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

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

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

Top canonical pathways associated with acute phase of STEMI.

<p>Ingenuity Pathway Analysis of gene sets differentially expressed on the first day of myocardial infarction versus 6 months after MI or versus control group was performed. Functional categories are represented on the x-axis. The significance is expressed as the negative exponent on the p-value calculated for each function on the y-axis of the diagram, increasing with bar height.</p

Expression data from microarray experiments for chosen genes.

<p>The y-axis represents the log2 normalized intensity of the gene and the x-axis represents analyzed groups. The line inside the box and whiskers represents the median of the samples in a group. Points present relative expression levels in individual patients at admission (blue), at discharge (green), 6 month after MI (violet) and from control group (red). Numbers indicate the coded identity of a particular patient. SOCS3– suppressor of cytokine signaling 3; ST14– MT-SP1/matriptase; AQP 9– aquaporin 9; MYBL1– v-myb myeloblastosis viral oncogene homolog (avian)-like 1; STAB1– stabilin 1; ASGR2– asialoglycoprotein receptor 2.</p