A substantial amount of genetic variability is known to exist in natural populations.

Transcription

1 FREQUENCY-DEPENDENT SELECTION AT THE LAP LOCUS IN DROSOPHILA MELANOGASTER R. NASSAR Kansas State University, Manhattan, Kansas Manuscript received March 14, 1978 Revised copy received June 5,1978 ABSTRACT Results of fitness estimates for the Lap locus in Drosophila melanogaster revealed that under crowded media conditions gene frequency equilibrium was maintained by frequency-dependent selection. Evidence was obtained that indicated that mating and egg-to-adult viability were frequency dependent. A substantial amount of genetic variability is known to exist in natural populations. An important problem is finding the mechanism that maintains such variability. KOJIMA (1971b) argued for frequency-dependent selection as an important mechanism that acts to maintain genetic variation in natural populations. Evidence for this type of selection in Drosophila has been presented by KOJIMA and TOBARI (1969a,b), KOJIMA and YARBOROUGH (1967), PETIT (1958), EHRMAN (1966,1968), and NASSAR, MUHS andcoo~ (1973). No doubt, more experimentation will be needed to adequately assess the importance of the role of frequency-dependent selection in the maintenance of genetic variability. We report in this study on selection experiments regarding the Lap locus in Drosophila melanogaster. Evidence is obtained that indicates that frequencydependent selection acts to maintain variation at the Lap locus under crowded culture conditions. MATERIALS AND METHODS The material for this study came from two lines that were homozygous for fast (DF) and slow (Ds) moving bands at the Lap locus (3-98.3). These lines were isolated through singlepair matings from a wild-type population collected in Lawrence. Ten females of the proper genotype initiated each line. In the wild-type population, the frequency of the fast allele was about 0.7 and was presumed to be at equilibrium. To determine if a cross between the two lines would reconstitute the parent population and reestablish the same frequency equilibrium, we brought together 100 mated females in the proper ratio from each line such that the frequency of the fast allele was at 0.5. After ten generations of mating, the frequency changed to At 15 generations the frequency was zlc This frequency corresponded to that in the wild-type population. The possibilty was excluded that inversons (like the Payne inversion) were present on the right arm of chromosome 3 of the wild-type population. This was based on the finding that there was a normal crossover rate between the Lap and Acph. ( ) loci. Also, there was the regular crossover rate between ebony (3-70.7) and taxi (3-91) when these were balanced against chromosomes from the wild-type population. Genetics 91: February, 1979.

2 328 R. h-assar At the initiation of the first experiment the lines were at generation 12 of mass mating in /z pint bottles. Four types of crosses were made (FF x FF, FF x SS, SS x FF and SS x SS) and, after two days, males and females were separated and 100 mated females from the four types of crosses were brought together in a half-pint bottle containing 46 to 50 cc of cornmeal- Karo medium and allowed to lay eggs for either three days or 12 hours. Different proportions of females from each of the four crosses were chosen so that the genotypes laying eggs were in Hardy-Weinberg proportions in which the frequencies of the Lap F allele were 0.2, 0.50, 0.7 and 0.8. There were two replicates for each frequency. In the next generation, the three genotypes were scored and their frequencies observed. Estimates were taken on the means of the number of eggs laid and eggs hatched per FF and SS female. For each of FF x FF, FF x SS, SS x FF and SS x SS crosses females were separated, after two days of mating, into vials (one female to a vial). Each vial contained a piece of green-colored food (1 cm x 1 cm x /z cm) fastened with paraffin wax to the end of a strip of index card (1 cm x 4 cm). Each female was allowed to lay eggs on the green food for three days, after which females were discarded and eggs laid per female counted. After 36 hr from the time of egg count, vials were re-examined for the number of eggs that were not hatched. A second experiment was started from the same lines approximately one year later. Three replications were established and are still being maintained. Each replication (half-pint bottle with 45 to 50cc of medium) was initiated from 100 inseminated females, four of which came from the cross FF x FF, 16 from FF x SS, 16 from SS x FF and 64 from SS x SS. Replicates were kept separate, and each generation (up to ten) electrophoresis was run on over 400 pupae and the genotypic frequencies of FF, FS and SS were determined (Table 2). On the seventh and eighth day after emergence, all flies were transferred to a new bottle to start a new generation. Parents were discarded after three days of egg laying and larvae were under crowded media conditions. A third experiment was initiated in order to determine if mating among males was frequencydependent. Three FS virgin females were crossed to three males (1 FF, 1 FS, 1 SS) in a vial and replicated over a number of vials. After two days of mating, the females were separated (one female to a vial), allowed to lay eggs for two days and electrophoresis was run on at least 12 pupae per vial to determine the type of mating (FS x FF, FS x FS or FS x SS). The same experiment was repeated with three FS virgin females crossed to ten males (7 FF, 2 SF and 1 SS) in a vial. The experiment for FS females was also repeated for each of FF and SS females. Throughout this work, flies were maintained at room temperature under discrete generations. Electrophoresis was performed on the pupae just before eclosion. Daily random sampling commenced (in all replicates simultaneously) on the first day of adult emergence and ended about six days later. In the analysis of results, data were pooled over replicates. This was justified on the grounds that no significant differences in genotype frequencies occurred among replicates and that replicates had nearly equal sample sizes. The electrophoresis technique was as described in NASSAR, MUHS and COOK (1973). STATISTICAL ANALYSIS In the first experiment, the fitness of an offspring genotype (FF, FS or SS) over one generation was determined as the ratio of its observed to expected frequency. The latter was the Hardy-Weinberg frequency, assuming no fitness differences among the genotypes. The variance of the fitness estimate of genotype i is P, ( 1 -Pc) /Pt N, where P, = observed frequency of genotype i = n,/n P, = expected frequency of genotype i (Hardy-Weinberg) N = sample size Characters that contributed to fitness in this experiment were the number

