Institute of Genetics, University of Nottingham, Queens Medical Centre, United Kingdom
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Abstract |
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Introduction |
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An advantageous mutation spreading to fixation in such a region would drag the linked neutral variants to fixation along with it. This phenomenon has been termed a selective sweep and the reduction in linked diversity described as being the result of hitch-hiking (Maynard Smith and Haigh 1974
). The effects of hypothetical selective sweeps have recently been identified in the D. melanogaster genome (Nurminsky et al. 1998
). Whereas the expected genealogy of alleles linked to, but showing some recombination with, an advantageous nucleotide substitution can be complex (Kaplan, Hudson, and Langley 1989
; Stephan, Wiehe, and Lenz 1992
; Barton 1998
), if there is zero recombination in a chromosome, the occurrence and subsequent fixation of a single advantageous mutation would result in the fixation of that chromosomal variant in the population. Polymorphic sites will reappear within the population in time, but as the variants are caused by recent mutation events, they are likely to have low frequencies. A differing explanation for the correlation between recombination and gene diversity is that it is created by the effects of weakly deleterious mutations. There will be a loss of neutral variants because of their linkage to deleterious sites, and this has been termed background selection (Charlesworth, Morgan, and Charlesworth 1993
). As neutral variants are constantly being lost through this process, the overall effect of background selection is to lower the effective size of a population. Because of the continual nature of background selection, the expected coalescent process of a sample of alleles evolving under background selection will be almost exactly the same as a neutral coalescent with a smaller effective size. The distribution of frequencies at variable sites will thus be as expected under neutrality. One consequence is that whereas the expected value of the D statistic of Tajima (1989)
will be strongly negative following a selective sweep, as the samples will show an unexpectedly high number of low-frequency sites, the expectation of D will be approximately zero under background selection. It is intuitively obvious that D will be reduced after a selective sweep with no recombination, and even if there is some recombination between the sampled locus and the site of the sweep, an excess of low-frequency sites, and thus a negative D, will still be expected (Braverman et al. 1995
). However, samples of D. melanogaster alleles in low-recombination regions show values of D which are close to zero. This suggests that selective sweeps cannot, on their own, explain the reduction in variability seen in these low-recombination regions.
The ideal test to resolve between the theories, however, would be to look in the regions where there is the minimum amount of recombination, such as the fourth chromosome. The fourth chromosome of D. melanogaster has many unusual features; it is often referred to as a minichromosome as it is made up of roughly 1 Mb of euchromatin (Locke et al. 1999
). Individuals can be viable as monoploids, triploids, and tetraploids, whereas aneuploidy for chromosomes two or three results in death (Hochman 1976
). Much of the noncoding regions consist of repetitive sequences (Locke et al. 1999
), and the polytene chromosome appears diffuse and is similar to ß-heterochromatin. It has long been known that the chromosome does not undergo meiotic recombination under natural conditions (Hochman 1976
). However, recombination does occur if the chromosome is polyploid (Hochman 1976
), under heat shock (Grell 1971
), treated with X-rays (Williamson, Parker, and Manchester 1970
), or if the individual is a recombination-defective meiotic mutant (Sandler and Szauter 1978
).
Sequencing of a kilobase region of the gene cubitus interruptus Dominant by Berry, Ajioka, and Kreitman (1991)
in 10 lines of D. melanogaster showed no nucleotide substitutions. The same region was sequenced in nine lines of D. simulans, and only a single nucleotide substitution was found in one line. Despite the lack of variation within each species, the divergence of the gene between the two species was about 5%, which is typical for these species. This suggests that some mechanism of selection is causing the chromosomes to share recent common ancestry within each species. The initial interpretation of these data was that selective sweeps may be occurring (Berry, Ajioka, and Kreitman 1991
; Charlesworth 1992
) in each species, whereas more recent studies have suggested that background selection could be the cause (Charlesworth 1994
; Charlesworth, Jarne, and Assimacopoulos 1994
; Charlesworth, Charlesworth, and Morgan 1995
).
In order to try to resolve which mechanism is acting on the chromosome, we have screened the fourth chromosomes of 11 strains of D. melanogaster for polymorphic sites. As nucleotide polymorphisms are extremely rare on this chromosome, the markers we have used are retrotransposons. Such markers have been used, for example, in determining speciation events in salmonid fish (Murata et al. 1996
). However, we are using them as polymorphisms between individuals of the same species.
