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Lecture 21: Random
mating continued,
assortative mating,
and linkage
disequilibrium
Poe, ''Sonnet: To Science'' (1829) SCIENCE! true daughter of Old Time thou art! Who alterest all things with thy peering eyes. Why preyest thou thus upon the poet's heart, Vulture, whose wings are dull realities? How should he love thee? or how deem thee wise, Who wouldst not leave him in his wandering To seek for treasure in the jewelled skies, Albeit he soared with an undaunted wing? Hast thou not dragged Diana from her car? And driven the Hamadryad from the wood To seek a shelter in some happier star? Hast thou not torn the Naiad from her flood, The Elfin from the green grass, and from me The summer dream beneath the tamarind tree?
Lecture 21 reading
Primary reading - DF - Chapter 9, pp. 189-
Background - C & H - Chapter 5, pp. 156 (start with “In addition to”)-160 (stop with end of “What can cause linkage disequilibrium?”)
Lecture 20 reading
Primary reading - DF - Chapter 9, pp. 189-
Background - C & H - Chapter 1, Chapter 2, pp. 9-
Revised lecture syllabus 10 Oct Lecture 20 - Genetic Variation and random mating 12 Oct Lecture 21 - Random mating, assortative mating, linkage disequilibrium 15 Oct Lecture 22 - Inbreeding 17 Oct Lecture 23 - Mutation and migration 19 Oct Lecture 24 - Genetic Drift 22 Oct Lecture 25 - Drift-migration equilibrium and F-stats 24 Oct Lecture 26 - Quantitative Genetics I 26 Oct Lecture 27 - Quantitative Genetics II 29 Oct SECOND MID-TERM EXAM (lectures 14-25) 31 Oct Lecture 28 - Fitness 2 Nov Lecture 29 - Artificial selection 5 Nov Lecture 30 - Natural Selection 7 Nov Lecture 31 - Sexual Selection 9 Nov Lecture 32 - Geographic variation 12 Nov Lecture 33 - Molecular Evolution I 14 Nov Lecture 34 - Molecular Evolution II 16 Nov Lecture 35 - Species and Speciation 26 Nov Lecture 36 - Allopatric speciation 28 Nov Lecture 37 - Sympatric speciation 30 Nov Lecture 38 - The fossil record 3 Dec Lecture 39 - Macroevolution 5 Dec Lecture 40 - Macroevolution 7 Dec Lecture 36 - Human population structure
Gene pool
- All alleles at all gene loci of all individuals of the population
- Population geneticists often also use the term “standing variation” to describe the gene pool at the point when you start studying it. The standing variation is the result of mutations in the past. For example, if you are a plant breeder trying to make a bigger tomato, you first study the variation that exists now (the standing variation) before you try to add mutations (new variation).
A population - color is determined by one gene, with 2 alleles showing partial dominance.
How to quantify variation - discrete variation Allele, genotype, and phenotype frequencies
(Continuous variation is quantified in terms of means and variances).
We need numbers to do population genetics. There are three types of frequencies that we need.
6 C W
total
20
The third kind of number is perhaps the most important
(6+5)/20=0.
5 C W,^ 5 CR^ 4 C R
We need numbers to do population genetics. There are three types of frequencies that we need.
How to relate allele frequencies and genotype frequencies? Two different ways.
First, some nomenclature for frequencies of alleles A and a. Freq. A = p, freq. a = q.
We will use P, H, and Q for the genotype frequencies of AA, Aa, and aa.
So, this is one way, but must have partial or codomiance.
The other way - assume random mating - the Hardy-Weinberg Equilibrium - HWE
Random mating does not change allele frequencies
Heterozygotes are most common when alleles are at intermediate frequencies.
How do we know if a population really is in Hardy- Weinberg Equilibrium (HWE)?
Degrees of freedom is calculated as
df = (g - 1) - (a - 1)
where g is the number of genotypes and a is the number of alleles
Nonrandom mating Assortative mating positive negative Inbreeding (next lecture)
http://www.falconrybirds.com/Pics/eb/eb_x2.jpg
Hedrick, P. 2005. Genetics of populations, Jones and Bartlet, p. 294.
European buzzard, Buteo buteo
Positive assortative mating
Genotype AA Aa aa FrequencyP H Q AA P P^2 PH zero Aa H PH H^2 zero aa Q zero zero Q^2
What are frequencies of each type of mating? No longer random mating!
Thought example: if 25 red males, 25 blue males, 25 red females, and 25 blue females (n = 100, freq. red organisms = 0.50, freq. blue = 0.50) start a new population, then the frequency of blue x blue matings (out of 50 matings total) is 25/50 = 0.50. In other words, blue x blue mating frequency is not Q 2 but Q!
Genotype (^) AA Aa aa Frequency (^) P H Q AA P P 2 /(1-Q) PH/(1-Q) zero Aa H PH/(1-Q) H^2 /(1-Q) zero aa Q zero zero Q
This is wrong
This is correct
Positive assortative mating
Hedrick, P. 2005. Genetics of populations, Jones and Bartlet, p.
So, positive assortative mating reduces H and increases P and Q - as you would expect intuitively. No change in allele frequencies. Negative assortative mating does the opposite.
So far we have only talked about one gene (one locus) at a time. Expanding to two genes (two loci) brings in some complications.
http://www.countrysideinfo. co.uk/devon_bap/images/
pin thrum
So far we have only talked about one gene (one locus) at a time. Expanding to two genes (two loci) brings in some complications.
An important point - single genes come to HWE in one generation, but two genes come to an equilibrium very slowly if linkage is tight.
