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# Relative Fitness and Absolute Fitness using Selection Coefficient

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The coefficient for selection between Zid+ and Zid- in common garden experiment of an individual being treated with AZT is 0.036, indicating selection for Zid-.

What are the relative fitnesses of Zid- and Zid+?

Absolute fitness of Zid+ in AZT treated people is 1.040. What's the Absolute fitness for Zid-?

https://brainmass.com/biology/genetics/relative-fitness-absolute-fitness-selection-coefficient-456283

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Fitness is an indicator of the rate of growth of a given genotype within a population. Absolute fitness (wabsolute) is a ratio of the number of individuals with a particular genotype in a given generation divided by the number of individuals with that genotype in the previous generation.

wabsolute of genotype A = Number in generation n / Number in generation n-1
Number indicates the number of individuals with genotype A in the given generations.

Relative fitness (wrelative) is the ratio of the absolute fitness of a given genotype divided by the absolute fitness of the most fit genotype. The relative fitness of the most fit genotype would be 1.

wrelative of A = wabsolute of genotype A / wabsolute of reference genotype
Reference genotype is the genotype with the highest wabsolute. The relative fitness of the rest of the genotypes is measured in reference to this most fit genotype.

Selection coefficient (s) is given by s = 1 - w relative. The only way to get a coefficient of 1 is to have w relative equal to 0. Thus, a coefficient of 1 indicates that the genotype is selected against because of no fitness. This is the case with a lethal genotype. A coefficient of 0 would indicate high fitness because the only way to get a zero is to have w relative equal to 1. Reference genotype should have a coefficient of 0 because the relative fitness is 1.

Since we are given the selection coefficients and not the actual number of individuals, we have to start backwards from the selection coefficient. Use the given selection coefficient of Zid- to calculate the relative fitness of Zid-.

S(Zid-) = 1 - wrelative
0.036 = 1 - wrelative
w(Zid-) = 0.964

Given multiple genotypes, there should be at least 1 genotype that is most fit. This genotype is used as a reference to calculate relative fitness of all genotypes and itself has a relative fitness of 1. Since Zid- has a relative fitness of less than 1, that leaves only Zid+ as the possible genotype with a relative fitness of 1. Zid+ must have a relative fitness of 1. The selection coefficient for Zid+ must be 0.

S(Zid+) = 1 - w
0 = 1 - w
w(Zid+) = 1

Relative fitness of Zid+ would be a ratio of absolute fitness of Zid+ divided by itself.

wrelative of Zid+ = wabsolute of Zid+ / wabsolute of reference genotype
Since Zid+ is the reference genotype, the formula becomes:
wrelative of Zid+ = wabsolute of Zid+ / wabsolute of Zid+
1 = 1.040/1.040

Relative fitness of Zid- would be a ratio of absolute fitness of Zid- divided by absolute fitness of Zid+ (reference genotype). Using the value of relative fitness calculated above for Zid-, this gives us:

wrelative of Zid- = wabsolute of Zid- / wabsolute of Zid+
0.964 = wabsolute of Zid- /1.040
wabsolute of Zid- = (0.964)(1.040)
wabsolute of Zid- = 1.00256

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