3 Results

3.1 Data overview

Thirteen studies were available for meta-analysis, and 9 studies involved multiple cases. From these, we obtained a total of 70 correlations between erosion depth and crop yield (Supplementary material Data S1), and 205 crop yield data with erosion treatments (Supplementary material Data S2). Among them, maize, wheat, and soybeans were subjects of 8, 50, and 12 studies, respectively (Figure 3). The following erosion depths were included (Figure 5): 5 cm, 6 cm, 10 cm, 12 cm, 15 cm, 18 cm, 20 cm, 25 cm, 30 cm, 40 cm (9 cases), 50 cm (9 cases), 60 cm (6 cases), and 70 cm (7 cases). Both positive and negative correlation coefficients were reported between erosion depth and yield reduction, with r ranging from -0.4739 to 0.9999.
Geographically, research areas were located in Asia (34%), North America (63%), and Africa (3%). None of the studies were located in Europe or Australia. Relatively, soil erosion gets more attention in high-yield areas. Both negative and positive values of the Pearson correlation coefficient were reported for studies in Asia and North America.

3.2 Meta-analysis

We found evidence that crop yield followed consistent patterns of change in response to soil erosion worldwide. Crop yield negativity responded to soil erosion no matter the intra-assay variance existed or not, which supports our hypothesis. Overall, soil erosion had a significant positive effect on crop yield reduction (estimate: 1.7861; p<.0001; 95%CI [1.4396, 2.1327]), and a significant negative effect on crop yield (estimate: -0.5523; p=.0002; 95%CI [-0.8473, -0.2574]). Since crop yield is usually associated with plant height and seed size, we did meta-analysis for the two indexes using relevant publications (Supplementary material Data S3). The results definitely showed that both of them significantly and negatively responded to erosion. For Data S1, the effect was highly heterogeneous among experiments (Qt=608.4312, p < .0001). The reliability of this result was tested by a fail-safe number (Fail-safe N: 1432840). As expected for a correlation between erosion and percent yield loss, there was a significant residual heterogeneity (Qt=608.43, p<.0001) in the hierarchical mixed-effects meta-analysis for grain type (Qt= 9039.7297, p<.0001), soil type (Qt=8231.2124,p<.0001), measure (Qt= 8579.4537,p<.0001), latitude (Qt= 9031.5350, p < .0001), and longitude (Qt = 9029.1165, p < .0001); we tried to explain this with different modifiers. Grain_type (Qm= 0.9014, p = 0.6372), soil_type (Qm= 6.5215, p = 0.4803), measure (Qm= 5.7817, p = 0.2161), latitude (Qm = 0.0766, p = 0.7820), and longitude (Qm = 0.2347, p = 0.6281) had no significant effect on effect size. There were no significant differences between multiple levels of soil types, grain types, and measures (Figure 3).
All erosion depths except 5 cm and 6 cm exhibited statistically significant effects on crop yield (p < 0.05) (Figure 5). Effect sizes in 8.8% of cases were negative. When erosion depth was higher than 20 cm, crop yield was reduced. When erosion depth was higher than 60 cm, the effect sizes (lnRR) were similar (Figure 4). The cumulative effect size of erosion at 5, 10, 15, 20, 25, and 30 cm was -0.17, -0.38, -0.78, -0.76, NA, and -1.01, respectively, indicating a decreasing trend with increasing erosion depth (Figure 5). The effect degree of erosion was significantly different between 5 - 10 cm and 10 - 15 cm erosion depth intervals (Figure 6).