Scientists often use genetic data to figure out how closely related different organisms are. One common way they do this is by using something called a Markov substitution model. This model helps them understand how changes, or substitutions, happen in molecular sequences over time. The general time reversible model, or GTR, is a popular choice for DNA data. It's easy to work with because it's available in a closed form.

However, for more complex biological stuff, like when evolutionary rates change differently over time for different lineages (called heterotachy), scientists need different models. One such model is the GTR with rate variation (GTR + Γ). But these models don't always have easy-to-calculate solutions, and they don't automatically help with Bayesian analysis.

In this study, scientists combined both methods into a new approach. They included rate variation and heterotachy into a hierarchical Bayesian framework based on GTR. This means they can use both stochastic gradient descent for optimization and Hamiltonian Markov chain Monte Carlo for Bayesian inference.

They tested this method by looking into the origins of the eukaryotic cell within the context of the universal tree of life. Their findings suggest that the two-domain theory might be correct. This theory says that the eukaryotic cell comes from the combination of two different types of cells.

How Bayesian Inference is Helping Us Understand Evolution Better

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