This study—based on systematic testing of 30 different wheat crop models against field experiments—shows that many wheat models simulate yields well, but with reduced accuracy at higher temperatures. Extrapolation of the model ensemble response indicates that global wheat production will fall by 6% for each 1 °C increase in temperature. Crop models are essential tools for assessing the threat of climate change to local and global food production1. Present models used to predict wheat grain yield are highly uncertain when simulating how crops respond to temperature2. Here we systematically tested 30 different wheat crop models of the Agricultural Model Intercomparison and Improvement Project against field experiments in which growing season mean temperatures ranged from 15 °C to 32 °C, including experiments with artificial heating. Many models simulated yields well, but were less accurate at higher temperatures. The model ensemble median was consistently more accurate in simulating the crop temperature response than any single model, regardless of the input information used. Extrapolating the model ensemble temperature response indicates that warming is already slowing yield gains at a majority of wheat-growing locations. Global wheat production is estimated to fall by 6% for each °C of further temperature increase and become more variable over space and time.

Fluorescence polarization, nuclear magnetic resonance, and electron spin resonance experiments on appropriately labeled proteins give information about various angular correlation functions or correlation times for the reorientation of the label. Expressions are derived relating these correlation functions and times to the rotation rate of the rigid protein and the rates of the internal rotations between the label and the protein. The effective correlation time for the label is simply a series of factors times the correlation time for the rigid protein. Each internal rotation which is much faster than the protein rotation contributes a single factor ½(3 cos²θ−1)², where θ is the angle from the internal rotation axis of interest to the next internal rotation axis, or, for the last internal rotation, to the label axis of interest. The effect of internal rotations which are much slower than the protein rotation rate is the same as the effect of averaging over molecules with a permanent geometry corresponding to the possible orientations about the internal rotation axis.