Comp 790-087

Comp 790-087

• Administrative Details• Course Overview• Coalescent Theory?

04/21/23 1Comp 790– Introduction & Coalescence

Genetics, Evolution, andthe Coalescent Theory

Course Overview

• Synopsis– Graduate-level project course– Guided reading, discussions, and project with write-up

• Website– To appear at:

http://www.unc.edu/courses/2009spring/comp/790/087/

• Course Grading– Class Participation 10%– 2 In-class Presentations 40%– Final Project, Presentation, & Write-up 50%


Syllabus

• ⅓ Guided reading/discussion of text

• ⅓ Student presentations of recent papers

• ⅓ Project Proposals

04/21/23 Comp 790– Introduction & Coalescence 3

Coalescent Theory

• Ancestral properties can be inferred from extant populations

• Alternatives to Correctness– Most-Likely – Most Parsimonious– Other optimality criteria

• Background– Biology (genetics)– Statistics– Computational Modeling


Non-Classical Genetics

• Coalescence differs from classical genetics– Analysis rather than synthesis– Depends on models, which attempt to explain

observations– Less emphasis on Darwin’s natural selection

• Considers population dynamics– Isolation– Bottlenecks


Historical Human Migrations


Population Dynamics

• It is helpful to view evolutionary trees in the contexts of geography and population structure

• These factors affect the prevalence and distribution of genes

• Genetic diversity largely depends on population isolation and population bottlenecks, as well as– Constant population size (resource limited)– Sudden increases in population (explosions)– Patterns of growth (exponential, uniform, etc.)

04/21/23 Comp 665 – Introduction & Signals 7

It’s About Genes

• Genetics is most clearly understood by considering its subject to be genes rather than organisms

• Organisms are merely vessels for assuring the survival of genes

• Successful genes live on long after their host organism • An objective of a gene is to replicate itself


“[Genes] that survived were the ones that built survival machines for themselves to live in. But making a living got steadily harder as new rivals arose with better and more effective survivial machines. Survival machines got bigger and more eloborate, and the process was cumulative and progressive…”

-- Dawkins, The Selfish Gene

Why Computer Science

• Classically, genetics, both generative (classical) and coalescent (population) has focused on mathematical/statistical models

• As model complexity increases, it becomes harder to find closed-form solutions

• Relies more and more on computational modeling to ascertain structure

• Also, complicated models often lead to common models… today’s subject


Wright-Fisher Model

• One of the first, and simplest models of population genealogies was introduced by Wright (1931) and Fisher (1930).

• Model emphasizes transmission of genes from one generation to the next

• For simplicity we’ll first focus on a fixed population size, each with a distinct gene variant


Simple Haploid Model

• Rules– Antecedent genes

are chosen randomly, with replacement, from their parental generation

– No selection– Fixed population

size


G0: ['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J']

G1: ['J', 'A', 'H', 'B', 'I', 'E', 'D', 'G', 'A', 'B']

G2: ['A', 'J', 'E', 'G', 'D', 'E', 'B', 'I', 'A', 'A']

G3: ['A', 'A', 'E', 'J', 'I', 'A', 'I', 'A', 'J', 'B']

G4: ['E', 'A', 'B', 'B', 'A', 'E', 'A', 'A', 'A', 'A']

G5: ['A', 'A', 'B', 'A', 'A', 'E', 'A', 'A', 'A', 'B']

G6: ['A', 'A', 'A', 'A', 'A', 'A', 'A', 'B', 'A', 'A']

G7: ['B', 'A', 'A', 'B', 'A', 'A', 'A', 'A', 'A', 'A']

What will this population eventually look like?

Assumptions of Wright/Fisher

• Discrete and non-overlapping generations• Haploid individuals• Populations size is constant• All individuals are equally fit• No population of social structure• Genes segregate independently


Some Graphical Abstractions

• Replace letters with colors

• Draw lineages• Sort topologically


Repeats


Every population results in just one gene

Onset of Uniformity

• 10000 trials• Mode = 11 (616)• Mean = 17.5


Diploid Model

• Our model is obviously too simple, let’s add more realism

• Organisms are diploid (have 2, perhaps different, copies of each gene)

