Population Genetics Models of Competition Between Transposable ...

Copyright Ó 2006 by the Genetics Society of America DOI: 10.1534/genetics.105.052241

Population Genetics Models of Competition Between Transposable Element Subfamilies Arnaud Le Rouzic*,1 and Pierre Capy*,†,2 *Laboratoire E´volution, Geńe´tique et Spećiation, CNRS, 91198 Gif-sur-Yvette, France and †Universite´ Paris-Sud 11, Faculte´ des Sciences d’Orsay (IFR 115, Geńome: Structure, Fonction, Evolution), 91405 Orsay, France Manuscript received October 11, 2005 Accepted for publication July 24, 2006 ABSTRACT Transposable elements are one of the major components of genomes. Some copies are fully efficient; i.e., they are able to produce the proteins needed for their own transposition, and they can move and duplicate into the genome. Other copies are mutated. They may have lost their moving ability, their coding capacity, or both, thus becoming pseudogenes slowly eliminated from the genome through deletions and natural selection. Little is known about the dynamics of such mutant elements, particularly concerning their interactions with autonomous copies. To get a better understanding of the transposable elements’ evolution after their initial invasion, we have designed a population genetics model of transposable elements dynamics including mutants or nonfunctional sequences. We have particularly focused on the case where these sequences are nonautonomous elements, known to be able to use the transposition machinery produced by the autonomous ones. The results show that such copies generally prevent the system from achieving a stable transposition–selection equilibrium and that nonautonomous elements can invade the system at the expense of autonomous ones. The resulting dynamics are mainly cyclic, which highlights the similarities existing between genomic selfish DNA sequences and host–parasite systems.

G

ENES usually represent a minor part of the genomes, and most of the DNA content of a eukaryote nucleus consists of intergenic repeated sequences. Some of them, such as telomeric or centromeric sequences, appear to play fundamental roles in the cell, whereas the others do not seem to provide any adaptive feature and have been sometimes called ‘‘junk DNA’’ (Wong et al. 2000). Some moderately repetitive sequences, the transposable elements (TEs), often constitute a significant proportion of the genomes (15% in Drosophila, 45% in Homo sapiens, and up to 70% in Zea mays; Deininger and Roy-Engel 2002). These elements are known to be able to move and duplicate into the genome through various transposition mechanisms (Capy et al. 1998), allowing them to remain despite some harmful effects (deleterious insertions, deletions, or ectopic recombinations). After several decades of both experimental and theoretical studies, the coevolution between genes and their intragenomic parasites is still a major research area. A respectable amount of theoretical work on TE invasion has been already carried out. Almost all models confirm that an autonomous element, even if it is significantly deleterious for its host, is able to invade the genome of all the individuals of a population, pro-

1 Present address: Linaeus Centre for Bioinformatics, Uppsala University, SE-751 24 Uppsala, Sweden. 2 Corresponding author: Laboratoire E´volution, Geńe´tique et Spećiation, CNRS, 91198 Gif-sur-Yvette, France. E-mail: [email protected]

Genetics 174: 785–793 (October 2006)

vided its transposition rate is high enough to counterbalance its elimination through natural selection (Hickey 1982; Charlesworth et al. 1994; Le Rouzic and Deceliere 2005). Invasive TEs may then diffuse to the other populations of a species (Quesneville and Anxolabe´he`re 1998; Deceliere et al. 2005). The majority of these models predicts the occurrence of an equilibrium state between transposition vs. deletion, selection, and transposition regulation. This equilibrium state is supposed to stabilize the average TE genomic copy number, but the time needed for such a process is still debated (Ohta 1986; Tsitrone et al. 1999). Moreover, the existence of such a stable equilibrium is far from being demonstrated experimentally. First, several new TE amplifications have been reported in the last century, such as the P (Anxolabe´he`re et al. 1988), hobo (Bonnivard et al. 2000), and I (Kidwell 1983) invasions in Drosophila melanogaster and even more families in D. simulans (Vieira et al. 1999) and in maize (San Miguel et al. 1996). Therefore, if all the TE families of a genome are able to achieve a stable equilibrium, genomes that are recurrently invaded by new TEs should be in constant expansion, which is probably not the case (Petrov 2001). Second, genome sequencing suggests that most of the TE copies of a genome are deleted and nonfunctional (e.g., Prak and Kazazian 2000; Deininger and Roy-Engel 2002; Bowen et al. 2003). Some families do not even show any functional copies, suggesting that some TE families are frequently lost, probably not only through genetic

