MARTIN L. TRACEY. Division of Biological and Medical Sciences, Brown University, Providence, R. I

Transcription

1 SEX CHROMOSOME TRANSLOCATIONS IN THE EVOLUTION OF REPRODUCTIVE ISOLATION* MARTIN L. TRACEY Division of Biological and Medical Sciences, Brown University, Providence, R. I Manuscript received May 1, 1972 Revised copy received June 19,1972 ABSTRACT Haldane s rule states that in organisms with differentiated sex chromosomes, hybrid sterility or inviability is generally expressed more frequently in the heterogametic sex. This observation has been variously explained as due to either genic or chromosomal imbalance. The fixation probabilities and mean times to fixation of sex-chromosome translocations of the type necessary to explain Haldane s rule on the basis of chromosomal imbalance have been estimated in small populations of Drosophila melanogasier. The fixation probability of an X chromosome carrying the long arm of the Y(X.YL) is approximately 30% greater than expected under the assumption of no selection. No fitness differences associated with the attached YL segment were detected. The fixation probability of a deficient Y chromosome is 300% greater than expected when the X chromosome contains the deleted portion of the Y. It is suggested that sex-chromosome translocations may play a role in the establishment of reproductive isolation. N organisms with cliff erentiated sex chromosomes, hybrid sterility or invia- I bility is generally expressed more frequently in the heterogametic sex than in the homogametic sex. This widely applicable observation is known as Haldane s rule (HALDANE 1922). For example, interspecific crosses in the genus Drosophila have produced viable and fertile F, females (homogametic sex) in approximately forty percent of the cases studied. The F, males (heterogametic sex) from these crosses were inviable or sterile in 100 of the 101 cases reported (EHRMAN 1962). Furthermore, F, male sterility has been observed in intraspecific crosses between semispecies of Drosophila paulistorum (PEREZ-SALAS and EHRMAN 1971 ) and between geographic strains of Drosophila birchii (AYALA 1965 and BAIMAI 1970). Two alternative, though not mutally exclusive, explanations of Haldane s rule have been proposed. The first, which may be called the genic imbalance theory, ascribes heterogametic inviability or sterility to the differential modification of sex-linked genes which are necessary developmental complements of genes in the autosomes or the Y chromosome (HALDANE 1922; MULLER 1940). The second explanation of Haldane s rule (HALDANE 1932) was based on Stern s experiments with X-Y translocations (STERN 1929 and 1936) and may be termed the chromosomal imbalance theory. Stern produced an X-Y translocation stock of Drosophila * Research supported by PHS Grants GM and GM Genetics 72: October 1972.

2 318 M. L. TRACEY melanogaster. The Y chromosomc of this stock was deficient, and the missing arm of the Y chromosome was attached to the X chromosome. Since all of the Y chromosomal material was present, this stock was fertile inter se. On the other hand, crosses between males from the translocation stock and females from a normal stock of flies produced sterile F, males. Haldane suggested that this type of chromosomal translocation might explain most of the heterogametic hybrid sterility or inviability observed. Chromosomal rearrangements involving the sex chromosomes have occurred in many different groups of organisms, particularly in those organisms where sex determination is of the balance type (LEWIS and JOHN 1963 and 1968). Nevertheless, the processes by which these rearrangements become fixed in populations have not been studied. The simplest evolutionary scheme of %eterogametic sex sterility, in accordance with the chromosomal imbalance theory would be as follows: Part of the Y chromosome is translocated to the X chromosome in the germ line of a male and the resulting X.Y product is transmitted to his female progeny. (Male progeny which receive the deficient Y chromosome will be inviable or sterile.) The homozygous viability of such X.Y chromosomes depends on the position of the break points (NICOLETTI and LINDSLEY 1960), and the X.Y chromosome may become fixed in a finite population if it is not seriously detrimental in the homozygous state. Once this X.Y chromosome is fixed, or reaches a high frequency in the population, genes on the Y chromosome which are covered by the translocation may subsequently be lost without detriment. Such deficient Y chromosomes may become fixed in the population. The loss of genes may occur either through partial deletion of the covered segments of the Y or through accumulation of nonfunctional point mutations (NEI 1970). Natural populations analogous to Stern s translocation stocks might arise in this manner. In organisms where the Y chromosome contains sex-determining loci, the model suggested here is only plausible when the translocated segment of the Y chromosome does not include the sexdetermining loci. To test some aspects of this hypothetical scheme, experiments were conducted with X- Y translocations in Drosophila melanogaster. The two experiments were specifically designated to estimate both the fixation probability and the mean time to fixation of an X.Y chromosome and a Y chromosome consisting of a centric fragment. The experimental results were then compared with the theoretical expectations. Some experimental work has been done to test the applicability of stochastic theory to gene frequency changes (KERR and WRIGHT 1954a, b; WRIGHT and KERR 1954; BURI 1956). However, no studies of the fixation probabilities or fixation times of genes or chromosomes represented only once in the initial populations have been reported. In the experiments reported below, all of the experimental populations were initiated with either the X.Y or the Y fragment present in only a single individual. This was done to simulate the mutational origin of such chromosomes. Since the populations studied were, of necessity, very small, the approximation to the natural situation was rather poor. Nevertheless, the present study does add a new element to the available data dealing with stochastic changes of gene or chromosome frequencies.

