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Reconstructible phylogenetic networks: do not distinguish the indistinguishable.

Pardi F, Scornavacca C - PLoS Comput. Biol. (2015)

Bottom Line: This identifiability problem is partially solved by accounting for branch lengths, although this merely reduces the frequency of the problem.For any given set of indistinguishable networks, we define a canonical network that, under mild assumptions, is unique and thus representative of the entire set.While on the methodological side this will imply a drastic reduction of the solution space in network inference, for the study of reticulate evolution this is a fundamental limitation that will require an important change of perspective when interpreting phylogenetic networks.

View Article: PubMed Central - PubMed

Affiliation: Laboratoire d'Informatique, de Robotique et de Microélectronique de Montpellier (LIRMM, UMR 5506) CNRS, Université de Montpellier, France; Institut de Biologie Computationnelle, Montpellier, France.

ABSTRACT
Phylogenetic networks represent the evolution of organisms that have undergone reticulate events, such as recombination, hybrid speciation or lateral gene transfer. An important way to interpret a phylogenetic network is in terms of the trees it displays, which represent all the possible histories of the characters carried by the organisms in the network. Interestingly, however, different networks may display exactly the same set of trees, an observation that poses a problem for network reconstruction: from the perspective of many inference methods such networks are "indistinguishable". This is true for all methods that evaluate a phylogenetic network solely on the basis of how well the displayed trees fit the available data, including all methods based on input data consisting of clades, triples, quartets, or trees with any number of taxa, and also sequence-based approaches such as popular formalisations of maximum parsimony and maximum likelihood for networks. This identifiability problem is partially solved by accounting for branch lengths, although this merely reduces the frequency of the problem. Here we propose that network inference methods should only attempt to reconstruct what they can uniquely identify. To this end, we introduce a novel definition of what constitutes a uniquely reconstructible network. For any given set of indistinguishable networks, we define a canonical network that, under mild assumptions, is unique and thus representative of the entire set. Given data that underwent reticulate evolution, only the canonical form of the underlying phylogenetic network can be uniquely reconstructed. While on the methodological side this will imply a drastic reduction of the solution space in network inference, for the study of reticulate evolution this is a fundamental limitation that will require an important change of perspective when interpreting phylogenetic networks.

No MeSH data available.


A non-reticulating evolutionary history (left) and a reticulating evolutionary history (right).The black lineages are those leading to a sampled set of taxa 𝓧. The horizontal jagged lines represent reticulation events. Note that, whereas representing the scenario on the left with a phylogenetic tree on 𝓧 is straightforward, for the one on the right several options are possible. We show three alternative representations in Fig. 9.
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pcbi.1004135.g008: A non-reticulating evolutionary history (left) and a reticulating evolutionary history (right).The black lineages are those leading to a sampled set of taxa 𝓧. The horizontal jagged lines represent reticulation events. Note that, whereas representing the scenario on the left with a phylogenetic tree on 𝓧 is straightforward, for the one on the right several options are possible. We show three alternative representations in Fig. 9.

Mentions: Moreover, we allow multiple lengths for an edge in a network, but not in a tree. For example, in Fig. 6, network has an edge with two lengths (λ7 + λ12 + λ14 and λ7 + λ11 + λ13 + λ14). The motivation behind multiple lengths lies in the observation that, whereas each edge in a phylogenetic tree describing the evolution of non-reticulating organisms trivially corresponds to a unique evolutionary path in the underlying real evolutionary history, when reticulate events have occurred this is not necessarily true: Fig. 8 and Fig. 9 show that some evolutionary scenarios can either be represented using multiedges (multiple edges with the same endpoints) or edges with multiple lengths. Although these two options are mathematically equivalent, graphically the second one leads to more compact representations, and this is why we choose to allow multiple lengths rather than multiedges. For our purposes we only need to consider the case where e has a finite set of lengths (Λ(e) = {λ1(e), …, λk(e)}).


