Fig. 3. Potential yield (YIELDPOT)

Fig. 3. Potential yield (YIELDPOT) in winter wheat (a) and spring barley (c) as a function of SOC and the residual plots from the full model (excluding SOC) for winter wheat (b) and spring barley (d) (note the axes are transformed). The solid line is the estimated regression line, whilst the dotted lines demonstrate the 95% confidence interval for the line.yields at zero N application (YIELDN0) and N use efficiency (NUE). The data included in this analysis has been collected from a large number of locations rather than from a single experiment, so factors other than SOC were not controlled. Therefore, there may be variables which are confounded with SOC, i.e., factors that are correlated with SOC, making it difficult or impossible to infer a causal relationship between SOC and the response variable, because the effect might as well be caused by the confounding variable. For example, a confounding variable could be clay content. Increasing clay content would typically be expected to have a positive influence on potential yield. However, many Danish sandy soils with a low clay content hold considerable amounts of organic matter. This can be attributed to intensive dairy production (involving manure application and cultivation of perennial grass crops, and thus increased SOC levels) typically located in regions with sandy soils and soils with a higher content of charred material from previous land-uses (Taghizadeh-Toosi et al., 2014). These two relationships would produce a negative relationship between SOC and potential yield, not because SOC has a negative effect, but because SOC is negatively correlated with clay and clay has a positive effect on potential yields (due todeeperrootdevelopmentandhighercapacityforplantavailable water). The statistical analysis was thus conducted with the aim of removing the effect of as many of the confounding variables as possible.