786

A. Le Rouzic and P. Capy

drift from a high-copy-number equilibrium point. In fact, the whole-genome content in TEs is subject to recurrent mutations leading to numerous nonactive copies and other TE-derived sequences that interfere with the normal transposition mechanism. Such a process may lead to uncommon dynamics (Kaplan et al. 1985; Brookfield 1991, 1996; Quesneville and Anxolabe´he`re 2001), and the long-term evolution of a TE family might be much more complex than a stable, flat equilibrium. Modeling the mutations of TEs is, however, not straightforward. TEs generally show several features, which can be more or less affected by a mutation. For instance, a modification in a TE sequence (e.g., in the terminal repeats of DNA-based transposons and of some retroelements) may lead to the loss of mobility, but the element will still be able to produce efficient proteins and thus will contribute to the transposition of the other elements from the same family. On the other hand, mutations or deletions in the coding sequence will not affect the moving ability of a so-called ‘‘nonautonomous’’ copy, which can still spread to the genome due to other autonomous corresponding elements. In this article, we propose to split the mutations affecting TEs into two categories: (i) those affecting the moving capacity of the element and (ii) those concerning the coding capacity (‘‘activity’’) of the element. Our objective is to understand, through a population genetics model, the long-term dynamics of interactions between canonical autonomous copies and their derived mutant forms. MATERIALS AND METHODS We analyzed the dynamics of a TE family in a diploid, panmictic population, using both determinist and stochastic approaches. In all cases, a TE copy is characterized by its transposition (i.e., duplication) rate u, its deletion (or excision) rate v, and its activity a. The activity represents the aptitude for the production of transposition-related proteins, which will participate in the transposition of all the genomic copies from the same family. The transposition activity of a genome for this family is a, the average of the activities of all its copies. On the other hand, the transposition rate u is a measure of a given copy’s own transposition capacity (e.g., its aptitude to use the transposition machinery). The transposition frequency of a copy is a u and depends both on the transposition capacity of this copy and on the average activity of the genome. A copy is also characterized by its additive impact s, generally ,0, on the host fitness (the fitness of an individual carrying n copies is wn ¼ 1 1 s n). Determinist approach: Following Charlesworth and Charlesworth (1983), the variation of the average copy number n between two generations in an infinite population is Dn nSn 1 nðu vÞ; where Sn ¼

@ ln wn : @n

We consider two types of elements, named 1 and 2, that are supposed to be mobilized by the same transposition machin-

ery. If the respective activities of elements 1 and 2 are a1 and a2, then the average transpositional activity of a genome carrying, respectively, n1 and n2 elements of types 1 and 2 will be a ¼ ðn1 a1 1 n2 a2 Þ=ðn1 1 n2 Þ. Then the transposition frequencies of the two kinds of elements are, respectively, u1 a and u2 a. For simplicity, both types are assumed to have the same impact on fitness. When n1 ?1 and n2 ?1, if the mutation rates from type 1 to 2 and from 2 to 1 are, respectively, m12 and m21, the average copy numbers vary as Dn1 n1 ðSn 1 a u1 vÞ n1 m12 1 n2 m21 Dn2 n2 ðSn 1 a u2 vÞ n2 m21 1 n1 m12 : However, when n1 or n2 is small, our simulations have shown that the transposition frequency of form i cannot be approximated by ui a, since some genomes are deprived of one or both forms. For instance, the true transposition frequency of type 1 will be u1 a1 when type 2 is absent from the genome, which becomes probable if n2 is low. The bias is particularly strong if one of the elements is not autonomous (a ¼ 0), since it is not able to transpose alone. If the copies are supposed to be randomly distributed among individuals—i.e., n1 and n2 follow a Poisson distribution—then Pðn1 ¼0Þ ¼ e n1 and Pðn2 ¼0Þ ¼ e n2 , where Pðn1 ¼0Þ and Pðn2 ¼0Þ are, respectively, the probability of being absent from a genome for elements 1 and 2. Therefore, the copy number variation for both forms can be satisfactorily approximated as follows: Dn1 n1 ðSn 1 ðð1 Pðn2 ¼0Þ Þ a 1 Pðn2 ¼0Þ a1 Þ u1 vÞ n1 m12 1 n2 m21 Dn2 n2 ðSn 1 ðð1 Pðn1 ¼0Þ Þ a 1 Pðn1 ¼0Þ a2 Þ u2 vÞ n2 m21 1 n1 m12 : Stochastic simulations: This model was also implemented in an object-oriented simulation program, available at http:// www.pge.cnrs-gif.fr/bioinfo/Dyet. The simulations were initialized with a population of size N ¼ 1000 in which 1000 elements (i.e., 1 copy per genome on average) were randomly dispatched in a diploid genome constituted by 2n ¼ 6 chromosomes of 100 cM each. Reproduction: Generations are not overlapping. The population has a constant size N and comprises as many males as females. In each generation, N zygotes are created from the N parents of the previous generation. For each offspring, two parents, i.e., one male and one female, are randomly drawn P P proportionally to their fitness value w ¼ 1 1 si , where si is the sum of the selective impacts (,0) of all the copies carried by the individual. A gamete is then generated from the genome of each parent: the number of crossovers is determined following a Poissonian process, the recombination positions being uniformly distributed. Both gametes are finally merged to give a complete, reproductive individual. Transposition: Transposition takes place just after fertilization, (in other words, both germinal and somatic tissues have the same genotype). A TE copy i is defined by its transposition rate ui and its activity ai. If the average activity of the elements present in the genome is noted a, then the transposition probability of the element i will be ui a while the deletion probability is vi (i.e., deletion is not dependent on the transpositional activity). The duplicated copy has exactly the same features compared to that of the template, except for its position in the genome; the insertion probability in the genome follows a uniform distribution. Mutations: In each generation (i.e., when a gamete is generated), the TE copies can mutate, either through their transposition rate u or their activity a, with the respective

Transposable Element Dynamics

787

mutation rates mu and ma. If a mutation occurs, a random number e is generated from a Gaussian distribution with an average of 0 and a standard deviation of 1. A new value for the parameter is then computed for the mutated element, centered on the former value of the parameter, and dispersed following factors respectively termed du and da. The random factor is added directly to the former value for activity a (a9 ¼ a 1 e da) and after a log transformation for parameter u (log(u9) ¼ log(u) 1 e du), because transposition rates are usually >1, and nearly half of symmetrical mutations would decrease the rate below 0 without this transformation. Even if a , 0 and a . 1 can be considered as realistic situations (respectively, regulatory and superactive copies), we limited the activity to the interval [0; 1].

