator joins haplotypes 3, 4, and 5 into a 1-step clade. Similarly, the terminal 0-step clade 7 is joined to the internal 0-step clade 6 by a single mutational step. The internal


FIGURE 2.-The haplotype categories defined by the nesting algorithm discussed in the text. The haplotypes enclosed by solid lines indicate the 1-step clades and are designated by Roman numer- als. The dashed lines enclose the 2-step clades that are designated by Greek letters. Finally, a thick, solid line indicates the partitioning of the cladogram into two 3-step clades, designated by Roman letters.

haplotype 6 is not within a single mutational step of any other terminal O-step clade, so haplotypes 7 and 6 form another 1-step clade. After repeating this procedure for all the terminal haplotypes, only internal haplotypes 1 and 2 have not been placed within a 1-step clade. Both haplotypes 1 and 2 are adjacent to a 1-step clade defined by the initial procedure (haplotype 2 is one mutational step from the 1-step clade consisting of haplotypes 3 , 4 and 5 ; haplotype 1 is one step from the 1-step clade consisting of haplotypes 15 and 16). Hence, both haplotypes 1 and 2 are now regarded as “terminal,” and moving back one mutational step from either one joins the two together. Hence, haplotypes 1 and 2 form a l-step clade. Figure 2 shows the 1-step clades defined by this operation. These l-step clades are designated with Roman nu- merals. As can be seen from Figure 2, a total of l l 1- step clades are defined (I through XI). Of these, 111, IV, V, VI, VIII, IX and XI are terminal, and I, 11, VI1 and X are internal. The 2-step clades defined by these I-step clades are also indicated in Figure 2 and are designated by Greek letters. Of these five 2-step clades, 8, y and e are terminal, and a and 6 are internal. The 2-step clades in turn define two 3-step clades, indicated by a partition in Figure 2 and labeled A and B. Going back one mutational step from these 3-step clades would join the entire cladogram into a single unit. Hence, the 3-step level represents the final level of nesting in this example.

The nested design given by Figure 2 is not balanced at any level. This can be expected to be a general property of nested designs defined in this manner. Hence, we execute the NANOVA using the least- squares, multiple regression technique outlined on

TABLE 2

Nested analysis of variance of alcohol dehydrogenase activities in D. melanogaster


3-Step clades 138.33 1 138.33 366.50*** 2-Step clades 0.88 3 0.29 0.78 I-Step clades 12.93 6 2.16 5.71** O-Step clades 19.14 14 1.37 3.62** Error 6.04 16 0.38

*** Significant; the 0.1%level. ** Significant at the 1 % level. The 41 lines are nested into 25 distinct haplotypes (O-step clades),

which in turn are nested into 1 1 l-step clades, which in turn are nested into five 2-step clades, which in turn are nested into two 3- step clades, as discussed in the text and illustrated in Figure 2.

pages 981-983 of NETER, WASSERMAN and KUTNER (1985).

The results of the NANOVA of ADH activity are given in Table 2. As with the standard ANOVA, a highly significant phenotypic association is detected between strata and ADH activity. Unlike the ANOVA, the NANOVA gives immediate insight into the nature and location of the phenotypically important effects. The most significant phenotypic effect by far is at the 3-step clade level. Since there are only two 3-step clades, this highly significant effect is associated with the transitional step between clades A and B in Figure 2 ( i . e . , the arrow connecting haplotypes 1 and 15).

Other significant phenotypic effects are found at the 1-step and O-step levels (Table 2). Many transitional arrows are associated with these levels, so further localization is necessary. Fortunately, in a NANOVA, it is possible to decompose the total sum of squares at any one level into the independent components that contribute to it. For example, the 1- step clade sum of squares can be subdivided into four independent sums of squares; namely, the sums of squares for the 1-step clades nested within a particular 2-step clade (only four of the five 2-step clades contribute to this sum of squares because, as shown in Figure 2, the 1-step clade VI contains identical data to the 2-step clade y because of a missing intermediate haplotype category). Likewise, the O-step sum of squares can be decomposed into eleven independent sums of squares, each representing the sum of squares of the O-step clades nested within eleven 1-step clades. Table 3 shows the resulting decompositions of the 1- step and O-step sums of squares. Since the sums of squares at any one level are independent, F tests can be used to localize the phenotypic effects in a level.

