Genetic Dissection of Hybrid Incompatibilities Between Drosophila simulans and D. mauritiana. I. Differential Accumulation of Hybrid Male Sterility Effects on the X and Autosomes

Corresponding author: Yun Tao, Harvard University, 16 Divinity Ave., Cambridge, MA 02138., ytao{at}oeb.harvard.edu (E-mail)

Communicating editor: M. A. F. NOOR

	ABSTRACT

TOP ABSTRACT MATERIALS AND METHODS RESULTS DISCUSSION APPENDIX LITERATURE CITED

The genetic basis of hybrid incompatibility in crosses between Drosophila mauritiana and D. simulans was investigated to gain insight into the evolutionary mechanisms of speciation. In this study, segments of the D. mauritiana third chromosome were introgressed into a D. simulans genetic background and tested as homozygotes for viability, male fertility, and female fertility. The entire third chromosome was covered with partially overlapping segments. Many segments were male sterile, while none were female sterile or lethal, confirming previous reports of the rapid evolution of hybrid male sterility (HMS). A statistical model was developed to quantify the HMS accumulation. In comparison with previous work on the X chromosome, we estimate that the X has 2.5 times the density of HMS factors as the autosomes. We also estimate that the whole genome contains 15 HMS "equivalents"—i.e., 15 times the minimum number of incompatibility factors necessary to cause complete sterility. Although some caveats for the quantitative estimate of a 2.5-fold density difference are described, this study supports the notion that the X chromosome plays a special role in the evolution of reproductive isolation. Possible mechanisms of a "large X" effect include selective fixation of new mutations that are recessive or partially recessive and the evolution of sex-ratio distortion systems.

POPULATION genetics theory predicts that sex chromosomes (X or Y) have unique evolutionary dynamics that differ from the autosomes (HALDANE 1924 ). For example, newly arisen X-linked mutations have a greater substitution rate under selection than autosomal mutations have, provided they are recessive (or partially recessive) and favorable to the heterogametic sex (CHARLESWORTH et al. 1987 ). The higher substitution rate of new recessives that favor the heterogametic sex may hold even for "sexually antagonistic" mutations that are detrimental to the homogametic sex (RICE 1984 ). However, the opposite result is obtained by considering adaptation to a sudden environmental change in which mutations that were previously deleterious and held in mutation-selection balance become beneficial and fixed by selection. In this case, X-linked genes evolve more slowly than autosomal genes, regardless of dominance (ORR and BETANCOURT 2001 ).

If X-linked loci evolve faster than autosomal loci, interspecific trait differences should map disproportionately to the X chromosome (i.e., a "large X" effect). At one time, it was argued that the faster evolution of the X chromosome is a general pattern in Drosophila. "The genes having the greatest effect on hybrid sterility and inviability are X-linked" (COYNE and ORR 1989 , p. 181). This suggestion of a large X arose from classic backcross analyses of hybrid incompatibilities (DOBZHANSKY 1936 ). In all case studies of this kind that followed, the X chromosome shows a disproportionate contribution to hybrid incompatibility. However, as pointed out by WU and DAVIS 1993 , the large X effect could be an observational artifact in this type of experiment due to the hemizygosity of the X chromosome. Although the X chromosome appears to be hosting a disproportionately large amount of hybrid incompatibility, the difference may actually be due to the masking of the recessive incompatibility factors on autosomes. Meaningful comparison of the contributions of the X and autosomes requires an experimental design that removes the confounding effect of dominance and provides sufficient resolution to detect quantitative differences in the density of genetic factors affecting the trait.

As a paradigm of studying the genetics of speciation, the X chromosome in Drosophila simulans and D. mauritiana has been intensively mapped for hybrid male sterility (HMS). Employing an introgression approach, COYNE and CHARLESWORTH 1986 , COYNE and CHARLESWORTH 1989 localized three "major" factors, each closely linked to one visible marker. A major factor is defined as a single locus or a cluster of closely linked loci ("minor" factors) that can cause complete sterility. With additional markers, Wu and co-workers covered the three regions surrounding these major factors (60% of the X chromosome) by more introgressions (PEREZ et al. 1993 ; CABOT et al. 1994 ; PEREZ and WU 1995 ; DAVIS and WU 1996 ). They carefully analyzed a smaller coverage (40% of the X) and mapped nine minor factors (reviewed in WU and HOLLOCHER 1998 ; two factors mapped in 9A–10E are not taken into account due to the relative lower resolution in this region).

Recent genetic analyses of autosomal sterility factors in D. simulans and D. mauritiana hybrids have removed the complications due to dominance by comparing homozygous introgressions on the autosomes with hemizygous introgressions on the X. With this design, HOLLOCHER and WU 1996 suggested a similar density of HMS factors on the X and the second chromosomes, while TRUE et al. 1996B inferred (qualitatively) a higher density on the X than on the two major autosomes. Unfortunately, the genetic resolution of these studies was not fine enough to give a reliable conclusion.

Here we report an introgression experiment designed to finely map HMS factors on the third chromosome with a resolution similar to that on the X chromosome. The basic idea of constructing the introgression lines follows that of TRUE et al. 1996B by tracking P[w⁺]-tagged D. mauritiana fragments in repeated backcrossings to D. simulans. However, several improvements have been made to the original scheme. We were able to estimate the lengths of introgressed D. mauritiana fragments by using 38 allele-specific oligonucleotide (ASO) markers (LIU et al. 1996 ; ZENG et al. 2000 ), as well as the 38 P[w⁺] inserts themselves. The ASO markers were used to identify and produce a set of introgressions that covered the entire chromosome, avoiding a potential problem in the original scheme where selection during backcrossing might have biased against the recovery of introgressions with heterozygous effects in females. Fertility and viability effects of the introgressed segments were carefully assayed as homozygotes in a manner that permits comparison to previously published work on the X chromosome. A statistical model was developed and used to estimate the ratio of densities of HMS factors on the X and third chromosomes as 2.5:1. This result strongly supports the conclusion that the X chromosome plays a special role in the evolution of hybrid incompatibility.

