Making a functional diploid: from polysomic to disomic inheritance
Summary
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One little understood feature of polyploid speciation is the transition from polysomic to disomic inheritance, and much recent attention has focused on the role of pairing genes in this process.
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Using computer simulations we studied the effects of mutations, chromosomal inversions, chiasma, neofunctionalization, subfunctionalization and selection on the evolution of disomic inheritance in a polyploid over 10 000 generations.
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We show that: the evolution of pairing genes is not essential for the establishment of disomic inheritance, as genetic drift, coupled with a threshold for homologue pairing fidelity, is sufficient to explain the transition from polysomic to disomic inheritance; high rates of recombination increase the number of generations required for disomic inheritance to become established; both neofunctionalization and subfunctionalization speed up the transition to disomic inheritance.
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The data suggest that during polyploid species establishment, selection will favour reduced chiasma number and/or more focused distribution. The data also suggest a new role for subfunctionalization in that it can drive disomic inheritance. The evolution of subfunctionalization in genes across the genome will then act to maintain genes in syntenic blocks and may explain why such regions are so highly conserved.
Introduction
How do autopolyploid animal and plant species that have undergone one or more rounds of whole-genome duplication become established in nature? A potential difficulty concerns the transition from polysomic inheritance, where a chromosome can combine at meiosis with one of several partners (homologues), to disomic inheritance, where specific chromosome pairs form and segregate regularly. This paper models the evolution of disomic inheritance from a population of tetraploids with polysomic inheritance.
Polyploids may arise through chromosome duplication within a species (autopolyploidy) or in association with interspecific hybridization (allopolyploidy). In nature this distinction is not clear cut and is influenced by taxonomic partitioning of natural variation; for example, autopolyploids of Prospero autumnalis arise from diploids with substantially different genotypes (Vaughan et al., 1997). In synthetic autotetraploids of rye, which were made from different diploid accessions, the less similar the parental genomes, the fewer the number of chromosomes that formed quadrivalents at meiosis (Jenkins & Chatterjee, 1994). In theory, with the evolution of disomic inheritance, the genomes of an autopolyploid will diverge through drift, as a consequence of a lack of recombination between all combinations of homologues. By contrast, an allopolyploid begins part way along that journey, inheriting, from the start, some divergence between chromosome pairs. Yet, unless the genomes are sufficiently diverged, homoeologous pairing may still occur: for example, there is some homoeologue pairing in the allopolyploids Tragopogon mirus and Tragopogon miscellus (Lim et al., 2008). As with autopolyploids, once regular disomic inheritance is established, differences between homologues/homoeologues will become exacerbated. Thus, in meiotic terms, there is little difference between autopolyploids and allopolyploids: what matters is disomic inheritance and the formation of regular chromosome pairs.
In a newly formed tetraploid, the homologous chromosomes may pair in any combination, forming univalents, bivalents, trivalents or quadrivalents. All arrangements except bivalent formation are prone to aberrant chromosome segregation (Synbenga, 1975). The problem arises upon segregation in anaphase I. For example, how multivalent chromosomes align on the metaphase I plate, the distribution of chiasma along the chromosome and the direction that segregating multivalents and univalents take at anaphase I will all influence the outcome. In addition, how a quadrivalent at anaphase I segregates can lead to any number from all four to no copies of the chromosome at a particular pole. Segregation may be further complicated by the distribution of chiasma (e.g. a quadrivalent that formed in prophase I may form chiasma focused at a recombination hot spot). Such a quadrivalent will then segregate into two bivalents at anaphase I, while the same quadrivalent with chiasma connecting both arms may not (Synbenga, 1975; Fig. 1); see also Cifuentes et al. (2010) for further discussion of meiosis in autotetraploids.
Diagrammatic representation of a quadrivalent with two chiasma, that resolves into two bivalents at metaphase I (above). The same quadrivalent, but with four chiasma, remains a quadrivalent at metaphase I (below).
Regular pairing and segregation is essential for fertility, but is frequently absent in polyploids, resulting in aneuploid gametes and individuals even after thousands of generations (Synbenga, 1975). For example, this instability can be observed in synthetic polyploids of Brassica (Gaeta et al., 2007), natural recent (< 90 yr) polyploid species Tragopogon mirus and T. miscellus (2008) and in Triticum aestivum (wheat), which is estimated to have formed c. 10 000 yr ago (Levy & Feldman, 2002).
