Human genealogy reveals a selective advantage to moderate fecundity

Abstract

Life-history theory suggests that the level of fecundity of each organism reflects the effect of the trade-off between the quantity and quality of offspring on its long-run reproductive success. The present research provides evidence that moderate fecundity was conducive to long-run reproductive success in humans. Using a reconstructed genealogy for nearly half a million individuals in Quebec during the 1608–1800 period, the study establishes that, while high fecundity was associated with a larger number of children, perhaps paradoxically, moderate fecundity maximized the number of descendants after several generations. Moreover, the analysis further suggests that evolutionary forces decreased the level of fecundity in the population over this period, consistent with an additional finding that the level of fecundity that maximized long-run reproductive success was below the population mean. The research identifies several mechanisms that contributed to the importance of moderate fecundity for long-run reproductive success. It suggests that, while individuals with lower fecundity had fewer children, the observed hump-shaped effect of fecundity on long-run reproductive success reflects the beneficial effects of lower fecundity on various measures of child quality, such as marriageability and literacy, and thus on the reproductive success of each child.

The influential life-history theory suggests that fecundity of organisms reflects the impact of the fundamental trade-off between the quantity and quality of offspring on long-run reproductive success. Central to the theory is the supposition that there exists a level of fecundity beyond which the number of descendants in the long run diminishes^1–4. A negative association between the quantity and quality of offspring has been documented in a wide variety of species, ranging from plants to humans. In particular, researchers uncovered an inverse relationship between the number of seeds and their size, as well as between the quantity and quality of offspring within and across mammals^5–9. Furthermore, a trade-off between fertility on the one hand and offspring survival probability and education on the other hand has been documented for preindustrial human societies^10–14.

Nevertheless, as established theoretically, in contrast with a prevailing perception, the presence of a trade-off between the quantity and quality of offspring is merely a necessary, but not sufficient, condition for the existence of a level of fecundity beyond which a higher level would have a negative effect on reproductive success in the long run (Supplementary Section 1). In particular, the proposed theory suggests that, a priori, in an environment in which the carrying capacity was an order of magnitude greater than the size of the founder population, an individual with the highest level of fertility could have had the largest reproductive success if the direct contribution of any additional child to her long-run reproductive success would be larger than the adverse indirect effect of this child on the quality of her children and their long-run reproductive success. However, if the impact of investment in the quality of children on their potential income, and thus their reproductive success, is sufficiently large, an intermediate level of fecundity would generate the highest reproductive success and would therefore be favoured by natural selection.

The extensive exploration of the trade-off between quantity and quality of offspring, while confirming an important building block of the theory, has therefore not shed direct light on the effect of a reduction in quantity, and the associated investment in offspring quality, on long-run reproductive success. Moreover, existing attempts to examine the effect of fertility on long-run reproductive success in preindustrial societies have been largely inconclusive^15,16. The lack of evidence that reduced fertility is a fitness-maximizing reproductive strategy in humans has recently induced researchers to consider alternative determinants of the number of children in preindustrial societies, underlying the trade-offs between reproductive and somatic effort, as well as between reproductive and mating effort¹⁷. In contrast, the present study and the evidence that it provides may rekindle interest in the importance of the quantity–quality trade-off in the understanding of the determinants of observed fertility in preindustrial societies.

This study explores the effect of fecundity on long-run reproductive success in a human population. Using a reconstructed genealogy for nearly half a million individuals, based on the parish registers of the Saint Lawrence Valley in Quebec during the 1608–1800 period, we trace the number of descendants of early inhabitants of this Canadian province in the subsequent four generations. As depicted in Fig. 1, a marriage over this period signalled a deliberate attempt to conceive. A sharp spike in birth rates occurs starting in the 35th week after marriage, and nearly one-third of births occurs within the 36–44 weeks time interval. Hence, using the protogenesic interval (PI; that is, the time interval between the date of marriage and the first live birth) as a proxy for fecundity over this period, and thus as a source of variation in family size, the research establishes that while higher fecundity was associated with a larger number of children, moderate fecundity is associated with the maximum number of descendants after several generations. Furthermore, the analysis examines the potential mechanisms that govern the non-monotonic effect of fecundity on long-run reproductive success.

Fig. 1 |. Time between marriage and first birth.

Weeks elapsed from marriage to first birth of 53,154 mothers in Quebec during the 17th to 18th century, truncated at 142 weeks.

The research finds that the maximum long-run reproductive success is attained by individuals with a moderate PI (that is, those whose first delivery occurs 65–74 weeks after their marriage, depending on the statistical specification, relative to a sample median of 53 weeks and a sample mean of 62 weeks). In particular, compared with highly fertile individuals whose first child is born 38 weeks after the marriage, those individuals have on average 0.35–0.55 fewer children, but 0.63–0.66 more grandchildren, 9.5–17.2 additional great-grandchildren, and 16.0–32.4 additional great-great-grandchildren. Moreover, in light of the heritability of fecundity^18–21 and the heritability of PI in particular (Supplementary Section 5), the analysis suggests that evolutionary forces decreased the level of fecundity in the population over this period, as reflected by a predicted 4-week increase in the PI, consistent with the finding that the level of fecundity that maximized long-run reproductive success was above the population mean and median.

