Reconstructing recombination network from sequence data: the small parsimony problem

The small parsimony problem is studied for reconstructing recombination networks from sequence data. The small parsimony problem is polynomial-time solvable for phylogenetic trees. However, the problem is proved NP-hard even for galled recombination networks. A dynamic programming algorithm is also developed to solve the small parsimony problem. It takes O(dn2(3h)) time on an input recombination network over length-d sequences in which there are h recombination and n - h tree nodes.     

The ancestry of a sample of sequences subject to recombination

In this article we discuss the ancestry of sequences sampled from the coalescent with recombination with constant population size 2N. We have studied a number of variables based on simulations of sample histories, and some analytical results are derived. Consider the leftmost nucleotide in the sequences. We show that the number of nucleotides sharing a most recent common ancestor (MRCA) with the leftmost nucleotide is approximately log(1 + 4N Lr)/4Nr when two sequences are compared, where L denotes sequence length in nucleotides, and r the recombination rate between any two neighboring nucleotides per generation. For larger samples, the number of nucleotides sharing MRCA with the leftmost nucleotide decreases and becomes almost independent of 4N Lr. Further, we show that a segment of the sequences sharing a MRCA consists in mean of 3/8Nr nucleotides, when two sequences are compared, and that this decreases toward 1/4Nr nucleotides when the whole population is sampled. A measure of the correlation between the genealogies of two nucleotides on two sequences is introduced. We show analytically that even when the nucleotides are separated by a large genetic distance, but share MRCA, the genealogies will show only little correlation. This is surprising, because the time until the two nucleotides shared MRCA is reciprocal to the genetic distance. Using simulations, the mean time until all positions in the sample have found a MRCA increases logarithmically with increasing sequence length and is considerably lower than a theoretically predicted upper bound. On the basis of simulations, it turns out that important properties of the coalescent with recombinations of the whole population are reflected in the properties of a sample of low size.     

A heuristic method to reconstruct the history of sequences subject to recombination

Summary Sequences subject to recombination and gene conversion defy phylogenetic analysis by traditional methods since their evolutionary history cannot be adequately summarized by a tree. This study investigates ways to describe their evolutionary history and proposes a method giving a partial reconstruction of this history. Multigene families, viruses, and alleles from within populations experience recombinations/gene conversions, so the questions studied here are relevant for a large body of data and the suggested solutions should be very practical. The method employed was implemented in a program, RecPars, written in C and was used to analyze nine retroviruses.     

Reconstructing ancestral character states under Wagner parsimony

The problem of assigning optimal character states to the hypothetical ancestors of an evolutionary tree under the Wagner parsimony criterion is examined. A proof is provided for the correctness of Farris's well-known, but previously unproven, algorithm for solving this problem. However, the solution is not, in general, unique, and Farris's method obtains only a subset (generally only one) of the possible solutions. Algorithms that discover other solutions and that resolve ambiguities through the imposition of ancillary criteria are developed and discussed. A method for determining the optimal length of a given tree without actually assigning character states to hypothetical ancestors is described.     

Reconstructing evolutionary graphs: 3D parsimony

The increasing recognition that symbioses have greatly altered evolution through genome fusions is creating a need for algorithms that can reliably detect and reconstruct fusions. Here, we generalize the bootstrappers gambit algorithm (a quartet method) in order to permit it to analyze both bifurcations and fusions under a single mathematical model, and thereby detect past genomic branchings and endosymbioses. This new method, 3-dimensional parsimony, can be applied to aligned sequences, such as gene, indel, or other genomic presence/absence sequences. It also provides a statistical measure of support for each possible graph. The usefulness of this method is demonstrated by applying it to the ring of life.     

Ontogenetic Sequence Analysis: using parsimony to characterize developmental sequences and sequence polymorphism

Ontogenetic sequences are a pervasive aspect of development and are used extensively by biologists for intra- and interspecific comparisons. A tacit assumption behind most such analyses is that sequence is largely invariant within a species. However, recent embryological and experimental work emphasizes that ontogenetic sequences can be variable and that sequence polymorphism may be far more prevalent than is generally realized. We present a method that uses parsimony algorithms to map hierarchic developmental patterns that capture variability within a sample. This technique for discovering and formalizing sequences is called the "Ontogenetic Sequence Analysis" (OSA). Results of OSA include formalized diagrams of reticulating networks, describe all most parsimonious sequences, and can be used to develop statistics and metrics for comparison of both intraspecific and interspecific sequence variation. The method is tested with examples of human postnatal skeletal ossification, comprising a time-calibrated data set of human hand and wrist epiphyseal unions, and a longitudinal data set of human wrist ossification. Results illustrate the validity of the method for discovering sequence patterns and for predicting morphologies not represented in analytic samples. OSA demonstrates the potential and challenges of incorporating ontogenetic sequences of morphological information into evolutionary analyses.     

