30Bread wheat expanded its habitats from a small core area of the Fertile Crescent to global 31 environments within ~10,000 years. Genetic mechanisms of this remarkable evolutionary 32 success are not well understood. By whole-genome sequencing of populations from 25 33 subspecies within genera Triticum and Aegilops, we identified composite introgression 34 from these wild populations contributing 13%~36% of the bread wheat genome, which 35 tremendously increased the genetic diversity of bread wheat and allowed its divergent 36 adaptation. Meanwhile, convergent adaption to human selection showed 2-to 16-fold 37 enrichment relative to random expectation in Triticum species despite their drastic 38 differences in ploidy levels and growing zones, indicating the vital importance of adaptive 39 constraints in the success of bread wheat. These results showed the genetic necessities 40 of wheat as a global crop and provided new perspectives on leveraging adaptation 41 success across species for crop improvement. 42
43Bread wheat (Triticum aestivum. ssp. aestivum) is one of the most successful crops on 44 earth since the Neolithic Age. Within only a few millennia, wheat expanded its habitat 45 from a small core area within the Fertile Crescent to a broad spectrum of diverse 46 environments around the globe, making it the most widely grown crop in the world 1,2 . 47Despite, wheat serving as one of the keystone crops for global food security, offering ~20% 48 of calories and proteins of human diet 3 , new environments resulting from climate change 49 may compromise its production 4,5 . Understanding the genetic mechanisms of the 50 adaptation success is key to productive and stable wheat production in the future. 51 52 Bread wheat (2n = 6x = 42, AABBDD) is an allohexaploid species, comprising of A, B, 53 and D subgenomes. It originated from two successive rounds of polyploidization within 54 genera Triticum and Aegilops, forming tetraploid wheat (AABB) and hexaploid wheat 55 (AABBDD), respectively 6 . By fusing genomes previously existing in different 56 environments, polyploidization brought broader adaptability to bread wheat 7 . However, 57 the same polyploidization process combined with the domestication bottleneck induced 58 severe diversity reduction to the ancestral population of bread wheat 8,9 , which was likely 59 impeding its range expansion. Recent studies identified that introgression from wild 60 emmer (T. turgidum. ssp. dicoccoides, AABB) could increase the diversity of bread 61 wheat 10,11 . Nevertheless, given the complex taxonomic groups within genera Triticum and 62Aegilops plus their unresolved phylogeny ( Supplementary Table 1) 12-14 , understanding 63 the diversity recovery of bread wheat from introgression may be still far from enough. In 64 addition to the obscurity of the divergent adaptation, questions on the convergent side of 65 the adaptation coin remain to be addressed. The evolution of wheats, or Triticum species, 66 is deeply rooted in human selection for agronomic traits, which almost excl...