This figure summarizes the results from our analyses to determine parameters used in the simulations. For full detail, see Appendix, section ‘Major considerations in constructing the simulations’. (A) Finding the correct value for the composite trait . In each simulated family, offspring are split by sex and ranked by their composite trait. Due to occasional use of back-up crosses, the average rank of actual breeders is greater than 1. We vary to find the value where actual breeders in the LS lines have the best (lowest) rank. We find = -0.571 to show the best match for males and -0.605 for females. For subsequent analyses we set to be -0.57. (B) Increase in inbreeding over the course of the Longshanks experiment. The lines show the change in identity between two alleles between diploid individuals, , over 20 generations, as calculated from the pedigree (light shade); the average of 50 neutral simulations without selection (dotted line); or the average of 50 simulation replicates with selection intensity at = 0.584 (; thick, dark line). While the trajectories based on pedigree or neutral simulations are indistinguishable, inbreeding increases slightly faster under selection (thick line). The black line shows the increase in identity expected under a Wright–Fisher model with the actual population sizes; under this model, and are close to each other, and to , with equal to the harmonic mean, 24.8. The large dot (with error bar showing the interquartile range among chromosomes) at right show the actual , estimated from the decline in average over 17 generations. Small filled dots show the estimates from each of the 20 chromosomes. Open dots show 40 replicate simulations, made with the same pedigree and the same selection response and sub-sampling from the simulated chromosome according to the actual map length of each of the mouse chromosomes (Cox et al., 2009). The simulation agrees well with the observed genome-wide average. Most of the observed data from chromosomes fall within a range comparable to simulated replicates (compare large dot with open dots), with LD being the likely source of this excess variance. (C) Three different schemes to seed founder haplotypes. We simulate founder haplotypes that are consistent with observed genotypes (shown here as black, white and gray dots as the two homozygous and the heterozygous states) by directly sampling from founder individuals in each LS line. Under the linkage equilibrium scheme, we sample from the list of allele counts at all SNPs. This produces founder haplotypes that carry no linkage disequilibrium (‘no LD'). Under the random assignment scheme, we sample according to each individual (shown as ‘diplotypes' within the box for easy comparison). At heterozygote sites in each individual (arrowheads), we randomly assign the alleles to the two haplotypes. This produces founder haplotypes that show minimal LD that is consistent with the observed genotypes (‘min LD'). Under the ‘max LD' assignment scheme, we also sample according to each individual, except that we consistently assign its haplotypes 1 and 2 with reference (white) and alternate (black) alleles, respectively. This maximizes LD in the founder haplotypes (‘max LD'). (D) Simulated vs. expected allele frequency shifts. The distribution of minor allele frequencies q0 at generation 17 is compared with the distribution expected with no selection (blue) or with selection (red), given a frequency of 1, 4, 12 or 28 minor alleles out of 56 founding alleles. The black line shows the diffusion limit, calculated for scaled time , with estimated to be 51.7 and 48 in LS1 and LS2 respectively, from the rate of increase in , calculated from the pedigree in panel A above. (E) Significance threshold values under varying LD from 100 simulated replicates (blue: no selection; red: observed selection response in the actual experiment, ; see panel C on LD assignment methods). In order to account for non-independence of adjacent windows due to linkage, a distribution of genome-wide maximum ∆z2 was used to determine the significance threshold at each LD level. ∆z2 is the square of arcsine transformed allele frequency difference between F0 and F17; this has an expected variance of 1/2Ne per generation, independent of starting frequency, and ranges from 0 to π2. As seen in previous panels, increasing selection pressure does produce greater shifts in ∆z2 despite using the same pedigree due to a relatively greater proportion of additive genetic variance . However, a far greater impact on ∆z2 is due to changes in LD. This is because weak associations between large numbers of SNP can greatly inflate the variance of ∆z2. Of the three LD levels, ‘max LD' likely produced overly conservative thresholds, whereas ‘min LD' may lead to higher false positives. We have opted conservatively to use maximal LD in our analysis.