Modeling the evolution of protein domain architectures using maximum parsimony

Domains are basic evolutionary units of proteins and most proteins have more than one domain. Advances in domain modeling and collection are making it possible to annotate a large fraction of known protein sequences by a linear ordering of their domains, yielding their architecture. Protein domain architectures link evolutionarily related proteins and underscore their shared functions. Here, we attempt to better understand this association by identifying the evolutionary pathways by which extant architectures may have evolved. We propose a model of evolution in which architectures arise through rearrangements of inferred precursor architectures and acquisition of new domains. These pathways are ranked using a parsimony principle, whereby scenarios requiring the fewest number of independent recombination events, namely fission and fusion operations, are assumed to be more likely. Using a data set of domain architectures present in 159 proteomes that represent all three major branches of the tree of life allows us to estimate the history of over 85% of all architectures in the sequence database. We find that the distribution of rearrangement classes is robust with respect to alternative parsimony rules for inferring the presence of precursor architectures in ancestral species. Analyzing the most parsimonious pathways, we find 87% of architectures to gain complexity over time through simple changes, among which fusion events account for 5.6 times as many architectures as fission. Our results may be used to compute domain architecture similarities, for example, based on the number of historical recombination events separating them. Domain architecture "neighbors" identified in this way may lead to new insights about the evolution of protein function.     

Reconstructing the evolution of agarics from nuclear gene sequences and basidiospore ultrastructure

Traditional classifications of agaric fungi involve gross morphology of their fruit bodies and meiospore print-colour. However, the phylogeny of these fungi and the evolution of their morphological and ecological traits are poorly understood. Phylogenetic analyses have already demonstrated that characters used in traditional classifications of basidiomycetes may be heavily affected by homoplasy, and that non-gilled taxa evolved within the agarics several times. By integrating molecular phylogenetic analyses including domains D1–D3 and D7–D8 of nucLSU rDNA and domains A–C of the RPB1 gene with morphological and chemical data from representative species of 88 genera, we were able to resolve higher groups of agarics. We found that the species with thick-walled and pigmented basidiospores constitute a derived group, and hypothesize that this specific combination of characters represents an evolutionary advantage by increasing the tolerance of the basidiospores to dehydration and solar radiation and so opened up new ecological niches, e.g. the colonization of dung substrates by enabling basidiospores to survive gut passages through herbivores. Our results confirm the validity of basidiospore morphology as a phylogenetic marker in the agarics.     

Inference of homologous recombination in bacteria using whole-genome sequences

Bacteria and archaea reproduce clonally, but sporadically import DNA into their chromosomes from other organisms. In many of these events, the imported DNA replaces an homologous segment in the recipient genome. Here we present a new method to reconstruct the history of recombination events that affected a given sample of bacterial genomes. We introduce a mathematical model that represents both the donor and the recipient of each DNA import as an ancestor of the genomes in the sample. The model represents a simplification of the previously described coalescent with gene conversion. We implement a Monte Carlo Markov chain algorithm to perform inference under this model from sequence data alignments and show that inference is feasible for whole-genome alignments through parallelization. Using simulated data, we demonstrate accurate and reliable identification of individual recombination events and global recombination rate parameters. We applied our approach to an alignment of 13 whole genomes from the Bacillus cereus group. We find, as expected from laboratory experiments, that the recombination rate is higher between closely related organisms and also that the genome contains several broad regions of elevated levels of recombination. Application of the method to the genomic data sets that are becoming available should reveal the evolutionary history and private lives of populations of bacteria and archaea. The methods described in this article have been implemented in a computer software package, ClonalOrigin, which is freely available from http://code.google.com/p/clonalorigin/.     

Likelihood, parsimony, and heterogeneous evolution

Evolutionary rates vary among sites and across the phylogenetic tree (heterotachy). A recent analysis suggested that parsimony can be better than standard likelihood at recovering the true tree given heterotachy. The authors recommended that results from parsimony, which they consider to be nonparametric, be reported alongside likelihood results. They also proposed a mixture model, which was inconsistent but better than either parsimony or standard likelihood under heterotachy. We show that their main conclusion is limited to a special case for the type of model they study. Their mixture model was inconsistent because it was incorrectly implemented. A useful nonparametric model should perform well over a wide range of possible evolutionary models, but parsimony does not have this property. Likelihood-based methods are therefore the best way to deal with heterotachy.     