3 Lap LOCUS IN DROSOPHILA 329 of eggs laid and egg hatchability per FF and SS female parent and larva-to-adult viability of the offspring genotypes (FF, FS or SS). The two are confounded. If we combine eggs laid and percent hatchability into eggs hatched and let the fitness of FF and SS female parents with regard to this character be f l and f2, we obtain the following model. Genotype of female parent FF ss Ftness due to eggs hatched fl fs Genotype of hatched larvae FF FS ss P2f 1 Expected frequency - z Fitness due to larva-adult viability U1 U, U3 Expected frequency of emerging adults P2flU1 2Pdfl+ f,)u, Q2f2U3 W 2w W Observed frequency of emerging adults n,/n n,/n n3jn N = n1 + n2 + n3 z = P fl + P 9(fl+ f,) + Q2fz w = EP2flUl + 2Pdf,+ fdu, + 92fzU31 The maximum likelihood estimates of the fitness values - - w 2w fzu3 n1 nz n3 are - W p2n 2pqN q2n nzqz (fl+fz)uz On the other hand, the relative fitnesses are given as 1 ;- - 2n3pq 2fJJ3 and - -- and -, respectively. and n1q2 flu1 (fz+fl) U2 --=- flu for SS, FS and FF, respectively. It is clear that if fl = f2, n3p2 f2u3 then fitness will be due solely to viability. In experiment two (I O generation experiment), the enumeration of the genotypes was at the adult stage (the pupae that were analyzed can be safely regarded as newly emerging adults). A generation was from adult to adult and not, as commonly assumed, from zygote to zygote (PROUT 1965; CROW and KIMURA 1970). This is shown below. Genotype (adult) FF FS ss Frequency Fitness Genotype (zygote) Fiiness The set (el, 62, 6,) from adult to zygote might include fertility, survival to time of mating and differential mating. The set (e4, e,, e,) from zygote to adult would include fecundily and viability if adult enumeration is just after emer-

