One-way migration

Migration There are two populations (x and y), each with a

different frequency of A alleles (px and py). Assume migrants are from population x, and residents

are population x; unidirectional). After migration, m is the migrant portion of the

population y, and (1-m) is the resident portion of the population y. py’ is the p after migration: py’ = m x px + (1-m) x py dpy = m x px + (1-m) x py – py dpy = m x px + py – m x py – py dpy = m x px + m x py dpy = m(px-py)

Change in allele frequency with one-way migration (m = 0.01)

Natural Selection The interaction between alleles

and environment shapes the direction of the change in allele frequencies resulting in evolution of adaptable traits.

Fitness and coefficient of selection (s) Darwinian fitness is defined as the relative

reproductive ability of a genotype. The genotype that produces the most

offspring is assigned a fitness (W) value of 1. Selection coefficient (s) equals (1-W) AA produces on average 8 offspring Aa produces on average 4 offspring aa produces on average 2 offspring.

WAA = 1.0; sAA = 1-1 = 0 WAa = 0.5; sAa = 1-0.5 = 0.5 Waa = 0.25; saa = 1-0.25 = 0.75

How to calculate change in allele frequency after selection

AA Aa aa

Initial genotypic frequencies

p2 2pq q2

Fitness WAA WAa Waa

Frequency after selection

p2 WAA 2pq WAa q2 Waa

Relative frequency after selection

p2 WAA/WMEAN 2pq WAa /WMEAN q2 Waa /WMEAN

Wmean = p2 WAA + 2pq WAa + q2 Waa

Possibilities

1. WAA = WAa = Waa: no natural selection

2. WAA = WAa < 1.0 and Waa = 1.0: natural selection and complete dominance operate against a dominant allele.

3. WAA = WAa = 1.0 and Waa < 1.0: natural selection and complete dominance operate against a recessive allele.

4. WAA < WAa < 1.0 and Waa = 1.0: heterozygote shows intermediate fitness; natural selection operates without effects of complete dominance.

5. WAA and Waa < 1.0 and WAa = 1.0: heterozygote has the highest fitness; natural selection/codominance favor the heterozygote (also called overdominance).

6. WAa < WAA and Waa = 1.0: heterozygote has lowest fitness; natural selection favors either homozygote.

Selection against a recessive lethal phenotype

Recessive trait result in reduced fitness.

Frequency of the recessive allele decreases over time.

Not completely eliminated since present in heterozygotes.

Heterozygote superiority

Distribution of malaria and frequency of Hb-s allele leading to sickle cell disease in homozygotes.

Balance between mutation and selection When an allele becomes rare, changes in

frequency due to natural selection are small.

Mutation occurs at the same time and produces new rare alleles.

For a complete recessive allele at equilibrium: q = õ/s If homozygote recessive is lethal (s = 1) then q

= õ

Model 1 Simulate the change in allele frequencies directly

by mathematical modeling of the forces that act on them. Set initial values for p and q; Set initial sample size (effective population size); Set the HWE as the null model (p2 + 2pq + q2 = 1); Allow for forces such as mutation rate, migration, genetic

drift, and selection to act on the null model. Estimate the change in allele frequencies over time using

iterations (i.e., the program loops over for a number of generations as given by the arguments).

Model 2 Simulate individuals of a population(s) having DNA

sequence polymorphisms, and allow them to evolve randomly or under certain forces.

Set initial number of individuals (N at t = 0, equals to the effective size of the population, Ne);

Generate a null matrix for N x K x G, where K = 2 (diploid), and G equals to the number of genes considered (start with a single gene, if else assume genes are not linked for simplicity).

Set the total number of alleles (Nk, start with Nk = 2) for each G. Set the initial number of homozygotes, heterozygotes for G. Allow for the individuals mate randomly to produce offspring, iterate to

simulate generations; for simplicity assume that all individuals die after reproduction. E.g., annual plants where Nt+1 = bNt + 0 Nt

Allow for forces to act on the null model, and test their effects on the allelic evolution.