Genes that regulate the formation of bivalents and inhibit univalent and multivalent formation (generally called pairing control genes) are likely to be important in the transition from polysomic to disomic inheritance (for reviews see Jenczewski & Alix (2004) and Cifuentes et al. (2010)). The best-characterized example is in wheat, where the Ph genes play a major role in regular bivalent pairing and ensure disomic inheritance. Deletion of Ph genes results in meiotic pairing between homoeologous chromosomes (Moore, 2002). This is exploited in wheat breeding to drive alien gene characters into breeding lines. Similarly, in the allopolyploid Brassica napus, the PrBn locus influences the frequency of homoeologous pairing in haploid plants (Nicolas et al., 2009; Cifuentes et al., 2010).
In meiosis there is a strong drive for synaptic pairing of chromosome arms, as even, for example, haploids of rye (Santos et al., 1994) and yeast (Loidl et al., 1991) will synapse with a nonhomologous partner in the absence of their homologue. There has been much discussion as to whether the genes influencing pairing in polyploid meiosis also occur in the diploid parents, or whether they adapted or evolved subsequent to polyploidy (see reviews by Jenczewski & Alix (2004) and Cifuentes et al. (2010)). In wheat, the major locus restricting homoeologous pairing, Ph1, includes multiple copies of cdk-like genes, probably arising through local duplications and insertions. These are not found at homoeologous loci and therefore are likely to have arisen subsequent to polyploidy (Al-Kaff et al., 2008). Furthermore wheat lines lacking the Ph1 locus are not restored to regular pairing by the addition of homoeologous loci from diploid relatives tested (see review by Jenczewski & Alix, 2004).
Here, we ask: Is the divergence, or evolution, of pairing control genes, like those in wheat (Griffiths et al., 2006; Colas et al., 2008) and Brassica (Jenczewski & Alix, 2004; Liu et al., 2006) a prerequisite for the evolution of disomic inheritance? How does recombination affect the transition from polysomic to disomic inheritance? How is the generation time to disomic inheritance affected by chromosome inversions and the evolution of neofunctionalization (new beneficial genes arising from duplicate copies) and subfunctionalization (the divergence of tissue-specific function in duplicate gene copies)?
To address these issues we designed a computer model simulating the evolution of disomic inheritance from a population of autopolyploids with polysomic inheritance. Our approach offers a number of advantages: processes taking thousands of generations can be examined more quickly than is possible even using microorganisms; selective regimes can be precisely specified; replication of experiments is easily conducted; and the entire gene pool can be output in every generation, allowing detailed examination of the population’s genetic structure and unambiguous identification of disomic inheritance.
Description
Model outline
We used a computer model to simulate the evolution of a population of 50 autopolyploids, each starting with four identical chromosomes. We examined the divergence and pairing pattern of the chromosomes over 10 000 generations of mutation, recombination and selection, with and without chromosome inversions, neofunctionalization and subfunctionalization. Pseudocode giving the overall scheme of our model is shown in Fig. 2 and explained in detail in this text.
Pseudocode illustrating the structure of the model.
The model analysed did not necessarily use biologically realistic values for the parameters tested, as our intention was not to make quantitative predictions, but rather to illustrate the effects of changes to the parameters (see the Discussion). Pilot studies were used to identify combinations of values such that when populations did become functionally diploid, they did so neither too rapidly (< 100 generations) nor too slowly (> 10 000 generations).
The model was written in mathematica 5.0 (Wolfram Research Inc., Champaign, IL, USA) and the source code is available in the Supporting Information Notes S1.
The starting population
The starting population was closed, consisting of 50 autotetraploid individuals, each with four identical 100-base chromosomes (a–d) each carrying two 20-base genes that were specified in advance.
Chromosome pairing efficiency
At the model start, the four identical chromosomes can pair in three different ways (a-b and c-d; a-c and b-d; and a-d and b-c). The first step is to decide which of these will occur. The model aims to reflect the drive to form most similar pairs as observed in autotetraploids of rye (Jenkins & Chatterjee, 1994). However, we do not want to exclude the possibility of mispairings. We achieve this using Eqn 1, which calculates pairing efficiency for each combination of chromosome pairs. So, with the pairing ab/cd we calculate the pairing efficiency of a and b, and of c and d, and average these two numbers to produce a mean pairing efficiency. We repeat this with the other possible pairings. One of these three possible pairings is then chosen to produce gametes for the next generation in proportion to these mean pairing efficiencies. So, if the three pairing efficiency scores were 100, 50 and 50, respectively, the first pairing would be twice as likely to be chosen as either of the other two, and the second and third pairings would be just as likely to be chosen as each other.
