Farmers' decision to adopt new management or production system depends on production risk. Grain yield data was used to assess production risk in a field experiment composed of two cropping systems (CNV and ORG), each with eight subsystems (two levels each of crop rotation (2-yr and 4-yr), tillage management (conventional, CT and strip, ST), and fertilizer input (fertilized, YF and non-fertilized, NF)). Statistical moments, cumulative yield (CY), temporal yield variance (TYV) and coefficient of variation (CV) were used to assess the risk associated with adopting combinations of new management practices in CNV and ORG. The mean-variance-skewness (M-V-S) statistics derived from yield data separated all 16 subsystems into three clusters. Both cropping systems and clustered subsystems differed as to their ability to maintain a constant yield over years, displayed different yield cumulative probabilities, exhibited significant and different M-V-S relationships, and differed as to the reliability of estimating TYV as a function of CY. Results indicated that differences in management among cropping systems and subsystems contributed differently to the goal of achieving yield potential as estimated by the cumulative density function, and that certain low-input management practices caused a positive shift in yield distribution, and may lower TYV and reduce production risk.

Production risk influences farmers’ decision to adopt a new management practice or a production system [

Quantifying treatment main effects in cropping systems experiments provides valuable information that can be augmented by examining the interaction between years and treatment [

Crop yields and their temporal variances are influenced by management factors, especially crop rotations [

A long-term cropping systems experiment was established in 2002 on a land area of about 3.0 ha as a split-plot randomized complete block design with four replications (i.e., blocks). The experimental site was uniformly cropped for one year prior to the start of the experiment. The predominant cropping system practiced by farmers in this part of the upper Midwest of the United States (45°41′N, 95°48′W at 370 meters above sea level) is based on conventional management of a 2 yr corn-soybean crop rotation using conventional tillage and external inputs (fertilizer, herbicides, etc.). Sixteen subsystems were formulated as combinations of two levels each of cropping systems (conventional and organic), crop rotation (2-yr of corn (

Fertilizer rates (inorganic N source for the conventional and animal manure N source for the organic cropping system) were determined for each crop on the basis of annual soil analyses and regional N recommendations. The Nitrogen Decision Aid software (

Grain yield in each of eight years (2002–2009) was measured from a central 15 m^{2} mechanically harvested strip per plot of corn, soybean, and wheat and adjusted to a moisture content of 15.5, 13.0, and 13.5%, respectively. Total dry matter yield of alfalfa was measured on two 0.5 m^{2} subplots per plot harvested three times per year, and adjusted to a moisture content of 15.0%. Measured yield data were expressed in Mg ha^{−1} for each subsystem and then used for further statistical analyses and modeling. Annual and total yields were used to calculate annual and cumulative yield means (years 1 to 8), medians, temporal yield variances, coefficients of variation, skewness, and kurtosis and to construct yield frequency distributions for each cropping system. The M-V-S estimates for subsystems were used to cluster them into three distinct groups (Clusters), based on results of a preliminary principal components analysis (see below).

Principal Components Analysis (PCA) was used to identify possible associations (i.e., loadings on the first PC) and quantify the amount of total variation accounted for by statistical descriptors, central moments, two cropping systems (Conventional and organic), their components (i.e., crop rotations, tillage, and fertility management options), and the resulting 16 subsystems. The correlation matrix between variables was used in the analyses to give variables equal weight after standardizing the variances to a value of 1. The results of PCA were used to classify the 16 subsystems into those with significant positive, negative, or no significant loadings on PC1. Two demarcation lines at the ±0.2 loadings separate these subsystems (Figure

Loadings of, calibration (

Repeated measurements analysis using REML with first-order autoregressive (AR1) models appropriate for equally spaced data (i.e., annual yield estimates) and an option to allow for heterogeneous variances over years, was used on annual yield data of all subsystems [

Two modeling approaches were employed to evaluate and compare yield and temporal variance of both cropping systems and those of clustered subsystems; these were

Cumulative yields with significant regression coefficients were reported in the validation PLS models (

Principal components analysis captured a large portion (

The three-way relationship between S and the other two central moments (M-V) was positive and significant (r: S/M-V = 0.75;

Three-dimensional plots of central moments (mean yield, variance, and skewness, M-V-S, (a); total yield, variance, and skewness, (b) for 16 subsystems in a long-term cropping systems experiment.

The magnitude and level of significance of bivariate M-V-S correlation coefficients varied between cropping systems and clusters within systems (Table

Simple bivariate correlation coefficients between mean-variance-skewness in two cropping systems and three subsystem clusters of these systems.

