Boundary line models for soil nutrient concentrations and wheat yield in national‐scale datasets

Abstract

In boundary line analysis a biological response (e.g., crop yield) is assumed to be a function of a variable (e.g., soil nutrient concentration), which limits the response in only some subset of observations because other limiting factors also apply. The response function is therefore expressed by an upper boundary of the plot of the response against the variable. This model has been used in various branches of soil science. In this paper we apply it to the analysis of some large datasets, originating from commercial farms in England and Wales, on the recorded yield of wheat and measured concentrations of soil nutrients in within-field soil management zones.We considered boundary line models for the effects of potassium (K), phosphorus (P) and magnesium (Mg) on yield, comparing the model with a simple bivariate normal distribution or a bivariate normal censored at a constant maximum yield. We were able to show, using likelihood-based methods, that the boundary line model was preferable in most cases. The boundary line model suggested that the standard RB209 soil nutrient index values (Agriculture and Horticulture Development Board, nutrient management guide (RB209), 2017) are robust and apply at the within-field scale. However, there was evidence that wheat yield could respond to additional Mg at concentrations above index 0, contrary to RB209 guidelines.Furthermore, there was evidence that the boundary line model for yield and P differs between soils at different pH and depth intervals, suggesting that shallow soils with larger pH require a larger target P index than others. Highlights• Boundary line analysis is one way to examine how soil variables influence crop yield in large datasets. • We showed that boundary line models could be applied to large datasets on soil nutrients and crop yield. • The resulting models are consistent with current practice for P and K, but not for Mg. • Models suggest that more refined recommendations for P requirement could be based on soil pH and depth. K E Y W O R D Sagricultural management, fertilization, modelling

Boundary line analysis and machine learning models to identify critical soil values for major crops in Guatemala

“…Similar to Shatar and McBratney (2004), we found the flexibility of the spline function worked well for identifying soil variable thresholds. Another common method used in BLA is the linear plateau function (Hajjarpoor et al., 2018; Lark et al., 2020). However, within our study a linear plateau would not accurately capture the parabolic effect of pH.…”

“…Compared to more advanced statistical methods for estimating boundary lines, the approach presented here does have some limitations. BLA methods have been criticized for their lack of statistical grounding and inconsistency in methods, which can produce differing results depending on methods used (Lark et al, 2020). However, in this case data used were non-normal which prevented calculation of boundary lines using more robust methods such as the maximum likelihood approaches used by Milne et al (2006), Lark and Milne (2016), or Lark et al (2020).…”

“…Subsequent approaches have calculated boundary lines manually using maximum values from data clouds (Hajjarpoor et al., 2018; Lewandowski & Schmidt, 2006), or divided the environmental variable into “buckets” or moving windows along the x ‐axis to take the maximum or upper quantile of each bucket (Schmidt et al., 2000; Shatar & McBratney, 2004). Some researchers have also used more advanced statistical methods to derive boundary lines, though these methods have been less widely applied (Lark & Milne, 2016; Lark et al., 2020; Makowski et al., 2007; Milne et al., 2006).…”

Assessing land suitability for rainfed paddy rice production in Zambia

“…These might use process models, or surveys of actual paddy rice yields at locations across Zambia or an analysis of proxy variables for crop yield, e.g. from remote sensor data, both to compare these between the suitability classes obtained here, but also to explore other non-linear effects of multiple factors, possibly using a modelling method such as boundary line analysis (Lark et al, 2020). Furthermore, this study has considered biophysical factors which might control land suitability, but farmers' decisions are not based only on biophysical limitations (Rossiter, 1995).…”

Boundary-Line Approach Macro-Nutrient Standards for Opuntia ficus-indica (L.) Miller Variety “Rojo Pelón” Fruiting

“…The boundary-line is formed when all values for two variables are plotted and a line enclosing most of these points is established (Michael et al 1985). The boundary-line represents the limiting effect of the independent variable on the dependent one (Webb 1972;Lark 1997); then, it is assumed that all values below such a line result from the effect of another independent variable or a combination of variables that are limiting the dependent variable (Webb 1972). Detailed information regarding B-LA can be obtained from Blanco-Macías et al (2010) and Ali (2018).…”