Proc. Nati. Acad. Sci. USA Vol. 77, No. 2, pp. 1091-1095, February 1980 Genetics Enzyme null in natural populations of : Frequencies in a North Carolina population (allozymes/enzyme deficiencies) ROBERT A. VOELKER, CHARLES H. LANGLEY, ANDREW J. LEIGH BROWN*, SEIDO OHNISHI, BARBARA DICKSON, ELIZABETH MONTGOMERY, AND SANDRA C. SMITHt Laboratory of Animal Genetics, National Institute of Environmental Health Sciences, Research Triangle Park, North Carolina 27709 Communicated by C. Clark Cockerham, November 26,1979

ABSTRACT A Raleigh, NC, population of Drosophila that will be underestimated and, concomitantly, the melanogaster was sampled for the presence of enzyme null al- detrimental'effects of nulls on fitness will be overestimated. leles at 25 loci. No nulls were found at any of five X-linked loci. This paper reports data on the frequency of null alleles (see Nulls were recovered at 13 of 20 autosomal loci; the weighted mean frequency for all 20 autosomal loci was estimated to be Methods for definition) at 25 allozyme loci in a Raleigh, NC, 0.0025. A consideration of the effects of these null alleles on population of Drosophila melanogaster. The loci to be screened viability strongly suggests that, although they may contribute were selected on the basis of detectability of nulls by starch gel to so-called polygenic variation, they are not representative of electrophoresis. The two criteria for inclusion of a locus were: the entire genome. (i) the enzyme must be present in sufficiently high concentra- The existence of allozyme polymorphisms in natural popula- tion to be reliably scorable in single fly assays after starch gel tions of most species is now well documented (1). The signifi- electrophoresis; and (ii) because of the technique for detection, cance of allozyme variation to the fitness and evolution of at least two mobility variants were necessary at each locus. Of populations is much less well understood. Whereas in some cases nearly 30 enzymes in category i, only one was eliminated be- there is suggestive evidence that individuals carrying a par- cause no variant could be found; because of the necessity ticular allozyme genotype may have greater viabilities and of staining larval or pupal homogenates, which would have fertilities than other genotypes at the locus in question, at the inordinately increased the amount of work involved in vast majority of polymorphic enzyme loci there is no evidence screening, several other (polymorphic) loci were eliminated. that the various electrophoretically detectable alleles are not The remaining 25 loci include ones that are highly polymorphic equivalent in biological function. Of potentially greater im- in natural populations as well as ones that are monomorphic portance to overall fitness are enzyme deficiencies genetically (i.e., no variant alleles had been reported prior to our discovery attributable to so-called "null" alleles. Individuals hemizygous, of them for the construction of our "tester" stocks). Thus, the homozygous, or heterozygous for null alleles at loci coding for sample of loci should not be biased towards detecting nulls at the production of enzymes might be expected to have reduced loci that are polymorphic in natural populations or that are fitnesses, with the depression in fitness being correlated with associated with deleterious effects. the importance of the enzyme function to overall metabo- lism. METHODS Surveys of electrophoretic variation have provided little in- Definition of Enzyme Null Allele. In this report the term formation about the frequencies of null alleles in natural pop- "null" denotes an allele that specifies a product that shows no ulations. In most surveys nulls go undetected, because a null/ catalytic activity as a monomer or homomultimer (depending active allele heterozygote would be indistinguishable from a on the locus) in our