	MATERIALS AND METHODS

TOP ABSTRACT MATERIALS AND METHODS RESULTS DISCUSSION APPENDIX LITERATURE CITED

Experimental design:
A two-stage protocol was used to introgress fragments of the D. mauritiana third chromosome into a D. simulans genetic background (Fig 1). A salient feature of these schemes is to follow the introgression by tagging the D. mauritiana segments with P[w⁺]-inserts, which are semidominant markers with various eye colors (from pale orange to deep red) because of position effects. Usually, the homozygous P[w⁺] flies, with two copies of P[w⁺]-inserts, have darker eyes than heterozygous flies. In most cases, the eye color differences are clear-cut. For convenience, the heterozygous P[w⁺] fly is called "orange eyed" and the homozygous fly is called "red eyed" throughout the text.

View larger version (14K): In this window In a new window Download PPT slide   Figure A1. An example for the pdf of z (Equation A4). The parameters are = 1.0, = 1.0 (for I), ... , = 10.0 (for X).

In stage I, females of sim 1 x 1 JJ, a highly inbred D. simulans stock (LIU et al. 1996 ), were crossed to males of P[w⁺]-insert D. mauritiana males. These P[w⁺]-insert strains were described previously (TRUE et al. 1996A ). Orange-eyed female progeny were then backcrossed to sim 1 x 1 JJ for five generations [backcross (BC)5], by which time approximately one-third of hybrid males were fertile (DAVID et al. 1976 ). For each line, 20–40 orange-eyed males from BC5 were singly crossed to the females of simB, a D. simulans stock visibly marked on the X and the second chromosomes. Using the visible and ASO markers, several sublines for each P[w⁺] insert were selected. All sublines were isogenic for the whole genome except one single introgressed D. mauritiana segment surrounding the P[w⁺]-insert. To maintain these sublines, the hybrid chromosomes were transmitted only through males (Fig 1A).

In stage II, shorter introgressions were made. Most of the sublines from stage I had relatively long (greater than one-third of the whole chromosome) D. mauritiana segments, which might host many HMS factors. For high-resolution mapping, much shorter D. mauritiana segments were developed. From the cross in Fig 1B, 100 or more orange-eyed males were singly mated to simB females. After sublines had been established, recombinants yielding shorter introgressions were identified by genotyping the males with appropriate ASO markers.

A total of 259 introgressions (28 from stage I and 231 from stage II) were selected and kept as the set of lines for various phenotypic assays. Each line was given a serial number in the format ##.##, where the number preceding the dot represents the P[w⁺]-insert and the number following the dot represents one of several sublines tagged by the same P[w⁺]. The cytological positions of all P[w⁺]-inserts used are summarized in the Fig 4 legend. All lines but one (20.11) have just one uninterrupted segment of D. mauritiana introgressed.

View larger version (27K): In this window In a new window Download PPT slide   Figure 2. Testing male fertility of introgression lines. (A) Homozygous introgression males and females were assayed for fertility by mating tests. (B) For the lines tested in A as sterile or lethal, a second-round test was carried out to make sure that sterility or lethality was not caused by spontaneous mutations. The genuine hybrid sterility/lethality should still be observed if testing trans-heterozygous males or females produced by crossing these lines inter se. The two parental lines for each trans-heterozygote were independently derived and were tagged with different P[w+]. Usually, one parental line had a longer introgressed segment that covered the shorter one from the other parental line. Introgressions through females were checked by ASO markers to exclude recombinants. The second chromosome is not shown. Also see the Fig 1 legend.

View larger version (14K): In this window In a new window Download PPT slide   Figure 3. Two ways of measuring male fertility are highly correlated. Individual fertility was assayed consecutively by mating test and sperm motility (sperm index x: 1–4). Progeny counts (y) were transformed in logarithm scale by Log10(y + 0.01). Each individual of the 146 genotypes was checked for appropriate ASO markers to exclude any recombinants from data analysis. An average of 12.2 and 20.9 individuals per genotype were sampled for scoring sperm index and mating test, respectively. The sample size for mating test was larger because some individuals were not observed for sperm motility. The two measures are highly correlated (R2 = 0.62, P < 10-6 after z-transformation; SOKAL and ROHLF 1995 , p. 575) and a logistic curve is well fitted (y = 7.49 - 7.82/(1.41 - 1.53e-x)) (R2 = 0.74, P << 0.001).

View larger version (68K): In this window In a new window Download PPT slide   Figure 4. Homozygous male fertility of introgressions on the third chromosome. Bars represent the introgressed D. mauritiana segments in an otherwise pure D. simulans background. The boundaries for each introgressed segment are defined by ASO markers as well as P[w+]-inserts. Serial numbers of sublines are labeled at the right of bars, with the digits before dots corresponding to P[w+]-inserts (open triangles at top). A total of 218 lines were tested, including 25 lines that had already been made and kept as homozygotes. The ASO markers and P[w+]-inserts are positioned according to polytene bands. Fertile introgressions cover the whole third chromosome except one gap (solid arrow). Males with homozygous introgressions covering this gap had their fertility severely reduced and sired predominantly female offspring (TAO et al. 2001 ). A total of 38 D. mauritiana P[w+]-insert lines were used in this study. These lines have been described before (TRUE et al. 1996A , Table A1): 1 [61CD(I)], 3 [61CD(II)], 4 [62BC], 5 [62E], 6 [63C], 7 [64C], 8 [65A], 9 [65CD], 11 [66D], 12 [66EF], 15 [67BC(II)], 16 [67DE], 18 [69D], 20 [71A(II)], 21 [71F72A], 23 [72EF(II)], 25 [75C(II)], 26 [76C], 27 [78CD], 28 [79F], 32 [83AB], 29 [82A], 31 [82E], 33 [84DE], 45 [93EF], 44 [92E], 42 [91BC], 41 [91A], 40 [90B], 38 [87EF], 37 [86EF], 35 [86AB], 46 [95A(I)], 48 [96E], 49 [97A], 50 [98DE], 51 [99A(I)], and 54 [99D]. Note that the cytological positions are based on the D. melanogaster map. There is an inversion at 84F–93F between D. melanogaster and the D. simulans triad (LEMEUNIER and ASHBURNER 1976 ; indicated by bent arrows facing each other). The cytological locations of 32 and 40 determined by TRUE et al. 1996A were not correct. The current locations of 32 and 40 were inferred from meiotic recombination data obtained in this study: 32 is between 28 and 29, and 40 is distal to ASO marker Akt1 (89B9).

