# 10: Introduction to Birth-Death Models

This chapter introduces birth-death models and summarized their basic mathematical properties. Birth-death models predict patterns of species diversity over time intervals, and can also be used to model the growth of phylogenetic trees. We can visualize these patterns by measuring tree balance and creating lineage-through-time (LTT) plots.

• 10.1: Plant Diversity Imbalance
The diversity of flowering plants (the angiosperms) dwarfs the number of species of their closest evolutionary relatives. There are more than 260,000 species of angiosperms . The clade originated more than 140 million years ago, and all of these species have formed since then. One can contrast the diversity of angiosperms with the diversity of other groups that originated at around the same time. For example, gymnosperms, which are as old as angiosperms, include only around 1000 species.
• 10.2: The Birth-Death Model
A birth-death model is a continuous-time Markov process that is often used to study how the number of individuals in a population change through time. For macroevolution, these “individuals” are usually species, sometimes called "lineages" in the literature. In a birth-death model, two things can occur: births, where the number of individuals increases by one; and deaths, where the number of individuals decreases by one.
• 10.3: Birth-death models and phylogenetic trees
The main complication in phylogenetic studies of birth-death models is that we get a “censored” view of the process, in that we only observe lineages that survive to the present day.
• 10.4: Simulating Birth-Death Trees
We can use the statistical properties of birth-death models to simulate phylogenetic trees through time. We could begin with a single lineage at time 0. However, phylogenetic tree often start with the first speciation event in the clade, so one can also begin the simulation with two lineages at time 0 (this difference relates to the distinction between crown and stem ages of clades.
• 10.5: Tree topology, tree shape, and tree balance under a birth-death model
Tree topology summarizes the patterns of evolutionary relatedness among a group of species independent of the branch lengths of a phylogenetic tree. Two different trees have the same topology if they define the exact same set of clades. This is important because sometimes two trees can look very different and yet still have the same topology.
• 10.6: Lineage-through-Time Plots
The other main way to quantify phylogenetic tree shape is by making lineage-through-time plots. These plots have time along the x axis (from the root of the tree to the present day), and the reconstructed number of lineages on the y-axis. Since we are usually considering birth-death models, where the number of lineages is expected to grow (or shrink) exponentially through time, then it is typical practice to log-transform the y-axis.
• 10.S: Introduction to birth-death models (Summary)