Bayesian approach for maize yield response to plant density from both agronomic and economic viewpoints in North America

Abstract

Targeting the right agronomic optimum plant density (AOPD) for maize (Zea mays L.) is a critical management decision, but even more when the seed cost and grain selling price are accounted for, i.e. economic OPD (EOPD). From the perspective of improving those estimates, past studies have focused on utilizing a Frequentist (classical) approach for obtaining single-point estimates for the yield-density models. Alternative analysis models such as Bayesian computational methods can provide more reliable estimation for AOPD, EOPD and yield at those optimal densities and better quantify the scope of uncertainty and variability that may be in the data. Thus, the aims of this research were to (i) quantify AOPD, EOPD and yield at those plant densities, (ii) obtain and compare clusters of yield-density for different attainable yields and latitudes, and (iii) characterize their influence on EOPD variability under different economic scenarios, i.e. seed cost to corn price ratios. Maize hybrid by seeding rate trials were conducted in 24 US states from 2010 to 2019, in at least one county per state. This study identified common yield-density response curves as well as plant density and yield optimums for 460 site-years. Locations below 40.5 N latitude showed a positive relationship between AOPD and maximum yield, in parallel to the high potential level of productivity. At these latitudes, EOPD depended mostly on the maximum attainable yield. For the northern latitudes, EOPD was not only dependent on the attainable yield but on the cost:price ratio, with high ratios favoring reductions in EOPD at similar yields. A significant contribution from the Bayesian method was realizing that the variability of the estimators for AOPD is sometimes greater than the adjustment accounting for seed cost. Our results point at the differential response across latitudes and commercial relative maturity, as well as the significant uncertainty in the prediction of AOPD, relative to the economic value of the crop and the seed cost adjustments.

Figure 1

Data description. (A) Geographical datapoint distribution within the continental US territory (the size of the bubbles represents the number of years). This map was created with the ggplot2 package in R; (B1) Yield distribution (raw data); (B2) Plant density distribution (raw data); and (C) Relationship between Bayes estimated agronomic optimum plant density (AOPD) and yield_AOPD for each site-year of the dataset ranging from 2011–2019 period.

Figure 2

Yield-latitude relationships. (A) Relationship between commercial relative maturity (CRM) and latitude. (B) Relationship between latitude and yield_AOPD (B1), and between yield_AOPD and latitude (B2), (C) AOPD distribution for high and low yield_AOPD at locations North (C1) and South (C2) of 40.5 N.

Figure 3

Cluster geographic distribution. (A) Cluster frequency for locations with more than 7 observed years. This map was created with the ggplot2 package in R; (B) Yield response to plant density for: (B1) Group I (S): Southern latitudes (i.e., below 40.5 N), (B2) Group II (N): Northern latitudes (above 40.5 N). Clusters are numbered in increasing order, according to their yield distribution.

Figure 4

(A) Cost/price ratio evolution through the years for the US. (B) EOPD variation at different latitude and price/cost ratio combinations. (C) EOPD vs. AOPD regression for (C1) Group I (S) and (C2) Group II (N); dashed lines represent the 1:1 relationship.