( Eqn 1)
Fitness effects of sequence identity on chromosome pairing. The function was chosen to give a steep increase in pairing efficiency between 80% and 90% sequence identity; above 80%, chromosome pairing is efficient and there is little or no fitness cost to an individual. Below 80%, chromosome pairing is poor and the consequent fitness of individuals (Fp) is low. This function corresponds to imposing a fitness cost caused by, for example, multivalent formation and aberrant chromosome segregation at meiosis when chromosomes do not pair properly.
Generating gametes and the next generation of tetraploids
Once the probabilities of generating gametes from any particular pair of chromosomes is calculated, we produce gametes for each individual in turn. But before the gametes are generated the chromosomes undergo mutation, recombination and inversions at prespecified frequencies. Finally, we calculate the fitness of the individual, based on pairing efficiency and on the presence or absence of genes and variants, as described in Eqn 2, and use this to determine how many gametes this individual will contribute to the gene pool which will form the next generation; individuals with greater fitness will pass more gametes into the gene pool. From this pool of gametes, 2n are chosen at random, where n is the population size, and randomly combined to produce a new parental generation.
Determining fitness, neofunctionalization and subfunctionalization
( Eqn 2)
In examining subfunctionalization, individuals required at least one copy of each original gene or both copies of two variant forms of that gene (again variant forms were specified in advance). Individuals with these variants had no greater fitness than individuals with the original form of the gene.
Mutation, recombination and inversions
Mutation rate was constant (0.001 per base per generation). Recombination between paired chromosomes, r, occurred at frequencies of 0.2 or 0.4. Double or single crossovers occurred with relative frequencies of r2 and r (1 − r), respectively. The position of crossovers was random and symmetrical. Three inversion rates (i) – 0, 0.5 and 1.0 – were used. Inversions occurred between randomly chosen bases.
The generation time to disomic inheritance
Defining the fixation of disomic inheritance in a population was determined empirically. The approach taken was to identify a random chromosome from the population and assign to it all chromosomes with which it had ≥ 80% sequence identity, thus forming group 1; a threshold of 80% was used in line with our assumptions about pairing in Eqn 1. From the remaining chromosomes, another one was selected at random and all of those remaining chromosomes with which it had ≥ 80% sequence identity were assigned to it, forming a second group. Because the precise composition of the groups can vary depending on the choice of chromosomes chosen at each stage, this was repeated to produce four groups and the whole process repeated five times. The results were averaged to produce mean sizes of the two largest groups of chromosomes. If, for five consecutive generations, the two largest groups contained between them ≥ 75% of the total number of chromosomes in the population, and if they differed in size by ≤ 10% of the total number of chromosomes in the population, then disomic inheritance was deemed to have evolved in the first of these five generations. Our pilot studies showed that the populations never reverted to polysomic inheritance from this point. Where disomic inheritance had not occurred by generation 10 000, the replicate was truncated and assigned a value of 10 000. For each set of conditions, between 47 and 99 replicates were carried out depending on computer run time.
Results
Identification of the number of generations to diploidization
Figure 4 shows, for three independent runs of our evolutionary model over 10 000 generations, the number of chromosomes in the two largest groups of chromosomes in the population. In early generations, when there is little divergence between the chromosomes, then most chromosomes in the population cluster together as a single group of similar chromosomes. Hence, the largest group contains close to 200 chromosomes, while the second largest group is small, with only a few chromosomes; this second group consists mainly of chromosomes with recent inversions and mutations. At low mutation frequency, or in the presence of high recombination, this situation may remain stable for the duration of the simulation, and the population as a whole is behaving with tetrasomic inheritance (Fig. 4a). When the population evolves disomic inheritance (Fig. 4b), the chromosomes separate into two groups, each containing roughly half of the chromosomes in the population. In this situation chromosomes from one group are unlikely to mutate sufficiently to move between groups. At this stage the population is acting like an amphidiploid, with disomic inheritance. The situation in Fig. 4(c) arises if there is no selection for pairing fidelity. Here the chromosomes are free to drift, and the population consists entirely of numerous small groups of chromosomes, reflected by the two largest groups typically containing fewer than 25 chromosomes (Fig. 4c).
