Enumeration of Ancestral Configurations for Matching Gene Trees and Species Trees

Disanto, Filippo; Rosenberg, Noah A.

doi:10.1089/cmb.2016.0159

Cited by 19 publications

(36 citation statements)

References 25 publications

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“…An alternative approach for inferring the root suggested by Allman et al (2011b) is to use maximum likelihood of the unrooted gene trees. This method has not yet been implemented; however, likelihood calculations for rooted gene tree topologies scale exponentially in the number of taxa (Degnan and Salter, 2005; Wu, 2012; Rosenberg, 2007; Disanto and Rosenberg, 2016a,b), suggesting that this method will not scale well in the number of taxa. Furthermore, the only current method available for calculating unrooted gene tree probabilities is to sum gene tree probabilities over all possible root locations.…”

Section: Discussionmentioning

confidence: 99%

Inferring rooted species trees from unrooted gene trees using approximate Bayesian computation

Alanzi

Degnan

2017

Molecular Phylogenetics and Evolution

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Methods for inferring species trees from gene trees motivated by incomplete lineage sorting typically use either rooted gene trees to infer a rooted species tree, or use unrooted gene trees to infer an unrooted species tree, which is then typically rooted using one or more outgroups. Theoretically, however, it has been known since 2011 that it is possible to consistently infer the root of the species tree directly from unrooted gene trees without assuming an outgroup. Here, we use approximate Bayesian computation to infer the root of the species tree from unrooted gene trees assuming the multispecies coalescent model. It is hoped that this approach will be useful in cases where an appropriate outgroup is difficult to find and gene trees do not follow a molecular clock. We use approximate Bayesian computation to infer the root of the species tree from unrooted gene trees. This approach could also be useful when there is prior information that makes a small number of root locations plausible in an unrooted species tree.

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Section: Discussionmentioning

confidence: 99%

Inferring rooted species trees from unrooted gene trees using approximate Bayesian computation

Alanzi

Degnan

2017

Molecular Phylogenetics and Evolution

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“…We recall some results of Disanto and Rosenberg (2017) on the number of configurations possessed by a tree.…”

Section: Known Resultsmentioning

confidence: 99%

“…In Section 2.3, we recall properties of generating functions and analytic combinatorics. Following Wu (2012), in Section 2.4 we define ancestral configurations, and we review enumerative results from Disanto and Rosenberg (2017). In Section 2.5, we relate ancestral configurations to the additive tree parameters of Wagner (2015).…”

Section: Preliminariesmentioning

confidence: 99%

“…In this section, following Disanto and Rosenberg (2017), we review features of the objects on which our study focuses: the ancestral configurations of a gene tree G in a species tree S. In our framework, exactly one gene lineage has been selected from each species, and we assume G and S have the same labeled topology t.…”

Section: Ancestral Configurations For Matching Gene Trees and Speciesmentioning

confidence: 99%

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On the Number of Non-equivalent Ancestral Configurations for Matching Gene Trees and Species Trees

Disanto

Rosenberg

2017

Bull Math Biol

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An ancestral configuration is one of the combinatorially distinct sets of gene lineages that, for a given gene tree, can reach a given node of a specified species tree. Ancestral configurations have appeared in recursive algebraic computations of the conditional probability that a gene tree topology is produced under the multispecies coalescent model for a given species tree. For matching gene trees and species trees, we study the number of ancestral configurations, considered up to an equivalence relation introduced by Wu (Evolution 66:763-775, 2012) to reduce the complexity of the recursive probability computation. We examine the largest number of non-equivalent ancestral configurations possible for a given tree size n. Whereas the smallest number of non-equivalent ancestral configurations increases polynomially with n, we show that the largest number increases with [Formula: see text], where k is a constant that satisfies [Formula: see text]. Under a uniform distribution on the set of binary labeled trees with a given size n, the mean number of non-equivalent ancestral configurations grows exponentially with n. The results refine an earlier analysis of the number of ancestral configurations considered without applying the equivalence relation, showing that use of the equivalence relation does not alter the exponential nature of the increase with tree size.

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“…Both questions are naturally related, as precise counting results often translate into efficient sampling algorithms [24,48]. The former (counting) question has been studied by Rosenberg et al in the case of the multispecies coalescent model [13][14][15][16][17]38]. However similar questions have not been explored as thoroughly for evolutionary models including gene duplication, gene loss and HGT.…”

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confidence: 99%

Counting and sampling gene family evolutionary histories in the duplication-loss and duplication-loss-transfer models

2020

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Given a set of species whose evolution is represented by a species tree, a gene family is a group of genes having evolved from a single ancestral gene. A gene family evolves along the branches of a species tree through various mechanisms, including -but not limited to -speciation (S), gene duplication (D), gene loss (L), horizontal gene transfer (T). The reconstruction of a gene tree representing the evolution of a gene family constrained by a species tree is an important problem in phylogenomics. However, unlike in the multispecies coalescent evolutionary model that considers only speciation and incomplete lineage sorting events, very little is known about the search space for gene family histories accounting for gene duplication, gene loss and horizontal gene transfer (the DLT-model).In this work, we introduce the notion of evolutionary histories defined as a binary ordered rooted tree describing the evolution of a gene family, constrained by a species tree in the DLT-model. We provide formal grammars describing the set of all evolutionary histories that are compatible with a given species tree, whether it is ranked or unranked. These grammars allow us, using either analytic combinatorics or dynamic programming, to efficiently compute the number of histories of a given size, and also to generate random histories of a given size under the uniform distribution. We apply these tools to obtain exact asymptotics for the number of gene family histories for two species trees, the rooted caterpillar and the complete binary tree, as well as estimates of the range of the exponential growth factor of the number of histories for random species trees of size up to 25. Our results show that including horizontal gene transfer induce a dramatic increase of the number of evolutionary histories. We also show that, within ranked species trees, the number of evolutionary histories in the DLT-model is almost independent of the species tree topology. These results establish firm foundations for the development of ensemble methods for the prediction of reconciliations.

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Enumeration of Ancestral Configurations for Matching Gene Trees and Species Trees

Cited by 19 publications

References 25 publications

Inferring rooted species trees from unrooted gene trees using approximate Bayesian computation

Inferring rooted species trees from unrooted gene trees using approximate Bayesian computation

On the Number of Non-equivalent Ancestral Configurations for Matching Gene Trees and Species Trees

Counting and sampling gene family evolutionary histories in the duplication-loss and duplication-loss-transfer models

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