THE EVOLUTION OF RESTRICTED RECOMBINATION AND THE ACCUMULATION OF REPEATED DNA SEQUENCES

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THE EVOLUTION OF RESTRICTED RECOMBINATION

AND THE ACCUMULATION OF REPEATED DNA

SEQUENCES

BRIAN CHARLESWORTH,' CHARLES H. LANGLEY* AND WOLFGANG STEPHAN'

School of Biological Sciences, University of Sussex, Brighton BNI 9QG, England

Manuscript received April 9, 1985 Revised copy accepted December 13, 1985

ABSTRACT

We suggest hypotheses to account for two major features of chromosomal organization in higher eukaryotes. T h e first of these is the general restriction of crossing over in the neighborhood of centromeres and telomeres. We propose that this is a consequence of selection for reduced rates of unequal exchange between repeated DNA sequences for which the copy number is subject to stabilizing selection: microtubule binding sites, in the case of centromeres, and the short repeated sequences needed for terminal replication of a linear DNA molecule, in the case of telomeres. An association between proximal crossing over and nondisjunction would also favor the restriction of crossing over near the centromere. T h e second feature is the association between highly repeated DNA sequences of n o obvious functional significance and regions of restricted crossing over. We show that highly repeated sequences a r e likely t o persist longest (over evolutionary time) when crossing over is infrequent. This is because unequal exchange among repeated sequences generates single copy sequences, and a population that becomes fixed for a single copy sequence by drift remains in this state indefinitely (in the absence of gene amplification processes). In- creased rates of exchange thus speed up the process of stochastic loss of repeated sequences.

N this paper, we propose some evolutionary hypotheses to account for two

I

major features of the genetic and molecular evolution of the chromosomes of eukaryotes. T h e first such feature is the reduced frequency of genetic recombination in the neighborhood of centromeres and telomeres. A lowered probability of genetic exchange in meiosis in these regions has been most clearly documented in Drosophila melanogaster (LINDSLEY and SANDLER 1977;

YAMAMOTO and MIKLOS 1978; SZAUTER 1984), but a relative contraction of t h e genetic map near centromeres and/or telomeres is observable in several

Present address: Department of Biology, T h e University of Chicago, I103 Fast 57th Street, Chicago, Illinois

'

Present address: Laboratory of Genetics, National Institute of Environmental Health Sciences, Research Present address: Physikalische Chemie 1 , Technische Hochschule Darmstadt, 6100 Darmstadt, West Cer- 60637.

Triangle Park, North Carolina 27709. many.

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948 B. CHARLESWORTH, C. H. LANGLEY AND W. STEPHAN

other well-studied species, such as maize (NEUFFER and COE 1974), tomato (KHUSH and RICK 1968) and barley (RICK 1971). We suggest here that this reduction in crossover frequencies is the consequence of natural selection for a lower frequency of unequal exchange between repeated sequences of DNA of functional significance that are located in these chromosomal regions. This suggestion is based on a simple population genetics model, and we show that it is consistent with a range of facts about the cytogenetics and molecular organization of centromeres and telomeres.

T h e other phenomenon that we shall discuss is the tendency for highly repeated DNA (HRDNA) sequences, of no apparent functional significance, to be concentrated in regions of restricted crossing over (JOHN and MIKLOS 1979;

SIMS et al. 1984). Many inconclusive attempts (reviewed by JOHN and MIKLOS

1979) have been made to interpret this association. We shall show here that the rate of loss from a population of a family of HRDNA, due to natural selection and genetic drift, increases with the rate of unequal exchange between members of the family. It follows that regions of restricted crossing over will tend to contain a higher-than-average abundance of HRDNA, if there is some long-term evolutionary steady state between the generation of new repeated sequences by amplification processes (SCHIMKE 1984) and the forces leading to loss. Similarly, HRDNA sequences that rarely undergo exchange will persist longest.

RESTRICTED CROSSING OVER NEAR CENTROMERES AND TELOMERES

Centromeres: We start with the observation that the structure of the centromeres of eukaryotes with very small chromosomes, such as yeast, is appar- ently very simple (BLACKBURN and SZOSTAK 1984). According to PETERSON and RIS (1976), the yeast centromere lacks an identifiable structure, such as kinetochore, and each chromosome is attached to a single microtubule. In contrast, the chromosomes of mammals and most other higher organisms pos-

sess a highly differentiated kinetochore, through which many microtubules attach to a large stretch of specialized chromatin (RIS and WITT 1981; RIEDER

1982). It seems reasonable to suppose that this complex kinetochore may have a basic unit of organization similar to that of the yeast centromere. Recent genetic and molecular analyses of the yeast centromere and its associated chromatin indicate that a specific DNA sequence is recognized by a protein, perhaps

a microtubule-associated protein (BLOOM, FITZGERALD-HAYES and CARBON

1983; BLACKBURN and SZOSTAK 1984; CARBON 1984), which is presumably involved in attachment of the microtubule to the chromosome.

Although very small chromosomes often do show differentiated kineto- chores, it is usually the case that chromosomes without differentiated kineto- chores are small (e.g., the chromosomes of Physarum, various yeasts, Neuro- spora and the microchromosomes of birds; see KUBAI 1975; PETERSON and RIS

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mosomes presumably led to the multitubule spindle fiber and to multiple centromeric microtubule binding sites.

