Fundamentals of Evoluon Fundamentals of Evoluon EEEB G6110 EEEB - - PowerPoint PPT Presentation

Fundamentals of Evoluon Fundamentals of Evoluon

EEEB G6110 EEEB G6110

Session 12: Demography Session 12: Demography

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Today's topics Today's topics

• 1. The coalescent
• 2. Coalescent simulaons
• 3. Structured coalescent
• 4. Species trees
• 4. Forward simulaons
• 5. Assignment

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Wright-Fisher Model Wright-Fisher Model

Each generaon randomly sample alleles from the parental generaon. By incorporang a finite populaon size (N) into our sampling probabilies we can esmate the expected change in allele frequencies due to dri. A discrete me model in which each generaon is composed of 2N copies of each

• gene. Each subsequent generaon 2N new copies are randomly drawn from the

previous generaon. The probability of obtaining k copies of allele p the next generaon is:

( ) (1 − p 2N k pk )2N−k

hps:/ /en.wikipedia.org/wiki/Genec_dri#Wright.E2.80.93Fisher_model

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Wright-Fisher Model Wright-Fisher Model

A neutral evoluonary process (no selecon) can be modeled using the WF model in which allele frequencies change over me by genec dri.

Source: Alexei Drummond

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Characteriscs of the coalescent Characteriscs of the coalescent

The coalescent is a mathemacal descripon of the genealogical process arising in idealised populaons. It focuses on one or more genealogies (i.e., trees) underlying the history of a sample

• f chromosomes.

It is a probabilisc model, which implies that it describes the distribuon of genealogies. The principle idea is that genealogy holds all the informaon we need to know about

• ur populaon (under a neutral evoluonary scenario).

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The coalescent for The coalescent for two sequences two sequences

In one generaon these two sequences either came from the same parent ( )

• r they came from different parents (

) The probability that these two sequences coalesced t generaons ago can be calculated from these two probability statements:

1 2N

1 −

1 2N

(1 − )

1 2N

t−1 1

2N

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The distribuon of coalescent mes The distribuon of coalescent mes

There are ways pairs of lineages can pick the same parent. Probability of coalescence scales quadracally with lineage count.

Pr(coal) = ( ) = i 2 1 2N i(i − 1) 4N

( )

i 2

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Expected waing me to coalescence Expected waing me to coalescence

This is a . If each generaon there is a probability of an event occurring, we expect to wait generaons for the event to occur.

E[ ] = Ti 4N i(i − 1)

geometric distribuon

1 x

x

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Connuous me limit Connuous me limit

With per-generaon probability of an event small, but many generaons, then the discrete me geometric distribuon approximates to a connuous me . Thus, we assume to be exponenally distributed with mean:

1 x

exponenal distribuon

Ti E[ ] = Ti 4N i(i − 1)

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Set of coalescent intervals with waing mes Set of coalescent intervals with waing mes

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Set of coalescent intervals with waing mes Set of coalescent intervals with waing mes

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Set of coalescent intervals with waing mes Set of coalescent intervals with waing mes

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Pairwise genec diversity Pairwise genec diversity

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Time to the most recent common ancestor (TMRCA) Time to the most recent common ancestor (TMRCA)

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Coalescent paerns can esmate populaon growth/decline Coalescent paerns can esmate populaon growth/decline

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Coalescent paerns can esmate populaon growth/decline Coalescent paerns can esmate populaon growth/decline

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Coalescent simulaon exercise. Coalescent simulaon exercise.

hps:/ /mybinder.org/v2/gh/genomics-course/f12-coalescent/master?filepath=fundamentals-msprime.ipynb

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Coalescent simulaon exercise. Coalescent simulaon exercise.

hps:/ /mybinder.org/v2/gh/genomics-course/f12-coalescent/master?filepath=fundamentals-msprime.ipynb

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Reading for next session Reading for next session

Read both of these: Gene tree discordance, phylogenec inference and the mulspecies coalescent Inferring the Joint Demographic History of Mulple Populaons from Muldimensional SNP Frequency Data

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