4 330 R. NASSAR gence. With this model in mind, it is seen that the expected genotype frequencies of adults in the next generation are: (Pile, + P1,02/2) 284 P,, = - S S = sum of three numerators. Given the changes in gene frequencies observed to occur over ten generations, our interest is to find a selection model that best fit the data. This was done by estimating, for a given model, the fitness parameters (e s) and then testing by means of a x2 statistic for the goodness-of-fit of the model to the data. The parameters were estimated by either of two methods, minimum x2 (MCS) or maximum likelihood (ML). For the MCS procedure, the x2 statistic is defined as where i = ith generation j = jth genotype in ith generation Xii = observed number of genotype j in generation i Ni = total number of genotypes in generation i NiPij = expected number of genotype j in generation i. The Pij s are determined by equation (2) and are functions of the 0 s in a specified model. Equation (3) was evaluated numerically on the computer for all possible combinations of the e s, taken at intervals of The set of 0 s that gave the minimum x2 value was selected as the estimate of the fitness parameters in the model. The asymptotic properties of the MCS estimators are known to be similar to those of ML estimators, and for large samples (as is the case here) the choice between ML or MCS is determined on the ground of computational convenience (KENDALL and STUART 1967). As is well known, the numerical procedures that can be used to solve for the e s in the nonlinear ML equations do not always converge to give a solution. This is particularly true for models with many parameters. In this case, MCS has a definite advantage over ML. Minimum x2 estimation of fitness was apparently first used by LEVINE, PAVLOVSKY and DOBZHANSKY (1954). For the ML procedure, the logarithm of the likelihood function is 10 3 L = constant + 2=11=1.X.X Xij In (Pij). (4) Equation (4) is nonlinear in the 8 s and requires an iterative procedure to obtain

5 Lap LOCUS IN DROSOPHILA 33 1 a solution. We have used FISHER S maximum likelihood scoring method. The procedure is sufficiently well known not to need detailed explanation. For more information on the method, the reader is referred to BAILEY (1961, Appendix 1). Two methods were used to compute Pij in equation (4). The methods were similar to those used by DUMOUCHEL and ANDERSON (1968). The first method (conditional) was to substitute for Pi-,,i in the right-hand side of (2) the observed relative frequency of genotype j in generation i-1 (X~-l,j/Ni-l). The second method (unconditional) was to begin with the known initial genotype frequencies and apply equation (2) repeatedly to obtain Pij at any generation i. Programs were written and tested by generating genotype frequencies over ten generations for a given genetic model of selection with specified 6 s and then using the generated data and a modification of it (frequencies of genotypes were perturbed from their generated values) to estimate the known 6 s. It was observed that the unconditional method of scoring gave estimates with smaller variance than those obtained from the conditional analysis. DUMOUCHEL and ANDERSON (1968) have also reported on the superiority of the unconditional analysis. For this study, the ML fitness estimates were obtained using the unconditional analysis. The method of scoring converged readily for certain models of selection. In such cases, it converged to the same solution starting with different initial values for the 6 s. For some models, the method did not converge even when a grid search was performed to locate starting values for the 6 s that maximized the likelihood function. When the scoring method did not converge or converged to give inadmissible estimates, we used MCS. In the framework of the general model (adult-zygote-adult fitness), we have considered two types of models as shown below: (1) Constant fitness (first model) ; and (2) frequency-dependent fitness (other models). Model FF FS ss 1. Overdominance 1 -e e, 2. WRIGHT (1969) 1 +e,+e,p, e3 + 8,(1 - P,) 3. KOJIMA (1971a) 1 + 8,(ijl - PJ (Pi - fi,) P;) 1 + B,(E, - 2P,P,) 1 + e,@, - P, ) The overdominance (constant fitness) and frequency-dependent fitness models were chosen for this analysis because of the importance given to these two models as mechanisms to explain the maintenance of genetic polymorphism at many loci. It is commonplace to suggest that an overdominance model or a frequencydependent fitness model may be responsible for maintaining a large amount of balanced polymorphism. It is deemed useful, therefore, to analyze these two models for evidence on the type of balanced selection operating in the population. For the KOJIMA model, P, is the gene-frequency equilibrium. The estimates of Pl from generations 10, 15 and 35 were 0.559, 0.543, 0.549, respectively. These estimates were based on 300 observations each. This leaves no doubt that the population was in equilibrium, and P was taken to be 0.55, the mean of the three