• Sexual reproduction• Half female, Half Male


['AA', 'BB', 'CC', 'DD', 'EE', 'FF', 'GG', 'HH', 'II', 'JJ']['CF', 'AG', 'BI', 'CH', 'CH', 'EG', 'EG', 'EH', 'EI', 'DG']['CE', 'IE', 'CG', 'HE', 'HE', 'FG', 'IG', 'BE', 'BG', 'HE']['CB', 'EI', 'HE', 'HI', 'HE', 'CG', 'EF', 'EI', 'HF', 'GI']['EE', 'HF', 'BC', 'IG', 'BH', 'HI', 'BI', 'EF', 'HG', 'HC']['CH', 'BH', 'BH', 'EI', 'BH', 'BE', 'BI', 'HC', 'EH', 'IH']['BE', 'BE', 'IB', 'BE', 'BH', 'BH', 'BH', 'HH', 'CB', 'EH']['BH', 'EC', 'BB', 'BB', 'IC', 'BH', 'EH', 'EH', 'BE', 'EB']['CE', 'BE', 'BE', 'BE', 'CH', 'BE', 'CB', 'HE', 'IB', 'CB']['EH', 'BB', 'BB', 'BH', 'EC', 'EE', 'EC', 'CE', 'CI', 'CE']['CI', 'BE', 'EC', 'BE', 'BC', 'BC', 'BE', 'BE', 'BE', 'BC']['EB', 'EB', 'BB', 'CB', 'EB', 'CC', 'IB', 'BC', 'IE', 'CB']['BB', 'EC', 'BE', 'BC', 'CC', 'CC', 'EI', 'BI', 'BC', 'BC']['EB', 'CB', 'CC', 'BC', 'BB', 'CC', 'BI', 'CC', 'BC', 'CC']['BC', 'BC', 'CC', 'BC', 'BC', 'EC', 'BB', 'BC', 'BC', 'BB']['BB', 'BC', 'CB', 'CC', 'CB', 'CC', 'CB', 'CB', 'CE', 'CB']['CC', 'CB', 'CC', 'CB', 'BB', 'CC', 'CB', 'CC', 'CC', 'BC']['CC', 'CC', 'CC', 'BB', 'CC', 'BC', 'CC', 'CC', 'CC', 'CB']['CC', 'BC', 'CC', 'CC', 'CC', 'CC', 'CC', 'CB', 'CC', 'CC']['CC', 'BC', 'BC', 'CC', 'CC', 'CC', 'CC', 'CC', 'BC', 'CC']['CC', 'CC', 'CC', 'BC', 'CC', 'CC', 'CC', 'CC', 'BC', 'CB']['CC', 'BC', 'CC', 'CC', 'CC', 'CC', 'CC', 'CC', 'CC', 'CC']['CC', 'CC', 'CC', 'CC', 'CC', 'BC', 'CC', 'CC', 'CC', 'CC']['CC', 'CC', 'CC', 'CC', 'CC', 'CC', 'CC', 'CC', 'CC', 'CC']

MalesFemales

Same Result


['AA', 'BB', 'CC', 'DD', 'EE', 'FF', 'GG', 'HH', 'II', 'JJ']['AG', 'BF', 'AI', 'EJ', 'DH', 'AH', 'CH', 'AI', 'DI', 'AH']['BI', 'AI', 'FA', 'AC', 'GH', 'AH', 'BI', 'DH', 'FI', 'AH']['HH', 'AI', 'BH', 'II', 'AI', 'AI', 'GI', 'AD', 'IA', 'AA']['HG', 'IG', 'ID', 'IA', 'ID', 'HG', 'HI', 'AA', 'AI', 'IA']['IA', 'DG', 'DH', 'HA', 'GA', 'DI', 'GH', 'GG', 'II', 'IH']['HI', 'GI', 'GH', 'DH', 'GG', 'HH', 'II', 'HI', 'ID', 'GH']['HH', 'GI', 'HI', 'HI', 'HH', 'IH', 'HH', 'HI', 'GG', 'HH']['GH', 'HH', 'HH', 'HH', 'IH', 'II', 'HH', 'HI', 'HG', 'HH']['HI', 'HG', 'HH', 'HH', 'IH', 'HH', 'GH', 'HH', 'HI', 'HH']['HH', 'HH', 'HH', 'HI', 'HG', 'HH', 'HH', 'HH', 'HH', 'IH']['HH', 'HH', 'HH', 'HH', 'HH', 'HH', 'IH', 'GH', 'HH', 'GH']['HI', 'HH', 'HG', 'HG', 'HH', 'HI', 'HG', 'HG', 'HH', 'HH']['GG', 'GH', 'HI', 'HH', 'IG', 'GH', 'IG', 'HG', 'HH', 'HH']['IH', 'HH', 'HG', 'HI', 'GH', 'HH', 'GI', 'IG', 'HH', 'GH']['IH', 'HG', 'HG', 'IH', 'HH', 'HG', 'II', 'HH', 'HG', 'IH']['II', 'HI', 'HI', 'HH', 'HH', 'HH', 'IH', 'HH', 'GI', 'HH']['IH', 'II', 'HH', 'HH', 'II', 'HH', 'HH', 'IH', 'HH', 'HH']['HH', 'HH', 'HH', 'II', 'IH', 'IH', 'IH', 'HH', 'IH', 'IH']['IH', 'HH', 'IH', 'II', 'IH', 'HH', 'HH', 'II', 'IH', 'IH']['HI', 'II', 'IH', 'IH', 'IH', 'HH', 'HI', 'IH', 'HI', 'HH']['IH', 'HH', 'HI', 'HI', 'HH', 'HI', 'HH', 'II', 'IH', 'HH']['II', 'HH', 'HH', 'HH', 'HH', 'HH', 'HI', 'HH', 'HH', 'II']['IH', 'HI', 'HI', 'HH', 'HI', 'HH', 'HH', 'HH', 'IH', 'HI']['IH', 'HH', 'HI', 'IH', 'HH', 'HH', 'HI', 'HI', 'HI', 'HH']['HI', 'HH', 'HH', 'HH', 'HH', 'HH', 'HI', 'HI', 'HH', 'HH']['HH', 'HH', 'IH', 'HH', 'HI', 'HH', 'HH', 'HH', 'HH', 'HH']['HH', 'HH', 'HH', 'IH', 'HH', 'HH', 'HH', 'HH', 'HH', 'HH']['HH', 'HH', 'HH', 'HH', 'HH', 'HH', 'HH', 'HH', 'HH', 'HH']

