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In mathematics a process where new discrete states are reached from current states following random transition probabilities independently from the past pathways is called Markov chain.

ASHEs simulate haplotype states transitions under a Wright-Fisher model formulated in terms of Markov chains. (Montecarlo algorithm?) At each generation (t), any new haplotype is sampled randomly from the parental pool, stored in a temporary vector and a copy subsequently reintroduced in the parental pool. After a given number of samplings (k) the temporary pool will become the new generation of haplotypes (t+1) and processed n times (generations) in the same way (Figure 1).

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Figure 1. Flow chart of the basic Markov chain/Wright-Fisher algorithm implemented in ASHEs.

- one-ancestral-population module (OAP)
- two-ancestral-population module (TAP).

Each project describes the model of population history to be simulated over the chosen time window.

Title: SIM1

Module: TAP

Data type: Multistate

GroupX: 5,000 9-locus YSTR haplotypes

Parameters

Nm: 10 or 100 or 1000

Mutation rate: 0.00185

Increment rate: 1

Iterations: 200

Generations: 200

Distance function: DHS or FST2

Output file: SIM1.csv

Variables

Calculate distance: true

Calculate group X P: false

Calculate group X H: false

Calculate group X N: false

Calculate group Y P: false

Calculate group Y H: false

Calculate group Y N: false

(INSERT TABLE)

DHS performed much better than FST, being more linear with time (from 2 to 12 times higher α values) and having much lower variance (from 3,6 to 5 times lower CV values). Both the distributions show deviation from linearity (low R2 values) in the case of a marked founder effect (migrant size around 10).

We calculated confidence intervals of the probability distributions of J1 frequencies over the last 1,350 years (54 generations assuming 25 years per generation) from two source populations (GroupX0B, GroupX0A) showing the current frequency levels either in Berbers (p0B) or Arabs (p0A). Before starting simulations the haplotype of choice in the data box should be clicked. In both cases the simulation gave observed J1 frequencies largely comprised in the confidence intervals expected by random fluctuations (Figure 2).

Title: SIM2

Module: OAP

Data type: Binary

GroupX: 477 30-locus binary haplotypes

Parameters

Mutation rate: 1x10-8

Increment rate: 1.014

Iterations: 100

Generations: 54

Output file: SIM2.csv

Variables

Calculate distance: false

Calculate group X P: true

Calculate group X H: false

Calculate group X N: false

Figure 2. Random fluctuactions of Arab (in green) and Berber (in red) J1 frequencies over the last 54 generations: Mean values (thick line) and 95% CI intervals (dotted lines).

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*F*-Statistics for the analysis of population structure.*Evolution*, 38: 1358–1370. - Wright S (1921). Systems of mating. I. The biometric relations between offspring and parent. Genetics 6: 111-123.
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Last edited May 16, 2009 at 9:22 AM by merlitti, version 3