Course outline Evolution: When violations in H-W assumptions cause changes in the genetic composition of a population Population Structure: When violations in H-W assumptions cause changes in the distribution of alleles within/across populations Unit 2: Evolution and Pop. Structure (a.k.a. violations in H-W assumptions) Unit 2.1: genetic drift Unit 2.2: natural selection Unit 2.3: mutation Unit 2.4: migration Unit 2.5: assortative mating Unit 2.6: inbreeding Consider adding some PCA plots, etc. to show population structure.

Course outline Evolution: When violations in H-W assumptions cause changes in the genetic composition of a population Population Structure: When violations in H-W assumptions cause changes in the distribution of alleles within/across populations Unit 2: Evolution and Pop. Structure (a.k.a. violations in H-W assumptions) Unit 2.1: genetic drift Unit 2.2: natural selection Unit 2.3: mutation Unit 2.5: assortative mating Unit 2.6: inbreeding Unit 2.4: migration

Migration Feb 16, 2015 HUGEN 2022: Population Genetics J. Shaffer Dept. Human Genetics University of Pittsburgh

Objectives At the end of the lecture you should be able to 1.identify whether scenarios constitute genetic migration 2.recognize the qualitative effects of migration 3.solve and interpret problems under various migration models

Hardy-Weinberg assumptions diploid organism sexual reproduction nonoverlapping generations random mating large population size equal allele frequencies in the sexes no migration no mutation no selection

Hardy-Weinberg assumptions diploid organism sexual reproduction nonoverlapping generations random mating large population size equal allele frequencies in the sexes no migration no mutation no selection

Big Picture: Population Structure Definition: –person-perspective: individuals in a population fall into genetically- distinct groups –allele perspective: alleles are distributed across the population in some way other than expected due to chance alone Population Structure vs. Hardy-Weinberg –The H-W Law tells us that if assumptions are met, alleles will be distributed across genotype groups with the following frequencies: p 2, 2pq, q 2 –For population structure to occur, H-W assumption must be violated –Which processes cause population structure? non-random mating based on broad range of cultural and phenotypic characteristics (i.e. ethnicity) migration bringing two or more genetically distinct populations together

Migration Definition: –the movement of alleles among subpopulations Two viewpoints for population structure: –a meta-population may be divided into subpopulations geographical regions ethnic groups –people more often mate within their subpopulation, but there is some mixing –from the point of view of the meta-population, the population structure is an example of non-random mating –from the point of view of the subpopulation, the population structure is an example of migration

Key point: genetic migration For the purpose of studying population genetics, migration does NOT necessarily involve people migrating from one geographical place to another Migration from the genetic standpoint is only interested in movement of alleles among subpopulations Examples: –Sailors land on island, mate with natives, and then sail on –European settlers mate with native Americans –Mixing of people of African ancestry and European ancestry in North America Counter example: –Entire island population moves from a volcanically active island to an uninhabited nearby island (i.e. NO genetic migration)

Effects of migration Qualitative –Migration among populations is “homogenizing” allele frequencies of each population move toward the average do not confuse homogenous with homozygous –Affects the entire genome simultaneously –Speed of homogenization dependent on rate(s) of migration among populations Quantitative –difficult to accurately model; we will do math under some very simple models of migration

general migration model to understand how allele frequencies change in population i, we need to know: 1.migration rates, m ij (i.e., m to from ), among all populations m ij is the P(next generation allele comes from pop. j into pop. i) 2.allele frequencies, P(A) = p j, for all populations

general migration model allele frequency for population i after one generation of migration is: m 11 m 12 m 13 m 14 2m 21 m 22 m 23 m 24 3m 31 m 32 m 33 m 34 4m 41 m 42 m 43 m 44 from to p1p1 p3p3 p2p2 p4p4

example: general model four populations, 1-4, with allele frequencies 0.1, 0.2, 0.3, 0.4, respectively what is the allele frequency of population #2 after one generation of migration? Example from to = (p 1 )(m 21 ) + (p 2 )(m 22 ) + (p 3 )(m 23 ) + (p 4 )(m 24 ) = (0.1)(0.01) + (0.2)(0.85) + (0.3)(0.09) + (0.4)(0.05) = = must be known

general migration model What if we have a lot of populations? –migration matrix becomes bigger –we probably can’t accurately know all of the migration rates –migration rates among the network probably change from one generation to another Make some simplifications –trade off between accuracy and feasibility

general migration model What if we have a lot of populations? –migration matrix becomes bigger –we probably can’t accurately know all of the migration rates –migration rates among the network probably change from one generation to another Make some simplifications –trade off between accuracy and feasibility … quickly becomes a real mess!

general migration model What if we have a lot of populations? –migration matrix becomes bigger –we probably can’t accurately know all of the migration rates –migration rates among the network probably change from one generation to another Make some simplifications –trade off between accuracy and feasibility … quickly becomes a real mess!