MalesFemales['AA', 'BB', 'CC', 'DD', 'EE', 'FF', 'GG', 'HH', 'II', 'JJ']['EF', 'EI', 'DI', 'BF', 'EJ', 'BI', 'AI', 'CI', 'EJ', 'EI']['FB', 'EE', 'EI', 'JB', 'FE', 'BJ', 'JE', 'EI', 'EE', 'DI']['FJ', 'IE', 'FE', 'JE', 'EJ', 'FI', 'FE', 'BJ', 'EB', 'FJ']['FF', 'II', 'EB', 'FI', 'EI', 'EJ', 'EB', 'IB', 'EI', 'EF']['FE', 'IE', 'BE', 'BB', 'BE', 'EB', 'EB', 'IE', 'BI', 'FJ']['BB', 'FE', 'FE', 'EE', 'EE', 'BJ', 'II', 'EE', 'BE', 'FE']['BB', 'EB', 'EB', 'EE', 'EI', 'EE', 'FI', 'EE', 'EE', 'EE']['EF', 'BE', 'BE', 'EE', 'BE', 'IE', 'BI', 'EE', 'EE', 'EE']['EE', 'BE', 'FE', 'EB', 'EE', 'BE', 'BE', 'BE', 'FE', 'EE']['EF', 'EE', 'EE', 'EE', 'EE', 'EE', 'FE', 'EB', 'BE', 'EE']['EE', 'FB', 'EE', 'EE', 'EE', 'EB', 'EE', 'EE', 'EE', 'EE']['EE', 'EE', 'EE', 'EE', 'EE', 'EE', 'EE', 'BE', 'EE', 'EE']['EE', 'EE', 'EE', 'EE', 'EE', 'EE', 'EE', 'EE', 'EE', 'EE']

['AA', 'BB', 'CC', 'DD', 'EE', 'FF', 'GG', 'HH', 'II', 'JJ']['AF', 'AJ', 'AF', 'CG', 'BG', 'BH', 'AH', 'EG', 'DG', 'DJ']['AA', 'AH', 'CA', 'AJ', 'BJ', 'GB', 'AB', 'GH', 'BB', 'AA']['JH', 'AB', 'AA', 'AG', 'AB', 'JB', 'AH', 'AA', 'AA', 'AG']['GA', 'AA', 'AG', 'BH', 'AB', 'BA', 'GA', 'AA', 'AA', 'AA']['AA', 'AA', 'AA', 'AA', 'AG', 'AA', 'AA', 'AA', 'AB', 'AA']['AA', 'AA', 'AB', 'AA', 'AA', 'AA', 'AA', 'AA', 'AA', 'AA']['BA', 'AA', 'AA', 'AA', 'AA', 'BA', 'AA', 'AA', 'AA', 'AA']['AB', 'AA', 'AA', 'AB', 'AA', 'AA', 'AA', 'AA', 'AA', 'AA']['AA', 'AA', 'BA', 'AA', 'BA', 'AA', 'AA', 'AA', 'AA', 'AA']['AA', 'AA', 'AA', 'BA', 'BA', 'AA', 'AA', 'AA', 'AA', 'AA']['AA', 'AA', 'AA', 'AA', 'AA', 'AA', 'BA', 'AA', 'BA', 'AA']['AA', 'AA', 'AA', 'AA', 'AA', 'AA', 'AA', 'AB', 'AB', 'AA']['AA', 'AA', 'AA', 'AA', 'AA', 'AA', 'AA', 'AA', 'AA', 'AA']

MalesFemales

MalesFemales

Similar Distributions

• 10000 trials• Mode = 24 (291)• Mean = 35.5

• These statistics are almost exactly 2x the haploid (Mode = 11, Mean = 17.5)


Punnett Squares

AA x BB A A

B AB AB

B AB AB


AB x AB A B

A AA AB

B AB BB

What if we introduce inbreeding, by choosing mates from common litters,in successive generations

AB x BB A B

B AB BB

B AB BB

Different Problem?


