“…‘Albeli’ species included C. candidus, C. albellus , C. muelleri , and C. heglingus (for lakes Neuchâtel, Brienz, Lucerne, and Walen), and ‘Balchen’ species included C. palea, C. alpinus, C. litoralis , and C. duplex (for lakes Neuchâtel, Brienz, Lucerne, and Walen). To first confirm the independent evolution of each ‘Balchen’ and ‘Albeli’ species-pair within each of these four lakes, as indicated by the phylogeny, F4 statistics were calculated across a four-taxon tree (as used in 42 ), allowing us to estimate the degree of correlated allele frequencies between ‘Balchen’ and ‘Albeli’ individuals within and between lake-systems. First, loci were pruned based on linkage disequilibrium using the script ldPruning.sh (https://github.com/joanam/scripts/raw/master/ldPruning.sh), resulting in 1,315,105 SNPs.…”