RESULTS

Transposition ability mutants: If the transposition machinery is usable by all the copies of a TE family, then these copies are certainly competing for this limited resource. Figure 1 represents the theoretical evolution of the copy number when a mutant copy with a different transposition ability (u) is introduced into the population. If the mutant is less competitive than the wild copies, it will quickly disappear, while a ‘‘better’’ mutant will invade the population and progressively replace the former element. This suggests that there is no polymorphic equilibrium state for transposition ability. However, the replacement is relatively long (several thousand generations if the mutant increases its transposition rate by 10%), and recurrent mutations may lead to the coexistence, in the genome, of several TE subfamilies. We also ran some simulations in which mutant copies regularly appear. Even if mutations are bidirectional, i.e., mutants can have lesser or higher transposition rates than the copy from which they derive, only better mutants are able to invade (Figure 2). This result can be reproduced even if the appearance frequency of these mutants is very rare (,1%, results not shown). Intragenomic selection thus always leads to more efficient elements. However, the greater the average transposition rate, the higher the average copy number in the population will be, since high transposition rates will modify the transposition–selection–deletion equilibrium. In our simulations, the transposition rate grows until copies are so numerous that the fitness of individuals decreases to 0 and the population is extinct. Activity mutants: The higher transposition rate copies are not necessarily those with the highest protein production. Indeed, some copies cannot produce any functional transcript (a ¼ 0), but are still able to transpose because of the other genomic copies from the same family. Nonautonomous forms of a TE are certainly frequent, since most nonsynonymous substitutions or deletions in the open reading frame will probably result in such a mutant. When introduced in a population, an activity mutant does not seem to invade or to be eliminated, whatever the direction of the mutation (inactive

Figure 1.—Determinist dynamics of a mobility mutant. A functional element (u ¼ 0.015, v ¼ 0.001, a ¼ 1, s ¼ 0.01) is introduced at the first generation with an average of 1 copy per individual. After 2000 generations, when the copy number is stabilized (transposition–selection equilibrium), a mutant copy with the same features except for u is introduced (five copies in all individuals, to make the plots more easily readable). (a) If the mobility of the mutant is lower than that of the wild element (u ¼ 0.014), the mutant will be eliminated. (b) If the mutant has a better mobility (u ¼ 0.016), it will progressively invade the population.

or superactive mutant, see Figure 3). This result suggests that polymorphic equilibria between autonomous and nonautonomous copies can be maintained over a long period, even if the average genomic copy number is reduced because of an overall decrease in the transposition rate. Recurrent mutations: Inactivation mutations are probably recurrent, and nonautonomous copies are likely to be progressively accumulated in the genome. Since a decreases at the same time, the average copy number of both autonomous and nonautonomous copies tends toward 0, with an increased risk of loss for the element. Simulations show that this loss is frequent in small populations (N , 500). However, for larger populations, the element is never lost since its copy number evolves in a cyclic way. Indeed, when the average copy number per genome is high, all genomes have both active and nonautonomous copies, and the transposition rate of all these copies is exactly the same: the active copies are not advantaged compared to mutant copies. However,

788


Figure 2.—Evolution of the genomic copy number (a) and the transposition rate (b) in a stochastic simulation. One thousand TEs (u ¼ 0.02, s ¼ 0.01, v ¼ 0.001) are introduced in a population of size N ¼ 1000. The transposition rate u can mutate in both directions with the rate mu ¼ 104 and the amplitude du ¼ 0.1 (see materials and methods). The shaded level is proportional to the distribution frequency of the copy number (a) and of the transposition rate (b). Only higherrate mutants are conserved and replace the former TE after a short polymorphic stage, and the average transposition rate thus grows regularly, shifting the transposition–selection equilibrium toward a higher copy number. When the copy number per genome becomes too high, the whole population could disappear (vertical solid line).

when the copy number per genome is low, autonomous copies always transpose, whereas nonautonomous copies transpose only when wild elements are present in the same genome. The average transposition rate of active copies thus becomes higher than that of mutant elements, and the active copies will start another invasion cycle. The results of both analytical and simulation models generally agree quite well. Figure 4 presents the copy number evolution for autonomous (a ¼ 1) and nonautonomous (a ¼ 0) copies for several parameter sets. The first cycle is generally different from the following ones, because the initial state is particular, since there are no mutant copies during the very first steps of the invasion. In some situations, analytical results suggest a decrease in the amplitude of the cycles, which is reversible, however, in the corresponding simulations. The stochasticity due to genetic drift certainly induces little change in the wild and mutant copy numbers and thus leads to the start of new invasion cycles. Nonautonomous TE families: However, some nonautonomous TEs are so different from the active copies that

Figure 3.—Determinist dynamics of an activity mutant. Whatever the activity of the mutant—(a) lower, a ¼ 0.8, or (b) higher, a ¼ 1.2—both mutant and wild elements will coexist in the genome. All the parameters are the same as those in Figure 1, except activity.

