Proc. Nati. Acad. Sci. USA Vol. 82, pp. 8552-8556, December 1985

Detection of simple polygenic segregations in a natural population (/Drosophila melanogaster/dominance modifiers) JAMES N. TH6MPSON, JR.,* AND C. G. N. MASCIE-TAYLORt *Department of Zoology, University of Oklahoma, Norman, OK 73019; and tDepartment of Physical Anthropology, Cambridge University, Cambridge CB2 3DZ England Communicated by Hampton L. Carson, August 7, 1985

ABSTRACT Penetrance frequencies were used to quantify MATERIALS AND METHODS segregating polygenic effects in a natural population of Drosophila melanogaster. When males from a series of 100 Polygenic modifiers offormation ofthe fifth-longitudinal (L5) isofemale strains were crossed to females from a veinlet line vein were scored in 100 isofemale strains collected around a (ve) single watermelon on a single day in 1973 in Oklahoma City, that had been selected for shortened veins, gaps commonly Oklahoma. The bait was exposed for less than 6 hr before appeared In the fifth longitudinal (L5) vein in the ve/+ collections were made. A localized natural D. melanogaster heterozygotes. We were able to assign each strain to one of six population is extremely difficult to identify with certainty. In significantly different clusters, based upon the pattern of sampling 100 separate genomes collected at the same time polygenic modifiers of ve dominance segregating in each strain. from the same location, however, we have done our best to We conclude that the extensive range of phenotypic variation obtain flies from the same population. in vein-forming ability is actually based upon a relatively Each female had been inseminated before collection, simple underlying polygenic structure that is consistent with though the number ofinseminations could not be determined. segregation of only a small dumber of alleles or allele combi- Flies were immediately isolated in separate food vials, and nations in the wild population. the progeny of each female were mass-transfei-red at each generation to minimize sampling effects in culture. Each Polygenic segregation plays a central role in the adaptability isofemale strain consequently carried a limited sample of the of a pool. Yet only a few studies have attempted more total allelic variation segregating in the population. than a superficial analysis of the polygenic structure of The manipulation of environmental variables or the pres- natural populations (1-5). This is not particularly surprising, ence ofa major mutation has frequently been used to uncover cryptic polygenic variation (10). Such variation can be traced since polygenic loci are rarely identifiable individually and to the segregation of polygenic alleles that have effects not their effects are often masked by environmental factors. In usually expressed overtly in typical wild-type individuals. In spite of these limitations, however, some aspects of this study, the polygenic modifiers of vein formation in each polygenic architecture are detectable under highly controlled isofemale strain were categorized by crossing 10 single males conditions, as biometrical analysis (6), whole- from each line to females from a veinlet (ve, chromosome 3, substitutions (7, 8), and isofemale-strain surveys (9) clearly locus 0.2) line that had been selected for reduced vein length demonstrate. (ve Short). This selected veinlet line provided increased One key conclusion from such studies is that relatively few sensitivity in the detection of segregating modifiers, partic- loci are required to account for the majority of the response ularly those affecting the L5 vein (12, 13). to artificial selection (10). Unfortunately, the degree to which The frequency ofterminal L5-vein gaps (i.e., gaps between this can be extended to natural populations is almost com- the end of the L5 vein and the wing margin) was determined pletely unknown. Although many loci could theoretically from 20 male and 20 female wings scored per culture (a total contribute to quantitative variation in a population, a limited of400 wings from each ofthe 100 isofemale strains). Only one number of polygenic combinations may occur at high fre- wing was scored from each fly, and gaps in other veins were quency as a result of selection for polygenic balance. Indeed, rare. Single males had been used as parents of each culture. this is a major, testable prediction from Wright's shifting- Thus, the 40 wings scored for each replicate provide an balance theory of genetic architecture (11). estimate ofthe average ve/+ gap penetrance associated with In this study, we outline a method by which polygenic the samples of from the segregating isofemale can be assessed in natural and we line. segregation populations, Cluster analyses were carried out by the unweighted pair test the prediction that only a limited number of polygenic group method with arithmetic averages (UPGMA; ref. 14) combinations are common in a population. To do this, we using NT-SYS, a package ofmultivariate statistical programs have surveyed polygenic modifiers ofwing-vein formation in (15). Other statistical analyses were performed using the 100 separate isofemale strains of Drosophila melanogaster statistical package for the social sciences (SPSS; ref. 16). collected from a single location. The polygenic makeup and All lines and crosses were maintained on an agar, oatmeal, patterns of segregation in these lines were studied by using and molasses medium seeded with live yeast. Temperature cluster- and discriminant-analysis techniques. The results was 25 ± 0.50C. strongly suggest that, at least at one level, the polygenic structure of a natural population can be comparatively simple. RESULTS

