From the website (accessed 2015-12-16):
These are a series of geographically accurate and publicly accessible map tiles that represent the ancient Mediterranean world in a variety of different periodizations, released under the CC BY-NC 3.0 license. The map tiles are hosted on Mapbox servers courtesy of ISAW, and are created by Ryan Horne from AWMC data produced by Richard Talbert, Jeffrey Becker, Ryan Horne, Ross Twele, Audrey Jo, Ray Belanger, Steve Burges, Luke Hagemann, Ashley Lee, and others. They were built from shapefiles originally created by the AWMC using ArcGIS and QGIS. The data was derived from from VMap0 and OSM, then further modified by the AWMC, generally following the Barrington Atlas. Bathymetric data is largely built from SRTM 30 PLUS (copyright notice here) with additional work by the AWMC, with GDAL tools utilized to produce hillshade and color-relief rasters. The shapefiles and rasters were brought into TileMill, then uploaded to Mapbox, where they were combined with data from OSM and MapBox to produce the finished tile set. Detailed information on each data layer can be found here: http://awmc.unc.edu/wordpress/tiles/map-tile-information.