Unequal exchange between these repeated sites would lead to variation in the number of binding sites

per

chromosome (KRUEGER and VOGEL 1975;

PERELSON and BELL 1977; OHTA 198 1 ; OHTA and KIMURA 198 1 ; TAKAHATA

1981). Chromosomes with a number that deviates from the optimum may suffer an imbalance of spindle forces at disjunction, leading to nondisjunction events and aneuploidy, with a consequent reduction in fitness. Natural selection will therefore favor a reduction in crossing over in the centromeric region. In APPENDIX 1, we present an explicit model of this selection process and show that a population with zero recombination around the centromere is stable to invasion by mutants which cause recombination and associated unequal exchange.

If the kinetochore found at the centromere of most animal chromosomes is organized around an optimal number of microtubule binding sites, then it is not surprising from the above considerations that crossing over is restricted in these regions, as mentioned in the Introduction. T h e only optimum number of binding sites that would not favor the evolution of restricted recombination would be one. It is interesting to note that yeast has only one binding site and does not exhibit a centromeric reduction in crossing over comparable in magnitude to that of Drosophila (MORTIMER and SCHILD 1980; CLARKE and CAR- BON 1980). There is a similar lack of evidence for a centromere effect in filamentous fungi, such as Neurospora and Aspergillus (FINCHAM, DAY and RADFORD 1979), but the structure of the centromere is at present unknown in these species. Our hypothesis leads to the expectation of a single binding site. It should be noted that there is little or no HRDNA in Aspergillus (TIMBER- LAKE 1978).

Telomeres: WALMSLEY et al. (1 984) have proposed a model of the terminal replication of linear chromosomes that requires the existence of a terminal block of repetitive DNA sequences. There is now clear molecular evidence from yeast and Tetrahymena for the presence of such specialized telomeric repeated sequences (BLACKBURN and SZOSTAK 1984). If there were an optimum number of repeats for efficient telomeric replication, the argument used above for centromeres applies, and reduced recombination in telomeric regions would be favored by natural selection. There is, however, evidence that the size of the block of telomeric sequences in yeast and Tetrahymena is under some degree of control by replicative mechanisms (BLACKBURN and SZOSTAK

1984; WALMSLEY and PETES 1985). This might reduce any effect of unequal exchange on the number of copies of the repeats, although WALMSLEY and PETES (1 985) have demonstrated the existence of stable genetic variants of telomere length in yeast. Recombination can take place in the yeast telomere under some experimental circumstances (DUNN et al. 1984), so that any selection for restricted crossing over has not been completely successful.

Relative contraction of the genetic map near telomeres has been well documented in Drosophila species (STURTEVANT and TAN 1937; MATHER 1939;

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950 B. CHARLESWORTH, C. H. LANGLEY AND W. STEPHAN

other species is less clear, although observations on grasshopper species have demonstrated an effect of telomeric chromatin in repressing chiasma formation in its neighborhood (MIKLOS and NANKIVELL 1976; NAVAS-CASTILLO, CABRERO

and CAMACHO 1985).

A M O U N T OF H R D N A I N R E L A T I O N TO RECOMBINATION R A T E

In this section, we shall develop some population genetics models in order to study the relationship between rate of crossing over and the number of copies of members of HRDNA families. Our objective is to show that the association between HRDNA and regions of restricted crossing over, mentioned in the Introduction, may be a consequence of evolution rather than an inherent functional property of HRDNA.

We assume that a given chromosome carries a tandemly repeated DNA

sequence. There may be variation in the number of copies of members of this sequence between different representatives of this chromosome present in a given generation, such that x, is the frequency of chromosomes with

i

copies. A new generation is formed by random sampling of independent gametes, after allowing copy number to be modified by the processes of unequal exchange and amplification. T h e individuals formed from these gametes may then be exposed to selection on copy number. Our models of these processes are as follows.

Unequal exchange: T h e frequency and properties of meiotic and somatic exchange in HRDNA families are at present unknown, although they seem to be low frequency events (JOHN and MIKLOS 1979; CARPENTER and BAKER

1982) as far as sequences located in heterochromatin are concerned. A rate of approximately lop4 per kilobase per generation is, however, likely for the nonheterochromatic human “minisatellite” repeated sequence recently isolated by JEFFREYS, WILSON and THEIN (1985). Large changes in the amount of heterochromatin in specific chromosomal regions have been observed in hu- mans (CRAIG-HOLMES, MOORE and SHAW 1975; SEABRIGHT, GREGSON and

MOULD 1976; NAGAGOME et al. 1977), suggesting that unequal exchanges can involve a large number of repeats and can cause a major change in copy number between parental and daughter chromosomes. T h e same is true for the classical Bar duplication of D. melanogaster (STURTEVANT 1925), although this involves euchromatin rather than heterochromatin. Various models of unequal exchange have been proposed (KRUEGER and VOCEL 1975; PERELSON

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ditioned on an exchange having occurred), we have

Qjk = 1. i

T h e net probability of such an event occurring is denoted by yQljk, where

is the rate of exchange.

Gene amplification: Gene amplification is a blanket term for poorly understood processes of mutational increases in the copy numbers of DNA sequences

(SCHIMKE 1984). It is not necessary for our purposes here to develop detailed models of such changes. We can represent the probability that a chromosome with j copies of a given sequence generates a daughter with i

(i

2 j ) by ay,

such that C, ay = 1. In the absence of other forces, gamete frequencies obey the standard multiallelic recurrence relations

x i =

r,

agj, j

and the change in mean copy number i =

zi

ixi, is

A i = a,(i

-

j ) x j .

y (3)

In the simplest case, when there is only one class of mutant sequence with copy number iA, produced at rate a from all other sequences, we have

AT = a ( i ~

-

9.