Reconstructing ancestral genome content based on symmetrical best alignments and Dollo parsimony

MOTIVATION: Gene duplications and losses (GDLs) are important events in genome evolution. They result in expansion or contraction of gene families, with a likely role in phenotypic evolution. As more genomes become available and their annotations are improved, software programs capable of rapidly and accurately identifying the content of ancestral genomes and the timings of GDLs become necessary to understand the unique evolution of each lineage. RESULTS: We report EvolMAP, a new algorithm and software that utilizes a species tree-based gene clustering method to join all-to-all symmetrical similarity comparisons of multiple gene sets in order to infer the gene composition of multiple ancestral genomes. The algorithm further uses Dollo parsimony-based comparison of the inferred ancestral genes to pinpoint the timings of GDLs onto evolutionary intervals marked by speciation events. Using EvolMAP, first we analyzed the expansion of four families of G-protein coupled receptors (GPCRs) within animal lineages. Additional to demonstrating the unique expansion tree for each family, results also show that the ancestral eumetazoan genome contained many fewer GPCRs than modern animals, and these families expanded through concurrent lineage-specific duplications. Second, we analyzed the history of GDLs in mammalian genomes by comparing seven proteomes. In agreement with previous studies, we report that the mammalian gene family sizes have changed drastically through their evolution. Interestingly, although we identified a potential source of duplication for 75% of the gained genes, remaining 25% did not have clear-cut sources, revealing thousands of genes that have likely gained their distinct sequence identities within the descent of mammals. AVAILABILITY: Query server, source code and executable are available at http://kosik-web.mcdb.ucsb.edu/evolmap/index.htm .     

Reconstructing recent human evolution.

The two most distinct models of recent human evolution, the multiregional and the recent African origin models, have different retrodictions concerning specific archaic-recent population relationships. The former model infers multiple regional archaic-modern connections and the ancient establishment of regional characteristics, whereas the latter model implies only an African archaic-all modern relationship, with recent (late Pleistocene) development of regionality. In this paper, four late archaic groups from Europe, southwest Asia, Africa and East Asia are compared with various fossil and recent Homo sapiens crania or cranial samples. The results of Penrose shape comparisons narrowly favour a late archaic African-modern special relationship over an East Asian-modern one, with European and southwest Asian Neanderthal groups much more distant. No specific archaic-recent regional relationships are indicated in the shape analyses, nor in separate examinations of patterns of regionality, which indicate a recent origin for present day regionality. The Skhul-Qafzeh sample provides an excellent shape intermediate between the archaic and recent samples.     

The evolution of recombination

The selective forces responsible for the evolution of genes mediating recombination are discussed. These genes originated because of their role indna repair. In eukaryotes, their role in repair is not sufficient to account for the evolution of meiosis and syngamy. Therefore, a “hitch-hiking” explanation is required, according to which a recombination gene gets a lift in frequency from the high-fitness genes to which it is linked. Such hitch-hiking models are reviewed: collectively they provide an adequate explanation for the maintenance of sex and recombination in eukaryotes. In prokaryotes, the main selective force favouring recombination isdna repair: the cross-overs caused by recombination may occasionally have important evolutionary effects, but they are the consequences, rather than the causes, of the evolution of recombination in prokaryotes. In both prokaryotes and eukaryotes, recombination genes also cause specific, repeatable and adaptive rearrangements of the genetic material.     

Reconstructing evolution: gene transfer from plastids to the nucleus

During evolution, the genomes of eukaryotic cells have undergone major restructuring to meet the new regulatory challenges associated with compartmentalization of the genetic material in the nucleus and the organelles acquired by endosymbiosis (mitochondria and plastids). Restructuring involved the loss of dispensable or redundant genes and the massive translocation of genes from the ancestral organelles to the nucleus. Genomics and bioinformatic data suggest that the process of DNA transfer from organelles to the nucleus still continues, providing raw material for evolutionary tinkering in the nuclear genome. Recent reconstruction of these events in the laboratory has provided a unique tool to observe genome evolution in real time and to study the molecular mechanisms by which plastid genes are converted into functional nuclear genes. Here, we summarize current knowledge about plastid-to-nuclear gene transfer in the context of genome evolution and discuss new insights gained from experiments that recapitulate endosymbiotic gene transfer in the laboratory.     