We performed in situ hybridization using seven retrotransposon probes. Despite being mildly deleterious to their host, retrotransposons have certain advantages as markers. Unlike class II elements, such as the P element, retrotransposons have no innate excision mechanism. Therefore, once a copy inserts, it will remain at that location, although the chromosome bearing it may be lost by selection or drift. There may be occasional deletions which nonspecifically remove Drosophila DNA, including retrotransposons, and we include the possibility of element loss in some of the simulations below (Petrov, Lozovskaya, and Hartl 1996
; Petrov and Hartl 1998
). The rate of transposition of these elements is sufficiently low, so that if two or more strains of D. melanogaster show the same occupied site, it is more likely, under most population models, to be the result of common ancestry than of independent insertion events. In situ hybridization allows the entire chromosome to be screened, for a particular element, in a single step. The location of the element can be determined to the nearest lettered subdivision using the maps produced by Lefevre (1976)
. Whereas the technique only allows localization to the polytene band, and thus insertions of the same element family at the same apparent location in different strains might be many kilobases apart, multiple insertions of this kind would often be expected to create homoplasies in the tree of the chromosomes. We do not see such homoplasies in our results, and in the analysis below, we condition upon an assumption of an absence of apparent homoplasies, but not an absence of multiple insertions into the same site, as detected by in situ hybridization.
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Materials and Methods |
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Molecular Biology
The salivary glands of third instar larvae were removed and their polytene chromosomes prepared for in situ hybridization on poly-l-lysinecoated slides. The probes were biotinylated plasmids. The biotin was incorporated on Boehringer Mannheim biotin-16-dUTP via nick translation. Bound probe was visualized using Vector Laboratories' VECTASTAIN Elite ABC kit and diaminobenzidine tetrahydrochloride, darkened with nickel chloride. Prepared slides were washed in 2x standard saline citrate, 1x phosphate-buffered saline (PBS), and 1x PBS/0.1% Triton solutions. The polytene chromosomes were visualized using Giemsa's stainimproved R66 solution. The locations of element insertion sites were determined viewing the fourth and other chromosomes using an objective with 100x magnification.
Bands in division 101 are particularly difficult to determine. Both roo and 297 have two insertion sites in this division; these have been labeled and ß, with the more distal sites being termed
and the proximal sites, ß.
Six of the retrotransposable elements are long terminal repeat (LTR) retrotransposable elements; these are 412 (provided by D. Finnegan), mdg-1, mdg-3, roo, and 297 (provided by K. O'Hare), and opus-2217 in Charlesworth, Lapid, and Canada (1992)
(provided by B. Charlesworth). One non-LTR retrotransposon was used, 2156 (provided by B. Charlesworth).
Simulations
In order to test the power of the data to resolve between the hypotheses, simulated phylogenetic trees were created using a coalescent approach, upon which mutations were created.
Creating the PhylogeniesBackground Selection
The sample is modeled using a coalescent process with an effective size of Nb (greatly reduced relative to the census population size because of the effects of background selection). Following Hudson (1990)
, the time of a coalescent starting with i lineages is obtained by selecting a random number P in the range 01, and then calculating the coalescence time from
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Creating the PhylogeniesSelective Sweeps
Random trees are created as above, except that now the population size is not treated as constant. The size is constant recently, but during the period of the selective sweep prior to this, the population size is treated as being that of the subset of the population possessing the advantageous allele sweeping through. It is assumed that there is no background selection in this model, and the effective diploid population size after the selective sweep event is the same as that of the other autosomes, and is symbolized by N. The last selective sweep affecting the chromosome is assumed to have reached fixation T generations ago. Prior to this, the proportion of the population which possessed the advantageous allele spreading to fixation, and which thus could have been ancestors of the alleles in the sample, was increasing, and thus diminished as one follows time backwards in the coalescent process. Using an argument analogous to that of Stephan, Wiehe, and Lenz (1992)
and Braverman et al. (1995)
, we say that T generations ago, the wild-type allele (being replaced by a codominant allele with a selective advantage of s) had been reduced to one copy, and the frequency of the wild-type allele t generations earlier than T would be est/(2N + est). The frequency of the advantageous mutant allele would thus be 2N/(2N + est). The number of copies of the advantageous allele T + t generations ago would thus be 4N2/(2N + est).
