Phylogenetic MCMC algorithms are misleading on mixtures of trees

Markov chain Monte Carlo (MCMC) algorithms play a critical role in the Bayesian approach to phylogenetic inference. We present a theoretical analysis of the rate of convergence of many of the widely used Markov chains. For N characters generated from a uniform mixture of two trees, we prove that the Markov chains take an exponentially long (in N) number of iterations to converge to the posterior distribution. Nevertheless, the likelihood plots for sample runs of the Markov chains deceivingly suggest that the chains converge rapidly to a unique tree. Our results rely on novel mathematical understanding of the log-likelihood function on the space of phylogenetic trees. The practical implications of our work are that Bayesian MCMC methods can be misleading when the data are generated from a mixture of trees. Thus, in cases of data containing potentially conflicting phylogenetic signals, phylogenetic reconstruction should be performed separately on each signal.     

Comment on "The geometry of musical chords"

Tymoczko (Reports, 7 July 2006, p. 72) proposed that the familiar sonorities of Western tonal music cluster around the center of a multidimensional orbifold. However, this is not true for all tonal progressions. When prototypical three-voice cadential progressions by Bach converge on the tonic, the chords migrate from the center to the edge of the orbifold.     

Comment on "Reconstructing the origin of Andaman islanders"

On the basis of mitochondrial DNA sequence analyses, Thangaraj et al. (Brevia, 13 May 2005, p. 996) proposed that Andaman islanders descended from the first humans to migrate out of Africa. We identified mitochondrial DNA from two northeast Indian Rajbanshi individuals that shares three specific mutations with the M31a lineage observed in the Great Andamanese, which suggests that the predecessor of haplogroup M31 originated on the Indian subcontinent.     

Comment on "A vestige of Earth's oldest ophiolite"

Furnes et al. (Reports, 23 March 2007, p. 1704) reported the identification of an ophiolite sequence within the approximately 3.8-billion-year-old Isua supracrustal belt. However, they did not acknowledge that the belt contains supracrustal rocks and mafic dikes of different ages, nor did they demonstrate that the proposed components of the ophiolite are coeval.     

Comment on "A hydrogen-rich early Earth atmosphere"

Tian et al. (Reports, 13 May 2005, p. 1014) proposed a hydrogen-rich early atmosphere with slow hydrogen escape from a cold thermosphere. However, their model neglects the ultraviolet absorption of all gases other than H2. The model also neglects Earth's magnetic field, which affects the temperature and density of ions and promotes nonthermal escape of neutral hydrogen.     

Comment on "Asymmetric coevolutionary networks facilitate biodiversity maintenance"

Bascompte et al. (Reports, 21 April 2006, p. 431) used network asymmetries to explain mathematical conditions necessary for stability in historic models of mutualism. The Lotka-Volterra equations they used artificially created conditions in which some factor, such as asymmetric interaction strengths, is necessary for community coexistence. We show that a more realistic model incorporating nonlinear functional responses requires no such condition and is consistent with their data.     

Comment on "Dispersal limitations matter for microbial morphospecies"

Telford et al. (Brevia, 19 May 2006, p. 1015) reported that freshwater diatoms exhibit regional-scale richness-pH relationships that depend substantially on regional habitat availability. On this basis, the authors argued that, despite their microscopic size, diatoms are not ubiquitously dispersed. Here, I describe my demonstration that their primary evidence against the ubiquitous dispersal hypothesis is spurious.     

Comment on "Large-scale sequence analysis of avian influenza isolates"

Obenauer et al. (Research Articles, 17 March 2006, p. 1576) reported that the influenza A virus PB1-F2 gene is evolving under strong positive selection, as documented by an extremely high ratio of the number of nonsynonymous nucleotide substitutions to the number of synonymous substitutions (dN/dS). However, we show that this observation is likely to be an artifact related to the location of PB1-F2 in the +1 reading frame of the PB1 gene.     

Comment on "Impacts of biodiversity loss on ocean ecosystem services"

Worm et al. (Research Articles, 3 November 2006, p. 787) investigated the importance of biodiversity to marine ecosystem services across temporal and spatial scales. In projecting the extent of future fisheries collapse, we argue that the authors inappropriately extrapolated beyond their available observations and used data on marine reserves and fishery closures that are not representative of global fisheries.     

Comment on "Dynamics of dpp signaling and proliferation control"

Wartlick et al. (Research Articles, 4 March 2011, p. 1154) reported that growth rates in the Drosophila wing disc correlate with increasing Dpp signaling levels, suggesting that the rate of Dpp increase determines the cell-cycle length. Contradicting their model, we found that cells in which the increase of Dpp signaling levels was genetically abrogated grew at rates comparable to those of wild-type cells.