Mean yields have grown rapidly over the second half of the 20th century and are now several times larger than yield levels around 1900. Minimum and maximum yields increased, too, indicating that yield losses have been better mitigated (higher minima) and that yield potentials did increase (higher maxima). But these trends have stalled in recent decades on a substantial fraction of the cultivated area (at least one quarter) for several crops: wine, winter wheat, barley, oats, durum wheat and sunflower. This is, in particular, not the case for maize. A stalling in growth rates is also observed for maximum yields in the majority of those crops. Minimum yields are not increasing further in some of the stagnating crops, possibly indicating that harvest losses are already at a basal level that is hard to decrease further.

The very high correlation between trends of yields and of N and K 2 O fertilizer application is to be expected given the strong negative influence of insufficient nutrient supply on average yield levels15 (though fertilization timing and crop-specific dosage are not recorded in this departmental data set). Durum wheat and wine show lower correlations with N, and durum wheat even negative correlation with K 2 O trends. This may indicate that lacking nutrients are not the main yield-limiting factors for wine and durum wheat. Yield trends are not correlated with P 2 O 5 supply, though, and again even strongly negative for durum wheat. A possible explanation is the shape of the trend for P 2 O 5 application (SI Fig. 11): it decreases substantially after 1980, but yields do not – indicating that the comparably low amount of P 2 O 5 addition is already sufficient for current yield levels, as French soils are rich in phosphate16, and phosphate is an element that accumulates in soils being adsorbed on clay particles (iron and aluminium oxides) from previous years of application17,18,19. Trend shape may also explain the lower correlation of yields with K 2 O in comparison to N. Since the fertilizer application data used here is not crop-specific, it is difficult to draw conclusions about nutrient supply and yield trends for single crops. A further caveat is that only the application rates of mineral fertilizer were considered, but organic fertilizer application can be equally important in some departments16. Finally, increased fertilizer application rates are not the only reason for increased yields, as enhanced genotypes, changing soil attributes and management choices also play a decisive role.

The Northern parts of France seem to offer consistently better growing conditions for crops, evidenced by significantly higher mean yields, with maize and wine as the only exceptions. Reasons for better crop growth in the North include more favourable temperatures (especially for winter crops), higher precipitation, deeper soils with high levels of organic matter20 and a higher fertilizer use (SI Fig. 10). Given the uneven distribution of crop performance in France, it would be interesting to evaluate whether the current allocation of crops and croplands is optimal – similar to a study by Ben-Ari and Makowski21 who calculated stability gains in major crops by re-distributing crop land fractions over the globe into regions with lower variability. The widening of the intra-country productivity gap (between clusters) over time may indicate that non-climatic and non-edaphic growing conditions could be improved in regions showing low yield levels. Furthermore, follow-up investigations on, for example, the share of weather-dependent yield variation, may benefit from stratifying the country into productivity regions to avoid blending of results with confounding non-weather factors.

The increase in absolute yield variability (standard deviation), but decrease in relative variability (CV) over the last century is presumably driven by the increase of genetic potential and thus maximum attainable yields, and by the prevention of severe loss events, likely due to more intensive management (irrigation, fertilizer use, fungicide and herbicide applications). For barley, oats, sunflower and wine, however, recent decades have shown no further decrease of relative yield variability, and even an increase in some departments – which is consistent with slower growth or stagnation of yields. Increased yield variability in recent years (in contrast to an overall decrease since 1900) may be due to increased climate variability, which has to be investigated in a further study. Absolute yield variation may be related to irrigation, as claimed by Hawkins, et al.11, but the results obtained here are counterintuitive (SI Fig. 13). Though some crop standard deviations are significantly correlated with the nationally aggregated area equipped for irrigation (from FAO4), the correlation direction is positive and thus unrealistic as more irrigation is expected to reduce yield variation11. The two crops with negative correlation are sunflower and wine, which are rarely irrigated in France. Furthermore, maize standard deviation is increasing over time, and not diminishing as stated by Hawkins, et al.11. Overall this analysis highlights the importance of sub-national analyses of crop growth with crop-specific irrigation data (which are not yet available) rather than on aggregate national level.