3 SEX CHROMOSOME TRANSLOCATIONS 319 MATERIALS AND METHODS Chromosomes: In order to facilitate scoring, chromosomes with visible markers were used in all experiments (LINDSLEY and GRELL 1968). The X.Y chromosome used was yfcar.yl. Since the Yfi segment was not marked, a doubly inverted X chromosome (yscs1zn49 wsca) was used as the analogue of the normal X. Due to the almost complete suppression of recombination, this allowed scoring of the Y portion of the X.Y chromosome by identification of the X-associated markers. The Y chromosome from the (y sr31zn49 w sc8) or "winscy" stock was used as the normal Y, and a YS centric fragment carrying the normal allele of yellow, y+, served as the analogue of the deficient Y. In the following the X, X.Y, Y and YS chromosomes will be designated by X, X', Y and Ys respectively. The markers associated with these chromosomes allow phenotypic identification of all genotypes: XX-yellow, white; XX-yellow; X'x'- yellow, forked, carnation; XY-yellow, white; X'Y-yellow, forked, carnation; and XYS-forked, carnation. Since T(X.Y) stocks are occasionally unstable (MULLER 194.9), the following crosses were made at the outset of the experiment to confirm the expected effects of these chromosomes on male fertility: (1) XX? x X'YS$ 8, (2) X'X'P? x XY$ 8, (3) XX'?? x X'YS8 8, (4) XX' 0 0 X XY 8 8. As expected the XYS males from crosses (1) and (3) were sterile, while all other progeny were fully fertile. Progeny from crosses (3) and (4) were collected and used to initiate the experiments. Experimental populations: Small populations were used to estimate fixation probabilities, because both time and facilities were limited. This, however, should pose no serious problem in extension of the estimates to larger populations as long as the fitness relationships remain constant. One hundred and fortyfour populations consisting of 4 XY males, 3 XX females, and a single XX' female were set up to detennine the probability of fixation of the X' chromosome. One hundred and twenty-nine replicate populations were set up to estimate the probability of fixation of the YS chromosome. As in the X' set, the YS chromosome was present in the initial populations at the lowest possible frequency; these populations consisted initially of 4 X'X' females, 3 X'Y males and a single X'YS male. Population size in these vial cultures was artificially held equal to eight. The parents were allowed to mate and lay eggs for seven days, and were then discarded. Their progeny were scored on the thirteenth day. Male parents for the next generation were collected from the progeny population by selecting the first four males scored. Female parents were selected by collecting virgins whose genotypes were identical to those of the first four females scared. This technique was followed over all generations in both the X' cultures where there were three female genotypes and in the YS cultures where all females were X'X'. Populations in which the X' or YS chromosome was either lost or fixed were discontinued. For the remainder of this paper the various combinations of parental genotype frequencies will be called states and denoted by a combination of a two digit number and a three digit number separated by a semi-colon. The first two digits represent the numbers of XY and X'Y parental males, while the three digits after the semi-colon refer to the number of XX, XX' and X'X' female parents respectively. In the Ys experiments the first two digits designate the numbers of X'Y and X'YS males. RESULTS The frequency distributions of the X' chromosome in these populations for generations 0 to 17 are given in Table 1. Populations in which the X' chromosome was either lost or fixed are recorded separately from those in which it had been lost or fixed in a previous generation. The distribution of chromosome frequency reached approximate stable form very rapidly. The distributions from generations 5 to 17 were almost identical, although the absolute frequencies declined every generation. In the absence of selection the expected number of generations

