Phylogenies from dynamic networks

The relationship between the underlying contact network over which a pathogen spreads and the pathogen phylogenetic trees that are obtained presents an opportunity to use sequence data to learn about contact networks that are difficult to study empirically. However, this relationship is not explicitly known and is usually studied in simulations, often with the simplifying assumption that the contact network is static in time, though human contact networks are dynamic. We simulate pathogen phylogenetic trees on dynamic Erdős-Renyi random networks and on two dynamic networks with skewed degree distribution, of which one is additionally clustered. We use tree shape features to explore how adding dynamics changes the relationships between the overall network structure and phylogenies. Our tree features include the number of small substructures (cherries, pitchforks) in the trees, measures of tree imbalance (Sackin index, Colless index), features derived from network science (diameter, closeness), as well as features using the internal branch lengths from the tip to the root. Using principal component analysis we find that the network dynamics influence the shapes of phylogenies, as does the network type. We also compare dynamic and time-integrated static networks. We find, in particular, that static network models like the widely used Barabasi-Albert model can be poor approximations for dynamic networks. We explore the effects of mis-specifying the network on the performance of classifiers trained identify the transmission rate (using supervised learning methods). We find that both mis-specification of the underlying network and its parameters (mean degree, turnover rate) have a strong adverse effect on the ability to estimate the transmission parameter. We illustrate these results by classifying HIV trees with a classifier that we trained on simulated trees from different networks, infection rates and turnover rates. Our results point to the importance of correctly estimating and modelling contact networks with dynamics when using phylodynamic tools to estimate epidemiological parameters.Author summary: Understanding whether and how transmission patterns are revealed by branching patterns in phylogenetic trees for pathogens remains a challenging research question. Besides the diversification of the pathogen, branching patterns depend strongly on the host contact structure as it shapes opportunities for the pathogen to reproduce. However, the host contact network is often difficult to study, in particular as it evolves in time. In this paper we perform a simulation study on three different dynamic networks, on which we simulate transmission trees. We use a simple Erdős-Renyi random network and two more realistic networks with skewed degree distribution, where one is also clustered. We convert transmission trees into phylogenetic trees and analyze them with different tree statistics like imbalance measures, counts of small substructures, and measures containing the branch lengths. We study the tree features with principal component analysis and with supervised learning methods, and find that network dynamics and network type can strongly influence the shape of phylogenetic trees. This implies that using phylogenetic trees from a mis-specified network type and dynamic can lead to poor phylodynamic estimation of transmission parameters. We illustrate this with HIV phylogenetic trees constructed from viral sequences of patients in the Dutch ATHENA cohort, and from sequences of the Los Alamos Sequence database.