Starting with Ohno, a range of models has been proposed to predict the fates of paralogous gene pairs resulting from duplications. These models can be categorized by their assumptions: they can be either neutral or involving natural selection, and can consider the early stage of duplication, i.e. when the duplication is not yet fixed in the species or start with the assumption that the gene duplication has just been fixed (recently reviewed in [11]).

Immediately after the gene duplication event, the two copies are assumed to be identical and therefore functionally redundant. At this stage, there should be no selective pressure against any loss-of-function mutation affecting either copy. As a result, it is believed that most instances of gene duplications will eventually result in the loss of one of the copies (pseudogenization or nonfunctionalization). However, the relaxation of purifying selection (due to the initial redundancy) may allow some amount of divergence and occasionally can let one copy acquire a new function and be subsequently maintained by natural selection (neofunctionalization). This scenario is essential for the creative role of duplication envisioned by Ohno [1]. Force et al.[12] suggested that the presence of two redundant genes may drive the fixation of complementary degenerative mutations in both of copies, with higher probability in gene regulatory regions. At the end of this process, both gene copies are required to perform the set of functions originally performed by a single gene (subfunctionalization). These two scenarios are not mutually exclusive and may act jointly [13]. Besides these models, the maintenance of functionally redundant copies (without functional divergence) could be adaptive under specific circumstances, either through dosage effect or as a means of genetic robustness against deleterious mutations [14-16] and therefore also explain the fixation of duplications in species [11].

Functional analyses have been performed in order to determine the relative importance or the interaction between these different models. The occurrence and the characteristics of functional divergence of paralogous genes can be addressed either through the regulatory or protein-coding sequence angle.

Whole-genome expression profiles revealed divergent expression patterns between paralogous gene pairs, providing indirect evidence for subfonctionalization and/or neofunctionalization [17]. Similar conclusions were also drawn from studies of polyploid species for which duplicated genes were instantly fixed in the species founder individual [18-20]. More specific and detailed functional analyses revealed several cases of paralogs undergoing neofunctionalization or subfunctionalization [21,22].

Beside differences in gene expression, rates of molecular evolution can be used to qualify the constraints experienced by genes. In particular, contrasting the rate of protein-changing (non-synonymous) substitution (dN) and the rate of silent (synonymous) substitution (dS) at the nucleotide level allows qualifying the type of selection acting on individual gene copies after a duplication event. The intensity of purifying selection is often estimated through the ratio ω=dN/dS. Values of ω<1 are interpreted as evidence for purifying selection (the lower ω, the stronger purifying selection). Following pseudogenization, ω=1 is expected (no constraint). Last, amino acid sites exhibiting ω>1 are likely directly targeted by positive selection. As an example, the evolutionary fate of ten genes recently duplicated by retrotransposition in mice was studied by contrasting synonymous and non-synonymous rates [23]. Gene duplications have been the subject of many functional and molecular studies in plants [24,25], but here we aimed at analysing specifically the selective constraints exerted on duplicated genes through analysis of their rates of substitution. In order to shed light to the temporal variation of selective constraints acting on duplicated genes following their duplication, we focused on the evolution of fairly recent duplicated genes at a time scale appropriate for coding sequence evolution rates analysis. Such study can provide insight about the relative role of relaxation of purifying selection and positive selection in the fate of duplicated genes.

We investigated rates of molecular evolution of three duplicated gene pairs in the genus Medicago (L.), therefore maximizing the amount of available phylogenetic signal. We selected gene pairs involved directly or indirectly in the symbiotic interaction between legumes and nitrogen-fixing bacteria (rhizobia). The first genes code for polygalacturonases, which are enzymes involved in the degradation of polysaccharides. One member (Pg11) is involved in pollen tube elongation and the other (Pg3) in the tip growth of the infection threads during the establishment of the symbiosis with nitrogen-fixing bacteria Sinorhizobium sp [26]. The second genes are Lax (Like-Aux1). They are auxin efflux carriers and play an important role in auxin-controlled processes such as tissue growth and in particular development of nodules.

Mutualistic host-symbiont interactions present the interest of combining several features we can expect will promot fast evolution. Mutualisms are often based on nutrient exchanges and involve strong selective pressures, since both costs and benefits are important. The interaction with a biotic partner can cause shifting selective optima, especially if there are conflicts of interest. Finally, in contrast with host-pathogen interactions, mutualisms can involve the evolution of novel structures by both partners. The legume-rhizobium symbiosis evolved relatively recently, around 60 million years ago, culminating with the emergence of a specific organ, the root nodule [27]. Therefore, the genes underlying rhizobial symbiosis in legumes are likely to record the signatures of past selective pressures caused by the emergence and diversification of symbiosis as well as pressures linked to their current function. Due to a whole-genome duplication event that occurred approximately 58 Myr ago [28], legumes are therefore a good model to examine the changes of selective pressures over time for duplicated genes.

Models describing the evolutionary fate of duplicated genes once the duplication is fixed in the species suppose different forms of selective pressures [11]. First, according to the neofunctionalization model, i.e. evolution of a new function through functional divergence of one of the duplicated copies, selective pressures are expected to be asymmetrical between paralogs [1]. The copy fulfilling the ancestral function is expected to remain under purifying selection while the other copy is expected to experience a short period of relaxed constraint and then positive selection driving the acquisition of its new function. Second, the subfunctionalization model envisions the fixation of complementary degenerative mutations [12]. Under this model, relaxation of purifying selection is expected during the period of functional redundancy, and may allow the fixation of at least two complementary degenerative mutations (one in each gene). When both copies are jointly required to fulfil the ancestral gene function, purifying selection is still expected to be prevalent to maintain both copies. Although both models have been functionally validated, they are not exclusive and more complex scenarios combining the steps cited previously have been devised [15,25].

