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Core Ideas Soybean seed yield response to plant density is dependent on yield environment.Low yield environments required higher plant densities than high yield environments.Plant density mainly affected per‐plant seed number.No differences in plant survival were observed among yield environments. Inconsistent soybean [Glycine max (L.) Merr.] seed yield response to plant density has been previously reported. Moreover, recent economic and productive circumstances have caused interest in within‐field variation of the agronomic optimal plant density (AOPD) for soybean. Thus, the objectives of this study were to: (i) determine the AOPD by yield environments (YE) and (ii) study variations in yield components (seed number and weight) related to the changes in seed yield response to plant density for soybean in North America. During 2013 and 2014, a total of 78 yield‐to‐plant density responses were evaluated in different regions of the United States and Canada. A soybean database evaluating multiple seeding rates ranging from 170,000 to 670,000 seeds ha−1 was collected, including final number of plants, seed yield, and its components (seed number and weight). The data was classified in YEs: low (LYE, <4 Mg ha−1), medium (MYE, 4–4.3 Mg ha−1), and high (HYE, >4.3 Mg ha−1). The main outcomes were: (i) AOPD increased by 24% from HYE to LYE, (ii) per‐plant yield increased due to a decrease in plant density: HYE > MYE > LYE, and (iii) per‐plant yield was mainly driven by seed number across plant densities within a YE, but both yield components influenced per‐plant yield across YEs. This study presents the first attempt to investigate the seed yield‐to‐plant density relationship via the understanding of plant establishment and yield components and by exploring the influence of weather variables defining soybean YEs.

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Core Ideas Soybean yield response to seeding rate was dependent on yield environment. Optimum seeding rate increased as yield environments were reduced. Seeding rate could be reduced by 18% for high‐yielding relative to low‐yielding environments, without penalizing yields. Planting date interacts with seed yield response to seeding rate, optimum seeding rates increase with late planting. For high‐yielding environment, late planting time decreased yields regardless of the seeding rate. Optimizing seed inputs while increasing farming profit is the main purpose of variable rate seeding (VRS) technology adoption. Previous studies in corn (Zea mays L.) suggested that optimal seeding rates increase as yield productivity level increased. For soybean [Glycine max (L.) Merr.], optimal yield‐to‐seeding rate by yield level has not been fully investigated, representing a scientific knowledge gap. Therefore, a dataset was collected from 109 replicated field trials from Southern Brazil (2180 experimental units) presenting the following objectives: (i) identify the optimum seeding rate at varying yield levels (herein termed as yield environments), and (ii) explore the contribution of management factors (i.e., seeding rate, planting date, row spacing, maturity groups, growing season, yield environment, and ecological region) on soybean seed yield. Hierarchical modeling and Bayesian statistical inference were used to predict optimum seeding rate at varying yield environments, while conditional inference tree analysis was explored to identify and rank factors contributing to yield variation. The main results were: (i) soybean seeding rate increased from high‐ to low‐yielding environments; (ii) seeding rate could be reduced by 18% in high‐yielding (>5 Mg ha−1) relative to the low‐yielding (<4 Mg ha−1) environments, without penalizing yields. For improving site‐specific soybean seeding rate prescriptions, future studies should focus on the physiological mechanisms underpinning yield formation and on understanding the main factors (soil × plant × weather) contributing to the differential optimum seeding rate response.