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Horse domestication revolutionized warfare and accelerated travel, trade, and the geographic expansion of languages. Here, we present the largest DNA time series for a non-human organism to date, including genome-scale data from 149 ancient animals and 129 ancient genomes (>= 1-fold coverage), 87 of which are new. This extensive dataset allows us to assess the modem legacy of past equestrian civilisations. We find that two extinct horse lineages existed during early domestication, one at the far western (Iberia) and the other at the far eastern range (Siberia) of Eurasia. None of these contributed significantly to modern diversity. We show that the influence of Persian-related horse lineages increased following the Islamic conquests in Europe and Asia. Multiple alleles associated with elite-racing, including at the MSTN "speed gene," only rose in popularity within the last millennium. Finally, the development of modem breeding impacted genetic diversity more dramatically than the previous millennia of human management.
In the limit we analyze the generators of families of reversible jump processes in the n-dimensional space associated with a class of symmetric non-local Dirichlet forms and show exponential decay of the eigenfunctions. The exponential rate function is a Finsler distance, given as solution of certain eikonal equation. Fine results are sensitive to the rate functions being twice differentiable or just Lipschitz. Our estimates are similar to the semiclassical Agmon estimates for differential operators of second order. They generalize and strengthen previous results on the lattice.
In this article we analyse the structure of Markov processes and reciprocal processes to underline their time symmetrical properties, and to compare them. Our originality consists in adopting a unifying approach of reciprocal processes, independently of special frameworks in which the theory was developped till now (diffusions, or pure jump processes). This leads to some new results, too.
In the limit 0 we analyse the generators H of families of reversible jump processes in Rd associated with a class of symmetric non-local Dirichlet-forms and show exponential decay of the eigenfunctions. The exponential rate function is a Finsler distance, given as solution of a certain eikonal equation. Fine results are sensitive to the rate function being C2 or just Lipschitz. Our estimates are analogous to the semiclassical Agmon estimates for differential operators of second order. They generalize and strengthen previous results on the lattice Zd. Although our final interest is in the (sub)stochastic jump process, technically this is a pure analysis paper, inspired by PDE techniques.