In light of the inherent uncertainty in the process of human reproduction, this study attempts to identify the causal effect of fecundity on long-run reproductive success by isolating the random component of the PI (Fig. 2). Given the social norm observed in preindustrial Quebec, in which marriage marked the intention to conceive a child, the analysis exploits the time interval between the date of first marriage and first birth (that is, the PI) as a source of variation in fertility, reflecting the probability of successful conception (that is, fecundability). The PI is affected by genetic predisposition, socioeconomic and environmental conditions, and the realization of the randomness in the occurrence of a pregnancy in a given monthly cycle among couples that are actively engaged in an attempt to conceive.

Fig. 2 |. Overview of the proposed hypothesis.

The effect of fecundity of the head of lineage on long-run reproductive success is established by isolating the impact of the random component of the PIs (that is, the time interval from marriage to first birth) of the head of lineage, accounting for the marriage age, as well as the genetic predisposition towards fecundity, as captured by variations in PI across siblings.

This study attempts to isolate the random variations in the PI by accounting for a range of confounding genetic, socioeconomic and environmental factors that may have affected PI, reproductive success and quality of offspring. In particular, environmental factors are accounted for by focusing on a homogeneous founder population in a single geographical location in a given time period. Cultural, socioeconomic and genetic factors that may affect fecundity are accounted for by focusing on variations in PI across siblings, while confounding socioeconomic characteristics are further accounted for by controlling for the parental marriage age, literacy status and gender. While the empirical analysis exploits the random variation in PI to identify the causal effect of fecundity on the number of descendants after four generations, it further establishes that the effect of the phenotypic variance in PI (that is, including non-random components) on long-run reproductive success is qualitatively similar (see Supplementary Sections 2 and 3 for additional information on the empirical strategy, independent variable and analysis).

Results

The effect of fecundity (as proxied by the time interval from marriage to first birth (that is, PI)) on reproductive success is estimated initially using linear regression models. As presented in Table 1, accounting for the potentially confounding effects of birth year and age of marriage (columns 1–4), gender, stoppage age (that is, the age at last birth) and literacy (as captured by the signature status on the marriage certificate), as well as factors shared by heads of lineages originating from a common mother (that is, lineage fixed effects (columns 5–8)), the analysis suggests that the number of children is linearly and negatively affected by PI. In particular, an additional year from marriage to first birth results in a reduction of 0.77 children (column 1) or 0.54 children (column 5).

Table 1 |.

Effect of fecundity (proxied by PI) on the number of descendants of heads of lineages born no later than 1685

	log[number of descendants in generation]
	Generation 1	Generation 2	Generation 3	Generation 4	Generation 1	Generation 2	Generation 3	Generation 4
Column number	1	2	3	4	5	6	7	8
PI	−0.080***	0.137	0.509**	0.830***	−0.077***	0.208	0.535***	0.810***
	(0.024)	(0.180)	(0.232)	(0.311)	(0.011)	(0.130)	(0.181)	(0.258)
PI2		−0.054	−0.174**	−0.290***		−0.089**	−0.210***	−0.325***
		(0.058)	(0.075)	(0.099)		(0.042)	(0.059)	(0.084)
Literacy					−0.027*	0.044	0.125***	0.109*
					(0.014)	(0.032)	(0.046)	(0.066)
Male					−0.028*	0.025	0.085*	0.036
					(0.015)	(0.031)	(0.043)	(0.063)
Lineage fixed effects	No	No	No	No	Yes	Yes	Yes	Yes
Stoppage age fixed effects	No	No	No	No	Yes	Yes	Yes	Yes
Number of observations	3,798	3,798	3,798	3,798	3,798	3,798	3,798	3,798
Adjusted R2	0.018	0.013	0.026	0.301	0.799	0.442	0.296	0.355
Joint significance level of PI and PI2	<0.001	0.439	0.055	0.007	<0.001	0.002	<0.001	<0.001
Level of PI at the peak		1.256	1.463	1.431		1.163	1.272	1.247

This table presents the results of a series of OLS regressions of the number of children (generation 1), grandchildren (generation 2), great-grandchildren (generation 3) and great-great-grandchildren (generation 4) on the fecundity and squared fecundity of heads of lineages born before the end of 1685 (as proxied by their PI measured in years; that is, PI and PI2). Birth year and marriage age dummy variables are included as controls in all columns. Furthermore, the specifications in columns 5–8 account for lineage fixed effects (that is, the estimation is based on variation across heads of lineages who are siblings, as opposed to all heads of lineages, as estimated in columns 1–4), as well as dummy variables for gender, stoppage age, literacy (as proxied by marriage certificate signatures) and unknown literacy status. Standard errors (clustered at the level of the firstborn) are reported in parentheses.

