Segmental interpolation surface: a tool to dissect environmental effects on plant water-use efficiency in drought prone scenarios

Abstract

Water use efficiency (WUE), defined as the ratio of biomass (B) produced per unit of water transpired (E) by plants, is an important determinant of plant productivity. A mathematical approach was developed with the purpose explaining the WUE of two forage legumes (clover and birdsfoot trefoil). The approach applied involved an interpolation method by cubic spline which results in the smoothest curve that fits the set of data points obtained experimentally. The results obtained show the importance of recognizing the WUE as a function of two variables, one represents the supply ({theta}) and the other represents the demand (D). It is important to note that these surfaces generated by the model allowed the estimation of the WUE value for any value of {theta} and any value of D, showing it is able to dissect the effect of both environmental variables on WUE. From the surface generated by the model, a scalar field plot (SFP) was created. Analysis of these SFPs allowed decomposing the environmental effect on B and E parameters defining WUE. The SFPs allow identify, in one picture, what are the environmental conditions and what variable are explaining a high WUE in both species. Spline application for generating SFP could have a significant impact on the quantitative understanding of the WUE and our study represents a first step towards an analytical and integrated view of this parameters.\n\nMathematics Subject Classification 92B05 65D05 65D07 65D10