Theta0 and mutation rate

Theta0 is equal to the expected number of mutations that occur in one chromosome in one generation in the infinite-sited model. GADMA can scale all values of demographic model parameters due to known value of Theta0. However, it is not always possible to find it. There is a way to solve this problem: one can set Theta0 to None or just not specify it at all, so GADMA will take it as 1.0 and after launch one can scale result values due to found Theta0.

The alternative way to set Theta0 is to specify both mutation rate and length of the sequence in the parameters file instead. Then Theta0 will be calculated automatically.

# param file
...
Mutation rate: 2.35e-8
Sequence length: 4.04e6
...

Estimating Theta0

If mu is the neutral mutation rate per site per generation and L is the length of the sequence, then:

Theta_0 = 4 * mu * L

Note

L is the effective sequence length, which accounts for losses in alignment and missed calls.

Note

mu should be estimated based on generation time. One can leave Time per generation option in the parameter file unspecified (then time on the model’s plots will be in the genetic units), but one should recalculate mu!

For example (Gutenkunst et al, 2009):

We estimate the neutral mutation rate mu using the divergence between human and chimp. Comparing aligned sequences in our data, we estimate the divergence to be 1.13%. Assuming a divergence time of 6 million years and a mean generation time for human and chimp over this interval of 25 years, we have

mu = 0.0113 * 25 / (2 * 6 * 10^6) = 2.35 * 10^{-8} (per generation).

Changing Theta0

If GADMA was launched with one Theta0 and now one wants to use another or if it was launched with default Theta0 = 1 and now one has estimated its real value, model’s parameters can be simply scaled:

Let a = Theta0_NEW / Theta0_OLD,

Size of population / a,

Time / a,

Migration rates * a,

Split percent stay the same.

Examples of Theta0 and time for generation

The following tables produce different possible values for the demographic model inference for three populations of modern people: YRI, CEU, CHB.

Examples of different values of generation time and its influence on mu and Theta0:

FS filename	Gen. time (years)	`mu` (per site per gen.)	`L` (base pair)	`Theta0` (per chr. per gen.)
YRI_CEU_CHB.fs	25 (Gutenkunst et al., 2009)	2.35 * 10^{-8} (Gutenkunst et al., 2009)	4.04 * 10^6 (Gutenkunst et al., 2009)	0.37976
YRI_CEU_CHB.fs	24 (Lapierre et al., 2017)	2.26 * 10^{-8} (Gutenkunst et al., 2009)	4.04 * 10^6 (Gutenkunst et al., 2009)	0.36521
YRI_CEU_CHB.fs	29 (Jouganous et al., 2017)	1.44 * 10^(-8) (Jouganous et al., 2017)	4.04 * 10^6 (Gutenkunst et al., 2009)	0.23270
YRI_CEU_CHB.fs	24 (Lapierre et al., 2017)	1.2 * 10^(-8) (Jouganous et al., 2017)	4.04 * 10^6 (Gutenkunst et al., 2009)	0.19392

In Gutenkunst et al. 2009 generation time for human populations was equal to 25 years and mutation rate mu was estimated as 2.35 * 10^(-8). If one wants to change time for one generation to 24 years, one needs to scale mu: mu / 25 * 24 = 2.26 * 10^(-8).

In Jouganous et al. 2017 generation time was grater - 29 years and mutation rate was equal to 1.44 \* 10^(-8). To change generation time to 24, one needs to change value of the mutation rate: muNEW = mu / 29 * 24 = 1.2 * 10^(-8). Theta0 is calculated then by the formula above.

Note

There is another more practical example of changing theta after run.