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Boundary line (BL) methodology is widely used to assess yield gaps and infer causes, yet different BL fitting methods can produce inconsistent outputs and recommendations. This study compared binning, BOLIDES, quantile regression, and the censored bivariate normal model (cbvn) across England, East Africa, and an Ethiopian nutrient omission trial, testing agreement, estimating critical nutrient concentrations, and gathering stakeholder preferences.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/evaluating-boundary-line-fitting-approaches-for-detecting-yield-limiting-factors-and-critical-soil-nutrient-concentrations/154107/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/evaluating-boundary-line-fitting-approaches-for-detecting-yield-limiting-factors-and-critical-soil-nutrient-concentrations/154107.png","ImageObject",300,407,{"name":92,"@type":93},"Cart","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-07","2026-08-28",true,{"@type":102,"interactionType":103,"userInteractionCount":52},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"Why is boundary line (BL) methodology important for closing yield gaps?","Question",{"text":112,"@type":113},"BL methodology benchmarks crop yield and helps identify the likely causes of yield gaps by estimating most-limiting factors and critical nutrient concentrations.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"Which boundary line fitting methods are evaluated in the study?",{"text":117,"@type":113},"The study compares four BL fitting approaches: binning, BOLIDES, quantile regression (QR), and the censored bivariate normal model (cbvn).",{"name":119,"@type":110,"acceptedAnswer":120},"What is the study’s key finding about critical nutrient concentration estimation?",{"text":121,"@type":113},"Most critical nutrient concentration estimates fall within the cbvn uncertainty interval, but deviations occur in some datasets; the study recommends cbvn for critical nutrient estimation due to its uncertainty quantification.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},154107,1787888095,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":52,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":129,"read_time":144,"preview_page_count":4},18829141979164,"https://eur-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8","European Journal of Agronomy 170 (2025) 127744  \n| Evaluating boundary line fitting approaches for detecting yield-limiting factors and critical soil nutrient concentrations\u003Cbr>C. Miti a,b ,∗, A.E. Milne b, K.E. Giller c, R.M. Lark a\u003Cbr>a School of Biosciences, University of Nottingham, Sutton Bonington Campus, Loughborough, Leicestershire LE12 5RD, UK b Net Zero and Resilient Farming, Rothamsted Research, Harpenden, Hertfordshire AL5 2JQ, UK\u003Cbr>c Plant Production Systems, Wageningen University, P.O Box 430, 6700AK Wageningen, The Netherlands |  | |\n| --- | --- | --- |\n| A R T I C L E I N F O\u003Cbr>Dataset link: [https://CRAN.R-project.org/pack](https://CRAN.R-project.org/pack)age=BLA, [https://data.cimmyt.org/dataset.xht](https://data.cimmyt.org/dataset.xht)[ml?persistentId=hdl:11529/11015](ml?persistentId=hdl:11529/11015)\u003Cbr>Keywords:\u003Cbr>Boundary lines\u003Cbr>Most-limiting factor\u003Cbr>Critical nutrient concentration | A B S T R A C T\u003Cbr>Closing the crop yield gap is critical to meeting rising global food demand driven by population growth. The boundary line (BL) methodology is widely used to assess yield gaps and identify its causes. However, the lack of a standard BL fitting method can lead to inconsistencies in outputs and recommendations. This study compared four BL fitting methods, binning, BOLIDES, quantile regression (QR), and the censored bivariate normal model (cbvn), in determining the most-limiting factor and critical values (􀁸crit ) across three datasets from England (Dataset 1), East Africa (Dataset 2), and a nutrient omission-trial from Ethiopia (Dataset 3). The most-limiting factor was identified using the Law of the Minimum and experimentally via omission-trials. Agreement among BL fitting methods and between BL methodology and omission-trials was tested using Cohen/Fleiss 􀀔-statistic. The consistency of 􀁸crit from BL fitting methods was assessed using the 95% confidence interval (CI) of cbvn and compared to RB209 guidelines (Dataset 1 only). Additionally, stakeholder preferences/opinions on BL fitting methods were gathered via workshops in Nairobi and Harare. Results showed BL fitting methods generally identified the most-limiting factor consistently (􀀔 > 0.4), but inconsistencies were observed for binning and QR methods. Experimentally-determined most-limiting factors were inconsistent with BL outputs (􀀔 \u003C 0.2). While most 􀁸crit estimates fell within the cbvn CI, deviations occurred, especially in Dataset 2. BL fitting methods often underestimated 􀁸crit compared to RB209 guidelines. Stakeholder exercise showed no evidence (p = 0.56) against the null hypothesis of uniform ranking of BL fitting methods. The study highlights that while BL fitting methods show general consistency, discrepancies with experimentally determined results exist. Despite consistent results, cbvn is recommended for critical nutrient estimation due to its uncertainty quantification, supporting probabilistic insights for agronomic decisions. |  |\n\n1. Introduction  \nGlobal increase in population coupled with the adverse effects of climate change and the reduction in agricultural land due to degradation threatens future global food security (Giller et al., 2021; Kopittke et al., 2019). To counter this, agricultural production must be increased. This can be achieved by agricultural intensification through closing crop yield gaps which can avoid the need for expansion of the landarea under agriculture (Godfray et al., 2010; Foley et al., 2011). The process to close the yield gap should start with its quantification and the determination of its possible causes. Management options can be identified and policies adopted that favour the identified management options (FAO and DWFI, 2015). Various methods for bench-marking yield to determine the yield gaps have been described (FAO and DWFI, 2015). One method, which has been widely used in many agronomic  \nstudies, is the boundary line methodology (Sadras, 2020). This methodology allows for bench-marking yie","cbCaijY6T2U23A51","https://ap.wps.com/l/cbCaijY6T2U23A51","pdf",3116977,17,"English","# Introduction\n## Boundary line methodology overview\n## Development of boundary line fitting methods","[{\"question\":\"Why is boundary line (BL) methodology important for closing yield gaps?\",\"answer\":\"BL methodology benchmarks crop yield and helps identify the likely causes of yield gaps by estimating most-limiting factors and critical nutrient concentrations.\"},{\"question\":\"Which boundary line fitting methods are evaluated in the study?\",\"answer\":\"The study compares four BL fitting approaches: binning, BOLIDES, quantile regression (QR), and the censored bivariate normal model (cbvn).\"},{\"question\":\"What is the study’s key finding about critical nutrient concentration estimation?\",\"answer\":\"Most critical nutrient concentration estimates fall within the cbvn uncertainty interval, but deviations occur in some datasets; the study recommends cbvn for critical nutrient estimation due to its uncertainty quantification.\"}]","Evaluating boundary line fitting approaches for detecting yield-limiting factors and critical soil nutrient concentrations | PDF",43]