A generalized Robinson-Foulds distance for labeled trees

Background: The Robinson-Foulds (RF) distance is a well-established measure between phylogenetic trees. Despite a lack of biological justification, it has the advantages of being a proper metric and being computable in linear time. For phylogenetic applications involving genes, however, a crucial aspect of the trees ignored by the RF metric is the type of the branching event (e.g. speciation, duplication, transfer, etc). Results: We extend RF to trees with labeled internal nodes by including a node flip operation, alongside edge contractions and extensions. We explore properties of this extended RF distance in the case of a binary labeling. In particular, we show that contrary to the unlabeled case, an optimal edit path may require contracting “good” edges, i.e. edges shared between the two trees. Conclusions: We provide a 2-approximation algorithm which is shown to perform well empirically. Looking ahead, computing distances between labeled trees opens up a variety of new algorithmic directions. Implementation and simulations available at https://github.com/DessimozLab/pylabeledrf

A generalized Robinson-Foulds distance for labeled trees.

The Robinson-Foulds (RF) distance is a well-established measure between phylogenetic trees. Despite a lack of biological justification, it has the advantages of being a proper metric and being computable in linear time. For phylogenetic applications involving genes, however, a crucial aspect of the trees ignored by the RF metric is the type of the branching event (e.g. speciation, duplication, transfer, etc). We extend RF to trees with labeled internal nodes by including a node flip operation, alongside edge contractions and extensions. We explore properties of this extended RF distance in the case of a binary labeling. In particular, we show that contrary to the unlabeled case, an optimal edit path may require contracting "good" edges, i.e. edges shared between the two trees. We provide a 2-approximation algorithm which is shown to perform well empirically. Looking ahead, computing distances between labeled trees opens up a variety of new algorithmic directions.Implementation and simulations available at https://github.com/DessimozLab/pylabeledrf

Evolution of resistance to COVID-19 vaccination with dynamic social distancing

The COVID-19 pandemic has led to an unprecedented global response in terms of social lockdown in order to slow the spread of the virus 1,2. Currently the greatest hope is based on world-wide vaccination3,4. The expectation is that social and economic activities can gradually resume as more and more people become vaccinated. Yet, a relaxation of social distancing that allows increased transmissibility, coupled with selection pressure due to vaccination, will likely lead to the emergence of vaccine resistance 5. Here we analyze the evolutionary dynamics of COVID-19 in the presence of dynamic lockdown and in response to vaccination. We use infection and vaccination data of 6 different countries (Israel, US, UK, Brazil, France and Germany) to assess the probability and timing for the wave of vaccine resistant mutant2. For slow vaccination rates, resistant mutants will appear inevitably even if strict lockdown is maintained. For fast vaccination rates (such as those used in Israel) the emergence of the mutant can be prevented if strict lockdown is maintained during vaccination. Our mathematical results provide quantitative guidelines for a combined vaccination and lockdown policy that minimizes the probability of emergence of vaccine resistance variants for current and future vaccination programs