₍₄₎

Natural selection: T h e relation between Darwinian fitness and copy number of HRDNA is at present unknown. We shall assume that the fitness of individuals with

i

copies, w i t is in general a decreasing function of

i,

since we are not considering multigene families with specific functions, such as histone or ri- bosomal RNA genes, which presumably h a i e optimal numbers of repeats

(CROW and KIMURA 1970, p. 293). It is possible that HRDNA sequences are completely neutral as far as copy number is concerned, in which case wi is independent of

i.

It seems to us more likely that there is some upper limit to the copy number that can be tolerated, such that fitness is zero beyond this level il (wi = 0 for i

>

a),

since cells with indefinitely large quantities of HRDNA must have substantially altered properties, such as long division times

(CAVALIER SMITH 1978; 1985; JOHN and MIKLOS 1979).

Consequences of the models: infinite populations: We shall first consider the case in which population size is so large that the effects of genetic drift can be ignored. We thus expect that the mean copy number in the population will eventually reach an equilibrium value that is determined by the interaction between selection, unequal exchange and amplification, analogous to the mutation-selection balance equilibrium for a single locus (CROW and KIMURA

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952 B. CHARLESWORTH, C. H . LANGLEY AND W. STEPHAN

would expect unequal exchange to increase the variance in copy number for a given regime of selection and amplification and, thereby, to increase the power of selection to reduce copy number, leading to a lower equilibrium mean copy number

(4

OHTA 1983). Some insight into the magnitude of this effect can be obtained, using the simple model of amplification of (4), and assuming an additive selection function such that w, = 1

-

s

(i

- 1) (s

is assumed to be so small that the limit D is not attained by sequences present in the population). It is easily seen for a haploid population that, in the absence of exchange and assuming iA

>>

1,

h A = -%A( 1

-

xA)SiA

+

a( 1

-

X A ) , _{( 5 )}

where xA is the frequency of the amplified sequence, and 1

-

XA is the fre-

quency of the sequence with copy number 1. It follows that the equilibrium mean copy number with no exchange is given by

io = a/s (a 5 SiA) ( 6 4

It is difficult to obtain a general expression for equilibrium mean copy number in the presence of exchange. However, STEPHAN (1986) has obtained an approximate expression for the case of additive selection with the following specific exchange model of TAKAHATA (1981):

where

c = 2 / ( j

+

k)

( j

+

k

even) (7b)

( 7 4

c = 2 ( j

+

k)/((

j

+

k)'

-

11 ( j

+

k

odd).

This provides a representation in which the probability of obtaining a given exchange product falls off symmetrically with the deviation of its length from the mean of the parental strands.

If the rate of unequal exchange, 7, is sufficiently large that i 5 O.l7y/s,

STEPHAN'S equation (23) gives the following approximate expression for the change in mean:

Under the above condition on y, the denominator may be approximated by

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Some values of io and i7 are given below for the case

iA

= 1,000:

a/s 125 250 500 1,000 2,000 4,000 8,000

80 125 250 500 1,000 1,000 1,000 1,000

It will be seen that, for a/s sufficiently small in relation to iA,

iy

exceeds io. This is presumably d u e to the fact that, when the population is segregating for both the single copy and amplified sequences, ample variance exists for selection on copy number even in the absence of exchange; unequal exchange simply introduces variants for which the copy numbers all exceed 1. For a / s

sufficiently close to

iA,

Zo

>

F7,

but the magnitude of the effect is not large and declines to zero as a/s increases. OHTA’S (1983, Figure 1) numerical results for a related model are in qualitative agreement.

T h e general conclusion from these results is that unequal exchange may cause a reduction in mean copy number when selection is sufficiently weak, but that the effect is not large and is certainly inadequate to explain the discrepancy in the amount of HRDNA between regions of low and high crossing over. T h e effects of finite population size, to be discussed in the next section, are likely to be of much greater significance, especially as the deter- ministic forces are likely to be weak.

Consequences of the models: finite populations: We shall consider here in detail only the case for which the product of population size and recombination rate (Ney) is sufficiently small that the population is usually fixed for a single chromosome with some copy number

i.

Results for more general cases will be presented in another paper (STEPHAN 1986). T h e assumption of small Ney is, of course, appropriate in relation to the properties of heterochromatin. As described in APPENDIX

2,

it means that (when y

>

0), there is a low rate of production by unequal exchange (meiotic or somatic) of chromosomes with variant copy number, each of which has a low probability of fixation. Ulti- mately, a chromosome with copy number i = 1 will be fixed, and the population will be trapped in this state in the absence of amplification. (If amplification is occurring, the population will remain in this state for a long time until the process is restarted by the fixation of a new repeated sequence.)

In APPENDIX 2, we show that the rate of approach of the probability distribution of copy number to the state with i = 1, in the absence of amplification, is an increasing function of the rate of crossing over y, under quite general assumptions. This is simply because a higher value of speeds up the generation of variant chromosomes and, hence, facilitates the fixation of chromosomes with only one copy of the sequence. It follows that, if two regions in the genome with different rates of crossing over are compared, the concentration of HRDNA is likely to be much higher in the region with the lower rate. An explicit formula for the mean time to absorption at copy number 1 can be found in the case of linear selection (STEPHAN 1986). This assumes the form

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for the distribution of unequal exchange products, w i t h j =

k.