Three plots revealing potential scenarios of our evolutionary model. In each case, the size of the largest (black squares) and second largest (grey squares) groups of chromosomes are shown after each generation. When most of the chromosomes in the population are of a single type, the largest group will contain nearly all of the 200 chromosomes in the population; when the population is functionally disomic, there will be two roughly equal groups with c100 chromosomes each. In (a) the population remains with tetrasomic inheritance for the duration of the experiment. This is manifested by chromosomes remaining throughout sufficiently similar to each other that most group together. In (b) the population evolves disomic inheritance around generation 1350, after which, chromosomes from each of the two clusters are unlikely to pair. In (c) there was no selection for pairing efficiency (i.e. Fπ in Eqn 2 was removed and all pairing combinations were equally fit). In such a case the chromosomes diverge independently of each other and similar chromosomes drift apart.
Factors influencing the generation time to disomic inheritance
Figure 5 shows the time to disomic inheritance in number of generations, for each replicate. The variance within each set of conditions was high, reflecting the stochasticity inherent in evolutionary processes. However, several patterns were apparent. Disomic inheritance occurred more rapidly at the lower rates of recombination, and when redundant copies of the duplicated genes could acquire new functions that conferred fitness benefits (neofunctionalization); inversion rate had no effect (Table 1, Fig. 5). Neofunctionalization and subfunctionalization were not prerequisites for the evolution of disomic inheritance, which occurred in their absence. When there was no selection for chromosome pairing efficiency, disomic inheritance did not occur. In the presence of subfunctionalization and neofunctionalization the mean generation time to disomic inheritance was significantly reduced (neofunctionalization: F1,853 = 406.71, P < 0.001; subfunctionalization: F2,213 = 54.79, P < 0.001)) (Fig. 5). However the relative effects of neofunctionalization and subfunctionalization cannot be compared because they are dependent on the choice of selection coefficients, which differed in each case.
(a) The number of generations to disomic inheritance under varying recombination and inversion rates and with, or without, neofunctionalization. (b) The number of generations to disomic inheritance under three conditions (from left to right): (1) neither subfunctionalization nor neofunctionalization (no selection); (2) subfunctionalization alone; (3) neofunctionalization alone. Squares show median values, with error bars showing first and third quartiles. Post-hoc Tukey tests showed significant (α = 0.05) reductions in the generation time to disomic inheritance owing to both subfunctionalization and neofunctionalization when compared with the control. Note that the relative effects of neofunctionalization and subfunctionalization cannot be directly compared because they depend on the choice of selection coefficients, which differ in each case.
| Factor | df | F | P |
|---|---|---|---|
| Neofunctionalization (φ) | 1 | 267.65 | < 0.001 |
| Recombination rate (ρ) | 1 | 113.26 | < 0.001 |
| Inversion rate (ι) | 2 | 2.57 | 0.077 |
| Φ × ρ | 1 | 0.00 | 0.979 |
| φ × ι | 2 | 1.29 | 0.277 |
| ρ × ι | 2 | 0.19 | 0.830 |
| φ × ρ × ι | 2 | 0.24 | 0.787 |
| Error | 528 | ||
| Total | 539 |
Discussion
Our results indicate that pairing genes are not needed to drive the transition from polysomic to disomic inheritance in polyploids. We show that neofunctionalization and subfunctionalization reduce the time required for this transition, while increasing the rate of recombination has the opposite effect. Of critical importance is our supposition, expanded on below, that a derived feature of subfunctionalization is the conservation of syntenic blocks and genes in a colinear arrangement.
Parameters chosen for model
The parameters of our model were selected to test the effects of those parameters we deemed likely to influence the evolution of disomic inheritance. They were not designed to be realistic values, but values that tested the effects of the phenomena on the generation time to disomic inheritance within the constraints set up by the simplicity of our model. In designing the parameters of the model it became clear that in any case the data are either not available or vary widely between species, with no species offering all the parameters together.