The publication costs of this article were defrayed in part by page charge The Oklahoma population is highly polymorphic for payment. This article must therefore be hereby marked "advertisement" polygenic modifiers of vein formation. This is readily seen in in accordance with 18 U.S.C. §1734 solely to indicate this fact. Fig. 1, which shows mean L5-vein-gap frequencies in 100 8552 Downloaded by guest on September 30, 2021 Evolution: Thompson and Mascie-Taylor Proc. Natl. Acad. Sci. USA 82 (1985) 8553

30 -

20-

E 10 z

0 50 100 150 200 250 Total number of wings with gaps FIG. 1. Distribution of mean frequencies of L5-vein-gap expression in 100 isofemale strains of D. melanogaster. Each mean is based upon average ve/+ penetrance in 10 replicate crosses. genetically heterogeneous isofemale strains. The phenotypic loci would increase the complexity of segregational patterns, variation among crosses is high, ranging from 0 to 40 vein as would environmental factors and differences in allele gaps in the 40 wings scored per cross. Superficially, this frequency within an isofemale line. approximates a Poisson distribution, although there is evi- Thus, this experimental approach is based upon a simple dence of significant residual variance (Kolmogorov-Smirnov prediction. If segregational patterns characteristic of each test, P < 0.001). isofemale line fall into a small number of significantly Variation in gap penetrance is not due to genetic heteroge- different categories, the polygenic basis of the trait must be neity in the ve Short selection line used as the outcross standard. comparatively simple. There are several statistical ways to This was shown by mating each of 75 single males from 75 determine whether an underlying group structure exists different isofemale lines to 2 virgin ve Short females. The within a data set. For this study, we have used cluster- females were then separated and placed singly in culture vials. analysis techniques in the NT-SYS package to evaluate the A total of 20 male and 20 female wings were scored in each of overall degree of similarity in the distribution of gap frequen- the replicates of each tested male. Although there was highly cies in comparisons among all pairs of isofemale strains. significant variation among males (X74 = 1020, P < 0.001), The function of cluster analysis is to assess the degrees of variation among ve Short females (i.e., variation among repli- similarity among pairs of quantitative comparisons. In this cates, within males) was not significant (X25 = 79) instance, the comparisons we want to make are between pairs The correlation between males and females was 0.863. of phenotypic distributions, such as those in Fig. 2. Resem- Thus, approximately 74.5% (r2 = 0.8632) of the variance in blance is quantified by the Z value generated by the gap frequencies is due to genetic differences among lines. Kolmogorov-Smirnov two-sample test (19, 20), which is used These are almost exclusively autosomal polygenes, since to evaluate the probability that two independent samples effective sex-linked loci are rare in this sample (17). The have been drawn from the same population or from popula- remaining 25.5% of the variance can be accounted for by tions having the same distribution. It is sensitive to distribu- uncontrolled environmental effects and by sex-limited differ- tion qualities such as location, dispersion, and skewness (19). ences in development (for example, males commonly express In our study, the Kolmogorov-Smirnov Z values are used vein defects more strongly than do females; ref. 13). as measures of "distance"-that is, as measures of the A phenotypic distribution such as this is consistent with degree of similarity or separation between pairs of L5-vein- most models of the polygenic structure of natural popula- gap phenotype distributions. Hierarchical cluster analyses tions. A continuous distribution is commonly considered were performed to identify isofemale strains that produce strong evidence for a broad range of underlying genotypes similar phenotypic distributions of test progeny. The produced by segregation at many loci. However, the infor- dendrogram in Fig. 3 illustrates the six distinct clusters of mation that is actually provided by such analyses is also strains that are revealed by this analysis. compatible with the idea that only a few or gene Separate cluster analyses taking into account the slight complexes are segregating (18). Our objective, therefore, was differences between male and female expression and varia- to try to resolve this apparent continuity of strain phenotypes tion among replicate assays gave essentially identical results, into groups that share similar segregational patterns. as did the SAS (statistical analysis system) package of tree In the progeny ofeach cross between the ve Short standard and cluster procedures. But cluster techniques do not them- females and a male from a wild-type line, only one pair of selves imply statistical significance. To substantiate the tested second and third chromosomes is segregating. If the existence of these six groups, we assigned each of the 100 genetic basis of the trait is relatively simple, the phenotypes strains to the appropriate cluster and performed a discrimi- produced by the segregation ofallelic variants will tend to fall nant analysis to determine the predictive value of the cluster into a small number of patterns, such as those in Fig. 2. classifications (Table 1). Males that are homozygous for a suppressing allele at an It is clear from Table 1 that there are distinct differences in important polygenic locus (A'Al), for example, would tend to the average gap frequencies of the six groups. Before any produce offspring with no L5 gaps, whereas those homozy- function was removed in the discriminant analysis, Wilks' X gous for the enhancing allele (A2A2) would tend to result in was 0.079 (X2o = 241.16, P < 0.001). This indicates that gaps in most individuals, depending upon the action and considerable discriminatory power exists in the variable magnitude of the segregating polygenic alleles they carry. being tested (the larger X is, the less discriminatory power is Heterozygous tested males would produce progeny com- present). Furthermore, the primary discriminant function posed ofa mixture ofgap and non-gap carriers and having, on (eigenvalue = 11.3, canonical correlation = 0.96) correctly average, an intermediate degree of expression. Additional classified 77% of the grouped cases, with the major source of Downloaded by guest on September 30, 2021 8554 Evolution: Thompson and Mascie-Taylor Proc. Natl. Acad Sci. USA 82 (1985)