in vitro gel staining assay. Such nulls may homozygote for an active allele. However, a few nulls have been produce no or a protein that is nonfunctional. For ex- reported in several Drosophila species (1-5), usually at ample, a-glycerolphosphate dehydrogenase functions as an frequencies under 5%. In mammals, esterase nulls have been aggregation of two subunits that are products of a-Gpdh. A reported at appreciable frequencies in Microtus agrestis (6) mutant allele was scored as a null if its product failed to function and in Mus musculus (7). as a mutant homodimer even if there was residual activity in Neel (8) has recently summarized the types of null alleles a heterodimer consisting of that mutant subunit and one normal observed in human populations and their potential importance. subunit. Estimates of frequencies of null alleles in humans have been Detection of Null Alleles. The procedure used for the de- obtained from data on the frequency of individuals affected tection of null alleles is shown in Fig. 1. A chromosome ex- with traits having, a known autosomal or X-linked recessive tracted from a wild fly was made heterozygous with each of two mode of inheritance. However, this method of estimation may mobility variants at the locus in question. Failure of the ex- underestimate the frequency of nulls because only individuals tracted chromosome (allele) to produce a heterozygous phe- affected with pathological conditions seek medical treatment notype when heterozygous with either allele suggested a null and are thereby detected. Consequently, nulls will not be de- allele. Such putative nulls were retested to confirm their failure tected at loci where homozygosity or hemizygosity does not to produce a heterozygous electrophoretic pattern. Stocks of result in pathological conditions. Moreover, if persons exhibiting all confirmed nulls were established. pathological conditions are but a subset of all null hemi- or The overall scheme for scoring the 25 loci is shown in Fig. homozygotes at a given locus, the frequency of null alleles at 2. The symbolism is as follows: B = In(1)FM7,B; Cy =

The publication costs of this article were defrayed in part by page * Present address: Imperial Cancer Research Fund, Mill Hill Labo- charge payment. This article must therefore be hereby marked "ad- ratories, Burtonhole Lane, London NW7, United Kingdom.. vertisement" in accordance with 18 U. S. C. §1734 solely to indicate t Present address: Department of Bacteriology and Immunology, this fact. University of North Carolina, Chapel Hill, NC 27514. 1091 Downloaded by guest on September 28, 2021 1092 Genetics: Voelker et al. Proc. Natl. Acad. Sci. USA 77 (1980)

SM I ,Cy.t-4GpdhF/c-Gpdhs QQXbwv'/-- Gpdh?d'C Select: e-Gpdh?/'- Gpdh9 '-Gpdh?/SM ,Cy b-GpdhF

F If e-Gpdh? is: w-Gpdh Y-Gpdh8 o-GpdhSF i-GpdhnuIl K-Gpdhf C-Gpdh5 .-KGpdhF.-(GpdhS .-tGpdhF-c-GpdhS K-GpdhF K-Gpdhs Expected _ _ Electrophoretic _ __ _ are: __

Origin FIG. 1. Procedure for detection of null alleles. The failure of an extracted allele to produce a heterozygous with either of two different mobility variants suggests the presence of a null allele. In(2LR)SM1,Cy; btvl = In(2LR)bwvl,bwvl; Ubx = to explain our failure to recover nulls on the X chromosome. If In(3LR)TM6,Ubx; SbSer = In(3LR)TM3,SbSer; Sb = Sb in we assume a frequency of 0.0020 nulls per locus on the X standard sequence. Further details of the balancer chromosomes chromosome, the probability that we would observe 3061 (Fum, and mutant symbols are given in ref. 9. The designation "tester" Hex-A, Gpt, and Zw) alleles and not see any nulls is (1 - denotes a chromosome carrying alleles of electrophoretic mo- 0.0020),'"l = 0.002. Thus, the explanation must lie in their bilities different from those of the respective balancer chro- frequency of occurrence or in their associated deleterious ef- mosome for the loci