## 4 Discussion  
We first extracted data from a public database to determine the changes in water temperature (Figure 2). Data showed that even in adjacent sea areas, water temperature could have monthly average differences of 1 \({}^{\circ}\)C-2 \({}^{\circ}\)C, along with clearer annual variations. Figure 5: Network diagram of Bayesian network analysis of NMR and NGS data: (**A**) is a network calculated using NMR data; (**B**) is a network calculated using NGS data. Both diagrams were bootstrapped. Orange squares show hot water condition, and the number indicates elapsed months. On the other hand, blue squares show cold water condition, and the number indicates elapsed months. Green squares show metabolites (in (**A**)) or the phylum of bacteria. The thickness of the arrow indicates the strength of the tie, and the thicker the arrow, the stronger it is. An arrow indicated by a dashed line represents a weak connection. The same metabolite with different number shows different peaks in NMR measurements. The causes of this were mainly the weather and differences in the number of hours of sunshine. The annual range of variation of the water temperature in the seas near Japan was ~15 \({}^{\circ}\)C. It was speculated that cold water would limit the efficiency of enzymatic reactions as well as the replication of microorganisms to some extent [34]. The distribution of Mahalanobis' distances for groups classified was confirmed using i-means. Both studied groups had a data structure close to the center (Figure 3). Similar to the physiochemical state, the stable state of biological phenomena was considered to be the state of less energy dispersion [32]. Therefore, samples with Mahalanobis' distances close to the center of the group were considered to be in a stable state, whereas those with long Mahalanobis' distances were in an unstable one. Specifically, we defined samples as being in an unstable state when they were more than one standard deviation away from the center of the group to which they belonged. To clarify the association between stable/unstable state and water temperature estimated from Mahalanobis' distances, we analyzed the association rules using an a priori algorithm. We previously reported that this method was able to detect nonnumerical factor association rules from biological states, for example the relationship between creatine content in muscle and animal habitat [31]. Therefore, it is considered possible to analyze data on the relationship between data stability and nonnumerical information, such as water temperature change. Indeed, correlations were found between state stability and ranking of numerical or nonnumerical information. Figure 4A indicates that if the water temperature remained below 20 \({}^{\circ}\)C for a while, the growth of fish would be difficult, and fish meat would transition to an unstable state. This might be attributable mainly to the inhibition of enzymatic reactions. It is known that low-temperature conditions may reduce oxidative stress [35]. Our findings indicated that if the water was maintained at a high temperature (Figure 4B), the muscular metabolite state would likely be stable. This supports the hypothesis that enzymatic reactions are important for stabilizing the state. In addition, the intestinal microbiota of fish appears to be affected during the transition between cold and hot conditions, possibly because it acts as an intermediate factor in environment changes. Finally, we attempted to predict the cascade with temperature at the most upstream by the Bayesian network analysis. In the cold water state, the a priori algorithm showed that anserine could be at low levels, but just before that, it was related to beta-alanine concentrations, which was reasonable because anserine is a compound of beta-alanine and methylhistidine. Therefore, it could be stated that the Bayesian network was working. In other words, fluctuations in inosine and IMP signals, which connected temperature and beta-alanine, are predicted to be involved in the final anserine concentration.