DIFFERENTIATION OF A MULTIGENE FAMILY BETWEEN POPULATIONS

Differentiation of a multigene family between populations is investigated under the forces of intrachromosomal unbiased gene conversion, neutral mutation, recombination, and random drift. The infinite-site model without recombination within the gene is employed, and the average numbers of the different sites between pairs of genes at the same locus and at different loci from two populations that divided some time ago are calculated as functions of time. Since differentiation is a relative concept in which differences between populations are expressed in comparison with those within a population and since there is most likely a reduction in population size after the division of populations, the time-dependent behavior of the corresponding quantities within a population is also investigated using approximate and numerical methods. It is found that intrachromosomal unbiased gene conversion promotes differentiation at the same locus but promotes or retards that between different loci, depending on the parameters in a recently divided population.     

On the divergence of genes in multigene families

Statistical properties of the amount of divergence of genes in multigene families are studied. The model considered is an infinite-site neutral model with unbiased intrachromosomal conversion, unbiased interchromosomal conversion, and recombination. By considering the time back to the most recent common ancestor of two genes, both the probability of identity and the moments of S, the number of sites that differ between two sampled genes, are obtained. We find that if recombination rates are large or conversion is always interchromosomal, then the expectation of S is 4N mu n where N is the population size, mu is the rate of mutation per generation per gene and n is the number of genes in the gene family, as the conversion rates approach zero, the moments of divergence do not approach the moments of divergence with conversion rates equal to zero, and it is possible for a decrease in the rate of intrachromosomal conversion to result in a higher probability of identity, but a greater mean divergence of the two genes.     

On the divergence of members of a transposable element family

Statistical properties of the amount of divergence of members of a transposable element family are studied. The analysis is based on the model proposed by Langley et al. [5], describing the evolution of a family of selectively neutral transposable elements in a finite haploid population of size 2N. By considering the time back to the most recent common ancestor of two copies, both the probability of identity and the moments of the number of sites that differ between two sampled copies are obtained. Our analytic results are consistent with the numerical results of Ohta [8] for a similar model. The effects of gene conversion are also examined. In agreement with Slatkin [9], we find that gene conversion has a minimal effect on the probability of identity providing that the rate of deletion is sufficiently large.     

Repeat-induced point mutation and the population structure of transposable elements in Microbotryum violaceum

Repeat-induced point mutation (RIP) is a genome defense in fungi that hypermutates repetitive DNA and is suggested to limit the accumulation of transposable elements. The genome of Microbotryum violaceum has a high density of transposable elements compared to other fungi, but there is also evidence of RIP activity. This is the first report of RIP in a basidiomycete and was obtained by sequencing multiple copies of the integrase gene of a copia-type transposable element and the helicase gene of a Helitron-type element. In M. violaceum, the targets for RIP mutations are the cytosine residues of TCG trinucleotide combinations. Although RIP is a linkage-dependent process that tends to increase the variation among repetitive sequences, a chromosome-specific substructuring was observed in the transposable element population. The observed chromosome-specific patterns are not consistent with RIP, but rather suggest an effect of gene conversion, which is also a linkage-dependent process but results in a homogenization of repeated sequences. Particular sequences were found more widely distributed within the genome than expected by chance and may reflect the recently active variants. Therefore, sequence variation of transposable elements in M. violaceum appears to be driven by selection for transposition ability in combination with the context-specific forces of the RIP and gene conversion.     

The Cohesive Population Genetics of Molecular Drive

The long-term population genetics of multigene families is influenced by several biased and unbiased mechanisms of nonreciprocal exchanges (gene conversion, unequal exchanges, transposition) between member genes, often distributed on several chromosomes. These mechanisms cause fluctuations in the copy number of variant genes in an individual and lead to a gradual replacement of an original family of n genes (A) in N number of individuals by a variant gene (a). The process for spreading a variant gene through a family and through a population is called molecular drive. Consideration of the known slow rates of nonreciprocal exchanges predicts that the population variance in the copy number of gene a per individual is small at any given generation during molecular drive. Genotypes at a given generation are expected only to range over a small section of all possible genotypes from one extreme (n number of A) to the other (n number of a). A theory is developed for estimating the size of the population variance by using the concept of identity coefficients. In particular, the variance in the course of spreading of a single mutant gene of a multigene family was investigated in detail, and the theory of identity coefficients at the state of steady decay of genetic variability proved to be useful. Monte Carlo simulations and numerical analysis based on realistic rates of exchange in families of known size reveal the correctness of the theoretical prediction and also assess the effect of bias in turnover. The population dynamics of molecular drive in gradually increasing the mean copy number of a variant gene without the generation of a large variance (population cohesion) is of significance regarding potential interactions between natural selection and molecular drive.     

