In any case, the conclusions are worth mentioning in themselves. For the Ashkenazi:
We obtained an improved fit for a population composed of ~2,300 ancestors 200 generations before the present; this population exponentially expanded to reach ~45,000 individuals 34 generations ago. After a severe founder event, the population was reduced to ~270 individuals, which then expanded rapidly during 33 generations (rate r ~ 0.29) and reached a modern population of ~4,300,000 individuals.And, for the Maasai:
Optimizing a model of exponential expansion and contraction (Figure 1A), we obtained a good fit to the observed IBD frequency spectrum (Figure 6), suggesting that an ancestral population of ~23,500 individuals decreased to ~500 current individuals during the course of 23 generations (r ~ -0.17). We note that this result might not be driven by an actual gradual population contraction in the MKK individuals, but it most likely reflects the societal structure of this seminomadic population. ... We thus used the village model to analyze the MKK demography and relied on coalescent simulations to retrieve its parameters: migration rate, size, and number of villages that provide a good fit for the empirical distribution of IBD segments.We observed a compatible fit for this model, in which 44 villages of 485 individuals each intermix with a migration rate of 0.13 individuals per generation (Figure 6).If I understand this correctly, it appears that Maasai (MKK) individuals share long IBD segments not because their population has contracted (and hence they're all descended from a limited number of founders, as is the case for Ashkenazi Jews), but rather because their social structure follows the "village model" in which people share shallow ancestry (and hence long IBD) with other people in their "village" and exchange genes with other "villages".
The American Journal of Human Genetics, 25 October 2012 doi:10.1016/j.ajhg.2012.08.030
Length Distributions of Identity by Descent Reveal Fine-Scale Demographic History
Pier Francesco Palamara et al.
Data-driven studies of identity by descent (IBD) were recently enabled by high-resolution genomic data from large cohorts and scalable algorithms for IBD detection. Yet, haplotype sharing currently represents an underutilized source of information for population-genetics research. We present analytical results on the relationship between haplotype sharing across purportedly unrelated individuals and a population’s demographic history. We express the distribution of IBD sharing across pairs of individuals for segments of arbitrary length as a function of the population’s demography, and we derive an inference procedure to reconstruct such demographic history. The accuracy of the proposed reconstruction methodology was extensively tested on simulated data. We applied this methodology to two densely typed data sets: 500 Ashkenazi Jewish (AJ) individuals and 56 Kenyan Maasai (MKK) individuals (HapMap 3 data set). Reconstructing the demographic history of the AJ cohort, we recovered two subsequent population expansions, separated by a severe founder event, consistent with previous analysis of lower-throughput genetic data and historical accounts of AJ history. In the MKK cohort, high levels of cryptic relatedness were detected. The spectrum of IBD sharing is consistent with a demographic model in which several small-sized demes intermix through high migration rates and result in enrichment of shared long-range haplotypes. This scenario of historically structured demographies might explain the unexpected abundance of runs of homozygosity within several populations.