Genetic aspects of populations, Hardy-Weinberg equilibrium

Population
What is a population from genetic point-of-view? It is a group of inbreeding individuals of the same species that inhabit the same space (prescribed geographical area) and time. The key to a population is that they must be able to interbreed.

Within any given population there is variation (differencies) of/in:
 * phenotypes; the proportion of individuals within a population that are of a particular phenotype is phenotype frequency
 * genotypes; the proportion of individuals within a population that are of a particular genotype is genotype frequency
 * alleles; the proportion of all copies of a gene in a population that are of a particular allele type is allelic frequency

The gene pool is the sum total of all of the alleles (of one locus) present and carried by the population.
 * Gametic gene pool – sum of all alleles in gametes.
 * Zygotic gene pool – sum of all alleles in zygotes.

For a gene with 2 alleles, A and a:
 * NAA is the number of AA homozygotes
 * NAa is the number of heterozygotes Aa
 * Naa is the number of aa homozygotes
 * NAA + NAa + Naa = N, number of individuals in population

Estimating/calculating of allele frequencies in a population
 * with three distinct phenotypes for a trait (e.g. in MN blood group system)
 * Let p = frequency of allele A, and q = frequency of a. Then:
 * pA = (2NAA + NAa) / 2N
 * qa = (2Naa + NAa) / 2N
 * Variant procedure: Calculating allele frequencies from (known) frequencies of genotypes AA, Aa, aa
 * pA = fAA + ½ fAa
 * qa = faa + ½ fAa
 * p + q = 1


 * where (only) two distinct phenotypes exist (i.e., in allelic relation of full dominance/recessivity); estimate of frequency of unfavourable (mutant, deleterious, recessive) allele (Rh blood group system, tasting of PTC or AR diseases)



Genotype frequencies
If frequency of allele A in a population is p, frequency of allele a in a population is q:
 * the probability that both the egg and the sperm contain the A allele is p x p = p2
 * the probability that both the egg and the sperm contain the a allele is q x q = q2
 * the probability that the egg and the sperm contain different alleles is (p x q) + (q x p) = 2pq

Hardy-Weinberg Equation
A population that is not changing genetically is in Hardy-Weinberg equilibrium (1908). It comes if these 5 assumptions are correct:
 * Hardy-Weinberg law
 * Random mating (panmixia)
 * Large population size (N approaching infinity)
 * No migration between populations
 * No (or negligible) mutations
 * Natural selection does not affect alleles being considered

If these assumptions are true, it follows that:
 * Allele frequencies remain constant from one generation to the next
 * After one (or more) generations of random mating (breeding), the genotype frequencies (for a 2-allele gene with allele frequencies p, q) are in the proportions: p2(AA) : 2pq(Aa) : q2(aa), and population will be in H-W equilibrium. Var.: H-W equilibrium in a large population will be reached after one generation of (random) breeding.
 * For a population to be in Hardy Weinberg equilibrium, the observed genotype frequencies must match those predicted by the equation p2 + 2pq + q2.

(relation between frequencies of alleles and frequencies of genotypes)
 * Graphic demonstration of H-W equilibrium



Multiple alleles
Multinomial expansion for two alleles a and b with frequencies p and q p2 + 2pq + q2 is a binomial expansion of (p + q)2
 * p2(AA) + 2pq(Aa) + q2(aa) = (p + q)2 = (1)2 = 1

For three alleles a, b and c with frequencies p, q and r, the multinomial expansion is (p + q + r)2 which expands into: p2+ q2 + r2 + 2pq + 2pr +2qr , where the first 3 terms being homozygotes and the remaining three heterozygotes.
 * p + q + r = 1		p2+ q2 + r2 + 2pq + 2pr +2qr = 1