If we have a coalescent process starting with i lineages generations into the selective sweep phase (with time being read backwards, i.e., T +
generations ago), then if we are t -
generations into this coalescent process, the probability of a coalescent event in a short time
t, which we can call
P (where P is the probability of a coalescence by time t), is given by
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Making the Mutations
It is assumed that the ancestral fourth chromosome has x element insertions. There are 56 distinguishable mutation events which are possible, representing eight chromosomal divisions and seven element families. As a given chromosomal division could contain more than one element of a given family, an array is defined in which each lineage has a certain number of insertions in each of the 56 boxes. The ancestral chromosome has x of the boxes with exactly one insertion, and the rest with none. The mutational events of each of the 56 boxes in each of the branches of the phylogeny are considered in turn. The rate of insertion of any element into any chromosomal division is assumed to have a constant expectation of µ per generation, and the rate of loss of any element is yµ. Thus, y represents how many times more likely it is that an element will be lost from an occupied division than that an element of a given family will be inserted into a previously empty division.
For any branch and any box, therefore, the expected number of new insertions is time x µ, where time is the length of the branch in generations. With probability 1 - exp(time x µ), which is approximately time x µ if this is small, the number of elements in the box is increased by one. If there are m elements in the box at the start of a branch, then with probability 1 - exp(-time x µym), which is approximately time x µym if this is small, the number of elements in the box is decreased by one.
There are three ways in which an insertion of a given element into a given division can have a frequency greater than 1 in the sample, and yet not be fixed. Firstly, if x > 0, an insertion could be descended from an element present in the ancestral chromosome, which has been deleted in some of the descendants. Secondly, the insertion, although a unique event, could be an insertion into a branch which has multiple descendants in the sample. Thirdly, there could be more than one insertion of the same type, occurring independently in different branches of the tree. Each process would create a site frequency greater than 1, but in the first and the third cases, but not in the second, there would be a possibility that homoplasy would be detected in the data. For this reason, once the mutations have been placed on the tree, all site-element combinations with a frequency above 1 in the sample are examined in all possible pairwise combinations, and for each pair, we see if there is evidence for homoplasy. In this context, a pair of sites are said to show evidence for homoplasy if all the four combinations are seen: (++), (+-), (-+), and (--), where (++), for example, represents the presence, in at least one individual in the sample, of elements at both sites.
Once the tree has been created and the mutations placed on the tree, the simulated genotypes of the sample are examined. If n is the total number of site-element combinations occupied in at least one of the individuals of the observed sample, we see if the number of sites in the simulated sample is n. If it is, the tree is retained provided that the homoplasy test shows no homoplasious combinations of sites.
For each type of simulation, background selection and selective sweep models with different values of T, µ are chosen by trial and error such that the average n in the simulated data matches the n observed. s is always 0.005 in the selective sweep models. Then large numbers of simulations are performed, and from each of those retained in the analysis (retained because there are n sites and no homoplasies), we record the number, j, of what we call internal sites. These are sites where more than one chromosome in the sample possesses the site, and more than one chromosome lacks it. j can thus range from 0 to n. n - j is defined as the number of external sites. Thus, the expected frequency distribution of j (given n and the model) is observed. In addition, for simulations retained in the analysis, and thus with n sites, we observe ki (the number of chromosomes occupied out of 11) of the ith site in the sample, and calculate the mean number of differences between the chromosomes in the sample by
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Results |
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The data show the number of variable element-division combinations to be 16, and the number of sites found more than once in the sample (internal sites) to be seven. Thus, in the simulations, we tried a background selection model and many selective sweep models, differing in the time to the selective sweep, and adjusted the insertion rate until the expected number of insertion sites was 16.
From the data, Tajima's D has a value of minus 0.905. This is not significantly different from 0, but the inaccuracy of the infinite sites model implies that D would be expected to be weakly positive, given neutrality.
The initial simulations assumed that there was no deletion process, i.e., y = 0. Consequently, as there were no sites fixed in the sample, the number of sites in the ancestral chromosome, x, must also be zero.
