DROSOPHILA MELANOGASTERI

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1 A MODEL OF THE NEGATIVE CORRELATION BETWEEN MALE RECOMBINATION AND TRANSMISSION FREQUENCY IN DROSOPHILA MELANOGASTERI YUICHIRO HIRAIZUMI Department of Zoology, The Uniuersity of Texas at Austin, Austin, Texas Manuscript received December 19, 1978 Revised copy received April 9, 1979 ABSTRACT A model is proposed to account for the phenomenon of negative correlation between male recombination (e) and transmission frequency (k) in Drosophila melanogaster. The model assumes that, in some stage or stages of development, the male recombination elements cause a particular event that does not occur in normal males and that this event, in turn, induces with certain probabilities male recombination and/or sperm dysfunction. The regression equations of e on k predicted by the model were compared with those actually observed. There was generally excellent agreement between them. is now a well-established fact that many natural populations of Drosophila Izelanognster contain genetic elements that induce male recombination in nontrivial frequencies (see MATTHEWS and HIRAIZUMI 1978 for reference). These elements, which may be called male-recombination elements, have been found to be associated with several other genetic characteristics, such as a higher frequency of spontaneous mutation (SLATKO and HIRAIZUMI 1973; KIDWELL 1973; KIDWELL and KIDWELL ; KIDWELL, KIDWELL and SVED 1977), high sterility (KIDWELL and KIDWELL 1975a; KIDWELL, KIDWELL and IVES 1977), and a distorted transmission frequency (HIRAIZUMI 1971, 1977; KIDWELL, KIDWELL and SVED 1977; MATTHEWS et az. 1978). During the past five years, intensive studies on the male-recombination system have been carried out in this laboratory, and it has been reported repeatedly that the frequency of male recombination is correlated with the degree of distortion in transmission frequency. For simplicity, let k be the frequency of the second chromosome (= 2) associated with male recombination recovered among nonrecombinant progeny of the backcross mating, +/+ 0 x x/+ d. If the transmission ratio is Mendelian and if the two segregating genotypes have the same viability, one would expect that 50% of the progeny will receive the z chromosome, and thus k = 0.5. However, when the x chromosome carries male recombination elements, one will find a much reduced recovery frequency of the x chromosome among progeny, and thus k < 0.5. * This wolk \\as supported by Public Health Service Research Grant, GhI GerietiL, 93 : October, 1979

2 45 0 Y. HIRAIZUMI The frequency of male recombination (= 0) and the k value are different among different genotypes, and even among different individual males within a genotype. It has been shown (HIRAIZUMI 1971, 1977; MATTHEWS et al. 1978) that a genotype (or individual male) associated with a larger value of 0 generally exhibits a smaller IC value. In order to make a further analysis of this phenomenon of negative correlation, however, a large body of data is needed, since the frequency of male recombination, O, is generally small, of the order of a few percent. In the past few years, many experiments relating to this system have been carried out in this laboratory; a large amount of data, some published, much unpublished, has been accumulated, and it has now become possible to make further analyses on the negative correlation and to construct a formal model for this phenomenon. MATERIALS AND METHODS The second chromosome lines of Drosophila melunoguster employed in this study are listed below. cn bw: a second-chromosome line marked with two recessive eye color mutants, cn (cinnabar eye color, 2R, 57.5) and bw (brown eye color, 2R, 104.5). al dp cn bw; a second-chromosome line carrying four recessive mutants, al (aristaless, ZL, 0.01), dp (dumpy wing, ZL, 13.0), cn and bw. b pr c px: a second-chromosome line carrying four recessive mutants, b (black body color, 2L, 48.00), pr (purple eye color, 2L, 54.4), c (curved wing, 2R, 75.5), and px (plexus wing vein, 2R, 100.5). a2 dp b pr c px sp; a second-chromosome line carrying seven recessive mutants, al, dp, b, pr, c, pz, and sp (speck, 2R, 107.0) Tokyo: a standard wild-type second-chromosome line which has been maintained for more than 15 years by backcrossing, through males, to females from the standard cn bw stock. In previous extensive tests, this stock showed practically no male recombination. T-007: a second-chromosome line isolated in 1970 from a natural population in Harlingen, south Texas. This chromosome, when made heterozygous with a marked laboratory chromosome, is known to induce male recombination, a high frequency of mutation, and to show, in heterozygous males, a transmission frequency of about instead of the Mendelian expectation of 0.5. T-006: a line with properties similar to those of the T-007 chromosome. This line was lost accidentally a couple of years ago. Recombinant lines Various recombinant chromosome lines were generated, by crossing over, from females of the genotypes T-O07/ul dp b pr c px sp, T-O07/b pr c px, and T-O66/b pr c px. Those will not be listed here, but they are shown in tables, which will be presented later. SLATKO and HIRAIZUMI (1975) showed that the major elements, named Mr for Male recombination, were located near the pr+ locus, so that the recombinant chromosome types with the pr+ allele may be considered to carry the Mr elements. All remaining types, which carry the pr marker, may not contain Mr, but they contain some chromosome segments from the original T-007 chromosome, and thus contain the elements for male recombination, as discussed by MATTHEWS et al. (1978). Crosses Mating types from which the k and the e values were estimated were as follows. The chromosome indicated as z is the one that carries the male-recombination elements, either the major