If the initial copy number of the population is

io,

such that 1

<<

io

<<

0, the mean time to absorption at 1 is

-

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954 B. CHARLESWORTH, C. H. LANGLEY AND W. STEPHAN

Equation (1 0) is appropriate for very weak selection on copy number, which may well be realistic for HRDNA. As expected from the general argument of APPENDIX 2, both equations show that the time to absorption at copy number

i

= 1 is inversely proportional to y. If repeated sequences are occasionally regenerated by gene amplification processes, we would expect from these results that the steady-state probability distribution of copy number will be such that mean copy number is highest with low values of y.

These results assume 4Ney

<<

1 (for a diploid species). A similar analysis for the case of 4Ney

>

1 yields a much weaker dependence of absorption time on

y (STEPHAN 1986). It thus appears that the greatest effect of rate of crossing over on concentration of HRDNA is in the neighborhood of zero crossing over, so that a large difference would be expected between regions such as centric heterochromatin and other regions of the genome, but only smaller differences where crossing over is more frequent.

It has been pointed out to us by BRUCE WALSH that unequal exchange within a chromatid between homologous units of a repeated sequence may occur and may result in the deletion of one or more units

(CJ:

WALSH 1985, figure 1). Evidence for this process is available in the literature (LEHRMAN et al. 1985;

WALSH 1985). This would, in itself, produce a decrease in mean copy number and would accelerate the tendency toward loss of repeated sequences in regions where exchange are frequent.

DISCUSSION

Restricted crossing over: In the second section of this paper, we have proposed that the reduction in the rate of crossing over near centromeres and telomeres is an evolutionary response to selection for prevention of unequal exchange between sequences subject to stabilizing selection for an intermediate copy number. Since centromeres and telomeres are frequently associated with HRDNA sequences, it could be argued that this suppression of crossing over is a direct physical property of these sequences (cJ: JOHN and MIKLOS 1979). Several facts suggest, however, that this is not the case.

T h e original observations of the “centromere effect” were in Drosophila experiments in which rearrangements placed genes that are normally distal into proximal positions (BEADLE 1932; MATHER 1939). These experiments clearly indicated a regional suppression of recombination near the centromere. Later experiments involving deletions of HRDNA proximal to the centromere have also supported the view that the centromere, as opposed to its associated HRDNA, is the source of the reduction of recombination in that region

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More recent experiments with mutations that affect recombination indicate an independent, specific and cis-acting reduction associated with the centromere itself (SZAUTER 1984). A “telomere effect” is indicated by the Drosophila genetic maps, but the location of the relevant determinant is not as clearly demonstrated.

It may seem puzzling at first that the centromere or telomere is capable of exerting such long-range effects in suppressing euchromatic recombination, which (in the case of the

D.

melanogaster X centromere) can extend over a block of DNA constituting one-third of the chromosome. T h e mechanism of this suppression is not understood, but the genetic evidence for its existence is strong. Furthermore, several studies of quantitative genetic variation in rates of crossing over in Drosophila have yielded evidence for region-specific effects extending over large stretches of chromatin (CHARLESWORTH, MORI and

CHARLESWORTH 1985). If this kind of effect were to be exerted by a centromeric or telomeric factor, the observations we have discussed could easily be explained.

Another possible advantage to crossover suppression in the neighborhood of the centromere is suggested by the data of CATTRALL, BAIRD and GARBER (1978) on Ustilago violacea, which show that nondisjunction at meiosis I is tightly correlated with crossing over near the centromere. It is interesting to note that the U. violacea map shows evidence for proximal clustering of loci (E. D. GARBER, personal communication), suggesting that there may be crossover suppression near the centromere, unlike other species of fungi that have been studied intensively (FINCHAM, DAY and RADFORD 1979). Similarly, in yeast there is evidence that chromosome loss in mitosis is correlated with proximal recombination events (CAMPBELL and FOGEL 1977; CAMPBELL 1980). Recent data on autosomal nondisjunction in

D.

melanogaster also suggest a relation between proximal crossing over and nondisjunction (CHARLESWORTH,

MORI and CHARLESWORTH 1985), although other explanations cannot be completely ruled out at present. If crossing over near the centromere interferes with disjunction, for example by preventing normal chiasma terminalization (CATTRALL, BAIRD and GARBER 1978), there would be an obvious advantage to its suppression (cf. APPENDIX 1).

A further conclusion from the Drosophila experiments is that large blocks of centromeric HRDNA behave as almost completely nonrecombinogenic

(SZAUTER 1984). Some evidence for effects of centric heterochromatin in ac- tively suppressing crossing over in adjacent euchromatin has been cited

(YAMAMOTO and MIKLOS 1978; JOHN and MIKLOS 1979), but most of those cases are hard to distinguish from concomitant changes in proximity to the centromere or from mechanical effects of disturbances in pairing (cf. SUZUKI

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9 5 6 B. CHARLESWORTH, C. H . LANGLEY AND W. STEPHAN

evidence cited earlier on human minisatellite DNA (JEFFREYS, WILSON and

THEIN 1985) shows that tandemly repeated, nontranscribed DNA sequences a r e not inherently incapable of recombination. It therefore seems either that controls on recombination within proximal heterochromatin (supplementary to the effect of the centromere) have been established or that the centromeric region has become enriched for sequences which are poor substrates for recombination. From the results of the third part of this paper, such poorly recombinogenic sequences a r e expected to persist longest over evolutionary time. (Purely mechanical effects on recombination of large blocks of heterochromatin cannot be ruled out, of course.)

Accordingly, we propose that the evolutionary accumulation of highly repeated DNA in the neighborhood of centromeres and telomeres may be a dual process: there is a preferential accumulation of repeated sequences in the neighborhoods of these structures, d u e t o these neighborhoods having been selected for reduced rates of crossing over, and the HRDNA sequences which accumulate a r e those with low rates of exchange, even in regions outside the influence of centromeres or telomeres.