indicated. The loci screened and their ge- fects. netic map locations are given in Table 1. The map locations are To determine whether the distribution of null alleles over from refs. 10-12 and our unpublished results. The electro- autosomal loci was random, we calculated x2 values for good- phoretic and staining conditions are as in refs. 12-15. The wild ness of fit for a 2 X 20 homogeneity test and for a Poisson dis- males used in the screen were captured in a 2-week period at tribution. Both methods indicated significant interlocus het- the Farmer's Market in Raleigh, NC, during June 1977. All erogeneity in the distribution of null alleles. One possible reason crosses were carried out at room temperature with cornmeal/ for the heterogeneity is differences in rates at the molasses/agar medium. various loci, for which there is suggestive evidence (unpublished results of R. A. Voelker, H. E. Schaffer, and T. Mukai and of RESULTS AND DISCUSSION R. R. Racine, C. H. Langley, and R. A. Voelker). The frequencies of nulls recovered at the 25 loci are presented The autosomal data were examined for correlations between in Table 2. No nulls were recovered at the five X-linked loci. null frequency and (i) estimated allozymic heterozyosity in the Nulls were recovered at 13 of the 20 autosomal loci; the population sampled and (ii) subunit molecular weight. The weighted mean frequencies for all loci and for only the auto- correlation between estimated heterozygosity and null fre- somal loci are 0.0020 and 0.0025, respectively. quency was not significant. The correlation between subunit Our failure to recover any nulls on the X chromosome may molecular weight and null frequency, calculated from molec- be attributable to several factors. First, Pgd is a known lethal ular weight estimates from refs. 17 and 18, unpublished results, as a null hemizygote (16); because wild males (hemizygous) and a personal communication from C.-Y. Lee, was also not were sampled, the recovery of Pgd nulls was precluded. Be- significant. This observation is perhaps surprising in view of cause nulls have not previously been recovered at Fum, Hex-A, reported positive correlations between subunit molecular and Gpt, it is not known whether they are associated with re- weights and heterozygosities at enzyme loci (19, 20)-i.e., the duced viability or fertility effects; any reduction in fitness would greater the size of a subunit, the greater the number of nucle- have severely decreased the probability of recovering nulls at otide pairs that can mutate to give altered structure or function these loci. Zw (G-6pd) is the only one of the five X-linked loci (or both). The null allele frequencies have also been tested for at which null hemizygotes are known to survive; their fitness association with the metabolic role of the enzymes by dividing in nature might be expected to be reduced although no data are the loci into those that interact primarily with a narrow range available that bear on that question. Sampling error is unlikely of intracellular metabolites ["group I" (21)] and those whose

Cy/bwVI;Ubx/Sb 99 X +/7;+/+;+/+ d X B/tester I 99 Cy/bwVI;Ubx/Sb~ot~y/+;Ubx/+ d Score: +/B. +/testerI Loci scored: Pgd,Fum,Hex-AGptZw Establish Cy/+; Ubx/+ Stock bw V4+; Ubx or Sb/+dCM X bolancer/tester9 9 Score: +/balancer, +/tester Tester Loci Scored IEa Got-2,oC- Gpdh,cMdh,AdhDip-AHex-C Ma Est-6, Odh, Est-C, Acph-l, Tpi IEb;Mb Pgk, Pgi, MenXdh,Aldox,mMdh Mc Idh, Pgm, Ald FIG. 2. The set of crosses used to extract X and second and third chromosomes and screen them for 25 loci. Downloaded by guest on September 28, 2021 Genetics: Welker et al. Proc. Natl. Acad. Sci. USA 77 (1980) 1093

