A diffusion model for the fate of tandem gene duplicates in diploids

Suppose one chromosome in one member of a population somehow acquires a duplicate copy of the gene, fully linked to the original gene's locus. Preservation is the event that eventually every chromosome in the population is a descendant of the one which initially carried the duplicate. For a haploid population in which the absence of all copies of the gene is lethal, the probability of preservation has recently been estimated via a diffusion approximation. That approximation is shown to carry over to the case of diploids and arbitrary strong selection against the absence of the gene. The techniques used lead to some new results. In the large population limit, it is shown that the relative probability that descendants of a small number of individuals carrying multiple copies of the gene fix in the population is proportional to the number of copies carried. The probability of preservation is approximated when chromosomes carrying two copies of the gene are subject to additional, fully non-functionalizing mutations, thereby modelling either an additional cost of replicating a longer genome, or a partial duplication of the gene. In the latter case the preservation probability depends only on the mutation rate to null for the duplicated portion of the gene.     

The probability of preservation of a newly arisen gene duplicate.

Newly emerging data from genome sequencing projects suggest that gene duplication, often accompanied by genetic map changes, is a common and ongoing feature of all genomes. This raises the possibility that differential expansion/contraction of various genomic sequences may be just as important a mechanism of phenotypic evolution as changes at the nucleotide level. However, the population-genetic mechanisms responsible for the success vs. failure of newly arisen gene duplicates are poorly understood. We examine the influence of various aspects of gene structure, mutation rates, degree of linkage, and population size (N) on the joint fate of a newly arisen duplicate gene and its ancestral locus. Unless there is active selection against duplicate genes, the probability of permanent establishment of such genes is usually no less than 1/(4N) (half of the neutral expectation), and it can be orders of magnitude greater if neofunctionalizing mutations are common. The probability of a map change (reassignment of a key function of an ancestral locus to a new chromosomal location) induced by a newly arisen duplicate is also generally >1/(4N) for unlinked duplicates, suggesting that recurrent gene duplication and alternative silencing may be a common mechanism for generating microchromosomal rearrangements responsible for postreproductive isolating barriers among species. Relative to subfunctionalization, neofunctionalization is expected to become a progressively more important mechanism of duplicate-gene preservation in populations with increasing size. However, even in large populations, the probability of neofunctionalization scales only with the square of the selective advantage. Tight linkage also influences the probability of duplicate-gene preservation, increasing the probability of subfunctionalization but decreasing the probability of neofunctionalization.     

A Population-Genetic Lens into the Process of Gene Loss Following Whole-Genome Duplication

Whole-genome duplications (WGDs) have occurred in many eukaryotic lineages. However, the underlying evolutionary forces and molecular mechanisms responsible for the long-term retention of gene duplicates created by WGDs are not well understood. We employ a population-genomic approach to understand the selective forces acting on paralogs and investigate ongoing duplicate-gene loss in multiple species of Paramecium that share an ancient WGD. We show that mutations that abolish protein function are more likely to be segregating in retained WGD paralogs than in single-copy genes, most likely because of ongoing nonfunctionalization post-WGD. This relaxation of purifying selection occurs in only one WGD paralog, accompanied by the gradual fixation of nonsynonymous mutations and reduction in levels of expression, and occurs over a long period of evolutionary time, “marking” one locus for future loss. Concordantly, the fitness effects of new nonsynonymous mutations and frameshift-causing indels are significantly more deleterious in the highly expressed copy compared with their paralogs with lower expression. Our results provide a novel mechanistic model of gene duplicate loss following WGDs, wherein selection acts on the sum of functional activity of both duplicate genes, allowing the two to wander in expression and functional space, until one duplicate locus eventually degenerates enough in functional efficiency or expression that its contribution to total activity is too insignificant to be retained by purifying selection. Retention of duplicates by such mechanisms predicts long times to duplicate-gene loss, which should not be falsely attributed to retention due to gain/change in function.     

