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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.


Two networks with edge lengths N1, N2 displaying the same set of trees 𝓣(N1) = 𝓣(N2) = {T1, T2, T3}.For any choice of edge lengths λ1, λ2, …, λ12 for N1, we define a family of edge length assignments for N2, parameterized by x, y (with -y < x < min{λ6, λ5 + λ8}, 0 < y < λ7).
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pcbi.1004135.g003: Two networks with edge lengths N1, N2 displaying the same set of trees 𝓣(N1) = 𝓣(N2) = {T1, T2, T3}.For any choice of edge lengths λ1, λ2, …, λ12 for N1, we define a family of edge length assignments for N2, parameterized by x, y (with -y < x < min{λ6, λ5 + λ8}, 0 < y < λ7).

Mentions: Unfortunately, accounting for edge lengths only solves some of the identifiability problems for phylogenetic networks. Consider networks N1 and N2 in Fig. 3: for any set of edge lengths for N1, there exist an infinity of edge length assignments for N2 that make these two networks display exactly the same set of trees with the same edge lengths. In the following, we say that networks such as N1 and N2 are indistinguishable.


Reconstructible phylogenetic networks: do not distinguish the indistinguishable.

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

Two networks with edge lengths N1, N2 displaying the same set of trees 𝓣(N1) = 𝓣(N2) = {T1, T2, T3}.For any choice of edge lengths λ1, λ2, …, λ12 for N1, we define a family of edge length assignments for N2, parameterized by x, y (with -y < x < min{λ6, λ5 + λ8}, 0 < y < λ7).
© Copyright Policy
Related In: Results  -  Collection

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

pcbi.1004135.g003: Two networks with edge lengths N1, N2 displaying the same set of trees 𝓣(N1) = 𝓣(N2) = {T1, T2, T3}.For any choice of edge lengths λ1, λ2, …, λ12 for N1, we define a family of edge length assignments for N2, parameterized by x, y (with -y < x < min{λ6, λ5 + λ8}, 0 < y < λ7).
Mentions: Unfortunately, accounting for edge lengths only solves some of the identifiability problems for phylogenetic networks. Consider networks N1 and N2 in Fig. 3: for any set of edge lengths for N1, there exist an infinity of edge length assignments for N2 that make these two networks display exactly the same set of trees with the same edge lengths. In the following, we say that networks such as N1 and N2 are indistinguishable.

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.