Rates of movement and distribution of transposable elements in Drosophila melanogaster: in situ hybridization vs Southern blotting data.

Genomic copy numbers and the rates of movement of nine families of transposable elements (TEs) of Drosophila melanogaster were estimated in two sets of mutation accumulation lines: Beltsville and Madrid. Southern blotting was used to screen a large number of samples from both genetic backgrounds for TEs. The Madrid lines were also screened by in situ hybridization of TEs to polytene chromosomes, in order to obtain more detailed information about the behaviour of TEs in the euchromatin. Southern blotting data provided evidence of insertions and excision events in both genetic backgrounds, occurring at rates of approximately 10(-5) and 10(-6) per element copy per generation, respectively. In contrast, in situ data from the Madrid background presented a completely different picture, with no evidence for excisions, and a significantly higher rate of transposition (1.01 x 10(-4)). Direct comparison of the two data sets suggests that the Southern blotting technique had serious deficiencies: (i) it underestimated element abundance; (ii) it revealed less than 30% of the new insertions detected by in situ hybridization; and (iii) changes in the size of restriction fragments from any source were spuriously identified as simultaneous insertion-excision events. Our in situ data are consistent with previous studies, and suggest that selection is the main force controlling element spread by transposition.     

The Evolution of Multigene Families under Intrachromosomal Gene Conversion

A model for the evolution of the probabilities of genetic identity within and between loci of a multigene family in a finite population is formulated and investigated. Unbiased intrachromosomal gene conversion, equal crossing over between tandemly repeated genes, random genetic drift and mutation to new alleles are incorporated. Generations are discrete and nonoverlapping; the diploid, monoecious population mates at random. Formulas for the equilibrium values of the probabilities of identity and a cubic equation for the rate of convergence are deduced. Numerical examples indicate the following. The amount of homology at equilibrium generally decreases as the mutation rate, the population size and the number of repeats increase; it may increase or decrease with increasing crossover rate. The intralocus homology has an intermediate minimum, whereas the interlocus homology increases, as the rate of gene conversion increases. The intralocus homology decreases, whereas the interlocus homology increases, as the proportion of symmetric heteroduplexes increases. The characteristic convergence time can be sufficiently short to imply that intrachromosomal gene conversion may be an important mechanism for maintaining sequence homogeneity among repeated genes. The convergence time decreases as the conversion rate and the proportion of symmetric heteroduplexes increase; although exceptions occur, it generally increases as the population size and the number of repeats increase; it may increase or decrease with increasing crossover rate.     

Population genetics models of transposable elements

The control of transposable element copy number is of considerable theoretical and empirical interest. Under simple models, copy numbers may increase without limit. Mechanisms that can prevent such an increase include those in which the effect of selection increases with copy number, those in which the rate of transposition decreases with copy number, and those where unlimited increase in copy number is prevented by the consequences of functional heterogeneity in the transposable element family. Finite population sizes may attenuate the power of natural selection to act on transposable element copy number in a number of ways that may be of particular importance in laboratory populations. First, a small host population size will create occasional periods in which the variance between individuals in copy number is diminished, and with it the power of natural selection, even when the expected variance is Poisson. Second, small population sizes will produce high-frequency transposable element sites, systematically reducing the variance in copy number. The consequences will be particularly profound when the selective damage of transposable elements follows from their heterozygosity, as when ectopic exchange limits copy number. This revised version was published online in August 2006 with corrections to the Cover Date.     

A study of ten families of transposable elements on X chromosomes from a population of Drosophila melanogaster

Data were collected on the distribution of ten families of transposable elements among fourteen X chromosomes isolated from a natural population of Drosophila melanogaster, by means of in situ hybridization to polytene chromosomes. It was found that, with the exception of roo, the copy number per chromosome followed a Poisson distribution. There was no evidence for linkage disequilibrium, either within or between families. Some pairs of families of elements were correlated with respect to the identity of the sites that were occupied in the sample, although there was no evidence for a correlation with respect to the sites at which elements attained relatively high frequencies. Elements appeared to be distributed randomly along the distal part of the X chromosome. There was, however, a strong tendency for elements to accumulate at the base of the chromosome. Element frequencies per chromosome band were generally low, except at the base of the chromosome where bands in subdivisions 19E and 20A sometimes had high frequencies of occupation. These results are discussed in the light of models of the population dynamics of transposable elements. It is concluded that they provide strong evidence for the operation of a force or forces opposing transpositional increase in copy number. The accumulation of elements at the base of the chromosome is consistent with the idea that unequal exchange between elements at non-homologous sites is such a force, although other possibilities cannot be excluded at present. The data suggest that the rate of transposition per element per generation is of the order of 10(-4), for the elements included in this study.     