Molecular evolution of the chalcone synthase multigene family in the morning glory genome

Plant genomes appear to exploit the process of gene duplication as a primary means of acquiring biochemical and developmental flexibility. Thus, for example, most of the enzymatic components of plant secondary metabolism are encoded by small families of genes that originated through duplication over evolutionary time. The dynamics of gene family evolution are well illustrated by the genes that encode chalcone synthase (CHS), the first committed step in flavonoid biosynthesis. We review pertinent facts about CHS evolution in flowering plants with special reference to the morning glory genus, Ipomoea. Our review shows that new CHS genes are recruited recurrently in flowering plant evolution. Rates of nucleotide substitution are frequently accelerated in new duplicate genes, and there is clear evidence for repeated shifts in enzymatic function among duplicate copies of CHS genes. In addition, we present new data on expression patterns of CHS genes as a function of tissue and developmental stage in the common morning glory (I. purpurea). These data show extensive differentiation in gene expression among duplicate copies of CHS genes. We also show that a single mutation which blocks anthocyanin biosynthesis in the floral limb is correlated with a loss of expression of one of the six duplicate CHS genes present in the morning glory genome. This suggests that different duplicate copies of CHS have acquired specialized functional roles over the course of evolution. We conclude that recurrent gene duplication and subsequent differentiation is a major adaptive strategy in plant genome evolution.     

A Diffusion Approach to Approximating Preservation Probabilities for Gene Duplicates

Consider a haploid population and, within its genome, a gene whose presence is vital for the survival of any individual. Each copy of this gene is subject to mutations which destroy its function. Suppose one member of the population somehow acquires a duplicate copy of the gene, where the duplicate is fully linked to the original gene’s locus. Preservation is said to occur if eventually the entire population consists of individuals descended from this one which initially carried the duplicate. The system is modelled by a finite state-space Markov process which in turn is approximated by a diffusion process, whence an explicit expression for the probability of preservation is derived. The event of preservation can be compared to the fixation of a selectively neutral gene variant initially present in a single individual, the probability of which is the reciprocal of the population size. For very weak mutation, this and the probability of preservation are equal, while as mutation becomes stronger, the preservation probability tends to double this reciprocal. This is in excellent agreement with simulation studies.     

Probabilistic cross-species inference of orthologous genomic regions created by whole-genome duplication in yeast

Identification of orthologous genes across species becomes challenging in the presence of a whole-genome duplication (WGD). We present a probabilistic method for identifying orthologs that considers all possible orthology/paralogy assignments for a set of genomes with a shared WGD (here five yeast species). This approach allows us to estimate how confident we can be in the orthology assignments in each genomic region. Two inferences produced by this model are indicative of purifying selection acting to prevent duplicate gene loss. First, our model suggests that there are significant differences (up to a factor of seven) in duplicate gene half-life. Second, we observe differences between the genes that the model infers to have been lost soon after WGD and those lost more recently. Gene losses soon after WGD appear uncorrelated with gene expression level and knockout fitness defect. However, later losses are biased toward genes whose paralogs have high expression and large knockout fitness defects, as well as showing biases toward certain functional groups such as ribosomal proteins. We suggest that while duplicate copies of some genes may be lost neutrally after WGD, another set of genes may be initially preserved in duplicate by natural selection for reasons including dosage.     

Loss of duplicate gene expression in tetraploid Chenopodium

Genetic analyses indicate that single-banded leucine aminopeptidase (LAP) phenotypes in tetraploid Chenopodium reflect homozygosity for null alleles at either locus of a polyduplicated pair. Other duplicated isozyme loci show simplification to the diploid phenotype. Loss of duplicate gene expression in the LAP system has occurred independently in putatively specialized taxa occupying the distributional periphery of a New World tetraploid complex. The geographic/taxonomic pattern of genetic variation suggests that fixation of null alleles is mediated by stochastic genetic phenomena associated with migration. Plants homozygous for null alleles at both LAP loci show no detetable activity in assays involving several exopeptidase substrates, although growth and fertility of double-null plants are not markedly reduced. Our data confirm that loss of duplicate gene expression can occur in isozyme systems of polyploid plant taxa. Thus, lack of electrophoretically detectable duplicate gene expression is not a certain indication of diploidy. However, loss of duplicate gene expression in population systems known to be of allopolyploid origin is a clear indication of phyletic derivation.     

Evolutionary preservation of redundant duplicated genes

Gene duplication events produce both perfect and imperfect copies of genes. Perfect copies are said to be functionally redundant when knockout of one gene produces no 'scoreable', phenotypic effects. Preserving identical, duplicate copies of genes is problematic as all copies are prone to accumulate neutral mutations as pseudogenes, or more rarely, evolve into new genes with novel functions. We summarise theoretical treatments for the invasion and subsequent evolutionary modification of functionally redundant genes. We then consider the preservation of functionally identical copies of a gene over evolutionary time. We present several models for conserving redundancy: asymmetric mutation, asymmetric efficacy, pleiotropy, developmental buffering, allelic competition and regulatory asymmetries. In all cases, some form of symmetry breaking is required to maintain functional redundancy indefinitely.     