4 320 M. L. TRACEY TABLE 1 The distribution of the number of X chromosoms in each generation among the N=8 uial populations Generations X ffrequency I , Lost in a given generation Previouslylost Fixed in a given generation Previously fixed Ne ,...,,.... The total number of replicates was reduced by one in generations eight and fourteen. An insufficient number of flies, less than four males and females, had emerged by the thirteenth day in both cases and these populations were arbitrarily classified as extinct. This problem was not encountered in any of the other populations. required for the stable distribution of chromosome frequency to be reached is more than 2Ne generations where Ne is the effective population size (KIMURA 1955). Ne was estimated over the first eight generations as the product of the expected to observed variance ratio and the actual population size, (Si/S;)N, for the segregating populations. The estimated Ne increases rapidly over this period from a low of 4.8 in the first generation to approximately 7 in the last four generations for which Ne was estimated. The harmonic mean of Ne is approximately 6.4. The expected time to distributional stability is therefore more than 13 generations, which is more than twice the observed time of approximately 6 generations. The frequency distributions for the Ys chromosome are given in Table 2; as in Table 1, populations which were lost or fixed in a given generation are recorded separately from those lost or fixed in previous generations. The mean frequency of the Ys chromosome increased dramatically in the first generation and the frequency was maintained at a high level thereafter. As in the X experiment the estimated Ne shows an apparent positive correlation with mutant chromosome frequency; the harmonic mean of Ne over the first four generations is approximately 2.1. In this case the Ys chromosome was fixed or lost so rapidly, that it is impossible to determine the number of generations required for attainment of the stable chromosome frequency distribution.

5 ~~~~ ~ SEX CHROMOSOME TRANSLOCATIONS 32 1 TABLE 2 The distribution of the number of YS chromosomes in each generation among the N=8 uial populations Generat YS frequency Lost in a given generation Previously lost Fixed in a given genera tion Previously fixed Ne I , I Relative Fitnesses: The data in Tables 1 and 2 are presented in the form of chromosome frequency distributions for populations of constant size, N=8. However, the entire progeny populations of all vials was examined each generation. Genotype fitnesses can be estimated from both sets of data since the parental genotype frequencies as well as the genotype frequencies for both the total population of progeny and the randomly selected set of four males and four females were known. Two components of fitness were estimated separately for males and females from various parental populations or states: 1) fertility and 2) viability (zygote to census age survival). The estimation procedures used were straightforward, but tedious. A single example will be sufficient to illustrate the method. Relative male fertility (fxp/fxpy) was estimated from the eight population states composed of both male genotypes and a single female genotype. The female progeny produced by such states may readily be attributed to specific matings, SO that the relative male fertilities can be estimated from these states. Consider, for example, female state 400, and let ~ Z(XX)$+~ and n(xx ) t+l be the frequencies (numbers) of homozygous and heterozygous zygotes among the progeny. Since all parental females are XX, the zygotic frequencies depend solely on the frequencies, N(.) t, and fertilities, f, of the parental males. Furthermore, the genotypic frequencies of the female progeny, N(.) t+l, may be accurately represented as the product of the zygotic frequencies and viabilities. Thus, n(xx)t+1= fxyn(xy)t N(XX)t+1= uxxn(xx>t+1 n(xx >t+1= fx*yn(x Y)t N(XX )t+1= vxrn(xx )t+1 Combining these expressions, the relative fertility of XY to X Y is estimated by -- fxp _N(XX )t+l N(X Y) t UX X fx Y N(X X )t+l N(XY)t UXX Similarly, we have for female state 004 fn _N(XX),+l N(X Y)t UX X, and -- for female state 040 fx Y N(X X )t+l N(XY)t uxx

6 322 M. L. TRACEY TABLE 3 Relative fitnesses estimated from the X chromosome fixation experiment and the YS chromosome fixation experiment FERTILITY VIABILITY FITNESS Relative fitness XY/X?Y xx/xxt X~Xf/XX~ X YS/X Y t i f C i Total 0.94 i k 0.09 {N= k Total {N= Where no standard error is given, estimates were computed from single state data. * Data used were from a separate experiment where no N=8 counts were available (TRACEY, 1971). The N(.) s denote the numbers of flies of the parenthesized genotypes, the f s and U S the fertilities and viabilities of the subscripted genotypes, and the subscripts t and tl-i identify the parental and progeny generations respectively. To compute these relative fertilities, populations of identical state were collected over all generations and the progeny genotype frequencies were calculated. The differences, if any, attributable to generations have been ignored, because there were too few replicates of most states in any given generation to provide meaningful frequency estimates. Independent estimates of the female viability from states 40;040 and 04;040 were employed to correct for differential female viability in estimating relative male fertility. Estimates of relative viability and fertility are presented in Table 3. Where values from more than a single state were calculated, only the mean weighted by the number of states is given. The tabulated fitness estimates show that the XY males had a higher fitness than the X Y males, and that this was due primarily to their higher fertility. The relatively large values of the standard errors associated with both fxy/fx,y and fx,yn/fx,y are mainly due to the female-state dependency of relative male fertility. For example, in the X experiments fxy/fx,y was 3.10k0.58 for state 400, that is when all females were XX. When all females were heterozygous, state 040, the estimated relative fertility was 0.96i-0.17; and when all females were homozygous for the X chromosome the estimated relative fertility was equal to 0.41 t0.01. Male fertility clearly depends on female state in these populations. In the Ys experiments reported here and in experiments designed to test the relative mating ability of X Y and X Ys flies (TRACEY 1972), the advantage of X Ys males is seen to be dependent on the frequency of the Ys chromosome and this dependency increases the magnitude of the standard errors associated with the relative fertility estimates in Table 3. Both the XX and X X females were less viable and less fertile than their heterozygous counterparts over all states and they were approximately equal to each other. Female fitness was overdominant.

