For obstacles in the form of horizontal circular cylinders, these voids are thin and can evolve symmetrically and periodically beneath the cylinder.
It is observed that the dynamic profiles of mound in horizontal aquifer evolve symmetrically about the center of the basins (Fig. 2a).
Phylogenetic analyses show that Atlantic salmon paralogs are evolving symmetrically, and they have been retained in the genome by purifying selection.
One of the main findings of genomic studies is that duplicate genes do not evolve symmetrically [ 48], i.e. they do not evolve at the same rate, due either to differences in recombination rate or to relaxation of negative selection and/or an increase in positive selection.
A large class of unusually symmetric pairs of paralogs is to be expected: firstly, some paralogs may have duplicated a significant and unknown time since the nearest preceding speciation and thus evolved for the unknown time as a single copy, not accumulating any differences; and secondly, even after duplication, paralogs may be evolving unusually symmetrically due to concerted evolution.
Interestingly, even when we control the average substitution scores by ensuring that for each asymmetrically evolving domain, we only sample a symmetrically evolving domain with average substitution score within 10 percentile using the pooled dataset, we still see a significant enrichment of low scores in the asymmetrically evolving pairs (Wilcoxon test P-value = 0.0005).
We found that the substitution scores for the asymmetrically evolving domains were significantly lower compared to those for symmetrically evolving domains (Wilcoxon test P-value ranged from 0.04 to 2.9e-05 2.9e-05 fore fish species).
Functional gene groups defined by Gene Ontology terms were found for S. salar gene duplicates that displayed either substantial or very small to no differences in selection constraints (i.e. evolving asymmetrically or symmetrically, respectively).
Figure 5C demonstrates that, in the pattern already presented on Figure B, the average difference between SNPs Ka/Ks estimates (faster paralogs – slower paralogs) is, predictably, close to 0 for symmetrically evolving paralogs pairs but significantly increases in the paralog pairs with the highest asymmetry.
Do asymmetrically evolving paralogs diverge in their expression tissue specificity greater than more symmetrically evolving ones?
We also found that asymmetrically evolving domains are targeted for qualitatively different substitutions as compared to symmetrically evolving domains, consistent with a functional divergence between duplicated genes.
