Temporal evolution properties

Children under 18 years are divided into four groups (Li et al., 2017a, 2017b): under 1 year old (babyhood), 1–6 years old (toddlerhood), 7–13 years old (school age), and 14–17 years old (adolescence). We use the sex ratio of a population, which is defined as the number of males per 100 females, to reflect the gender characteristics.

Informal adoption is most prevalent among females under 1-year-old (average age is 269.25 days after birth). The number of cases decreases with age (Fig. 1), indicating that birth families tend to give children away as early as possible. Children after age 7 are rarely adopted informally (only 2.12% of the total number of adoptions). Informal adoptions from 1924 to 2018 generally showed the characteristics of one peak and two poles (Fig. 2); the number was highest in 1990 and reached extremes value in 1960 and 2015, respectively. Considering the data characteristics and major events in China and some cases with explicit reasons for adoptions (Supplementary Fig. 1), we divided 1924–2018 into the following six stages (Supplementary Table 1 and Fig. 2).

Fig. 1: Gender-age pyramid of informal adoption.

The inset shows the results of further subdivision of children under 1-year-old into ten grades.

Fig. 2: Time evolution process of informal adoption.

According to the curve pattern and major events and certain circumstances in China, 1924–2018 was divided into six periods.

(I) Fuzzy burst period (1924–1954). Because of limitations on the amount of data, the characteristics of informal adoption were rather vague. The average age of the children was close to 3 years (971.88 days). The average sex ratio was 110.20, and it fluctuated sharply approximately 1942. Adopted children were relatively concentrated ((G_{Xt}) is 24.60). Henan had the largest share of adoptions (13.20% of period I), which may be related to the famine that broke out in Henan during 1942–1943 (Muscolino, 2011). Theodore White (Lary, 2010) noted that some people gave their children to others for survival during the famine, and doing so was not prohibited at that time.

(II) Unstable rise period (1955–1978). Informally adopted children during this period (average age was 412.96 days) were younger than those during the previous period. Children in early childhood were targeted, and the gender ratio was relatively balanced (mean sex ratio was 101.88). Around 1960, the number of informal adoptions increased and reached the extreme value, and there were slightly more females among children under 1-year-old and more males among children 1 to 6 years old. During this period, China experienced the Great Chinese Famine (1959–1961), which stands out in world history as the most devastating famine on record (Gale Johnson, 1998). During this period, most families who gave away their children did so because they were too poor to raise them. Influenced by son preference, families often gave up female children in infancy, and they gave up male children only when the families struggled to survive (Das Gupta et al., 2003). In 1958, China began to implement a strict household registration system. Since then, informally adopted children may have been able to register in time due to a lack of documents such as birth certificates.

(III) Rapid rise period (1979–1992). The number of informal adoptions increased sharply and peaked in 1990. The average age of adopted children dropped to the minimum (162.86 days). The sex ratio of children under 1-year-old was stable at a low level after 1982 (lower than 30). Since the 1980s, informal adoption has been the most prevalent among females under 1-year-old. These data are likely be mainly related to the gender preference and birth control policy. In traditional Chinese society, only the males of the family can inherit the land and have the responsibility to continue the family line (Das Gupta et al., 2003). Therefore, the son preference is deeply rooted in many families. In 1979, China began to implement a strict one-child policy. Extra-birth families faced a series of problems, such as fines and difficulties in household registration (Sten, 1995; Zhu, 2003; Hesketh et al., 2005). To avoid punishment and have a chance to raise a male, families often chose to give up female babies. Thus, strict birth control heightened discrimination against daughters (Kane and Choi, 1999; Das Gupta et al., 2003). Girls’ rights are seriously impaired. In terms of spatial distribution, (G_{Ot}) dropped to a minimum, indicating that informal adoption was widespread at that time.

(IV) Sharp decline period (1993–2012). In 1990, China agreed to fulfill its obligations to uphold the outcomes from the Convention on the Rights of the Child. Subsequently, China enacted and revised a series of laws to protect children’s rights. In 1992, the authorities began to manage informal adoption and enacted the Adopting Law of the People’s Republic of China (Sten, 1995). The number of informal adoptions decreased, and the average age rose to 344.16 days. The implementation of the law greatly reduced the number of informal adoptions, as was confirmed in interviews with the Civil Affairs Bureau of a city in China. Additionally, the widespread use of sex-selective technology reduced total numbers but exacerbated gender discrimination. The sex ratio reached a minimum of 28.94.