7 SEX CHROMOSOME TRANSLOCATIONS 323 Cage populations containing equal numbers of X and X chromosomes (set 1) or X and X chromosomes from which the YL arm had been removed by recombination (set 2) were initiated in order to assess the effect on fitness of the attached YL segment. Two replicates cages were initiated with 200 males and 200 females per cage at Hardy-Weinberg frequencies, and an initial X-chromosome frequency of 0.5. The cages were maintained for ten generations on a discrete generation schedule and a11 adults were classified each generation. The mean population size was 2046 * 118 in the set 2 cages where the X chromosome did not carry YL, and 2553*329 in the set 1 cages where the YL was present on the X. The mean frequency of the X chromosome was 0.44k0.01 in set 1 while the equivalent frequency in set 2 was 0.45*0.02. Similar replicate populations were initiated at X chromosome frequencies of 0.2 and 0.8 and followed for a number of generations. All of the populations converged toward an equilibrium frequency of approximately 0.45 ( TRACEY, unpublished data). Under the assumption of overdominance, the expected equilibrium frequency of the X chromosome may be calculated from the fitness estimates of Table 3. The observed convergence of chromosome frequency 0.42 Exp f (X ) = 0.42 i = 0.53 and the close agreement between observed and expected equilibrium frequencies (even where the YL arm has been detached) provide a strong argument for acceptance of the overdominant fitness model and for the hypothesis of no YL effect on fitness. Two cage populations were maintained as a check on the fitnesses estimated from the Ys experiments as well. These cages were initiated with 500 males and 500 females at equal Y and YS chromosome frequencies, and maintained on a discrete generation schedule. Over the 32 generations during which these cages were polymorphic the population size was approximately 2,000 in each cage. The frequency of the YS chromosome reached 0.90 by the third generation in both cages and was maintained at or above this level until the Y* chromosome was fixed in both cages. The Ys chromosome was fixed in both cages between generations 26 and 30. The frequency of the Ys chromosome was maintained at approximately 0.97 * 0.01 over roughly twenty-five generations. Since the relative fertility of X Y and X YS males is frequency dependent, 0.97 is most probably the stable equilibrium frequency of the Ys chromosome. And it seems reasonable to suggest that the fixation of this chromosome was due to drift rather than to selective fixation. Again, the cage studies are in good accord with the relative fitnesses estimated from the small populations. Estimation of the probabilities of fixation and mean times to fixation: As noted above, the frequency distribution of the X chromosome reached approximate steady state much earlier than expected under the assumption of no selection. It is of interest to see how the observed distribution deviated from the theoretical one in each generation. The theoretical distribution was computed under the hypothesis of no selection by using the Markov chain method of probability theory, In the present case any population of four males can be classified into

8 324 M. L. TRACEY one of the five different states, 0, 1, 2, 3, and 4, according to the nuniber of X chromosomes present. Similarly, any population of four females can be classified into one of nine different states. Therefore, there are 45 possible states with a population of four males and four females. We denote by sij the state of a population where i X chromosomes are present in males and i X chromosomes are present in females. If there is no selection, the transition probability from state sij in one generation to Smn in the next generation (pijmn) can be obtained by where Piimn = piim.pii.n m Pijm- = 2 (z,)(i/zn,) (I-i/2Nf) N~-k (2) k=o (j/nm) nz-k (I -i/n,) *+ and Nf and N, represent the number of females and males respectively. Therefore, if the initial state frequencies are given, the state frequencies in the tth generation can be computed by the method of matrix multiplication. These state frequencies are easily converted into the chromosome frequency distribution required. Computations were done on an IBM 360 computer. Both experimental and expected means and variances of chromosome frequency in segregating populations ere presented in Figure 1. The expected values were computed for the case of no selection using the Markov chain method outlined above. The results show that the means and variances of the chromosome

