Population Genetics: The Hardy-Weinberg Law Consider a single gene that has only two alleles (A and a). There is complete dominance, though this is not really important because we will deal primarily with genotypes rather than phenotypes.

Genotype and allele frequencies Genotype frequencies (what fraction of the population is made up of each genotype?) D = f(AA); H = f(Aa); R = f(aa) Allele frequencies (what fraction of the genes in the population is made up of each allele?) Since each gamete carries only one copy of each gene, “allele frequency” and “gamete frequency” are synonymous. p = f(A) and q = f(a)

To go from genotype frequencies to allele frequencies p = D + ½ H q = R + ½ H

After random mating D = p2 H = 2pq R = q2

Conclusions of Hardy-Weinberg Law Given certain conditions, the genotype and allele frequencies of a population do not change over time. In other words, the population does not evolve. Therefore, we must examine what the conditions are, and what happens if they are not met. By specifying the conditions under which evolution does not occur, H-W law identifies the potential causes of evolution and allows us to study them.

Conditions for H-W Equilibrium Large, statistically predictable population. Closed population; no immigration / emigration. No net mutation. Random mating. Equal reproductive success of all genotypes.

Population Size In a small population, gene frequencies can change merely due to chance. Change in a small population: genetic drift Temporarily small populations: bottlenecks Populations that grow from a small pool of initial colonists: founder effect

Migration = “Gene Flow” Only has an effect if the migrants are genetically different from the population as a whole. A potential problem with introduction of exotic animals and plants. But gene flow can also be a force keeping two populations similar, so they don’t evolve differences between them.

Mutation Definition – heritable change in DNA. Usually caused by errors in replication. Mutation can be caused by radiation or certain chemicals (mutagens). However, cells have elaborate mechanisms to detect and repair mutations.

Mutation and population genetics Mutation alone could change a population, if there were a strong net mutational pressure. for example, if allele A mutates to a at a steady rate But in reality, mutation is very rare and usually random in direction. Mutation is very important as the ultimate source of all genetic variability.

Non-random mating Inbreeding – mating with relatives reduces heterozygosity Assortative mating – choosing mates based on phenotype positive (mating like with like): has similar effects to inbreeding negative (mating with different phenotype): increases variability of population

Differential reproductive success If one genotype reproduces more successfully than others, its genes will become more common in future generations. This is a formal statement of Darwin’s concept of natural selection. Can be modeled mathematically: Fitness (W) = reproductive success, with the most successful genotype assigned a value of W=1. Selection coefficient (s) = 1-W

What about continuous variation? Traits like height, weight, etc. are controlled by many genes (polygenic inheritance). Could try to analyze using Hardy-Weinberg for multiple genes, but it gets too complicated. Instead, we can simply look at the results of selection on the phenotype. This approach is called “quantitative genetics”.

3 Patterns of Natural Selection Directional selection: One extreme more fit than the other. Causes population mean to shift over time. Stabilizing selection: Both extremes are less fit than the intermediates. Causes population to become less variable. Disruptive selection: Both extremes are more fit than the intermediates. Causes population to become more variable, perhaps to have distinct polymorphisms (different forms).

Directional selection on polygenic traits can cause new phenotypes to appear in a population. This appears to contradict the basic idea that selection does not create characters but only “sifts” existing variability, but in fact is easy to explain based on polygenic inheritance. Assume that height of a giraffe is controlled by 5 genes, with the recessive form making the animal tall. If the genes act additively, the chance of being homozygous tall for a given gene is q2 and the chance of being homozygous tall for all eight genes is (q2)5 or q10. If tall alleles are relatively rare (say q=0.2), then the chance of finding an extremely tall giraffe is 0.210 = 1x10-7 or one in ten million. Since there are not ten million giraffes in the world, you would be very unlikely to ever see such an animal. On the other hand, if selection drives q up to 0.8, then the chance of finding an extremely tall giraffe is 0.810 which is about 0.1, or one in ten giraffes, a fairly common occurrence.

Sources of genetic variation Mutation, while rare, is the ultimate source of variability. Mutations include: Point mutation: replacing one base with another. Frame-shift mutations: adding or deleting a base. Chromosomal rearrangements: inversions/translocations Additions or losses of chromosomes (aneuploidy) Additions of whole sets of chromosomes (polyploidy)

Recombination Recombination is a very powerful force for making new genotypes with existing variation. Recombination includes: independent assortment during meiosis, which combines maternal with paternal traits. crossing-over, which separates linked genes fertilization, which combines alleles into a new generation. Meiosis and sexual reproduction have probably evolved as a means of generating variation, because variation leads to adaptability.