Gene duplication within the Green Lineage: the case of TEL genes

Recent years have witnessed a breathtaking increase in the availability of genome sequence data, providing evidence of the highly duplicate nature of eukaryotic genomes. Plants are exceptional among eukaryotic organisms in that duplicate loci compose a large fraction of their genomes, partly because of the frequent occurrence of polyploidy (or whole-genome duplication) events. Tandem gene duplication and transposition have also contributed to the large number of duplicated genes in plant genomes. Evolutionary analyses allowed the dynamics of duplicate gene evolution to be studied and several models were proposed. It seems that, over time, many duplicated genes were lost and some of those that were retained gained new functions and/or expression patterns (neofunctionalization) or subdivided their functions and/or expression patterns between them (subfunctionalization). Recent studies have provided examples of genes that originated by duplication with successive diversification within plants. In this review, we focused on the TEL (TERMINAL EAR1-like) genes to illustrate such mechanisms. Emerged from the mei2 gene family, these TEL genes are likely to be land plant-specific. Phylogenetic analyses revealed one or two TEL copies per diploid genome. TEL gene degeneration and loss in several Angiosperm species such as in poplar and maize seem to have occurred. In Arabidopsis thaliana, whose genome experienced at least three polyploidy events followed by massive gene loss and genomic reorganization, two TEL genes were retained and two new shorter TEL-like (MCT) genes emerged. Molecular and expression analyses suggest for these genes sub- and neofunctionalization events, but confirmation will come from their functional characterization.     

Preservation of duplicate genes by complementary, degenerative mutations

The origin of organismal complexity is generally thought to be tightly coupled to the evolution of new gene functions arising subsequent to gene duplication. Under the classical model for the evolution of duplicate genes, one member of the duplicated pair usually degenerates within a few million years by accumulating deleterious mutations, while the other duplicate retains the original function. This model further predicts that on rare occasions, one duplicate may acquire a new adaptive function, resulting in the preservation of both members of the pair, one with the new function and the other retaining the old. However, empirical data suggest that a much greater proportion of gene duplicates is preserved than predicted by the classical model. Here we present a new conceptual framework for understanding the evolution of duplicate genes that may help explain this conundrum. Focusing on the regulatory complexity of eukaryotic genes, we show how complementary degenerative mutations in different regulatory elements of duplicated genes can facilitate the preservation of both duplicates, thereby increasing long-term opportunities for the evolution of new gene functions. The duplication-degeneration-complementation (DDC) model predicts that (1) degenerative mutations in regulatory elements can increase rather than reduce the probability of duplicate gene preservation and (2) the usual mechanism of duplicate gene preservation is the partitioning of ancestral functions rather than the evolution of new functions. We present several examples (including analysis of a new engrailed gene in zebrafish) that appear to be consistent with the DDC model, and we suggest several analytical and experimental approaches for determining whether the complementary loss of gene subfunctions or the acquisition of novel functions are likely to be the primary mechanisms for the preservation of gene duplicates. For a newly duplicated paralog, survival depends on the outcome of the race between entropic decay and chance acquisition of an advantageous regulatory mutation.Sidow 1996(p. 717) On one hand, it may fix an advantageous allele giving it a slightly different, and selectable, function from its original copy. This initial fixation provides substantial protection against future fixation of null mutations, allowing additional mutations to accumulate that refine functional differentiation. Alternatively, a duplicate locus can instead first fix a null allele, becoming a pseudogene.Walsh 1995 (p. 426) Duplicated genes persist only if mutations create new and essential protein functions, an event that is predicted to occur rarely.Nadeau and Sankoff 1997 (p. 1259) Thus overall, with complex metazoans, the major mechanism for retention of ancient gene duplicates would appear to have been the acquisition of novel expression sites for developmental genes, with its accompanying opportunity for new gene roles underlying the progressive extension of development itself.Cooke et al. 1997 (p. 362)     

Divergence pattern of duplicate genes in protein-protein interactions follows the power law

