Detecting Lineage-Specific Shifts in Diversification: A Proper Likelihood Approach.

The branching patterns of molecular phylogenies are generally assumed to contain information on rates of the underlying speciation and extinction processes. Simple birth-death models with constant, time-varying, or diversity-dependent rates have been invoked to explain these patterns. They have one assumption in common: all lineages have the same set of diversification rates at a given point in time. It seems likely, however, that there is variability in diversification rates across subclades in a phylogenetic tree. This has inspired the construction of models that allow multiple rate regimes across the phylogeny, with instantaneous shifts between these regimes. Several methods exist for calculating the likelihood of a phylogeny under a specified mapping of diversification regimes and for performing inference on the most likely diversification history that gave rise to a particular phylogenetic tree. Here, we show that the likelihood computation of these methods is not correct. We provide a new framework to compute the likelihood correctly and show, with simulations of a single shift, that the correct likelihood indeed leads to parameter estimates that are on average in much better agreement with the generating parameters than the incorrect likelihood. Moreover, we show that our corrected likelihood can be extended to multiple rate shifts in time-dependent and diversity-dependent models. We argue that identifying shifts in diversification rates is a nontrivial model selection exercise where one has to choose whether shifts in now-extinct lineages are taken into account or not. Hence, our framework also resolves the recent debate on such unobserved shifts. [Diversification; macroevolution; phylogeny; speciation].

Additional Analytical Support for a New Method to Compute the Likelihood of Diversification Models.

Molecular phylogenies have been increasingly recognized as an important source of information on species diversification. For many models of macroevolution, analytical likelihood formulas have been derived to infer macroevolutionary parameters from phylogenies. A few years ago, a general framework to numerically compute such likelihood formulas was proposed, which accommodates models that allow speciation and/or extinction rates to depend on diversity. This framework calculates the likelihood as the probability of the diversification process being consistent with the phylogeny from the root to the tips. However, while some readers found the framework presented in Etienne et al. (Proc R Soc Lond B Biol Sci 279(1732):1300-1309, 2012) convincing, others still questioned it (personal communication), despite numerical evidence that for special cases the framework yields the same (i.e., within double precision) numerical value for the likelihood as analytical formulas do that were independently derived for these special cases. Here we prove analytically that the likelihoods calculated in the new framework are correct for all special cases with known analytical likelihood formula. Our results thus add substantial mathematical support for the overall coherence of the general framework.

Hierarchical folding and reorganization of chromosomes are linked to transcriptional changes in cellular differentiation.

Mammalian chromosomes fold into arrays of megabase-sized topologically associating domains (TADs), which are arranged into compartments spanning multiple megabases of genomic DNA. TADs have internal substructures that are often cell type specific, but their higher-order organization remains elusive. Here, we investigate TAD higher-order interactions with Hi-C through neuronal differentiation and show that they form a hierarchy of domains-within-domains (metaTADs) extending across genomic scales up to the range of entire chromosomes. We find that TAD interactions are well captured by tree-like, hierarchical structures irrespective of cell type. metaTAD tree structures correlate with genetic, epigenomic and expression features, and structural tree rearrangements during differentiation are linked to transcriptional state changes. Using polymer modelling, we demonstrate that hierarchical folding promotes efficient chromatin packaging without the loss of contact specificity, highlighting a role far beyond the simple need for packing efficiency.