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Inversion length and breakpoint distribution in the Drosophila buzzatii species complex: is inversion length a selected trait?

There is a long history of theoretical models and empirical tests dealing with the relationship between inversion length and the processes generating and maintaining paracentric inversions in the Drosophila genus. Wallace (1954) and Crumpacker and Kastritsis (1967) first proposed a relationship between length and success of inversions and postulated that rare inversions were generally short while well-established inversions were at least moderately long. Olvera et al. (1979) tried to confirm this relationship in D. pseudoobscura, and showed that rare inversions were more often short than polymorphic and widespread ones (see also Ruiz et al. 1984 for similar results in D. buzzatii). Moreover, Van Valen and Levins (1968) fit length data from a selected subset of inversions of the Drosophilidae family to different theoretical models. They found a deficiency of small inversions with respect to a uniform breakage probability model. Krimbas and Loukas (1980) in D. subobscura and Brehm and Krimbas (1991) in D. obscura found a deficiency of small and large inversions when compared with the expectations of the same model. All these results seem to indicate that moderately sized inversions are favored by natural selection.

Distribution of inversion breakpoints has also been subjected to extensive study. Position of breakpoints can be considered in two different ways: (1) as the chromosomal band in which the break occurs (band location); and (2) as the relative position along the chromosome. According to band location, non-random distribution of breakpoints and hot spots with repeated breaks have been observed in several Drosophila species (Krimbas and Loukas 1980; Tonzetich et al. 1988; Lemeunier and Aulard 1992), but not in D. pseudoobscura (Olvera et al. 1979). The distribution of breakpoints with regard to relative position seems also to be nonrandom in Drosophila, with regions near the centromere showing more breaks (Tonzetich et al. 1988; Krimbas and Powell 1992).

Obviously, length and position of breakpoints are related and must be studied simultaneously. Information on both is essential to understand the processes underlying the origin and success of chromosomal inversions. However, none of the previous studies has considered these two variables at the same time. In addition, all studies have been carried out either using a single species (D. pseudoobscura, Olvera et al. 1979; D. subobscura, Krimbas and Loukas 1980; D. obscura, Brehm and Krimbas 1991; D. melanogaster, Lemeunier and Aulard 1992), or lumping together heterogeneous data from many species (Van Valen and Levins 1968; Tonzetich et al. 1988). In the former case, fixed inversions cannot be analyzed and compared. In the latter, the observed patterns may be difficult to interpret. Furthermore, none of the previous studies has tested for the effect of the species (or its phylogenetic affinities) on the length of inversions.

The Drosophila buzzatii species complex is a closely related set of 12 species belonging to the mulleri subgroup of the Drosophila repleta species group. Eleven formally described species have been ascribed to the buzzatii complex (Wasserman 1992; Ruiz and Wasserman 1993; Tidon-Sklorz and Sene 1995). In addition, the populations of D. serido of central-western Brazil (D. serido IV) very likely represent a separate, and as yet undescribed, species (Tosi and Sene 1989; Silva and Sene 1991). All buzzatii complex species have similar basic karyotypes consisting of four pairs of almost equal-length acrocentric autosomes, one pair of dot autosomes, a long acrocentric X, and a Y chromosome. Its chromosomal phylogeny has been established by comparing the banding patterns of the various species and also by the observation of the polytene chromosomes in many interspecific hybrids (Ruiz and Wasserman 1993). Results fully congruent with the proposed chromosomal phylogeny have been obtained by sequencing the mitochondrial cytochrome oxidase genes of eight of the 12 species (Spicer 1995) and by comparative gene mapping between D. buzzatii (one of the species in the complex) and D. repleta (the reference species for all cytological studies in the group) (Ranz et al. 1997). The complete and reliable record of its extant inversion polymorphism and chromosomal evolution, and the availability of a sample of inversions induced in D. buzzatii by introgressive hybridization (Naveira and Fontdevila 1985), makes this complex a suitable species set for the study of the evolutionary sequence from the origin to the fixation of inversions.


