Lactase Persistence & Genetic Selection Simulator

1. Population Genetics & Selection Engine Wright-Fisher Stochastic Model

Historical Scenarios:

Initial Allele Freq (p₀) 0.010

Selection Coeff (s) 0.080

Effective Pop Size (Nₑ) 5,000

Pastoralism Epoch (Gen) 40

Dominance Model (h)

Replicate Monte Carlo Runs 5

Gen: 0 (~10,000 BP) p(LP): 1.0% Tolerant Adults: 2.0%

LP Allele Freq (p)

0.010

Ancestral (q)

0.990

Genotypes (LL / Lp / pp)

0.0% / 2.0% / 98.0%

Phenotype Lactose Tolerant

2.0%

2. Molecular Mechanism: MCM6 Enhancer & LCT Promoter Transcriptional Regulation

Small Intestine: Lactose Hydrolysis

Lactase cleaves lactose disaccharide into absorbable glucose + galactose.

Brush Border Lactase: 95% Blood Glucose Rise: +28 mg/dL

Large Intestine (Colon): Bacterial Fermentation

Undigested lactose fermented by gut microbiome into H₂, CH₄, and SCFAs.

Breath H₂ Level: 6 ppm (Normal) Osmotic Symptoms: None

🧬 The Evolutionary Paradox

Lactase non-persistence (hypolactasia) is the ancestral mammalian phenotype: across ~70% of human adults, lactase enzyme synthesis naturally ceases after weaning. However, with the advent of dairy pastoralism ~10,000 years ago, rare regulatory mutations in the MCM6 gene conferred unprecedented selective advantages (s ≈ 0.05 – 0.15), representing one of the strongest signatures of positive selection in the entire human genome.

🔬 Convergent Evolution

Lactase persistence is a striking example of convergent cultural-genetic evolution. Distinct single-nucleotide polymorphisms arose independently in different dairying pastoralist populations:
• -13910*T in European Funnelbeaker & Yamnaya cultures
• -14010*C in East African pastoralists (Maasai, Tutsi)
• -13915*G in Afro-Asiatic Arabian camel-herders

📐 Mathematical Formalism

Under dominant selection with selection coefficient s:
p' = (p²(1+s) + pq(1+s)) / w̄ where w̄ = 1 + s(1 - q²). Finite population drift is computed per Wright-Fisher binomial sampling: k ~ Binomial(2N, p') and p_{t+1} = k / (2N).