Heterozygous males from all introgression lines were fertile. To remove the confounding effects of dominance, the fertility of each autosomal introgression was assayed in homozygous condition (Fig 2A). Red-eyed homozygotes were produced by crossing orange-eyed males and females of the same line. For each line tested, at least 10 red-eyed males or females were assayed for fertility. Fertility was assayed in a mating test by crossing red-eyed flies of one sex with the tester stock D. simulans w; e, where e (ebony) was used to detect nonvirgins. For each tested individual, the flanking ASO markers on maternally derived D. mauritiana segments were checked to exclude recombinants.

During the introgression process and the later stock maintenance, spontaneous lethal and sterile mutations may have accumulated. Because the introgression chromosomes were transmitted through the nonrecombining male, lethal and sterile mutations may significantly accumulate through Muller's ratchet. Assuming that the lethal mutation rate is 0.005 per chromosome per generation (SIMMONS and CROW 1977 ), the frequency of lethal chromosomes is expected to be 1 - (1 - 0.005)²⁰ = 9.5% in a stock maintained for 1 year (20 generations/year). If the sterile mutation rate is 15% of that of lethals (TRUE et al. 1996B ), then the frequency of spontaneous sterility should be 1.5%. Both amounts are sufficiently high that they cannot be ignored. Thus introgressed lines tested as sterile or lethal by the method in Fig 2A could be due to spontaneous mutations. To address this issue, we retested the sterile and lethal lines by producing trans-heterozygotes from two independently derived lines (tagged by different P[w⁺]-inserts), usually with one shorter introgression nested within the other longer one (Fig 2B). Similar to Fig 2A, the maternal chromosome was checked for ASO markers to exclude recombinants. Introgressions that were lethal or sterile when homozygous, but not when trans-heterozygous, in this test are assumed to carry spontaneous mutations that arose during the course of the experiment. This method tests for mutations in the vicinity of the P-insert and not throughout the entire chromosome.

Drosophila stocks:

• D. mauritiana-1: w (white, 1–1.5 on the D. melanogaster map) is from J. Coyne; this stock was the progenitor for constructing the P[w⁺]-insert lines (TRUE et al. 1996A ).

• D. mauritiana-2: w; P[w⁺], 38 lines of independent inserts on the third chromosome (TRUE et al. 1996A , Table A1); for convenience, we renumbered the lines (see Fig 4 legend).

• D. simulans-1, 13w (white, 1-4.1); D. simulans-2, nt (net, 2-0); D. simulans-3, Ubx/D (Ultrabithorax 3-71, Delta 3-64); D. simulans-4, w; e (ebony, 3-72): These stocks were also provided by J. Coyne. The descriptions of the mutations can be found in LINDSLEY and ZIMM 1992 .

• D. simulans-5: 13w 1 x 1 JJ is a line constructed by sib-pair mating for 20 generations from 13w (LIU et al. 1996 ).

Construction of D. simulans simB: D. simulans is a very polymorphic species in its DNA sequence and so is D. mauritiana, but to a lesser degree (HEY and KLIMAN 1993 ). Due to their recent common ancestry, they share some alleles. To develop molecular markers, it is necessary to make both species fixed for alleles as much as possible. For this purpose, the highly inbred stock 13w 1 x 1 JJ was used. However, this stock is extremely weak. To remedy this problem, we constructed a stock with the third chromosome homozygous and isogenic to that of 13w 1 x 1 JJ, but with the first and second chromosomes potentially heterozygous and derived from several different stocks (D. simulans stocks 1–3 described above). We first obtained female w/w; nt/+; D/+, with the notable characteristic that nt becomes dominant in the presence of D. We then crossed this female to 13w 1 x 1 JJ males and backcrossed the male progeny w; nt/II; D/III to females of 13w 1 x 1 JJ. The stock simB (w; nt; III) was then obtained by pair mating w; nt/II; III. Here, II and III represent the isogenic second and third chromosomes from 13w 1 x 1 JJ. The fourth chromosome was not followed.

Purging of standing lethal and sterile mutations: It is possible that some standing lethal and sterile mutations in the P[w⁺]-tagged D. mauritiana chromosome could be introgressed into the D. simulans background. To avoid this problem, we performed a pseudo-extraction to purge any sterile and lethal mutations in the vicinity of the P[w⁺]-insert. Because of the lack of balancers in D. mauritiana, we can make a segment around the P[w⁺]-insert isogenic in a statistical sense only. Males from P[w⁺]-insert stocks were crossed to w. Single F₁ males were then backcrossed to w. F₂ males and females heterozygous for the P[w⁺]-insert from the same line were crossed. The three genotypes (P[w⁺]/P[w⁺], P[w⁺]/+, and +/+) were counted in the F₃ progeny. Five pair matings of homozygous P[w⁺]-insert (P[w⁺]/P[w⁺]) were set up and their progeny (F₄) counted. Homozygous P[w⁺] individuals in F₃ would be less than expected (25%) if there are linked lethal mutations. Similarly, the number of F₄ progeny would be smaller if male and/or female sterile mutation(s) are nearby. For each P[w⁺] line, 5–10 third chromosomes were extracted. Among the 304 chromosomes extracted, 17 (5.6%) chromosomes (with 14 different P[w⁺]-inserts) were found to be subvital or lethal. Two chromosomes (0.7%) did not produce any viable homozygous P[w⁺] flies at all. Three chromosomes (1%) were detected with sterile mutations. The standing lethal and sterile mutations in the P[w⁺]-insert stocks were therefore 0.01 per chromosome. For each P[w⁺]-insert line, one extracted chromosome line with a combined maximum of viability and fertility was selected for later experiments. All flies were raised with standard cornmeal molasses agar medium at room temperature (21°–24°).

Molecular markers:
ASO markers (SAIKI et al. 1986 ) were used throughout this study. The ASO probes are pairs of 15-mers with the same sequences but one or more species-specific substitutions. Each member of the pair can hybridize specifically to DNA of one species but not the other. The ASO probes were developed using the following steps:

1. From FlyBase (http://flybase.bio.indiana.edu/), known D. melanogaster gene sequences in a particular cytological region were identified. For the most part, exonic sequences flanking intron(s) were used for designing PCR primers.