6 332 R. NASSAR estimates. Model 4 is similar to a model on frequency-dependent selection used by O DONALD (1969). E,, E, and E3 in this model represent the relative frequencies of the three genotypes at equilibrium. They were also estimated at generations IO, 15 and 35. The average estimates over generations were 0.313, and 0.212, respectively. Different combinations of the above models were used in specifying the adultzygote and zygote-adult fitnesses. In addition, equal fitness values for the three genotypes at the adult-zygote stage was used. In such a case, selection was assumed to act only in the zygote-adult stage. For each model, estimates of 8 s were obtained and the fit of the expected genotype frequencies (obtained from the estimates of the fitness values for a certain model) to the observed genotype frequencies was tested by x2. The degrees of freedom for the xz were 2n-p, where n is the number of generations and p the number of fitness parameters that were estimated. Our interest was not in estimating parameters as such, but rather in determining the type of selection operating in the population. For this reason, we have not presented errors of estimates in Table 3, but emphasized rather the xz statistic for goodness of fit. RESULTS AND DISCUSSION For the three-day egg laying period of Table 1, it seems clear that for the 0.8 F allele frequency, the S/S genotypic fitness was larger than either the F/F or F/S genotypic fitness. For 0.7 allele frequency, the genotypic fitnesses were about the same, and for 0.5 and 0.2 allelic frequencies, the F/F genotypic fitness was TABLE 1 Fitness estimates for the three genotypes (FF, FS and SS) as a function of their frequencies in the population Egg-la ng 3 days 12 hours SaFpC Pqpn. Sample Popn. F freq. size size FF FS ss size size FF FS ss OM MO e t t 1.034& 0.610t 0.04Q a 0.510e 0.531t C t 0.511& k t

7 Lap LOCUS IN DROSOPHILA 333 larger than was the S/S or the F/S genotypic fitness. For the 12-hour egg laying period, the F/F genotypic fitness was always larger than the S/S fitness and was either larger than or equal to the F/S fitness at all F allelic frequencies. Data for the frequencies of FF, FS and SS genotypes over 10 generations are presented in Table 2. In Table 3, we present the genetic models that gave better fit to the data as judged by the xz for goodness of fit. It is seen that the best fit to the observed genotype frequencies of Table 2 was the frequency-dependent selection model 3 (Table 3, x ; = ~ 19.8). Also, the zygote-adult frequencydependent model 2 gave a good fit to the data (x,", = 26.64). Neither x2 value was significant at the 5% level. All other models of constant fitness or mixed constant and frequency-dependent fitness showed a significant x2 goodness of fit and were not as good in fitting the observed data. In estimating fitness in the one-generation experiment oi Table 1, our enumeration was at the adult stage. The generation interval was taken to be from adult to adult and not as commonly assumed from zygote to zygote. Normally, if adults are allowed to mate at random and if fertility differences (or other fitness differences) exist among the mating genotypes, fitness (as measured here) will be frequency dependent in the sense that gene frequency will be confounded in the fitness estimate. We have avoided this difficulty by making all possible matings among the lines separate and then bringing only mated females together in the proper Hardy-Weinberg ratios. From ( 1 ), the observed frequency of a genotype divided by its expected frequency (as fitness was estimated) is the maximum likelihood estimate of the fitness of the genotype divided by the mean fitness of the three genotypes concerned. As such, a comparison of the fitnesses of the two homozygotes and the heterozygote at a certain gene frequency (say 0.2) should not be affected by that frequency. Hence, if the relative magnitude of genotypic fitnesses changes from one frequency to another, then that should be taken as evidence of frequency-dependent selection. TABLE 2 Observed frequencies of FF, FS and SS genotypes at the Lap locus over ten generations Genotype frequency Generation FF FS ss Q

