A hunter-gatherer-farmer population model: Lie symmetries, exact solutions and their interpretation

The Lie symmetry classification of the known three-component reaction-diffusion system modelling the spread of an initially localized population of farmers into a region occupied by hunter-gatherers is derived. The Lie symmetries obtained for reducing the system in question to systems of ODEs and constructing exact solutions are applied. Several exact solutions of traveling front type are found, their properties are identified and biological interpretation is discussed

Correlation of rs2200733 genotype (CC and CT vs. TT) with diameter of pulmonary veins (in millimetres).

<p>For calculation a recessive effect was assumed.</p><p>Data presented as median (1^st–3^rd quartile).</p

Pairwise linkage disequilibrium (LD) scores (r2) among 4q25 SNPs.

<p>Pairwise linkage disequilibrium (LD) scores (r2) among 4q25 SNPs.</p

Characteristics of study and control groups.

<p>Data presented as: n (%).</p><p>*mean (SD).</p><p>SD – standard deviation.</p><p>ND – no data; NA – not applicable.</p

Haplotypes found for 4q25 SNPs with independent effects on AF risk (i.e. rs2200733-rs10033464-rs17570669-rs6838973 haplotypes).

<p>Haplotypes found for 4q25 SNPs with independent effects on AF risk (i.e. rs2200733-rs10033464-rs17570669-rs6838973  haplotypes).</p

The rs10757278 polymorphism and long-term survival in the derivation group.

<p>No significant differences were observed between the genotypes.</p

Baseline characteristics of the validation group based on rs10757278 genotype (risk allele for MI- G).

<p>eGFR- estimated GFR, mean values with standard deviations are given, unless otherwise specified.</p

The rs10757278 polymorphism and long-term survival - subgroup of high-risk patients (GRACE risk score ≥155) from the derivation group.

<p>GG high-risk homozygotes had significantly higher probability of survival compared to other genotypes (p = 0.032 after adjustment for Bonferroni correction, log-rank test).</p

Linkage disequilibrium of investigated SNPs.

<p>Linkage disequilibrium of investigated SNPs.</p

Percentages of specific genotypes and associated mortality rates.

1<p>p = 0.007; ²p = 0.019; ³p = 0.011; chi-2 tests for 3 genotypes; all p values adjusted for Bonferroni correction.</p