The paper starts off well:
However, a wide range of times since the most recent common ancestor (TMRCAs) has been proposed for J1 and its subclades (between 36 and 10 KyBP), and different conflicting scenarios have been depicted to explain their current distribution.Unfortunately I wasn't able to locate in the paper/supp info any mention of the mutation rate assumed in this paper which leads the authors to come out in support of a pre-historical "hunter-gatherer" mode of dispersal for J1. Naturally I'm very skeptical of archaeological conclusions based on TMRCA, both because most of the literature leads to age overestimates, and because population movements may be both older and younger than TMRCAs, and TMRCAs of modern Y-chromosomes tell us virtually nothing about them.
UPDATE (Apr 21): A reader alerts me of the fact that the mutation rate is shown in Supplementary Table 4, where a uniform distribution between the germline (0.0028) and "evolutionary" rate (0.00069) is assumed. As I don't think there is any merit to the evolutionary rate for large haplogroups, the ages presented in the paper should be divided by ~1.5, although as always, these carry fairly wide uncertainty margins.
European Journal of Human Genetics doi:10.1038/ejhg.2009.58
J1-M267 Y lineage marks climate-driven pre-historical human displacements
Sergio Tofanelli et al.
The present day distribution of Y chromosomes bearing the haplogroup J1 M267*G variant has been associated with different episodes of human demographic history, the main one being the diffusion of Islam since the Early Middle Ages. To better understand the modes and timing of J1 dispersals, we reconstructed the genealogical relationships among 282 M267*G chromosomes from 29 populations typed at 20 YSTRs and 6 SNPs. Phylogenetic analyses depicted a new genetic background consistent with climate-driven demographic dynamics occurring during two key phases of human pre-history: (1) the spatial expansion of hunter gatherers in response to the end of the late Pleistocene cooling phases and (2) the displacement of groups of foragers/herders following the mid-Holocene rainfall retreats across the Sahara and Arabia. Furthermore, J1 STR motifs previously used to trace Arab or Jewish ancestries were shown unsuitable as diagnostic markers for ethnicity.