2. Two stocks, w of D. mauritiana and 13w 1 x 1 JJ of D. simulans, were used as the reference strains for comparing DNA sequences. PCR products from the two species were directly sequenced and checked for nucleotide substitution. Any substitutions except those involving G to C are useful for designing ASO probes.

3. DNA target fragments were amplified by PCR and dot-blotted to N⁺ nylon filter. The filter was probed with ³²P-labeled ASO at appropriate temperatures.

4. Eight individual males from each reference strain were probed to determine whether ASO alleles were fixed in each strain.

At the first stage of the introgression, we used a total of 28 ASO markers, among which 23 had been developed in previous studies (LIU et al. 1996 ; ZENG et al. 2000 ). We made some improvements on 5 of the 23 markers for more sensitive probes. At the second stage, we developed 10 more (Table 1). Unfortunately, two of them, Hsr and kni, were not fixed in all D. mauritiana stocks. A total of 38 ASO markers were used in this study.

Single-fly genotyping:
A single fly was ground in 50 µl grinding solution (10 mM Tris pH 8.2, 1 mM EDTA, 25 mM NaCl, 0.2 mg/ml Proteinase K) in a 1.5-ml Eppendorf tube. After a 15-min digestion at room temperature, the tube was incubated at 95° for >2 min and chilled on ice briefly before being stored at -20°.

PCR reactions were set up with 1 µl DNA extraction prepared as above in a volume of 10 µl reaction mixture [2.5 ng/µl primer mix each, 0.25 units of Taq polymerase, 1x Taq buffer, 1.65 mM MgCl₂, 150 µM dNTP]. The temperature regimes for all ASO markers were the same except the annealing temperatures (Table 1). For a large number of PCR reactions, 96-well plates were used. The PCR product was denatured with 100 µl alkaline solution (0.4 M NaOH, 15 mM EDTA) and transferred to N⁺ nylon filter by using a 96-well dot-blot apparatus. The filter was baked at 80° for >2 hr and then hybridized sequentially with ³²P-labeled species-specific ASO probes. After being washed at a temperature appropriate for each ASO probe, signals from the filter were detected by a Molecular Dynamics (Sunnyvale, CA) phosphorimager.

Fertility assay:
In the mating test, the number of tester females, duration of mating, and ambient temperature may cause variation in progeny counts (data not shown). To minimize this variation, we used a test regime of 1 male (female) x 3 virgin females (males) for 7 (8) days at room temperature. The number of males tested per line has a mean ± SD of 14 ± 12 with a range of 1–111.

For females, fertility was tested by crossing a single virgin female to three D. simulans w; e males (<3 days old). On the eighth day, the flies were cleared. Females still alive were collected for genotyping. Vials in which the female and/or all three males were dead were excluded from data analysis. The progeny were sorted and counted by eye color and sex on the thirteenth, sixteenth, and nineteenth days. The number of females tested per line has a mean ± SD of 7 ± 3 with a range of 1–16. A female was considered fertile if she produced any progeny; otherwise she was considered sterile.

Males (<3 days old) were singly crossed with three virgin females of D. simulans w; e (<3 days old) for 7 days. Females were discarded and males were collected on the seventh day for later genotyping. Offspring were counted by sex and eye color on the thirteenth, sixteenth, and nineteenth days. We included for data analysis only the vials in which the male and at least one female were still alive at the time of collection and the male was the correct genotype. Because the carrying capacity for 7 ml medium in each vial is 100 (rarely >200) flies, this method can be regarded as quantitative for those males with fertility well below 100 flies.

Male fertility classification:
In previous analyses of X-chromosome introgressions, fertility was classified primarily on the basis of sperm motility. DAVIS and WU 1996 defined a sperm index with four classes based on the number of motile sperm present in the seminal vesicles. Classes 1–4 have 0, 1–25, 25–100, and >100 motile sperm, respectively. Introgression lines were classified as sterile, quasi-sterile, subfertile, and fertile, according to sperm index and qualitative results of multiple-male mating tests.

In our study, fertility was estimated primarily from the number of progeny produced in single-male mating tests, because sperm motility is very difficult to measure quantitatively. However, a calibration experiment was conducted to define fertility classes (by progeny number) that are comparable to the classes used by DAVIS and WU 1996 for the X chromosome. In this experiment, both sperm index evaluation and mating tests were performed on males from each of 146 different genotypes. On the seventh day of the mating test, multiple males for each genotype were dissected and the sperm index was scored according to DAVIS and WU 1996 . Fig 3 shows a plot of the average sperm index vs. average progeny number for each genotype. The two measures are well correlated, but some exceptions do occur. For instance, there are genotypes having no detected motile sperm, which nevertheless produced a few offspring and vice versa. However, in this study and in the study of DAVIS and WU 1996 no males had many motile sperm but produced no progeny, against the expectation that behavioral problems (i.e., failure to mate) were a common cause of sterility in the mating test.

Here we use a fertility classification system based solely on progeny number that was designed to be comparable to the sperm index system of DAVIS and WU 1996 : sterile (<0), quasi-sterile (0–10), subfertile (10–45), and fertile (>45 progeny per male tested). Table 2 shows that both the distribution of sperm index values within a fertility class and the average for each class are very similar for the autosome (this study) and the X chromosome (DAVIS and WU 1996 ).

Estimating the lengths of introgressed segments:
The positions of ASO and P[w⁺]-insert as landmarks were ordered on the polytene map of D. melanogaster and segment lengths were estimated as the number of bands between landmarks (HEINO et al. 1994 ). Each introgressed segment of D. mauritiana has up to five landmarks: a central P[w⁺]-insert flanked by a pair of ASO markers on each side. The left boundary of the segment was generated by recombination between the outer member (now a D. simulans allele) and the inner member (still D. mauritiana) of the left pair (and similarly for the right boundary). In some cases, the boundary falls between the P[w⁺]-insert and an ASO marker. For the purpose of length calculation, these boundaries are assumed to lie at the midpoint of the interval defined by each pair of landmarks. Overall, a total of 76 landmarks were used for measuring the introgressions, providing a resolution of 30 polytene bands per landmark. This level of resolution is comparable to that (20 bands) on the finely mapped 40% of the X chromosome (reviewed in WU and HOLLOCHER 1998 ).

