Climate and landscape mediate patterns of low lentil productivity in Nepal

The STATA statistical program was used to estimate the maximum likelihood estimation of parameters for Eqs (2) and (3) based on a Cobb-Douglas type functional form. Our dataset contained 128 cases of complete crop failure and, hence, reported zero yield; these cases were omitted from the stochastic frontier analysis in order to avoid biased estimates of the production function. However, to crosscheck the robustness of our findings we esti- mated a Tobit model [66], which can accommodate zero output (yield) data, in addition to the stochastic frontier production function. The Tobit model has been widely applied when the dependent variable contains an accumulation of observations at zero [67–71]. The definitions and summary statistics of all variables included in the model are presented in the Table 1. The quantity of the lentil grain yield harvested by the farmers is the dependent variable, which is regressed with a number of farm input variables. The farm input variables used in the current stochastic frontier analysis are of two types. The first type of variable included in the models are continuous in nature and are: cultivated lentil land, labor, non- labor capital, amount of seed, amount of nitrogen, phosphorus and potassium, and amount of rainfall and average temperature during the lentil production period. The second type of vari- ables included in the models are dummy in nature and are related to soil types, diseases, water- logging, variety, and production ecologies for lentil farming. Finally, we also included the

interaction of rainfall with lowland production ecology in the model. The variables used for technical efficiency analysis are presented in Table 1 and most of the variables are included in the model as suggested by Bravo-Ureta and Pinheiro [72]. Some of the variables used in technical inefficiency determinant analysis are based on site-specific con- siderations. Inclusion of a gender variable in the model differentiates the potential role of gen- der in technical efficiency; in our case almost 80% of households were headed by a male. Furthermore, farming experiences influence the technical efficiency of lentil farming and we expect that farming experience is positively associated with technical efficiency. We included cultivated land and lentil-specialized farms (i.e. >50% of winter cropped area in lentil) as potential technical efficiency determinants. While we expect that cultivated land has an inverse relationship with technical efficiency as farmers with limited land resources may have incen- tives to increase yields through meticulous crop and input management [73], the lentil-special- ized farms are expected to have a positive relationship. Finally, we included the on-farm labor wage rate and labor availability variables; the former is expected to have a negative relationship with technical efficiency while the latter is expected to have a positive relationship. Simulating Stemphylium blight disease severity simulation using the Stempedia model The Stempedia model predicts the potential severity of Stemphylium blight disease and associ-

ated yield reductions in lentil based on sowing date, first flowering date, and daily weather; model performance has been verified in western Nepal [49]. The model assumes that inoculum does not limit disease progression. In our study, Stempedia is used to predict mean and inter- annual variations in disease severity risk in Banke district as a representative production envi- ronment for lentil in western Nepal. Crop characterization data was derived from on-farm and on-station experimental trials conducted in the region. To drive the model, long-term (1985– 2015) weather data for rainfall and minimum and maximum temperature were used from Banke district, with additional data for solar radiation and relative humidity retrieved from NASA’s POWER datasets [74]. Lentil variety Khajura-2, commonly grown by farmers in the western Terai, was used for the simulations. The model was run for nine different seeding dates at 10-day intervals starting from 1st October to 20th December. Seeding time of lentil PLOS ONE Climate and landscape mediate low lentil productivity PLOS ONE | https://doi.org/10.1371/journal.pone.0231377 April 16, 2020 6 / 19