To test for a relationship between RCI and predictive factors, all variables were centered and RCI was regressed against a set of covariate data in a linear mixed model including US state as a random effect to account for regional differences . We included interactions for which we had a priori hypotheses . The model was estimated using the R package `lme4`64. Two model assumptions are violated in the above model, requiring updated estimates of the parameters’ standard errors. First, because RCI is a derived statistic with an unusual domain, the index is not distributed according to a known distribution family and violates the assumption of normality in the residuals. Second, residuals showed high spatial autocorrelation at multiple scales and with an unknown structure, necessitating a non-parametric approach. Both violations are likely to shrink standard errors of the estimated parameters, leading to overconfident estimates; to illustrate, in the case of spatial autocorrelation, if the explanatory variables are randomly located in relation to crop rotation, spatial autocorrelation in crop rotation would falsely inflate significance. An algorithm for sparsely distributed spatial data, derived by Lahiri 2018, was implemented in R . Spatial block bootstrapping involves iteratively resampling data in spatial blocks to mimic the generation of autocorrelated data. Choice of block size is nontrivial, and choosing the optimal block is an open question, but blocks should be larger than the scale at which autocorrelation operates. Using the R package `gstat`to compute a variogram of the residuals generated by the naive LMM, hemp drying racks we determined that range was 400815m. We used this as the dimension of each spatial block . We repeated this bootstrap with a range of possible spatial block sizes and found that this inference on parameters was robust to the choice of block size .
RCI scores have statistically clear correlations with land capability, mean rainfall, distance to the nearest bio-fuel plant, and field size, as well as with several interactions between these variables . Standard errors from the spatially blocked bootstrap were much larger than uncorrected naive confidence intervals, reflecting that accounting for spatial non-independence is necessary to estimate uncertainty of parameter estimates. Rotational complexity decreased with NCCPI, a proxy for land capability. We find that land of higher inherent capability is more likely to be used for lower complexity rotations. Rotational complexity decreased with average rainfall during the growing season. Fields with ample precipitation during the growing season are more likely to have simplified rotations. Though the relationship between the proximity of the nearest grain elevator and a field’s rotational complexity is not statistically clear , RCI showed a clear increase with distance to the nearest bio-fuel plant. Fields that are closer to bio-fuel plants are therefore more likely to have simplified rotations. Rotational complexity decreased with field size, with larger fields being more likely to have simplified rotations. Two of the interactions included in the model show statistically clear relationships. There is a positive interaction between land capability and field size, with higher quality land associated with decreasing RCI on small fields and slightly increasing RCI on large fields . The interaction between land capability and rainfall variance show a negative effect on RCI, with highly variable rainfall accentuating land capability’s impact on RCI . Interpretations of the relationship that each variable has with rotational complexity are shown in Table 4. Though each change is associated with a small shift in average RCI across the region, these can represent massive shifts in regional land management.
As crop rotations continue to simplify in the Midwestern US despite robust evidence demonstrating yield and soil benefits from diversified rotations, our ability to explain and understand these trends will come in part from observing the biophysical and policy influences on farmers’ crop choices at one key scale of management: the field. By developing a novel metric, RCI, that can classify rotational complexity over large areas at the field scale, we open the door to regional analyses that can address the unique landscape conditions that impact farmers’ field-level management choices and their subsequent influence on rotational simplification. We find that as farmers are pushed towards simplification by broad federal policies , physical manifestations of these policies like bio-fuel plants are correlated with intensified simplification pressures. Similarly, we see that the pressure to build soils and boost crop yields through diversified rotations intensifies in fields with lower land capability, while conversely the negative effects of cropping system simplifications are accentuated on the region’s best soils.RCI uses the sequence of cash crops on a given field as a proxy for crop rotation, and sorts these sequences into scores based on the sequence’s complexity and potential for agro-ecosystem health. Because this metric has not been used in previous analyses, we verified RCI’s validity through comparisons to previous estimates of rotational prevalence in the region. For example, two separate surveys of farmers in the Midwestern US showed that between 24% and 46% report growing “diversified rotations”which we consider to be an RCI of greater than 2.24 . In the present study, 34% of fields had an RCI greater than 2.24. This and further comparisons of RCI to previous work show that RCI is capable of capturing previously-noted trends in the region.
