Fig 1.
(A–C) Large-scale to small-scale overviews of the network. Each node represents a food, and nodes are connected through links that reflect the similarities between the nutrient contents of foods. The network in (A) is composed of animal-derived (left) and plant-derived (right) foods. A part of the animal-derived foods is magnified in (B), which shows seven different clusters of foods. The members of one of these clusters, the cluster ‘Finfish (with some shellfish and poultry)’, are shown in (C). In (A–C), each node is colored according to the food category. The size of each node corresponds to the nutritional fitness (NF) of the food (Fig. 2A and 2B). For visual clarity, we only show the topologically-informative connections between the foods (represented by links with the same thickness), and we omit six foods that have loose connections to the network (see S1 Appendix, Section 3.3 for details).
Fig 2.
Characteristics of nutritional fitness (NF).
(A) Flow chart for calculating NF. See S1 Appendix, Section 4.1 for the detailed procedures of the flow chart. At the end, we assign NF = log(f+1)/log(N+1) to each food, where f is the number of irreducible food sets that include the food, and N is the number of all irreducible food sets. An irreducible food set is defined as a set of different foods that satisfies the following two conditions: it meets our daily nutrient demands in its entirety, and no set is a superset of another set. We limit the number of different foods in each irreducible food set and the total weight of foods therein (Materials and Methods section). A large NF suggests that the food is nutritionally favorable. (B) NFs of foods, sorted in descending order. (C) NF versus price (per weight) for each food (gray). The blue line indicates the average prices along NFs. (D) NFs of foods (average and standard deviation) in each food cluster of the protein-rich category. Clusters are abbreviated as follows. F1: Finfish (with some shellfish and poultry); L: Animal liver; M: Milk; S: Shellfish (with some mollusks); E: Eggs; FP: Finfish and poultry (with some veal); PR: Pork (with some veal); B: Beef (with some lamb and poultry); F2: Finfish (mixed); PL: Poultry (with some beef and lamb).
Table 1.
Examples of bottleneck nutrients for high nutritional fitness (NF).
For each food category, we list the two most favorable and two most unfavorable bottleneck nutrients based on the regression coefficients (Materials and Methods section). If the total number of favorable or unfavorable bottleneck nutrients for a given food category was less than two, we listed all. The full list of bottleneck nutrients is available in Table C in S1 Appendix, which indicates choline is a favorable bottleneck nutrient in every food category.
Fig 3.
Correlations between the abundances of two nutrients (one nutrient is favorable and the other nutrient is unfavorable for NF) across the foods in each food category.
For highly synergistic nutrient pairs (Φij > 2.0; blue) and the other pairs (Φij ≤ 2.0; grey), we present the respective averages and standard deviations of the correlations (see the Materials and Methods section and S1 Appendix, Section 6.2).
Table 2.
Synergistic bottleneck pairs for high NF, which are composed of non-bottleneck nutrients.
For each food category, we list synergistic bottleneck pairs (Φij > 2.0) composed of nutrients (in the second and third columns) that are not bottleneck nutrients themselves for high NF in that food category. Only food in which a given pair of nutrients exhibits the strongest synergism (among multiple foods) for high NF is shown in the fourth column. In the fifth column, ‘F’ (‘U’) denotes that the nutrient is ‘favorable’ (‘unfavorable’) for a high NF of the food in the fourth column (see the Materials and Methods section). For example, ‘F, U’ indicates that a nutrient in the second column is favorable, whereas the nutrient in the third column is unfavorable. This table shows only the cases with a definite ‘F’ or ‘U’ (Materials and Methods section). Foods in the low-calorie category do not have synergistic pairs of non-bottleneck nutrients.
Fig 4.
The nutrient-nutrient network.
Each node represents a nutrient, and the nodes are connected through correlations between the abundances of nutrients across all foods. The network is composed of three major groups of nutrients that are densely connected to one another through positive correlations. Between groups, nutrients have only sparsely positive or frequently negative correlations (S1 Appendix, Section 7.3): the top and left side is for the first group, the right side is for the second group, and the bottom side is for the third group. Each node is colored according to the nutrient type. The shape of each node indicates the hierarchical or ‘taxonomic’ level of a nutrient, from ‘Highest’ (a general class of nutrients) to ‘Lowest’ (a specific nutrient). The color and thickness of each link correspond to the sign and magnitude of the correlation, respectively. Here, we only show the significant nutrients and correlations described in S1 Appendix, Section 7.2, and we omit seven nutrients which don’t have significant correlations with any others. We also omit amino acids because their correlations with other nutrients are very similar to the correlations of the total protein with others (thus, these correlations are redundant for visualization).