Abstract
Based on compilation of a large number of archaeological and palaeosol 14C-ages, the Summed Probability Method is used to reconstruct population history and climatic patterns on the Chinese Loess Plateau during the period 8.5–3.5 cal. ka BP. During this period, the population experienced two major expansion periods and several climatic fluctuations. The first population expansion began at around 7.8 cal. ka BP, and the second at around 5.8 cal. ka BP. During the first period, although already in combination with cultivation of broomcorn millet the population growth was supported mainly by hunting and gathering. With the switch from broomcorn millet to foxtail millet, plant cultivation became the major factor promoting a second population increase. In this paper, we demonstrate that, initially, suitable climate and agriculture both can facilitate population growth and climate events had a significant influence on demographic fluctuations. However, when reaching the threshold of land capacity, population became increasingly more sensitive towards climate fluctuations.
Introduction
Prehistoric demography dynamics and its relationship with climate variability have become a major topic during recent years. Although many different proxies (e.g. site numbers, site density, size and distribution) can be used to reconstruct population size, the basic shortcoming of all methods is due to limited time resolution (Wang et al., 2014a). In order to circumvent the dating problems, Rick (1987) was the first to use summed probability distributions (SPDs) of calibrated radiocarbon data to reconstruct trends in prehistoric populations. Because of the high achievable dating precision, in combination with the availability of continuous time-series, the method is now steadily gaining in importance (Williams, 2012). Whereas Quaternary geologists apply the method to reconstruct fluvial histories in relation to climate variability (e.g. Chiverrell et al., 2011; Howard et al., 2009; Wang et al., 2014b), in archaeology it can be used to study the relationship between population dynamics and climate (e.g. Kelly et al., 2013; Munoz et al., 2010; Shennan et al., 2013; Smith et al., 2008). The advantages and disadvantages of the method have been thoroughly discussed, and the critical discussion has helped in promoting its application over the world (Ballenger and Mabry, 2011; Bamforth and Grund, 2012; Miller and Gingerich, 2013; Steele, 2010; Surovell et al., 2009; Weninger et al., 2011; Williams, 2012).
The method has been introduced to China in recent years (Barton et al., 2007, 2009; Dong et al., 2013; Ma et al., 2012), but up to now only used to analyse individuals sites with small area. The situation changed with a recent research paper that was published online (Wang et al., 2014a) where the method is used to reconstruct the population dynamics of the whole of China during the past 50 ka. The paper also includes a discussion of climate effects. Another recent study has demonstrated that the frequency distribution of Chinese Loess Plateau (CLP) palaeosol dates can be used to reconstruct the monsoon intensity (Wang et al., 2014b). Until now, we are still lacking in regional study that discusses the relationship between population dynamics and climate change. Regional studies are important since China has complex topographic diversities and regional climate change may not follow the macroclimate change (Maher and Hu, 2006).
The CLP is a cradle of Chinese civilization with a long Neolithic history. Located in the transition regions from humid to arid of China, the CLP is sensitive to climate change and influenced strongly by the Asian monsoon. The CLP therefore provides an ideal region for environmental archaeology research (An et al., 2005). The effect of climate change on cultural evolution has been discussed in many aspects. The majority of previous studies have focused on the impact of cold/dry climate switches, events which are shown to have had dramatic effects in terms of cultural shifts, geographic site distributions, in comparison to warm/humid climate switches that facilitated population expansion and culture diffusion (An et al., 2006; Dong et al., 2013; Liu and Feng, 2012; Lv and Zhang, 2008; Mo et al., 1996; Pang and Huang, 2003; Wang et al., 1993; Wu and Liu, 2004). In our working area, the CLP, with a more complex climate pattern (Zhao et al., 2010), the main problem for discussion of climate–culture interaction is the low dating resolution of the Loess profiles used in Holocene climate reconstructions, as well as the lack of high resolution lake cores (Zhao et al., 2010). On the other hand, most of the modern discussion was limited to a relatively small area such as the Western Loess Plateau (An et al., 2004; Mo et al., 1996) or the Guanzhong Basin (Lv and Zhang, 2008; Pang and Huang, 2003). Little work has been done to discuss this relationship on the whole CLP level. This is probably on one hand because the culture types are not uniform over such large areas and the time and spatial framework of each culture type was not clear especially in the Western Loess Plateau because of insufficient archaeological investigation. The application of the Summed Probability Method provides a chance to evaluate the association between Holocene population dynamics and climate change on the CLP through correlating directly the archaeological and the palaeosol data for the past 10 ka.
