TreeToy is a Java applet that can simulate the genealogical coalescent process in cases where population size changes over time. The goal of the applet is to help people develop an intuition for the outcomes expected under different population histories.


The major components of the TreeToy applet are the genealogy, the population history, the mismatch distribution, the frequency spectrum, the parameters and the "Draw Tree" button. To do a simulation, enter parameters of interest into the spaces provided, and click on the "Draw Tree" button. The results of the simulation will be placed in the genealogy, mismatch and frequency spectrum panels. The history panel will display the history you specified.

Observations about gene genealogies:

1) When population size has increased, genealogies are more comb-like than under constant population size or population decrease.

2) Branching events tend to be clustered around the time of population increase.

Observations about the mismatch distribution:

1) When population size has increased (i.e. when Growth Factor is greater than 1) the mismatch tends to form a wave, and the high point (mode) of the wave tends to occur at about Tau differences between sequences. For example if Tau is 8, the mode of the mismatch distributions occurs at about 8 differences.

2) If Growth Factor goes up, but Theta0 is held constant, the wave described gets more smooth and stable, but it does not change its shape much.

3) If Theta0 goes up but Growth Factor is held constant, the shape of the wave changes: it gets flatter and flatter. It can take large sample sizes to see this.

These three observations are what enable Alan Rogers's method of moments to infer population history from the mismatch distribution.

Observations about the site frequency spectrum:

1) Regardless of population history, mutations with low frequencies are, on average, more common than mutations with high frequencies. However, population growth causes the appearance of more low-frequency variants. Population decrease causes the appearance of more high-frequency variants. It can take large sample sizes to see this.

2) With population increase, frequency spectra get more stable.