('A', 'A') ('B', 'B') [('A', 'B'), ('A', 'B'), ('A', 'B'), ('A', 'B')]('A', 'B') ('A', 'B') [('A', 'A'), ('A', 'B'), ('A', 'B'), ('B', 'B')]('A', 'B') ('A', 'A') [('A', 'A'), ('A', 'A'), ('A', 'B'), ('A', 'B')]('A', 'A') ('A', 'B') [('A', 'A'), ('A', 'B'), ('A', 'A'), ('A', 'B')]('A', 'B') ('A', 'B') [('A', 'A'), ('A', 'B'), ('A', 'B'), ('B', 'B')]('A', 'B') ('B', 'B') [('A', 'B'), ('A', 'B'), ('B', 'B'), ('B', 'B')]('A', 'B') ('A', 'B') [('A', 'A'), ('A', 'B'), ('A', 'B'), ('B', 'B')]('A', 'B') ('A', 'B') [('A', 'A'), ('A', 'B'), ('A', 'B'), ('B', 'B')]('A', 'B') ('A', 'B') [('A', 'A'), ('A', 'B'), ('A', 'B'), ('B', 'B')]('A', 'B') ('B', 'B') [('A', 'B'), ('A', 'B'), ('B', 'B'), ('B', 'B')]('A', 'B') ('A', 'B') [('A', 'A'), ('A', 'B'), ('A', 'B'), ('B', 'B')]('A', 'A') ('A', 'B') [('A', 'A'), ('A', 'B'), ('A', 'A'), ('A', 'B')]('A', 'B') ('A', 'A') [('A', 'A'), ('A', 'A'), ('A', 'B'), ('A', 'B')]('A', 'B') ('A', 'A') [('A', 'A'), ('A', 'A'), ('A', 'B'), ('A', 'B')]('A', 'A') ('A', 'B') [('A', 'A'), ('A', 'B'), ('A', 'A'), ('A', 'B')]('A', 'A') ('A', 'B') [('A', 'A'), ('A', 'B'), ('A', 'A'), ('A', 'B')]('A', 'A') ('A', 'B') [('A', 'A'), ('A', 'B'), ('A', 'A'), ('A', 'B')]('A', 'A') ('A', 'B') [('A', 'A'), ('A', 'B'), ('A', 'A'), ('A', 'B')]('A', 'A') ('A', 'B') [('A', 'A'), ('A', 'B'), ('A', 'A'), ('A', 'B')]('A', 'A') ('A', 'A') [('A', 'A'), ('A', 'A'), ('A', 'A'), ('A', 'A')]

('A', 'A') ('B', 'B') [('A', 'B'), ('A', 'B'), ('A', 'B'), ('A', 'B')]('A', 'B') ('A', 'B') [('A', 'A'), ('A', 'B'), ('A', 'B'), ('B', 'B')]('A', 'B') ('A', 'A') [('A', 'A'), ('A', 'A'), ('A', 'B'), ('A', 'B')]('A', 'B') ('A', 'A') [('A', 'A'), ('A', 'A'), ('A', 'B'), ('A', 'B')]('A', 'B') ('A', 'B') [('A', 'A'), ('A', 'B'), ('A', 'B'), ('B', 'B')]('A', 'B') ('A', 'B') [('A', 'A'), ('A', 'B'), ('A', 'B'), ('B', 'B')]('A', 'B') ('B', 'B') [('A', 'B'), ('A', 'B'), ('B', 'B'), ('B', 'B')]('B', 'B') ('B', 'B') [('B', 'B'), ('B', 'B'), ('B', 'B'), ('B', 'B')]

('A', 'A') ('B', 'B') [('A', 'B'), ('A', 'B'), ('A', 'B'), ('A', 'B')]('A', 'B') ('A', 'B') [('A', 'A'), ('A', 'B'), ('A', 'B'), ('B', 'B')]('A', 'B') ('A', 'B') [('A', 'A'), ('A', 'B'), ('A', 'B'), ('B', 'B')]('A', 'A') ('A', 'A') [('A', 'A'), ('A', 'A'), ('A', 'A'), ('A', 'A')]

Parents Offspring Parents Offspring

Parents Offspring

Distributions


Next time

• Commonly occurring distributions– Geometric– Exponential


Documents

Comp 790-087