4.-

2-

A fly- 6-

4- Hr-i

10 a=

._ '4-4 z.0

z HIn lii- 4 IF Fi1

AinF n nnnH n

4- 20 on CH r H 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Number of wings with gaps FIG. 2. Vein-gap frequencies in six representative isofemale strains. In each strain, 20 wings were scored in the progeny of 10 individually tested males. The phenotypic frequencies therefore provide an estimate of the effects of polygenic vein modifiers segregating in each isofemale strain.

error (12 strains) being associated with cluster 2, which is ing as few as one or two effective factors segregating in this phenotypically very similar to cluster 3. Thus, we appear to population. In support of this interpretation, a whole-chro- be conservative in defining as many as six clusters-a result mosome assay was carried out using an inbred standard one would certainly not have anticipated on the basis of some marked with the recessive eye color mutations brown (bw, common views of polygene complexity. chromosome 2) and scarlet (st, chromosome 3) (see ref. 21 for Since this test is sensitive to the frequency of segregating crosses). The F1 progeny of a cross between a high-gap strain polygenic alleles or complexes in each strain, a total of five (no. 60) and a "no-gap" strain (no. 23) was intermediate in different cluster categories could be produced by even a expression, and chromosome substitution with the bw; st single locus at high frequency in the population. The original standard showed that gap loci were concentrated on chro- pair ofparents ofeach isofemale strain might contribute from mosome 2. The presence of minor ve-dominance-modifier zero to four gap-enhancing polygenic alleles and, thus, activity in available standard mapping strains precluded more determine the probabilities of segregating five different ar- extensive studies at this time, but the present evidence rays of frequency distributions. supports the hypothesis that only a very small number of Our results are, therefore, consistent with a model involv- polygenic factors are segregating. Downloaded by guest on September 30, 2021 Evolution: Thompson and Mascie-Taylor Proc. Natl. Acad. Sci. USA 82 (1985) 8555 Number Cluster of number strains 1 15

