**1. Introduction**

Improper nitrogen (N) managemen<sup>t</sup> in current crop production systems has become a growing concern among governments, scientists and farmers around the world [1–3]. Optimizing N managemen<sup>t</sup> in agriculture is crucially important for food security, environmental protection, and sustainable development [3–5]. This is particularly true for China, the world's largest producer, consumer and importer of chemical fertilizers [6,7]. Chinese scientists have been promoting a regional optimal N managemen<sup>t</sup> (RONM) strategy to avoid significant over- or under-application problems [5,8]. If it were adopted for maize (*Zea mays* L.) production across China, more than 1.4 million tons N fertilizer and 18.6 million tons of greenhouse gas (GHG) emission would be reduced [9]. Such strategy can be easily adopted by farmers and won't increase their costs. However, due to the significant field-to-field and within-field variability of indigenous soil N supply and crop N demand, this fixed rate and timing strategy will unavoidably result in sub-optimal N managemen<sup>t</sup> in di fferent fields within a region [8,10]. There is a growing interest in China to develop alternative strategies to further improve N use e fficiency (NUE) by better matching N supply with crop N requirement in both space and time [5,6]. Accordingly, it is necessary to determine key factors influencing maize response to N rate and evaluate the potential benefits of alternative N managemen<sup>t</sup> strategies first.

The first and most important factor to consider is soil type di fferences, especially soil texture, which regulates many soil processes such as water retention and infiltration, soil organic matter mineralization and nutrient dynamics and, therefore, influences soil N availability and crop yield [11–14]. There are about 17 di fferent soil types, according to the United States Department of Agriculture (USDA) Soil Taxonomy, in Lishu county, Jilin Province, Northeast China [15]. Recent research indicated that N requirements for maize varied spatially due to the spatial heterogeneity of soil texture [16]. The optimal N rate should be determined according to variability in these soil properties that influence soil N availability or crop response to available N [17]. Loamy clay and loamy sand are two representative soil textures in Northeast China. The loamy clay soil generally has a higher soil organic matter (SOM) content, higher water holding capacity, and stronger ability to fix NH4-N than loamy sand [18]. Loamy sand soils, on the other hand, have generally lower SOM and water holding capacity, but due to greater aeration, they are usually characterized by a higher N mineralization rate than the loamy clay soils [19], causing higher risks of N leaching losses [20]. A recent study from Northeast China indicated that there was a weak parabolic relationship between N rate and maize root length in loamy clay and clay loam soils, but not in the loamy sand soil [21]. That study reported that root length and grain yield were both maximized at the optimal N rate (ONR) of 168–240 kg N ha−<sup>1</sup> across soils and years. Results of Qiu et al. [22] indicated that ONR ranged between 140 and 210 kg ha−<sup>1</sup> for maize in Northeast China across site-years. The results of studies conducted in North America indicated that the maize grown in fine-textured soils had significantly greater response to added N than the maize grown in medium-textured soils [23].

In addition to soil type and soil texture, weather conditions can also have a strong impact on crop growth, soil water and nutrient dynamics, and crop response to N fertilization. Precipitation and temperature have been found to significantly a ffect maize grain yield, soil mineral N, and maize response to N [24–27]. The interaction between soil properties and weather conditions controls the soil water and nutrient availability as well as crop yield potential during the growing season [28,29]. Due to the spatial and temporal variations in crop N demand and soil N supply and losses, crop responses to N fertilizer may vary both between and within soils under di fferent weather conditions [30–32]. This can result in significant changes of ONR in space and time [33–35]. It has been found that maize yield response to N fertilization could be enhanced by abundant and well-distributed rainfall, and accumulated maize heat units [23]. Therefore, weather conditions should also be taken in account when determining the ONR for di fferent soils.

Planting density is often considered one of the most important crop managemen<sup>t</sup> practices to improve grain yield and NUE for maize production [36–38]. An optimal planting density is needed together with a matching optimal N rate to ensure appropriate aboveground and underground plant growth through different utilization of solar radiation and soil nutrients [38–40]. Hence, the maximum maize grain yield in a specific environment (related to soil and weather conditions) may be achieved [41].

So far, few studies have explored the effects of soil type (texture), weather condition, and planting density on the economic optimal N rate (EONR) for maize production, especially in Northeast China. Therefore, the objectives of this study were to (1) determine the EONR as affected by soil type, weather condition and planting density, and (2) evaluate the potential benefits of applying soil-specific (SS), soil- and year-specific (SYS), and soil-, year- and density-specific (SYDS) EONR for maize production in Northeast China.
