In order to find the frequency of recurrent mutation frequency, we will work on equilibrium frequency. It’s the fact natural selection can not eliminate mutant genes because it will keep forming by mutation.
a gene mutates and gives A gene. take m as the mutation rate from a to A per generation. Ignore back mutation. the frequency of a as q and A as p
Fitness is give as
| aa | Aa | AA |
| 1 | 1-s | 1-s |
equilibrium works in the way in regard to mutant gene A. if the frequency of A is higher than the equilibrium, Natural selection removes more A genes than mutation creates, and the frequency decreases and vice versa if frequency is lower than equilibrium.
equilibrium is given as
Rate of loss of A gene by selection= Rate of gain of A gene by mutation
Equilibrium frequency is given as P*
We can calculate the rate per generation of creation of A gene by mutation. Each mutant A gene is formed from a gene and the chance of formation of A gene from a gene is mutation rate.
Total rate of creation of A genes by mutation= m(1-p)
and A gene can survival rate gives as 1-s or s chance of dying
Total rate of loss of A gene by mutation = ps
At the equilibrium gene frequency p* given as
m(1-p*)=p*s
m-mp* = p*s
p*= m/(s+m)
m in denominator is very small so it becomes
p*=m/s equation means gene frequency of mutation at equilibrium is equal to ratio of mutation rate to its selective disadvantage. equilibrium frequency is very important in terms it describes the rate of loss of gene is equal to gain
so eq p=m/s gives rough estimate of mutation rate of a harmful mutation. if the mutants are rare they are present in heterozygous combination and have frequency at birth as 2pq if p is very small q= 1 and 2pq= 2p
now N is another factor given as frequency of mutant bearers. this is equal to frequency of heterozygote = 2p so N= 2p and p=N/2
now p= m/s and m=ps
m=N/2(s) if the mutation is highly dangerous , s=1 and m=N/2
The mutation rate can be calculated as half the birth rate of mutant type
Chondrodystrophic Dwarfism:
This is dominant deleterious mutation in human.
Chondrosdystrophic dwarfism is a dominant deleterious mutation in humans.
In the study, 10 births out of 94,075 had the gene, a frequency of 10.6 × 10−5 The estimate
of the mutation rate by the above method is then m = 5.3 × 10−5
However, it is possible o estimate the selection coefficient, enabling a more accurate estimate of the mutation rate another study, 108 chondrodystrophic dwarves produced 27 children; their
457 normal siblings produced 582 children. The relative fitness of the dwarves was(27/108)/(582/457) = 0.196; the selection coefficient s = 0.804. Instead of assuming s=1, we can use s = 0.804. Then the mutation rate is sN/2 = 4.3 × 10−5, a rather lower figure because with lower selection the same gene frequency can be maintained by a lower mutation rate. A similar method is used to find mutation for recessive alleles but the equation is different for that.
Reference: Evolution Book by Mark Ridley