Macroevolutionary Rates of Species Interactions: Approximate Bayesian Inference from Cophylogenies

Understanding the macroevolutionary dynamics of species interactions such as parasitisms, commensalisms, and mutualisms is an important goal in evolutionary ecology. To this end, statistical inference from time-calibrated cophylogenies holds promising potential. However, such inference cannot yet quantify the rates of different types of speciation and extinction that occur in the host and symbiont clades on the same timeline. Here we present an Approximate Bayesian Computation (ABC) approach that infers rates of six types of speciation or extinction from a cophylogenetic system: (i) host speciation, (ii) symbiont speciation without host-switching, (iii) symbiont speciation with host-switching, (iv) cospeciation, (v) host extinction, and (vi) symbiont extinction. The ABC approach relies on a novel design of summary statistics based on the density curves of pairwise Branch Length Differences (BLenD) of the cophylogeny, which are informative about the relative relationships (ratios) between the six speciation/extinction rates in a single cophylogeny. Here we describe two levels of inference that differ in informativeness and data requirement: the first level infers speciation/extinction rates relative to the total net diversification rate of the cophylogeny without needing information on the time frame of the cophylogeny; the second level infers absolute speciation/extinction rates in units of events per lineage per million years using information on the time frame of the cophylogeny. When the target cophylogeny is sufficiently large, both levels of inference achieve clearly improved accuracy relative to the prior, and both are reasonably honest about uncertainty. Using a cophylogenetic dataset of Batesian mimicry of Pachyrhynchus by Doliops weevils, we show (1) that the first level of inference is sufficient to quantify the relative rates of different speciation/extinction processes within the target cophylogeny and (2) that the second level of inference allows potentially comparing speciation/extinction rates in the target cophylogeny to those in another cophylogeny (i.e., cross-cophylogeny comparisons). We discuss potential improvements for the use of the BLenD curves as summary statistics for simulation-based inference, including potential applications in machine learning approaches. Understanding speciation and extinction rate variation within and between cophylogenetic systems, enabled by this approach and an increasing availability of time-calibrated cophylogenies, has potential implications for various areas in ecology and evolution such as host conservatism, trait-driven diversification, and pathogen spillover risk.