Wheat (Triticum aestivum L.) grain yield response to plant density is inconsistent, and the mechanisms driving this response are unclear. A better understanding of the factors governing this relationship could improve plant density recommendations according to specific environmental and genetics characteristics. Therefore, the aims of this paper were to: i) execute a synthesis-analysis of existing literature related to yield-plant density relationship to provide an indication of the need for different agronomic optimum plant density (AOPD) in different yield environments (YEs), and ii) explore a data set of field research studies conducted in Kansas (USA) on yield response to plant density to determine the AOPD at different YEs, evaluate the effect of tillering potential (TP) on the AOPD, and explain changes in AOPD via variations in wheat yield components. Major findings of this study are: i) the synthesis-analysis portrayed new insights of differences in AOPD at varying YEs, reducing the AOPD as the attainable yield increases (with AOPD moving from 397 pl m^-2 for the low YE to 191 pl m^-2 for the high YE); ii) the field dataset confirmed the trend observed in the synthesis-analysis but expanded on the physiological mechanisms underpinning the yield response to plant density for wheat, mainly highlighting the following points: a) high TP reduces the AOPD mainly in high and low YEs, b) at canopy-scale, both final number of heads and kernels per square meter were the main factors improving yield response to plant density under high TP, c) under varying YEs, at per-plant-scale, a compensation between heads per plant and kernels per head was the main factor contributing to yield with different TP.

Since 1980, average wheat (Triticum aestivum L.) yields have remained nearly stagnant in the southern Great Plains (SGP) and stagnant in the state of Oklahoma. Yield stagnation can sometimes be attributed to a relatively small gap between current and potential yields, but the magnitude of the yield gap for this region has not been well quantified. The objective of this study was to determine the wheat yield and production gaps in Oklahoma at state and county levels. This involved estimation of attainable yield (Y_a) using a frontier yield function and water‐limited potential yield (Y_p) using estimated transpiration and transpiration efficiency. Yield gap and production gap relative to Y_a and Y_p were calculated using grain yields and harvested area for 19 counties. Current average yield (Y_c) was 2.06 Mg ha⁻¹ at the state level, well below the maximum recorded yield at the plot level of 6.59 Mg ha⁻¹. The Y_p of current wheat varieties is far above Y_c in Oklahoma, and Y_c represents 74% of Y_a but only 30% of Y_p at state level. For growing season rainfall (GSRF) amount <250 mm wheat yields were often water‐limited. However, average GSRF was 471 mm, and yield was typically limited by factors other than GSRF amount. Production exhibited greater temporal variability than yield, and production gap may be a better indicator than yield gap for regions with highest potential to increase production. Low yields and yield stagnation in Oklahoma cannot be attributed to a small remaining yield gap, nor to inadequate GSRF amount.

There is limited information on agronomic practices affecting wheat ( Triticum aestivum L.) yield in intensively managed dryland systems despite the opportunity to narrow the existing yield gap ( Y _G ). We used a unique database of 100 intensively managed field‐years entered in the Kansas Wheat Yield Contest during the 2010 to 2017 harvest seasons to (i) quantify the Y _G , (ii) describe wheat management, and (iii) identify management opportunities and weather patterns associated with yield. We simulated wheat water‐limited yield ( Y _w ) using Simple Simulation Modeling–Wheat (SSM‐Wheat) model for each field‐year to estimate Y _G as the difference between Y _w and actual yield ( Y _a ) and used 11 statistical approaches to test the association of management practices and weather variables with Y _a . Wheat Y _a averaged 5.5 Mg ha ⁻¹ , and simulated Y _w averaged 6.4 Mg ha ⁻¹ , resulting in a Y _G of 0.9 Mg ha ⁻¹ (15% of Y _w ). High‐yielding fields had lower maximum and minimum temperatures and greater cumulative solar radiation and precipitation during grain fill. Varieties susceptible to fungal diseases responded to foliar fungicide (0.8–1.4 Mg ha ⁻¹ ), whereas resistant varieties did not. Seeding rate was negatively associated with Y _a , as yield quantile 0.99 was 7.5 Mg ha ⁻¹ and decreased by 2.7 Mg ha ⁻¹ for every 100‐seed m ⁻² increase in seeding rate above 305 seeds m ⁻² . In‐furrow P fertilizer, previous crop, tillage practice, and N timing were also associated with Y _a . We conclude that fields entered in yield contests have closed the exploitable Y _G , and there are opportunities to improve Y _a through improved management in regions with stagnant wheat yield.