This study is based on the 86 inversions described so far in the D. buzzatii species complex (Ruiz and Wasserman 1993; Kuhn et al. 1996) and 18 inversions induced in a laboratory strain of D. buzzatii by introgressive hybridization with D. koepferae (Naveira and Fontdevila 1985). According to their evolutionary success, naturally occurring inversions were grouped as fixed, polymorphic, or rare. Only those inversions found in all individuals of one or more species were considered fixed. Polymorphic inversions are those segregating within a species in at least two different localities. Inversions fixed in one species but segregating in a different one (2[f.sup.2], 2[e.sup.7, and 2[t.sup.6]) were also considered polymorphic. Finally, inversions found in only one locality, and usually in very low frequency, were considered rare (Ruiz and Wasserman 1993). Physical length and position of breakpoints were determined using maps of the polytene chromosomes of the buzzatii complex species (Ruiz and Wasserman 1993) and the original descriptions of the inversions. These maps are a cut-and-paste reconstruction of the D. repleta polytene chromosomes (Wharton 1942) from which these species differ by a small number of inversions (Ruiz and Wasserman 1993). The full data set is available from the authors upon request.

Relative length of each inversion (l) was measured as the distance between the two breakpoints divided by the total length of the chromosome. Two different kinds of analysis were carried out. First, different classes of inversions were compared using analysis of variance and non-parametric tests. Second, observed length distributions were compared to those predicted by four theoretical models that assume different breakpoint distributions. The four models are: (1) Uniform Breakage Probability Model: assumes that distribution of breakpoints of inversions is uniform along the chromosome (Federer et al. 1967; Van Valen and Levins 1968); (2) Van Valen and Levins' Model: a truncated version of the previous model, with very short inversions (l [less than] 0.1) being excluded (Federer et al. 1967; Van Valen and Levins 1968); (3) Non-uniform Breakage Probability Model: derived from the first model by relaxing the assumption that the probability of a break is uniform along the chromosome; it allows for unequal break probabilities in different regions of the chromosome, although it assumes that breaks distribute uniformly inside each region (see Appendix for its derivation); (4) Truncated Non-uniform Breakage Probability Model: derived from the third model, it excludes very short inversions (l [less than] 0.1).

The positions of inversion breakpoints were analyzed as the relative distance from each break to the centromere (relative position) and as the chromosomal band where the break is located (band location). For the study of the relative position of breakpoints, chromosomes were divided into three regions (proximal, central, and distal), each one-third the total length; and the observed number of breakpoints in each region was compared to a uniform distribution. The study of the band location of breakpoints was limited to chromosome 2, which harbors 61 out of the 86 inversions described in the buzzatii complex. Using the usual procedure (Tonzetich et al. 1988; Lemeunier and Aulard 1992), chromosome 2ab, the putative ancestral sequence of the buzzatii complex (Ruiz and Wasserman 1993), was divided into 74 equal-length segments, and the number of breakpoints in each segment was recorded. The number of segments is arbitrary, but large enough for the expected number of breakpoints per segment to approximate a Poisson distribution.


Length of Inversions

To evaluate the factors associated with inversion length we carried out a log linear analysis (Sokal and Rohlf 1995) with length, chromosome, and evolutionary success as variables. Only the interaction between length and success was significant (G = 29.10; df = 5; P [less than] 0.001). The chromosome does not have an effect on inversion length, i.e. inversions on different chromosomes have similar lengths. Interaction between chromosome and success was not significant either: fixed, polymorphic, and rare inversions have a similar distribution in the different chromosomes, with a marked accumulation of inversions in chromosome 2 in all three cases.

Figure 1 shows the length distribution of fixed, polymorphic, and rare inversions. The differences between them are obvious. Analysis of variance showed significant differences in length between the three types of inversions (F = 5.74; df = 2, 83; P = 0.005). Post hoc comparisons using Newman-Keuls test showed that mean length of rare inversions is significantly lower than that of polymorphic (P = 0.004) and fixed inversions (P = 0.025). Polymorphic and fixed inversions do not have significantly different means (P = 0.59), but very different variances (Levene's test: F = 9.12; df = 1, 60; P = 0.004).

