*2.1. Plague Data*

To measure the historical plague outbreak in Europe, we adopted a detailed geo-referenced plague dataset digitalized by Buntgen, et al. [ ¯ 17]. The database records the starting year of each human plague outbreak in Europe at the city-scale. We counted the number of cities identified with plague outbreak in each year and transformed the database into a time series. Only data from Europe was counted, as Europe was selected for our study region. Slightly di fferent from the original dataset, which used the number of total plague outbreak count as its unit, the transformed dataset adopted in this study used the number of cities with plague outbreak count as our unit. Over the AD1347–1760 period, a total of 6764 plague outbreaks were recorded in Europe. The year with the most extensive plague outbreak is AD1630, with a record 119 cities a ffected by the plague. Out of 414 units of observation, plague quiet years are recorded 14 times. Zero-inflation of the dataset should not be considered as a problem.

## *2.2. Climate Data*

We considered three sets of climate data, namely temperature, precipitation, and scPDSI, for our analysis in this study. They were common parameters for historical study relating to climate-human relationships and were found strongly significant in influencing plague dynamics over time and space [18,19].

The temperature and precipitation dataset included for analysis are acquired from the climate reconstruction provided by Büntgen, et al. [20]. This climatic reconstruction was made possible through surveying 1547 sets of tree ring chronologies from Europe for the reconstruction of past climatic variability of Europe at its continental scale in annual resolution. Particularly, the time series for temperature data is calibrated into temperature anomaly with respect to the period of AD1901–2000. The vast coverage of raw data from this dataset ensured the reliability and validity of climate reconstruction. Thus, the dataset has been widely adopted in other historical studies of Europe [21].

Another set of climatic variables adopted in this study originated from the Old World Drought Atlas (OWDA) project of Cook et al. [22]. Our study considered self-calibrated Palmer Drought Severity Index (scPDSI) as the projection of the natural hydroclimatic environment. As such, the PDSI reconstruction by Cook et al. [22] provides an ideal extended record of natural wetness/dryness variability for the pre-industrial era of Europe. The OWDA was developed from dendrochronological records over the European continent and calibrated with high-quality instrumental scPDSI gridded data from the Royal Netherlands Meteorological Institute. Our study retrieved available data points, which have a spatial resolution of half-degree longitude-by-latitude grid, from our study area and further aggregated relevant grids of the same year into a time series for our analysis.

## *2.3. Economic Data*

For historical economic parameters, we selected wheat price, consumer price index (CPI), and real wages as variables for our estimations. The historical wheat price is extracted from the database created by Allen [23]. We extracted the data from each city and determined whether they fell onto our study region. The raw data is first standardized by [(xi − xmean)/xs.d.], then we calculated the averaged standardized wheat price of Europe. The historical CPI data comes from Allen [23]. We calculated the averaged standardized CPI by the same method as suggested in wheat price. We here averaged the standardized real wages of laborers and standardized real wages of building craftsmen based on the database from Allen [23].

#### *2.4. Structural Equation Modeling*

We applied structural equation modeling (SEM) [24] to test for the relative importance of climatic variables and economic variables on plague dynamics, and whether climate change has a direct influence on plague dynamics. To do this, we first constructed all the hypothetical pathways that fully detailed the causality amongs<sup>t</sup> variables within the system being studied [25]. Then, mathematically, the total pathway added up together as a series of linear regression. The technique hypothetically decomposed all the correlations of two variables into direct effects that pinpointed the causal influence of one factor on another and indirect effects that passed through other variables in the model and non-casual mediating predictors resulting from a common cause [26]. From the full casual model, the sum of direct effects and all indirect effects mediated by other variables between the predictor and response variable would yield total effect. In SEM, by assuming that all of the important variables and pathways were labeled, every effect listed in path analysis was considered linear, additive and unidirectional, and that residuals were presumably uncorrelated [27]. In this study, as also shown in Figure 1, the response variable is plague outbreak. We hypothesized that climate change and economic fluctuations (including wheat price, CPI, and real wage) may directly cause plague outbreak. Also, climate change may indirectly cause plague outbreak by influencing wheat price, which then will affect CPI and real wage.
