Climate and landscape mediate patterns of low lentil productivity in Nepal

ranges from 1.09 to 7.18, with a mean value of 2.12 in the case of the Tobit model, indicating no signal detection for multicollinearity. Furthermore, the Cobb-Douglas type production function in agriculture is expected to follow a constant returns to scale (CRS), i.e., doubling all of the inputs increases the output by the same proportion [77]. However, since environment and/or climate related variables (rainfall and temperature) are not under the farms direct con- trol and doubling these inputs may result excessive waterlogging and/or extreme drought in crop leading to crop senescence, we excluded these variables while conducting test against con- stant returns to scale. This means that the sum of partial production elasticities should be one and the test on respective regression coefficient failed to reject the null hypothesis that their sum is one, indicating the existence of constant returns to scale in the production function. Parameter estimates in the stochastic production function for lentil farming in western Nepal. The maximum likelihood estimates for the parameters in the stochastic frontier model as defined in Eq (2) are presented in Table 3. The slope coefficient defines the output elasticity of inputs and the estimated signs of parameters are as expected. The result from max- imum likelihood estimates for the parameters in the stochastic frontier model and Tobit model indicated that lentil production in the wet years was significantly and negatively affected by higher rainfall and waterlogging (Table 3). These results indicate that a 1% increase in sea-

sonal rainfall decreases lentil yield by 0.40% in the stochastic frontier model and the impact magnitude is even higher (1.57%) in the Tobit model. There is a significant interaction effect of rainfall with land type on grain yield, where a 1% increase in rainfall in lowland areas decreases lentil yield by 0.22% in the stochastic frontier model and by 0.36% in the Tobit model (Table 3). The stochastic frontier model shows that farms that suffered waterlogging had a 16.7% lower yield and the impact magnitude in the Tobit model is much higher at 43.6%. A more modest temperature effect was observed with a 1% increase in the average tem- perature decreasing lentil yield by 1.25% in the stochastic frontier model and by 3.4% in the Tobit model. The stochastic frontier model showed that the occurrence of disease in lentil fields signifi- cantly reduces grain yield. Farmers who reported the presence of disease had a 31.5% lower lentil yield than the farmers who did not report disease problems. However, the coefficient of disease was not significant in the Tobit model (Table 3). Among the farmers who do not lose their crop, 78% reported incidence of disease and harvested 206 kg ha-1 lower yields. In gen- eral, farmers could not identify the specific diseases that affect their fields; based on observa- tions from the pathologists from the Nepal Agricultural Research Council (NARC), Stemphyllium leaf blight is the most common and damaging disease of lentil in western Nepal. As expected, our findings are consistent with economic theory that shows that the partial

production elasticities for land, labor, and capital inputs are positively associated with output, and these variables are statistically significant (P< 0.05) in both of the models. However, the magnitude of the elasticities for land, labor, and capital varies across two models. While the magnitude of elasticities for land is larger in the stochastic frontier model (0.798) than in the Tobit model (0.397), the elasticities for labor and non-labor capital are smaller in the stochastic frontier model than in the Tobit model. Seed rate and soil type had a significant positive effect (P < 0.01) on lentil productivity in both models. Yield reduction was significantly higher in the field where improved seed varieties were grown. Similarly, seeding method had significant effect on grain yield, where grain yield was significantly lower for farmers who practiced relay seeding rather than other seeding methods. Further, the model coefficient for nitrogen is positively associated with yield in the stochas- tic frontier model, while this coefficient sign is reversed in the Tobit model, likely because pro- portionally more farmers who applied nitrogen also experienced crop failure. Since this association is unlikely to be causal since applied fertilizer rates were low in all surveyed fields, PLOS ONE Climate and landscape mediate low lentil productivity PLOS ONE | https://doi.org/10.1371/journal.pone.0231377 April 16, 2020 10 / 19