Philosophy of Biology

Formalisations of Evolutionary Biology 515

There are 9 different combinations (genotypes). For each genotype a fitness
co-efficientWican be assigned. In addition, for each genotype a frequency can be
assigned based onp 1 andq 1 ,p 2 andq 2 (for locus 1 and locus 2 respectively). Let
that frequency beZi. The product of the frequency of a genotype and the fitness of
that genotype is the contribution to the average fitness of the populationmade
by that genotype. The sum of the contributions of all the genotypes represented
in the population is the average fitnessof the population. Hence, the average
fitnessfor a population

=

∑

ZiWi.

Consider the following calculation for a single population.

P 1 =. 7

p 2 =. 4

Sincep 1 +q 1 =1andp 2 +q 2 = 1, the value ofqcan be determined from the value
ofp. Hence the value of p alone is sufficient to determine the genotype frequencies
of the population.
In accordance with the Hardy-Weinberg equilibrium, the genotype frequencies
can be calculated by multiplying the frequencies of the allelic combinations at
each locus in the two loci pair. The resulting frequencies with assigned fitnesses,
frequency-fitnesses, and the average fitness for the population is shown in the
following table:

Genotype Frequency Fitness Frequencey×

ZWFitness

AABB 0.784 0.85 0.06664

AABb 0.23522 .0.48 0.108192

AAbb 0.1764 0.54 095256

AaBB 0.0672 0.87 0.058484

AaBb 0.2016 0.65 0.13104

Aabb 0.1512 0.32 0.048384

aaBB 0.0144 0.61 0.008784

aaBb 0.0432 1.2 0.05184

aabb 0.0324 1.13 0.036612

w= 0.605212

By plotting the average fitnessof each possible population in a two loci system
with the assigned fitness valuesWi, an adaptive landscape for the system can be