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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). Because IW has an out-of-phase association with EW
10
and drought or flood shows an in-phase association with internal wars (Fig. S2, S3), peaks of
11
external aggression wars often occur after peaks of internal wars (Fig. 1), resulting in out-of-phase
12
association between EW and drought or flood (Fig.2). Thus, time-lag and co-varying effect together
13
can explain many phase inconsistencies.
14
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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