Gene amplification: T h e models proposed here incorporate the mechanism of gene amplification as an initiating and fundamental force. Little is actually known about this phenomenon in most organisms; however, the interpretation of the studies of both gene amplification and of the mechanism and control of chromosomal DNA replication indicate that the underlying molecular steps that lead to gene amplification are likely to be common to most species of eukaryotes. In higher organisms, the initiation and pattern of chromosomal DNA replication a r e not as rigidly fixed as in plasmids, viruses and bacteria

(MECHALI and KEARSEY 1984). Depending on many developmental and environmental factors, the number, distribution and timing of initiation sites along the chromosome of higher eukaryotes can vary (CALLAN 1973; BLUMENTHAL,

KRIEGSTEIN and HOGNESS 1973; VARSHANSKY 1981). This lack of complete synchrony and determination can lead to differential or disproportionate replication of various regions. T h e disposition of these disproportionately repli- cated segments is thought to be an important source of gene amplification

(SCHIMKE 1984). T h e rate of gene amplification is not generally known, but stable duplications of a given region probably occur at a rate of

per cell generation at several loci in cultured mammalian cells (reviewed in

SCHIMKE 1984). A rate of 1 0-5 was obtained for the rosy region of Drosophila by GELBART and CHOVNICK (1979). If the rate of random gene amplification is high throughout the genome, it is likely that duplications and higher repeats would accumulate over evolutionary time, given the generally mild selection against duplications (LINDSLEY et al. 1972).

It is also noteworthy that the gene amplification events observed in tissue culture experiments often occur at the original site of the sequence, but they occasionally involve the transposition of the amplified sequence to another chromosome (see references in SCHIMKE 1984). This transpositional gene amplification could be the basis for the spread of HRDNA among the chromo-

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somes. Transpositional insertions are known to occur in centric heterochromatin (RUBIN 1983).

Noncentromeric heterochromatin: T h e Y and W chromosomes of the het- erogametic sex in species with chromosomal sex determination are frequently largely genetically inert and heterochromatic (BULL 1983). CHARLESWORTH (1978) has suggested that this genetic inertness is a consequence of the

oper-

ation of “Muller’s ratchet” (MULLER 1964; FELSENSTEIN 1974; FELSENSTEIN and YOKOYAMA 1976; HAICH 1978), the process by which random genetic drift causes a gradual increase in the mean number of deleterious mutations per chromosome when genetic recombination is absent. As pointed out by CHARLESWORTH (1 985), the insertion of transposable elements is analogous to mutation, so that “Muller’s ratchet” might cause the accumulation of transposable elements on the Y or other regions of restricted crossing over, provided that excision rates of transposable elements are sufficiently small. T h e process of random fixation of genes in permanently heterozygous regions sheltered from recombination, studied by NEI (1970), would also play a role if population size is sufficiently small. Finally, as noted by BULL (1983, p. 259), the selective impact of insertions of new genetic material into regions which are genetically inert is likely to be minimal. For these reasons, we might well expect the accumulation of repetitive DNAs (both HRDNA by transpositional gene amplification and transposable elements) in regions of restricted crossing over, such as the Y chromosome. There is extensive evidence for the accumulation of both middle repetitive and highly repetitive DNA on Y and W chromosomes in a variety of species (e.g., see STEINEMANN 1982; COOKE, SCHMIDTKE and COSDEN 1982; TONE et al. 1984).

A similar tendency to accumulate repeated DNA would be expected for balanced lethal systems involving chromosome rearrangements, in which a por- tion of the genome is maintained heterozygous in the absence of crossing over. Such systems are rare in nature. In Drosophila, two instances have been re- ported from natural populations (DOBZHANSKY and PAVLOVSKY 1955; MITRO- FANOV and POLU~KTOVA 1982). In both cases, the inversions were found to be associated with lethals such that all (or most) individuals are heterokarotypic. These examples are limited to local populations and may not survive over evolutionary time to become fixed in a species.

If such a balanced lethal inversion should survive many generations, the model presented above indicates that HRDNA may accumulate in the region of the chromosome where the inversion suppresses recombination. A spectac- ular example of a balanced lethal associated with the accumulation of HRDNA

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958 B. CHARLESWORTH, C. H. LANGLEY AND W. STEPHAN

thality of homokaryotypes and, thus, the elimination of recombination in the inverted segment. Gene amplification and transposition led to the slow accumulation of HRDNA. Since recombination and, hence, unequal exchange were reduced, natural selection was less effective at stemming the amplification of the sequences. Eventually, the amount of HRDNA on this single chromosome reached the present enormous level of 5% of the total genomic DNA.

This work was supported in part by a Science and Engineering Research Council Visiting Fellowship to C.H.L., a fellowship from the Deutsche Forschungsgemeinschaft to W.S. and a grant from the Louis Block Fund of the University of Chicago to B.C. We thank DEBORAH CHARLES- WORTH, MONTGOMERY SLATKIN, JANICE SPOFFORD, BRUCE WALSH and a reviewer for their com- nients on the manuscript.

LITERATURE CITED

BAKER, W. K., 1958

BEADLE, G. W., 1932

Crossing over in heterochromatin. Am. Nat. 92: 59-60.

A possible influence of the spindle fibre on crossing over in Drosophila.

T h e molecular structure of centromeres and telo- Proc. Natl. Acad. Sci. USA 18: 160-165.