3 MALE RECOMBINATION.4ND TRANSMISSION FREQUENCY 45 1 elements, Mr (SLATKO and HIRAIZUMI 1975), or the minor elements (MATTHEWS et al. 1978), or both. (1) 2to3cnbw 0 x lcnbw/x 8. (2) 5 a1 dp cn bw 0 x I a1 dp en bw/x 8. In these two mating types, tww to four-day-old males were mated individually to females of the same age, and they were kept in a vial for seven days, then discarded. Fly counts were completed on the 19th day from the date when the mating was initiated. (3) 5 al dp cn bw 0 x 1 a1 dp cn bw/t This was the mating type reported by HIRAIZUMI (1977). Briefly, one- to three-day-old males were individually mated to five young virgin females and kept in a vial for three days. They were then transferred to a second vial for another three days. Transfers were repeated, with addition of new virgin females, until the fifth vial, or until the male became sterile (for details, see HIRAIZUMI 1977). A MODEL OF NEGATIVE CORRELATION Let N be the number of functional sperm produced by a normal genotypic male for a certain period. For simplicity, we shall consider a heterozygous +/cn bw male where + is the second chromosome without the male recombination elements. There will be no male recombination, and no distortion in transmission frequency; thus, half (N/2) of the functional sperm will carry +, and the other half will carry the cn bw chromosomes. Now consider a male of the genotype x/cn bw, where x is the second chromosome associated with the male recombination elements. HIRAIZUMI (1977) found that, in the a1 dp cn bw female x T-O07/al dp cn bw male matings, the average number of a1 dp cn bw progeny was approximately the same as that of the control, Tokyo/al dp cn bw male matings. We may therefore assume that the x/cn bw male will produce approximately N/2 functional sperm carrying cn bw. The number of functional sperm containing the x chromosome will be smaller than N/2. MATTHEWS (1977, and manuscript in preparation) showed that this reduction was due to dysfunction of the sperms containing the z chromosome during spermiogenesis. In addition to those sperms with the parental-type chromosomes, there will be some sperm that have recombinant chromosomes, either cn or bw. Let us, for simplicity, call the group of sperm containing either recombinant chromosomes (regardless of whether they are functional or dysfunctional) or the dysfunctional x chromosomes affected, and the rest unaffected. We shall then have the following four groups of sperm: (1) Unaffected, functional sperm containing either cn bw or x chromosomes. (2) Affected, functional sperm containing recombinant chromosomes, either cn or bw. (3) Affected, dysfunctional sperm containing recombinant chromosomes, either cn or bw. (4) Affected, dysfunctional sperm containing x chromosomes. As mentioned previously, k and o are negatively correlated. This implies that the actual frequency of dysfunctional sperm is positively correlated with 0. The simplest explanation for this relationship might be as follows.

