Proc. Nat. Acad. Sci. USA Vol. 69, No. 9, pp. 2474-2478, September 1972 Is the Gene the Unit of Selection? Evidence from Two Experimental Plant Populations (barley/enzyme polymorphisms/gametic phase disequilibrium/linkage disequilibrium/ natural selection/coadaptation) M. T. CLEGG*, R. W. ALLARD, AND A. L. KAHLER Department of Genetics, University of California, Davis, Calif. 95616 Communicated by Th. Dobzhansky, June 29, 1972 ABSTRACT The dynamics of gametic frequency ment of selection intensity over loci along the chromosome. change have been analyzed in two experimental plant and Lewontin (8), assuming multiplicative heterosis, populations. Individual plants were scored for their geno- Franklin type at four enzyme loci, and four-locus joint gametic find that when recombination falls within certain critical frequencies were estimated from the genotypic data over ranges high correlations in allelic state accumulate rapidly generations. Striking correlations developed in allelic state along the chromosome; the effect of these correlations is to over loci, including correlations between nonlinked loci, as restrict the gametic pool to few gametic types, usually per- these populations evolved. Furthermore, the same pair of four-locus complementary gametic types came into fectly complementary to one another. These authors speculate marked excess in the late generations of both populations. that selection acts, not on single loci, but upon chromosomal The results demonstrate that natural selection acted to blocks composed of highly interacting sets of loci. structure the genetic resources of these populations into Theoretical analyses of models involving two or more loci sets of highly interacting, coadapted gene complexes. it clear that the behavior of multilocus systems They also provide evidence, at the level of the gene, that thus make selection operating on correlated multilocus units is an cannot, in general, be predicted from single-locus theory. important determinant of population structure. There is, however, a paucity of experimental data on the dynamics of multilocus systems, especially for systems in- Sexual reproduction and genetic recombination are capable volving more than two loci. Predominantly self-pollinating of producing a virtually infinite array of genotypes. The populations of plants are favorable materials for such studies, potential diversity is especially striking in view of current since the intense inbreeding that occurs in such populations estimates that indicate that at least one-third of electro- is expected to lead to drastic restriction of recombination phoretically detectable loci are polymorphic (1-4). A par- among all loci, including unlinked loci, with effects on equilib- ticularly challenging issue in population genetics is to deter- ria equivalent to very tight linkage. This paper reports a mine how natural selection sorts out from the vast number of study of gametic frequency change at four enzyme loci in potential arrays of genotypes those arrays that confer high two experimental populations of barley (Hordeum vulgare L.), fitness on the population. Measurement of correlations in in which the mating system is one of more than 99% self- allelic state over loci in the gametic pool provides an impor- fertilization. The results show clearly the buildup of striking tant test of the extent to which natural selection reduces the correlations between loci, including unlinked loci, and they potential genotypic frequency distribution. provide experimental evidence, at the level of the gene, that Theoretical and numerical investigations show that com- selection operating on such coadapted (9) multilocus units plex relationships exist between selection, linkage, effective is an important determinant of population structure. population size, and mating system when two or more loci are considered simultaneously. Exact treatments of two-locus MATERIALS AND METHODS symmetric viability models in which random mating and in- The two experimental plant populations studied are barley finite population size are assumed show that up to seven in- Composite Crosses II and V (hereafter abbreviated CCII terior equilibria are possible, and that equilibrium points .are and CCV). CCV was synthesized from 30 parents represent- given by complex functions of the recombination fraction ing the major barley growing regions of the world (10). The and viabilities (5). If population size is finite, recombination parents were crossed in all possible pairs, the resulting F1 is restricted and, through the vagaries of sampling, wide hybrids were again paircrossed, and this cycle was repeated fluctuations in disequilibria may result (6). Inbreeding due until a single grand F1 hybrid was obtained. The F2 seed from to