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Introduction - Developing Darwin's Computer

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Lecturer: Alexei Drummond

Darwin's Computer

Detail from the only illustration in the Origin of Species (Darwin, 1859)

https://www.evogeneao.com/en/explore/tree-of-life-explorer

Descent with modification in populations

15 possible trees of 4 individuals/species

105 possible trees of 5 individuals/species

945 possible trees of 6 individuals/species

How many trees are there?

$n$	#trees
4	15	enumerable by hand
5	105	enumerable by hand on a rainy day
6	945	enumerable by computer
7	10395	still searchable very quickly on computer
8	135135	about the number of hairs on your head
9	2027025	greater than the population of Auckland
10	34459425	$\approx$ upper limit for exhaustive search
20	$8.2 \times 10^{21}$	$\approx$ upper limit of branch-and-bound searching
48	$3.21 \times 10^{70}$	$\approx$ the number of particles in the Universe
136	$2.11 \times 10^{267}$	number of trees to choose from in the “Out of Africa” data (Vigilant et al. 1991)

Computing Darwin's Tree of Life

Bayesian reconstruction of phylogenetic trees

Yang & Rannala (1997), Mau, Newton & Larget (1998)

What we really want is the probability of the tree given the data.

We can compute that from the likelihood using Bayes Theorem:

This is known as the Posterior probability of the tree. Using the Markov chain Monte Carlo algorithm we can produce a sample of trees that have high posterior probability.

The posterior distribution on Darwin's Finches

This posterior probability distribution was computed using Markov chain Monte Carlo implemented in the BEAST software package (Drummond et al, 2012).

The posterior distribution of larger trees

Produced using DensiTree (Bouckaert, 2012)

Elaborations of the phylogenetic model

Basic model: (posterior proportional to likelihood × prior)

$$p(T|D) \propto \Pr(D|T) \; p(T)$$

Substitution model:

$$p(T,\color{green}{Q}|D) \propto \Pr(D|T,\color{green}{Q}) \; p(T) \; \color{green}{p(Q)}$$

Substitution model and tree branching process prior:

$$p(T,\color{green}{Q},\color{blue}{\Theta}|D) \propto \Pr(D|T,\color{green}{Q}) \; p(T|\color{blue}{\Theta}) \; \color{green}{p(Q)} \; \color{blue}{p(\Theta)}$$

Elaborations of the model: Evolution is happening right now!

Modelling phylogenetic data sampled through time

Drummond and Rodrigo (2000), Drummond et al (2002)

Rapidly evolving microbes
Ancient DNA
Cancer
Somatic evolution
Languages
et cetera

$$p(T,\color{green}{Q},\color{blue}{\Theta},\color{red}{\mu}|D) \propto \Pr\{D|\color{red}{\mu} T,\color{green}{Q}\} \; p(T|\color{blue}{\Theta}) \; \color{green}{p(Q)} \; \color{blue}{p(\Theta)} \; \color{red}{p(\mu)}$$

A calibrated phylogenetic inference

Origin of the HIV epidemic in the Americas, Gilbert et al (2007)

A phylogenetic reconstruction of samples of HIV-1 virus. Each tip represents a single infected individual from whom a blood sample has been taken.

Estimation of

evolutionary trees
divergence times
evolutionary rates
population history
infectious disease parameters
migration rates
and more…

Also: Drummond & Rambaut, 2007; Drummond et al., 2012; Bouckaert et al., 2014; Suchard et al., 2018; Baele et al., Nat Methods, 2025

>42,000 scientific studies have cited the six BEAST papers,
>3,200 last year alone (2025)

Phylodynamics

Statistical phylogenetics and
population genetics models

Mathematical epidemiology,
non-linear dynamical models

Goal: the integration of immunological, genomic and epidemiological data in a single coherent predictive model.

Coalescent theory: $p(g|\Theta)$

$\Theta$ $g$

$$p(g,\color{green}{Q},\color{blue}{\Theta}|D) \propto \Pr\{D|\mu g,\color{green}{Q}\} \; p(g|\color{blue}{\Theta}) \; \color{green}{p(Q)} \; \color{blue}{p(\Theta)}$$

Trees inside trees

Modelling diversity and divergence
Central to understanding diverse areas including speciation genomics and host-symbiont co-evolution is building up a statistically rigorous model of the patterns of divergence and diversity spanning multiple species/hosts, multiple genes / gene families and multiple individuals per species/host.

$$p(T,\color{purple}{S}|D) \propto \Pr\{D|T\} \; p(T|\color{purple}{S}) \; \color{purple}{p(S)}$$

$$p(t_1,t_2,\ldots,t_N,\color{purple}{S}|D) \propto \prod_i \Pr\{D_i|t_i\} \; p(t_i|\color{purple}{S}) \; \color{purple}{p(S)}$$

Phylogenies and the fossil record

An example of node dating with BEAST from Subramanian et al (Biology Letters, 2013)

Final Perspectives

Evolutionary biology has become a multidisciplinary analytical science, with major input from computer scientists, statisticians, mathematicians and physicists.
Evolutionary biology is not just an historical science. Rapidly evolving natural systems, low-cost high-throughput sequencing and high-throughput automated experimental evolution platforms, all add up to the potential to close the loop between experimental and theoretical evolutionary biology.
A common set of evolutionary modelling principles can inform us on diverse questions including human population history, the spread of viral epidemics and the age of fossils.