Yield stagnation is detected on substantial fractions of the cropping area for major crops, and is more likely in departments with high average yields. Stagnation could be caused by several factors. First, a physiological yield potential could have been reached22. If stagnation is due to asymptotically decreasing growth when reaching the genetic potential, this would manifest in three further observations: (i) a stalled growth for maximum yields, (ii) higher inter-annual relative variation (i.e. higher CV due to the negative skewness of yield residuals; although higher yield variability may also be caused by more variation in climate, we assume stagnation as an additional, independent source of increased yield variation) and (iii) higher average yields in departments with stagnation as compared to those without stagnation. Except for winter wheat (see also below), none of the crops detected as stagnating fulfils all three criteria.

Second, climatic conditions could recently have changed such that no further increase of crop yields is possible without adequate adaptation, even if the genetic potential was not yet reached. An increased sensitivity of crops to climate variation could be an indicator for a climatic cause of stagnation. The still increasing minimum yields, though, suggest that losses due to adverse climate are not a major reason for mean stagnation (except for wine and sunflower). Previous assessments have indicated that climate change is already visible in crop trends11,12,23,24,25 – thus the question of how much climate changes causes crop stagnation should be further studied.

Third, political decisions, for example in the Common Agricultural Policy (CAP) of the European Union, and an ensuing change of financial incentives or quotas for certain crops could have contributed to lower investment in breeding or a decrease in input use. An example for arbitrary limitation of yield growth is wine: wine yields are stagnating in many French departments. But (reported) yields are kept at an upper threshold for two reasons: limitations of the regional wine-growers labelling associations (termed AOC for Appellation d’Origine Contrôlée) that install a cap on the amount produced, and a preference of the market for quality rather than quantity. An analysis of political causes for yield stagnation would therefore be a valuable extension of this study.

Fourth, changes in crop rotation (like a lower share of legumes or increasing shares of serial monoculture) or soil carbon content could have contributed to stalled growth, as already speculated by Brisson, et al.5. For these assessments, detailed and time-resolved data sets on crop rotation and soil carbon contents are required, which are currently not available on the required spatial level.

Fifth, marginal costs for management interventions could have reached a balance where a further investment into crop production, for example with fertilisation or irrigation, does not pay off at harvest time – resulting in a stable level of both management input and yields, but no further harvest increases. This may partly be the case for potatoes and rapeseed, where yields in departments with stagnation are lower (significantly only for potatoes), which may hint to a secondary importance of these crops and also less investment therein. Changing demand for certain crops may also account for stalling investments and ensuing yield stagnation. The necessary data set on management input for such an analysis does, to our knowledge, not yet exist. The fertilizer data used here is not crop-specific and does not permit such a detailed analysis of reduced input leading to reduced increases.

Sixth, and finally, an increase of relative area share in favour of organically grown crops may lead to average yield stagnation as organic yields are usually lower than those on conventional fields26,27. Yet the share of organic agriculture in France is only about 2.8% for cereals28, such that an increased share of organic agriculture is not assumed as a major reason for stagnation.

Previous studies on yield stagnation in France only treated wheat and maize. The geographic pattern of wheat stagnation detected by Michel and Makowski9 is comparable to ours (Fig. 4). Brisson, et al.5, though analysing only a subset of departments, find stagnating wheat yields for most areas in their subset, and especially in regions with higher average yields – which is in line with our findings. On the national level, we detect a stagnation of wheat yields (SI Fig. 3), in accordance with Calderini and Slafer6, Lin and Huybers8 and Grassini, et al.10. Ray, et al.7 stated wheat yields as stagnating in 80% of crop areas – which is slightly higher than our estimate of 70% of its cropping area (spring and winter wheat combined). Regarding maize, Ray, et al.7 state to find no detectable stagnation in 90% of the area, where we similarly find 97% as non-stagnating, while Grassini, et al.10 identified maize as stagnating on national level – which we do not (despite national yields increasing at lower rates or occasionally decreasing after 2000; Fig. 1). The selection of the best-fitting model among different linear formulations, as practiced by Grassini, et al.10, may thus not be apt for such analysis due to too rigid model formulations.