These F tests are also shown in Table 3. As can be seen, the stronger l-step effect is localized to the 1- step clades nested within the /3 2-step clade. A second phenotypic association is localized to the 1-step clades nested within the 6 2-step clade. Two phenotypic

~


TABLE 3

Decomposition of the sums of squares for the 1-step and 0-step levels into their independent components nested within the next

higher level


]-Step clades Within (Y 1.50 1 1.50 3.98 Within /3 5.74 2 2.87 7.61** Within 6 5.38 2 2.69 7.12** Within 6 0.31 1 0.31 0.82

Total 1-step 12.93 6 2.16 5.17** 0-Step clades

Within I 0.18 1 0.18 0.47 Within I1 1.26 2 0.63 1.66 Within I11 0.01 1 0.01 0.04 Within 1V 0.80 2 0.40 1.06 Within V 0.15 1 0.15 0.39 Within VI 0.39 1 0.39 1.02 Within VI1 0.00 1 0.00 0.00 Within VI11 10.49 2 5.25 13.90** Within IX 1.66 1 1.66 4.39 Within X 4.14 1 4.14 10.97** Within XI 0.06 1 0.06 0.16

Total 0-step 19.14 14 1.37 3.62**

** Significant at the 1 % level.

effects are also localized within the 0-step clades. The stronger effect is localized to the 0-step clades nested within 1-step clade VIII. The other effect is localized to the 0-step clades nested within 1-step clade X. Since there are only two 0-step clades nested within 1-step clade X, this last phenotypic effect is associated with the transition between haplotypes 22 and 23.

Figure 3 highlights the inferences that are drawn from the NANOVA given in Tables 2 and 3. This figure localizes within the cladogram five regions that may be associated with phenotypically important mutations as implied by the NANOVA results. Caution must be applied in equating these five regions to five different phenotypically important mutations. First, two of these regions contain only a single transitional arrow between two haplotypes, but the remaining three have seven possible transitional steps. Second, although the F tests at any one level of nesting are independent of one another, contrasts between levels need not be. A strong phenotypic contrast at one level of nesting could potentially yield significant F-tests at the next higher level of nesting when the lower level effect is strong and/or effects a substantial portion of the higher level clade. Such a “spillover” effect would cause significant phenotypic effects to be associated with adjacent arrows in the cladogram, with the effects associated with the higher level clade transitions being potentially spurious. As can be seen from Figure 3, three potentially adjacent effects (the between clades A and B contrast, the within clade 6 contrast, and the within clade VI11 contrast) are indicated by the NANOVA. It is important to perform additional sta-

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9- 8-10 18 FIGURE 3.-The initial detection and localization of phenotypi-

cally important mutations on the cladogram as inferred from the results of the nested ANOVA (Tables 2 and 3). Asterisks indicate transitional arrows associated with a phenotypically important mutation. Polygons enclosing an asterisk and more than one arrow indicate the possible transitional steps in the cladogram with which the phenotypic effect is most strongly associated.

tistical tests to localize the effects of ambiguous position as shown in Figure 3 and to check for potential “spillover” effects.

These goals are achieved through multiple comparison statistics. However, unlike the ANOVA for which one needs a multiple contrast procedure that is appropriate for exploratory data analysis, the NANOVA has already defined the set of relevant contrasts. In particular, only seven contrasts are relevant; the contrasts of the clades on the opposite sides of the transitional arrows enclosed in Figure 3. Because the number of contrasts is small and known a priori, it is possible to use multiple-comparison statistics that are much more powerful than those given by the Scheffe method. In particular, the Bonferroni multiple comparison method (NETER, WASSERMAN and KUTNER 1985) is much more powerful than the Scheffe method when the number of contrasts (which must be known a priori) is small compared to the number of factors (in this case, the number of haplotypes, which is 25). Table 4 presents the results obtained with the Bonferroni method as applied to the seven relevant comparisons defined by the NANOVA. As can be seen, the within P phenotypic effect detected in Table 3 is clearly localized to the transitional arrow leading to 1-step clade IV. Similarly, the within VI11 phenotypic effect is clearly localized to the transition between haplotypes 17 and 19. However, the statistical significance of the effect nested within 2-step clade 6 totally disappears with this analysis. Hence, the within 6 effect in the original NANOVA is most likely a spillover from the clade VI11 effect that is nested within it. Figure 4 summarizes the statistical inferences possible with the NANOVA followed by multi-


TABLE 4

Multiple comparisons on the contrasts needed to localize the phenotypically important mutations with ambiguous positions,

as shown in Figure 3

Contrast

111 vs. IV 111 vs. v IV vs. v VI1 vs. VI11 VI1 vs. IX

Within VI11 17 vs. 18 17 vs. 19

Within 0

Within 6

Bonferroni significance

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Five levels of significance were evaluated: 50%, 20%, lo%, 5%, and 1%.

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9- 8-10 18 FIGURE 4.-The final detection and localization of phenotypi-

cally important mutations on the cladogram as inferred from the results of the nested ANOVA and Bonferroni’s method of multiple comparisons (Table 4).

ple comparisons with the Bonferroni method. Note that the four arrows associated with significant phenotypic effects are non-adjacent7 so the results cannot be explained by a spillover effect. Hence, we conclude that four different phenotypically important mutations have occurred.