Statistics:
The outcome of a male fertility test for an introgression line is determined by the total cumulative HMS effect, which depends on the number of HMS factors residing in the line and the magnitudes of their individual effects. We would like to estimate these quantities from the observations, namely, the lengths of the introgressed D. mauritiana segments and the level of male fertility. More specifically, we wish to estimate the relative densities of HMS factors on the X vs. autosomes. For these purposes, we derived a statistical model to account for the HMS accumulation under the following assumptions: The HMS factors have a Poisson distribution along a chromosome; the effect of each factor follows an exponential distribution; and the effects are additive.

In the Appendix we have shown that the accumulated effect (z) of HMS on an introgressed segment of length L has a probability density function (pdf),

(1)

where and are parameters for the Poisson and exponential distributions, respectively. The notation (z) is a function with a value of 1 when z = 0 and 0 when z 0. The mean and variance for distribution (1) are L/ and 2L/², respectively. The cumulative density function (cdf) of z on an introgression of length L is

which can be obtained numerically.

For estimating parameters in the model, male flies are assigned to one of three classes: fertile when z < ₁, semifertile (quasi-sterile and subfertile) when ₁ < z < ₂, and sterile when z > ₂. The two parameters are the thresholds where fertility shifts classes. Note that fertility classes of quasi-sterile and subfertile are pooled because of their small sample sizes. There are two observations for each line: the length of its introgression L_i and its fertility class s_i (where s_i = S, SF, or F, indicating whether the line is sterile, semifertile, or fertile, respectively, and i = 1, 2, ... , M, where M is the total number of introgression lines tested). We assume that the magnitudes of effect of HMS factors on the X have the same distribution as those on the third (i.e., they share the same but have different 's). The likelihood for all observations O = (s₁, L₁, s₂, L₂ ... s_M, L_M) can be written as

(2)

where M = M_X + M₃. M₃ and M_X are the numbers of introgression lines for the third and the X chromosomes, respectively, while ₃ and _X are the corresponding parameters of the Poisson distribution. For each line, 1 or 0 is assigned to each of the three logical variables S, SF, and F according to the fertility observed.

The five parameters in the likelihood function are not identifiable. However, if one of the parameters (say ₁) is fixed as a scalar, the remaining four parameters can be uniquely determined (identifiable). Although these four parameter values depend on the scalar chosen, the biologically important ratios _X/, ₃/, and _X/₃ are independent of the scalar. Equation 2 obviously can be modified to fit the observations on the X and the third chromosomes separately, as

(3)

where j indexes the X or third chromosomes.

We maximized the likelihood (Equation 2 or Equation 3) by using the observations from the X and third chromosomes either jointly or separately through a Markov chain Monte Carlo (MCMC) technique, using the Metropolis algorithm (GELMAN et al. 1995 , chap. 11). We arbitrarily set ₁ = 1 and chose initial values for the other four parameters (, _X, ₃, and ₂). The parameter estimates that maximize the likelihood functions were obtained from the MCMC after 1000 iterations of burn-ins. In the MCMC simulation, the absolute values of , _X, and ₃ sometimes did not converge well, but the value of ₂ and the ratios of _X/ and ₃/ always converged nicely.

	RESULTS

TOP ABSTRACT MATERIALS AND METHODS RESULTS DISCUSSION APPENDIX LITERATURE CITED

Spontaneous mutations distinguished from hybrid incompatibilities:
Sterility and lethality detected by the protocol of Fig 2A could be due to spontaneous mutations rather than to hybrid incompatibility. The test protocol in Fig 2B was used to distinguish these two situations. If spontaneous mutations arose in independent lines during the course of the experiment, they were unlikely to be allelic to each other. Several lines were found to contain spontaneous mutations: two homozygous male sterile lines (31.1 and 31.2), two homozygous female sterile lines (51.4, 51.11), and seven homozygous lethal lines (16.3, 20.2, 20.7, 20.11, 20.16, 20.23, and 20.25). Since most of the spontaneous mutations were clustered within a particular P[w⁺]-insert line (as indicated by the number preceding the dot in the line name), there may be only four independent mutations (one male sterile in line 31, one female sterile in line 51, and one lethal in each of lines 16 and 20). Thus, for the 38 P[w⁺]-insert lines used in this study, the spontaneous mutation rate is on the order of 2.5% for male or female sterility and is on the order of 5% for lethality.

"Faster male" evolution—much larger accumulation of HMS than of hybrid female sterility:
In this study, we tested 218 introgression lines for homozygous male fertility and 173 lines for homozygous female fertility. Among the 145 lines tested for fertility in both sexes, 67 lines are male infertile (30 steriles, 22 subfertiles, 15 quasi-steriles) while none are female infertile. Thus, there is a clear difference in density of male vs. female hybrid sterility factors. A similar difference in fertility between the sexes was reported previously by TRUE et al. 1996B . However, in the earlier experiment, there was a possible bias because the lines were established by repeated backcrossing of heterozygous females. This protocol may have selected against factors with a heterozygous effect on female fertility. Furthermore, the extent of coverage of the autosomes by introgressions was not determined, so the possible magnitude of selection was unknown. In the experiment reported here, the lengths of introgressions were defined by ASO and P[w⁺] landmarks and it was determined that these segments cover the entire third chromosome, eliminating any possible bias in coverage. Therefore, the density difference in male vs. female sterility is now very well established.

The density of HMS factors on the X is estimated to be 2.5 times higher than that on the third chromosome:
In this study we also observed the lengths of the third chromosome introgressions tested for male and female fertility as homozygotes. In Fig 4, we graphically show the 218 lines tested for male fertility. Similar observations on 265 introgressions, which cover 60% of the X chromosome, were obtained from previous studies (PEREZ et al. 1993 , Figure 4; CABOT et al. 1994 , Figure 5; PEREZ and WU 1995 , Figure 2; DAVIS and WU 1996 , Figure 3). The descriptive statistics are summarized in Table 3. The X chromosome appears to have a substantially higher number and/or larger effects of individual HMS factors than the third chromosome. Only very short introgressions on the X can be fertile and lengths that are sterile on the X frequently are fertile on the third chromosome.