8 334 R. NASSAR

9 Lap LOCUS IN DROSOPHILA 335 If one wishes to compare the fitness of the same genotype across gene frequencies without those frequencies affecting the comparison, one ought to compare relative fitness of a genotype, because at any given gene frequency the relative fitness of genotype i to j is seen from (1) to be independent of gene frequency. Strictly speaking, the expected value of this relative estimate is infinite because there is a positive probability that nj equals zero. However, in computing the expectation, one can exclude the case nj = 0 without any serious error. The expectation turns out to be biased. The magnitude of the bias, however, is not serious enough to affect interpretation of results. Thus, it is meaningful, for the sort of data in Table 1, to compare genotypic fitnesses within any given allele frequency. Comparing across frequencies would only be meaningful if relative fitnesses are compared. Fitness as seen from (1) includes viability of the offspring genotypes confounded with fecundity (defined as eggs hatched) of the FF and SS maternal genotypes. It is possible to correct the fitness estimates for fecundity by obtaining estimates of the latter. Estimates of fecundity are necessarily obtained on genotypes laying eggs separately. It must be assumed that these estimates hold when genotypes lay eggs together in one bottle and that fecundity of a genotype is not affected by its frequency in the population. Such assumptions may not be unrealistic. Estimates of the average numbers of eggs laid and eggs hatched per FF and SS female genotype for each of the FF x F'F, FF X SS, SS X FF and SS X SS are presented in Table 4. These estimates indicate that there were no significant differences among the crosses with regard to the average number of eggs laid or eggs hatched per female. The data for FF x FF and FF x SS were pooled to obtain estimates for FF. Estimates for SS were obtained by pooling the data for SS X FF and SS X SS. The pooled estimates for SS and FF were very similar, indicating that there was no selection for fecundity in the one-generation experiment and that the fitness estimates (Table 1) represent mostly larva-to-adult viabilities. The conclusion from Table 1 is that viability seems to be frequency dependent, especially under crowded conditions (three-day egg laying period). The results from selection over ten generations also support the fact that zygote-adult fitness TABLE 4 Average number of eggs laid and eggs hatched per female for each of the FF X FF, FF x SS, SS X FF and SS X SS crosses and for pooled FF X FF, FF x SS and SS X FF, SS X SS FF x FF FF x SS SS x FF ss x ss Eggs laid f f t 1.91 Eggs hatched f f t t 1.79 No. of females Pooled data FF x (FF, SS) ss x (FT, SS) Eggs laid f k 1.34 Eggs hatched t

10 336 R. NASSAR is frequency dependent (model 2, Table 3). There is an indication also that introducing frequency-dependent fitness at the adult-zygote stage improved the fit to the data somewhat (model 3, Table 3). Under our laboratory conditions, it seems likely that the adult-zygote fitness may be due in large part to differential mating. There are several reports in the literature on frequency-dependent mating. Results in Table 5 indicate that frequency-dependent mating is present, thus supporting the finding from model 3. In Table 5, the heterogeneity x2 for the FF, FS and SS female data within a male ratio was not significant. This indicates that the female genotype did not seem to affect the male mating frequencies. It is also clear that the frequencies with which FF, FS and SS males mated to FF, FS or SS females did not follow the 1 : 1 : 1 or the 7: 2: 1 ratio. Since the heterogeneity x2 was not significant, the data were pooled within a male ratio. From the pooled data, one sees that the observed mating frequencies of males did not fit the null hypotheses of 1: 1 : 1 or 7:2: 1. The x2 in each case was highly significant. When the expected ratio of mating frequencies (under the null hypothesis) was 1: 1: 1, it was seen that the ratio of observed to expected mating frequency for each of FF, FS and SS males was 1.08, 1.56 and 0.36, respectively. When the ratio of mating frequencies was 7:2: 1, similar estimates gave 0.57,2.53 and Hence, the fitness of a given male genotype (attributed to the frequency of mating of that genotype) seems to be inversely proportional to the frequency of the genotype in the cross. Although these data are not complete, it nevertheless strongly suggests that the mating is frequency-dependent among males. Data are not available on the mating frequency among females. In TABLE 5 Mating frequencies of FF, FS and SS males (in the radios 1:l:l and 7:2:1) to each of FF, FS and SS females Males (1 FF, 1 FS, 1 SS) (1 FF, 1 FS, 1 SS) (1 FF, 1 FS, 1 SS) Females 3 FF 3 FS 3 ss Pooled data Matings with Observed Expected Observed Expected Observed Expected Observed Expected O/E F'F males FS males SS males Heterogeneity x2 = 0.80 x: = 7.81* x', = 6.89* x', = 8.69* x: =22.59** Males (7 FF, 2 FS, 1 SS) (7 FF, 2 FS, 1 SS) (7 FF, 2 FS, 1 SS) Females 3 FF 3 FS 3 ss Pooled data Matings with Observed Expected Observed Expected Observed Expected Observed Expected O@ FF males FS males SS males Heterogeneity xz = 7.36 x: = 12.43* = 37.82** xi = 6.82* x: = ** * Significant at the 5% level. ** Significant at the 1 % level.