BLACKBURN, E. H. and J. W. SZOSTAK, 1984 meres. Annu. Rev. Biochem. 53: 163-194.

BLOOM, K. S., M. FITZGERALD-HAYES and J. CARBON, 1983 Structural analysis and sequence organization of yeast centromeres. Cold Spring Harbor Symp. Quant. Biol. 47: 1175-1 185.

in Drosophila melanogaster. Cold Spring Harbor Symp. Quant. Biol. 38: 205-223.

nia.

BLUMENTHAL, A. B., H. G. KRIEGSTEIN and D. S. HOGNESS, 1973 T h e units of DNA replication

BULL, J. J., 1983 Evolution of Sex Determining Systems. Benjamin-Cummings, Menlo Park, Califor-

Crossing over in the distal euchromatin of homozygous I n ( l ) r s t 3 . Drosophila

BRAVER, G., 1956

Inform. S e w . 3 0 105.

Symp. Quant. Biol. 47: 1165-1 173.

in yeast. Genetics 96: 613-625.

mitotic recombination in a yeast disomic haploid. Genetics 85: 573-585.

CALLAN, H. G., 1973 DNA replication in the chromosomes of eukaryotes. Cold Spring Harbor

CAMPBELL, D. A., 1980 Association of disomic chromosome loss with EMS-induced conversion

CAMPBELL, D. A. and S. FOGEL, 1977 Association of chromosome loss with centromere-adjacent

CARBON, J. 1984

CARPENTER, A. T. C. and B. S. BAKER, 1982 O n the control of the distribution of meiotic Yeast centromeres: structure and function. Cell 37: 351-353.

exchange in Drosophila melanogaster. Genetics 101: 8 1-84.

Crossing over and nondisjunction. Bot. Gaz. 13: 266-270.

CATTRALL, M. E., M. L. BAIRD and E. D. GARBER, 1978 Genetics of Ustilago uiolacea. 111.

Nuclear volume control bv nucleoskeletal DNA. selection for cell CAVALIER SMITH, T., 1978

volume and cell growth rate, and the solution of the C-value paradox. J. Cell. Sci. 34: 247- 278.

CAVALIER SMITH, T. (editor), 1985 Cell volume and the evolution of eukaryote genome size. pp. 105-185. In: Natural Selection and Genome Size. John Wiley & Sons, Chichester, West Sussex, England.

Recombination modification in a fluctuating environment. Genetics CHARLESWORTH, B., 1976

(13)

959

CHARLESWORTH, B., 1978

CHARLESWORTH, B., 1985

Model for evolution of Y chromosomes and dosage compensation.

Recombination, genome size and chromosome number. pp. 489-5 13. In: Natural Selection and Genome Size, Edited by T. CAVALIER-SMITH. John Wiley & Sons, Chichester, West Sussex, England.

CHARLESWORTH, B. and D. CHARLESWORTH, 1973 Selection of new inversions in multi-locus genetic systems. Genet. Res. 21: 167-183.

CHARLESWORTH, B., 1. MORI and D. CHARLESWORTH, 1985 Genetic variation in recombination in Drosophila. 111. Regional effects on crossing over and effects on non-disjunction. Heredity

Isolation of a yeast centromere and construction of functional

Characterization of a human Y chromosome Proc. Natl. Acad. Sci. USA 7 5 5618-5622.

5 5 209-222.

CLARKE, L. and J. CARBON, 1980

COOKE, H. J., J. SCHMIDTKE and J, R. GOSDEN, 1982

CRAIG-HOLMES, A. P., F. B. MOORE and M. W. SHAW, 1975 small circular chromosomes. Nature 287: 504-509.

repeated sequence and related sequences in higher primates. Chromosoma 87: 49 1-502.

Polymorphism of human C-band heterochromatin. 11. Family studies with suggestive evidence of somatic crossing over. Am. J. Hum. Genet. 27: 178-189.

CROW, J. F. and M. KIMURA, 1970 An Introduction to Population Genetics Theory. Harper & Row,

DORZHANSKY, T. and 0. PAVLOVSKY, 1955 An extreme case of heterosis in a Central American New York.

population of Drosophila tropicalis. Proc. Natl. Acad. Sci. USA 41: 289-295,

linear plasmids by recombination. Cell 3 9 191-201. DUNN, B., P. SZAUTER, M. L. PARDUE and J. W. SZOSTAK, 1984

EWENS, W. J., 1979 Mathematical Population Genetics. Springer-Verlag, Berlin.

FELSENSTEIN, J., 1974 T h e evolutionary advantage of recombination. Genetics 7 8 737-756.

FELSENSTEIN, J. and S. YOKOYAMA, 1976 T h e evolutionary advantage of recombination. 11. In-

FINCHAM, J. R. S., P. R. DAY and A. R. RADFORD, 1979 Fungal Genetics. University of California

GELRART, W. M. and A. CHOVNICK, 1979 Spontaneous unequal exchange in the rosy region of

HAIGH, J., 1978 T h e accumulation of deleterious genes in a population-Muller’s ratchet. Theor.

JEFFREYS, A. J., V. WILSON and S. L. THEIN, 1985 Hypervariable ‘minisatellite’ regions in human

JOHN, B. and G. L. G. MIKLOS, 1979 Functional aspects of satellite DNA and heterochromatin. lnt. Rev. Cytol. 58: 1-1 14.

KHUSH, G . S. and C. M. RICK, 1968 Cytogenetic analysis of the tomato genome by means of deficiencies. Chromosoma 23: 452-484.

Population genetics of unequal crossing over. J. Mol. Evol. 4: Transfer of yeast telomeres to

dividual selection for recombination. Genetics 83: 845-859.