island model of migration many populations; migration rates among all –population of interest is an “island” –collectively call all of the other populations together a “continent” P(A) for each population, p p = average p over all populations (p of meta-population) –does not change over time (think of whole-world allele freq.) m = migration rate –P(next-gen. allele in island comes from the continent) –1 – m = P(next-gen. allele is from the island)

island model of migration simplifying assumptions: –continental population very large compared to island migration FROM continent TO island may meaningfully impact genetic composition of island migration FROM island TO continent has negligible impact on genetic composition of continent island population has negligible effect on p –migrant allele frequency = p ignores population substructure within the continent

island model as general model p0p0 p islandcontinent island1-mm continent to from = (p 0 )(1-m) + (p)(m) m from islandfrom migrants in the next generation:

island model over time for the next generation: p 1 = p 0 (1 – m) + pm For t generations: p t = p + (p 0 – p)(1 – m) t After many, many generations (1 – m) ∞ = 0 p ∞ = p

island model example specifics the continental population has p = island population has p 0 = 0 m = 0.01 i.e. 1% of alleles from continent, 99% from island what is p 10 ? p 100 ? p 1000 ? how many generations until p = 0.4? Example

island model example p 0 = 0.0 m = 0.01 p = 0.6 p t = p + (p 0 – p)(1 – m) t p 10 = (0.6) + (0 – 0.6)(1 – 0.01) 10 p 10 = p 100 = p 1000 = Example

Migration example p 0 = 0.0 m = 0.01 p = 0.6 How many generations until p t = 0.4 in the subpopulation of interest? p t = p + (p 0 – p)(1 – m) t (0.4) = (0.6) + (0 – 0.6) (1 – 0.01) t (0.4) = (0.6) + (-0.6) (0.99) t (0.6 – 0.4) / (0.6) = (0.99) t = 0.99 t t = log(0.3333) / log(0.99) t = Example

More models for humans one-way “racism” model (variant of island model) –offspring of mixed parentage are all members of one of the parental groups –example: African Americans two-way racism model (example of general model) –child of mixed parentage are distinct and from a new population of their own –example: Anglo-Indians migrant pop. admixed pop. parental pop. 1 admixed pop. parental pop. 2

one-way racism as general model admixedmigrant admixed1-mm migrant to from = p A1 = (1-m)(p A ) + (m)(p M ) from admixedfrom migrants in the next generation: migrant pop. admixed pop. pApA pMpM m for t generations: p At = p M + (p A0 – p M )(1-m) t comments –p M not dependent on t because migration is one way –what happens to p At in the long run? It approaches p M

Example: one-way racism model How much admixture is there in U.S. African American population? –clinical and historical interest We need to know: p At, p M, p A0, t and solve for m p At = p M + (p A0 – p M )(1-m) t We will consider a study of populations from Claxton, GA Caucasian African American Example

Example: one-way racism model Where do we get values for our variables? p A0 = original allele frequency in African Americans prior to admixture p At = current allele frequency in the admixed population p M = allele frequency in the migrating population t = number of generations since admixture These values must be estimated from what we can measure now Because of all this uncertainty, we cannot be confident in the results of a single locus. Instead, test many loci to see if the results are consistent –remember, migration effects all loci simultaneously! Example

Example: one-way racism model the data for an example locus: p A0 = (measured from West Africa) p At = (current Claxton African Americans) p M = (current Claxton Caucasians) t = 15 (historical record of time of max. slave influx to Claxton area) p At = p M + (p A0 – p M )(1-m) t = (0.474 – 0.507)(1-m) 15 m = 1 – ( ) 1/15 m = Interpretation: On average, over 15 generations, 2.4% of the alleles in each generation of African Americans came from Caucasians Example

two-way racism as general model admixedmigrant 1migrant 2 admixed1-m A1 -m A2 m A1 m A2 migrant migrant to from = p A1 = (1-m A1 -m A2 )(p A ) + (m A1 )(p M1 )+ (m A2 )(p M2 ) from admixed from migrants 1 in the next generation: pApA p M2 m A1 for t generations: p At = p M + (p A0 – p M )(1-m) t where: parental pop. 1 admixed pop. parental pop. 2 m A2 p M1 from migrants 2 and m = m A1 + m A2

Wahlund’s effect reduction in heterozygosity in the meta-population due to population substructure –suppose each subpopulation is in HWE p 2, 2pq, q 2 –suppose allele frequencies differ among subpopulations –meta-population is not in HWE it has an excess of homozygotes Sidebar

Wahlund’s effect reduction in heterozygosity in the meta-population due to population substructure –suppose each subpopulation is in HWE p 2, 2pq, q 2 –suppose allele frequencies differ among subpopulations –meta-population is not in HWE it has an excess of homozygotes Sidebar extreme case: subpop. 1 in HWE: p 1 = 1.0 p 2 = 100% 2pq = 0 q 2 = 0 subpop. 2 in HWE: p 2 = 0 2pq = 0 q 2 = 100% meta-pop. not in HWE

Summary Migration –from meta-population viewpoint: homogenizing –from subpopulation viewpoint: source of variation general model –island model –one- and two-way racism models