The impact of the biological network structures on the divergence between the two copies of one duplicate gene pair involved in the networks has not been documented on a genome scale. Having analyzed the most recently updated Database of Interacting Proteins (DIP) by incorporating the information for duplicate genes of the same age in yeast, we find that there was a highly significantly positive correlation between the level of connectivity of ancient genes and the number of shared partners of their duplicates in the protein-protein interaction networks. This suggests that duplicate genes with a low ancestral connectivity tend to provide raw materials for functional novelty, whereas those duplicate genes with a high ancestral connectivity tend to create functional redundancy for a genome during the same evolutionary period. Moreover, the difference in the number of partners between two copies of a duplicate pair was found to follow a power-law distribution. This suggests that loss and gain of interacting partners for most duplicate genes with a lower level of ancestral connectivity is largely symmetrical, whereas the "hub duplicate genes" with a higher level of ancient connectivity display an asymmetrical divergence pattern in protein-protein interactions. Thus, it is clear that the protein-protein interaction network structures affect the divergence pattern of duplicate genes. Our findings also provide insights into the origin and development of biological networks.     

Evolutionary simulations to detect functional lineage-specific genes

MOTIVATION: Supporting the functionality of recent duplicate gene copies is usually difficult, owing to high sequence similarity between duplicate counterparts and shallow phylogenies, which hamper both the statistical and experimental inference. RESULTS: We developed an integrated evolutionary approach to identify functional duplicate gene copies and other lineage-specific genes. By repeatedly simulating neutral evolution, our method estimates the probability that an ORF was selectively conserved and is therefore likely to represent a bona fide coding region. In parallel, our method tests whether the accumulation of non-synonymous substitutions reveals signatures of selective constraint. We show that our approach has high power to identify functional lineage-specific genes using simulated and real data. For example, a coding region of average length (approximately 1400 bp), restricted to hominoids, can be predicted to be functional in approximately 94-100% of cases. Notably, the method may support functionality for instances where classical selection tests based on the ratio of non-synonymous to synonymous substitutions fail to reveal signatures of selection. Our method is available as an automated tool, ReEVOLVER, which will also be useful to systematically detect functional lineage-specific genes of closely related species on a large scale. AVAILABILITY: ReEVOLVER is available at http://www.unil.ch/cig/page7858.html.     

Asymmetric Functional Divergence of Young, Dispersed Gene Duplicates in Arabidopsis thaliana

One prediction of the classic Ohno model of gene duplication predicts that new genes form from the asymmetric functional divergence of a newly arisen, redundant duplicate locus. In order to understand the mechanisms which give rise to functional divergence of newly formed dispersed duplicates, we assessed the expression and molecular evolutionary divergence of a suite of 19 highly similar dispersed duplicates in Arabidopsis thaliana. These duplicates have a K _sil equal to or less than 5 % and are specific to the A. thaliana lineage; thus, they predictably represent some of the youngest duplicates in the A. thaliana genome. We found that the majority of young duplicate loci exhibit asymmetric expression patterns, with the daughter locus exhibiting reduced expression across all tissues analyzed relative to the progenitor locus or simply not expressed. Furthermore, daughter loci, on the whole, have significantly more nonsynonymous substitutions than the progenitor loci. We also identified four pairs of loci which exhibit significant (P < 0.05) evolutionary rate asymmetry, three of which exhibit elevated dN/dS in the duplicate copy. We suggest, based on these data, that functional diversification initially takes the form of asymmetric regulatory divergence that can be a direct consequence of the mode of duplication. The reduced and/or absence of expression in the daughter copy relaxes functional constraint on its protein coding sequence leading to the asymmetric accumulation of nonsynonymous mutations. Thus, our data both affirm Ohno’s prediction while explaining the mechanism by which functional divergence initially occurs following duplication for dispersed gene duplicates.     

Gene and Allelic Genealogies at a Gametophytic Self-Incompatibility Locus

The properties of gene and allelic genealogies at a gametophytic self-incompatibility locus in plants have been investigated analytically and checked against extensive numerical simulations. It is found that, as with overdominant loci, there are two genealogical processes with markedly different time scales. First, functionally distinct allelic lines diverge on an extremely long time scale which is inversely related to the mutation rate to new alleles. These alleles show a genealogical structure which is similar, after an appropriate rescaling of time, to that described by the coalescent process for genes at a neutral locus. Second, gene copies sampled within the same functional allelic line show genealogical relationships similar to neutral gene genealogies but on a much shorter time scale, which is on the same order of magnitude as the harmonic mean of the number of gene copies within an allelic line. These results are discussed in relation to data showing trans-specific polymorphisms for alleles at the gametophytic self-incompatibility locus in the Solanaceae. It is shown that population sizes on the order of 4 X 10(5) and a mutation rate per locus per generation as high as 10(-6) could account for estimated allelic divergence times in this family.     