A particular problem was the chromosome pairing efficiency algorithm, which is intrinsic to the model and assumes a strong drive for bivalent formation and that most appropriate pairs will form. Our approach was to follow as best we could the observation of pairing preferences in four lines of autotetraploid rye (Secale cereale), each containing homologous sets of chromosomes with different degrees of similarity to each other (Jenkins & Chatterjee, 1994). In these lines, the authors observed a stronger preference for bivalent formation than would be expected by mathematical models and that the lines favoured bivalent formation between the most similar pairs. These observations led us to use a steep curve in our chromosome pairing efficiency algorithm. There are few data, as far as we are aware, that could guide us as to the position at which to place our pairing fidelity threshold, except that it is known that some bivalents form between heterologues in haploid wheat lines where the homologous partner is absent (Wang, 1988). It is not known over which sequences pairing actually happens, although presumably it is at low copy or unique sequences. Studies on the integration of DNA into Arabidopsis thaliana has revealed that repeat sequence divergence by as little as 0.16% can substantially inhibit somatic recombination (Opperman et al., 2004). By contrast, Okumura et al. (1987) reported recombination between human satellite DNA that showed 20–30% divergence. Given these data, and that heterologues can pair in the absence of homologues, we set the chromosome pairing efficiency parameter at 80% threshold below which pairing efficiency is zero.
In angiosperms, somatic and germ-line mutations both contribute to genetic change, the former increasing with the number of cell divisions in the germ line (Klekowski et al., 1989). Angiosperms may have particularly high somatic mutation rates compared with some other eukaryotes (Kejnovsky et al., 2009). Indeed, analyses of mutation frequencies of transgenes in Arabidopsis thaliana that restore the activity of a ß-glucuronidase reporter are estimated to be 10−6 to 10−7 mutation events per base pair of gene analysed, which exceeded estimates from other eukaryotes and bacteria by at least 100-fold (Kovalchuk et al., 2000). In the context of polyploid evolution these values may all be inappropriate, particularly in early stages of polyploid formation where dramatic restructuring of the genome can occur, stimulated by the ‘genomic shock’ of polyploidy (Adams & Wendel, 2005). We chose for our analysis a mutation rate of 10−3 per base per generation, a value selected for the effective run times of our model. More realistic values only increased the run time of our experiments because reduced mutation rates meant that the evolution of disomic inheritance was slower.
In our model we varied inversion rates, experimenting with values of 0, 0.5 and 1 inversion per generation, the upper values exceeds rates that might be expected in nature, although spontaneous chromosome aberration rates at c. 0.1% for a range of chromosome anomalies have been reported in hybrid Tradescantia plants (Giles, 1940). Rarely, inversions can be common (e.g. all individuals of a population of Paeonia decomposita were heterozygotes for paracentric inversions; Wang et al., 2008). We were surprised that even the high values we used did not have significant effects on the generation time to disomic inheritance. In nature, inversions may inhibit recombination in heterozygotes and reduce fitness, which can lead to elevated sequence divergence frequencies at rearranged regions when populations separate into independent lineages (Navarro & Barton, 2003). Our model will also lead to drift at inversions because inverted chromosomes are less likely to pair with chromosomes not containing the same inversion, leading over time to increased isolation from the rest of the chromosome set. However, inversions had no effect on the evolution of disomic inheritance (F2,853 = 2.26, P = 0.105), although we had hypothesized at the start of our experiments that inversions might speed up the transition to disomic inheritance because they could potentially rapidly produce divergent groups of chromosomes.
We also varied chiasma frequencies between 0.2 and 0.4 crossovers per generation. It is typical for bivalents to have one to three chiasma per bivalent (Synbenga, 1975), typically those with two or more chiasma having at least one chiasma in each arm of the chromosome. For any individual fraction of chromosomal DNA the rate of recombination will vary enormously. In humans it is estimated there is a hotspot of recombination every 50–100 kb where the most extreme hotspots have a cross-over event every 110 meioses (0.9 cM) (Myers et al., 2006) and in A. thaliana hotspots may exceed 120 cM Mb−1 while elsewhere in the genome the value is, or is close to, zero (Mezard, 2006).