Study area
The CLP covers an area of some 440,000 km2 in the upper and middle reaches of China’s Yellow River which includes almost all of Shanxi and Shaanxi provinces, parts of Gansu province and the Ningxia Hui Autonomous Region (Liu, 1985). The loess–palaeosol sequence has accumulated to a depth of 120–300 m during the last 2.6 million years (Ding et al., 2002). The plateau generally has a semi-humid and semi-arid climate, with extensive monsoonal influence. Winters are cold and dry, while summers are warm and humid. Rainfall tends to be heavily concentrated in summer. The mean annual temperature range is 2–15°C, and the mean annual precipitation decreases from 700 to 150 mm from southeast to northwest (Li et al., 2003). The vegetation types include, in order, temperate forest, temperate forest-steppe, temperate steppe, temperate desert-steppe and temperate steppe-desert from southeast to northwest along the precipitation gradient (He et al., 2004).
It is reasonable to call the CLP the cradle of Chinese civilization. From what is presently known, the development of Neolithic cultures began ca. 8 cal. ka BP. According to the widely applied geographic partitioning and cultural terminology Partition, the Huanghe drainage basin has been divided into three different regional systems and cultural types including Gan-qing, Central Plain and Shandong cultural regions (Yan, 1987). The eastern part of the CLP (Shanxi–Shaanxi province) is a part of the Central Plain culture region, while the western part of the CLP (eastern part of Gansu province and southern part of Ningxia province) is divided into Gan-qing cultural region. The prehistoric culture sequence is broadly defined by the Laoguantai (also called Dadiwan; 8–7 cal. ka BP), Yangshao (7–5 cal. ka BP), Longshan (4.9–4 cal. ka BP) cultures on the Eastern Loess Plateau and Dadiwan (7.8–7 cal. ka BP), Yangshao (7–5 cal. ka BP), Majiayao (5.3–4 cal. ka BP), Qijia (4.3–3.6 cal. ka BP) and Siwa (3.6–2.6 cal. ka BP) cultures on the Western Loess Plateau (Xie, 2002; Yan, 2008).
Material and method
Radiocarbon dates from archaeological context are used to calculate the summed probability as a proxy for prehistoric demography since a larger population will result in more production and deposition of cultural carbon, therefore providing more determinations (Holdaway and Porch, 1995; Munoz et al., 2010; Peros et al., 2010; Surovell and Brantingham, 2007). With sufficient numbers of radiocarbon dates from large regions, numerous sites and investigators, the changes in their frequency distributions are widely approved to be a reliable indicator of the population fluctuations (Anderson et al., 2011; Kuzmin and Keates, 2005; Peros et al., 2010).
The radiocarbon dates were obtained mainly from published archaeological 14C-ages as given in datasets, reports and papers. We have referenced in particular the recently published (online) database of Wang et al. (2014a). All dates were given in years BP (Before Present) on the 14C-scale and are based on the Libby half-life of 5568 years with 1σ (68% confidence) standard deviation (SD). To avoid misunderstandings, we use the term 14C-BP.
