Root-zone salinity: I. Selecting a product-yield index and response function for crop tolerance

Six empirical functions were compared for describing the product yields of agricultural crops grown while subject to increasing levels of root-zone salinity. The four nonlinear functions fit the test data from a spring wheat (Triticum aestivum L., cv. Biggar) experiment conducted in Canada's Salt Tolerance Testing Facility closer than the two linear functions. Although each of the four nonlinear declining functions could reasonably describe the data, the modified compound-discount equation recorded the lowest root mean square error and the highest R-2 value. Additional response data using the nonlinear discount function obtained from 33 separate trials averaged 11% closer in statistical fit and 45% lower in statistical error than the best linear function. The discount function {Y-r = 1/(1 + [(C/C-50)(exp(SC50))]} follows a sigmoidal form and relates relative yield (Y-r) to a measure of root-zone salinity (C) such as the solute concentration with an electrical conductivity of an equivalent saturated soil paste extract (ECe). This function features two parameters, the salinity level producing 50% of the nonsaline crop yield (C-50) and the absolute value of the general decline in relative yield with salinity at and near C50, the steepness constant (s). These parameters combine to form a single-value, salinity-tolerance index (ST-Index) consisting of the 50% reduction in crop yield (C50) plus the tendency to maintain some product yield as the crop is subjected to increasing salinity levels approaching C-50, i.e., ST-Index = C-50 + s(C-50). The ST-Index for the Biggar wheat registered 6.44. Approximations for C-50 and s can be derived from the threshold salinity (C,) and declining slope (b) parameters of the threshold-slope linear response function [Y-r = 1 - b(C - C-t)]. Procedures for converting C-t to C-50 and b to s offer linkages between these linear and nonlinear response function parameters, and are further explored in this paper's companion. The resulting ST-Index-values equal 6.56, 9.43, and 5.67 for sample field (corn, Zea mays L.), forage (alfalfa, Medicago sativa L. and falcata L.), and vegetable (radish, Raphanus sativus L.) crops, respectively.