When reconstructing phylogenetic character histories, biologists aim to identify distinct evolutionary trajectories, or paths of character state evolution. However, biologists typically wish to summarize the information representing large numbers of potential character histories for a single phylogeny. For discrete characters, few approaches exist for summarizing the number of unique evolutionary trajectories beyond the frequency of specific events (i.e., state transition types) or the time lineages spend in each state. Here, we introduce a framework for summarizing the evolutionary trajectories of discrete character histories by compressing them into trajectory trees, where branches represent unique character-evolution pathways rather than lineages. This framework includes a novel compressed tree representation, called a scenario tree, that retains temporal information, ensuring that each root-to-tip path represents a unique, temporally explicit evolutionary trajectory. We describe and apply several approaches to summarize phylogenetic trees into transition trees. We include visual summaries, such as consensus trajectory trees, trajectory tree tanglegrams, and 'trajectory-through-time plots', to compare how unique evolutionary trajectories accumulate across lineages and state transitions. We also include quantitative summaries, such as the time spent in unique evolutionary trajectories and the number of transitions that follow unique character-state transitions. We use our new trajectory-wise summaries to evaluate the adequacy of commonly used continuous-time Markov models of character evolution, which are memoryless and consider only the rates between pairs of states. We conducted multiple simulation-based experiments demonstrating the utility of our novel trajectory-wise approaches. We also apply our new trajectory-wise approaches to Greater Antillean Anolis lizard biogeography and ecomorph evolution, and find that Anoles evolved along considerably more unique evolutionary trajectories than expected under simulations of our best-fitting character evolution model. The number of unique evolutionary paths accumulated in an early burst pattern relative to simulated trajectories, with this burst being more intense than expected across all character state transition events.
McHugh, S. W., Landis, M. J.
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