Drosophila duplicate genes evolve new functions on the fly

Gene duplication is thought to play a key role in phenotypic innovation. While several processes have been hypothesized to drive the retention and functional evolution of duplicate genes, their genomic contributions have never been determined. We recently developed the first genome-wide method to classify these processes by comparing distances between expression profiles of duplicate genes and their ancestral single-copy orthologs. Application of our approach to spatial gene expression profiles in two Drosophila species revealed that a majority of young duplicate genes possess new functions, and that new functions are acquired rapidly—often within a few million years. Surprisingly, new functions tend to arise in younger copies of duplicate gene pairs. Moreover, we found that young duplicates are often specifically expressed in testes, whereas old duplicates are broadly expressed across several tissues, providing strong support for the hypothetical “out-of-testes” origin of new genes. In this Extra View, I discuss our findings in the context of theoretical predictions about gene duplication, with a particular emphasis on the importance of natural selection in the evolution of novel phenotypes.     

Chromosome mapping and phylogenetic analysis of the cytosolic acetyl-CoA carboxylase loci in wheat

The cytosolic isoform of plant acetyl-CoA carboxylase is a multidomain enzyme involved in the synthesis of very-long-chain fatty acids and in secondary metabolism. Chromosome mapping of wheat identified one locus containing cytosolic acetyl-CoA carboxylase genes (Acc-2) and a related partially processed pseudogene (Psi-Acc-2) in the distal region of the long arm of wheat homoeologous group 3 chromosomes. Multiple copies of the Acc-2 genes, whose presence was suggested by sequence analysis, are likely to be arranged in tandem repeats. At least three out of five genes cloned from hexaploid wheat map to this locus. Another locus containing Acc-2--related sequences is present in the distal region of the long arm of chromosome 5D. The identity of the hybridizing DNA present at this locus remains unknown. A system based on PCR-cloning and DNA sequence analysis of acetyl-CoA carboxylase genes was developed to address various phylogenetic and systematics questions in grasses. It was applied to reconstruct the phylogeny of the Acc-2 genes from D- and S-genome Aegilops and A-genome Triticum diploid species, AABB- and AAGG-genome tetraploid wheat, and AABBDD-genome hexaploid wheat, as well as from rye and barley. The combined cytogenetic and molecular evolution approach allowed assignment of gene sequences included in phylogenetic analysis to specific loci on homoeologous chromosomes. Recurring gene duplication followed by chromosome translocation and/or possible loss of some gene copies, as well as loss of introns, occurred in the gene family in different plant lineages. Two major Acc-2 clades appeared before the divergence of barley and rye. Nucleotide substitution rates in different parts of the Acc-2 gene were assessed. This analysis of the Acc-2 loci provides detailed information regarding evolutionary events at a low--copy-number locus containing important functional genes. These events are likely to be common and to play a significant role in shaping grass genomes.     

Reciprocal gene loss following experimental whole-genome duplication causes reproductive isolation in yeast

Whole-genome duplication has shaped the genomes of extant lineages ranging from unicellular fungi to vertebrates, and its association with several species-rich taxa has fueled interest in its potential as a catalyst for speciation. One well-established model for the evolution of reproductive isolation involves the reciprocal loss of redundant genes at different loci in allopatric populations. Whole-genome duplication simultaneously doubles the entire gene content of an organism, resulting in massive levels of genetic redundancy and potential for reciprocal gene loss that may produce postzygotic reproductive isolation. Following whole-genome duplication, different populations can potentially change or lose gene function at different duplicate loci. If such populations come back into contact any F1 hybrids that are formed may suffer reduced fertility as some of the gametes they produce may not carry a full complement of functional genes. This reduction in hybrid fertility will be directly proportional to the number of divergently resolved loci between the populations. In this work, we demonstrate that initially identical populations of allotetraploid yeast subjected to mutagenesis rapidly evolve postzygotic reproductive isolation, consistent with the divergent loss of function of redundant gene copies.