Recent claim of declining climate resilience in European wheat is not supported by the statistics used

Kahiluoto et al. (1) claim that climate resilience of wheat has declined over the past years in Europe. They make several strong statements, including that some countries are “response diversity deserts.” These conclusions are not supported by the statistics used. Here, I review their definitions of these statistics and raise questions regarding their interpretation.

Yield Response

Yield response is computed for each cultivar as the “relative difference in yield between the extreme categories” (1) based on a classification of a given agroclimatic variable. The cultivar-by-category means are computed from a linear mixed model lacking all lower-order interactions, which are likely to be important, given the complexities of the data (2, 3). It is also unclear how the difference was turned into a relative one (i.e., What is the denominator of the ratio computed?).

Response Diversity

Cultivars are clustered using yield responses to 43 agroclimatic variables. Shannon’s index $H=-{\displaystyle \sum _{k=1}^K{p}_k\ln p_k}$ is computed for each country and year, where p_k is the proportion of cultivated area for cluster k. The value of H is independent of how different or similar the responses are between clusters. Any observed change of H over years (figure 1 of ref. 1) is only due to change of cluster areas. Any change in genotypic composition of clusters over years is not reflected in the analysis. Thus, H does not inform about a change in the responses. To assess any change in diversity of the responses, it would be necessary to compute measures of variability among the responses themselves, such as variances.

Climate resilience is not properly defined, but the authors state that response diversity is a key determinant of climate resilience. Throughout the paper, the notion of climate resilience seems to be synonymous with that of response diversity (figures 1 and 3 of ref. 1) and so suffers from the same problems.

Yield stability is defined in terms of a pooled SD (SD_pooled) of yield responses of cultivars within clusters. The rationale for this definition is unclear. Yield stability is usually defined as a cultivar-specific property based on the variability of yields in different environments for the same cultivar (4, 5), and this can include the response to environmental gradients (4, 6). By contrast, SD_pooled is a between-cultivar measure of variability. It is also not clear why a small SD_pooled is deemed desirable, because this would correspond to a reduced variability (or “diversity”) of responses.

Figure 2 of ref. 1 shows that SD_pooled declines with accumulating number of clusters obtained by Ward’s method, which merges clusters so that within-cluster variance is minimized. This plot just shows that the Ward method worked properly. But the authors conclude that “combining cultivars from different clusters increases the yield stability under weather variability.” This conclusion is unwarranted. If we combine cultivars from all clusters and then ask how variable the responses are, we need to also account for the between-cluster variance, but SD_pooled only accounts for within-cluster variance. Suppose we decide to select all cultivars, then the variability between cultivars should be the same no matter how many clusters were previously formed.