they have probably not been generated by several independent mutation events from complete copies. Our previous results show that, without any mutations, the copy number of both forms will be stabilized in an equilibrium state. Nevertheless, nonautonomous TE families could have different dynamic features compared to the corresponding autonomous elements. For instance, the selective impact may be lower, since nonautonomous copies are much smaller than complete elements. Simulations were run, setting different selective impacts for both forms, and results are presented in Figure 5. Since the mutation rate is 0, there are two absorbing states: (i) the autonomous copy is lost (there is no more transposition, and all TEs are lost) and (ii) the nonautonomous copy is lost (the autonomous copy will then reach a stable equilibrium state). However, the time necessary to reach one of these states can be .10,000 generations, and fluctuations, similar to those observed when mutations are allowed, can be observed. Moreover, the final state seems to be highly unpredictable and depends mainly on genetic drift. Conditions for cyclic dynamics: Simulations were run to test the range of parameters for which these cyclic dynamics are observable, and the occurrence of successive invasions and regressions seems to be the general


789

Figure 4.—Dynamics of TE autonomous copies and their corresponding nonautonomous mutants. Populations are initialized with an average of one autonomous copy per individual. The columns represent, respectively, (i) the evolution of the average total copy number per genome (i.e., autonomous plus nonautonomous) in a single simulation (N ¼ 200 individuals), (ii) the same with N ¼ 2000 individuals, (iii) the evolution of the average copy number for autonomous and nonautonomous copies in the same simulations as those in column ii (initial state is 1 autonomous and 0 nonautonomous), and (iv) the same dynamics predicted by the determinist model. Each line represents a different parameter set. (a) s ¼ 0.01, u ¼ 0.02, v ¼ 0.001, ma ¼ 0; (b) s ¼ 0.005, u ¼ 0.02, v ¼ 0.001, ma ¼ 0.0005; (c) s ¼ 0.005, u ¼ 0.02, v ¼ 0.001, ma ¼ 0.005; (d) s ¼ 0.005, u ¼ 0.015, v ¼ 0.001, ma ¼ 0.001. In a, there is no mutation and the dynamics correspond to the invasion of a single, active element.

rule. Moreover, some situations, where the transposition rate is so high that no realistic equilibrium exists, might become more plausible when some active elements are mutated toward nonautonomous copies. Finally, we tested more complex activity mutation models, such as reversible mutations or continuous steps between a ¼ 1 and a ¼ 0 (results not shown). The cycles are then sometimes less defined, leading to a more chaotic evolution, but the copy number generally failed to achieve a stable equilibrium.

DISCUSSION

Mutations of transposable elements: Even if the theoretical framework concerning genome evolution is still fragmentary, a considerable amount of data are

now available with the multiple complete genome sequences (e.g., Adams et al. 2000; Lander et al. 2001). Sequenced organisms show striking differences in their TE content. Some of them, such as bacteria or yeasts, have a low number of TEs, almost all of them being functional (Sawyer et al. 1987; Wilke et al. 1992). Others, such as Plasmodium and other protista parasites, show only very mutated TE-derived sequences or no recognizable TE at all (Gardner et al. 2002). On the other hand, D. melanogaster has many active elements and even more inactive elements (Bartolome´ et al. 2002), sometimes from families with no corresponding active copy in this genome (Quesneville et al. 2003). H. sapiens has a huge number of TE sequences, but very few of them are potentially active (Lander et al. 2001). Extreme differences also exist when the nature of TE content (e.g., DNA vs. RNA transposition-mediated

790


Figure 5.—Examples of simulations of the evolution of the total genomic copy number when there are no mutations between autonomous and nonautonomous forms. Five repetitions with the same initial state are plotted. Initially, 1000 autonomous and 1000 nonautonomous elements are present in the genome of the N ¼ 1000 individuals of the population. The nonautonomous copy (a ¼ 0, u ¼ 0.02, v ¼ 0.001, s ¼ 0.005) is less deleterious than the active copy (a ¼ 1, s ¼ 0.01). If the nonautonomous element is lost, the copy number stabilizes to the expected transposition–selection equilibrium (one simulation among five). If the autonomous copy is lost, there is no more transposition, and all copies are finally lost.

TEs) is considered. For all these organisms, among defective copies, some, but not all, are still mobilizable. As modified elements are in a majority, numerous examples of TE mutations are available. Unfortunately, most of them present important internal deletions or truncations, leading to nonfunctional elements, which are not able to move or to produce any functional protein. It is likely that these ‘‘pseudogenes’’ are progressively eliminated and cannot be considered as a successful TE subfamily: they are rather a consequence of the success of the corresponding active element. If their impact on fitness is negligible, in our model they are no longer considered as TEs. However, nonautonomous copies, i.e., those capable of moving without producing active transposition-related proteins, are also frequent in the genomes, and widespread nonautonomous TE families have indeed been described, such as MITE or SINE elements (Weiner 2002; Holyoake and Kidwell 2003). While activity mutants are relatively easy to evidence, transposition ability mutants, if they exist, are certainly much more difficult to detect, since it is not enough merely to know their sequence. However, even if there is no direct evidence, some interesting mutant TEs have already been studied. Artificial changes in the sequence of some DNA transposons do seem to improve the cis-interaction between the element and the transposase protein, e.g., for the mariner element (Auge´-Gouillou et al. 2001), the Tn5 bacterial insertion sequence (Zhou et al. 1998), or the reconstituted Sleeping Beauty element (Cui et al. 2002). Furthermore, in Drosophila, some mutant elements could be