9 SEX CHROMOSOME TRANSLOCATIONS 325 frequency increased in the early generations of the experiment, as theoretically expected (KIMURA 1955). However, the increase was more rapid than expected for both the mean and variance. The mean frequency of the X' chromosome is considerably higher than expected until generation thirteen. It is lower than expected during the last four generations of the experiment. Similarly, the variance is initially larger than expected, and it is smaller than expected in seven out of the last eight generations. While these shifts must be interpreted cautiously due to the decline in absolute frequency, they are predictable on the assumption of an overdominant fitness model. STATE 22:400 b5& STATE 31;310 Ne = 4.4(61) OBSERVED EXPECTED 0 BS E RVE D EXPECTED STATE 31 ;400 Ne = 6.7(44) n BS E RVE D L FIGURE &.-Frequency STATE 40;310 Ne = 4.8(78) n EXPECTED 0 BSE RVE D EXPECTED distributions of the X' chromosome for various states. The expected distributions were computed for the neutral case and the effective population sizes were estimated from ratios of the expected to observed variances. The number of replicate popukations for each state is given in parentheses after the effective population size estimate. All of the state comparisons are significantly different from the neutral expectation (P < 0.005) except state 31;040 for which 0.6 < P < 0.7.

10 326 M. L. TRACEY The effects of selection may be readily seen in Figure 2. Here the observed and expected X chromosome frequency distributions are compared for five parental states. The two dimorphic female states (40;310 and 31;310) show an increased X frequency which may be attributed to female overdominance. This effect is not observed in the monomorphic states at the same X frequency. In these states the X-chromosome frequency increases, apparently owing to the higher fertility of XY males with XX females mentioned above. The X frequency distributions for parental state 31;040 are in good agreement, perhaps because this state is close to the theoretical chromosome frequency equilibrium point and XX females show little mating preference. It has previously been reported that experimental data of this type may exhibit a dependence of Ne on gene or chromosome frequency (BURI 1956). A dependence of this type may be seen in the estimates of Ne in Figure 2 as well as in those recorded in Table 1. The positive correlation between X frequency and Ne observed in these experiments reflects a clear departure from the binomially predicted frequency distribution. Comparison of the estimates of Ne for different genotypic states at identical chromosome frequency (22;400 us 31 ;310 and 31;400 us 40;310) shows that Ne is smaller for the dimorphic female states. This is due, in large part, to the higher fitness of XX females. Clearly the actual distribution is compounded of binomial elements with associated genotypic fitnesses which may vary from state to state. The probability of ultimate fixation and the average time until fixation may be compared with their expectatioiis in the absence of selection. For the neutral case the probability of ultimate fixation, u(x ), is equal to the initial X chromosome frequency. In the present experiment it is The average time until fixation, T( I), in generations, is equal to approximately 24 generations (4N,; KIMURA and OHTA 1969). The average time until loss, T(O), is approximately 5 generations [(2N,/N) log, (2Ne)]. The computer simulations confirmed these theoretical expectations for the case of neutral genes or chromosomes. The fixation experiment or the X chromosome was not continued until all populations were either lost or fixed. Therefore, it was necessary to estimate u(x ), T (1) and T(0) by assuming that the rates of loss and fixation after generation 17 were equal to the mean rates during the period of approximate steady state, generations 5 to 17. The probabilities of ultimate loss and fixation obtained in this manner are and respectively. The observed fixation probability is approximately 30% higher than expected. The estimated times to loss or fixation were 7.6 and 15.8 generations respectively. Thus the time until loss is longer than the expected time, while the time until fixation is shorter than the expected time. Since the fitness relationships are overdominant, these discrepancies are not surprising, and the fixation probabilities and mean times to loss and fixation should be compared with the expectations under selection. Dominance of a favorable allele or chromosomn invariably increases its probability of ultimate fixation above that of the neutral case. However, for over- dominant situations the probability of ultimate fixation may be either smaller or greater than that predicted for the neutral case (ROBERTSON 1962). In general

