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1 SUPPLEMENTARY MATERIALS 2 Table S1 3 Table S2 4 Figure S1 5 Figure S2 6 Figure S3 7 Figure S4 8 9 Wavelet analysis 10 Wavelet analysis is ideally suited for investigating non-stationary time series and particularly causal 11 links of multiple non-stationary time series (Cazelles et al. 2008; Zhang et al. 2009). The continuous 12 wavelet transform decomposes the time series into both time and frequency components, the 13 calculation of the wavelet power spectrum quantify in the time-frequency domain the distribution of 14 the variance of the time series (Cazelles et al. 2008; Grinsted et al. 2004). Wavelet coherency was 15 used to present coherencies between two non-stationary time series. Then wavelet coherency aims 16 to identify significant associations between two time series of specific frequency-time domain 17 (Cazelles et al. 2008; Grinsted et al. 2004), while cross-correlation function (CCF) method 18 measures overall associations for the whole frequency-time domain. The overall CCF associations 19 are often determined by predominant associations of some frequencies, which often mask weak 20 associations of the other frequencies or time periods (Bloom et al. 2007). 21 For our analyses, the Morlet wavelet was used. The significance levels were computed with an 22 appropriate bootstrapping scheme, the ‘Beta-Surrogate’ (Rouyer et al. 2008); 1000 ‘Beta-Surrogate’ 23 series was used. The significance level was set at p < 0.05. These bootstrapped series using 1/f 24 spectrum models has taken the highly auto-correlated nature of the environmental time series into 25 account (Rouyer et al. 2008). To complete the coherency analysis, a phase analysis has been 26 performed. The arrows in wavelet coherence figures represent the phase difference between two 1 1 time series, in-phase or positive (pointing to the right) relationships or out-of-phase or negative 2 (pointing to the left) relationships. For more details, please see Cazelles et al. (2008) and Zhang et 3 al. (2009). 4 The coherencies between frequency of all wars (AW) and temperature of entire China (T), 5 between frequency of internal wars (IW) and T, and between external aggression wars (EW) and T 6 are shown in Fig. S1a, Fig. S2a and Fig. S3a, respectively. T shows predominant out-of-phase 7 associations with AW and EW (especially around 320-yr periodic band), resulting in a significant 8 CCF between them (Fig. 2). T shows about equivalent in-phase and out-of-phase association with 9 IW, resulting in a non-significant CCF between the (Fig. 2). These results generally support the 10 CCF results in Fig. 2. The phase inconsistencies can be caused by several factors (see below) [Insert Fig. S1, S2, S3 here] 11 12 The coherencies between AW and frequency of flood (F), between IW and F, and between EW 13 and F are shown in Fig. S1b, Fig. S2b and Fig. S3b, respectively. Around the 320-yr band, F shows 14 predominant out-of-phase association with AW and EW, not with IW. However, F shows 15 predominant and consistent in-phase association with IW. These results generally support the CCF 16 results in Fig. 2. 17 The coherencies between AW and frequency of drought (D), between IW and D, and between 18 EW and D are shown in Fig. S1c, Fig. S2c and Fig. S3c, respectively. D shows predominant 19 out-of-phase with EW, not with AW or IW. However, D shows predominant in-phase association 20 with IW around the 320-yr periodic band. These results also generally support the CCF results in 21 Fig. 2. 22 The coherencies between AW and locust plague (L), between IW and L, and between EW and 23 L are shown in Fig. S1d, Fig. S2d and Fig. S3d, respectively. L shows predominant in-phase 24 association with AW and IW, about equal out-of-phase and in-phase associations with EW. However, 25 L shows predominant in-phase association with EW around 320-yr periodic band. These results also 26 generally support the CCF results in Fig. 2. 2 1 The coherencies between AW and rice price (RP), between IW and RP, and between EW and 2 RP are shown in Fig. S1e, Fig. S2e and Fig. S3e, respectively. RP shows predominant in-phase 3 associations with AW, EW and IW. These associations are consistent around 320-yr periodic band. 4 These results also generally support the CCF results in Fig. 2. 5 The coherency analysis results generally agree with the CCF results in Fig. 2. Furthermore, 6 coherency analysis reveals drought and flood show predominant and consistent in-phase association 7 with IW around the 320-yr periodic band. The predominant out-of-phase association between EW 8 and F is likely caused by the co-varying effect between EW and IW (see below). Coherency 9 analysis also reveals that phase inconsistencies often occur around the 160-yr periodic band. These 10 inconsistencies can be caused by several factors (see below) 11 There is significant out-of-phase relationship between EW and IW (Table S1). This is 12 reasonable because if a dynasty faces more EW, the whole society has to unite together to fight the 13 common invaders, resulting in less IW. Similarly, high level of EW may occur in a dynasty after it 14 is weakened by a high level of IW. The co-varying effect between EW and IW may cause changes 15 of phase relationship (arrow directions) between war-frequency of EW or IW and T. For example, 16 low temperature may increase EW, because high level of IW may