François Mariotti
email: francois.mariotti@agroparistech.fr

Jean-François Huneau

Hélène Fouillet

No Nutritional Lessons Can Be Learned from a Misspecified

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Dear Editor: 1

In an article published recently in The Journal of Nutrition, Vieux et al. used a diet optimization model 2 to conclude that nutritionally adequate diets need to contain approximately >50% animal protein [START_REF] Vieux | Approximately Half of Total Protein Intake by 64 Adults must be Animal-Based to Meet Non-Protein Nutrient-Based Recommendations with 65 Variation Due to Age and Sex[END_REF]. 3

We have many concerns about this work. 4

Diet modeling using optimization can be used for two purposes: to identify which is the "best" diet in 5 a well-established context, which is useful to inform food-based dietary guidelines (2), or to analyze a 6 nutritional question, which is useful to characterize and understand nutrient issues and dietary 7 levers. In this latter case, which is that addressed by Vieux et al., because diet modeling results 8 depend on the data used and the constraints applied (3, 4), a sensitivity analysis must be conducted 9 to explore how the chosen constraints influence or restrict the solutions identified (5). This is critical 10 to establish the overall significance of the results. Here, unfortunately, the authors provided hardly 11 any indications regarding the influence of their chosen constraints, while they drastically narrowed 12 the domain of feasible dietary solutions, all combined with a flawed research strategy, as we will 13 argue below. 14

Regarding the constraints chosen, the greatest possible consumption of each food item and group 15 was set at the 95 th percentile of intake in the old survey used by the authors, for reasons of 16 theoretical "acceptability". It is difficult to agree that intakes higher than the 95 th percentile 17 consumption observed 16 years ago are simply unattainable in our current context of marked food 18 transition. The food repertoire was also very short, especially regarding plant protein (n=2 for 19 legumes; n=2 for plant-based meat substitutes, vs n=19 for meat) (1). In particular, while legumes are 20 acknowledged as a cornerstone of nutrient-rich healthy plant-based diets, it is striking that they 21 remained embedded in the "starchy food" group and restricted to two food items (boiled beans and 22 lentils). Furthermore, no information was given about the dietary constraints (on the consumption of 23 food items or groups) that were active and therefore limiting for the identification of more plant-24 based dietary solutions. It is not reasonable to study potentially major changes to the share of 25 animal/plant protein based on the premise of such conservative -and indeed outdated -dietary 26 patterns, and capping the consumption of likely dietary levers at binding values. Indeed, such a 27 constraint on legume consumption has been waived in the modelling scenarios that underpin food-28 based dietary guidelines for French women (2). Current dietary guidelines advocating several 29 servings of legumes per week (6) would be considered impossible according to the authors' model. 30

The authors also chose to limit the deviation in food mass and number of food items from the 31 observed diet to arbitrary values, while it was precisely identified as increasing in line with the 32 potential share of plant protein. It was also unusually restrictive to constraint at the same or lower 33

Acknowledgments and statement of authors' contributions to manuscript 4

The authors' responsibilities were as follows: FM drafted the paper and all authors participated actively in critically reviewing of this draft and its revision and read and approved the final manuscript.

The authors report that no funding was received. FM has received research grants for PhD fellowships under his direction by AgroParisTech and INRAE from Terres Univia and Ecotone Foundation, under the aegis of the Fondation de France. . The Ecotone Foundation for biodiversity is founded by the Ecotone Group that sells mainly organic and plant-based foods. HF has received a research grant by INRAE from Roquette, which produces plant-based ingredients.

cost, as this simply discarded all dietary solutions at even a 1% higher cost. This constraint was 34 systematically binding, as recognized by the authors, but they did not investigate the effects of its 35 relaxation. Furthermore, the costs of the food items studied dated from 16 years ago. Given the food 36 price fluctuations seen since then and cruelly illustrated today, such a constraint is inappropriate 37 when trying to study a long-term dietary transition. Indeed, current diets would be considered 38 impossible using their model. 39

Lastly, the authors applied a research strategy that was conceptually flawed in modelling terms. After 40 determining modelled diets containing an increasing share of plant protein under an initial set of 41 constraints, the authors discarded some of the most plant-based solutions using a second set of 42 constraints as a posteriori criteria, such as protein intake adequacy. However, they were unable to 43 prove that another solution which satisfied these a posteriori constraints could not have been found 44 if they had been integrated beforehand. In particular, if a sufficient amount of protein in the 45 modelled diets had logically been required beforehand with other nutritional constraints of the same 46 type, it is possible and indeed likely that a solution would have been found for the share of plant 47 protein rejected by the authors. Diets containing >50% plant protein were thus ruled out due to 48 model misspecification, as a nutritional constraint was omitted. It is certain that an opposite 49 conclusion would have been reached if the authors had omitted the reference values for fiber or 50 saturated fatty acids, rather than protein. 51

In conclusion, there was no sensitivity analysis of the influence of the restrictive and questionable 52 constraints that prevented greener dietary solutions, combined with the a priori omission of a 53 nutritional constraint (sufficient protein intake) that was nevertheless used a posteriori to discard the 54 greenest dietary solutions inadequately built because of this misspecification. This invalidates the 55 authors' conclusion that diets containing <50% animal protein are intrinsically unable to ensure 56 nutritional adequacy. This misleading conclusion, as captured unfortunately by the paper's title, is 57 further contradicted by other literature findings (7-9). In particular, we recently modelled fully 58 nutritionally adequate diets containing only 20% animal protein (9). Diets with a lower share of 59 animal protein are also better for long-term health and the environment (8-10). Finally, because it 60 did not identify critical nutrients or analyze the influence of the many non-nutritional constraints 61 chosen, this work offers no information on what should be considered an obstacle to reducing the 62 share of animal products, which is the question at issue (5).