The archaeological dates were collected according to the principles of Wang et al. (2014a): (1) the 1σ SD of the 14C-ages should be less than ±400 14C-BP; (2) we have eliminated 14C-ages based on shells, unknown materials or materials inappropriate for dating; (3) we further eliminated 14C-ages that had weak (i.e. unreliable) association with human occupation such as ancient temples, pagodas or canoes and (4) whenever multiple dates were available for the same context at a site, the most reliable dating material was chosen. In total, 646 dates were collected from 122 sites (Figure 1, the detail is given in supplementary file, available online) and used for the following analysis.

Distribution of archaeological sites and Loess profile sites on the Chinese Loess Plateau (CLP) contributing radiocarbon dates to the database.
In order to reduce the over-representation of sites (or site-phases) for which scientists had conducted intensive archaeological investigations and dating efforts on one site, we calculate the occupation events using Ward and Wilson’s χ2 test (Ward and Wilson, 1978). Following this statistical test, we use the multiple dates to obtain a weighted average value for single sites (or site-phases). This procedure was implemented using the ‘test sample significance’ and ‘create pooled mean’ functions in the CALIB 7.0.2 program (Stuiver and Reimer, 1993): the averaged dates were then calibrated (95.4% confidence) and used to generate SPDs (applying the ‘sum probability’ option in CALIB 7.0.2) based on the IntCal13 calibration curve (Reimer et al., 2013). We also applied the empirical model put forward by Surovell et al. (2009) to correct for taphonomic bias by taphonomic processes (e.g. erosion and weathering) thereby causing over-representation of recent events relative to older events. Following correction, the data were standardized by Xi/Xmax, with Xi representing all single values for N dates (i = 1,…, N) and Xmax calculated as the oldest age-value in the series. Although Williams (2012) recommended secondary smoothing of the SPDs in an effort to remove the artificial effects of plateaus and steep-regions of the calibration curve on the SPD-shape for the last 11 ka, this smoothing may also change the shape of any real peaks in the SPD. Because the use of a 500-year floating window, as proposed by Williams (2012), will strongly impact the shape of any SPD, for our data we applied both a 200- and a 500-year smoothing procedure, and compared the differences in shape between the uncorrected and the smoothed SPD. As an additional check on the existence of artificial peaks or troughs (Williams, 2012), we also plotted the number of radiocarbon dates (using their weighted averages as described above) as well as the corresponding number of calibrated dates on both time-scales (14C and calendric). This test was deemed important since many authors take the peaks and troughs of SPDs as direct evidence for population fluctuations (Bamforth and Grund, 2012; Gamble et al., 2005; Shennan et al., 2013).
For purposes of comparison with the archaeological 14C-database, we collected a second and independent 14C-database for the palaeosols on the CLP. The palaeosols formed when the climate was warm and humid, and their development may therefore be expected to reflect prevailing climate change on a regional scale (Wang et al., 2014b). In order to date individual soil samples, as well as to generate an extended chronology for the overall soil development for the Holocene, in most cases bulk organic material is used for radiocarbon dating. The palaeosol dates were assembled according to the principles proposed by Wang et al. (2014b). In total, 151 14C-ages that cover the past 10 ka were collected from 52 sites (Figure 1, supplementary file, available online). The palaeosol 14C-ages were calibrated and processed by essentially the same procedures as for the archaeological 14C-ages. In both cases, we applied CALIB 7.0.2 software (Stuiver and Reimer, 1993) to generate the SPDs, with the application of the IntCal13 calibration curve (Reimer et al., 2013). As mentioned above, the distributions were then smoothed using a 200- and a 500-year floating window. Following smoothing, the data were standardized by the Xi/Xmax-method and are plotted on the cal BP-scale.