For all three studied paralogous gene pairs, the two copies exhibit different regimes of selection. This result suggests that these paralogous gene pairs have undergone at least some functional differentiation. Three different tests were used to qualify selective pressures governing the paralogs. The first one contrasted the average ω between paralog clades of the phylogeny and yielded significant differences only for Pg11/Pg3 (Table ​(Table1).1). The second test is specifically designed to detect positive selection affecting only a few sites of the sequence. We found signatures of positive selection in both Pg11a and Pg11c copies, and in Pg11 (Table ​(Table2).2). Finally, the clade model (Table ​(Table3)3) is a combination of branch and site models and allows investigating specifically the presence of sites evolving under divergent selective pressures between the paralogous genes and quantify its proportion. The clade model (M_D) detected a significant increase of ω in Pg11 due to the occurrence of positive selection, as detected by the site model M₈. For the paralogous pair Pg11a/Pg11c, branch models failed to detect any difference in selective pressure. Model D is more detailed and allows showing that sites under positive selection actually experience a stronger positive pressure in Pg11c than in Pg11a. Lax2 is the subject of an intense purifying selection whereas Lax4 harbours some sites (20% of sites) evolving quasi neutrally (ω=0.97). The combination of these different tests provides a more complete picture of the selective pressures at work on each set of paralog. Since each single test addresses a single hypothesis, the comparison of several complementary tests allows acquiring a more complete picture. However, the clade model, which accounts for both variation of ω among branches and amino acid position, appears as the most informative for qualifying changes of selective constraint during duplicated genes evolution [33]. The only drawback is that it does not test formally for positive selection.

We observed that the Pg3 and Pg11c gene copies were pseudogenes in several species: in M. littoralis and M. tricycla for Pg3 and in M. tornata, M. rigidula and M. polymorpha for Pg11c. Since the three genes are present and potentially functional in, at least, four other species among those studied, we can hypothesise that the mutations affecting the function of these gene copies occurred, in some phylum, after the two successive rounds of duplications leading to the presence of three copies. This observation suggests that redundancy between copies is sufficient to have allowed the loss of one copy in several species.

Functional redundancy generated by multiple copies also implies periods of relaxed selection pressures, except if duplication itself is advantageous as it is the case, for instance, for a positive dose effect of copy number [11]. Redundancy is expected to occur with a larger probability when divergence between copies is slowed as it is the case of gene conversion [34]. The phylogenetic miss positioning we observed for four genes copies (Figure ​(Figure1)1) may be explained by gene conversion. One way to test this hypothesis would be to sequence other individuals of M. tornata for example, in order to see if we could detect shared polymorphism between copies, which is a signature of gene conversion [11].

We detected sites under positive selection in Pg11 but not in Pg3. Rodriguez-Llorente et al.[26] suggested that Pg3 has been recruited by symbiosis after a duplication affecting an ancestral pollen-specific gene. The authors suggested that the modifications occurred essentially in the promoter region. Our results show that positive selection targeted both copies of Pg11 independently, possibly indicating the evolution of novel gene function. The polygalacturonase family contains members in organisms as distantly related as plants and eubacteria. In plants this gene family has been expanding dramatically through rounds of whole-genome duplications, segmental duplications and tandem duplications (66 and 59 copies in Arabidopsis thaliana and rice respectively) [35]. The high level of expansion of this family, generating periods of high redundancy, was probably accompanied by pseudogenization events, equivalent to those we detected in the Medicago genus. However as expression patterns are diverse between members of the family [35] subfunctionalization events were probably involved in the overall high retention rate of functional genes, notable in this family. Functional divergence among members of large gene families may also be driven by positive selection. Main examples in plants are disease resistance genes [36], transcription factors [37] or genes involved in development [38]. In our study, positive selection is detected in Pg11, resulting from the cumulative effects of positive selection in both Pg11a and Pg11c, the more recent duplicated gene pair we studied. Actually, this mode of selection does correspond to neither neofunctionalization nor subfunctionalization in their stricter definition. Subfunctionalization does not predict positive selection in either copy, while neofunctionalization predicts positive selection in only one copy (if detectable). Both copies could be under positive selection because they inherited, from the ancestral Pg11 gene, functions that imply regime of positive selection. Alternatively, neo-functionalization could involve adaptive differentiation of both copies (to avoid functional overlap), that would mediate adaptive evolution of both copies. Selection targets different sites in Pg11a and Pg11c and the strength of positive selection is different between them (Table ​(Table3).3). This observation is compatible with both models.

According to the clade models, the paralogs Lax2 and Lax4 experience different modes of selection. Both genes are mainly under purifying selection. Interestingly no pseudogenes were detected in Lax2 or in Lax4. The redundancy stage subsequent to the duplication generating Lax2 and Lax4 is not detectable anymore and may have been shorter than in Pg gene family. However, Lax4 appeared to be slightly, but significantly, less constrained than Lax2. According to the clade models (with 2 or 3 classes of sites, Table ​Table3)3) a relaxation of constraint is observed for about 20% of the sites for Lax4 relative to Lax2. This means either that Lax4 acquired a function that implies less functional constraints or that both genes underwent subfunctionalization in such a way that the protein sequence of Lax4 is less constrained. Currently, the precise functions of Lax2 and Lax4 are not known. Both paralogs are expressed in shoot and roots of nodulating plants of M. truncatula. Lax2 is found in Expressed Sequence Tag (EST) libraries built from different tissues (2 in early seed development, 2 in flowers, early seeds, late seeds and stems, 2 in mixed root and nodules, 1 in nematode-infected roots, in developing flowers and phosphate-starved leaf). Lax4 is not found in EST libraries but expression of Lax4 was detected in shoots and roots of nodulating plants of M. truncatula[39].