2324 Hominin evolution is characterized by progressive regional differentiation, as well as 25 migration waves, leading to anatomically modern humans that are assumed to have 26 emerged in Africa and spread over the whole world. Why or whether Africa was the source 27 region of modern humans and what caused their spread remains subject of ongoing debate. 28 We present a spatially explicit, stochastic numerical model that includes ongoing mutations, 29 demic diffusion, assortative mating and migration waves. Diffusion and assortative mating 30 alone result in a structured population with relatively homogeneous regions bound by 31 sharp clines. The addition of migration waves results in a power-law distribution of wave 32 areas: for every large wave, many more small waves are expected to occur. This suggests 33 that one or more out-of-Africa migrations would probably have been accompanied by 34 numerous smaller migration waves across the world. The migration waves are considered 35 "spontaneous", as the current model excludes environmental or other factors. Large waves 36 preferentially emanate from the central areas of large, compact inhabited areas. During the 37 Pleistocene, Africa was the largest such area most of the time, making Africa the statistically 38 most likely origin of anatomically modern humans, without a need to invoke additional 39 environmental or ecological drivers. 40 41 Introduction 42 -3 -43 Hominins are generally supposed to have originated in Africa and settled most of Africa and 44 the southern half of Eurasia in the early Pleistocene [1-5]. Fossil evidence suggests that 45 earliest Homo sapiens appeared in Africa during the late Middle Pleistocene (Jebel Irhoud, 46 Omo and Herto [6-8]). Anatomically modern humans (AMH) emerged, spread out of Africa 47 during the Late Pleistocene and now occupy the whole world as the only Homo species [9-48 13]. In the intervening time, a number of Homo species, such as Neanderthals, Denisovans, 49 Homo erectus, H. heidelbergensis, H. ergaster, etc. existed,. Pleistocene human evolution is thus characterised by differentiation, speciation, 51 migration waves and extinction events. Most authors assume that the out-of-Africa spread 52 of AMH involved one or more migration waves that replaced Homo species that existed at 53 the time with only limited genetic admixture, such as between Neanderthals and AMH [22-54 23]. Many studies have addressed the timing and origin of migration waves, as well as 55 migration paths [e.g. 24,22,25,26,13]. Apart from the major out-of-Africa event(s), AMH 56 populations experienced several more migration waves within already populated areas, 57 such as Africa [27][28] and Europe [29][30]. Considering this, it is not unlikely that more 58 migration waves occurred in the Pleistocene, but the sparse fossil record still makes it 59 difficult to detect any.
60Assuming that migration waves did happen, the question arises what caused them, 61 in particular the spread of AMH. Most authors favour some competitive advantage of AMH 62 ove...