Results
According to the previous studies, the sample size will affect the reliability of the 14C-age, and therefore also the shape of the SPD. Michczynska and Pazdur (2004) suggest that, for the time interval 0–12 cal. ka BP, a minimum number of 200 14C-ages with ΔT (mean SD) = 115 years is necessary, with statistically reliable results only achieved for 780 dates (when referenced to ΔT = 115 years). Similarly, Williams (2012) points out that summed probability diagrams based on less than 200–500 radiocarbon ages should be treated as provisional. The present studies are based on a total of 646 radiocarbon ages, with ΔT = 74 years. As can be taken from Figure 2, more than 90% of the 14C-ages have errors better than 125 years. Since the number of radiocarbon dates required to produce a robust SPD decreases with SD, we expect that our database is capable of producing results that are robust against chance statistical fluctuations.

Histogram (25-year bin) showing the cumulative proportions of the conventional 14C-ages arranged according to increasing standard deviations.
As shown in Figure 3d, when the data are evaluated using a 500-year moving average, the development of the CLP population can be divided into three phases. At around 8 cal. ka BP, we observe an initial population increase that corresponds to the introduction of Neolithic agriculture. After 7.8 cal. ka BP, the population strongly expands and then reaches a near-stable level which lasts until ~5.9 cal. ka BP. There follows a second large population expansion which lasts until ca 2.7 cal. ka BP, at which time the population size (as measured by the number of 14C-ages in the database) is twice as high in comparison to the previous phases. As deviations from this general development, there are two fluctuations at ages ca. 4.5 and 3.6 cal. ka BP. Finally, after ca. 3 cal. ka BP, the curve declines rapidly to very low levels. The 200-year moving average curve (Figure 3c) generally has the same trend as for 500-year smoothing, although the amplitude of the minor peak at 5.4 cal. ka BP (Figure 3d) is now attenuated (Figure 3c). According to the frequency distribution of the number of radiocarbon dates (using their mean; Figure 3a) and the number of calibrated dates (using their mean; Figure 3b) by 200-year time interval, three distinct fluctuations respectively existed at around 3.5, 4.1 and 4.7 ka BP (Figure 3a) and 3.7, 4.5 and 5.4 cal. ka BP (Figure 3b), respectively. As such, the 500-year floating window appears to (significantly) change the shape of the distribution for the 4.7 ka/5.4 cal. ka BP peak. We take this as an indication that the corresponding climate deterioration at this time was of shorter duration than the subsequent two climate events (cf. below). The initial population expansion of the CLP began about 1000 years later than the whole China (Wang et al., 2014a) and the fluctuations were not consistent with each other, reflecting a different growth trajectory probably because of regional environmental diversity and different adaptive strategies (Wang et al., 2014a).

Histograms and summed probability curve: (a) histogram of uncalibrated radiocarbon dates, (b) histogram of calibrated radiocarbon dates, (c) 200-year moving average summed probability curve and (d) 500-year moving average summed probability curve.
Turning now to the SPD of the palaeosol dates (Figure 4), we observe a (relative) increase in soil development that begins around 9 cal. ka BP, and which remains high until 3.2 cal. ka BP, with peaks at 8.2, 7.5, 6.5, 5.8 and 3.4 cal. ka BP and troughs at 7.8, 6.9, 5.9, 4.8 and 3.8 cal. ka BP. The curve shows an abrupt decline after 3.4 cal. ka BP. The general climate pattern reflected by the Summed Probability is consistent with that of other loess proxies for Holocene climate reconstruction (e.g. magnetic susceptibility, CaCO3 content; Huang et al., 2004), and the fluctuations correlate well with the result of arboreal pollen percentage from Lake Daihai located in the northern part of the CLP (Xiao et al., 2004).

Summed probability curve of 14C-ages on Holocene palaeosol layers: (a) 200-year moving average and (b) 500-year moving average.