Table 1. Enzyme loci screened and their genetic map positions Table 2. Frequencies of null alleles at 25 enzyme loci in a Enzyme Symbol Locus EC no. Raleigh, NC, population of D. melanogaster Locus n Nulls Frequency 6-Phosphogluconate dehydrogenase Pgd 1-0.6 1.1.1.44 Fumarase Fum 1-19.9 4.2.1.2 X chromosome Hexokinase A Hex-A 1-29.2 2.7.1.1 6-Pgd 799 0 0.000 Glutamate-pyruvate transaminase Gpt 1-42.6 2.6.1.2 Fum 770 0 0.000 Glucose-6-phosphate dehydrogenase Zw 1-63 1.1.1.49 Hex-A 760 0 0.000 Glutamate-oxaloacetate Gpt 794 0 0.000 transaminase Got-2 2-3.0 2.6.1.1 Zw (G-6pd) 737 0 0.000 3-Phosphoglycerate kinase Pgk 2-5.9 2.7.2.3 a-Glycerolphosphate Chromosome II dehydrogenase a-Gpdh 2-17.8 1.1.1.8 Got-2 782 3 0.004 Malate dehydrogenase Pgk 702 0 0.000 (cytoplasmic) cMdh 2-37.2 1.1.1.37 a-Gpdh 814 7 0.009 Alcohol dehydrogenase Adh 2-50.1 1.1.1.1 cMdh 815 2 0.002 Dipeptidase A Dip-A 2-55.2 3.4.-.- Adh 808 1 0.001 Phosphoglucose isomerase Pgi 2-58.6 5.3.1.9 Dip-A 767 2 0.003 Hexokinase C Hex-C 2-73.5 2.7.1.1 Pgi 716 1 0.001 Isocitrate dehydrogenase Idh 3-25.4 1.1.1.42 Hex-C 796 1 0.001 Esterase-6 Est-6 3-36.0 3.1.1.2 Phosphoglucomutase Pgm 3-43.4 2.7.5.1 Chromosome III Esterase-C Est-C 3-47.9 3.1.1.2 Idh 916 1 0.001 Octanol dehydrogenase Odh 3-49.2 1.1.1.73 Est-6 804 0 0.000 Malic enzyme Men 3-51.73 1.1.1.40 Pgm 913 0 0.000 Xanthine dehydrogenase ry 3-52.0 1.2.3.2 Est-C 758 4 0.005 Aldehyde oxidase Aldox 3-56.7 1.2.3.1 Odh 769 1 0.001 Malate dehydrogenase Men 734 6 0.008 (mitochondrial) mMdh 3-62.6 1.1.1.37 ry 575 0 0.000 Aldolase Ald 3-91.5 4.1.2.13 Aldox 739 9 0.012 Acid phosphatase-1 Acph-1 3-101.1 3.1.3.2 mMdh 723 0 0.000 Triosephosphate isomerase Tpi 3-101.3 5.3.1.1 Ald 912 0 0.000 Acph 799 1 0.001 Tpi 637 0 0.000 substrates are of extracellular or external origin ("group II"). There was no significant association between frequency of null Totals 19,339 39 alleles and metabolic role. reviewed in ref. the Weighted mean frequency, all loci = 0.0020. Weighted mean fre- Spencer (ref. 22, 1) reported frequencies quency, autosomal loci = 0.0025. of various visible mutants in a natural population of D. mulleri. Although the estimation is rather indirect, Lewontin concluded that Spencer's data [and other data of Alexander (23, 24)] sug- and includes six of the loci being screened in this study. Using gested a per locus mean mutant frequency of 0.0028. The our estimate of 4 = 0.0025, we obtain an h estimate of 0.00154. similarity of this frequency and the homozygous viabilities of Because reliable empirical estimates for h and s for allozyme these visible mutants to that of the allozyme loci surveyed loci are not available, we cannot meaningfully attempt to fur- suggests a simple interpretation that the loci are, in fact, bio- ther resolve this value. Nevertheless, we are left with the im- logically equivalent. The validity of this hypothesis must await pression that allozyme nulls are rare alleles which may very well further study of both types of genetic variation. be maintained by mutation-selection balance. It is of particular interest to determine the effects of nulls on The above estimate of hs may be an underestimate for nulls the fitness of the population. Because the highest frequency of in general for several reasons. First, from a biological per- nulls at any locus is only 0.012 (Aldox), it is clear that the fre- spective the sample of nulls that we recovered is likely to consist quency of homozygotes is very low (1 X 10-4 or less). Our null largely of nulls that have persisted in the population because frequency estimates and available null mutation rate estimates they have small heterozygous deleterious effects. A sample of (see below) are inconsistent with the assumption of complete newly arisen nulls might have a substantially greater /. Second, recessiveness by use of Haldane's equilibrium model (25). Thus, for statistical reasons, the estimation of hs involves the harmonic we look to an explanation that involves some selective action mean and the covariance between h and s, which is likely to on