4 452 Y. HIRAIZUMI In some stage or stages of development, the male recombination elements cause, with a certain probability, a particular event that does not occur in a normal male, and this event, in turn, induces with certain probabilities male recombination and/or sperm dysfunction. Let p be the probability that a sperm is affected as a result of such a particular event. We assume that 0 < p < 1. Among the affected sperm, let q be the probability that the sperm (whether functional or dysfunctional) contain recombinant chromosomes for a given region, say between cn and bw, and (1 - q) be the probability that the sperm contains the x chromosome and is dysfunctional. We assume that 0 < q < 1. Among the sperm containing either the cn or the bw recombinant chromosome, some of them will be functional and some dysfunctional. Lets be the probability that the sperm containing the cn recombinant chromosome is dysfunctional, and t be the probability that the sperm containing the bw recombinant chromosome is dysfunctional. We assume that O < s, t < 1. These situations are presented diagrammatically, with the probability for each event within parenthesis, in Figure 1. In Figure 1, x is the second chromosome associated with the male recombination elements. Male recombination is measured between the cn and bw loci on the cn bw chromosome, and between the a1 and bw loci when the a1 dp cn bw chromosome is used in place of the cn bw. The frequencies of functional sperm containing the x and the cn bw chromosomes are computed as follows. Let the frequency of functional sperm containing the x and the cn bw chromosomes be designated y and z, respectively. The frequency of dysfunctional sperm containing the x chromosomes is p ( 1-4). Thus, we obtain the relationship z = y + p( 1-4). The frequency of unaffected sperm is y + z = (1 - p). Solving these two equations simultaneously, we obtain: y=x(l +pq-2p), andz=1/2(1 -pq). Sperm \I i cn bw: All functional Unaffected x: All functional (I- P) < cn: 1/2 Recombinant bw:1/2 Affected (P) 7 Functiona! (I-s) Dys func t i ona I (s ) Functional (I-t) Dysfunctional (t ) (q) Parental x: All dysfunctional (I-q) FIGURE 1.-A diagram showing the relationships among various kinds of sperm types pro duced in z/cn bw males, where z is the second chromosome associated with male-recombination elements.

5 MALE RECOMBINATION.4ND TRANSMISSION FREQUENCY 453 The value of k can be calculated as follows. The value of o is generally small, of the order of a few percent (or less), SO that pq (2- s - t) is generally a small fraction. The fraction of sperm carrying the cn bw chromosome is i/e (1- pa), and the results of HIRAIZUMI (1977) mentioned earlier indicated that, even when the degree of distortion became large in the T-O07/al dp cn bw males, there was no demonstrable reduction in the number of functional a2 dp cn bw sperm produced for the vast majority of males. This implies that pq is a small fraction even if p is large. For a small value of pq, formulae (1) and (2) can be approximated as or (1-2k) = 2(1 - k) 20 q(2-s-t) = (1-2k) * (5) In (3) and (4) above, p is the only parameter appearing in both equations, and thus, in order to have some correlation between k and O, it is the candidate parameter that gives differential values of k and o among genotypes or individuals. Let us assume that, for a given region of chromosome where male recombination frequency is measured, the value of q, s and t are constant among genotypes (or among individuals within genotypes), and that only p can vary in value. Let q(2 - s - t) = 2c, where c is a constant. Then equation (6) can be written as Formula (7) shows that 0 can be expressed approximately as a linear function of k with a regression coefficient equal to -2c. We may choose the value of c to satisfy the relationship, O= c(1-2z),