The phenotypic effect on fertility of an introgressed segment depends on two variables: the number of factors and the magnitudes of their effect. Assuming that the number of factors has a Poisson distribution with parameter and that the magnitude of effect has an exponential distribution with parameter , we have derived a distribution of the cumulative effect that incorporates both variables (Appendix) and estimated the parameters with Markov chain Monte Carlo simulations. Since and are confounded in the observations, we assume that is the same for both the X and third chromosomes and estimate the relative densities of factors on these two chromosomes (_X/₃), as well as some other informative ratios of parameters.

Using quite different initial values, the MCMC simulation was run three times, each with 2000 iterations, either jointly or separately for the X and the third chromosomes. The estimates of ₂, _X/, ₃/, and _X/₃ converged very well (Table 4). The average ratio of _X/₃ is estimated as 2.5, which indicates that the X chromosome has 2.5 times the density of HMS factors as the third chromosome.

The number of HMS equivalents in the genome is 15:
An HMS "equivalent" is the minimum value of z (the cumulative negative effect on fertility) required to cause complete sterility (i.e., ₂ in our model). The number of HMS equivalents on a chromosome can be calculated as the expected value of z for the entire length of the chromosome (i.e., L/, where L is the number of bands in the chromosome) divided by ₂. Table 4 shows that the X and third chromosomes each have about five HMS equivalents. Although the X has a twofold higher density of HMS factors, it is about one-half the total length of the third chromosome (L₃ = 2200 and L_X = 981 in polytene bands; HEINO et al. 1994 ). Therefore, the X has roughly the same accumulation of HMS effects as the third chromosome (under our model where the distribution of individual factor effects does not differ between chromosomes). Since the second chromosome is about the same length as the third and the fourth chromosome is tiny, the total number of HMS equivalents in the genome is 15. Similarly, the number of hybrid male semisterile equivalents per chromosome is L/₁ and the total number for the genome is 25.

Each HMS equivalent could be considered as an introgressed D. mauritiana segment, nonoverlapping with other such segments and consisting of a set of "minor" HMS factors that together cause complete sterility. In a companion article (TAO et al. 2003 , this issue), we show by quantitative trait loci (QTL) mapping that the third chromosome contains 19 minor sterility factors. Similarly, 9 minor factors have been mapped on 40% of the X chromosome (WU and HOLLOCHER 1998 ). Thus the total number of the QTL (or minor genes) in the genome is 60 and, on average, every HMS equivalent consists of 4 minor genes (i.e., 60 minor genes/15 HMS equivalents). In other words, 4 minor genes together can cause complete sterility. By the same argument, one semisterile equivalent consists of 2.5 minor genes, which is consistent with the observation that adding one or two minor genes to a semifertile genotype can make it completely sterile (TAO et al. 2003 ).

	DISCUSSION

TOP ABSTRACT MATERIALS AND METHODS RESULTS DISCUSSION APPENDIX LITERATURE CITED

More hybrid male sterility than female sterility and lethality:
The much higher prevalence of hybrid male compared to female sterility and inviability has been reported previously (HOLLOCHER and WU 1996 ; TRUE et al. 1996B ). Here we support the earlier conclusions with some technical improvements in the experimental design. A potential bias against discovering female sterility in the study of TRUE et al. 1996B was removed by defining the lengths of introgressions and covering the entire third chromosome. Also, spontaneous mutations that occur during the experiment were identified and their frequencies account approximately for the low frequencies of female sterility and lethality observed by TRUE et al. 1996B (7 and 5%, respectively). Thus, there is no clear evidence that a single introgression causes female sterility or lethality due to hybrid incompatibility in D. simulans and D. mauritiana. However, there is evidence for an accumulation of minor female sterility factors. In a study by DAVIS et al. 1994 , homozygous introgressions on either the second or the third chromosome were female fertile, but simultaneous homozygosity on both chromosomes resulted in female sterility. Several possible causes of the difference in male vs. female hybrid sterility in Drosophila have been discussed at length in the literature, such as sexual selection for male reproductive characters and special properties of spermatogenesis (WU and DAVIS 1993 ).

Reliability of the large X effect:
A major conclusion of this study is that the X chromosome appears to contain 2.5 times the density of hybrid male sterility factors as the autosomes. Three caveats regarding this conclusion must be considered.

1. The observations on the X-linked and autosomal HMS were made in two different laboratories using different methodologies. The classification of the X-linked introgressions was based largely on sperm motility whereas that for the third chromosome was based on progeny number in mating tests. However, the progeny number classification system used here was designed to give equivalent results for the two systems and the calibration experiment reported here gives no indication of a bias toward detecting more sterility on the X.

2. Furthermore, this caveat concerning different methodologies has been addressed to some extent in the earlier study of TRUE et al. 1996B . In that study, P-element-marked introgressions were made throughout the X and both major autosomes. The fraction of hemizygous X introgressions that were male sterile was 50% greater than the fraction of homozygous autosomal segments. Unfortunately, the lengths of introgressed segments were not estimated directly in the TRUE et al. 1996B study, so the density difference could not be estimated quantitatively from those data and a possible difference in introgression length distributions could not be ruled out. Nevertheless, the TRUE et al. 1996B results qualitatively support the conclusions of the study reported here.

2. The 2.5-fold X vs. autosome difference reported here may be an overestimate due to biased sampling of the X chromosome. The three X chromosomal regions analyzed by Wu and colleagues had previously been implicated as hosting major HMS factors (COYNE and CHARLESWORTH 1986 , COYNE and CHARLESWORTH 1989 ), which could mean that they contain a higher density than the rest of the X chromosome. However, the distribution of sterile introgressions on the X in the study of TRUE et al. 1996B does not support this notion (see their Figure 4). Although there is a suggestion of more sterility near the centromere and less at the distal tip, this is probably an artifact of introgression length. Introgressions near the centromere may tend to be longer because of reduced recombination in that region, while those near the tip are shorter because of the edge effect. Consistent with this interpretation, only two HMS loci are finely mapped in one proximal region (PEREZ et al. 1993 ) while at least one HMS locus is mapped on the tip of the X chromosome (MASIDE et al. 1998 ). A similar pattern is apparent for the third chromosome in Figure 4 of TRUE et al. 1996B , even though genetic analyses indicate a fairly even distribution of HMS factors (TAO et al. 2003 ). Therefore, the sampling bias of the X chromosome may be very slight at most. We also note again that the study of TRUE et al. 1996B showed that the fraction of sterile X introgressions is 50% greater than the fraction of sterile third chromosome introgressions, even though the two chromosomes were sampled by the same methods in that study. Therefore, an excess of HMS factors on the X is supported by both studies, although the quantitative estimate of 2.5-fold reported here may represent an upper limit.

