**3. Results**

#### *3.1. Direct and Indirect Climatic E*ff*ect on Plague Outbreak*

Over our study period in AD1347–1760, our SEM results showed that temperature and precipitation variations would have a substantial indirect impact on plague outbreak in Europe through climate-induced fluctuations in wheat prices (Figure 2). Yet, the climatic influence, as implied from the SEM results, is never directly linked to plague dynamics.

**Figure 2.** Path diagrams for (**a**) Model 1: Temperature anomaly; (**b**) Model 2: Precipitation; (**c**) Model 3: PDSI, for the direct and indirect effects of climate change on plague outbreak. The residual variables (<sup>ε</sup>1, ε2, ε3, ε4) represent the unmeasured factors affecting the corresponding variable. Arrows represent the relationship of each pair of the variables, with the path coefficients stated next to the arrows. The path coefficients are standardized partial regression coefficients from linear regressions. We omit those statistically insignificant paths in the models, except for the path PDSI → Wheat Price. Red arrows represent statistically insignificant paths, while the black ones represent statistically significant ones.

Model 1 shows that temperature variation has a statistically-insignificant direct relationship with plague dynamics (Table 1).


**Table 1.** Correlation coefficients between each set of climatic/economic predictor and plague response. The correlation is decomposed into the direct and indirect effects, and the synergy of the direct and indirect effects gives the total effect.

> Significance level: \*\*\* *p* < 0.001, \*\* *p* < 0.05.

However, temperature would indirectly control the variations of plague frequency through wheat price fluctuations (intercept = −1.66, *p* < 0.001). In Model 2, precipitation displayed a similar pattern as temperature. The command of precipitation on plague dynamics is undertaken indirectly through the manipulation of wheat prices (intercept = 0.02, *p* < 0.001) during our study period. Likewise, the path model again denied the direct impact of precipitation on the plague outbreak. In Model 3, the estimation suggested that PDSI would have no directional effect on plague dynamics, both directly and indirectly. For each set of the path analysis, we also included selected economic factors to investigate the direct and indirect influence of climate change on plague dynamics. In all models, it is observed that, despite the climate-induced fluctuation, both wheat price and CPI have a direct effect on plague outbreak. The influence of wheat price and CPI was not mediated by other variables in the models when other factors were held constant. The models also universally demonstrated that the sensitivity of plague dynamics was indirectly correlated with the changes in wheat price via CPI. However, not all the economic variables tested were found relevant to plague outbreak. The historical real wage was not directly related to any variations of plague dynamics. By combining the direct effect and indirect effects of predictors, we were able to measure the total effect of both climatic variables and economic variables on plague outbreak. From the result, as indicated in Table 1, the total effect of temperature, precipitation, and CPI remained statistically negatively significant to any change of plague activity, while the effect of wheat price on plague was reported to be positive. In short, plague dynamics is favored by low temperature, dry environment, rising wheat price, and decreasing CPI.

#### *3.2. Long-Term Trends of Climate, Economic Changes, and Plague Outbreak*

In the process of creating SEM from climatic, economic, and plague data, we also looked for long-term trends between variables and checked for their consistency over our study period. In Figure 3, we laid out the general long-term sensitivity of plague dynamics and identified predictors deduced from SEM.

**Figure 3.** Long-term trend of plague outbreak with (**top left**) temperature anomaly; (**top right**) precipitation; (**bottom left**) wheat price; and (**bottom right**) CPI. The red lines represent the trends, and the green envelopes provide the 95% confidence interval areas.

Plague dynamics, as estimated, had a negative trend with temperature (Coef. = −0.007, *p* < 0.001, F = 8.24) (Table A1), implying that cooling would effectively trigger plague outbreak. For precipitation, the long-term trend is statistically insignificant to the plague dynamics. For the two economic variables tested here, wheat price exhibited a consistent positive trend with the plague dynamics (Coef. = 0.0126, *p* < 0.001, F = 60.24); whilst CPI also showed a similar trend (Coef. = 0.0062, *p* < 0.001, F = 16.20).

Over the 414 years of observation, temperature and precipitation both have a persistent impact on wheat price. It was estimated that the price of wheat drops with increasing temperature (Coef. = −0.319, *p* < 0.001, F = 23.81) and decreasing rainfall (Coef. = 10.519, *p* < 0.001, F = 23.81). At the same time, wheat price, because it is closely related to the economy, was itself positively correlated with CPI (Coef. = 1.029, *p* < 0.001, F = 2597.16).

We also compared the long-term trend of temperature influence between warm and cold periods. It should be noted that climatic control on plague and economic parameters behaved differently in warm and cold periods. During cold periods, the long-term trend of all studied relationships performed the same as the overall long-term trend observed (Figure 4, Table A2). However, during warm periods, temperature no longer exerted its effect on plague dynamics and wheat price (Figure 5, Table A3). From the statistical results we obtained, the sensitivity of plague dynamics was primarily controlled by wheat price (Coef. = 0.0122, *p* < 0.001, F = 12.04) and CPI (Coef. = 0.0093, *p* < 0.001, F = 8.66) within the warm phases. Such control was also revealed in the SEM models presented in the previous section, in which growing CPI and rising wheat price occurred together during the warm periods (Coef. = 1.065, *p* < 0.001, F = 691.12).

**Figure 4.** Long-term trend of plague outbreak with (**top left**) temperature anomaly; (**top right**) precipitation; (**bottom left**) wheat price; and (**bottom right**) CPI during the cold periods. The cold periods refer to the time with negative temperature anomaly. Red lines represent the trends, and the green envelopes provide the 95% confidence interval areas.

**Figure 5.** Long-term trend of plague outbreak with (**top left**) temperature anomaly; (**top right**) precipitation; (**bottom left**) wheat price; and (**bottom right**) CPI during the warm periods. The warm periods refer to the time with positive temperature anomaly. Red lines represent the trends, and green envelopes provide the 95% confidence interval areas.

In addition, the performance of the climatic variable differed in the dry and wet periods. Further analyses showed that temperature could not change the trend of plague outbreak during dry periods (Figure 6, Table A4). The pressure from the temperature on wheat price and plague outbreak did not exist at all during dry periods. However, in wet periods, the dynamics of plague activity increased with temperature cooling (Coef. = −0.0119, *p* < 0.001, F = 12.90), whilst increasing wheat price was also associated with decreasing temperature (Coef. = −0.524, *p* < 0.001, F = 32.18) (Figure 7, Table A5).

**Figure 6.** Long-term trend of plague outbreak with (**top left**) temperature anomaly; (**top right**) precipitation; (**bottom left**) wheat price; and (**bottom right**) CPI during the wet periods. The wet periods refer to the time with above-average precipitation over our study period. Red lines represent the trends, and the green envelopes provide the 95% confidence interval areas.

**Figure 7.** *Cont*.

**Figure 7.** Long-term trend of plague outbreaks with (**top left**) temperature anomaly; (**top right**) precipitation; (**bottom left**) wheat price; and (**bottom right**) CPI during the dry periods. The dry periods refer to the time with below-average precipitation over our study period. Red lines represent the trends, and the green envelopes provide the 95% confidence interval areas.