able to replace the wild copies at the population scale, such as the hobo element (Souames et al. 2003). Nevertheless, such an invasion is possible only if the transposition rate of wild elements is subobtimal, and the reasons why transposition rates are not higher remain unclear (Charlesworth and Langley 1986). Of course, if the transposition rate is too high, it would lead to an uncontrolled, exponential increase of the elements. However, an efficient mutant will invade despite its potentially catastrophic effects on the host’s population. Another explanation could be that increasing the transposition rate consists of bypassing the host’s regulation system. When an element ‘‘jumps’’ from one species to another one, which seems to occur frequently for numerous TE families (Kidwell 1992; Silva et al. 2004), its environment (e.g., the regulation system of the host) probably changes dramatically: on the one hand, the host is less able to regulate the transposition of an unknown TE, but on the other hand, the element could be less efficient in the use of the cellular machinery of a different host. An optimal element in the former species should then be more or less efficient in the new one. Transposition rates can indeed decrease when elements are artificially introduced into other species (Daniels et al. 1989; Montchamp-Moreau 1990), but must not be too low since after a horizontal transfer an element needs to have a moderately high transposition ability to invade its new host species actively (Le Rouzic and Capy 2005). Model discussion: As for any other model, our theoretical approach supposes multiple simplifications. The host species remains very simple, and its biology (panmixia, diploid genome, distinct sexes in simulations) is supposed to offer a ‘‘neutral’’ framework to focus on TE evolution—in addition to the fact that these features are very close to the biology of H. sapiens and Drosophila, both being intensively studied model species. The genome is modeled in a straightforward way (uniform recombination rate, uniform transposition rate, . . .), not taking into account the heterogeneity of observed TE insertion patterns. However, this probably does not affect significantly the population genetics of elements (copy number dynamics, for instance), but only prevents further analysis of the theoretical genomic distribution. Some TE features are also not precisely modeled, mainly because of a lack of knowledge about them. Selection against TE insertions, for instance, is not yet perfectly described. It appears that the fitness of a genome is decreased when it carries more TE copies, but the details of the selective pressures are still poorly known (Nuzhdin 1999; Le Rouzic and Deceliere 2005). Three main hypotheses are generally proposed to explain this deleterious effect: (i) a direct effect of the TE insertion (gene disruption for instance), (ii) the occurrence of ectopic recombinations between repeated copies leading to chromosomal abnormalities,


and (iii) the effect of the transposition process itself (production of poisonous proteins, chromosomal breaks, etc.). While the deleterious impacts of the first two processes are supposed to be related to the genomic content in TEs (generally modeled through a positive correlation with the copy number), the direct effect of transposition depends on the transpositional activity in the genome, whatever the copy number. This could have an important impact on the dynamics of nonautonomous elements: by decreasing the transposition rate, nonautonomous elements are associated with high-fitness individuals and are therefore positively selected. In this case, nonautonomous copies can invade without control (Brookfield 1991, 1996) and the dynamics of the system are similar to those of regulatory elements (Charlesworth and Langley 1986). On the contrary, our model considers that all kinds of elements have a deleterious effect (even if its amplitude could vary). Recent findings indeed suggest that even inactive copies could have a negative impact on fitness (see, for instance, Petrov et al. 2003) and that there is a clear correlation between fitness and copy number (Pasyukova et al. 2004). However, the hypothesis of the direct effect of transposition cannot be definitively ruled out and can be an explanation for the permissivity of some genomes to nonautonomous elements (SINEs elements in the mammalian group, for instance, Weiner 2002). Another misunderstood point lies in the effect of the accumulation of copies in the genome. While the average deleterious effect of TE insertions have been documented in some organisms (its average seems to be between 1 and 0.5% in Drosophila; Eanes et al. 1988; Houle and Nuzhdin 2004; Pasyukova et al. 2004), the effect of the presence of existing copies on the deleterious impact of new insertions is poorly known. Charlesworth and Charlesworth (1983) have indeed shown that no equilibrium can be achieved if the impact of new insertions decreases with the copy number, and a linear (such as in this article) or a multiplicative (Charlesworth and Langley 1986; Brookfield 1996) effect of insertions on fitness is generally used to avoid an uncontrolled invasion of the elements. However, in our model, the copy number is controlled not only by natural selection, but also by a process similar to transposition regulation (related to the presence of nonautonomous elements). Modifying the selection model or the individual impact of an insertion mainly changes the amplitude of the cycles, but not the general evolution, and realistic dynamics can be obtained even when no realistic equilibrium can be expected (in the same way, Kaplan et al. 1985 also got a copy number control by inactive copies in a neutral framework). Modeling TE dynamics through a transposition rate and a deletion rate is the most common way to design a general model (i.e., which is not supposed to cor-