3. The estimate of relative densities on the X chromosome and autosomes depends on an assumption that the distributions of magnitude of effect are the same, which may not be the case. Genes on the X and autosomes have different evolutionary dynamics (CHARLESWORTH et al. 1987 ; ORR and BETANCOURT 2001 ) that may lead to differences in either substitution rates or, possibly, the average effects of mutations that go to fixation. In either case, however, the observation of a difference in the load of HMS factors suggests that the X chromosome may play a special role in the evolution of hybrid incompatibility.

Implications of differential density in HMS factors:
There are two basic interpretations of a higher X vs. autosome density of HMS factors: (1) the rate of substitution of mutations is higher at X-linked than at autosomal loci or (2) the X chromosome contains a higher density of genes that have potential effects on male fertility. In humans, sex and reproduction-related genes seem to be disproportionately represented on the X chromosome (reviewed in SAIFI and CHANDRA 1999 ). However, two lines of evidence suggest that this is not the case in Drosophila. First, mutagenesis screens for male sterility have not revealed a biased distribution between the X and autosomes (LINDSLEY and TOKUYASU 1980 ). Second, there is evidence for a paucity of genes on the X that show male-biased expression (PARISI et al. 2003 ), indicating perhaps a deficiency of male-fertility-related genes on the X relative to autosomes. Therefore, an excess density of HMS factors on the X is most likely due to different substitution rates.

A higher rate of substitution on the X implies that evolutionary divergence leading to reproductive isolation occurs through selection rather than through random drift, because the expected substitution rate for neutral alleles is simply the mutation rate for both X and autosomal genes. However, it is possible that an X vs. autosome bias in mutation rate could result from a sex bias in mutation rate, since the X is overrepresented in the homogametic sex. There is evidence for a higher mutation rate in males for mammals (SHIMMIN et al. 1993 ; MAKOVA and LI 2002 ) and birds (ELLEGREN and FRIDOLFSSON 1997 ), but this would tend to make mutation rates on the X lower than those on the autosomes. In Drosophila, no evidence is found to support a sex-biased mutation rate (BAUER and AQUADRO 1997 ). There is also no evidence for a higher rate of substitution on the X vs. autosomes from sequence divergence studies (BETANCOURT et al. 2002 ), consistent with the notion that a majority of substitutions are neutral.

A higher rate of substitution on the X also implies that certain types of selection may occur more frequently than others. For example, population genetic theory shows that the substitution rate of newly arisen X-linked mutations is higher than that of new autosomal mutations, provided that the mutations are recessive or partially recessive (CHARLESWORTH et al. 1987 ). However, the opposite result is obtained by considering adaptation to a sudden environmental change in which mutations that were previously deleterious and held in mutation-selection balance become beneficial and fixed by selection. In that case, X-linked genes evolve somewhat more slowly than autosomal genes, regardless of dominance (ORR and BETANCOURT 2001 ). Thus, observation of a higher rate of substitution on the X would seem to favor the fixation of new mutations rather than the fixation of standing variation in the evolution of reproductive isolation. Perhaps a change in the direction of selective effect on a mutation is unusual, even though there are some well-documented cases, such as industrial melanism in moths (KETTLEWELL 1973 ).

If the estimated X vs. autosome ratio of 2.5:1 for HMS accumulation is equivalent to the relative fixation probability for newly arisen favorable mutations (R_X in CHARLESWORTH et al. 1987 ), we can derive some speculations about the degree of dominance of those mutations. Assuming a simple situation where selection is acting equally on the two sexes and d is the degree of dominance, R_X is roughly (2d + 1)/4d, showing that R_X > 1 when d < 0.5 (recessive or partially recessive mutations). Similarly, for genes expressed only in the heterogametic sex, as may be the case for a majority of male fertility genes, R_X is 1/2d. Thus, a value of d = 0.2 gives the R_X = 2.5 estimated here. This calculation implies that advantageous mutations fixed for spermatogenesis are moderately recessive.

The invasion of sex-ratio meiotic drive and its subsequent suppression is an additional mechanism that could account for the large X effect, as well as the rapid evolution of male (relative to female) hybrid sterility found in Drosophila. When the X and Y chromosomes in the heterogametic sex are not recombining (as is usually the case), sex-linked segregation distorters can invade the population more readily than autosomal ones can (FRANK 1991 ; HURST and POMIANKOWSKI 1991 ). Since sex-ratio distortion is not stable, suppressors (often autosomal) may also invade the population readily, rendering the distortion cryptic. Multiple cycles of distortion and suppression may occur, leading to genetic divergence that is distributed on both the X and autosomes, but tending to be more heavily represented on the X where the distortion initiates (unless multiple autosomal suppressors are required for each X-linked distorter). This genetic divergence may lead to sterility through disturbance of spermatogenesis in hybrids when the cryptic systems may become unsuppressed. The prevalence of this mechanism is not clear yet, but two apparent cases of cryptic sex-ratio drive in D. simulans (DERMITZAKIS et al. 2000 ; TAO et al. 2001 ) and another in D. pseudoobscura (ORR and PRESGRAVES 2000 ) have been reported. In one case, a suppressor is also causing hybrid male sterility (TAO et al. 2001 ). An attractive aspect of this meiotic drive theory is that it predicts a faster evolution of factors affecting the heterogametic sex, consistent with Haldane's rule. Indeed, a recent literature survey appears to show that there is faster female evolution in Lepidoptera, which have heterogametic females (PRESGRAVES 2002 ).