Regulation of Drosophila P element transposition.

Drosophila P transposable elements are the best-studied family of eukaryotic non-retroviral transposons. P element transposition is regulated in several different ways and has thus provided a unique system with which to study the control of DNA rearrangements and gene expression in metazoans. Recent genetic and biochemical experiments have begun to shed light on the mechanism of P element transposition and the mechanisms controlling the temporal and spatial patterns of transposition.     

High-frequency P element loss in Drosophila is homolog dependent

P transposable elements in Drosophila melanogaster can undergo precise loss at a rate exceeding 13% per generation. The process is similar to gene conversion in its requirement for a homolog that is wild type at the insertion site and in its reduced frequency when pairing between the homologs is inhibited. However, it differs from classical gene conversion by its high frequency, its requirement for P transposase, its unidirectionality, and its occurrence in somatic and premeiotic cells. Our results suggest a model of P element transposition in which jumps occur by a "cut-and-paste" mechanism but are followed by double-strand gap repair to restore the P element at the donor site. The results also suggest a technique for site-directed mutagenesis in Drosophila.     

Genomic parasites or symbionts? Modeling the effects of environmental pressure on transposition activity in asexual populations

Transposable elements are DNA segments capable of persisting in host genomes by self-replication in spite of deleterious mutagenic effects. The theoretical dynamics of these elements within genomes has been studied extensively, and population genetic models predict that they can invade and maintain as a result of both intra-genomic and inter-individual selection in sexual species. In asexuals, the success of selfish DNA is more difficult to explain. However, most theoretical work assumes constant environment. Here, we analyze the impact of environmental change on the dynamics of transposition activity when horizontal DNA exchange is absent, based on a stochastic computational model of transposable element proliferation. We argue that repeated changes in the phenotypic optimum in a multidimensional fitness landscape may induce explosive bursts of transposition activity associated with faster adaptation. However, long-term maintenance of transposition activity is unlikely. This could contribute to the significant variation in the transposable element copy number among closely related species.     

Rates of movement of transposable elements on the second chromosome of Drosophila melanogaster

The rates of movement of 11 families of transposable elements of Drosophila melanogaster were studied by means of in situ hybridization of probes to polytene chromosomes of larvae from a long-term mutation accumulation experiment. Replicate mutation-accumulation lines carrying second chromosomes derived from a single common ancestral chromosome were maintained by backcrosses of single males heterozygous for a balancer chromosome and a wild-type chromosome, and were scored after 116 generations. Twenty-seven transpositions and 1 excision were detected using homozygous viable and fertile second chromosomes, for a total of 235,056 potential sources of transposition events and a potential 252,880 excision events. The overall transposition rate per element per generation was 1.15 x 10(-4) and the excision rate was 3.95 x 10(-6). The single excision (of a roo element) was due to recombination between the element's long terminal repeats. A survey of the five most active elements among nine homozygous lethal lines revealed no significant difference in the estimates of transposition and excision rates from those from viable lines. The excess of transposition over excision events is in agreement with the results of other in situ hybridization experiments, and supports the conclusion that replicative increase in transposable element copy number is opposed by selection. These conclusions are compared with those from other studies, and with the conclusions from population surveys of element frequencies.     

A Model for DNA Sequence Evolution within Transposable Element Families

A quantitative model is proposed for the expected degree of relationship between copies of a family of transposable elements in a finite population of hosts. Special cases of the model (in which the process of homogenization of element copies either is or is not limited by transposition rate) are presented and illustrated, using data on mobile sequences from different species. It is shown that transposition will be expected, in large populations, to result in only a rather distant relationship between transposable elements at different genomic sites. Possible inadequacies of the model are suggested and quantified.     

What is the impact of transposable elements on host genome variability?

The spread of a transposable element family through a wild population may be of astonishing rapidity. At least three families of transposable genetic elements have recently invaded Drosophila melanogaster worldwide, including the P element. The mechanism has been a process of effectively replicative transposition, and, for the P element, has occurred notwithstanding the sterility induced by unrestricted movement. This element's invasion into D. melanogaster has been accompanied by the development of heterogeneity between P sequences, most of which now have internal deletions. Increasing evidence suggests that some deleted elements can repress P transposition, thereby protecting the host from the harmful effects of complete elements. Such repressing elements may rise to high frequencies in populations as a result of selection at the level of the host. We here investigate selective sweeps invoked by the spread of P sequences in D. melanogaster populations. Numerous high-frequency sites have been identified on the X chromosome, which differ in frequency between populations, and which are associated with repression of P-element transposition. Unexpectedly, sequences adjacent to high-frequency P-element sites do not show reduced levels of genetic diversity, and DNA variability is in linkage equilibrium with the presence or absence of a P element at the adjacent selected site. This might be explained by multiple insertions or through a selection for recombination analogous to that seen in 'hitchhiking'.     