This analysis also identifies the haplotype categories that are potential candidates for displaying phenotypic heterogeneity; they are simply those haplotypes on either end of the arrows associated with significant phenotypic effects. Unfortunately, small sample sizes within all of these haplotype categories prevent any meaningful analysis of within haplotype heterogeneity, so this problem is deferred to our next paper.

The next goal is to physically localize the phenotypically important mutations in the DNA region of interest. The cladogram strategy per se does not locate the physical position of these mutations. At this stage of the analysis, the rare recombinants can yield useful

information if they involve recombination between haplotypes that are separated by phenotypically important mutations in the cladogram. Of the four recombinants inferred by GOLDING, AQUADRO and LANGLEY (1 986), only one involves haplotypes that should differ in phenotypic effect. This is a haplotype category generated by recombination between haplotypes 17 and 3, which differ by the phenotypically important mutation associated with the haplotype 1 to haplotype 15 transition. Two lines fell into this recombinant category, with activities of 2.49 and 3.16, respectively (AQUADRO et al. 1986). These lines clearly cluster with the activities shown by 3-step clade A and lie completely outside the range of activities shown by clade B. Hence, these recombinants have the phenotypic state associated with clade A. As detailed in GOLDING, AQUADRO and LANGLEY (1 986), this recombinant haplotype has its ADH coding region and 3’ flanking sequence derived from haplotype 3 (a clade A haplotype). The region that is about 4-8-kb 5’ of the coding sequence is derived from haplotype 17 (clade B). The 4-kb 5’ region adjacent to the coding region is of ambiguous origin. Hence, the phenotypically important mutation is not in the 4-8-kb 5’ region. Interestingly, the mutation that defines the transition between clades A and B is 7 kb 5‘ of the coding region. Hence, the mutation that is most strongly associated with the phenotypic differences between clades A and B is definitely not the mutation respon- sible for the difference in ADH activity.

l f no direct information from recombinants is forth- coming, as is the case for the other phenotypically important mutations indicated in Figure 4, the cladistic approach at least suggests what haplotype contrasts should reveal the presence of the phenotypically important mutations. These are simply the haplotypes that are also the candidates for phenotypic heterogeneity. These haplotypes can be singled out for more detailed molecular analyses (such as additional restriction site mapping or sequencing) in order to further refine the haplotype associations and to identify and physically locate candidate mutational changes that may be causing the phenotypic change.

DISCUSSION

The above example illustrates the usefulness of the cladistic approach. Like any methodology, this approach has its limitations. First, the construction of the cladogram requires that recombination and gene conversion be relatively rare events. This seems to be a reasonable assumption for the ADH region, but may not be a good assumption for other DNA regions. However, when recombination is common throughout a region, the chances of a restriction marker displaying a strong association with a phenotypically important mutation are likewise diminished. There-


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fore, in cases with much recombination and gene conversion, a linkage analysis using pedigree data is a more appropriate design strategy.

The analysis requires that the phenotypic effects of the mutations are large enough to be detectable by appropriate statistical techniques. Moreover, if the rate of occurrence of such phenotypically important mutations was greater than that of the production of new restriction site polymorphisms, the cladistic approach would break down because there would be no clean association between clades (branches) and phenotypes. This situation is unlikely because many studies have revealed that phenotypically important mutations have a smaller rate of incorporation into the gene pool than neutral or nearly neutral variants (KIMURA 1983), and most of the polymorphic restriction sites occur in DNA regions that have no clear function. Nevertheless, our approach will be most successful when the number of phenotypically important mutations in the population is much smaller than the number of haplotypes used to construct the cladogram. To a certain extent, the experimenter has control over this requirement. One can generally cre- ate more haplotype diversity by mapping with more restriction endonucleases or by sequencing. If for some reason, however, the DNA segment being stud- ied is low in marker variability or has many mutations with small phenotypic effects, the cladistic approach will have limited usefulness.

Given the above caveats, the cladistic approach represents a useful and potentially powerful option for detecting associations between measured genotypic variation and phenotypic variation. The cladistic approach is not only convenient from a statistical point of view in dealing with restriction sites showing extreme disequilibrium, but it also takes advantage of the evolutionary prediction that mutations causing phenotypic effects should have these effects correlated with the historical structure inferred from restriction sites even if the restriction sites themselves have no direct phenotypic effects. This correlation is shown pictorially in Figure 5 which illustrates that lines clustered into the same clade because of their historical relationships are also strongly clustered phenotypically. Figure 5a represents a histogram of ADH activities for the total data set analyzed. Open areas represent observations from haplotypes found in clade A, solid entries from clade B. As can be seen, the overall distribution is distinctly bimodal, and this bimodality in ADH activity is primarily associated with the clade A vs. B difference. Figure 5b then shows just the activities for clade A, with open and solid entries indicating the two phenotypically distinct clade classes nested within this clade (I-step clade IV vs. the remainder of 3-step clade A). As is easily seen, the lines found within 1-step clade 1V are all phenotypi-