791

respond to a precise family of TEs) (Charlesworth and Charlesworth 1983; Kaplan et al. 1985; Charlesworth 1991; Le Rouzic and Capy 2005). In this context, the transposition rate represents any event that leads to a duplication of a copy, while a deletion models the loss of a copy from its insertion site. Numerous molecular processes can lead to these two kinds of events: homologous template-dependent process and excision for DNA elements and replicative transposition and recombination for RNA elements. A ‘‘deletion’’ may also correspond to a mutation that cancels both the functions of an element and its deleterious impact. However, amazingly, the resulting dynamics do not appear to be so different (Hua-Van et al. 2005), and a generic approach is probably pertinent. This similarity between the different TE classes can be also found in the existence of nonautonomous elements (MITEs for DNA elements, SINEs for RNA elements), which take advantage of their respective autonomous elements through different molecular mechanisms. Transposition rates can be experimentally determined and are usually estimated around or ,u ¼ 103 (Suh et al. 1995). In this article, we generally chose higher transposition rates, u ¼ 102, because (i) high transposition rates lead to faster dynamics, which is particularly convenient for time-consuming computer simulations, and (ii) the real transposition rate is less than u when nonautonomous elements are present. A similar choice has been made for the deletion rate, which has been fixed at v ¼ 0.001, while other experiments report lower rates (Suh et al. 1995). Our results suggest that transposition rate mutations certainly occur with a very low frequency, especially those increasing this transposition rate. Otherwise, more efficient mutants would segregate continuously, leading to an irrepressible growth of the TE family. On the contrary, mutations of activity can be moderately frequent without any damage to the host. However, if nonautonomous elements appear very often (i.e., with a rate equivalent to transposition), autonomous elements will be lost. This last possibility may concern some DNA elements, since their duplication is based partly on a DNA templaterepairing process, which is known to induce numerous substitutions and deletions (Engels et al. 1990). On the contrary, even if there are no mutations toward nonautonomous forms (some nonautonomous RNA elements could be in such a situation, since they are supposed to have a different origin), the general dynamics of the system are likely to be conserved. Cyclic dynamics: When transposition rate mutants are certainly rare and not able to maintain a stable polymorphism, activity mutants will lead to regular invasions followed by a regression stage. These invasion– regression cycles are observable for a wide range of parameters in our models and are still present even if the mutation model is strongly altered (e.g., by the occurrence of superactive or regulatory copies). Since

792


mutations from an active form to nonautonomous elements are not even necessary for such a periodic reinvasion of an almost lost TE family, it might well be a widespread phenomenon. More generally, the conditions necessary for cyclic dynamics are (i) a rather high expected copy number for the active element when the nonautonomous one is absent (i.e., more than a few copies per genome), (ii) an interference between wild and mutant elements (i.e., a decrease in the transposition rate when mutant copies are present), and (iii) a moderately low mutation rate from active to nonautonomous copies. The reason why the production of inactive copies does not lead to a stable equilibrium is that such a transposition regulation is not reversible: the transposition rate will remain low even if the copy number decreases, contrary to the other selfregulation models (Charlesworth and Charlesworth 1983). Mutations, leading to the appearance of modified copies interfering with complete elements, may thus play an important role in the limitation of the TE copy number. However, unlike natural selection and selfregulation, mutation does not induce an equilibrium state, but rather a regression stage, which is likely to be followed by recurrent reinvasion dynamics. The length of the predicted cycles is in the order of magnitude of the evolution timescale rather than the population genetics timescale; a complete cycle generally takes several thousand generations, which is certainly too long to be observable experimentally. Such recurrent amplifications have already been documented for several TE families, such as SINEs in primates (Ovchinnikov et al. 2002) or nonautonomous MITEs in plants (Santiago et al. 2002). This would suggest that, for some TEs at least, the maintenance in the genome can be achieved by such recurrent invasion stages. Conclusion: It is common to compare a genome with an ecosystem (Kidwell and Lisch 2001; Brookfield 2005; Mauricio 2005). In this framework, the autonomous element is a ‘‘host’’ for the defective copies (‘‘parasites’’). Multiplication of nonautonomous copies may indeed decrease the ‘‘reproduction rate’’ of complete copies, while parasitic mutant elements will take advantage of the presence of autonomous ones. Canonical transposable elements, usually considered as parasitic sequences (Doolittle and Sapienza 1980; Orgel and Crick 1980) in the genome of an organism, play the role of the victim when they are in competition with mobile but nonautonomous elements. The complexity of TE evolution thus appears to be partly due to such a multilevel parasitism (Leonardo and Nuzhdin 2002). Oscillations of population sizes in couples of interacting organisms are commonly encountered in ecology. What are the similarities between our TE dynamics models and existing predator–prey or host–parasite models? In other words, is this likeness relevant only to a vague, but convenient analogy, or is it an indication of a wide theoretical overlap between, on the one hand,

the well-studied and still developing area of interspecific interactions, and, on the other hand, the embryonic theory of genomic ecology (Bascompte and Rodriguez-Trelles 1998; Leonardo and Nuzhdin 2002; Brookfield 2005)? There are indeed striking correspondences between our simple dynamics equations and the basic Lokta–Volterra prey–predator model (Lokta 1925; Volterra 1926). Moreover, the probability of finding no host, which is the cause of the cyclic dynamics described above, is also frequently used in host–parasite models (Nicholson and Bailey 1935) (see Hassel 2000 for an overview). Even if it remains impossible to use directly ecological models in TE population genetic studies, partly because of deep discrepancies between their respective theoretical and conceptual frameworks, establishing a connection between them appears to be an exciting challenge for both communities. We are grateful to Hadi Quesneville and Ste´phane Dupas for helpful discussions. The two referees provided useful comments on the earlier version of this manuscript. The English text was reviewed by Malcolm Eden. This work was partly supported by the IFR 115, Geńome: Structure, Fonction, Evolution and by the GRD 2157 of the CNRS.