A branching-process model for the evolution of transposable elements incorporating selection

We have formulated a very general mathematical model to analyze the evolution of transposable genetic elements in prokaryotic populations. Transposable genetic elements are DNA sequences able to replicate and insert copies of themselves at new locations in the genome. This work characterizes the equilibrium distribution of copy number under the influence of copy number-dependent selection, transposition and deletion. Our principal results concern the equilibrium distribution of copy number in response to various selective regimes. For particular transposition patterns (e.g. unregulated transposition or copy number-dependent transposition), equilibrium distributions are calculated numerically for a variety of specific selection patterns. Selection is quantified through specification of the expected number of offspring for individuals of each type, which is generally a non-increasing function of copy number, in accord with the usual evolutionary speculations.     

The distribution of transposable elements within and between chromosomes in a population of Drosophila melanogaster. I. Element frequencies and distribution.

Data were collected on the distribution of nine families of transposable elements among second and third chromosomes isolated from a natural population of Drosophila melanogaster, by means of in situ hybridization of element probes to polytene chromosomes. It was found that the copy numbers per chromosome in the distal sections of the chromosome arms followed a Poisson distribution. Elements appeared to be distributed randomly along the distal sections of the chromosome arms. There was no evidence for linkage disequilibrium in the distal sections of the chromosomes, but some significant disequilibrium was detected in proximal regions. There were many significant correlations between different element families with respect to the identity of the sites that were occupied in the sample. There were also significant correlations between families with respect to sites at which elements achieved relatively high frequencies. Element frequencies per chromosome band were generally low in the distal sections, but were higher proximally. These results are discussed in the light of models of the population dynamics of transposable elements. It is concluded that they provide strong evidence for the operation of a force or forces opposing transpositional increase in copy number. The data suggest that the rate of transposition per element per generation is of the order of 10(-4), for the elements included in this study.     

A branching process for the early spread of a transposable element in a diploid population

Transposable elements (TEs) face significant challenges upon transfer into a new host population, invariably beginning their invasion with only a single element. The fate of this element is a product of its internal properties, the population dynamics of the host species, and genetic drift. We present a continuous-time multi-type branching process to model the early stages of TE spread. The model incorporates seasonal population size changes and is applicable to diploid hosts for prevalences up to 10%. We reproduce standard results of TE population dynamics and show that population growth may have a greater influence on reducing TE loss probability than a transpositional burst. These results are applied to the planned use of a TE to drive an antimalarial gene into an Anopheles gambiae population. The model favors a transgenic release immediately following the dry season when the An. gambiae population begins to grow. Increasing the number of transgenic hosts released has the greatest influence on reducing the probability of TE loss. Following release, the rate at which the TE increases its proportion in the population is most sensitive to its replicative transposition rate. The model recommends a replicative transposition rate greater than 0.1 per TE per generation to satisfy public health goals.     

Cloning and characterization of a transposable-like repeat in the heterochromatin of the darkling beetle Misolampus goudoti.

A long repeat unit of the PstI family in Misolampus goudoti (Coleoptera, Tenebrionodae) is characterized in this work. The 30 sequenced units have small differences in length (consensus 1169 bp), but very similar nucleotide composition (mean 61.1% A+T). PstI repeats contain a 36-bp-long inverted repeat at both the 5' and 3' ends, with a fully conserved 16-bp-long motif similar to those found in class II transposable elements. However, the transposable-like PstI repeats seems to be defective, since they do not encode for any protein related with transposition. Interestingly, energetically stable hairpins resembled the structure of a miniature interspersed transposable element, suggesting that the PstI satellite DNA family in M. goudoti may have originated from an ancestral active transposable element as also described in Drosophila guanche. The presence of transposable-like structure along with the non-detection of gene conversion or unequal crossing-over events suggest that transposition could be one of the putative molecular mechanisms involved in the strong amplification and (or) homogenization of these repeats. A putative transposition of PstI repeats allowing their genomic mobility also could explain why this satellite is widely distributed to all heterochromatic regions, telomeres, pericentromeric regions, and on the Y chromosome, whereas satellites of other tenebrionids lacking transposable-like structures are restricted only to pericentromeric regions.