POPULATION GENETICS PRIMER

Hardy-Weinberg Equilibrium, 2 Allele Case:

Genotype                                AA                  AA'                 A'A'

1st Gener. Frequency              .4                     .4                     .2

SO:     Frequency of A = [2(AA) + AA']/2 = .6 = p (= likelihood a particular GAMETE carries A)

            Frequency of A' = [2(A'A') + AA']/2 = .4 = q (=similar for A’)

SO: 2nd Gen. genotypes =      p²                    2pq                  q²

  (H-W Equilibrium)                = .36               = .48               = .16

AND THIS WILL STAY SAME INDEFINITELY if conditions of Hardy-Weinberg model are met (recalculate p and q to see this)

Measurement of Fitness:

FITNESS (w) is relative or proportional reproductive contribution of a given genotype (or individual of that genotype) to next generation. You can also apply this concept to alleles, in which case fitness is the proportional change in allele frequency from generation to generation -- the ratio of frequency next generation to frequency now). Since it is a relative measure -- always defined in context of some comparison (to previous frequencies or to other frequencies) -- the genotype with highest fitness may be assigned fitness = 1 and other fitness values rescaled proportionally.  This is common, though not universal practice. Intensity of selection AGAINST a genotype, 1- w = S, is called the SELECTION COEFFICIENT. SO:

I. Scenario A

Genotype                                AA                  AA’                A’A’              SUM

IF Fitness =                             w₀                   w₁                   w₂

and genotype freq.

    before selection =                p²                    2pq                  q²                    1

then proportionate 

  contrib. to next gen. =            p² w₀               2pqw₁             q²w₂  

SO, by way of an example, fitness of GENOTYPES of an asexual population could be calculated in following scenario as shown:

Genotype                    AA                  AA’                A’A’               p                      q

Freq. before sel.          .25                   .50                   .25                   .5                     .5

 (at birth generation 1)

Freq. after sel.             .35                   .48                   .17                   .59                   .41

 (at birth gen. 2)

Relative reprod.          .35/.25=          .48/.5=            .17/.25=

contribution                1.4                   .96                   .68

REL. FITNESS (w)    1.4/1.4             .96/1.4             .68/1.4

of genotype                             = 1                  = .7                 = .4

Sel. coeff, s                 0                      .3                     .6

NOTE that, strictly speaking, the above would be appropriate for an asexual organism; not necessarily for a sexual one...  IF you are looking at GENOTYPE/individual fitness for a SEXUALLY REPRODUCING organism, you would, ideally, want to know the proportion of offspring produced in a given generation by individuals of specific genotypes. (i.e., the second line above could be 'proportion of offspring  with parent of this type).  Of course, this gets complex very rapidly, since each offspring has two parents.  It's common to simplify in some way or another: for example, you might look only at female reproductive success and calculate fitness of 'maternal' phenotype.  Or the same for males. 

Fitness of ALLELES is more straightforward because it doesn't matter whether there's sexual recombination or not; it can always be calculated as follows (same scenario):

                                                A                     A’

Freq. before sel’n.                  .5                     .5

Freq. after sel’n                      .59                   .41

Relative contribution              .59/.5=1.18     .41/.5=.82

FITNESS, w                           1.18/1.18=1    .82/1.18=.69

Sel. coefficient, s                    0                      .31

II. Scenario B:

Just to illustrate that there are various ways of doing parallel things, consider three phenotypes, A, B, and C:

                                                A                     B                     C

In first cohort (generation)

at birth

            Number                      40                    40                    20

            Proportion                   0.4                   0.4                   0.2

Offspring born to each

phenotype to make second gen.

            Number                      60                    80                    60 

            Proportion                   0.3                   0.4                   0.3

Absolute fitness/relative

contribution                            0.3/0.4             0.4/0.4             0.3/0.2

                                                =0.75              =1.0                =1.5

Relative fitness (w)                 0.75/1.5           1.0/1.5             1.5/1.5

                                                = 0.5               =0.67              =1.0

(Note that you don’t need to know genotypes of 2^nd generation in this scenario – but you have to know how many offspring each individual has. 

ALSO NOTE that this population is increasing in total size; that doesn't really matter; we're only interested in proportions.

Finally, it doesn't matter here if population is sexually reproducing. BUT it gets more complicated if generations are overlapping...)