The number of species on the Earth remains highly uncertain, but our best estimates are around 10 million (Mora et al. 2011). This is a mind-boggling number, and far more than have been described. As far as we know, all of those species are descended from a single common ancestor that lived some 4.2 billion years ago (Hedges and Kumar 2009). All of these species formed by the process of speciation, the process by which one species splits into two (or more) descendants (Coyne and Orr 2004).
Some parts of the tree of life have more species than others. This imbalance in diversity tells us that speciation is much more common in some lineages than others (Mooers and Heard 1997). Likewise, numerous studies have argued that certain habitats are "hotbeds" of speciation (e.g. Hutter et al. 2017; Miller and Wiens 2017). For example, the high Andes ecosystem called the Páramo - a peculiar landscape of alien-looking plants and spectacled bears - might harbor the highest speciation rates on the planet (Madriñán et al. 2013).
In this chapter we will explore how we can learn about speciation and extinction rates from the tree of life. We will use birth-death models, simple models of how species form and go extinct through time. Birth-death models can be applied to data on clade ages and diversities, or fit to the branching times in phylogenetic trees. We will explore both maximum likelihood and Bayesian methods to do both of these things.