heterozygotes. The equilibrium frequency for a rare, slightly result in an underestimate of /i. Note that the estimate of /i deleterious is given by the equation (25) q - ,u/hs, in is weighted by mutation rate; thus, any correlation between ,u which, for our purpose, q is the frequency of a null allele, it is and hs can bias the estimate of hs. the mutation rate to null alleles, h is the measure of , The Reedy Creek population of D. melanogaster from Ra- and s is the reduction in fitness of the null homozygote. We will leigh, NC, has been extensively studied and is believed to be a generalize this equation to =i/hs to enable us to use our es- very large equilibrium population (27, 28). Estimates are timate of 4 and an available estimate of ,u. (Generalizing in this available for lethal frequencies, homozygous viabilities, and manner is not a formally valid procedure, but it does allow a heterozygous effects of lethal and of viability genes (27, crude approximation, subject to the limitations mentioned 29, 30). We would like to see whether our estimate of hs = below.) Two estimates of , are 9.65 X 10-6 (26) and 3.86 X 10-6 0.00154 from the Farmer's Market population (which we will (R. A. Voelker, H. E. Schaffer, and T. Mukai, unpublished re- assume is also in equilibrium because of its close proximity to sults) for five and seven second-chromosome loci, respectively; the Reedy Creek population) is interpretable within the we will use the latter because it is based on a larger data base framework of the above estimates. Downloaded by guest on September 28, 2021 1094 Genetics: Voelker et al. Proc. Natl. Acad. Sci. USA 77 (1980) Such an extrapolation from our results to the estimates above At present we have no firm answer to the question. (This po- (which were mostly derived from work using entire second tential shortcoming is not, however, unique to this study; nearly chromosomes) depends on whether our sample of loci is rep- all previous studies of frequencies and viability effects of lethal resentative of the entire second chromosome (or genome). genes and mutation rates and viability effects of polygenes in There are several reasons to believe that our sample of allozyme natural populations have used crossing schemes in which this loci (or allozyme loci in general) may not be representative of phenomenon might have occurred.) We may be able to provide the entire genome. evidence bearing on this question when we report in a subse- First, null homozygotes or null/deficiency heterozygotes at quent paper the results of our qualitative analyses of the nulls. 12 of the 13 loci (all except Pgi) are viable and fertile (ref. 31 In cases where only a single null was recovered at a locus, the and unpublished results). This is in contrast to the picture that question will remain unanswered. At loci where multiple nulls is emerging from saturation mapping studies of a number of were recovered from different wild males, concordance be- salivary gland chromosome regions; these studies suggest that tween two or more nulls in such qualities as amount of cross- approximately 80% of the bands are associated with a lethal- reacting material produced, electrophoretic mobility of mutant mutable site (refs. 32 and 33 and A. Schalet, personal commu- (nonfunctional) protein, residual enzyme activity, and allozyme nication). This discrepancy could be related to the natures of allele, lethal allele, sterility allele, and/or inversion associations the screens for mutants. Saturation screens frequently detect would provide strong evidence that the nulls were indeed only lethal and semilethal mutants although the loci might also present in nature and not a byproduct induced by a mutator be mutable to deleterious nonlethal alleles. On the other hand, factor(s). our screen is for nulls and would not detect lethal nonnulls. Preliminary observations of nulls