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. 2006 May;2(5):e68.
doi: 10.1371/journal.pgen.0020068. Epub 2006 May 26.

Discordance of species trees with their most likely gene trees

James H Degnan  1 , Noah A Rosenberg
Affiliations

Discordance of species trees with their most likely gene trees

James H Degnan et al. PLoS Genet. 2006 May.

Abstract

Because of the stochastic way in which lineages sort during speciation, gene trees may differ in topology from each other and from species trees. Surprisingly, assuming that genetic lineages follow a coalescent model of within-species evolution, we find that for any species tree topology with five or more species, there exist branch lengths for which gene tree discordance is so common that the most likely gene tree topology to evolve along the branches of a species tree differs from the species phylogeny. This counterintuitive result implies that in combining data on multiple loci, the straightforward procedure of using the most frequently observed gene tree topology as an estimate of the species tree topology can be asymptotically guaranteed to produce an incorrect estimate. We conclude with suggestions that can aid in overcoming this new obstacle to accurate genomic inference of species phylogenies.

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Conflict of interest statement

Competing interests. The authors have declared that no competing interests exist.

Figures

Figure 1
Figure 1. Anomalous Gene Trees for Four Taxa
Colored lines represent gene lineages that trace back to a common ancestor along the branches of a species tree with topology (((AB)C)D). The figure illustrates how a gene tree can have a higher probability of having a symmetric topology, in this case ((AD)(BC)), than of having the topology that matches the species tree. If the internal branches of the species tree—x and y—are short so that coalescences occur deep in the tree, the two sequences of coalescences that produce a given symmetric gene tree topology together have higher probability than the single sequence that produces the topology that matches the species tree. (a) and (b) Two coalescence sequences leading to gene tree topology ((AD)(BC)). In (a), the lineages from B and C coalesce more recently than those from A and D, and in (b), the reverse is true. (c) The single sequence of coalescences leading to gene tree topology (((AB)C)D).
Figure 2
Figure 2. The Anomaly Zone for the Four-Taxon Asymmetric Species Tree Topology
Branch lengths x and y (see Figure 1) are measured in coalescent time units.
Figure 3
Figure 3. The Production of Anomalies for n-Maximally Probable Species Tree Topologies with n = 5,6,7,8 (See Table 1)
The branch lengths x, y, and λ apply to each tree: in (a) and (b), x + y denotes the length of the red internal branch, and in (c) and (d), x and y are the lengths of the deeper and shallower red internal branches, respectively; the length λ denotes the branch length between the root of the species tree and the MRCA of species A and B. For each tree, the color of a branch represents the probability that coalescences occur on the branch. On an external branch, because there is only one gene lineage, coalescences cannot occur. Prior to the root, the probability is 1 that all lineages coalesce. During the time between the root of the species tree and the divergence of A and B—and of C and D in (b–d)—the probability that any coalescences occur can be made arbitrarily close to 0 by making the internal branches sufficiently short. Similarly, by choosing x and y to be sufficiently large, the probability that all available lineages coalesce on the red branches can be made arbitrarily close to 1. In (a), the species tree can be represented as (((AB)C)Z), where Z is (DE). By making the internal branch ancestral to D and E long, the subtree Z is similar to a single taxon, and the five-taxon tree behaves like the four-taxon asymmetric tree (((AB)C)Z), which produces the anomaly ((AB)(CZ)). Thus, in (a), the AGT is ((AB)(C(DE))). Similarly, the species tree topologies in (b), (c), and (d) have the form (((AB)(CD))Z) and produce anomalies (((AB)C)(DZ)); in (b), (c), and (d) Z is (EF), (E(FG)), and ((EF)(GH)), respectively. The anomalies occur by letting internal branches in subtrees ((AB)(CD)) and Z be sufficiently short and long, respectively.
Figure 4
Figure 4. A Wicked Forest
(a) The two long internal branches have length 2, and the two short internal branches have length 0.1. For this species tree the probabilities that a random gene tree has topology ψ i are 0.085 and 0.103 for i = 1 and i = 2, respectively. Hence ψ 2 is anomalous for σ 1. (b) The one long internal branch has length 4, the shortest internal branch has length 0.1, and the other two internal branches have length 0.3. For this species tree, the gene tree probabilities are 0.066 and 0.060 for topologies ψ 1 and ψ 2, respectively. Note that the two topologies disagree only on the placement of taxon D and that neither is 6-maximally probable.
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