If selective fixation of recessive mutations is the predominant cause of the "larger X" effect on HMS, we might also expect to see such an effect on other kinds of traits. However, if it is due to a more specialized mechanism such as the evolution of meiotic drive systems, the effect may be more restricted to traits related to spermatogenesis. The following summary of studies in Drosophila and Lepidoptera indicates that more work is needed to determine whether a large X effect occurs for other traits.

In Drosophila, a larger X effect is not clearly evident for traits other than hybrid male sterility (CHARLESWORTH et al. 1987 ). In some cases a larger X effect has been suggested for behavior (e.g., TAN 1946 ; EWING 1969 ; KAWANISHI and WATANABE 1981 ; KYRIACOU and HALL 1986 ; reviewed by REINHOLD 1998 ) and for morphology (e.g., TEMPLETON 1977 ; VAL 1977 ). However, the evidence is not strong because the level of genetic resolution in most studies is low and the number of genes affecting any one trait also may be low. In a relatively high-resolution study of interspecific divergence in genital morphology between D. simulans and D. mauritiana, the X was not overrepresented. About 10% (2/19) of QTL were on the X (ZENG et al. 2000 ), whereas the X represents 20% of euchromatic DNA. The morphological trait analyzed in that study (size and shape of the genital arch) represents the only qualitatively distinct morphological difference between those species.

There is stronger evidence for a large X effect on behavioral and morphological traits in Lepidoptera (reviewed by SPERLING 1994 ; PROWELL 1998 ; also see recent cases in JIGGINS et al. 2001 ; NAISBIT et al. 2002 ). Unlike Drosophila where the X chromosome is large, the X chromosome in Lepidoptera is generally very small, accounting for only 3% of the genome. Therefore, it appears unlikely, just by chance, that out "of a total of 77 traits, 39% are X-linked, 10% are maternal or Y-linked, and 51% are autosomally inherited" (PROWELL 1998 , p. 311). Many of these studies confound dominance with hemi/homozygous effect in comparing the X and autosomes, but even so, the degree of dominance would have to be considerably <0.20 to account for the large overrepresentation of the X. Unfortunately, there are no detailed genetic dissections of hybrid sterility in Lepidoptera, so we do not know whether a large X effect on that trait prevails in species where the female is heterogametic.

The results of the study reported here support the notion that X-linked genes play a special role in the evolution of reproductive isolation in Drosophila. Two possible mechanisms are the evolution of sex-ratio distortion systems and selective fixation of advantageous recessive mutations. Additional work on the generality of the large X effect across different traits and groups of organisms is likely to provide further understanding of these mechanisms.

	FOOTNOTES

² Present address: Monsanto Company, 800 N. Lindbergh Blvd., N2NA, St. Louis, MO 63167.

	ACKNOWLEDGMENTS

We thank Lynn Stam, Kristen Inoue, Jermaine Fuller, Lixia Jiang, and Jing Zhang for technical support during this study; J. A. Coyne for stocks; A. W. Davis and C.-I Wu for communicating on measuring male fertility; and D. A. Barbash, N. A. Johnson, C. H. Langley, S. V. Nuzhdin, M. Turelli and the UC Davis Evolution Discussion Group, J. Blumenstiel, R. J. Kulathinal, C. Castillo-Davis, C. Meiklejohn, J. Parsch, and J. Ranz for critical reading of various drafts of this article. We are grateful to two anonymous reviewers whose suggestions have improved this article in various aspects. We also thank Cecelia Laurie for advice on the MCMC technique. Y.T. thanks R. Fehon, D. Kiehart, J. Mercer, M. Rausher, and M. Uyenoyama for guidance. Y.T. was a recipient of a Catherine Stern Dissertation Year Fellowship of Duke University. This work was supported by National Institutes of Health grants 47292 and 65169.

Manuscript received January 22, 2003; Accepted for publication March 21, 2003.

	APPENDIX

TOP ABSTRACT MATERIALS AND METHODS RESULTS DISCUSSION APPENDIX LITERATURE CITED

STATISTICAL MODEL FOR THE ACCUMULATION OF HYBRID STERILITY
The model:
We make the following assumptions:

1. The number of discrete HMS factors (N) on a unit length of chromosome (one polytene band here) has a Poisson distribution with mean :
   

   

2. The magnitude of effect of each factor (w) varies as an exponential distribution with a mean of 1/:
   

   

3. The parameters and are homogeneous along the whole length of the chromosome (i.e., no hot spots). The cumulative effect (z) on a unit length of chromosome is
   

   (A1)

The pdf and cdf of z can be derived as described below:

The moment-generating function of z is

(A2)

The pdf of z is derived by taking a result from SEARLE 1971 (p. 49): For a noncentral ² distribution ²(n, ), the pdf is

with a known mgf,

(A3)

Comparing (A2) and (A3), let n = 0 and s = t/2 and introduce a function (u) (STUART et al. 1999 , p. 243):

The pdf of u, where u = 2z, is

Therefore, the pdf of z is

(A4)

From (A2), the expectation and variance for z are / and 2/², respectively. As an illustration, some pdf's of (A4) are shown graphically (Fig 1). (A4) is essentially a summation of Poisson(k|) x Gamma(z|k,) on k from 1 to infinity plus e^-(z):

In practice, we are more interested in the distribution of the hybrid sterility factors on the introgression with a length of L. For this, we substitute by L and the distribution of z has expectation and variance of L/ and 2L/², respectively.

Proof:
To prove that (A4) is the correct pdf of z, we use the Laplace transformation to show that LT[f(z)] = mgf of z, because by definition,

We have the Laplace transformation

Then,

and

Therefore, from (A4) we have

which is (A2), therefore proving that (A4) is the pdf of z.

If we assume that w has a Gamma distribution,

by the same derivation from (A1) to (A4), we have the distribution for z:

(A5)

We note that (A5) is essentially the same model as that intuitively proposed to account for mutation accumulation along a chromosome (KEIGHTLEY and OHNISHI 1998 , Equation 2). For this distribution, E(z) = /ß and Var(z) = (1 + )/ß². If E(z) and Var(z) can be estimated from mutation accumulation, the number of mutations (U) and their mean effect () can be obtained,

It is clear that U = E(z). However, without knowledge of the shape (defined by ) of the Gamma distribution of z, U and cannot be estimated reliably. For the assumption of equal eff