2 13

3 30

4 29

5 10

6 3

Il I I I I I I 1.50 1.25 1.0 0.75 0.50 0.25 0 Distance FIG. 3. Dendrogram showing the degree of similarity among six distinguishable clusters of strains. "Distance" is defined in the text. DISCUSSION inseminated before collection, though deviations from a single-pair mating pattern would affect this number (23)]. The The correspondence between genotypes and phenotypes of a 10 replicates, in turn, provided 10 independent measurements quantitative trait is not always a simple one. A number of of the phenotypic effect associated with the sample of different genotypes can produce the same phenotype, and, segregating autosomes in each line. If a large number of given genotype-environment interactions, the same geno- different polygenic loci or types of chromosomes had been type can be expressed in a variety ofways. Thus, even when segregating in the population, we would expect to find a selection favors a limited range of expression, extensive rather smooth distribution of phenotypic classes, whose polygenic variation can still remain in the gene pool. frequencies depended upon allele frequencies in the sample. The architecture of the genome must, therefore, include Although the overall distribution was fairly smooth, cluster mechanisms that minimize the segregation of maladaptive analyses allowed us to recognize a simple underlying pattern polygenic combinations. There are at least two ways in which in the array of phenotypes. this might be accomplished. First, selection could favor close The cluster analysis presented here measures a type of in - + genetic distance. It is based upon the degree of genetic linkages balanced combinations (+ -) of polygenic similarity between pairs of individuals as it is revealed in the loci affecting a particular trait (22). Alternatively, selection segregational patterns seen in their offspring. It is, in a sense, might act to eliminate all but a small number of loci having a measure of "genome" similarity, in which the statistical comparatively large effects. In this way, although many loci value produced by the Kolmogorov-Smirnov two-sample might still be segregating in the gene pool, few would test is the "distance" between two genomes. markedly alter the expression of the trait under most condi- The preliminary genetic analysis of several strains provid- tions. In either case, the expectation is that a survey of the ed further support for the hypothesis that a limited number of polygenic structure of a natural population would reveal a polygenic alleles or linked combinations contribute the ma- relatively small set of phenotypic (and perhaps genotypic) jority of the variance in L5-vein-forming ability in this categories. Our study was intended to test this prediction. population. We are clearly not yet in a position to count The 100 isofemale strains carried a sample of approximate- alleles or even to know whether we are dealing with separate ly 400 second and 400 third chromosomes from the popula- loci or with linked complexes. Yet as few as two loci are tion [2 of each per parent, since all females had been sufficient to account for the six phenotypic categories in this trait. Table 1. Characteristics of the groups identified by The inability to distinguish unambiguously between single cluster analysis alleles and linked complexes is not unique to this study. It is a limitation that has always inhibited the interpretation of No. of Gap frequency polygenic systems. In fact, it was precisely this that prompted Cluster strains Females Males Thompson and Thoday (24) to define a polygenic locus as "one or more closely linked genes" that contribute to the 1 15 0.67 ± 0.23 1.93 ± 0.84 variance in a specified quantitative character. 2 13 8.38 ± 1.59 6.46 ± 1.61 Essentially all populations carry polygenic alleles that 3 30 16.07 ± 1.21 14.33 ± 1.47 modify almost every measureable trait. Dissecting this mass 4 29 35.31 ± 1.95 32.52 ± 2.52 of variation, therefore, has important consequences for 5 10 69.10 ± 2.43 62.00 ± 3.61 understanding the genetic structure of natural populations. 6 3 114.00 ± 7.78 111.67 ± 11.55 Our results are consistent.with the idea that selection favor- L5-vein-gap frequencies (mean ± SEM) are given for strains, ing certain polygenic combinations can make the gene pool based upon wings scored in 200 flies ofeach sex per wild-type strain. less complex than it might initially appear. Downloaded by guest on September 30, 2021 8556 Evolution: Thompson and Mascie-Taylor Proc. Natl. Acad Sci. USA 82 (1985) We thank John Thoday, Roger Milkman, Gary Schnell, and Dan 12. Thompson, J. N., Jr., & Thoday, J. M. (1972) Heredity 29, Hough for valuable discussions. This work was supported by 285-292. National Science Foundation Grant BSR-8300025 and by funds for 13. Thompson, J. N., Jr. (1974) Heredity 33, 373-387. C.G.N.M.-T. from the University of Oklahoma Zoology Depart- 14. Sneath, P. H. A. & Sokal, R. R. (1973) Numerical Taxonomy ment in support of visiting faculty. (Freeman, San Francisco). 15. Rohlf, F. J., Kishpaugh, J. & Kirk, D. (1979) Numerical 1. Milkman, R. (1970) Adv. Genet. 15, 55-114. Taxonomy System of Multivariate Statistical Programs 2. Milkman, R. (1970) 65, 289-303. (SUNY, Stony Brook, New York). 3. Boyer, B. J., Parris, D. L. & Milkman, R. (1973) Genetics 75, 16. Nie, N. H., Hull, C. H., Jenkins, J. G., Steinbrenner, K. & 169-179. Bent, D. H. (1975) Statistical Packagefor the Social Sciences 4. Parsons, P. A. (1973) Behavioural and Ecological Genetics: A (McGraw-Hill, New York), 2nd Ed. Study in Drosophila (Clarendon, Oxford). 17. Thoday, J. M. & Thompson, J. N., Jr. (1985) Heredity 53, 5. Parsons, P. A. (1979) in Quantitative Genetic Variation, eds. 635-642. Thompson, J. N., Jr., & Thoday, J. M. (Academic, New York), pp. 61-79. 18. Thoday, J. M. & Thompson, J. N., Jr. (1976) Genetica 46, 6. Mather, K. & Jinks, J. L. (1982) Biometrical Genetics (Chap- 335-344. man and Hall, London), 3rd Ed. 19. Siegel, S. (1956) Nonparametric Statistics for the Behavioral 7. Thoday, J. M. & Gibson, J. B. (1972) Egypt. J. Genet. Cytol. Sciences (McGraw-Hill, New York). 1, 47-50. 20. Sokal, R. R. & Rohlf, F. J. (1969) Biometry (Freeman, San 8. Thompson, J. N., Jr., & Hellack, J. J. (1982) Can. J. Genet. Francisco). Cytol. 24, 235-241. 21. Thompson, J. N., Jr. (1975) Genetics 81, 387-402. 9. Parsons, P. A. (1980) Evol. Biol. 13, 175-217. 22. Mather, K. (1943) Biol. Rev. 18, 32-64. 10. Thompson, J. N., Jr., & Thoday, J. M. (1979) Quantitative 23. Milkman, R. & Zeitler, R. R. (1974) Genetics 78, 1191-1193. Genetic Variation (Academic, New York). 24. Thompson, J. N., Jr., & Thoday, J. M. (1974) Heredity 33, 11. Wright, S. (1980) Evolution 34, 825-843. 430-437. Downloaded by guest on September 30, 2021