2 Materials and Methods
2.1 Study selection
A literature search was conducted using keywords “soil erosion”,
“experiment” and “productivity” in Web of Science, Science Direct
and others. This resulted in a sample of 69 studies published from 1969
to March 2019. Different research methods may result in different yield
reduction rates due to erosion (Bakker et al., 2004). Most studies
explored erosion effects on productivity by observing crop yields in
field plots with different erosion levels (light, moderate, severe)
classified according to various criteria; in this case, erosion effects
on productivity cannot be accurately quantified (Duan et al., 2016; Lin
et al., 2019). We used only those studies that clearly specified erosion
depth. Then, crop yield variability was analyzed for six equidistant
soil erosion depths (i.e., 5, 10, 15, 20, 25, and 30 cm). More details
of the publication selection process can be found in Figure 1. The
geographical distribution of the studies selected for meta-analysis
included different areas across the globe as shown in Figure 2. Studies
were published between 1995 and 2015, and regarded as eligible if they
included the changing patterns of yield along erosion gradient, or yield
states of eroded and non-eroded soils. Each study reported data of one
or more relationships between yield and erosion depth were selected for
the following meta-analysis. Subsequently, only 13 out of the 41 studies
were selected after filtering titles, abstracts, and results. The
selected 13 studies explicitly quantified crop yield response along
erosion gradients.
2.2 Data processing
Crop yield data from different erosion depths at each site were
extracted. In this process, WebPlotDigitizer software (Burda et al.,
2017) was used to extract data from graphs, or data were directly
retrieved from tables and main text. In addition, soil types, grain
types, measure and geographical locations of each study were recorded.
Two soil types (i.e., clay loam and sandy clay loams) involved in the
dataset were standardized with China’s soil classification; and
undetermined soil types were set to “test”. Three grain species (i.e.,
maize, soybeans, and wheat) were involved. Other important information
that was expected to influence results was also collected, including
monitoring year, and management practices (i.e., fertilization,
fertilization add manure, irrigated site). Pearson’s correlation
coefficients (r) for the relationships of erosion depth-crop reduction
were either directly taken from the published studies, or calculated
using soil erosion depth and crop yield reduction if reported for
multiple plots.
2.3 Data analysis
Pearson’s correlation coefficient (r) for each case was normalized using
Fisher’s z transformation for an effect size, sample size was the
product of the number of repetitions and the number of erosion layers
(Peng et al., 2019). Subsequently, the log-response ratio (lnRR) of crop
yield in non-eroded and eroded treatments was used as the effect size in
our meta-analysis, and was calculated as follows:
\begin{equation}
lnRR=\ln{\ \left(T_{A}\right)}-ln\ (T_{B})\nonumber \\
\end{equation}where TA was the average crop yield under erosion
conditions, and TB was the average crop yield without
erosion (erosion depth equal to 0 cm) in the same environment. All
parameters in the meta-analytical models were estimated using maximum
likelihood method (Zuur et al., 2009). The possibility of publication
bias and temporal changes in effect size were examined using the
fail-safe number. The procedure of Fisher’s z and lnRR were conducted
using OpenMEE software (Wallace et al., 2017). Full analyses were
performed using the Metafor package (Viechtbauer, 2010) in R software
(version 3.5.2).
Meta-analysis assumes that individual studies are statistically
independent; thus, obtaining crop yield for multiple erosion levels or
several observations (e.g., cases in different site and year) from one
publication could violate the assumption of independence and create a
hierarchical dependence structure among the effect size estimates
(Stevens and Taylor, 2008). Hence, data were analyzed with multilevel
linear mixed-effect models using the ‘rma.mv’ function in Metafor
(Viechtbauer, 2010). Additionally, models were fitted with nested random
effect terms as follows: (ID |reference) (see Code
meta-analysis), which performs noise processing on similar or
non-independent cases, increasing the reliability of the analysis.