Polymorphic and rare inversions can be assigned to each species and their length can be compared among them. Analysis of variance showed significant differences in length between species for polymorphic inversions (F = 5.29; df = 9, 33; P [less than] 0.001) but not for rare inversions (F = 0.66; df = 7, 16; P = 0.70). To ascertain how the total variation among species is distributed among and within the three species clusters (stalkeri, martensis, and buzzatii) of the buzzatii complex (Ruiz and Wasserman 1993), we carried out a nested analysis of variance (Harvey and Pagel 1991). Results were unequivocal: the between-clusters level accounts for no variance, and all variation in inversion length is explained by the between-species (within clusters) level (Table 1). When the number of polymorphic inversions per species, rather than species, was used as the independent variable, a significant negative correlation between length and number of polymorphic inversions was found [ILLUSTRATION FOR FIGURE 2 OMITTED]. This correlation explains 39% of the variance in inversion length and persists when considering only inversions of chromosome 2 (r = -0.59; P [less than] 0.001). Species with many polymorphic inversions tend to have smaller inversions than those with fewer inversions.

Length distributions of the three types of inversions were compared to expected length distributions predicted by the four theoretical models (Table 2). Naturally occurring inversions (fixed, polymorphic, and rare) do not fit the uniform breakage probability model, not even after truncation of very short inversions (Van Valen and Levins' model). Except for rare inversions, the elimination of inversions of length less than 0.1 significantly improved fit of observed distributions to expected ones (Table 2). Fixed and polymorphic inversions, besides the deficiency of very short inversions, show a paucity of long and an excess of medium-sized inversions. Rare inversions present an excess of short inversions. When the non-uniform breakage probability model is considered, length distribution of polymorphic inversions shows an excellent fit to the expected truncated distribution (Table 2). Nevertheless, although different probabilities of breaks are considered, fixed inversions do not fit the non-uniform breakage probability model.
TABLE 1. Nested analysis of variance to test for differences
between clusters and between species (within clusters) in length
of polymorphic inversions.

Source of variation    SS      df     MS       F         component

Between clusters      0.0775    2   0.0387   0.73           0%
Between species       0.3715    7   0.0531   5.63(***)   58.9%
(within clusters)
Within species        0.3114   33   0.0094               41.1%

*** P [less than] 0.001.

Distribution of Inversion Breakpoints

The distribution of breakpoints according to relative position is given in Table 3. While rare inversions fit a uniform [TABULAR DATA FOR TABLE 2 OMITTED] distribution, significant differences between observed and expected distributions of breaks are found for fixed and polymorphic inversions. Breaks tend to accumulate in central regions of chromosomes. Further, for fixed inversions, breaks occur significantly more often in proximal regions than in distal regions (Table 3).

The distribution of the 122 inversion breakpoints according to their band location among the 74 segments established in chromosome 2 is shown in Table 4. When compared to the Poisson distribution a significant departure was found. Breakpoints are clustered, with segments that accumulate up to eight breaks and many segments showing no breaks at all. In several cases breaks fall apparently in the same chromosomal band. There are four bands with four (C6a, D1g, D5a, and E2e), one band with five (F6a), and one band with eight breakpoints (F2a). Considering that there are approximately 280 bands in chromosome 2, given a random distribution of breaks, the probability of a band having four, five, or eight breaks is 0.0014, 0.0001, or 4 [multiplied by] [10.sup.-8], respectively. When inversions were grouped according to evolutionary success, the breakpoint distribution of fixed inversions deviated significantly from the Poisson distribution, but those of polymorphic and rare inversions did not. However, when polymorphic and rare inversions were grouped, their distribution of breakpoints also departed significantly from the Poisson distribution (Table 4).


Inversions Induced by Introgressive Hybridization

The distribution of the 18 induced inversions among the five chromosomes is homogeneous (G = 7.29; df = 4; P = 0.12), and contrasts with that of naturally occurring inversions (Ruiz and Wasserman 1993). The mean length ([+ or -] SD) of induced inversions, 0.327 ([+ or -] 0.183), differs significantly from that of rare inversions (F = 9.29; df = 1, 40; P = 0.004) but not from that of polymorphic (F = 1.31; df = 1, 59; P = 0.26) or fixed inversions (F = 2.28; df = 1, 35; P = 0.14). Induced inversions, unlike natural inversions, fit the uniform probability model, with or without truncation of small inversions (Table 2). In addition, the relative position of their breakpoints did not show differences among the distal, central, and proximal region of chromosomes (Table 3).


