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

Results of pathway enrichment analysis.

Results of pathway enrichment analysis for genes whose expression in corneal epithelium was found to be correlated with the allergy status. Transcriptome data was obtained for males and females from both study groups. The Reactome database was chosen as the source of the pathways. (TIF)</p

Clinical characteristics of the examined patients with KTCN and control individuals.

The statistically significant differences, p ≤0.05 or p <0.001, are indicated.</p

Results of pathway enrichment analysis for genes whose expression in corneal epithelium was found to be related to the allergy status.

Results of pathway enrichment analysis for genes whose expression in corneal epithelium was found to be related to the allergy status.</p

Complete information on the qualitative and quantitative data/results of analyzes of behavioral, environmental, and socioeconomic aspects.

Complete information on the qualitative and quantitative data/results of analyzes of behavioral, environmental, and socioeconomic aspects.</p

The data/results of analyzes of the eye rubbing behavior.

The data/results of analyzes of the eye rubbing behavior.</p

Results of Pearson’s correlation.

Pearson’s correlation results between the expression of selected genes, TRIM8, JUNB, and LTBP3 (in TPM), in the cone (central) region of corneal epithelium and time spent using a computer after work. Values of regression and statistical significance are presented in plots.</p

Results of pathway enrichment analysis.

Results of pathway enrichment analysis for genes which expression in corneal epithelium was found to be correlated with the eye rubbing manner. The type of eye rubbing was indicated in response to presented photographs, included in Fig 1. Transcriptome data was obtained for males and females from both study groups. The Reactome database was chosen as the source of the pathways.</p

The identification of the eye rubbing manner in the examined individuals.

The photographs, numbered from 1 to 8, ranked ascending by their severity/potential harmfulness to the eyeball, included in the Questionnaire for the indication of the eye rubbing manner in the examined individuals. In the Questionnaire, the aspect of eye rubbing manner was verified using the multiple question method (Study Questionnaire, question no. 9: ‘Please select the photo that most closely resembles the way you rub your eyes’).</p

Additional statistical analyses.

Since the environmental, behavioral, and socioeconomic factors in the etiology of keratoconus (KTCN) remain poorly understood, we characterized them as features influencing KTCN phenotype, and especially affecting the corneal epithelium (CE). In this case-control study, 118 KTCN patients and 73 controls were clinically examined and the Questionnaire covering the aforementioned aspects was completed and then statistically elaborated. Selected KTCN-specific findings were correlated with the outcomes of the RNA-seq assessment of the CE samples. Male sex, eye rubbing, time of using a computer after work, and dust in the working environment, were the substantial KTCN risk factors identified in multivariate analysis, with ORs of 8.66, 7.36, 2.35, and 5.25, respectively. Analyses for genes whose expression in the CE was correlated with the eye rubbing manner showed the enrichment in apoptosis (TP53, BCL2L1), chaperon-related (TLN1, CTDSP2, SRPRA), unfolded protein response (NFYA, TLN1, CTDSP2, SRPRA), cell adhesion (TGFBI, PTPN1, PDPK1), and cellular stress (TFDP1, SRPRA, CAPZB) pathways. Genes whose expression was extrapolated to the allergy status didn’t contribute to IgE-related or other inflammatory pathways. Presented findings support the hypothesis of chronic mechanical corneal trauma in KTCN. Eye-rubbing causes CE damage and triggers cellular stress which through its influence on cell apoptosis, migration, and adhesion affects the KTCN phenotype.</div