Scholars carried out relevant research on the trade-off between fertility and longevity. In terms of number of births, most studies supported the negative relationship between number of births and longevity (Kitagawa and Hauser 1975. Beral 1985. Kvale et al. 1994. Green et al. 1988. Lund et al. 1990. Friedlander 1996). Bourg (2007) used complete cohort data to study that under natural fertility conditions, when the number of births increased, longevity would not decrease, but in the modern population, when women had more than five children, the mortality risk may increase. In order to overcome the direct consequences of pregnancy on death, Westendorp and Kirkwood (1998) limited the sample to postmenopausal women. They still found that the number of births was negatively correlated with women's longevity in women aged 60 and over, and a similar correlation was obtained when the sample was expanded to the age group of 50. Similar findings were also found in the study of Chinese samples. Based on the data of China Hainan centenarian cohort study, Zhu et al., (2021) found that compared with women aged 80–99, women over 100 had significantly fewer children, and there was also a negative correlation between female fertility and longevity in China's elderly population. However, due to the influence of population, social and economic level, the trade-off relationship between fertility and longevity was becoming more and more complex.
The mechanism of the trade-off relationship between fertility and longevity was as follows: first, in the gestational stage, there was a replacement relationship between the resources required for fertility and the resources used to maintain life (Kirkwood, 1977). A large number of reproductive activities exhausted the resources that could have been used to maintain life. Among them, Disposable Soma Theory (DST) believed that organisms need to invest more resources to maintain the integrity of somatic cells in order to live longer, but fertility consumed a large proportion of resources, resulting in the reduction of resources used to maintain somatic cells. The extension of longevity was at the cost of reducing reproductive behavior. We must reduce reproductive behavior in order to live longer. On the contrary, the more births, the shorter longevity. Second, in the stage of childbirth and parenting, reproductive behavior brought long-term negative cumulative effects to health through physiological or socio-economic factors. Multiple pregnancies and childbirth worsened women's health, increased the pressure of child care, and made men have greater economic pressure and excessive labor participation. From the perspective of health, the biological reaction brought by childbirth behavior increased the risk of coronary heart disease and obesity in the later stage for women (Bastian et al, 2005). Repeated pregnancy may also affect the metabolism of lipid and glucose for a long time, resulting in health problems such as obesity and arteriosclerosis (Skilton et al., 2009). In the long run, pregnancy and childbirth had a direct impact on women's health, especially the health status of high parity women was worse than that of low parity or non-fertility women, and high parity women faced higher risks of chronic diseases such as cardiovascular diseases, endocrine diseases and some cancers (Peters et al., 2016). The damage of fertility to physical health also existed in man groups. In some male animals, mating was usually dangerous, even suicidal mating. After mating, males died, such as mantis, salmon and bag shrew. From the perspective of social economy, life course theory held that health was a dynamic process that developed over time and was the result of the accumulation of a variety of risks and protective factors in the life process. Major events experienced by individuals in their life course, such as childbirth and abortion, may have a cumulative impact on health in old age (Liu et al., 2019). Among them, fertility was not only limited to women's physiological behavior, but also an important change for men and women to enter a new role in the life process, which changed the whole family structure. Accompanying fertility may bring about changes in individual social roles, social networks and social participation, which had a cumulative or even negative impact on the health of the elderly. According to the health production theory of Grossman (1972), health was not only a kind of consumer goods, but also an investment goods. Apart from the time of illness, part of the remaining time needed to be used for work to produce other goods, and the other part was used for leisure. Health can be produced only when work and leisure were matched together. When the mother had more children, she spent more time on child care and housework, which occupied the mother's leisure time and family resources, resulting in the mother not having too much time for health production. At the same time, having too many children required more social labor in exchange for parenting resources. According to the gender roles of parents within the family, men often engaged in more social labor. The more children and the more parenting resources they need, they needed to participate in more social labor. Excessive labor participation was detrimental to the health level, which caused negative accumulation of growth in their later years of health and life. The Hypothesis 1 was formulated accordingly:
There is a trade-off between the number of children and parental life expectancy in later life, with an increase in the number of children having a negative impact on life expectancy in later life.
When analyzing the relationship between fertility and longevity, the gender of children was also an important factor to be considered. Having sons and daughters may have different effects on parents' longevity. Boys grew faster during pregnancy and had a heavier average weight at birth (Loos et al., 2001. Marsal et al., 1996), larger body size may have higher lactation needs. The birth interval of women after giving birth to sons was often longer than that after giving birth to daughters (Mace and sear, 1997), and the mother may become more exhausted due to the production of male offspring. Helle et al., (2002) found that having a son brought a higher relative survival cost for the mother than having a daughter. The son shortened the life of the mother, while the daughter not. Van De Putte et al., (2003) found a similar conclusion in the study of a Flemish agricultural village in the 18th-20th century. The Hypothesis 2 was formulated accordingly:
Increases in the number of boys have a more pronounced negative impact on parental longevity in later life than the number of girls.
In addition, childbearing time also had an impact on parents' longevity, but this impact was adjusted by region and gender. In terms of regional differences, Doblhammer (2000) found that the mortality of women giving birth before the age of 20 was higher than that of women giving birth for the first time after the age of 20, and the mortality of late motherhood mothers was lower than that of young mothers. Westendorp and Kirkwood (1998) conducted a study on female samples from British noble families and found that there was a significant negative correlation between the time of giving birth and longevity, but there was a significant positive correlation between the age of first birth and longevity. Zeng and Jin(2004) also believed that late motherhood was significantly related to the health and longevity of the elderly in China. Hank (2010), based on the data of the German Socio-Economic Panel, found that in West Germany, early motherhood was accompanied by poor physical health, while in East Germany, late motherhood was accompanied by poor mental health. In terms of gender differences, early motherhood reduced the survival time of elderly women (Li and Zhang, 2017), and late motherhood was only related to women's longevity, but not for men (McArdle et al., 2006). The Hypothesis 3 was formulated accordingly:
The effect of the number of children on parental longevity is differentiated by gender, urban/rural and timing of childbearing.