11 SEX CHROMOSOME TRANSLOCATIONS 32 7 the direction of the deviation depends on the equilibrium gene frequency. If it is higher than about 0.4, the probability of fixation is higher than for the neutral case where this probability is equal to the initial frequency (NEI and ROYCHOUD- HURY, unpublished). If the equilibrium frequency is lower than this value, the probability of fixation is reduced. In these experiments the probability of ultimate fixation, u(x ), was estimated to bc approximately 30% greater than the expected value in the absence of selection. On the other hand, u (X) was estimated to be about 5% smaller than expected. The average time until fixation for the X chromosome was decreased by 30 %, while that of the X chromosome was increased by 30%. Since the equilibrium frequency of the X chromosome was approximately 0.45, these changes in U and T are in qualitative agreement with the predictions of an overdominant model. Ys chromosome frequency distributions can be computed by the Markov chain method. In this case only males are considered and selection is easily incorporated into the model by adjusting chromosome frequency prior to computation of the transition matrix. The expxted means and variances of Ys chromosome frequency in the segregating populations are plotted in Figure 3 for all generations of the experiment. The expectations were computed by assuming no selection. The observed means and variances plotted in Figure 3 were calculated for the segregating populations. From Table 2 and Figure 3 it is clear that the X Ys males were relatively more fit than the X Y males. The mean frequency of the Ys chromosome increases dramatically in the first generation and remains at a high frequency in the segregating populations. The drop in frequency observed G E N E R A T I O N FIGURE 3.-The means (circles) and variances (triangles) of the YS chromosome frequency in segregating populations. The solid lines represent the data from the fixation experiment, and the dashed lines represent the expected values in the absence of selection.

12 A ~ OBSERVED NEUTRAL FREQUENCY MAT I NG STATE 13;004 A 'A Ne = 3.1(35) OBSERVED NEUTRAL FREQUENCY MAT I NG STATE 22; OBSERVED k P, NEUTRAL FREQUENCY MAT I NG N = 1.4 (47) e STATE 31;004 FIGURE 4.-Frequency distributions of Ys chromosomes among the progeny of the three segregating male states. The expected distributions under neutral, frequency-dependent and matingsuccess selection models are presented for comparison. The expected distributions for these models were computed by adjusting the YS chromosome frequencies according to fitness estimates given in the text. The observed distributions are all different from the expected distributions (P < 0.001). The number of replicate populations for each state is given in parentheses after the effective population size estimate.

13 SEX CHROMOSOME TRANSLOCATIONS 325 at generation 7 is due to the low number (2) of segregating populations remaining. The large, but relatively constant, variance of chromosome frequency reflects the rapid rate at which these populations were lost or fixed. Expected Ys frequency distributions were computed for three different models over the three polymorphic male states: no selection, frequency-dependent selection, and differential mating success. The latter two models need not be distinct; they are separated here to emphasize that the estimates were obtained from separate experiments. For the selection models relative fitness estimates from the Ys fixation experiment were used in the frequency-dependent case (4.58 for state 31;004, 2.34 for state 22;004 and 1.67 for state 13;004), and estimates from a mating success experiment (TRACEY 1971) were used in the case of differential mating success (1.88 for state 31;004, 3.25 for state 22;004 and 2.64 for state 13;004). The observed and three expected distributions are given in Figure 4. x2 tests show that the fit to the observed distributions is poor for all three models (P < 0.001). The explanation of these discrepancies is, at best, tentative; however, it has been suggested that they are due to changes in female mating preferences which are induced by etherization (TRACEY 1971). Probabilities of ultimate loss and fixation as well as the average number of generations to loss or fixation may be directly estimated from the Ys fixation experiment. The theoretical probabilities of loss and fixation of the Ys chromosome are equal to the initial frequencies of the Y and Ys chromosomes for the neutral model, that is 0.75 and 0.25 respectively. The observed probabilities were u(y) = = (30/129) and u(y8) =0.767 = (99/129) respectively. The fertility advantage of X Ys males discussed above allows prediction of the high U (Y ) value; however, it is clear from examination of Figure 4 that simple selection models do not adequately account for the observed high rates of both loss and fixation. The same difficulty is encountered in comparing the observed and expected mean times to fixation. The average time to loss, T( 0), is 1.53; while the expected value in the absence of selection is Since, by all estimates, the X Y males were not as fit as the X YS males, the observed 40% reduction in time to loss is surprising. The observed and expected values of T( 1) were 1.90 and 4.37 respectively, and the X Ys males are, indeed, seen to reach fixation more rapidly than expected for the neutral case. It should be pointed out that these estimates of fixation probabilities were obtained from experiments conducted according to a two step model. The fixation of the X.YL chromosome occurs first. Subsequently, a deficient Y chromosome, complimented by the X-borne duplication, appears and eventually becomes fixed. It is conceivable that both steps occur concomitantly. That is the XYL and deficient Y chromosomes may be present simultaneously with the normal X and Y chromosomes. Preliminary experiments (TRACEY, unpublished results) indicate that overlap of the two phases of the model does not qualitatively affect the results reported here. DISCUSSION In the experiments reported above the X (X.YL) chromosome exhibited over-