Cropping system/cluster | Statistic mean/variance | Variance | Skewness |
---|---|---|---|

Conventional | Mean | 0.90^{***†} | −0.89*** |

variance | −0.74** | ||

Organic | Mean | 0.57* | −0.83*** |

variance | −0.33* | ||

Cluster 1 | Mean | 0.90*** | −0.89*** |

Variance | −0.72*** | ||

Cluster 2 | Mean | 0.37* | −0.58** |

variance | −0.44* | ||

Cluster 3 | Mean | 0.65** | −0.86*** |

variance | −0.59** |

^{†}Correlation coefficients followed by *, **, *** are significantly different at the 5, 1, and 0.1% level of probability, respectively.

Results of repeated measurements analyses are summarized in Table

Summary of repeated measurements analysis of variance of cumulative yield using restricted maximum likelihood with autoregressive correlations.

Number of years (d.f.) | |||
---|---|---|---|

2 | 5.22^{*†} | 3.92** | 0.23 n.s. |

3 | 9.10** | 17.44*** | 0.64 n.s. |

4 | 7.25*** | 42.18*** | 0.58 n.s. |

5 | 50.05*** | 71.05*** | 1.83** |

6 | 62.08*** | 79.62*** | 2.25** |

7 | 66.12*** | 80.84*** | 3.56** |

8 | 77.96*** | 79.55*** | 3.87** |

^{†}Values followed by *, **, *** are significantly different at the 5, 1, and 0.1% level of probability, respectively; n.s., not significant.

Most descriptive statistics and central moments differed significantly between conventional and organic cropping systems (Figures ^{−1}. Similarly, minimum and maximum yields of the conventional cropping system were much larger than those of the organic. The largest frequency in conventional cropping system was for the 35–40 Mg ha^{−1} yield category, followed by 30–35 Mg ha^{−1}; in the organic cropping system, it was 25–30 Mg ha^{−1}, followed by the 20–25 Mg ha^{−1} yield category. The distribution curve based on total yield of the organic cropping system was less skewed (0.098) than that of the conventional cropping system (0.27) which was positively skewed and with less kurtosis (−0.22 versus −0.79) although their respective medians were very close to their means. The larger mean yield of the conventional cropping system was associated with larger variance (68.4 Mg ha^{−1})^{2 }as compared to the organic cropping system (34.97); however, their long-term coefficient of variation values (21.19 and 22.26%, respectively) was almost equal.

Descriptive statistics, central moments, and empirical and normal cumulative density functions (CDF) of conventional (a) and organic (b) cropping systems.

Four subsystems, all belonging to the conventional cropping system, clustered together based on their M-V-S values to form Cluster 1 (Figure ^{−1} yield category, followed, in decreasing order, by 40–45 and 35–40 Mg ha^{−1} yield categories. The second cluster (Figure ^{−1} yield category, followed, in decreasing order, by the 30–35 and 35–40 Mg ha^{−1} yield categories. The third cluster (Figure ^{−1} followed by 25–30 Mg ha^{−1} yield category.

Statistical descriptors, central moments, and empirical and normal cumulative density functions (CDF) of 16 subsystems in three clusters (A, B, and C) based on their M-V-S means.

Temporal yield variance (TYV) of the conventional cropping system as a function of cumulative yield (CY) during eight years was predicted and validated by the following PLS model:

The remaining cumulative yields had positive impact on temporal yield variance. Except for the small

Temporal yield variance of the organic cropping system as a function of cumulative yield during the course of the experiment was predicted and validated by a simpler PLS model, as compared to temporal yield variance of the conventional cropping system:

Temporal yield variance for all four subsystems (within the conventional cropping system) in Cluster 1 (

Only a small (

Crop yield density estimation has been the subject of extensive empirical research, especially in risk analysis [

Farmers are mostly risk averse; they are primarily interested in knowing the probability of getting low yields that would lead to estimating risk [

The bivariate (Table

The design of this long-term experiment and the statistical analyses took into consideration the random temporal variation and prevented it from masking the real effects of fixed factors (i.e., subsystems, in this study) [

Posner et al. [

The reliability of using cumulative yield to predict temporal yield variance, although resulted in different model fit (

This and a few other similar studies [

Multivariate statistical analyses of annual and cumulative crop yields during the course of a long-term experiment identified stable and productive subsystems within each of conventional and organic cropping systems. The study provided evidences indicating that differences in management among cropping systems contributed differently to the goal of achieving the yield potential of each cropping system. Several statistical descriptors, including mean-variance-skewness of cumulative crop yields, were used to construct cumulative density functions and provided reliable indicators of yield stability in a long-term cropping systems experiment when subjected to repeated measurements, principal components, and partial least squares regression analyses. Results of the study may help farmers, agronomists, and crop consultants identify novel components of cropping systems that can be implemented on the farm with less external inputs and may result in reducing temporal variation of crop yields.