(V) Small fluctuation period (2013-). Adopted children were still predominantly younger than 1-year-old, with a decline in the average age. The sex ratio rebounded. Informal adoptions were more concentrated in space ((G_{Xt}) and (G_{It}) were 23.36 and 52.92, respectively), which was affected to some extent by the number of cases. These results showed that with the enhancement of living standards and legal awareness as well as the two-child policy launched in 2013, informal adoptions were fading. In addition, through the continuous advocacy of gender equality, the son preference was gradually weakening (Hou et al., 2018). The gap between males and females narrowed (mean sex ratio was 67.35).

According to the evolution process over the last 90 years, extreme poverty (Sten, 1995), severe natural disasters (famine) and strict birth control increased the number of informal adoptions. It was not until the 1970s that the son preference began to play a significant role in family decision-making. In the late twentieth century, Henan, Hebei and Shandong became the provinces where children were most likely to be given up.

Source and target provinces (Fig. 3)

In studies of child trafficking, scholars have used the quantity of trafficking cases (Li et al., 2017a, 2017b; Li et al., 2017a, 2017b; Li et al., 2018; Li et al., 2019) or the ratio of trafficking cases to the total population (Wang et al., 2018; Huang and Weng, 2019) in each province to identify provinces where this issue is prevalent. This approach may exaggerate or reduce the impact of the population. Therefore, we chose normalized quantities and degrees to identify the source and target provinces (Fig. 3) and concluded that Sichuan (2.00), Jiangsu (1.75) and Henan (1.66) were the most common source provinces. Henan (1.91), Hebei (1.79), Shandong (1.55) and Guangdong (1.18) were the vital target provinces. Among them, Henan was both a large source and target province.

Fig. 3: Standardized quantity and degree of informal adoptions.

Since the total number and degree of informal in- and out-adoptions are different, the raw data are incomparable. The normalized indexes are therefore used to select source and target areas.

Specifically, informal adoption showed a “inverse T” distribution, which was characterized by children being sent away from the central region in an eastern or western direction and into the coastal regions in a northern or southern direction”. The out-adoption provinces were relatively scattered in space ((G_{Ot}) is 22.04%) and mostly distributed in the central region of China. Sichuan, Jiangsu, Henan, Guangdong, Anhui, Hubei and Shandong were the provinces where sending out children was most common (normalized out-adoption number > 0.56). Jiangsu, Sichuan, Henan, Shaanxi, Anhui, Hubei and Chongqing were the top provinces with a wide range of destinations (normalized out-degree > 0.81). Although families in Shandong and Guangdong gave many children away, the links with other provinces were relatively weak because of the high proportion of within-province informal adoptions (47.43% and 53.64%, respectively). With regard to in-adoptions provinces, most are concentrated in the eastern coastal areas of China. The provinces with a large number of adoptions (normalized in-adoption number >0.50) were Henan, Hebei, Shandong, Fujian, Jiangsu and Guangdong. The provinces with a wider source (normalized in-degree >0.68) were Henan, Hebei, Shandong, and Guangdong.

Migration in the provinces

The ratio of in- to out-adoptions was used to represent the imbalance of migration (Fig. 4). The provinces with serious outflow were Hainan (0.22), Yunnan (0.25), Guizhou (0.26), Sichuan (0.26), and Xinjiang (0.28). Most of these provinces are in the western region of China and are among the least developed Chinese provinces. The northern half of the eastern region, which includes Hebei, Shandong, Tianjin and Beijing, along with Henan and Fujian, were the provinces with the largest number of inflows (ratio > 1.03).

Fig. 4: Geographical migration and ratio between informal in- and out-adoptions of each province.

Darker green indicates more children being adopted out of than into these provinces. Light green and yellow indicate little more children adopted out of than into these provinces. Red indicates that more children were adopted into these provinces. White indicates that the data are insufficient for a province. The lines represent interprovincial informal adoptions.

The proportion of within-province adoption reached 58.4%, and the interprovincial informal adopting paths were concentrated in the central and eastern parts of China (Fig. 4). Most of these are short-distance migrations from neighboring provinces to coastal provinces or Henan. In descending order of quantity, Shaanxi → Henan, Shanxi → Hebei, Jiangsu→Shandong and Shanxi → Henan were the paths with the highest incidence. In addition, Sichuan → Hebei and Sichuan → Henan were relatively distinct interprovincial paths. Similar to the properties of China’s population migration (Fan, 1995; Fan, 2005), informal adoption was mainly characterized by children being sent from poor provinces in south-central and southwestern China to the most developed provinces in the eastern region.