14 330 M. L. TRACEY dominance with respect to the cormal X chromosome for both viability and fertility, and a similar fitness relationship holds for the X chromosome from which the YL arm has been detached. Thus, the observed overdominance is unrelated to the translocation, and it is most likely due to the presence of the double inversion carried by the X chromosome. This may be due to either cumulative genic overdominance (HALDANE 1957) or associative overdominance (OHTA and KIMURA 1970). However, the distinctions between these theoretical alternatives are unimportant due to the small size of these populations and the rapid rates of loss and fixation in these populations. More importantly the presence of the YL segment does not have a detectable effect on fitness. Since X Y males carry a duplication of the YL arm, their reduced fertility may possibly be attributable to the presence of the duplication. However, X Y males show higher fertility than XY males in monomorphic X X populations (TRACEY 1971). Thus, the duplication does not appear to reduce fertility. On the other hand, both the X and Y chromosomes may contain genes which have sex-limited expressions. This is certainly true for the Y-linked fertility factors, and the observed frequency-dependent selection may be due to interactions between sexlimited loci. WRIGHT (1969) has shown that gene interaction produces frequency-dependent selection. Of course, such selection can occur in the absence of gene interactions under certain conditions. At any rate, it is quite conceivable that the operation of natural selection in X-Y translocation systems is considerably more complicated than it is for single genes. In the introduction it was pointed out that the sterility or inviability of the heterogametic sex has been explained by both genic and chromosomal inbalance theories. HALDANE (1922) argued that the observed excess of the homogametic sex was due to the death or sexual transformation of the heterogametic sex. His explanation was an sttempt to account for both phenomena; he attributed the preponderance of disturbances in the heterogametic sex to the requirement of nearly complete linkage in this sex where more than one factor affects sexual development. NEI ( 1969) expanded this suggestion and presented mathematical models for the evolution of sex chromosomes based on the requirement of tight linkage where sex determination depends on more than a single locus. He showed that where sex is determined by a reasonably large number of linked loci, each of which may have pleitropic effects, the opportunity for the accumulation of sex-limited interspecific differences is enhanced due to the number of loci involved. Crosses between species where one or more of these sex-linked loci have been lost or modified may then produce heterogametic inviability, sterility, or sexual transformation because the heterogametic sex receives only the sex chromosome of active elements from the homogametic parent. MULLER ( 1940) accepted and clarified HALDANE S genic imbalance explanation by emphasizing the physiological aspects of balance. He pointed out that many species-specific sex-chromosome loci are more strongly expressed than are similar autosomal loci, because many of these loci are recessive. In interspecific F, heterogametic hybrids these loci will be, unlike the autosomal loci, as strongly expressed as in the parental species. Consequently, these sex-linked loci will often

15 SEX CHROMOSOME TRANSLOCATIONS 33 1 be reflected in sex-chromosome-autosome imbalance. Feeling that such a mechanism was more important than translocational sterility, MULLER rejected HAL- DANE S second explanation which was based on sex chromosome translocations. Certainly, there are significant differences between genic and chromosomal mutations particularly with regard to the action of selection (JOHN and LEWIS 1966). For genic mutations at IOW frequencies, natural selection is generally ineffective. Chromosomal mutations, on the other hand, are subjected to the selective sieves of meiosis and mitosis very early in their history. Therefore, it is not surprising that most heritable variation within breeding groups is genic. However, species and often race differences are recognizable at the karyotypic level as well as at the genic level. In the genus Drosophila intraspecific chromosomal polymorphism is confined, in general, to paracentric inversions which do not necessarily reduce the fitness of heterozygotes due to the nonchiasmate nature of meiosis in males and the survival of only inner products in female meiosis. Examination of interspecific differences, on the other hand, shows that at least fifty-four fusions and thirty pericentric inversions have been fixed during the evolution of the species in this genus (PATTERSON and STONE 1952; WALLACE 1959). Chromosomal or genic mutations which are not well tolerated in the heterozygous condition, e.g. reciprocal translocations, seem appealing candidates for the formation of systems which may lead to the production of sexual isolation. However, if self-fertilization is not possible, such mutations generally have a very small probability of establishment (WRIGHT 1941). There is, however, a type of chromosomal rearrangement which is not subject to the severe selective strictures emphasized by WRIGHT, but which can produce hybrid inviability or sterility: sex chromosome translocations. While the universality of X-Y translocation type hybrid sterility or inviability is certainly equivocal, such a mechanism appears to have been incorporated in many groups of organisms (LEWIS and JOHN 1963). A number of Drosophila species exhibit Y polymorphism which may play a role in race differentiation. For example, Drosophila birchii is polymorphic for the Y chromosome-three types, the X chromosome-four types, and the IV chromosome-two types (BAIMAI 1969). Strains from Rabaul, New Britain and Cairns, Australia produce sterile male hybrids with the strains from New Guinea except Daru, when either parent is from Rabaul or the male parent is from Cairns (AYALA 1965; 1970 and BAIMAI 1970). The X and Y chromosomes from Rabaul and Cairns are unique to these populations, and the Daru Y is also unique (BAIMAI 1969). Furthermore, sexual isolation between these populations has been demonstrated even where the karyotypes are indistinguishable. This complex of populations is composed of genetically (chromosomal and genic) diverging groups. Since many of the interspecific karyotypic differences observed are deleterious in the heterozygous condition, most authors have ascribed their presence in natural populations to the effects of random genetic drift in small isolated populations (e.g., WHITE 1968 and CARSON 1970). Such explanations are clearly necessary for many of the rearrangements observed. Nevertheless, the present