Our starting population of 50 individuals is small, although many polyploid species do indeed start from very low numbers or even single individuals (Abbott & Lowe, 2004; Ainouche et al., 2004), and Thompson & Lumaret (1992) suggest that chance effects in small populations are particularly important in polyploid establishment. The rates of chromosomal divergence, including changes triggered by polyploidy and fusions/fission, are significantly higher among herbaceous species than woody ones, probably because of small to moderate effective population sizes and high seed dispersibility (Levin & Wilson, 1976). In nature, mutations arising may be become fixed through the action of selection and drift. The consequence of the low numbers of individuals in a population is that genetic drift will have a substantial effect on population dynamics; nevertheless, statistically significant data emerge from our analyses despite the small populations and vagaries of genetic drift. The establishment of strictly disomic inheritance may take many thousands of generations to evolve, indeed even in maize (Zea mays), a tetraploid thought to have evolved c. 11.4 million yr ago (Gaut & Doebley, 1997), quadrivalents can still form when it is treated with colchicine (Poggio et al., 1990).
Our approach in this study is qualitative, rather than quantitative. This arises partly from our intention to examine the types of effect that might in theory be observed in polyploidy evolution, rather than make detailed predictions about the magnitude of those effects in practice, and partly because of the difficulties of deriving accurate input values for many of our model variables, some of which are unavailable anyway.
Disomic inheritance can evolve through the actions of genetic drift in combination with selection favouring most similar pairs
Otto (2007) suggested that sequence divergence in autopolyploids may increase pairing fidelity over time leading to the evolution of disomic inheritance. Our results (Fig. 5) support this and that pairing genes are not required for the evolution of disomic inheritance, as regular chromosome pairing evolved in our model simply through the action of genetic drift in combination with selection against organisms with chromosome pairs that had low sequence identity. If our model reflects nature, then the drive to pairing can be simply manipulated via the stringency of chromosome pairing that results in stable bivalent formation. In terms of our model this is the threshold of association reflected in the shape of Fig. 3. We call this the ‘pair-matching’ hypothesis. Without selection for pairing efficiency, disomic inheritance did not evolve.
In nature there is some evidence for bivalent enhancing or controlling genes (for a review see Jenczewski & Alix, 2004). Indeed, deletion of Ph genes in wheat results in multivalent formation involving homoeologous chromosomes. The activity of these pairing genes is not well understood, although Ph1 is a Cdk-like gene involved in chromatin remodelling and DNA replication in meiotic and premeiotic cells, respectively (Colas et al., 2008). Such genes are likely to have a similar role in diploids and in the context of polyploidy their function was modified (see Cifuentes et al., 2010). While these genes are not a prerequisite for regular disomic inheritance, they have nevertheless been selected because they enhance polyploid fitness.
Pairing efficiency is thought to be initiated in prophase I using the genome scanning mechanisms of DNA strand invasion, base-pair matching and the homologous recombination pathway (Jordan, 2006); inadequate homology between chromosomes results in failure to synapse. We can envisage that pair matching operates through meiotic tolerance to mismatches (i.e. influenced by the meiotic genome scanning mechanisms; c.f. Jordan, 2006). Strand invasion is probably initiated across the genome, although this may occur at reduced frequencies in gene-poor regions (Mezard, 2006). Our model considers a ratio of genic to nongenic DNA of 2 : 3. In nature this typically exceeds 1 : 100 with much of the nongenic sequences in angiosperms being repetitive, especially retro-elements (Grover et al., 2008). It is unlikely that meiotic scanning mechanisms operate across repetitive sequences that are scattered around the genome as this would encourage the pairing of nonhomologous chromosomes. Instead, it is likely that meiotic scanning mechanisms operate predominantly in low-copy regions, including genic domains.
The role of recombination in the establishment of disomic inheritance
Although disomic inheritance evolved in 83% of runs without any selective mechanism beyond pair matching, this occurred more rapidly at lower rates of recombination, presumably because recombination reversed the progressive divergence of separate homologous pairs. Thus, in nature, it might be expected that there will be selective advantage for a lower recombination frequency in newly formed allopolyploids because it will favour the drifting apart of two sets of chromosomes. We present recombination rates of 0.2 and 0.4 for analysis – elevated rates from those found in nature. Despite these high recombination rates acting against the formation of disomic inheritance, it nevertheless evolved through drift in combination with selection for most similar pairs.