Our statistical analysis of the paracentric inversions of the D. buzzatii complex corroborates that inversion length is not a neutral trait, and provides strong support for the hypothesis that medium-sized inversions are favored by natural selection (Krimbas and Powell 1992). Successful inversions (fixed and polymorphic) show an accumulation of medium-sized inversions (0.1 [less than or equal to] l [less than or equal to] 0.4), while rare inversions are predominantly short. Furthermore, when polymorphic inversions are subdivided into two groups, polymorphic widespread and polymorphic endemic, according to whether they are present in more than or less than 25% of sampled localities of each species, significant differences in length are found (F = 18.53; df = 1, 41; P [less than] 0.001). Widespread are closer to fixed inversions, whereas endemic are closer to rare inversions [ILLUSTRATION FOR FIGURE 1B OMITTED]. Selection seems to generate a nearly gradual change in length, from small to medium sized, between less and more successful inversions.

Neither fixed nor polymorphic inversions fit the uniform breakage probability model (Table 2). Polymorphic inversions fit the truncated non-uniform breakage probability model. Fixed inversions do not, although fit improves significantly when the distribution of breakpoints is considered. Therefore, there exists a strong relationship between the nonuniform distribution of breakpoints and the observed length distribution. Figure 3 shows the expected proportion of breakpoints in the central region of chromosomes for inversions of different lengths. Medium-length inversions will show more breaks in the central region of chromosomes than expected [TABULAR DATA FOR TABLE 4 OMITTED] at random, as observed in our fixed and polymorphic inversions. On the other hand, for small inversions only a slight excess of breaks in the central region of chromosomes is expected, as observed in our rare inversions. So, two sources of evidence - that of length differences and that of different proportions of breakpoints in the central region of chromosomes among inversion classes with different evolutionary success - reinforce the hypothesis that selection is actively determining the length distribution of inversions.

Our sample of inversions induced by introgressive hybridization fit the uniform breakage probability model and their breakpoints did not show a regional clustering along the chromosomes. These results agree with that of Federer et al. (1967) with inversions induced by X-ray treatment and those of Tonzetich et al. (1988) with breaks induced by [Gamma]-irradiation. One could reasonably conceive that rare inversions would represent a sample of newly arisen inversions. However, they differ significantly in length from our sample of induced inversions and do not fit the uniform breakage probability model. Most rare inversions are probably not recently arisen, but rather have been floating in nature for a long time (Olvera et al. 1979). Seven of our rare inversions have been detected only once in the intensively studied species D. buzzatii and can be described as unique (Ruiz et al. 1984). Their mean length approximates to that of induced inversions and their length distribution does not differ from that of the uniform breakage probability model (G = 1.46; df = 4; P = 0.23) [ILLUSTRATION FOR FIGURE 1C OMITTED]. Thus, these could be representative of new inversions. The remaining 17 inversions are endemic to a single or a few localities, but probably have persisted there for many generations.

How could the relationship between length of inversions and their success be explained? First, the longer aft inversion, the higher the expected frequency of double crossing over within the inverted segment. Thus, selection is expected to operate against long inversions due to the semisterility of heterokaryotypes (Sturtevant and Beadle 1936; Navarro et al. 1997) and also due to the disruption of coadapted gene complexes. Second, the initial selective advantage of a newly arisen inversion is proportional to the epistasis between the trapped genes and their recombination rate (Charlesworth and Charlesworth 1973). To be highly successful, an inversion must usually have a minimum size, both to capture at least two epistatic genes and to capture genes separated by enough recombination rate. These two counteracting factors could explain the observed selection favoring medium-length inversions. Accordingly, small inversions would have only a relatively slight selective advantage that allows them to persist for a long time in the populations but not to increase in frequency or spread to a larger portion of the species range.

In our study a significant negative correlation between inversion length and number of polymorphic inversions per species was found. This pattern, not reported previously in the literature, seems to hold true over a wide taxonomic range of Drosophila species (M. Caceres, A. Barbadilla, and A. Ruiz, unpubl. data). How can we account for it? In some cases, in D. subobscura and other species, two nonoverlapping inversions in the same chromosome almost completely inhibit recombination in the region between them (Krimbas and Loukas 1980; Krimbas 1992). Thus, the recombination-reducing effect of an inversion occurring in a chromosome already segregating for another inversion may be much greater than expected by its length and span over the entire segment encompassing both inversions. In such cases, small inversions could be favored by selection and the average length of polymorphic inversions would decrease.