LITERATURE CITED Adams, M. D., S. E. Celniker, R. A. Holt, C. A. Evans, J. D. Gocayne et al., 2000 The genome sequence of Drosophila melanogaster. Science 287: 1185–1195. Anxolabe´he`re, D., M. G. Kidwell and G. Periquet, 1988 Molecular characteristics of diverse populations are consistent with the hypothesis of a recent invasion of Drosophila melanogaster by mobile P elements. Mol. Biol. Evol. 5: 252–269. Auge´-Gouillou, C., M. Hamelin, M. Demattei, M. Periquet and Y. Bigot, 2001 The wild-type conformation of the Mos-1 inverted terminal repeats is suboptimal for transposition in bacteria. Mol. Genet. Genomics 265: 51–57. Bartolome´, C., X. Maside and B. Charlesworth, 2002 On the abundance and distribution of transposable elements in the genome of Drosophila melanogaster. Mol. Biol. Evol. 19: 926– 937. Bascompte, J., and F. Rodriguez-Trelles, 1998 Eradication thresholds in epidemiology, conservation biology and genetics. J. Theor. Biol. 192: 415–418. Bonnivard, E., C. Bazin, B. Denis and D. Higuet, 2000 A scenario for the hobo transposable element invasion, deduced from the structure of natural populations of Drosophila melanogaster using tandem TPE repeats. Genet. Res. 75: 13–23. Bowen, N., I. Jordan, J. Epstein, V. Wood and H. Levin, 2003 Retrotransposons and their recognition of pol II promoters: a comprehensive survey of the transposable elements from the complete genome sequence of Schizosaccharomyces pombe. Genome Res. 13: 1984–1997. Brookfield, J., 2005 The ecology of the genome—mobile DNA elements and their hosts. Nat. Rev. Genet. 6: 128–136. Brookfield, J. F. Y., 1991 Models of repression of transposition in P-M hybrid dysgenesis by P cytotype and zygotically encoded repressor proteins. Genetics 128: 471–486. Brookfield, J. F. Y., 1996 Models and spread of non-autonomous selfish transposable elements when transposition and fitness are coupled. Genet. Res. 67: 199–209. Capy, P., C. Bazin, D. Higuet and T. Langin, 1998 Dynamics and Evolution of Transposable Elements. Landes Biosciences, Austin, TX. Charlesworth, B., 1991 Transposable elements in natural populations with a mixture of selected and neutral insertion sites. Genet. Res. 57: 127–134.

Transposable Element Dynamics Charlesworth, B., and D. Charlesworth, 1983 The population dynamics of transposable elements. Genet. Res. 42: 1–27. Charlesworth, B., and C. H. Langley, 1986 The evolution of self-regulated transposition of transposable elements. Genetics 112: 359–383. Charlesworth, B., P. Sniegowski and W. Stephan, 1994 The evolutionary dynamics of repetitive DNA in eukaryotes. Nature 371: 215–220. Cui, Z., A. Geurts, G. Liu, C. Kaufman and P. Hackett, 2002 Structure-function analysis of the inverted terminal repeats of the sleeping beauty transposon. J. Mol. Biol. 318: 1221–1235. Daniels, S. B., A. Chovnick and M. G. Kidwell, 1989 Hybrid dysgenesis in Drosophila simulans lines transformed with autonomous P elements. Genetics 121: 281–291. Deceliere, G., S. Charles and C. Bie´mont, 2005 The dynamics of transposable elements in structured populations. Genetics 169: 467–474. Deininger, P. L., and A. M. Roy-Engel, 2002 Mobile elements in animals and plants, pp. 1074–1102 in Mobile DNA II, edited by N. Craig, R. Craigie, M. Gellert and A. Lambowitz. American Society for Microbiology Press, Washington, DC. Doolittle, W., and C. Sapienza, 1980 Selfish genes, the phenotype paradigm and genome evolution. Nature 284: 601–603. Eanes, W. F., C. Wesley, J. Hey and D. Houle, 1988 The fitness consequences of P element insertion in Drosophila melanogaster. Genet. Res. 52: 17–26. Engels, W., D. Johnson-Schlitz, W. Eggleston and J. Sved, 1990 High-frequency P element loss in Drosophila is homolog dependent. Cell 62: 515–525. Gardner, M., N. Hall, E. Fung, O. White, M. Berriman et al., 2002 Genome sequence of the human malaria parasite Plasmodium falciparum. Nature 419: 498–511. Hassel, M. P., 2000 The Spacial and Temporal Dynamics of HostParasitoid Interactions. Oxford University Press, London/ New York/Oxford. Hickey, D. A., 1982 Selfish DNA: a sexually-transmitted nuclear parasite. Genetics 101: 519–531. Holyoake, A., and M. Kidwell, 2003 Vege and Mar: two novel hAT MITE families from Drosophila willistoni. Mol. Biol. Evol. 20: 163– 167. Houle, D., and S. V. Nuzhdin, 2004 Mutation accumulation and the effect of copia insertions in Drosophila melanogaster. Genet. Res. 83: 7–18. Hua-Van, A., A. Le Rouzic, C. Maisonhaute and P. Capy, 2005 Abundance, distribution and dynamics of retrotransposable elements and transposons: similarities and differences. Cytogenet. Genome Res. 110: 426–440. Kaplan, N., T. Darden and C. H. Langley, 1985 Evolution and extinction of transposable elements in Mendelian populations. Genetics 109: 459–480. Kidwell, M., 1983 Evolution of hybrid dysgenesis determinants in Drosophila melanogaster. Proc. Natl. Acad. Sci. USA 80: 1655–1659. Kidwell, M. G., 1992 Horizontal transfer. Curr. Opin. Genet. Dev. 2: 868–873. Kidwell, M. G., and D. R. Lisch, 2001 Transposable elements, parasitic DNA, and genome evolution. Evolution 55: 1–24. Lander, E., L. Linton, B. Birren, C. Nusbaum, M. Zody et al., 2001 Initial sequencing and analysis of the human genome. Nature 409: 860–921. Le Rouzic, A., and P. Capy, 2005 The first steps of transposable elements invasion: parasitic strategy vs. genetic drift. Genetics 169: 1033–1043. Le Rouzic, A., and G. Deceliere, 2005 The models of population genetics of transposable elements. Genet. Res. 85: 171–181. Leonardo, T., and S. Nuzhdin, 2002 Intracellular battlegrounds: conflict and cooperation between transposable elements. Genet. Res. 80: 155–161. Lokta, A. J., 1925 Elements of Physical Biology. Williams & Wilkins, Baltimore. Mauricio, R., 2005 Can ecology help genomics: The genome as ecosystem? Genetica 123: 205–209. Montchamp-Moreau, C., 1990 Dynamics of P-M hybrid dygenesis in P-transformed lines of Drosophila simulans. Evolution 44: 194–203.