Our data suggesting that reduced chiasma frequency in polyploids favours the evolution of disomic inheritance likely also holds for theoretical reasons. Recombination between chromosomes in polyploids can result in the formation of multivalents, which in turn can lead to aberrant segregation and reduced fertility (e.g. Synbenga, 1975). A reduced chiasma frequency per bivalent may ameliorate detrimental effects of multivalent formation in prophase I of meiosis. If chiasma are restricted to one per bivalent focused at a recombination hot spot, any quadrivalent that forms in prophase I will separate into two bivalents at metaphase I when the synaptonemal complex has dispersed and the bivalents can then segregate normally (see Fig. 1).
The role of subfunctionalization and neofunctionalization in driving disomic inheritance
Polyploidy results in the duplication of genes, leading to gene redundancy. The expected fate of these redundant genes is mutation and deletion, but in nature they are frequently maintained, perhaps through three mechanisms: (1) neofunctionalization, whereby one copy of the gene takes on a new function with a selective advantage; (2) subfunctionalization, whereby each copy of the gene takes on a tissue-specific (or time-specific) function; and (3) balanced gene drive or dosage compensation, whereby the gene copies are maintained to provide an appropriate stoichiometric balance of product in relation to different gene(s) (Semon & Wolfe, 2007; Freeling, 2008). There is a growing realization that this mechanism maintains genes, whose products form multisubunit complexes, for many millions of years following polyploidy (Birchler & Veita, 2010). By contrast, studies revealing patterns of duplicate gene retention following tetraploidy or local duplication point to a less important role for subfunctionalization than was previously thought (Freeling, 2008). Nevertheless subfunctionalization is regularly encountered in polyploids (Adams et al., 2003; Adams, 2007) and our studies suggest that it may play a role in the evolution of disomic inheritance. This role arises because once subfunctionalization occurs, there is a strong selection to maintain appropriate chromosome pairs, and once that is established genetic drift between individual pairs will exacerbate differences. It is of interest that tissue-specific expression of genes, perhaps providing evidence of subfunctionalization, has evolved (within the last 90 yr) in Tragopogon polyploids (Buggs RJA, Soltis DE and Soltis PS (pers. comm.)), despite polysomic inheritance still occurring in this species (Lim et al., 2008). Its occurrence in such materials argues against an alternative hypothesis that subfunctionalization evolves after the establishment of regular disomic inheritance.
Models predicting how subfunctionalization may evolve have been presented, which involve step-wise evolution of regulator elements (Lynch & Force, 2000; Force et al., 2005). However recent transcriptomics data from recently synthesized Gossypium allopolyploids reveal dramatic departures from expectation in the nature of the transcriptome, with high levels of genome-wide expression dominance of one or other of the parental genomes (Rapp et al., 2009). Potentially, such distortions of the transcriptome may provide the precursor for the evolution of subfunctionalization, which once established can drive disomic inheritance.
Given our prediction that subfunctionalization promotes regular chromosome pairing and disomic inheritance, an emergent property of subfunctionalization is genome stability. If gene subfunctionalization influences the activity of multiple genes across the genome, then deletion of a whole or part of the chromosome would be highly deleterious and selected against because of inappropriate gene activity. Even translocations between chromosomes can be deleterious for the same reasons. Therefore, we propose that the maintenance of duplicate genes, often in colinear arrangements and in syntenic blocks for long periods of time (e.g. in angiosperms for c. 125 million yr; Bowers et al., 2003) may be facilitated by subfunctionalized gene activity, a property that may arise early in polyploid evolution and act to drive disomic inheritance. Once fixed it then provides a barrier for chromosomal rearrangements. If such subfunctionalized genes evolve at positions scattered across the genome, perhaps at many hundreds of loci, the cumulative effects may be powerful drivers of disomic inheritance.
In the case of neofunctionalization, our model provided a strong selective advantage for neofunctionalization and it is no surprise that the allele became fixed. The derived effect of selecting for disomic inheritance may also be obvious with hindsight, although we think that this is the first time that neofunctionalization per se has been proposed as playing a role in the evolution of disomic inheritance. However the evolution of neofunctionalization may be too slow for this mechanism to be a powerful force in the evolution of disomic inheritance.
Acknowledgements
We thank Elizabeth McCarthy, Michael Chester and Professor Richard Nichols for useful discussions and Dr Eric Jenczewski and three anonymous referees whose contributions substantially improved the manuscript. We thank Grant Agency of the Czech Republic (521/07/0116) for support.
