China's Holocene crops did not spread as one farming frontier: millet, rice and wheat/barley each followed their own spatial opportunity structure
Synopsis
Holocene agriculture in China did not expand as one uniform farming frontier. Combining archaeological crop records with palaeoclimate, terrain and river-network data, a crop-specific dynamic non-local diffusion model estimates the relative probability of new crop records during 6000–2000 BP. Millet records were most associated with same-crop persistence and non-local diffusion, rice records most with humid-lowland environmental filtering, and wheat/barley records with corridor-like accessibility along the Hexi Corridor–Central Plains belts and higher frontier mobility.
Interpretation
Archaeological records of the three crop systems show a multicentred, asynchronous and crop-specific spatial pattern rather than the uniform outward movement of a single agricultural frontier. Earlier explanations of crop dispersal largely remained qualitative route descriptions or were confined to a single crop, region or cultural sequence, making it hard to compare whether different crops followed the same diffusion process at national scale. The compiled records show millet appearing early and widely across northern China and the Yellow River basin, rice concentrated in the Yangtze basin and adjacent humid lowlands, and the earliest wheat/barley evidence generally later and first concentrated in northwestern China, the Gansu-Qinghai region, Guanzhong and the Central Plains.
The model decomposes the relative probability of a new crop record into same-crop local persistence, non-local diffusion, dynamic environmental suitability and a diffusion-environment interaction, so the three mechanisms can be compared in one framework. The non-local diffusion term is a kernel built from distance decay, terrain costs, river-related accessibility and fixed crop-specific regional accessibility weights, implemented as weak, non-exclusive spatial modifiers rather than predefined route masks. The model runs on a 0.5° longitude-latitude grid with 300-year time windows over the main 6000–2000 BP interval, using a final dataset of 2,100 unique archaeological crop records: 1,223 millet, 450 rice and 427 wheat/barley.
Under one-step conditional simulation the full model showed consistent spatial-enrichment ability for new crop records in all three crop systems and outperformed spatial null models and sampling-intensity controls. Random expectation, a same-crop kernel density null model and a total-crop sampling-intensity kernel density null model served as controls, testing whether predictions reduced to randomness, previous same-crop clustering or general archaeological sampling intensity. AUC values for millet, rice and wheat/barley were approximately 0.94, 0.93 and 0.93, with AP about 0.17, 0.20 and 0.15; retaining only the top 5% of candidate cells by predicted probability captured top-5% recall of approximately 0.73, 0.68 and 0.74.
Counterfactual ablation separates the dominant mechanisms: same-crop persistence was the strongest predictor for all three, while non-local diffusion and environmental suitability contributed differently. Removing same-crop local persistence lowered AP by about 0.151, 0.186 and 0.147 for millet, rice and wheat/barley; removing non-local diffusion lowered AP by about 0.059 for rice and 0.038 for wheat/barley, with a smaller decline for millet; removing environmental suitability lowered rice AP by about 0.064, did not reduce millet AP and had only a minor effect on wheat/barley. In environmental-gating diagnostics rice showed the highest gating ratio, while wheat/barley showed the highest frontier mobility, with Q75 frontier velocities substantially higher than those of millet and rice, consistent with non-local or leapfrog-style expansion of an introduced crop.
Perspective
The model estimates the relative probability that archaeological crop evidence is observed, not the actual extent of cultivation, yield, dietary contribution or population movement; quantitative interpretation is restricted to 6000–2000 BP, and the decline in younger records reflects the temporal coverage of the source datasets rather than a decline in cultivation.
The environmental term is a composite suitability indicator, not the causal effect of a single climate variable or a physiological crop threshold; the non-local diffusion and accessibility terms are predictive spatial weights that cannot distinguish migration, exchange, technological adoption or cultural transmission; several spatial-accessibility parameters had only moderate support and are cautiously read as predictive weights rather than precise historical routes.