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

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

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

Nile Red staining of yeast lipid particles.

<p>Visualization of membranes composed of glycerophospholipids (red emission) and neutral lipids, triacyglycerols and steryl esters, in lipid particles (green emission). Cells were cultured overnight. The media were then supplemented with either 100 µM simvastatin or buffer and the cells were further grown with shaking for two hours at 30°C. To localize neutral lipids and glycerophospholipids in yeast cells, Nile Red staining was performed. Horizontal panels: upper glycrophospholipids at 543 nm excitation and 610 nm emission, middle neutral lipids at 488 nm excitation and 515/530 nm emission, lower merge of above panels. Vertical panels: B cells cultivated in buffer, S cells incubated for 2 h in buffer with simvastatin.</p

Two dimensional chromatography of glycerophospholipids.

<p>The levels of all major glycerophospholipids were diminished by treatment with simvastatin. Panels: 1, 3, 5 glycerophospholipids from cells harbouring the wild-type yeast, or the wild-type or mutated <i>hHMGR</i> gene, respectively. Panels 2, 4, 6 glycerophospholipids from simvastatin treated cells harbouring the wild-type yeast, or the wild-type or mutated <i>hHMGR</i> gene, respectively. Abbreviations: PC phosphtidylcholine, PE phosphtidylethanolamine, PS phosphatidylserine, PI phosphtidylinositol, PA phosphtidic acid, LP lysoglycerophospholipid, FA fatty acid, NL neutral lipids.</p

Differentially expressed genes common to both analyses: admission versus control and discharge versus control.

<p>Differentially expressed genes common to both analyses: admission versus control and discharge versus control.</p

Differentially expressed genes common to both analyses: admission versus 6 months after MI and admission versus control.

<p>Differentially expressed genes common to both analyses: admission versus 6 months after MI and admission versus control.</p

Validation of microarray data using qRT-PCR.

***<p>p<0.001; **p<0.01; *p<0.05; ^NS – not significant.</p><p>All genes abbreviations are explained in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0050054#pone-0050054-t002" target="_blank">Table 2</a>.</p