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"1 I

!I Adh Activity

FIGURE 5.-Histograms of alcohol dehydrogenase activity levels of 41 lines of D. melanogaster from the study of AQUADRO et al . (1986). The Adh activity units are nanomoles NAD reduced/min/ fly with ethanol substrate, adjusted for weight and general protein content. The interval width of the histograms is 0.5 activity units. (a) Histogram for the total data set, with open boxes indicating lines from clade A and solid boxes indicating lines from clade B. (b) Histogram for the 25 lines from clade A, with solid boxes indicating lines from clade IV and open boxes indicating the remaining clade A lines. (c) Histogram for the 16 lines from clade B. The stippled box indicates the line from clade 19, the solid boxes the lines from clade 23, and the open boxes the remaining clade B clades.

cally clustered in the high tail-end of this distribution. Finally, Figure 5c represents the ADH activity distribution of haplotypes from clade B, with different shadings indicating membership in the three clades with significant, phenotypic differences that are nested within clade B (O-step clade 19, O-step clade 23, vs. the remainder of 3-step clade B). As can be seen, there is one extreme outlier, and this corre- sponds to the phenotypic mutation that separates haplotype 19 from the remainder of the clade. The lines from haplotype 23 are phenotypically clustered in the lower tail of the remaining distribution. Thus, with the nested design defined by the cladogram, we were able to detect the phenotypic effects associated with the strong bimodality in the data set, the occurrence of outliers, and the extreme tails on the skewed ends of each mode.

Incorporating historical information into the statistical design can greatly increase power. Both the ANOVA (which ignores history) and the NANOVA

Cladistic Analysis of Phenotypes 35 1

revealed significant phenotypic heterogeneity within the ADH data set. In the standard ANOVA, the Scheffe contrast of clades A and B is significant, but when the Scheffe method was applied to all the comparisons given in Table 4, none of the comparisons were significant at even the 50% level, including the contrast that was significant at the 1% level with the Bonferroni procedure! Hence, the ANOVA of the ADH data would have identified only the major difference causing bimodality in ADH activity. The more subtle phenotypic differences (visually shown in Fig- ure 5 , b and c) would have gone undetected.

Even more importantly, there is no assurance that an investigator using an ANOVA approach with multiple comparisons would have even considered the contrasts given in Table 4. The nested design and the results of the initial NANOVA suggest to the investigator precisely what comparisons ought to be made. Otherwise, the comparisons one decides to perform are often based upon a subjective inspection of the data. Using the cladogram to define the nesting elim- inates the danger that some important phenotypic associations will be missed and that others may be an artifact of how one groups the various haplotype categories after inspecting their phenotypic values. The objectivity of the cladistic analysis is further enhanced because the nested design is determined from data reflecting the historical relationship between haplotypes and is constructed independently of any association that may exist between haplotypes and the phenotype of interest.

One can also argue for a nested design on biological grounds. Nesting strains within haplotypes are ob- vious and natural because these strains share the same genotype. However, some haplotypes share many of the same genetic site states as well, and the extent of sharing occurs in a nested fashion. Indeed, it is this nesting of shared genetic traits that allows the cladogram to be constructed in the first place. Hence, the design is a nested one biologically. It is well known that an ANOVA is less powerful than a NANOVA and may be misleading when applied to a design that is inherently nested (NETER, WASSERMAN and KUTNER 1985).

Finally, it is important to note that the cladistic approach is not limited to quantitative data, as illustrated by the ADH example, but it can also be applied to qualitative data as well. For qualitative data, one would use nested log-linear models for the statistical analysis (BISHOP, FIENBERG and HOLLAND 1975, p. 524) instead of the NANOVA used in this paper.

In summary, the cladistic analysis we outline in this paper has some limitations and is not applicable to all data sets. However, given these caveats and the success of the example presented, the cladistic analysis represents an excellent strategy for detecting associations

between measured genotypic variation and phenotypic variation at the population level.

We wish to thank RORK KUICK for his valuable statistical advice and STEPHEN HUMPHRIES for his useful suggestions on an earlier draft. We also thank BRUCE WEIR and JOSEPH FELSENSTEIN and two anonymous reviewers for their excellent suggestions that have greatly improved this paper. This work was supported in part by National Institutes of Health grants R01 AGO2246 to A.R.T. and R01 HL24489 to C.F.S.

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A Cladistic Analysis of Phenotypic Associations With ...Cladistic Analysis of Phenotypes 345 our analysis. It is important, however, to keep in mind that this cladogram is constructed