793

Nicholson, A. J., and V. A. Bailey, 1935 The balance of animal populations. Part 1. Proc. Zool. Soc. Lond. 3: 149–160. Nuzhdin, S. V., 1999 Sure facts, speculations, and open questions about evolution of transposable elements. Genetica 107: 129–137. Ohta, T., 1986 Population genetics of an expanding family of mobile genetic elements. Genetics 113: 145–159. Orgel, L. E., and F. H. C. Crick, 1980 Selfish DNA: the ultimate parasite. Nature 284: 604–607. Ovchinnikov, I., A. Rubin and G. Swergold, 2002 Tracing the LINEs of human evolution. Proc. Natl. Acad. Sci. USA 99: 10522–10527. Pasyukova, E., S. Nuzhdin, T. Morozova and T. Mackay, 2004 Accumulation of transposable elements in the genome of Drosophila melanogaster is associated with a decrease in fitness. J. Hered. 95: 284–290. Petrov, D., Y. Aminetzach, J. Davis, D. Bensasson and A. Hirsh, 2003 Size matters: non-LTR retrotransposable elements and ectopic recombination in Drosophila. Mol. Biol. Evol. 20: 880–892. Petrov, D. A., 2001 Evolution of genome size: new approaches to an old problem. Trends Genet. 17: 23–28. Prak, E., and H. Kazazian, Jr., 2000 Mobile elements and the human genome. Nat. Rev. Genet. 1: 134–144. Quesneville, H., and D. Anxolabe´he`re, 1998 Dynamics of transposable elements in metapopulations: a model of P elements invasion in Drosophila. Theor. Popul. Biol. 54: 175–193. Quesneville, H., and D. Anxolabe´he`re, 2001 Genetic algorithmbased model of evolutionary dynamics of class II transposable elements. J. Theor. Biol. 213: 21–30. Quesneville, H., D. Nouaud and D. Anxolabe´he`re, 2003 Detection of new transposable element families in Drosophila melanogaster and Anopheles gambiae genomes. J. Mol. Evol. 57(Suppl. 1): S50–S59. San Miguel, P., A. Tikhonov, Y. K. Jin, N. Motchoulskaia, D. Zakharov et al., 1996 Nested retrotransposons in the intergenic regions of the maize genome. Science 274: 765–768. Santiago, N., C. Herraiz, J. Goni, X. Messeguer and J. Casacuberta, 2002 Genome-wide analysis of the emigrant family of MITEs of Arabidopsis thaliana. Mol. Biol. Evol. 19: 2285–2293. Sawyer, S., D. Dykhuizen, R. DuBose, L. Green, T. MutangaduraMhlanga et al., 1987 Distribution and abundance of insertion sequences among natural isolates of Escherichia coli. Genetics 115: 51–63. Silva, J., E. Loreto and J. Clark, 2004 Factors that affect the horizontal transfer of transposable elements. Curr. Issues Mol. Biol. 6: 57–71. Souames, S., C. Bazin, E. Bonnivard and D. Higuet, 2003 Behavior of the hobo transposable element with regard to TPE repeats in transgenic lines of Drosophila melanogaster. Mol. Biol. Evol. 20: 2055–2066. Suh, D., E. Choi, T. Yamazaki and K. Harada, 1995 Studies on the transposition rates of mobile genetic elements in a natural population of Drosophila melanogaster. Mol. Biol. Evol. 12: 748–758. Tsitrone, A., S. Charles and C. Bie´mont, 1999 Dynamics of transposable elements under the selection model. Genet. Res. 74: 159–164. Vieira, C., D. Lepetit, S. Dumont and C. Biemont, 1999 Wake up of transposable elements following Drosophila simulans worldwide colonization. Mol. Biol. Evol. 16: 1251–1255. Volterra, V., 1926 Variazioni e fluttuazioni del numero d’individui in species animali conviventi. Mem. Acad. Nazionale Lincei 2: 31–113. Weiner, A., 2002 SINEs and LINEs: the art of biting the hand that feeds you. Curr. Opin. Cell. Biol. 14: 343–350. Wilke, C., E. Maimer and J. Adams, 1992 The population biology and evolutionary significance of Ty elements in Saccharomyces cerevisiae. Genetica 86: 155–173. Wong, G. K.-S., D. A. Passey, Y.-Z. Huang, Z. Yang and J. Yu, 2000 Is ‘‘junk’’ DNA mostly intron DNA? Genome Res. 10: 1672–1678. Zhou, M., A. Bhasin and W. Reznikoff, 1998 Molecular genetic analysis of transposase-end DNA sequence recognition: cooperativity of three adjacent base-pairs in specific interaction with a mutant Tn5 transposase. J. Mol. Biol. 276: 913–925. Communicating editor: T. H. Eickbush