45%c each, after some early difference. in. to account for the change in relative selective values. Hypothesis A: The fitness

Transcription

1 POP (,,-LA TION STUDIES IN PREDOMIINA TEL Y SELF-POLLINA TED SPECIES, IX. FREQUENCY-DEPENDENT SELECTION IN PHASEOLUS LUNATU S* BY JAMES HARDING, R. W. ALLARD, AND DALE G. SMELTZER UNIVERSITY OF CALIFORNIA (DAVIS) Communicated by G. L. Stebbins, May 27, 1966 In a study of three segregating populations of lima beans, Phaseolus lunatus L., Allard and Workman' found that the selective value of the heterozygote (Ss) was higher than the selective values of both homozygotes (SS and ss) for a locus which affects seed coat pattern in this predominantly self-fertilizing species. There was also a tendency for the selective advantage of the heterozygote to increase in the later generations of these hybrid populations. Two hypotheses can be advanced to account for the change in relative selective values. Hypothesis A: The fitness of heterozygotes increases as inbreeding causes their frequency to decrease in the population, i.e., selective values are frequency-dependent. Hypothesis B: The evolution of the genetic system involves formation of new combinations of genes which interact with the linkage blocks marked by the S/s locus in such a way as to enhance the advantage of heterozygotes. This paper reports the results of an experiment which was designed to evaluate these two hypotheses. Materials and Methods.-Population 65, one of the three populations studied by Allard and Workman, was selected for detailed analysis. Population 65 was derived from a hybrid between two highly inbred lines. The F1 hybrid was grown in the greenhouse, but the F2 and succeeding generations were grown under standard agricultural conditions. Each year the population was harvested in mass without conscious selection, and the next generation was established from a sample of approximately 3,000 seeds drawn at random from the harvest. Another sample of 2,500-5,000 seeds was used to determine the frequencies of the SS, Ss, and ss genotypes, which can be identified on a single-seed basis. Census data for the F2 through F14 generations, which are presented graphically in Figure 1, illustrate the pattern of change in genotypic frequencies which occurred in population 65. In the early generations the proportion of heterozygotes decreased rapidly, as expected inl a population in which there is 95% or more of self-fertilization. However, after the Fj generation the proportion of heterozygotes showed no further consistent decrease but instead fluctuated narrowly around an apparent equilibrium value of approximately 10%. The proportions of the two homozygotes appeared to stabilize around values of approximately 45%c each, after some early difference. in frequency. The materials for the present experiment were 50 the F13 and F14 generations of population 65, the F4 and F5 generations of a second mating between,0 - the same two inbred lines that were crossed to produce population 65, and two sets of contrived Q SS populations, designated "A'" and "B,'" which a were synthesized from samples drawn from these four generations. The A populations, which were designed to evaluate the effect of the frequency of heterozygotes on fitness (Hypothesis 10\ A), were prepared by removing all seeds that were phenotypically Ss from stocks of late generations 0 2 Fi Fi Fi Flo F12 F14 (F13 or F14) of population 65. These Ss seeds were GENERATION then added to samples of the remaining stock of FIG. L-Genotypic frequencies at the S/s homozygotes in various proportions to obtain locus in population 65 from the F2 through F14 populations with differing frequencies of heterozy- generations. 99

2 100 GENETICS: HARDING, ALLARD, AND SMELTZER PROC. N. A. S. TABLE 1 COMPOSITION OF POPULATIONS USED IN STUDIES OF RELATIVE FITNESS OF HETEROZYGOTES AT THE S/s LOCUS Proportion of outcrossing in Population iromozygote Heterozygote Heterozygote homozygote number generation generation frequency generation A Populations (check) F13 F, F13 F F13 F, F,3 F B Populations F13 F F,3 F F13 F F13 F F4 F F4 F (check) F4 F A Populations (check) F14 F F14 F F14 F F14 F F14 F F14 F F14 F B Populations F14 F, F14 F F14 F F14 F F14 F F, F F5 F (check) F5 F gotes. The A populations (Table 1) can be characterized as follows. Populations 1 and 12 were the unmodified F13 and F,4 generations, respectively, of the original population 65. In these two populations the frequencies of heterozygotes were allowed to remain at their natural values of 5.59 and 7.73%. Populations 2 through 4 (F,3) and populations 13 through 18 (F,4) were frequency-modified populations. In these populations the frequencies of heterozygotes were adjusted to values which ranged from approximately 2% to approximately 15%. It should be noted that the amount of outcrossing was unknown at the time these populations were synthesized and it was consequently not possible to obtain precisely the planned zygotic frequencies. Since only frequencies of heterozygotes and homozygotes were modified, and not the generation from which they were derived, the A populations provide a straightforward test of the null hypothesis that relative selective values are independent of the frequency of heterozygotes in the population. The B populations were prepared in a similar manner, but in addition to modification of the frequency of heterozygotes, the filial generations of homozygotes and heterozygotes were switched. Ss seeds taken from the early generations (F4, F,) were added to late-generation (F,3, F,4) stocks of homozygotes from population 65, and vice versa, in various proportions to obtain the populations shown in Table 1. Data from the B populations provide the comparisons necessary to test the null hypothesis that the fitness of heterozygotes does not change under selection, and the data can also be used to test the frequency-dependency hypothesis. Estimation of Selective Values.-In estimating the selective value of the heterozygote (w), the two homozygotes were treated as a single class with selective value of unity. Let f(n) be the observed frequency of Ss at gametogenesis in generation n, and f (n +1) be the zygotic frequency of Ss prior to selection in generation n + 1. Then f(n+l) 2tp(oa = p) + 1/2f(qn)(1 - t) h (1) where t is the proportion of outcrossing and p is the frequency of the s allele determined from