City-level properties

In general, the out-adoption cities were mainly distributed east of the Hu line (Fig. 5), which is consistent with the population distribution characteristics of China (Huanyong, 1990). The in-adoption cities were concentrated in the economically developed areas along the east coast (Fig. 6). Chongqing was the city where the phenomenon was most prevalent, with 638 children adopted out (or 4.15% of the total adopted-out children), followed by Shanghai (2.30%), Wuhan (1.67%), Xi’an (1.63%), Chengdu (1.50%), and Hefei (1.48%). On the other hand, Putian (4.44%), Chongqing (3.12%), Shanghai (3.05%) and Shijiazhuang (2.70%) had the largest inflows, followed by Zhengzhou (2.27%), Xuzhou (2.20%) and Beijing (2.13%). Most of these cities are municipalities and provincial capitals, which means that they are the economic centers and transportation hubs of the region. The average number of out-adoption (or in-adoption) cases in provincial capital cities was close to three times the total number, which indicates that there is a high tendency to select informal adoption in major cities.

Fig. 5: Geographical distribution of informal out-adoptions for each city.

Red indicates the largest number of children adopted out of these cities, followed by orange, yellow, dark green, and light green. White indicates that the data are insufficient for this province. The red dotted line is the dividing line of the population density in China, which is called the Hu Line.

Fig. 6: Geographical distribution of informal in-adoptions for each city.

Red indicates the largest number of children adopted into these cities, followed by orange, yellow, dark green, and light green. White indicates that the data are insufficient for this province. The red dotted line is the dividing line of the population density in China, which is called the Hu Line.

The proportions of within-province adoption and within-city adoption were 58.4% and 37.47%, respectively. In the migration network of informal adoption (Supplementary Fig. 2), Fuzhou (Fujian) → Putian (Fujian) was the strongest path, accounting for 2.87% of the total. After that, the strength of the paths dropped sharply. Suzhou (Anhui) → Xuzhou (Jiangsu) accounted for only 0.52% of the total paths. Nanping (Fujian) → Putian (Fujian), Jiaxing (Zhejiang) → Hangzhou (Zhejiang), and Datong (Shanxi) → Shijiazhuang (Hebei) comprised 0.39% of the total paths. Children were more likely to be adopted in provincial capital cities or cities with better economic conditions, although Putian has a strong attraction to surrounding cities, even provincial capital cities.

Information flow network between cities

We assumed that the supply and demand information on informal adoptions would go through the network. We used node betweenness (that is, the minimum number of paths between any node pairs through an intermediate node) to measure a city’s control degree of information flow between other cities. Higher values indicate that the city is more closely related to other clusters (Wang et al., 2018).

Table 1 shows the top 20 intermediary cities, most of which are located in central and eastern China and the Sichuan-Chongqing agglomeration. Chongqing, Shanghai and Beijing were the hub cities of Southwest China, East China and North China, respectively. As the highest-ranking prefecture-level cities, they all have the characteristics of having a large population density and convenient transportation and being regional economic centers. Wuhan (Hubei), Xi’an (Shaanxi), and Nanjing (Jiangsu) were provincial capitals that largely affected surrounding cities. Eastern coastal cities with better economic conditions (Suzhou (Jiangsu) and Xuzhou (Jiangsu)) also had higher node betweenness.

Table 1 Key cities with the highest node betweenness in city-level informal adoption network.

Table 2 shows that Luoyang → Chongqing has the highest edge betweenness, serving as a link to the informal adoption path between Henan and Chongqing, followed by Beijing → Xuchang. This indicates that Xuchang played a key role in the flow of Henan and Beijing. In general, the betweenness of edges was small, indicating that the single path had less control over the overall network, and the top 20 paths (2.93%) controlled only 2.61% of the total number of paths.

Table 2 Key informal adoption paths with the highest edge betweennesses in the city-level informal adoption network.

Since multiple occurrences of a connection result in path dependence (Garud and Rappa, 1994; Page, 2006), we believe that when the number of cases is > 2, a stable channel for information transmission has been formed. Figure 7 is a city-level informal adoption network constructed by the Yifan Hu proportional layout algorithm (Hu, 2005). Most of the cities are weakly connected (the network density is only 0.001), and some cities have formed the following four tight-knit clusters. The first cluster is the inland-coastal group: Xi’an, Zhengzhou, and Shanghai are key cities in the network and can pass information to the other 21 cities along the paths. Wuxi has become an intermediary city for inland and coastal information transmission. The second group is the Southwest-North China group. Chongqing and Shijiazhuang are the main target cities, while Dazhou plays a key role in connecting the two groups. Another group is the Putian network. This network is dominated by Putian, which consists of four prefecture-level cities in Fujian and one in neighboring Jiangxi. In the last group, Beijing is the main target, and the group consists of three other prefecture-level cities.

Fig. 7: City-level network of informal adoption based on the Yifan Hu algorithm layout.

The colors of the nodes represent the size of the centrality. Darker blue indicates that the node has weaker contact with other nodes, and darker red indicates that it has more connections with other nodes. The colors of the edges are the same as their source. A thicker edge represents a larger quantity of cases for the path. Cities in bold are provincial capital cities.

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