The background selection model used Nb = 2,000. For this model, the µ value which gives an expected n of 16 is 1.48 x 10-5 per element per division per generation. The selective sweeps all use N = 5 x 105 and s = 0.005. T has been varied, and for each T, a value of µ has been found that gives a mean number of 16 sites in the simulated trees. Thus, µ decreases with increasing T.
For each model, it is possible to observe the proportion of simulated trees in which there are a total of 16 sites and no homoplasies. For example, for the background selection model, 14,850 of 500,000 simulated trees met these two criteria. From these successful trees, we can observe the proportions of trees with all the possible numbers of internal sites (sites seen more than once and less than 10 times in the sample). Of the 14,850 successful trees, 842 or 5.67% had exactly the same number of seven internal sites as was seen in the data. The simulations also create distributions of the values of the mean number of differences between the chromosomes when 16 sites are present. Our distribution of site frequencies means that the 16 sites create a gene diversity of 4.218, i.e., two randomly chosen chromosomes show an average of 4.218 differences in the presence or absence of elements. This value is less than that expected under the background selection model with a total of 16 sites, as predicted from the negative D of Tajima, but more than that expected under any of the selective sweep models tried.
Table 3 shows the proportions of successful trees that had seven internal sites for each of the models tried. As can be seen, the likelihood of seven successful sites is reasonably high for the background selection model, very low for selective sweep models with low T, and quite high for selective sweep models with reasonably high T (above 50,000 generations to the sweep). Figure 2 shows the distribution of the numbers of internal sites in the simulations for the selective sweep model with T = 2,000, the selective sweep model with T = 100,000, and the background selection model. Even though the probabilities of the seven internal sites under the latter two models are similar, the overall distributions are very different.
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The relationship between the likelihood ratio from our data and the expected reduction in nucleotide variability on the fourth chromosome is shown in figure 4 . Thus, if one believed that the nucleotide variation on the fourth chromosome was 5% of that of chromosomal regions unaffected by background selection or sweeps, then our data would produce a likelihood ratio of around 10 in favor of background selection. If one believed that nucleotide variability on the fourth chromosome was 20% of that in chromosomes unaffected by background selection or sweeps, our data would be more consistent with the selective sweep model.
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The estimated insertion rates can be converted into transposition rates per element copy in the following way. As µ is the rate of insertion of a given family into a fourth chromosomal division, and as each fourth chromosomal division is around 0.166% of the total genome, the rate of insertion per genome, per element family, is around 600µ. If each family is represented by 30 element copies per haploid genome, the rate of transposition per element copy is 20µ. Thus, from the selective sweep model results in Table 3
, transposition rates per element copy range from 0.56 x 10-5 to 10.2 x 10-5. These rates are consistent with independent estimates of the rates of retrotransposon movement, e.g., those described by Charlesworth, Sniegowski, and Stephan (1994)
as "of the order of 10-4 or 10-5." Thus, the mutation rates required to create these insertion numbers cannot be used to resolve the timing of any selective sweep.
These simulations have all assumed an absence of insertion sites in the ancestral chromosome. However, if there were sites in the ancestral chromosome, these could have been lost in some or all of the descendant chromosomes, with the result that a site in the frequency range from two to nine chromosomes (an internal site) could be descended from a site in the ancestral chromosome which has been deleted in the ancestor(s) of two or more of the chromosomes in the sample. Thus, we repeated the simulations for T = 10,000, but now allowing y to be 1 or 5, and allowing x to range from 0 to 3. The results are shown in figure 5ac. Figure 5a shows the distribution of external sites when a single site was present in the ancestral chromosome, and with three y values (relative deletion rates) of zero, one, and five times the insertion rate. There is very little difference between the three distributions. The same is seen in figure 5b. Here, the distributions of external sites, when the deletion rate is equal to the insertion rate, are shown when there are zero to three sites in the ancestral chromosome. The corresponding distributions when the deletion rate is five times the insertion rate are shown in figure 5c. However, the higher the deletion rate, the lower the probability that the tree will be accepted because there will be a much higher probability of apparent homoplasies. Thus, with the deletion rate five times the insertion rate in figure 5c, the proportions of trees accepted, relative to the corresponding proportions for the equal rates simulations in figure 5b, are 99%, 72%, 57%, and 47% for zero, one, two, and three initial sites, respectively.