Press, Berkeley.

Drosophila melanogaster. Genetics 98: 849-859.

Pop. Biol. 14: 251-267.

DNA. Nature 314: 67-73.

KRUEGER, J. and F. VOGEL, 1975

KUBAI, D. F., 1975 T h e evolution of the mitotic spindle. Int. Rev. Cytol. 43: 167-227.

LEHRMAN, M. A., W. J. SCHNEIDER, T. C. SUDHOF, M. S. BROWN and D. W. RUSSELL, Mutation in LDL receptor: Alu-Alu recombination deletes exons encoding transmem-

T h e genetic analysis of meiosis in female Drosophila 201-247.

1985

brane and cytoplasmic domains. Science 227: 140-146.

(14)

960 B. CHARLESWORTH, C. H. LANGLEY AND W. STEPHAN

LINDSLEY, D. I,., L. SANDLER, B. S. BAKER, A. T. C. CARPENTER, R. E. DENNELL, J. C. HALL, P. Segmental aneuploidy and genetic gross structure of

Crossing over and heterochromatin in chromosomes of Drosophila melanogas-

Lack of specific sequence requirement for DNA replication

Telomeric satellite DNA functions in regulating

Inversion polymorphism in a natural popula-

MORIWAKI, D. and Y. N. TOBARI, 1975 Drosophila ananassae. pp. 513-535. Handbook of Genetics,

Vol. 3, Edited by R. C. KING. Plenum, New York.

Genetic map of Saccharomyces cerevisiae. Microbiol. Rev. 44: 519-571.

MUI.I.ER, H. J., 1964 T h e relation of recombination to mutational advance. Mutat. Res. 1: 2-9.

NAKAGOME, Y., T. KITAGAWA, K. IINUMA, E. MATSUNAGE, T. SHINODA and T . ANDO, Pitfialls in the use of chromosome variation for paternity dispute cases. Hum. Genet. A . JACOBS and G. L. G. MIKLOS, 1972

the Drosophila genome. Genetics 71: 157-184.

ter. Genetics 24: 413-435.

MECHALI, M. and S. KEARSEY, 1984

MIKLOS, G. L. G. and R. N. NANKIVELL, 1976 recombination. Chromosoma 5 6 143-167. MITROFANOV, V. G. and E. V. POLUEKTOVA, 1982 MAI'HER, K., 1939

in Xenopus eggs compared with high sequence specificity in yeast. Cell 38: 55-64.

tion of Drosophila imeretensis Sokolov (Drosophila littoralis Meig.). Genetika 18: 1849-1 855.

MORPIMER, R. K. and D. SCHILD, 1480

1977 27: 255-260.

NAVAS-CASTILLO, J., J. CABRERO and J. P . M. CAMACHO, 1985

carrying supernumerary chromosome segments in grasshoppers. Heredity 55: 245-248.

NEI, M., 1970 311-321.

Chiasma distribution in bivalents

Accumulation of non-functional genes on sheltered chromosomes. Am. Nat. 104

Corn (maize). pp. 3-30. In: Handbook of Genetics, Vol. 2, NEUFFER, M. G. and E. H. COE, 1974

Edited by R. C. KING. Plenum, New York.

OHTA, T., 198 1

OHTA, l., 1983

OHTA, T. and M. KIMURA, 1981

Population genetics of selfish DNA. Nature 292: 648-649.

Theoretical study on the accumulation of selfish DNA. Genet. Res. 41: 1-15.

Some calculations on the amount of selfish DNA. Proc. Natl. Acad. Sci. USA 78: 1129-1132.

PERELSON, A . and G. 1. BELL, 1977 Mathematical models for the evolution of multigene families

Electron-microscopic study of the spindle and chromosome

Some cytogenetic features of the genome in diploid plant species. Stadler

T h e formation, structure, and composition of the mammalian kinetochore

Structure of the mammalian kinetochore. Chromosoma 82: 153- by unequal crossing over. Nature 265: 304-310.

movement in the yeast Saccharomyces cerevisiae. J. Cell Sci. 22: 219-242.

Genet. Symp. 1 and 2: 153-174.

fiber. Int. Rev. Cytol. 79: 1-58.

170.

PETERSON, J. B. and H. RIS, 1976

RICK, C. M., 1971

KIEDER, C. l,., 1982

KIs, H. and P. L. WITT, 1981

KOBERTS, P. A., 1969 Some components of X-ray-induced crossing over in females of Drosophila

Dispersed repetitive DNA in Drosophila. pp. 329-361. In: Mobile Genetic

melanogaster. Genetics 63: 387-404.

RUBIN, G. M., 1983

Elements, Edited by J. A. SHAPIRO. Academic Press, New York. SCHIMKE, R. T., 1984

SEABRIGHT, M., N. GRECSON and S. MOULD, 1976 in a liveborn. Hum. Genet. 3 4 323-325.

Gene amplification in cultured animal cells. Cell 37: 705-713.

(15)

96

Chromosome 1 in crested and marbled newts (Triturus): an extraordinary case of heteromorphism and independent evolution. Chromosoma 8 9 169-185.

Multiple sex chromosomes in Drosophila miranda: a system to study the degeneration of a chromosome. Chromosoma 89: 59-76.

SIMS, S. H., H. C. MACGREGOR, P. S. PELLATT and H. A. HORNER, 1984

STEINEMANN, M., 1982

STEPHAN, W., 1986

STURTEVANT, A. H., 1925 Genetics 10: 117-147.