11 Lap LOCUS IN DROSOPHILA 337 model 3 (Table 3) the adult-zygote fitness was taken to be frequency dependent in the whole population, males and females. Model 3 (Table 3) was modified to include frequency-dependent itness among males only. No improvement in the fit to the data was observed, however. The 0 estimates (&, O2... 0,) were 2.45, 2.0, 0.75, 2.0, 3.75 and -0.9 and the x2 goodness of fit was 19.5, almost the same as for model 3. It is interesting to note that the difference between crowded and uncrowded culture conditions seems to be for the fitness of the SS genotype at 0.7 and 0.8 F allele frequencies. For crowded conditions, the fitness of the SS genotype increased with a decrease in the frequency of the S allele. No significant change in the fitness of the SS genotype was observed, however, under uncrowded conditions. Results indicate that, for uncrowded culture conditions, a frequencydependent equilibrium was not possible, at least in the range 0.2 to 0.8. The possibility exists that a frequency-dependent equilibrium could be maintained above a frequency of 0.8 for the F allele. It is clear, however, that the intensity of the frequency-dependent selection is reduced with a reduction in the level of crowding of the culture conditions. These results are in accord with findings by KOJIMA and HUANG (1972) and HUANG, SINGH and KOJIMA (1971). One cannot claim that selection was, in fact, due to the Lap locus itself. It is quite possible that selection was for other loci linked to the Lap locus. This study does not differentiate between these two possibilities. I thank the referees and W. W. ANDERSON for their comments. LITERATURE CITED BAILEY, N. T. J., 1961 Introduction to the Mathematical Theory of Genetic Linkage. Oxford University Press, London. CROW, J. F. and M. KIMURA, 1970 An Introduction to PopuZation Genetics Theory. Harper and Row, New York. DUMOUCHEL, W. H. and W. W. ANDERSON, 1968 The analysis of selection in experimental populations. Genetics 58: EHRMAN, L., 1966 Mating success and genotype frequency in Drosophila. Anim. Behavior 14: , 1968 Frequency-dependent mating success in Drosophila pseudoobscura. Genet. Res. 11: HAUNG, S. L., M. SINGH and K. KOJIMA, 1971 A study of frequency-dependent selection observed in the esterase-6 locus of Drosophila melanogaster using a conditioned media method, Genetics 68: KENDALL, M. C. and A. STUART, 1967 Griffin and Company Ltd., London The Advanced Theory of Statistics, Vol. 2, Charles KOJIMA, K., 1971a The distribution and comparison of Genetic Loads under heterotic selection and simple frequency-dependent selection in finite populations. Theoret. Pop. Biol. 2 : , 1971b Is there a constant fitness value for a given genotype? NO! Evolution 25: KOJIMA, K. and S. L. HUANG, 1972 Effects of population density on the frequency-dependent selection in the esterase-6 locus of Drosophila melanogaster. Evolution 26:

12 338 R. NASSAR KOJIMA, K. and Y. N. TOBARI, 1969a The pattern of viability changes associated with genotype frequency at the alcohol dehydrogenase locus in a population of Drosophila melanogaster. Genetics 61 : , 1969b Selective modes associated with karyotypes in Drosophila amnassae. 11. Heterosis and frequency-dependent selection. Genetics 63 : KOJIMA, K. and K. YARBROUGH, 1967 Frequency-dependent selection at the esterase 6 locus in Drosophila melanogaster. Proc. Natl. Acad. Sci. US. 57: LEVENE, H., 0. PAVLOVSKY and T. DOBZHANSKY, 1954 Interaction of the adaptive values in polymorphic experimental populations of Drosophila pseudoobscura. Evolution 8 : NASSAR, R. F., H. J. MUHS and R. D. COOK, 1973 Frequency-dependent selection at the Payne inversion in Drosophila melanogaster. Evolution 27 : ODONALD, P., 1969 The selective coefficients that keep modifying genes in a population. Genetics 62: PETIT, C., 1958 Le determination gknetique et psycho-physiologique de la compktition sexuelle chez Drosophila melanogaster. Bull. Biol. France et Belgique. 92 : PROUT, T., 1965 The estimation of fitness from genetic frequencies. Evolution 19: WRIGHT, S., 1969 Evolution and the Genetics of Populations. Volume 2, p Univ. Chicago Press, Chicago and London. Corresponding editor: W. W. ANDERSON