3 VOL. 56, 1966 GENETICS: HARDING, ALLARD, AND SMVELTZER 101 census data. The frequency of Ss after selection in generation n + 1 is expected to be where f(n+l) =Wf(n+l)I T If' 1 - fz(n+l)(1 - W). If fz(n+l) is the expected frequency of Ss in generation n + 1 anddf(n+l) is the frequency as determined from census data, then the maximum likelihood estimator for w is f2(n +l)[1 -znl[f~~~(2) -fz(n +1) ]- Experimiental Results. Populations 1 through 11 were grown in the field at Davis, California, in 1963, and samples were drawn from the seed harvested from each population to determine the frequencies of the genotypes SS, Ss, and ss. Estimates of outcrossing were also made in the generations from which seeds had been taken to synthesize the contrived populations (see column 5), Table 1). These census data and the estimates of outcrossing were used to estimate relative selective values according to (2). The results, which are shown in Figure 2, upper left, indicate that the relative selective values of the heterozygotes were not the same in different populations. Results for the A populations, in which only the frequency of heterozygotes was modified, suggest a negative regression of selective value on heterozygote frequency. In the corresponding B populations, both the generation and the frequencies of heterozygotes and homozygotes were varied. The significant regression of fitness on frequency of heterozygotes in the B populations indicates that frequency rather than generation was the more important variable. Particular note should be taken of the selective values of heterozygotes in populations 5-8 and 9 and 10. According to Hypothesis B, the selective values of the F4 heterozygotes in populations 5, 6, 7, and 8 should have been low, whereas they tended to be high. Similarly, the fitness values of the F13 heterozygotes in populations 9 and 10 should have been high, but the data show that their fitness values were not different from those of the F4 heterozygotes in population 11. The experiment was repeated on a larger scale in 1964 when populations 12 through 26 were grown under conditions similar to those of the 1963 experiment. The regression of relative selective values on frequency of heterozygotes was significant for both the A and B populations of 1964 (Fig. 2, upper right). The relative values for populations 22, 23, and 25 are particularly interesting because although the frequencies of heterozygotes were similar in these populations, the heterozygotes and homozygotes represent different generations. Population 25 was an unmodified F5, whereas in population 22, F1 heterozygotes were mixed with F14 homozygotes, and in population 23, the mixture was reversed. The similarity of selective values indicates that fitness values were independent of the generation of the homozygotes and heterozygotes. The data over years are combined for the A and for the B populations in Figure 2, lower left. The regression coefficients for both groups are highly significant and the slopes for the two types of populations do not differ significantly. This result clearly favors Hypothesis A. Further support for this hypothesis derives from the fitness value intercepts for the two groups. According to Hypothesis B, the A populations, in which only F13 and F14 heterozygotes occur, should have higher fitness

4 102 GENETICS: HARDING, ALLARD, AND SMELTZER PROC. N. A. S * A POPULATION4S A POPULATIONS o2~~~~~~~~~~~~~~~~~~~~~~~~~1 93.~~~~~~~~~~~~~~~~~~~4.0 Y X Y X POPULATIONS B POPULATIONS ~~~ *3 4.0 u. 10~~~~~~~~~~~~~~~~~~~~~~2 sz, =43 u33sb = 4 20*6 2~~~~~~~~~~~~~~~~~~~~~30 0~~~ ~~~~10 ~ -020 oil., *8.~" ~~~~~~~~~~~~~~~~ 1.0 Y Y X l FREQUENCY OFHETEROZYCOTES FREQUENCY OF HETEROZYGOTES o X.0t - Y= A POPULATIONS w1316 I4 W4.0 _.3 ol6~~~~~~~~~~~~~~~~n i>4.0.e , d A POPULATIONS ,0.6 Uj e~~ ~~2~ ~ ~~~~~~~~~~~~~~~~~4~ 0 10I1 r- 1.0 Y for thela 4ou9 n an B4n31 U B POPULATIONS -% POUAIN z 26A&BPPLTOS CL4.0- The3.0 fo 3l30 - e14 a i zygotes.~~~~~~~~ ,690 Th.4ns au necpsfrte w7.~3.31-1i7.080x7 ruswr eryeu,34.16 C 0.02 ~ FREQUENCY OP HIETEROZYGOTES PREQUENCY OPF.ETEROZYGOTES FIG. 2.-Regression of relative fitness on frequency of heterozygotes in populations in which the inecet frequency ar and/or eysmlrfrte generation of Sstw was modified. eas Upper left, 1963 data; upper right, 1964 data; lower lejft, comparison between types of populations over years; lower right, comparison between years over types of populations. values than the B populations, some of which include early generation heterozygotes. The fitness value intercepts for the two groups were nearly equa, 3.44 for the A populations and 3.36 for the B populations. The consistency of the frequency effect in the two years is apparent in Figure 2, lower right. The two regression values are highly significant and the slopes and intercepts are very similar for the two years. The data for all populations are combined in Figure 3. The close agreement with expectation according to the frequency-dependency hypothesis is clear. 1\Iean