STURTEVANT, A. H. and C. C. T A N , 1937

Recombination and the evolution of satellite DNA. Genet. Res. In press.

The effects of unequal crossing over at the Bar locus in Drosophila.

The comparative genetics of Drosophila Pseudoobscura

Interchromosomal effects on crossing over in Drosophila melanogaster. 11. A

An analysis of regional constraints on exchange in Drosophila melanogaster using recombination-defective meiotic mutants. Genetics 106: 45-7 1.

Mathematical study of the distribution of the number of repeated genes per chromosome. Genet. Res. 38: 97-102.

Low repetitive DNA content in Aspergillus nidulans. Science 202:

973-974.

Genus specificity and extensive methylation of the W chromosome specific repetitive DNA sequences from the domestic fowl, Gallus gallus domesticus. Chromosoma 8 9 228-237.

On the possibility of metabolic control of replicon “misfiring”: relationship to emergence of malignant phenotype in mammalian cell lineages. Proc. Natl. Acad. Sci.

Unusual DNA sequences

Genetic control of chromosome length in yeast. Proc.

How many processed pseudogenes are accumulated in a gene family? Genetics

Genetic studies on heterochromatin in Drosophila melanogaster and their implications for the function of satellite DNA. Chromosoma 66: 71- 98.

Communicating editor: B. S. WEIR and D. melanogaster. J. Genet. 3 4 415-432.

reexamination of X chromosome inversion effects. Genetics 48: 1605-161 7. SUZUKI, D. T., 1963

SZAUTER, P., 1984

~ A K A H A T A , N., 1981

TIMRERLAKE, W. E., 1978

TONE, M., Y. SAKAKI, T. HASHICUCHI and S. MIZIJMO, 1984

VARSHANSKY, H., 1981

USA 78: 3673-3677.

WALMSLEY, R. W., C. S. M. CHAN, B.-K. TYE and T. D. PETES, 1984

WALMSLEY, R. M. and T. D. PETES, 1985

associated with the ends of yeast chromosomes. Nature 310: 157-160.

Natl. Acad. Sci. USA 82: 506-510.

WALSH, J. B., 1985

YAMAMOTO, M. and G. L. G. MIKLOS, 1978 1 1 0 345-364.

APPENDIX 1: SELECTION FOR REDUCED CENTROMERIC CROSSING OVER

Consider a population in which there is variation in the number of copies of microtubule binding sites on a given chromosome, such that x, is the frequency of gametes with i sites. Let w, be the fitness of individuals with i and j sites o n the maternal and paternal chromosomes (w, = q,). We assume that there is some intermediate optimum number of attachment sites on a chromosome, such that the probability of nondisjunction or other segregational abnormalities increases as i deviates from the optimum io. hence, w, decreases as i and j

deviate from io; we thus have a case of stabilizing selection (CROW and KIMURA 1970, pp. 293-296), and standard theory can be applied. In the absence of crossing over, the system will behave like a single locus with multiple alleles, in which the maximum population mean fitness is attained when the population is fixed for gametes with copy number io. Selection

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population, it will cause the generation of gametes with i # io. By the argument of

CHARLESWORTH (1976, appendix I), it will thus suffer a selective disadvantage. Hence, a state of zero crossing will be evolutionarily stable.

Conversely, if the population initially has a nonzero rate of unequal crossing over, we may expect it to approach an equilibrium in which there is a distribution of values of i around io

(CROW and KIMURA 1970, pp. 293-296). This generates a corresponding distribution of gametic fitnesses, w, = 2, xJw0; as shown by CHARLESWORTH and CHARLESWORTH (1973), a dominant gene or a chromosomal rearrangement that completely suppresses recombination will be favored by selection if it is introduced into a gamete with a higher-than-average fitness. T h e r e is thus a pressure of selection for reducing the frequency of unequal crossing over, if it is initially nonzero.

B. CHARLESWORTH, C. H. LANGLEY AND W. STEPHAN

APPENDIX 2: COPY NUMBER CHANGE IN A FINITE POPULATION

We neglect gene amplification and assume also that the effective population size Ne is sufficiently small that the population is usually fixed for a single gamete type. In a diploid species, this requires 4Ney << 1 , so that n o successful new variants can be produced by unequal crossing over while a given one is on its way to fixation [a process that takes an average of 4N, generations if selection is negligible (CROW and KIMURA 1970, p. 432)]. If

there is an upper limit Q to copy number, the system occupies Q discrete states E, = (i = 1 , 2,

. . .

Q), and its dynamics can be described by a finite Markov chain. It is convenient to

consider the process of transition from state j to z on a time scale of units of (N<y)-I generations, since N , y is the number of recombination events taking place in the population each generation. Let p,] be the probability of transition from state j to state i on this time scale, and let r 4 be the probability of fixation of a variant with copy number i in a population fixed for j . (With negligible selection, r,, = 1/2N, where N is the population size.) We then have

P , = QIP-4 ( 1 # j ) (A. la)

(A. 1 b)

Two properties of the process follow immediately from standard theory (EWENS 1979,

chap. 2): El is the only absorbing state, since

P I

I = 1 and

pJl

< 1 for j > 1, and the eigenvalues X b of the matrix P =

{ p , ]

are also smaller than 1, except for X I = 1. It follows that the

process goes to absorption at E l (fixation for a copy number of unity). Furthermore, the rate of approach to absorption is increased by an increase in y, since on the time scale of

generations the process is described by the matrix PNey and, hence, by the eigenvalues if”’. If X2 is the second largest eigenvalue of P, XPy measures the asymptotic rate of flow of