Convergence is a central concept in evolutionary studies because it provides strong evidence for adaptation. It also provides information about the nature of the fitness landscape and the repeatability of evolution, and can mislead phylogenetic inference. To understand the role of adaptive convergence, we need to understand the patterns of nonadaptive convergence. Here, we consider the relationship between nonadaptive convergence and divergence in mitochondrial and model proteins. Surprisingly, nonadaptive convergence is much more common than expected in closely related organisms, falling off as organisms diverge. The extent of the convergent drop-off in mitochondrial proteins is well predicted by epistatic or coevolutionary effects in our “evolutionary Stokes shift” models and poorly predicted by conventional evolutionary models. Convergence probabilities decrease dramatically if the ancestral amino acids of branches being compared have diverged, but also drop slowly over evolutionary time even if the ancestral amino acids have not substituted. Convergence probabilities drop-off rapidly for quickly evolving sites, but much more slowly for slowly evolving sites. Furthermore, once sites have diverged their convergence probabilities are extremely low and indistinguishable from convergence levels at randomized sites. These results indicate that we cannot assume that excessive convergence early on is necessarily adaptive. This new understanding should help us to better discriminate adaptive from nonadaptive convergence and develop more relevant evolutionary models with improved validity for phylogenetic inference.

Carnivorous plants exploit animals as a nutritional source and have inspired long-standing questions about the origin and evolution of carnivory-related traits. To investigate the molecular bases of carnivory, we sequenced the genome of the heterophyllous pitcher plant Cephalotus follicularis, in which we succeeded in regulating the developmental switch between carnivorous and non-carnivorous leaves. Transcriptome comparison of the two leaf types and gene repertoire analysis identified genetic changes associated with prey attraction, capture, digestion and nutrient absorption. Analysis of digestive fluid proteins from C. follicularis and three other carnivorous plants with independent carnivorous origins revealed repeated co-options of stress-responsive protein lineages coupled with convergent amino acid substitutions to acquire digestive physiology. These results imply constraints on the available routes to evolve plant carnivory.

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14Phylogenetic inference requires a means to search phylogenetic tree space. This is usually 15 achieved using progressive algorithms that propose and test small alterations in the current tree 16 topology and branch lengths. Current programs search tree topology space using branch-17 swapping algorithms, but proposals do not discriminate well between swaps likely to succeed or 18 fail. When applied to datasets with many taxa, the huge number of possible topologies slows 19 these programs dramatically. To overcome this, we developed a statistical approach for proposal 20 generation in Bayesian analysis, and evaluated its applicability for the problem of searching 21 phylogenetic tree space. The general idea of the approach, which we call 'Markov katana', is to 22 make proposals based on a heuristic algorithm using bootstrapped subsets of the data. Such 23 proposals induce an unintended sampling distribution that must be determined and removed to 24 generate posterior estimates, but the cost of this extra step can in principle be small compared to 25 the added value of more efficient parameter exploration in Markov chain Monte Carlo analyses. 26Our prototype application uses the simple neighbor-joining distance heuristic on data subsets to 27propose new reasonably likely phylogenetic trees (including topologies and branch lengths). The 28 evolutionary model used to generate distances in our prototype was far simpler than the more 29 complex model used to evaluate the likelihood of phylogenies based on the full dataset. This 30 prototype implementation indicates that the Markov katana approach could be easily 31 incorporated into existing phylogenetic search programs and may prove a useful alternative in 32 conjunction with existing methods. The general features of this statistical approach may also 33 prove useful in disciplines other than phylogenetics. We demonstrate that this method can be 34 used to efficiently estimate a Bayesian posterior. 35