at many of the loci screened Perhaps a more important factor, however, is the essentiality in this study suggest that the biological effects on the carriers of the locus. Most routinely screened allozyme loci direct and null homozygotes may be minimal. We have hypothesized functions in intermediary metabolism, functions that can also that nulls are less likely to have strongly deleterious effects at be accomplished by duplicate systems (e.g., in mitochondria loci coding for enzyme function in intermediary metabolism and in the cytoplasm) or alternate pathways. As such, they are because of enzyme redundancy and alternate pathways. If this less likely to be lethal-mutable than genes that direct functions is correct, then mammalian systems might be expected to in a linear pathway and have no alternative mechanism to possess a still greater number of loci at which nulls might be produce a required end product. If most genes in the genome tolerable in view of the apparent greater redundancy of enzyme are of the latter type (as might be suggested by the 80% le- functions in mammals than in lower eukaryotes such as Dro- thal-mutability), then our sample of loci is atypical. Other ev- sophila. This might suggest that in humans significant numbers idence suggesting that allozyme loci are atypical comes from of nulls, including null homozygotes, go undetected because two-dimensional gel electrophoresis studies, which suggest that their biological effects are not sufficiently deleterious to present allozyme loci are much more variable than loci coding for pathological symptoms. This view contrasts with the prevailing abundant with unknown function (34). For the above impression (e.g., that most nulls in humans are associated with reasons, we are led to conclude that results from our sample of pathological conditions), an impression that no doubt derives allozyme loci are not applicable to an entire chromosome or the from their mostly having been detected in persons exhibiting genome. pathological conditions. A screen similar to the present carried In this report we have identified enzyme nulls to be rare al- out in humans would provide data bearing on this question. leles, mostly with mildly deleterious homozygous effects. In this This survey of null alleles at allozyme loci demonstrates their respect they are similar to viability polygenes postulated in occurrence at frequencies consistent with simple mutation- interpreting inbreeding depression (29, 30). The high degree selection balance. Our ongoing survey of another population of dominance (0.2) observed for polygenes could also pertain and subsequent analysis of the various null alleles will, we hope, to enzyme nulls that show only mildly deleterious effects when provide the necessary data to clarify many of the questions homozygous. This is particularly true for enzymes whose raised by this report. functions can be carried out by a duplicate enzyme or by an We thank the following for providing laboratory technical assistance alternate pathway. Thus, although we have not yet determined during this work: Diane Bartlett, Barbara Bynum, Sherri Baird Harper, that all our nulls have lesions in the structural gene, it seems Lynt Johnson, Allison Perry, Mark Robinson, and Benson Timmons. plausible to suggest that mutants of this type may contribute, We also thank Drs. C.