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Discussion |
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There is evidence that transposable elements have a weakly deleterious effect on their bearers, and this may be reflected in our data showing slightly fewer sites with nonunique frequencies than is expected under the background selection model. The mean number of differences between chromosomes is also reduced. It could be argued that retrotransposable element insertion sites are not a good choice of marker on account of their deleterious effects. However, the impact of weak selection will be to lower the frequencies of sites in the sample relative to the neutral expectation, and thus lower the proportion of internal sites and the mean number of differences between the chromosomes. This is expected by theory and confirmed by our simulations (results not shown here). Thus, as selection would make the data resemble those expected under selective sweeps, we can regard our use of neutral simulation, and the conclusion that background selection is occurring, as a conservative interpretation.
The weakly deleterious effect of insertions is also probably why, despite most chromosomes in the sample having at least one element insertion, it appears that the ancestral chromosome possessed no elements. A chromosome free of harmful elements is more likely to end up being ancestral. If a deletion process exists, it is possible that an internal site could be derived from a site present in the ancestor, but simulations with ancestral sites and a deletion process yield probability distributions for internal sites (fig. 5 ) that are very similar to those generated under an insertion process alone. This similarity is probably because if deletions occurred early, or more than once, the tree would have a high chance of showing homoplasy, and thus not being included in the analysis. It is possible that a hybrid selective sweep model could be produced. This model would include sites in the original chromosome spread by a selective sweep, followed by weak selection for one or more variants which had lost the ancestral site(s). This hybrid model might give a higher number of internal sites than are calculated under these neutral models. However, such a complex model would succeed because a series of selective sweeps were being postulated, the last of which had not reached fixation, and the resulting genealogy was mimicking that expected under neutrality. As selection can theoretically take any form, it is always possible to produce selective models which resemble the predictions of neutrality.
Our data are consistent with background selection, but are also consistent with a reasonably ancient selective sweep. The one published study of variation on the fourth chromosome (Berry, Ajioka, and Kreitman 1991
) revealed no variation at all, and thus, were one to explain these data with a selective sweep, the maximum likelihood estimate of the time of the sweep would be the present. However, these authors interpreted their data as suggesting a sweep 0.28N generations ago. For our N, this corresponds to 140,000 generations ago. A sweep at this time is even more consistent with our number of internal sites than background selection. However, this estimate of 0.28N generations is based on an assumption of a flat prior probability distribution of the timing of the most recent selective sweep, and can be regarded as inflated to an entirely arbitrary degree. Indeed, another analysis of the same results estimated a much more recent sweep (Charlesworth 1992
).
This discussion has focused on whether the data support the background selection model or the selective sweep model, as if these are simple alternatives and exactly one will be correct. However, both processes could be acting simultaneously, and even if a selective sweep were primarily responsible for the reduction in fourth-chromosome variability, it seems very probable that background selection (which is an inevitable consequence of deleterious mutation) must be playing a minor role also. Furthermore, other evolutionary models can also predict the correlation between recombination rate and genetic variability. In particular, the TIM model, created by Takahata and co-workers (Takahata, Iishi, and Matsuda 1975
; Takahata and Kimura 1979
) and discussed by Gillespie (1994)
is expected to create datasets which look quite like ours. This model postulates selection coefficients which vary randomly with time. It predicts a reduction in diversity in low-recombination regions, but with a negative Tajima's D of around -1 (Gillespie 1994
). However, there are also some problems with this model. The time-dependent changes in selection intensity seem intrinsically unlikely. Furthermore, Takahata and Kimura (1979)
suggest that if sufficient selected sites are linked together, the potential for temporally varying selection to lower variability will be reduced. With 83 genes on the fourth chromosome, it seems likely that the number of selected sites under selection would be too high for the TIM model to predict a major loss of variability.
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Acknowledgements |
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Footnotes |
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Keywords: retrotransposons
background selection
Drosophila melanogaster
fourth chromosome
Address for correspondence and reprints: John Brookfield, Institute of Genetics, University of Nottingham, Queens Medical Centre, Nottingham NG7 2UH, United Kingdom. john.brookfield{at}nottingham.ac.uk
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References |
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