6 454 Y. HIRAIZUMI where 0 and are the averages of o and of k among genotypes, or among individuals within a genotype. Thus, 0 (1-2k) - 0 (1-2k) (1-2k), or - 20 k. (1-2k) We shall now compute linear regression equations of o on k for several sets of data and determine if the predictions of formula (8) are in agreement. RESULTS Before tabulating and analyzing the data, the k value for each mating was adjusted for the differential viabilities of segregating genotypes. This was done by making control matings, cn bw 0 x Tokyo/cn bw 8 and a1 dp cn bw 0 X Tokyo/al dp cn bw 8, and estimating the viabilities of mutant phenotypes relative to that of the wild phenotype. The results of the following mating types were analyzed. (1) cn bw 9 X x/cn bw 8 mating type, where x is the second chromosome carrying the major or the minor elements of male recombination. Various z chromosome lines were isolated from al dp b PI c px sp/t-007 females. The values of k and o are listed in Table 1 and are shown in Figure 2. (2) cn bw 0 X x/cn bw 8 mating type, where various x chromosome lines were generated in the b pr c px/t-007 females. O.OD- e : *- e e e * e e * e l I *. e

7 MALE RECOMBINATION AND TRANSMISSION FREQUENCY TABLE I A list of the average k and 6 values for the matings, cn bw female x x/cn bw male, where x is either T-007 or one of the recombinant chromasome type generated in T-O07/al dp b pr c px sp females 455 Genotype T-007 a1 + + a1 dp aldpb ++++ c PZSP PXSP SP a1 + SP a1 + PX SP a1 + c PX SP a1 dp + SP a1 dp + PX SP a1 dp + c PX SP a1 dp b + PX SP a1 dp b + c px sp all others+ a1 dp b pr c px sp dp b pr c PX SP b pr c PX SP pr c PX SP a1 dp b pr + a1 dp b pr c + + a1 dp b pr c px + +++prc ++ ++b pr+++ a1 dp b pr + px sp all otherst - k' No. of matings 3, , ,822 Total ,058 The value of 8 was measured between the cn and bw loci. * Average k value after adjusting to the differential viabilities of cn bw and wild phenotypes. + All other multiple crossover types with pr+ (thus carrying the major elements, Mr). $ All other multiple crossover types with pr (thus lacking the Mr elements). Results are listed in Table 2. (3) cn bw 0 X x/cn bw8 mating type, where the x chromosome lines were isolated from the b pr c px/t-o66 females. The results are summarized in Table 3. (4) a1 dp cn bw 0 X x/al dp cn bw 8 mating type, where the x chromosome lines were generated from a1 dp b pr c p x sp/t-007 females. Results are shown in Table 4. The linear regression equation of o on k, weighted by the number of matings for each genotype, was then calculated for each of the four mating types, and these are summarized in Table 5. The regression equation predicted by formula (8) is also shown for each mating type. Table 5 clearly indicates that the agreement between observed and predicted regression equations is very good for each mating type.

8 456 Y. HIRAIZUMI TABLE 2 A list of the average k and 8 values for the matings, cn bw female x x/cn bw male, where x is one of the recombinant chromosome types generated in T-O07/b pr c px females Genotype ++++ b +++ -t- + c p.t +++px b pr c px i- pr c PX b pr++ b prc -I- Total E No. of matings ,923 The value of 0 was measured between the cn and bw loci. * Average k value after adjusting to the differential viabilities of cn bw and wild phenotypes. In the four sets of data above, the regression equations were examined among different genotypes. We now turn to examine the regression equation among individuals within a genotype. There is, however, one technical difficulty. When the regression equation among genotypes is examined, one may easily increase the number of replications for each genotype and thus obtain a large number of progeny per genotype. Hence the environmental and error variation within genotypes can be minimized. However, this can not be done for the analysis among individuals within genotypes. The number of progeny per mating in a culture vial is usually not large (approximately 60), and the resultant sampling errors associated with k and o when measured among individuals can be quite large. This would tend to result in the underestimation of the regression coefficient. TABLE 3 A list of the average k and 8 values for the matings, cn bw female x x/cn bw male, where x is either T-066 or one of the recombinant chromosome types generated in T-O66/b pr c px females Genotype T b c PZ +++PZ + pr c PZ b pr++ b prc + - k' No. of matings I Total The value of 0 was measured between the cn and bw loci. * Average k value after adjusting to the differential viabilities of cn bw and wild phenotypes,