mating system also reduces effective recombination by the grand F, hybrid was used to initiate the first generation lowering levels of heterozygosity, and very close inbreeding of CCV in 1941. The population has since been propagated in leads to drastic restriction of recombination with effects on large plots every year under normal agricultural conditions equilibria equivalent to those of very tight linkage (7). without conscious selection. Examination of the gametic in- Numerical investigations suggest that additional phe- put of the parental varieties indicates that frequencies of the nomena become involved when more than two, and especially various gametic types in the initial generation of this popula- when large numbers of, loci segregate simultaneously. Thus, tion deviated in a minor way from products of single-locus Sved (6) finds that apparent single-locus selective values are allelic frequencies. This initial gametic phase disequilibrium much greater than actual selective values due to reinforce- (also called linkage disequilibrium, which is a misnomer be- cause disequilibrium can occur without linkage) was of about * Present address: Division of Biological and Medical Sciences, the magnitude expected from sampling effects associated Brown University, Providence, R.I. 02912. with the small number of parents (11). 2474 Downloaded by guest on September 28, 2021 Proc. Nat. Acad. Sci. USA 69 (1972) Genes as Units of Selection 2475 CCII differs from CCV both in parentage and in method reduce the data to more managable proportions, we have of synthesis. The population was initiated in 1929 by pooling combined alleles to create two allelic classes per locus, one equal numbers of F1 hybrid seed from the 378 intercrosses consisting of the most-frequent allele (denoted allele 1) and among its 28 parents, which, like the parents of CCV, in- the other a "synthetic" allele consisting of all other alleles cluded a wide sample of the diversity of cultivated barley. combined (denoted allele 2). Population size and cultural practices were the same for this population as for CCV. Analyses of the gametic input of the Calculation of gametic input parental varieties indicates slightly greater gametic phase In calculating gametic inputs, it is convenient to adopt and disequilibrium in the initial generation of CCII than in CCV. extend the notation of Weir et al. (11). The relative frequency Moreover, there was less opportunity for recombination dur- of a heterozygous genotype is written as 2f(AiBjCkDl,AnBm- ing the synthesis of CCII than during the synthesis of CCV; CpDq), where genes AiBjCkDl were contributed by the same thus, the initial generation of CCII almost certainly deviated parental gamete, and the relative frequency of a four-locus further from gametic phase equilibrium than the initial joint homozygote is denoted f((AiBjCkD1,AiBjCkD1). Thus, generation of CCV. the relative frequency of a particular four-locus gamete can Four esterase loci, EA, EB, EC, and ED (hereafter desig- be found from the sums of appropriate genotypic frequencies. nated A, B, C, D) were simultaneously scored in each indi- For example in the diallelic case, vidual assayed in generations 5-7, 16-17, and 25-26 in CCV and 7-10, 17-20, and 39-42 in CCII. The formal genetics and f(ABCDl) = f(ABCD,,AB1C,Di) + f(AB,CD,,AB1C,D2) + assay techniques have been described (12). Three of these f(AB1CD,,AlBlC2D,) + f(A1BCD,,AlB2C1D,) + loci are very tightly linked, in the order B-0.0023 ± 0.0007 f(ABCD,,A2BCD,) + f(ABCD,,ABC2D2) + ± the fourth locus, D, is f(ABCD,,AB2ClD2) + f(ABCD,,A2BlCD2) + ---A--0.0048 0.0008--C, while f(AB,ClDl,,AB2C2D,) + f(ABC,D,,A2BC2D,) + inherited independently of the first three. f(A,BCD,,A2B2C,Dl) + f(AB,C,D,,AlB2C2D2) + Census data were obtained by analysis of 7-day-old seed- f(ABCD,,A2BC2D2) + f(A1BCD1,A2B2ClD2) + lings grown from the bulk seed harvest of the generations f(A,B,CD,,A2B2C2D,) + f(ABCD,,A2B2C2D2), selected for study. The seeds were germinated under ideal conditions and mortality was very low (<1%). Hence, the or, in general, f(ijkl) = E EE E f(ijkl,nmpq). census data obtained are effectively equivalent to enumera- n m p q tions made at the zygotic stage. Since progeny testing to determine the frequencies of the RESULTS various phases of multiply heterozygous individuals was The number of alleles of Loci A, B, C, and D introduced into impractical, the frequencies of such genotypes are unknown; CCII and CCV (10) were 3, 5, 3, and 5, and 4, 3, 3, and 4, consequently, in computing gametic input, we have assumed respectively. In both populations one allele generally pre- that the various phases of multiple heterozygotes were pres- dominated at each locus and one or more of the other alleles ent in equal frequency. For