The distribution of inversion breakpoints was studied as band location and as relative position. This allowed us to differentiate between content properties (those related with size, organization, or particular DNA sequence of each band) and positional properties (those related with the overall organization of chromosomes and selection for specific inversion length) as factors affecting the distribution of breaks (Tonzetich et al. 1988). Selection of small- and medium-length inversions could explain the accumulation of breakpoints in the central region of the chromosomes (Fig. 3). In addition, natural inversions breakpoints tend to concentrate in the proximal more than in the distal third of the chromosome. Such a pattern, found also in other species (Tonzetich et al. 1988; Krimbas and Powell 1992), could be explained by the deleterious effect of simultaneous crossovers in the inverted and proximal segments of an heterokaryotype, which favors inversions located near the centromere (Navarro et al. 1997). On the other hand, the non-random distribution of breakpoints according to band location is not surprising. Wasserman (1992) already noted that within the repleta group, although 208 inversions have been described, only 323 different breakpoints have been recorded. Moreover, in other species of Drosophila similar results have been found (Tonzetich et al. 1988; Krimbas and Loukas 1980; Lemeunier and Aulard 1992). Our analysis suggests that content differences between chromosomal segments cause the non-random distribution of breakpoints. Either the particular organization of DNA or target sites of break-producing agents could be involved. Transposable elements have been shown to induce chromosomal rearrangements in laboratory experiments with Drosophila (Lim and Simmons 1994). However, their implication in the generation of natural inversions remains unclear. To date, the molecular characterization of natural inversion breakpoints has provided no evidence of the action of transposable elements (Wesley and Eanes 1994; Cirera et al. 1995). In the buzzatii complex, bands C6a, D1g, D5a, E2e, F6a, and F2a are clear candidates for breakage hot spots. Further studies at the molecular level will allow their characterization and the distinction between the processes proposed for the generation of inversions.


We wish to thank sincerely A. Navarro for his computer assistance and H. Naveira for his introgressive hybridization data. We also thank A. Berry and A. Caballero for discussion of results and two anonymous referees for their valuable comments. Work was supported by a FI fellowship from the Comissionat per a Universitats i Recerca (Generalitat de Catalunya, Spain) to MC and grant PB95-0607 from the Direccion General de Investigacion Cientifica y Tecnica (Ministerio de Educacion y Ciencia, Spain) awarded to AR.


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Here we derive the formulae of the non-uniform breakage probability model. Consider a chromosome of length N sites (e.g., base pairs). Let [p.sub.1], [p.sub.2], and [p.sub.3] be the probabilities of a break to occur in the distal, central, and proximal regions, respectively, each of one third of the chromosome ([Sigma][p.sub.i] = 1). The probability of a break to occur at a given site within each of these regions is [p.sub.1]/(N/3), [p.sub.2]/(N/3), and [p.sub.3]/(N/3). The density probability function of an inversion of length L depends on the length of the inversion as follows. The total number of inversions of length L that can occur in the chromosome is (N - L + 1). All inversions of length between 2N/3 and N will have their breakpoints in the two extreme regions. [(2N/3) - L + 1] inversions of length between N/3 and 2N/3 will have their breakpoints in adjacent regions (distal and central or central and proximal), and the rest in the two extreme regions. Finally, [(N/3) - L + 1] inversions of length between 0 and N/3 will have their breakpoints within each region, and the rest in adjacent regions. When length of inversions is expressed relative to the total length of the chromosome (l) and N is assumed to be very large, the following continuous density functions are obtained:

For 0 [less than or equal to] l [less than or equal to] 1/3

[Mathematical Expression Omitted]

For 1/3 [less than or equal to] l [less than or equal to] 2/3

[Mathematical Expression Omitted]

For 2/3 [less than or equal to] l [less than or equal to] 1

f(l) = 18[(1 - l)[p.sub.1][p.sub.3]]
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Author:Caceres, Mario; Barbadilla, Antonio; Ruiz, Alfredo
Date:Aug 1, 1997
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