16 332 M. L. TRACEY work indicates that some sex-chromosome translocations may be fixed much more readily than autosomal reciprocal translocations, because they do not reduce the fitness of their carriers or of their offspring. They do, however, reduce the relative fitness of hybrid matings, and may provide a selective basis for strengthening of reproductive isolation. I wish to express appreciation to Dr. MASATOSHI NEI for advice and criticism throughout the course of this work. I also wish to thank Dr. JAMES F. KIDWELL, Dr. BRUCE R. LEVIN, Dr. FRAN- CISCO J. AYALA and Mr. JEFFREY POWELL for helpful criticism of the manuscript. LITERATURE CITED AYALA, F. J., 1965 Sibling species of the Drosophila serrata group. Evolution 19: , 1970 Speciation in an Australian group of sibling species of Drosophila. Symposio International De Zoofilogenia 1 : BAIMAI, V., 1969 Karotype variation in Drosophila birchii. Chromosoma 27: , 1970 Additional evidence on sexual isolation within Drosophila birchii. Evolution 24: 14Q BURI, P., 1956 Gene frequency in small populations of mutant Drosophila. Evolution 10: CARSON, H. L., 1970 Chromosome tracers of the origin of species. Science 168: EHRMAN, L., 1962 Hybrid sterility as an isolating mechanism in the geiius Drosophila. Quart. Rev. Biol. 37: HALDANE, J. B. S., 1922 Sex ratio and unisexual sterility in hybrid animals. J. Genet. 12: , 1932 The Causes of Evolution. Longmans, Green and Co., London. -, 1957 The conditions for coadaptation in polymorphism for inversions. J. Genet. 55: JOHN, B. and K. R. LEWIS, Chromosome variability and geographic distribution in insects. Science 152: KERR, W. E. and S. WRIGHT, 1954a Experimental studies of the distribution of gene frequencies in very small populations of Drosophila melanogaster. I. Forked. Evolution 8: , 1954b Experimental studies of the distribution of gene frequencies in very small populations of Drosophila melanogaster Aristapedia and spineless. Evolution 8: KIMURA, M., 1955 Solution of a process of random genetic drift with a continuous model. Proc. Natl. Acad. Sci. U.S. 41: KIMURA, M. and T. ORTA, 1969 The average number of generations until extinction of an individual mutant gene in a finite population. Genetics 63: LEWIS, K. R. and B. JOHN, 1963 Chromosome Marker. J. and A. Churchill, Ltd., London. -, 1968 The chromosomal basis of sex determination. Intern. Rev. Cytol. 23: LINDSLEY, D. L. and E. H. GRELL, 1968 Genetic Variations of Drosophila melanogaster. Carnegie Inst. Wash. Publ MULLER, H. J., 1940 Bearings of the Drosophila work on systematics, pp In: The New Systematics. Edited by J. S. HUXLEY. Clarendon Press, Oxford. -, 1949 The use of rearranged X s and Y s in facilitating class work with Drosophila. Drosophila Inform. Serv. 23: NEI, M., 1969 Linkage modification and sex difference in recombination. Genetics 63: , 1970 Accumulation of nonfunctional genes on sheltered chromosomes. Am. Naturalist 104:

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