English: Spectra of IBS sharing between simulated populations that differ only in admixture time. Each of the colored tract spectra in Figure A was generated from base pairs of sequence alignment simulated with Hudson R (2002). The IBS tracts are shared between two populations of constant size 10,000 that diverged 2,000 generations ago (= t_s), with one haplotype sampled from each population. 5% of the genetic material from one population is the product of a recent admixture pulse from the other population. Figure B illustrates the history being simulated. When the admixture occurred less than 1,000 generations ago, it noticeably increases the abundance of long IBS tracts. The gray lines in Figure A are theoretical tract abundance predictions, and fit the simulated data extremely well. To smooth out noise in the simulated data, abundances are averaged over intervals with exponentially spaced endpoints ${\displaystyle \left\{\lfloor 1.25^{n}\right\rfloor \}_{n\geq 1}}$.