class: center, middle, inverse, title-slide .title[ # Heterozygosity ] .author[ ### Jinliang Yang ] .date[ ### Feb. 9, 2024 ] --- # Systematic and dispersive processes ### Systematic process: mutation, migration, and selection - Bring the allele frequencies to stable equilibria at particular value -- ### Dispersive process - drift - Scatter the allele frequencies away from these equilibrium - Eventually lead to all alleles being either fixed or lost --- # Non-recurrent neutral mutation ### Infinite allele model (IAM) of mutation - Probability of the same mutation occurs more than once is very, very, very small -- ### Neutral model (new allele has no effect on fitness) - Probability new allele becomes fixed in the absence of selection = `\(\frac{1}{2N}\)` - If `\(\mu\)` is mutation rate at the locus, total number of new mutants = `\(2N\mu\)` - Probability of a new mutant being fixed `\(= 2N \mu \times \frac{1}{2N} = \mu\)` > Kimura, 1983 --- # Effective neutral mutation #### Probability of fixation of new mutation is influenced by selection - Favorable (beneficial) or unfavorable (deleterious) -- `\begin{align*} Pr(fixation) \approx \frac{1}{2N_e} \end{align*}` > Kimura, 1983 - __Effective neutral mutation__ is one a coefficient of selection `\(s\)` against it - Range from `\(s=0\)` (neutral) to `\(s=\frac{1}{2N_e}\)` or -- - `\(N_es < 1/2\)`: effectively neutral - `\(N_es > 1/2\)`: under selection --- # Effective neutral mutation ### `\(N_es < 1/2\)`: effectively neutral For example, inbred lines of mice resulting from sib matings have `\(N_e \approx 2.5\)` - To keep `\(N_es < 1/2\)`, `\(s\)` can be as high as 0.2 and this allele could become fixed due to drift and have a negative effect on fitness -- - The indication: favorable mutants are far too rare to counter balance the loss of fitness in small population!