Discussion
Population dynamics and correlation with climate change
Many authors have identified correlations between climatic and demographic change, and this in a wide variety of regions (e.g. Kelly et al., 2013; Munoz et al., 2010; Smith et al., 2008), including Wang et al. (2014a) for China, but their conclusions are by no means unanimously accepted (e.g. Buchanan et al., 2008; Maher et al., 2011; Shennan et al., 2013). On the CLP, most scholars working in this region apply large attention to the effects of climate change on cultural and in particular on economic evolution.The basic argument is that, on the environmentally sensitive CLP, climate amelioration affords favourable environments for agricultural production, thus promoting culture development and/or population expansion, whereas harsher climate conditions cause cultural decline in combination with demographic shift and/or movements (An et al., 2006; Lv and Zhang, 2008; Mo et al., 1996; Pang and Huang, 2003).
Our radiocarbon records suggest the existence of a correlation between population dynamics and climate change (Figure 5). Following the 8.2 cal. ka BP climate event, climate amelioration and population expansion began at the same time. Around 6.9 cal. ka BP, a cold–dry event occurred and population expansion was restrained and remained at a stable level until 6 cal. ka BP when the climate was humid and warm again during 6.8–6 cal. ka BP. From 5.8 to 3 cal. ka BP, there was a general warm and humid climate with three climate deterioration events, and we observe a second population increase which was maintained at a scale twice as high as during the previous period. Three climate deterioration events correspond well with three population fluctuations at around 5.4, 4.5 and 3.7 cal. ka BP. Of course, many factors may contribute to the decline in amplitude of calibrated age distribution (e.g. research focus, site visibility). In this particular case, as goes for the historic period (especially the past 2 ka), many archaeological sites are accurately dated by information given in ancient Chinese literature. This is visible in the decline of the probability distribution for these younger ages.

Comparison between summed probability of archaeological dates and palaeosol dates: (a) 200-year moving average summed probability curve of archaeological dates and (b) 200-year moving average summed probability curve of palaeosol dates.
Although the climate evidence generally correlates well with population size, there are some exceptions. From 8.5 to 3.5 cal. ka BP, during which the climate was consistently warm and humid, the population experienced two phases of growth (first: 7.8–5.9 cal. ka BP; second: 5.9–2.6 cal. ka BP) with large amplitude in the second phase than in the first. The fluctuation of the second phase appears to be more sensitive to climate change than the previous phase. From 5 cal. ka BP on, climate shows a trend towards cold and dry, but the population size remained high until at least 2.7 cal. ka BP. We conclude that climate is not the only factor that influences population dynamics.
Agriculture development and its relationship with population expansion
The emergence of agriculture is often considered to be a revolution in human history. It represents the period when humans adapted their cultural and economic behaviour to the environment. Northern China is thought to be the origin centre of rain-fed agriculture. Agriculture provides a stable source of food for prehistoric humans, which enables them to cope with seasonal food shortages and therefore promotes culture expansion (Jia et al., 2013). Flotation results (Figure 6) and stable isotope analysis of bones can show us the development process and character of agriculture on the CLP.

Abundance ratio of crops from the floatation results in the study area: Dadiwan (Liu et al., 2004), Qinan and Lixian (An et al., 2010), Xinglefang and Xiahe (Liu et al., 2013), Zhouyuan (The Zhouyuan Archaeology Team, 2004), Buziping (Jia et al., 2013), Taosi (Zhao and He, 2006), Qiaocun (Zhou et al., 2011), Lajia (The Team Study on Agriculture, 2011). The culture type and age of each site can be seen in Appendix 1 (available online).
