Génétique des Populations - Cours

• M6 – Génétique: Génétique des populations, fiche de cours n°5.

Introduction

• Objects of population genetics: study of allele and genotype frequencies in a population and factors modifying these frequencies across generations.
• Interests of population genetics: genetic counseling predicts the risk of having an affected child.
• Health policy anticipates disease frequency and population needs, adapting the healthcare system.
• It sheds light on ethical questions such as prenatal diagnosis involving balancing the risk of having an affected child against the risk of the diagnostic procedure and decisions regarding therapeutic abortions.
• Understanding the mechanisms of evolution needs molecular and mathematical bases.
• The biodiversity of living organisms results from genome evolution, and population genetics allows for better understanding of disease pathophysiology.

Definitions

• A population is the set of diploid individuals of the same species in a defined geographic area, interbreeding with each other.
• Examples of populations: humans in a defined territory and fish of a given species in a lake.
• The number of individuals in a population is denoted as N.
• A diploid individual has pairs of homologous chromosomes, one from each parent, with identical structure and nearly identical sequences.
• The number of chromosomes in an individual is 2N.
• A gene is a continuous DNA sequence present in two copies in each individual and can have variants or versions called alleles.
• Each individual has two alleles for a given gene A.
• In a population, a gene is present in n number of alleles at any given time: A1, A2, A3… An, where n ≤ 2N (the total number of chromosomes in the population).

Genotypes

• Genotypes refer to the combination of alleles an individual has for a particular gene.
• For the first chromosome, the allele can be A1, A2... or An, represented as the first allele Ai.
• For the second chromosome, the allele can also be A1, A2... or An, represented as the second allele Aj.
• If Ai = Aj, the individual is homozygous for gene A.
• If Ai ≠ Aj, the individual is heterozygous for gene A.
• The number of different genotypes can be calculated as n*(n+1)/2 with n being the number of alleles.
• With three alleles, the number of genotypes equals (3 x 4) / 2 = 6.

Frequencies

• Allele frequency (fAi) is the number of alleles Ai divided by 2N, where 2N is the total number of chromosomes in the diploid population.
• Genotype frequency (f(Ai, Aj)) is the number of individuals with genotype AiAj divided by N, the total number of individuals.

Populations in equilibrium

• A large population contains 1000+ individuals.
• A closed population contains no migration.
• A population in equilibirum contains no mutation.
• There is no selection.
• The genotype distribution is identical across males and females, and panmixia, random mating, happens.
• A stable population has couples with the same number of descendants.
• Allele frequencies at generation 0: fA1 = p = number of A1/2N, fA2 = q = number of A2/2N, with p + q = 1.

Frequencies to Generation 1

• A Punnett square illustrates the combinations: 25% A1A1, 25% A2A2, 50% A1A2.
• Necessary conditions of panmixia: random mating, equal probability of gametes (pangamy), and random merging of gametes.
• There is no selection.
• Allele frequencies are gamete frequencies: A1 = p, A2 = q.
• It allows calculating genotype frequencies from generation 1.
• (A1, A1): p², (A1, A2): 2pq, (A2, A2): q².
• Number of A1 alleles = 2 * N * p² + N * 2pq.
• Allele frequency: (N * 2p² + N * 2pq) / 2N = p² + pq = p, with 2N as the total number of alleles.
• A2 allele frequency = q² + pq = q.

Hardy-Weinberg Law

• Allele and genotype frequencies remain constant across generations.
• Only one initial condition needs to be unrespected.
• There is verification of the balance of a population.
• Observed genotype numbers are compared to calculated numbers using known allele frequencies.
• The Chi-squared test measures the difference.

Factors modifying the frequency of genotypes

• Non-application of the Hardy-Weinberg law is due to the emergence of specific situations.
• Small population size.
• The population contains migrations.
• There is a presence of mutations.
• There is a selection.

Hardy-Weinberg Applications

• Calculate genotype frequencies, calculate frequency of disease mutant genes.
• Identify factors modifying the frequencies of these genotypes.
• The Hardy-Weinberg law is also the law of non-evolution.
• Math is accurate, but isn't 100% true for humans in the long run.
• Frequency of disease alleles = q.
• Disease frequency = 2pq. Because q is small, then 2pq + q² ≈ 2q
• Example: Huntington's chorea: disease frequency is 1/20,000; allele frequency is (1/20,000)/2 = 1/40,000.
• Allele frequency = q.
• The disease frequency = q².
• Frequency of the porteurs = 2q.
• Example: Mucoviscidose, with a disease frequency of 1/2500, then the frequency = square root of 1/2500 = 1/50, causing the porteur genotype = 1/25

Factors Modifying Frequency

• Population Size: Small N population.
• Conditions: An allele Ai has a frequency of f = q.
• Gametes produce future generation alleles with 2N << draws = gametes to produce 2 children.
• Production of Gametes: Ai draws have a probability of q, don't have a probability of 1-q.
• Never drawing Ai for the total population (1-q)2N à leads to q = 0.
• Drawing exclusively Ai produces Ai with q2N à leads to q=1.
• Drawing X AI alleles (0 à 2N range) for the total population: binomial law (2N, q), N being the population total of q: the allele frequency.
• Binomial Law: Shows the link between the disappearance and allele frequency.
• A small population has an allele frequency trend towards 0 or 1.
• This is the notion of Dérive Génétique.
• The frequency of Hétérozygotes is multiplied for each generation to : 1-(1/2N).
• Migration in two cases contains different allelic frequencies. and a third case that is a mix of the two. A small population mix produces populations with a mix of issues.
• Mutations: a small mutation in one allele contains the sequence.
• An 1 allele with a mutation leads to A2 with frequency u.
• A1 to A2 : (A1-> A2) : u frequency.
• The allele start with frequency (A1) Po
• Generation post : frequencies of A1 = Po - UPo
• The result is a shift with a frequency of (A1) UPo
• At equilibrium and based on frequency A2 à constants with small mutations .

Population - Dérive Génétique

• Factor: dispersed frequencies, higher N (dispersed individuals, frequency variation).
• Small changes have potential for rapid changes, without having the same amplitude of variation.
• Genetics - can be more potential/efficient as the origin is smaller.
• Effect on derivation and genetics: diminishes genetics/can contribute to isolation

Selection

• Selection will occur if the individual contributes unequally to formation of the generation following. With value set between 0 and 1, as a coefficient. If the allele is lethal, the value is s=1.
• In each generation, the frequency/appearance of alleles can be factored: observed Frequency = (1-s) times calculated frequency.