5 VOL. 56, 1966 GENETICS: HARDING, ALLARD, AND SMIELTZER 103 population fitness is expected to be at a 50 maximum when d I l/df(n+l) = 0 1 l nax 0 26 ALL computed from the regression equation for 16 the combined data is 7.10 per cent, which 2 is very close to the actual values of per cent (1963) and 7.73 per cent (1964) observed in the original population 65. l X Discussion. The expected consequence 274 of frequency-dependent selection of the FREQUENCY OF HETEROZYGOTES type observed for the Sls locus is rapid FIG. 3.-Relationship between the freadjustment toward a highly stable non- quency of heterozygotes at the S/s locus in trivial equilibrium. When heterozygotes lima bean populations and their fitness relaare frequent, as in early generations of twe to homozygotes. populations derived from F1 hybrids between SS and ss strains, they have no seleetive advantage over homozygotes. Inbreeding is therefore expected to be the dominant force and it should reduce the proportion of heterozygotes in the population at the rapid rate of approximately one half per generation. This occurred in population 6.5. Should the frequency of heterozygotes fall below the assumed equilibrium value (dli /df, = 0) of approximately 7.10 per cent, their selective values increase until at very low frequency they produce up to three times as many progeny as homozygotes. The expected result is a rapid increase in the frequency of heterozygotes in the population. To determine whether this occurs in actual populations, an additional generation was grown of a synthetic population in which heterozygote frequency had been adjusted to the low value of approximately 2 per cent. A single generation was adequate to restore the frequency of heterozygotes near to the expected equilibrium value of 7 per cent, where it remained the following generation. Since the frequency dependency acts to maintain heterozygosity in the population, it is a potent force in the retention of segregational variability in this heavily inbreeding species. It is important to note that the frequency dependency associated with the Sls linkage block was measured directly on the fitness scale. This is in contrast to most previously reported cases where the measure was in terms of viability and/or mlorphological traits, e.g., Lewontin and Alatsuo,2 Sokal and Huber,3 and Sokal and Karten.4 Frequency dependenc(y on the fitness scale has been studied in Drosophila persimilis by Spiess,3 and it was offered as one explanation for an observed equilibrium in Moraba scurra by Lewontin and White.6 However, the observed equilibrium inl the latter case appears to be more simply explained oil the basis of the inbreeding expected to result from the low mobility of this wingless grasshopper.7 The biological basis of the frequency-dependent selection established in the present experiment is unknown. However, the pattern of the frequency dependency suggests a "neighborhood effect" in which the relative fitness of heterozygotes is affected by competition from other heterozygotes growing in proximity. Experiments to determine the effects of varying the frequency and density of heterozygotes within neighborhoods of known composition are now under way. In the present case the frequency dependency resulted from interactions between heterozygotes and homozygotes, but there is no reason to believe that similar interactions might not occur between different homozygotes, between different hetero-

6 104 GENETICS: HARDING, ALLIARD, AND SMELTZER PROC. N. A. S. zygotes, or even between different species. Frequency dependency in which rarity leads to enhanced fitness (apostatic selection of Clarke8) may therefore be a factor in the biology of communities, and hence it may be of interest in physiology, ecology, and agriculture as well as in population genetics. Summary. Relative fitness values associated with linkage block heterozygotes marked by the S/s locus were estimated in populations of lima beans in which the frequency of heterozygotes and/or degree of selection of the genetic background had been modified. The relative fitnesses of homozygotes and heterozygotes were independent of the generation from which they were derived, but there was a significant correlation between the frequency of heterozygotes and their selective value. The fitness of heterozygotes increased as their frequency in populations increased until, when they were at very low frequencies, heterozygotes produced about three times as many progeny as homozygotes. This frequency dependency acts to maintain a stable nontrivial equilibrium at the S/s locus and hence promotes the retention of segregational variability in these inbreeding populations. * This study was supported in part by grants from the National Science Foundation (GB-3246) and the National Institutes of Health (GM-10476). lallard, R. W., and P. L. Workman, Evolution, 17, (1963). 2 Lewontin, I1. C., and Y. MIatsuo, these PROCEEDINGS, 49, (1963). 3 Sokal, R. R., and I. Huber, Am. Naturalist, 97, (1963). Sokal, R. R., and I. Karten, Genetics, 49, (1964). 5Spiess, E. B., Evolution, 11, (1957). 6 Lewontin, R. C., and M. J. 1). White, Evolution, 14, (1960). 7 Allard, R. W., and C. Wehrhahn, Evolution, 18, (1964). 8 Clarke, B., Heredity, 17, (1962).