You're misinterpreting what the paper means when it says homogeneous. They're using it to describe the exact thing you are: the corridors and connections between areas, specifically places where domestication originated. They found, contrary to Diamond's assertions, that the locations of many of the places agriculture originated were actually cut off by very hostile terrain. Like how the fertile crescent is surrounded by deserts, but Diamond incorrectly uses it as an example of a place where it should have been easy to pass agriculture to surrounding areas.

> Our second set of analyses compared the distribution of ecological barriers to cultural transmission between 16 important areas of the globe: centres of agricultural origin. While the first set of analyses tests a key ecological assumption in Diamond's theory (ecological biases in cultural spread), it is this second set of analyses that tackles (and casts doubt upon) Diamond's overarching message: Eurasia benefitted from a more homogenous environment along its major corridors of cultural transmission. One of his most prominent arguments in this regard was that agriculture spread very rapidly out of the Fertile Crescent. Contrary to that view, we found that this particular region can actually experience stronger environmental barriers within the corridors of agricultural spread than those observed in other centres of agricultural origin. This trend is particularly observable when considering aridity turnover at both close- and long-range, as well as close-range topographic costs. The likely reason for this discrepancy is that even though the Fertile Crescent has access to a larger area of contiguous landmass at similar latitudes than many of its peers (Diamond's main argument), it is nevertheless more ecologically atypical for its surroundings. Most notably, the Fertile Crescent is nourished by rivers but surrounded by large deserts, and these strong gradients in access to water are further compounded by nearby changes in prevailing winds and elevation (Figure S15). These findings remind us that dramatic changes in habitat and climate can occur even within small spatial scales. In contrast to the Fertile Crescent (and other Eurasian areas), South Tropical China, the Lower-Middle Yangtze and the Chinese plateau stand out as having low aridity related costs compared with most centres of agriculture origin. South Tropical China also shows low to mid-range temperature turnover values. Both aridity and temperature regimes would have been important for the spread of rice agriculture (d'Alpoim Guedes & Butler, Reference d'Alpoim Guedes and Butler2014; Gutaker et al., Reference Gutaker, Groen, Bellis, Choi, Pires and Purugganan2020), although archaeological evidence shows that human-directed water management systems were developed early and were part of the success of rice as a crop in these regions (Fuller & Qin, Reference Fuller and Qin2009). Thus, humans were working towards hijacking the conditions that were set for their crops by the local environment, a finding that strengthens the need to consider cultural factors when understanding crop domestication. Our results show that close-range topographic travel costs are not trivial in South Tropical China, and the Lower-Middle Yangtze and the Chinese plateau show one of the highest barrier levels along this axis. Thus overall, we do not find a consensus of universal low environmental barriers to cultural spread in Eurasian areas, as hypothesised based on Eurasia's East–West dominant continental axis.