Homology in coding and non-coding DNA sequences: a parsimony perspective

Putative synapomorphy assessment (primary homology assessment) is distinct for DNA strings having a codon structure (hereafter, coding DNA) versus those lacking it (hereafter, non-coding DNA). The first requires the identification of a reading frame and of usually few in-frame insertions and deletions. In non-coding DNA, where length variation is much more common, putative synapomorphy assessment is considerably less straightforward and highly depends on the alignment method. Appreciating the existence of evolutionary constraints, alignments that consider patterns associated with specific putative evolutionary events are favored. Once the sequences have been aligned, the postulated putative evolutionary events need to be coded as an additional step. In order for the alignments and the alignment coding to be falsifiable, they should be carried out using justified and explicitly formulated criteria. Alternative coding methods for the most common patterns present in alignments of non-coding DNA are discussed here. Simpler putative synapomorphy assessment will not always correlate to more reliable phylogenetic information because simplicity does not necessarily correlate to the degree of homoplasy. The use of non-coding DNA can result in more laborious coding, but at the same time in more corroborated hypotheses, mirroring their accuracy for phylogenetic inference.     

Analysing recombination in nucleotide sequences

Throughout the living world, genetic recombination and nucleotide substitution are the primary processes that create the genetic variation upon which natural selection acts. Just as analyses of substitution patterns can reveal a great deal about evolution, so too can analyses of recombination. Evidence of genetic recombination within the genomes of apparently asexual species can equate with evidence of cryptic sexuality. In sexually reproducing species, nonrandom patterns of sequence exchange can provide direct evidence of population subdivisions that prevent certain individuals from mating. Although an interesting topic in its own right, an important reason for analysing recombination is to account for its potentially disruptive influences on various phylogenetic-based molecular evolution analyses. Specifically, the evolutionary histories of recombinant sequences cannot be accurately described by standard bifurcating phylogenetic trees. Taking recombination into account can therefore be pivotal to the success of selection, molecular clock and various other analyses that require adequate modelling of shared ancestry and draw increased power from accurately inferred phylogenetic trees. Here, we review various computational approaches to studying recombination and provide guidelines both on how to gain insights into this important evolutionary process and on how it can be properly accounted for during molecular evolution studies.     

A rate-independent technique for analysis of nucleic acid sequences: evolutionary parsimony

The method of evolutionary parsimony--or operator invariants--is a technique of nucleic acid sequence analysis related to parsimony analysis and explicitly designed for determining evolutionary relationships among four distantly related taxa. The method is independent of substitution rates because it is derived from consideration of the group properties of substitution operators rather than from an analysis of the probabilities of substitution in branches of a tree. In both parsimony and evolutionary parsimony, three patterns of nucleotide substitution are associated one-to-one with the three topologically linked trees for four taxa. In evolutionary parsimony, the three quantities are operator invariants. These invariants are the remnants of substitutions that have occurred in the interior branch of the tree and are analogous to the substitutions assigned to the central branch by parsimony. The two invariants associated with the incorrect trees must equal zero (statistically), whereas only the correct tree can have a nonzero invariant. The chi 2-test is used to ascertain the nonzero invariant and the statistically favored tree. Examples, obtained using data calculated with evolutionary rates and branchings designed to camouflage the true tree, show that the method accurately predicts the tree, even when substitution rates differ greatly in neighboring peripheral branches (conditions under which parsimony will consistently fail). As the number of substitutions in peripheral branches becomes fewer, the parsimony and the evolutionary-parsimony solutions converge. The method is robust and easy to use.      

Reconstructing patterns of reticulate evolution in plants

Until recently, rigorously reconstructing the many hybrid speciation events in plants has not been practical because of the limited number of molecular markers available for plant phylogenetic reconstruction and the lack of good, biologically based methods for inferring reticulation (network) events. This situation should change rapidly with the development of multiple nuclear markers for phylogenetic reconstruction and new methods for reconstructing reticulate evolution. These developments will necessitate a much greater incorporation of population genetics into phylogenetic reconstruction than has been common. Population genetic events such as gene duplication coupled with lineage sorting and meiotic and sexual recombination have always had the potential to affect phylogenetic inference. For tree reconstruction, these problems are usually minimized by using uniparental markers and nuclear markers that undergo rapid concerted evolution. Because reconstruction of reticulate speciation events will require nuclear markers that lack these characteristics, effects of population genetics on phylogenetic inference will need to be addressed directly. Current models and methods that allow hybrid speciation to be detected and reconstructed are discussed, with a focus on how lineage sorting and meiotic and sexual recombination affect network reconstruction. Approaches that would allow inference of phylogenetic networks in their presence are suggested.