## 3 Results  
First, we extracted data on water temperature published by the Japan Meteorological Agency. Since water temperature was reported as daily values, these were transformed into monthly data (Figure 2). This scatter plot shows that the temperature of all sea areas in this study tended to peak around August and reached their nadir from January to March. Since the temperature range was 15 \({}^{\circ}\)C-30 \({}^{\circ}\)C, we decided to regard 25 \({}^{\circ}\)C or more as \"hot\" water, 20 \({}^{\circ}\)C or less as \"cold\" water, and the range between these as \"lukewarm\" water. The shape represents the year. The color shows the measurement location in Figure 1. The point represents the monthly average. The horizontal line in the figure indicates the boundary of the temperature zone between hot and cold water. Next, we clustered data of fish collected in each sea area with water temperature using the i-means. We attempted to build multiple clusters; however, some types of fish only formed a single cluster; hence, we classified them into two groups. Using the cluster center and each variable weighted by the Mahalanobis' distance, the distance between each sample and the cluster to which it belonged was computed (Figure 3). The boxplot showed that the clusters were generally well-formed, indicating the clear differentiation of some samples. Figure 3: NMR data dotplot of Mahalanobis’ distance to the centers of groups separated by i-means. Score indicates Mahalanobis’ distance of the group classified by the i-means method. Dots indicate scores for individual samples, and the central horizontal line indicates the mean. The short vertical line represents the range of \(\pm 1\) standard deviation. It can be seen that some data deviate from the average. Figure 2: Changes in water temperature from 2011 to 2015. Subsequently, individual fish were ranked in the terms of NMR and NGS data and organized into quartiles. An association analysis was conducted with water temperature data (Figure 4). Figure 4A shows that unstable samples, with large deviations in Mahalanobis' distance, were more common in small Periciformes in a cold environment. A strong relationship between them was also shown via NMR. Low concentrations of anserine were strongly associated with unstable metabolism. However, the steady state, close to the vector center, was observed in hot water environments (Figure 4B). Gut microbe population occurrence, particularly proteobacteria, seemed to be associated with higher water temperature changes. Finally, we performed the Bayesian network analysis, an artificial neural network, using factors that were linked to unstable or temperature information in association analysis (Figure 5). We decided on a directed acyclic graph from origin data and bootstrapped to predict connection strength. In the NMR data, the fish metabolites that experienced the environmental effects of cold water showed a direct link with serine, valine, inosine, and glycerol (Figure 5A). There was also a strong connection between anserine and beta-alanine. However, the hot water conditions exerted only the direct effect of alanine and valine, but it appears to eventually affect organic acids (Figure 5A). In the result of NGS data, the cold water environment was strongly related to Gram-positive bacteria, such as actinobacteria and firmicutes, and was also weakly related to cyanobacteria (Figure 5B). Alternatively, the experience of the hot water environment appeared to be related to plantomycetes and proteobacteria. Moreover, the current hot water affected various other bacterial groups (Figure 5B). Figure 4: Network diagram of a priori association analysis of NMR and NGS data: (**A**) network of unstable state association factors; red boxes indicate categories; (**B**) network of stable state association factors; (**C**) network of NGS and temperature.