For sunflower, French growers assume a multitude of possible causes for stagnation, among which are slow genetic potential increase, climate change, non-optimal management on low-yielding soils or monoculture tendencies. It seems, though, that genetic progress for sunflower in experiments has been faster than on actual fields29, such that further explanations are necessary.

In sum, there has been consensus on wheat yield stagnation in a majority of French cropping areas, and we add further evidence to this. For maize, we find a stagnation in only few cropping areas and thus refute the statement by Grassini, et al.10 that maize yields have not improved in recent decades. Our results additionally show that stagnation is not limited to winter wheat but also affects substantial area shares of other crops.

The hypothesis of reaching a yield potential can only serve as a putative, but uncertain explanation for stagnating yields in the case of winter wheat, as there are hints from field trials that genetic gain in wheat yield potential has not stalled5,9. For all other crops that show stagnation further research for the cause(s) is needed, currently impeded by lacking data. Given this lack of knowledge, an outlook on future yield growth rates is furnished with uncertainty. It is obvious that an assumption of sustained yield growth into the future would at best be naïve, even when not accounting for climate change as an additional danger for harvests.

Our stagnation detection method, using a flexible scoring scheme, allows for assessing uncertainty of stagnation and is comparable between crops and departments. The stagnation score depends on the chosen absolute threshold of growth rates, and on the width of the temporal window used for testing (SI Fig. 5). But our results are only altered quantitatively, not qualitatively – that is, a substantial fraction of cultivation areas suffers from non-growing yields under any definition of stagnation. The choice of 0.25% as a detection threshold clearly distinguishes stagnation from growth rates in times of rapid increase, and also lies substantially below the increase rates deemed necessary for the near future2,3. Dependence of results on the choice of stagnation definition and threshold – from which all other studies cited above suffer similarly – is inevitable and reflects the fact that the question of stagnation remains open except for very clear cases.

The split of crops between spring and winter cultivars is of relevance, as in some cases (e.g. barley in Haute Saone) both spring and winter growth is considered as likely stagnating – but not so when yields of both varieties are combined. The reason is a changing area share, from exclusively spring barley (1940’s to 1970’s) to almost entirely winter barley in recent years. Since winter barley yields are, on average, higher than those of spring barley, the combined harvest of both crops keeps increasing when spring barley is replaced by winter barley, even when winter barley itself is not increasing any more. A further promotion of winter cultivars, where weather is appropriate, may therefore be helpful for sustaining combined yield growth. Such a split between spring and winter varieties is not usually performed in other studies, despite its obvious practical relevance.

During the time frame of this data set, the two world wars (1914–18 and 1939–45) occurred, with significant aftermaths for economic and agricultural life. The turmoil of these times is reflected in the data, with lower absolute yields (Fig. 1) and higher variability (Fig. 4), but also strong growth after the war in the 1940’s and 1950’s (Fig. 2) – possibly due to a base effect of low yields. It is, furthermore, not unlikely that the quality of the census procedure for recording agricultural performance suffered during war times such that values in these years are engrained with higher uncertainty.

In conclusion, French crop yields have developed to higher mean yields and lower relative variability over the full 20th and beginning of the 21st century. The continuation of these positive trends is of importance for local and global food availability, as France is a major producer of several staple crops like maize and wheat, and is exporting to many countries especially in Northern Africa. Yet recent stagnation for some crops, in particular for wheat, calls into question whether positive trends can be maintained, and merits further research into the underlying causes. In performing such examinations, crop-specific fertilizer dosage per department, the outbreaks and severities of pests and diseases (specific for each crop and department), the performance of field trials to assess recent gains in genetic potential, and a correlation with climate data are instrumental.