The ability to analyze rotations at the field scale across the entire Midwestern US allows us to ask how farmers optimize their rotations in complex economic and biophysical landscapes that include pressures to both simplify and diversify. Several biophysical and policy variables show statistically clear relationships with rotational complexity: high land capability, high rainfall during the growing season, and proximity to bio-fuel plants are all associated with rotational simplification. Given policy incentives, farmers often find that “corn on corn on dark dirt usually pencil out to be the way to go,” with farmers growing corn year after year when high quality soil is available. However, when that proverbial “dark dirt” is not available, calculations are not so simple. If growing conditions are sufficiently poor , these intensive corn systems may not be profitable, and farmers will have to rely more heavily on non-corn crops to maintain crop health and profitability in their fields. We see this dynamic at play with land capability in the present analysis. Despite—or rather because of— the fact that more diverse rotations improve soils, the most degrading cropping systems counter intuitively tend to occur on the highest quality land. Highly capable lands can be farmed intensively without dipping into a production “danger zone” in years with weather that is historically typical for the region, creating a pattern of land use that is likely to degrade these high quality lands in the long term and potentially jeopardize future yields, particularly in the face of climate change. Recent analyses show that enhanced drought tolerance and resilience for crops is one of the key benefits of diverse crop rotations. In the present analysis, mean rainfall during the growing season correlates positively with rotational simplification. Farmers may therefore be employing crop rotation in areas of low rainfall to achieve production levels that will keep a farm solvent, industrial rolling racks as was seen with rotational complexity increases in Nebraska during a drought period from 1999 to 200773. This trend is further accentuated by the negative interaction between land capability and rainfall variance in our analysis, where higher rainfall variability leads to even more diverse rotations on marginal lands. Proximity to bio-fuel plants, the main policy indicator in our model, showed a statistically clear trend towards rotational simplification, likely due to increased economic profits. Local corn prices increase by $0.06 – $0.12/bushel in the vicinity of a bio-fuel plant, amplifying incentives to grow corn more frequently. Wang and Ortiz Bobea were surprised not to find an impact of bio-fuel plant proximity on county-level frequencies of corn cropping in their own analysis, and the present analysis—done at a field rather than county scale—shows exactly this expected effect: corn-based rotations are simplified when in closer proximity to a bio-fuel plant. In the current economic and policy landscape, farmers are pushed to simplify rotations through more frequent corn cropping, especially in proximity to bio-fuel plants, while marginal soils and low rainfall pull fields towards more diverse rotations.
RCI’s ability to classify rotational complexity across large regions at the field scale and with low computational cost opens doors to future analyses that explore the interplay between localized landscape conditions, management choices, and agricultural, environmental, and economic outcomes. We see a strong potential to employ this metric not only in new regions, but in analyses that address how results from field experiments with crop rotation may scale up to regional levels. We also note that the metric should be used with caution. For example, because RCI cannot recognize functional groups in crop sequences , it cannot capture the added benefits that diverse functional groups often add to a rotation. In addition, though RCI includes a perennial correction that avoids penalizing multiple consecutive years of perennials the metric likely still underestimates the benefits of perennials in rotations. RCI is neutral to the soil benefits of annuals vs. perennials, while in practice the year-round cover and crop species mixes that often accompany perennials may boost soil benefits beyond those of annuals. Consecutive years of perennials are uncommon in our study area , and we encourage caution before applying the metric to regions with a more substantial perennial presence. We therefore recommend using RCI in studies that explore a wide range of cropping sequences where large differences in RCI are very likely to be meaningful, rather than as a tool to rank sequences that give similar scores. It is also important to note that, though the index can be applied to data of any sequence length, RCI values from different sequence lengths cannot be compared to each other; a rotation that results in a 2.2 from examining a six-year sequence will not be a 2.2 when examining a five or seven-year sequence. We also note that in using crop sequence as a proxy for crop rotation, RCI cannot fully capture the cyclical nature of true crop rotations. Because RCI examines a fixed number of years, it may “split up” identical rotations in ways that give slightly different scores or ABBAAB in a six-year sequence. As these discrepancies will decrease when longer sequences are considered, we recommend applying RCI to sequences that are as long or longer than the longest expected rotation in the study region.We hope to see RCI used in future analyses that extend beyond the Midwest; however, regional and historic patterns of crop production likely influence farmers’ rotational decisions and may render RCI scores calculated from disparate geographical regions difficult to interpret when called into direct comparison. We therefore see great promise in RCI as a rotational metric, and caution against applications that are overly narrow and overly broad .The time period chosen in this study, 2012 – 2017, coincides with the introduction of the Renewable Fuel Standard, or “bio-fuel mandate,” which took full effect in 2012. This policy mandates that 7.5 billion gallons of bio-fuel be blended with gasoline annually, and caused bio-fuel plants to open and local corn prices to soar across the Midwestern US. Now in 2021, there is significant political pressure both to maintain the bio-fuel mandate in its current state and to relax the standards, and new exemptions to the mandate have already caused several bio-fuel plants to close in the region. Given the link between bio-fuel plant proximity and rotational complexity, our analysis suggests that these closures, if continued, would likely be associated with an increase in mean RCI in the Midwestern US. Using our current model, simulations of randomly closing 20 of the 198 bio-fuel plants in the region lead to an increase of 0.003 in average RCI in the region, driven by greater distance to the nearest bio-fuel plant. In turn, increasing average RCI by 0.003 represents, for instance, the equivalent of 41,000 ha of cropland switching from corn-soy rotations to the most diverse rotation possible . Rotational simplification near bio-fuel plants is a pertinent example of the influence that policy can have on farm management decisions and its landscape repercussions.