9 MALE RECOMBINATION AND TRANSMISSION FREQUENCY 45 7 TABLE 4 A list of the auerage k and 8 values from the matings, a1 dp cn bw female x x/al dp cn bw male, where x is either T-007 or one of the recombinant chromosome types generated in T-O07/al dp b pr c px sp females - - Genotype k* 0 No. of matings T b c c PZSP b prc ff , b pr c PZSP Total ,452 The value of 0 was measured for the interval between al and bw covering almosst the entire second chromosome. * Average IC value after adjusting to the differential viabilities of al dp cn bw and wild phenotypes. One way to reduce this difficulty would be to transfer successively the parental flies of a mating to fresh culture vials so that the number of progeny per mating could be increased. Such a mating scheme was employed by HIRAIZUMI (1977), and the data reported in that paper can be used for the present purpose. Data are those included in Tables 1 and 2 of that paper, and the average number of progeny per mating was 225. This is shown below. (5) a2 dp cn bw 0 x T-O07/al dp cn bw 8 mating type. Regression equations are as follows: Observed: Predicted: o = (t ) (f ) k o = k The figures within parentheses are twice the standard errors, and the agreement between observed and predicted regression equations is satisfactory. DISCUSSION The results described in the previous section, when considered together, clearly indicate that the observed relationship between k and o among genotypes, as well as among individuals within a genotype, can be satisfactorily explained TABLE 5 Observed and predicted regression equations of 0 on k, 0 := a + bk, for each of the four mating types, (I) to (4), as shown in the text. Observed Predicted Mating type u[*z S.E.) b(*2 SE.) U b (1) ( f ), ( ) (2) ( f ) ( ) (3) ( t0.0120), ( ko.0250) (4) ( fo.0078) ( t0.0172)

10 45 8 Y. HIRAIZUMI by the following simple model: the value of p varies, but the other parameters, 9, s and t, remain constant among genotypes or among individuals within a genotype. Of course, the actual situation may not be this simple. There could be some correlation between p and q, s or t such that when p varies, the other parameters, or at least some of them, may also vary among genotypes. However, the excellent agreement between the two regressions, observed and predicted, suggests that such a correlation, if it exists, should be rather weak, and the negative correlation between k and 0 is mainly due to variation in p values. The p value for a normal male genotype is, of course, zero. Apparently, the male recombination elements operate to increase the value of p. The subsequent events leading to male recombination and/or sperm dysfunction appear to be independent of the activity of the male recombination elements since the values of q, s and t may be considered to be approximately constant among different genotypes. The parameters discussed above are those defined for sperm-the final products. Each of these parameters may actually consist of several events occurring at different developmental stages. For example, the value of 9 may actually be the total of several recombinational events that occurred at different developmental stages. As suggested by HIRAIZUMI et al. (1973), the effects of the male-recombination elements seem to occur in many stages of development causing phenotypic mosaicism, male recombination, and distorted transmission frequency. It may be that the male-recombination elements act as a kind of operator mutation, such that the sequences they control are transcribed through several stages of development. In a male of normal genotype, these sequences would remain suppressed through most developmental stages. The transcribed, or translated, product will then lead the chromosome to undergo a recombinational event. Like the case suggested for the Segregation Distorter (SD) system in Drosophila melanogaster (HARTL 1973), if the transcription takes place during spermiogenesis, it may cause dysfunction of the sperm that contain the male-recombination elements. All stocks used in the present study had the genetic background of the standard cn bw stock; only the second chromosome varied among genotypes. Under these conditions, p was the only parameter that vaned among different genotypes. It is quite possible that under different genetic backgrounds, the other parameters may also be modified, and thus will vary among different genotypes. For example, there may be a modifier that affects only the sperm dysfunction process, or a modifier that changes only the value of q. These will be interesting questions for future studies. I express my heartfelt thanks to JOHN WATSON for his help and many suggestions throughout the course of this investigation. LITERATURE CITED fin, D. L., 1973 Complementation analysis of male fertility among the segregation distorter chromosomes in Drosophila melanogaswr. Genetics 73 :

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