occur after EW (due to negative 17 associations), this may result in an in-phase association between IW and T. 18 19 Cool temperature-associated dynastic changes 20 The interaction between the Chinese agriculturalists and the nomads living further north has indeed 21 been a major force shaping Chinese history; the thousands kilometre long Great Wall was obviously 22 built under the pressure of frequent southward invasions by coalitions of pastoral nomadic societies 23 (see Dai & Gong 2000). The southern boundaries of pastoral nomadic societies have tended to 24 move southward to Chinese dynasties during the cold periods of the last two millennia (Wang 25 1996). According to historical records (e.g. Chen 1939), there are three major large southward 26 immigration phases of northern pastoral nomadic societies to the Chinese dynasties: during the 3 1 Eastern Jin Dynasty (AD 317-419) and the Southern and Northern Dynasties (AD 420-588), during 2 the Southern Song Dynasty (AD 1127-1279) and Yuan Dynasty (AD 1276-1367) and during the 3 Qing Dynasty (AD 1644-1911). These immigration phases generally correspond to the cold periods 4 in ancient China as defined by Zhu (1973) (also see Fig. S4). According to Wang (1996), the first 5 large-scale aggression by the Xiongnu, Xianbei, Jie, Di and Qiang societies occurred during the 6 Eastern Jin Dynasty, and the Southern and Northern Dynasty. The southern boundary of northern 7 pastoral nomadic societies was moved from N 41o42’ E 115o in Qin Dynasty (warm period) to N 8 30o24’ E 115o in Southern and Northern Dynasties (cold period). The second large-scale aggression 9 by northern pastoral nomadic societies (Mongol, Qidan, Nuzhen ect) occurred during the southern 10 Song Dynasty and Yuan Dynasty. The southern boundary of northern pastoral nomadic societies 11 was moved from N 44o00’ E 115o during the Sui and Tang Dynasties (warm period) to N 32o18’ E 12 115o in the Southern Song Dynasty (AD 1127-1279) (with a short but deep cold period). At the end 13 of the Song Dynasty, the southern boundary of the northern pastoral nomadic societies was moved 14 further south to N 22o30’ E 115o (southern edge of the Chinese mainland) during the Yuan Dynasty 15 (with a short but deep cold period). The third large-scale southward aggression was completed by 16 the Manchurian societies during the late Ming Dynasty (cold period). At the end of the Ming 17 Dynasty, the southern boundary of Qing Dynasty (within the period of the Little Ice Age, AD 18 1500-1900) was shifted to N 22o30’ E 115o (southern edge of the Chinese mainland) from that of N 19 42o40’ E 115o of the Ming Dynasty. The large and sustained southward migrations by nomads 20 triggered by climate cooling might thus have contributed significantly to collapses of some great 21 agricultural empires. As shown in Fig. S4, the collapses of the agricultural dynasties of the Han, 22 Tang, Northern Song, Southern Song, and Ming are closely associated with low temperature or 23 rapid decline of temperature, and immediately replaced by dynasties ruled by the northern nomads. 24 The Han was replaced by the Southern and Northern Dynasty ruled by northern nomads. The 25 Northern Song was converted into Southern Song after northern part was taken over by the 4 1 Mongolia societies, and finally the Southern Song was replaced by Yuan Dynasty ruled by the 2 Mongolian societies. The Ming was replaced by Qing ruled by the Manchuria societies. 3 A few recent studies attributed the collapses of the Tang and the Ming dynasties to drier 4 periods of weaker Asian summer monsoon (Yancheva et al. 2007; Zhang et al. 2008). However, 5 using historical climate records of China, Zhang & Lu (2007) argue that the collapse of Tang 6 Dynasty was not related to drought events because most of the cold winters during AD 700–900 7 were associated with relatively wet summers. Our results show that the great agricultural dynasties 8 of the Eastern Han (AD 25-220), the Tang (AD 618-907), the Song (AD 960-1279) and the Ming 9 (AD 1368-1643) experienced no obvious higher frequency of droughts or floods a few decades 10 before they collapsed (Fig. 1). The collapses of Eastern Han and Tang were much associated with 11 high level of internal wars which were likely induced by very high (to Han) or low temperature (to 12 Tang); the collapses of Song and Ming were much associated with high level of external aggression 13 wars which were likely induced by low temperature or rapid decline of temperature (Fig. 1). We did 14 not find significant links between high EW and high F or high D, instead, frequency of external 15 aggression war showed a negative association with drought and flood (Fig. 2), suggesting that the 16 collapses of the great agricultural empires were not caused by drought and flood events. The 17 negative association between external war and drought/flood is not known, probably being caused 18 by the co-varying effect of internal wars (D increases IW indirectly, IW may decrease EW; see 19 discussion below). 20 Associations of temperature with drought and flood 21 Recent studies have demonstrated that global warming may increase precipitation in China (e.g. 22 Webster et al. 1998, Yao et al. 2000, Liu et al. 2006). Indian summer monsoon (ISM) and East 23 Asian summer monsoon (EASM) are two key factors in influencing precipitation in China. 