After 8 cal. ka BP, broomcorn millet was gradually cultivated in many parts of northern China (Liu et al., 2004; Lv et al., 2009; Zhao, 2011), and the earliest (presently known) broomcorn millet remains in the Western Loess Plateau date to 7.8–7.3 cal. ka BP at the Dadiwan site (An et al., 2010; Barton et al., 2009; Liu et al., 2004). However, the primary human subsistence strategy at Dadiwan between 7.9–7.2 cal. ka BP was hunting, not farming. This is indicated by a brief and non-intensive agriculture (Barton et al., 2009). During the early Yangshao period, broomcorn millet was still the main crop rather than foxtail millet in the Western Loess Plateau (Liu et al., 2004). It was only later that agriculture replaced the hunter-gatherer economy, for example, around 6.5 cal. ka BP in Guanzhong Basin (Zhao, 2014). After 6 cal. ka BP, broomcorn millet was replaced by foxtail millet as the main crop (An et al., 2010; Liu et al., 2004; Zhao, 2014; Zhou et al., 2011). The most likely reason for this is that foxtail millet has a higher productivity, requires less water and is more disease-resistant than broomcorn millet (Zhao, 2014; Zhou et al., 2011). Stable isotopes measured on bones from the western CLP and the Guanzhong Basin indicate that humans, pigs and dogs were all heavily reliant on millet after 6 cal. ka BP (Barton et al., 2009; Pechenkia et al., 2005), and this is indicative of an increasingly intensive agricultural economy. At around the same time, millet agriculture expanded from northern China towards the Changjiang river, Chengdu Plain and even as far as the Qinghai-Tibetan Plateau (Guedes, 2010; Nasu et al., 2012; Zhao and Chen, 2011). Although not an equally important food, rice appeared in many sites of Shaanxi and Gansu province along the Wei River during the Holocene (An et al., 2010; Li et al., 2007b; Lv and Zhang, 2008) providing a complementary food resource for periods with suitable climate. After 4 cal. ka BP, wheat was introduced into the CLP, with steadily increasing proportion (Lee et al., 2007; Zhao, 2014). The increasingly diverse agricultural system is accompanied with an enhanced human resilience towards instable climate in late Holocene (An et al., 2014; Li et al., 2007a, 2007c; Zhao, 2014).
To conclude, in parallel with the cultivation of millet we observe an initial population boom. During this period (~8–6 cal. ka BP), climatic amelioration and agriculture both have important roles in the development of food resources. Nonetheless, hunting and gathering remain important and actually provide many of the main food resources. During this period, the climate generally supported a stable environment that provided favourable conditions both for wild plants and animals, as well as for plant cultivation.
After 6 cal. ka BP, an increasingly intensive agriculture with livestock breeding was established, with foxtail millet replacing broomcorn millet as major crop. Agriculture afforded the main food resource rather than hunting and gathering. New food production practices enabled people to establish permanent sites and expand their settlements, thus facilitating pronounced human population growth (Wang et al., 2014a). The increasingly diverse agricultural system also offered a certain degree of protection in the late Holocene, when the climate became colder and drier.Finally, climate was replaced by agriculture as the dominant factor in controlling population stability and growth.
During the second period, population fluctuations correspond well with climate deterioration events. However, the population size did not fluctuate significantly when climate deteriorated at around 7 and 5.9 cal. ka BP in the first period. As explanation, we propose that – when humans were becoming increasingly reliant on agriculture – the population size became more sensitive to climate change as shown in Figure 5. The main underlying reason would therefore be that, once the agricultural technology had reached a certain threshold, in combination with an increasingly stable demography, the economic system becomes more sensitive towards climatic fluctuations.
Conclusion
The population experienced two major expansion periods and several fluctuations. The first population expansion began at around 7.8 cal. ka BP, and the second at around 5.8 cal. ka BP. In addition, we observe three distinct population fluctuations at around 5.4, 4.5 and 3.7 cal. ka BP.
Suitable climate between 8.5 and 3.5 cal. ka BP facilitated demographic growth especially for the first period, during which hunting and gathering were the major economic factors. Climate variability had significant impact on population size, and caused a number of population fluctuations.
The development of agriculture finally became the major factor, promoting a second population boom when the increasingly intense and diverse agricultural system provided the necessary nutrition to support further population growth. Once the population scale had reached a certain threshold of land capacity, population became more sensitive and fragile to climate fluctuations.
Footnotes
Funding
This work was funded by National Key Technology R&D Program of China (Grant No. 2013BAK08B02).