-Y. Lee and A. Schalet for permission to cite their perhaps substantially, to so-called polygenic variation. unpublished results and Sue Bolton and Nancy Evans for typing the Smith et al. (35), in a variance component analysis of allo- manuscript. zyme data from populations of D. melanogaster from North Carolina, found apparent inbreeding (correlation within in- 1. Lewontin, R. C. (1974) The Genetic Basis of Evolutionary dividuals, particularly at Acph-1) and suggested that low Change (Columbia Univ. Press, New York). frequencies of null alleles 2. Ayala, F. J., Powell, J. R., Tracey, M. L., Mourio, C. A. & could account for the apparent in- Perez-Salas, S. (1972) Genetics 70, 113-139. breeding. The frequency of nulls observed at a-CGpdh in this 3. Prakash, S. (1974) Genetics 77,795-804. study accounts for the apparent inbreeding at that locus; the 4. Coyne, J. A. & Felton, A. A. (1977) Genetics 87,285-304. null frequencies do not, however, at the other six loci that they 5. Johnson, D. (1978),Evolution 32,798-811. studied. Thus, the frequency of nulls cannot be a general ex- 6. Semeonoff, R. & Robertson, F. W. (1968) Biochem. Genet. 1, planation for their observations. 205-227. A matter of some concern to us in this study is the possibility 7. Selander, R. K. & Yang, S. Y. (1969) Genetics 63,653-667. that some of our nulls may have been the products of hybrid 8. Neel, J. V. (1978) Can. J. Genet. Cytol. 20,295-306. dysgenesis (36-39), one facet of which includes elevated 9. Lindsley, D. L. & Grell, E. H. (1968) Genetic Variations of mutation rates. This phenomenon is observed when males, Drosophila melanogaster (Carnegie Institution of Washington, usually from Publication No. 627). nature, are crossed with certain types of females, 10. Maclntyre, R. J. & O'Brien, S. J. (1976) Annu. Rev. Genet, 10, usually a long-term laboratory culture. Because crosses of this 281-318. type were used in this study, the question arises as to what 11. Voelker, R. A., Leigh Brown, A. J., Ohnishi, S. & Langley, C. H. proportion of our nulls may be attributable to this phenomenon. (1978) Drosophila Inf. Serv. 53,200. Downloaded by guest on September 28, 2021 Genetics: 'Voelker et al. Proc. Natl. Acad. Sci. USA 77 (1980) 1095

12. Voelker, R. A. & Langley, C. H. (1978) Genetica 49,233-236. 27. Mukai, T., Watanabe, T. K. & Yamaguchi, 0. (1974) Genetics 13. Kojima, K.-I., Gillespie, J. H. & Tobari, Y. N. (1970) Biochem. 77,771-793. Genet. 4,627-637. 28. Mukai, T. & Voelker, R. A. (1977) Genetics 86, 175-185. 14. Langley, C. H., Tobari, Y. N. -& Kojima, K.-I. (1974) Genetics 29. Mukai, T. & Yamaguchi, 0. (1974) Genetics 76,339-366. - 78,921-936. 30. Mukai, T., Chigusa, S. I., Mettler, L. E. & Crow, J. F. (1972) 15. Chew, G. K. & Cooper, D. W. (1973) Biochem. Genet. 8, 267- Genetics 72, 335. 269. 31. O'Brien, S. J. & MacIntyre, R. J. (1978) in Genetics and Biology 16. Bewley, G. C. & Lucchesi, J. C. (1975) Genetics 79, 451-466. of Drosophila, eds. Ashburner, M. & Wright, T. R. F. (Academic, 17. Lee, C.-Y., Langley, C. H. & Burkhart, J. (1978) Anal. Biochein. New York), Vol. 2a, pp. 396-526. 86,697-706. 32. Lefevre, G. (1973) Cold Spring Harbor Symp. Quant. Biol. 38, 18. Sasaki, M. & Narise, S. (1978) Drosophila Inf. Serv. 53, 123. 591-599. 19. Koehn, R. K. & Eanes, W. F. (1977) Theor. Popul. Biol. 11, 33. B. H., M. & T. C. (1972) Genetics 71, 330-341. Judd, Shen, Kaufman, 20. Leigh Brown, A. J. & Langley, C. H. (1979) Nature (London) 139-156. 277,649-651. 34. Leigh Brown, A. J. & Langley, C. H. (1979) Proc. Natl. Acad. Sci. 21. Gillespie, J. H. & Kojima, K.-I. (1968) Proc. Natl. Acad. Sci. USA USA 76, 2381-2384. 61,582-585. 35. Smith, D. B., Langley, C. H. & Johnson, F. M. (1978) Genetics 22. Spencer, W. P. (1957) Univ. Texas Publ. 5721, 186-205. 88, 121-137. 23. Alexander, M. L. (1949) Univ. Texas Publ. 4920, 63-69. 36. Slatko, B. E. & Hiraizumi, Y. (1973) Genetics 75,643-649. 24. Alexander, M. L. (1952) Univ. Texas Publ. 5204, 73-105. 37. Kidwell, M. G. & Kidwell, J. F. (1975) J. Hered. 66,367-375. 25. Haldane, J. B. S. (1927) Proc. Cambridge Phil. Soc. 23, 838- 38. Golubovsky, M. D., Ivanov, Y. N. & Green, M. M. (1977) Proc. 844.. Natl. Acad. Sci. USA 74,2793-2795. 26. Mukai, T. & Cockerham, C. C. (1977) Proc. Natl. Acad. Sci. USA 39. Green, M. M. (1977) Proc. Natl. Acad. Sci. USA 74, 3490- 74,2514-2517. 3493. Downloaded by guest on September 28, 2021