24 Himalayan and Eurasian winter snow cover extent affects significantly the monsoon variability in 25 Asia (Kumar et al. 1999). EASM and ISM rainfalls have been shown to be negatively associated 5 1 with winter snow cover over the Himalaya or over Eurasia (e.g. Hahn & Shukla 1976; Dickson 2 1984; Liu et al. 2004, 2006; Ye & Bao 2005; Zhang et al. 2007). Global warming would 3 significantly increase the summer monsoon rainfall in Asia (Ueda et al. 2006), probably due to the 4 enhanced moisture transport from the surrounding oceans to the Asian continent (Jiang et al. 2005). 5 Thus, in cold periods, reduced EASM and ISM rainfalls would increase the frequency of droughts 6 in China. The increase of flood frequency in cold periods is probably caused by more typhoon 7 rainstorms in southern China (see Liu et al 2001; Leung et al. 2007; Liang & Zhang 2007). Our 8 previous studies indicated that increase of drought and flood in cold periods significantly increased 9 locust plagues in China due to increase of wet habitats in river banks or lake beaches associated 10 with drought or flood events (Zhang et al. 2009). 11 12 Inconsistencies in phase shift 13 Our wavelet analysis also reveals some inconsistencies in phase shift of war-frequencies with 14 temperature, drought/flood, price of rice and locust plagues around the periodic bands of 160-yr and 15 320-yr, especially around 160-yr periodic band. The underlying reasons may be not trivial. First, 16 phase shift may be caused by different responses of war-frequency to climatic variables due to 17 differences in abilities of a society to counter natural disasters, which may produce different 18 time-lag and then associations strength or even changes of phase shift of coherencies. Though 19 war-frequencies may response during increase or declines phases of climatic variables, the response 20 may not exactly or immediately follow the climatic variations. Second, the inconsistency of phase 21 shift between 160-yr and 320-yr may be caused by the coupling effect of two periods of prime 22 numbers. In theory, the predominant association between war-frequency and temperature around 23 320-yr would likely result in in-phase associations (pseudo-association) around 160-yr; and vice 24 versa. This may explain some inconsistencies of coherencies between the variables of this study. 25 The in-phase association between EW and T (Fig. 4b) around 160-yr band is likely a 26 pseudo-association. Thus, we need to use CCF methods to identify the significant predominant 6 1 associations, and then to use wavelet analysis to identify the periods where the predominant 2 associations occur. Third, inconsistency in phase shift may suggest that the effect may be different 3 at different frequency bands. For example, warm temperature increased locust plague in short 4 periodic band directly (Ma 1958), but we found cool temperature increased locust plague in long 5 periodic bands indirectly, through its positive association with drought which benefit locust plague 6 (Stige et al. 2007, and Fig. 2 in this study). Finally, some inconsistencies in phase-shift may be 7 caused by the co-varying effect between frequencies of external aggression war and internal wars 8 (see above). This co-varying effect may well explain the out-of-phase association between external 9 aggression wars and drought or flood (Fig. 2). 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Z. 1973 Preliminary study of climate change over past five millennia. Science in China 16, 226-256. 16 17 18 10 1 Figure Legends 2 3 Figure S1. Wavelet coherences analysis on association of the frequency of all wars with temperature 4 (a), flood (b), drought (c), locust plague (d) and rice price (e) in China during AD 10s-1900s. The 5 color codes for coherence values vary from dark blue (low values) to dark red (high values). The 6 5% significance levels computed based on 1,000 “Beta-Surrogate” series are shown as thick white 7 contour dashed-lines. The cone of influence where edge effects might distort the picture is shown in 8 a lighter shade. The arrows indicate the relative phase relationship (with in-phase pointing right, 9 out-of-phase pointing left). 10 11 Figure S2. Wavelet coherences analysis on association of the frequency of external aggression wars 12 with temperature (a), flood (b), drought (c), locust plague (d) and rice price (e) in China during AD 13 10s-1900s. For explanations, see Fig. S1. 14 15 Figure S3. Wavelet coherences analysis on association of the frequency of internal wars with 16 temperature (a), flood (b), drought (c), locust plague (d) and rice price (e) in China during AD 17 10s-1900s. For explanations, see Fig. S1. 18 19 Figure S4. Illustrations of times when the great agricultural empires of Chinese dynasties collapsed 20 for ①Han (and Three Kingdom) ②Sui and Tang ③Southern Song ④Northern Song ⑤Ming. 21 Temperature data for entire China are from Yang et al. (2002) (solid line, not detrended) and 22 temperature data for the Northern Hemisphere is from Mann and Jone (2003) (dashed line, not 23 detrended but standardized). Dynastic periods are defined by following Chen (1939) as: A. Han (BC 24 206-AD 220); B. Three Kingdoms (AD 220-280); C. Jin (AD 280-420); D. Southern and Northern 25 Dynasties (AD 420-589); E. Sui & Tang (AD 589-906); F. Five Dynasties and Ten Kingdoms (AD 26 907-959); G. Song (AD 960-1279); H. Yuan (AD 1276-1367); I. Ming (AD 1368-1643); J. Qing 11 1 (AD 1644-1911) 2 12