In this episode, we chat about phylogenetics with Xiang Ji. We start with a general introduction to the field and then go deeper into the likelihood-based methods (maximum likelihood and Bayesian inference). In particular, we talk about the different ways to calculate the likelihood gradient, including a linear-time exact gradient algorithm recently published by Xiang and his colleagues. Links: Gradients Do Grow on Trees: A Linear-Time O(N)-Dimensional Gradient for Statistical Phylogenetics (Xiang Ji, Zhenyu Zhang, Andrew Holbrook, Akihiko Nishimura, Guy Baele, Andrew Rambaut, Philippe Lemey, Marc A Suchard) BEAGLE: the package that implements the gradient algorithm BEAST: the program that implements the Hamiltonian Monte Carlo sampler and the molecular clock models