Calculation of Fitness and Selection Coefficient
Survival rate = the overall survival rate is the % of individuals born that survive to reproductive age. But often we can only measure the % that survive over some period of time, e.g. the survival rate of fledglings, the survival rate from one year to the next, or the survival rate through a winter storm.
Reproductive rate = for any given genotype or phenotype, the average number offspring born per individual.
Relative Fitness (w) is the survival and/or reproductive rate of a genotype (or phenotype) relative to the maximum survival and/or reproductive rate of other genotypes in the population.
Calculate the Relative Fitness (w) of each genotype by dividing each genotype's survival and/or reproductive rate by the highest survival and/or reproductive rate among the 3 genotypes. For example:
If only survival rates differ and reproductive rates are all equal, then the fitnesses are simply each survival rate divided by the highest survival rate.
DD |
Dd |
dd |
|
Survival rate |
10% |
10% |
20% |
Reproductive rate |
4 |
4 |
4 |
Relative fitness (w) |
10/20 = 0.50 |
10/20 = 0.50 |
20/20 = 1.0 |
If only reproductive rates differ and the survival rates are all equal, then fitnesses are each reproductive rate divided by the highest reproductive rate.
DD |
Dd |
dd |
|
Survival rate |
10% |
10% |
10% |
Reproductive rate |
8 |
8 |
4 |
Relative fitness (w) |
8/8 = 1.00 |
8/8 = 1.00 |
4/8 = 0.50 |
If both survival and reproductive rates vary among the genotypes, then divide each survival X reproductive rate by the highest survival X reproductive rate.
DD |
Dd |
dd |
|
Survival rate |
10% |
10% |
20% |
Reproductive rate |
10 |
8 |
6 |
Survival X Reprod. |
0.1 X 10 =1.0* |
0.1 X 8 = 0.8* |
0.20 X 6 = 1.2* |
Relative fitness (w) |
1.0/1.2 = 0.83 |
0.8/1.2 = 0.67 |
1.2/1.2 = 1.0 |
*On average, every DD born produces 1 viable offspring, while a typical Dd newborn produces 0.8 offspring and dd newborns average 1.2 offspring each.
Interpretation of fitness: wdd = 1.00 means the dd genotype is the most fit, most successful, of the 3 genotypes in that particular environment at that particular time (even though many may be dying young). The fitnesses of the other genotypes are some percentage of that highest fitness. For example, wDD = 0.9 means the DD individuals produce offspring on average at 90% of the rate of individuals with the most successful genotype with w = 1.0.
Selection coefficient is a measure of the relative strength of selection acting against a genotype. Calculate the selection coefficient (s) by subtracting each fitness value from 1.0 (that is, s = 1-w).
Interpretation of selection coefficient: sdd = 0.0 means genotype dd is not being selected against. That is, although they are dying, the dd individuals on average are dying less or produce more offspring than the other genotypes in the same population. sDD = 1.0 is total selection (DD individuals produce no viable offspring. sDD = 0.10 means each generation, DD individuals produce offspring on average at 90% of the rate of the dd individuals, or in other words, DD individuals on average have a 10% harder time producing offspring than dd individuals.
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This exersize assumes random mating among surviving adults in an infinitly large population. Graphs (that will be generated later) are predicted based on the fitness of each genotype and follow the modified Hardy-Weinberg formulat (p2w11 + 2pqw12 + q2w22) where w11 = the fitness of the A1A1 genotype, w12 = the fitness of the A1A2 genotype and w22 = the fitness of the A2A2 genotype.