# 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) |
(per site per gen.) |
(base pair) |
(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.