Reconstructible phylogenetic networks: do not distinguish the indistinguishable.

Pardi F, Scornavacca C - PLoS Comput. Biol. (2015)

A non-reticulating evolutionary history (left) and a reticulating evolutionary history (right).The black lineages are those leading to a sampled set of taxa 𝓧. The horizontal jagged lines represent reticulation events. Note that, whereas representing the scenario on the left with a phylogenetic tree on 𝓧 is straightforward, for the one on the right several options are possible. We show three alternative representations in Fig. 9.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4388854&req=5

pcbi.1004135.g008: A non-reticulating evolutionary history (left) and a reticulating evolutionary history (right).The black lineages are those leading to a sampled set of taxa 𝓧. The horizontal jagged lines represent reticulation events. Note that, whereas representing the scenario on the left with a phylogenetic tree on 𝓧 is straightforward, for the one on the right several options are possible. We show three alternative representations in Fig. 9.
Mentions: Moreover, we allow multiple lengths for an edge in a network, but not in a tree. For example, in Fig. 6, network has an edge with two lengths (λ7 + λ12 + λ14 and λ7 + λ11 + λ13 + λ14). The motivation behind multiple lengths lies in the observation that, whereas each edge in a phylogenetic tree describing the evolution of non-reticulating organisms trivially corresponds to a unique evolutionary path in the underlying real evolutionary history, when reticulate events have occurred this is not necessarily true: Fig. 8 and Fig. 9 show that some evolutionary scenarios can either be represented using multiedges (multiple edges with the same endpoints) or edges with multiple lengths. Although these two options are mathematically equivalent, graphically the second one leads to more compact representations, and this is why we choose to allow multiple lengths rather than multiedges. For our purposes we only need to consider the case where e has a finite set of lengths (Λ(e) = {λ1(e), …, λk(e)}).

Bottom Line: This identifiability problem is partially solved by accounting for branch lengths, although this merely reduces the frequency of the problem.For any given set of indistinguishable networks, we define a canonical network that, under mild assumptions, is unique and thus representative of the entire set.While on the methodological side this will imply a drastic reduction of the solution space in network inference, for the study of reticulate evolution this is a fundamental limitation that will require an important change of perspective when interpreting phylogenetic networks.

View Article: PubMed Central - PubMed

Affiliation: Laboratoire d'Informatique, de Robotique et de Microélectronique de Montpellier (LIRMM, UMR 5506) CNRS, Université de Montpellier, France; Institut de Biologie Computationnelle, Montpellier, France.

ABSTRACT
Phylogenetic networks represent the evolution of organisms that have undergone reticulate events, such as recombination, hybrid speciation or lateral gene transfer. An important way to interpret a phylogenetic network is in terms of the trees it displays, which represent all the possible histories of the characters carried by the organisms in the network. Interestingly, however, different networks may display exactly the same set of trees, an observation that poses a problem for network reconstruction: from the perspective of many inference methods such networks are "indistinguishable". This is true for all methods that evaluate a phylogenetic network solely on the basis of how well the displayed trees fit the available data, including all methods based on input data consisting of clades, triples, quartets, or trees with any number of taxa, and also sequence-based approaches such as popular formalisations of maximum parsimony and maximum likelihood for networks. This identifiability problem is partially solved by accounting for branch lengths, although this merely reduces the frequency of the problem. Here we propose that network inference methods should only attempt to reconstruct what they can uniquely identify. To this end, we introduce a novel definition of what constitutes a uniquely reconstructible network. For any given set of indistinguishable networks, we define a canonical network that, under mild assumptions, is unique and thus representative of the entire set. Given data that underwent reticulate evolution, only the canonical form of the underlying phylogenetic network can be uniquely reconstructed. While on the methodological side this will imply a drastic reduction of the solution space in network inference, for the study of reticulate evolution this is a fundamental limitation that will require an important change of perspective when interpreting phylogenetic networks.

No MeSH data available.