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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.


Illustration of Definition 3.P (edges in black) is a root-leaf path of N and thus both a wishbone and a crack of N. R and S (black) are cracks of N. Q (black) is a wishbone of N. All edges are assumed to have the (unique) length 1 unless otherwise displayed.
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pcbi.1004135.g014: Illustration of Definition 3.P (edges in black) is a root-leaf path of N and thus both a wishbone and a crack of N. R and S (black) are cracks of N. Q (black) is a wishbone of N. All edges are assumed to have the (unique) length 1 unless otherwise displayed.

Mentions: Fig. 14 illustrates the definitions above. Note that any root-leaf path P is both a wishbone and a crack, as P is the result of the union of P with itself, and P has a common prefix and a common suffix with P. Moreover, any sub-network R that can be obtained from a root-leaf path by attributing two lengths to one of its edges e is a crack. Finally, note that wishbones and cracks are networks, and thus the notion of isomorphism (Definition 5 in S1 Text) can be applied to them.


Reconstructible phylogenetic networks: do not distinguish the indistinguishable.

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

Illustration of Definition 3.P (edges in black) is a root-leaf path of N and thus both a wishbone and a crack of N. R and S (black) are cracks of N. Q (black) is a wishbone of N. All edges are assumed to have the (unique) length 1 unless otherwise displayed.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi.1004135.g014: Illustration of Definition 3.P (edges in black) is a root-leaf path of N and thus both a wishbone and a crack of N. R and S (black) are cracks of N. Q (black) is a wishbone of N. All edges are assumed to have the (unique) length 1 unless otherwise displayed.
Mentions: Fig. 14 illustrates the definitions above. Note that any root-leaf path P is both a wishbone and a crack, as P is the result of the union of P with itself, and P has a common prefix and a common suffix with P. Moreover, any sub-network R that can be obtained from a root-leaf path by attributing two lengths to one of its edges e is a crack. Finally, note that wishbones and cracks are networks, and thus the notion of isomorphism (Definition 5 in S1 Text) can be applied to them.

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.