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Warming due to climate change has profound impacts on regional crop yields, and this includes impacts from rising mean growing season temperature and heat stress events. Adapting to these two impacts could be substantially different, and the overall contribution of these two factors on the effects of climate warming and crop yield is not known. This study used the improved WheatGrow model, which can reproduce the effects of temperature change and heat stress, along with detailed information from 19 location-specific cultivars and local agronomic management practices at 129 research stations across the main wheat-producing region of China, to quantify the regional impacts of temperature increase and heat stress separately on wheat in China. Historical climate, plus two future low-warming scenarios (1.5 °C/2.0 °C warming above pre-industrial) and one future high-warming scenario (RCP8.5), were applied using the crop model, without considering elevated CO₂effects. The results showed that heat stress and its yield impact were more severe in the cooler northern sub-regions than the warmer southern sub-regions with historical and future warming scenarios. Heat stress was estimated to reduce wheat yield in most of northern sub-regions by 2.0%–4.0% (up to 29% in extreme years) under the historical climate. Climate warming is projected to increase heat stress events in frequency and extent, especially in northern sub-regions. Surprisingly, higher warming did not result in more yield-impacting heat stress compared to low-warming, due to advanced phenology with mean warming and finally avoiding heat stress events during grain filling in summer. Most negative impacts of climate warming are attributed to increasing mean growing-season temperature, while changes in heat stress are projected to reduce wheat yields by an additional 1.0%–1.5% in northern sub-regions. Adapting to climate change in China must consider the different regional and temperature impacts to be effective.

The nonlinear responses of species to environmental variability can play an important role in the maintenance of ecological diversity. Nonetheless, many models use parametric nonlinear terms which pre‐determine the ecological conclusions. Motivated by this concern, we study the estimate of the second derivative (curvature) of the link function in a functional single index model. Since the coefficient function and the link function are both unknown, the estimate is expressed as a nested optimization. We first estimate the coefficient function by minimizing squared error where the link function is estimated with a Nadaraya‐Watson estimator for each candidate coefficient function. The first and second derivatives of the link function are then estimated via local‐quadratic regression using the estimated coefficient function. In this paper, we derive a convergence rate for the curvature of the nonlinear response. In addition, we prove that the argument of the linear predictor can be estimated root‐nconsistently. However, practical implementation of the method requires solving a nonlinear optimization problem, and our results show that the estimates of the link function and the coefficient function are quite sensitive to the choices of starting values.