^*P<0.10;

^**P<0.05;

^***P<0.01.

For additional information, see the Methods and Supplementary Section 2.

However, there is a significant quadratic relationship between PI and the number of grandchildren (columns 2 and 6), great-grandchildren (columns 3 and 7) and great-great-grandchildren (columns 4 and 8). In particular, the peak of the estimated quadratic relation between the number of great-great-grandchildren and PI is for PI = 74 weeks (that is, 1.43 years; column 4) or 65 weeks (that is, 1.25 years; column 8). Interestingly, the PI associated with the peak of the hump is above the mean and median PI in the population (Supplementary Table 3), in accordance with the finding that evolutionary forces increased the mean PI in the population over the time period. Moreover, the interior hump-shaped relationship between the number of great-great-grandchildren and PI is highly significant (P = 0.0085 in column 4 or P = 0.0078 in column 8)²².

As established in Supplementary Table 5, the results in Table 1 are robust to the use of a more parsimonious specification, accounting only for the marriage age. Moreover, as established in Supplementary Section 12, the results are robust to accounting for the potentially confounding effects of remarriages, spousal migration, birth and death parish, month of marriage, month of birth of the firstborn, firstborn status, within-lineage birth order, patrilocal or matrilocal marriage status, distinct death and birth parishes, north or south shore parish, urban parish and longevity of the head of the lineage. Furthermore, as established in Supplementary Section 13, the results are robust to a range of sample restrictions based on gender, family size, marriage age, north or south shore parish, urban parish and other factors, as well as the inclusion of heads of lineage born over the entire period.

Using a generalized linear model (GLM) with a negative binomial distribution and logarithmic link function yields qualitatively similar findings (Supplementary Tables 4 and 5). In particular, Fig. 3 depicts the effect of PI on the number of descendants under the most parsimonious GLM specification (accounting only for the marriage age). Figure 3a shows a negative effect of PI on the number of children, reflecting the observation that, all else being equal, a shorter PI in the pre-demographic transition era increases the total number of children born in a family, whereas Fig. 3b depicts the hump-shaped effect of PI on the number of great-great-grandchildren.

Fig. 3 |. Predicted numbers of children and great-great-grandchildren.

a,b, Predicted number of children (a) and great-great-grandchildren (b) as a function of the PI of 3,798 heads of lineages, as derived from columns 5 and 8 of Supplementary Table 5. The shaded areas represent 95% confidence bands and the rugs at the bottom of the panels represent the distribution of the observations.

Moreover, the analysis suggests that evolutionary forces decreased the level of fecundity in the population over this period. In light of the heritability of PI (Supplementary Section 5) and the heritability of fecundity more generally^18–21, since the expected change in PI within each lineage weighted by fitness is insignificantly different from zero, it follows from the Price equation that the evolutionary change in PI is captured by the covariance between the fitness of the head of lineage i and the PI of this individual relative to the average fitness in the population^23,24. In particular, the evolutionary change in PI over these four generations, as captured by the covariance between the number of great-great-grandchildren of the head of lineage i and the PI, divided by the mean number of great-great-grandchildren in the population, is equal to 0.072 years (that is, 3.8 weeks). Hence, consistent with the finding that the level of PI that maximized long-run reproductive success was above the population mean (that is, 62 weeks), as well as the population median (that is, 53 weeks), evolutionary forces operated towards an increase in the mean PI over these 4 generations from 62.4 to 66.2 weeks.

This research identifies several mechanisms that contributed to the importance of moderate fecundity for long-run reproductive success. While individuals with lower fecundity had fewer children, the observed hump-shaped effect of fecundity on long-run reproductive success reflects the beneficial effects of lower fecundity on various measures of child quality and thus on the reproductive success of each child. In particular, the analysis establishes that lower fecundity indeed had: (1) a positive effect on the marriageability of children; (2) a negative effect on the age of marriage; and (3) a positive effect on the literacy of children²⁵. Thus, despite the positive effect of fecundity on the number of children, its adverse effect on child quality and the reproductive success of each child contributed to generating the hump-shaped relationship between fecundity and long-run reproductive success.

The proposed mechanisms are explored in Table 2, accounting for the head of the lineage’s birth year, marriage age, gender and literacy. This analysis establishes that: (1) the association between PI and the fraction of children who got married, among those who survived to the age of 40 years, is significantly positive (columns 1 and 2); (2) the association between PI and the average marriage age among offspring who got married is significantly negative (columns 3 and 4); and (3) the association between PI and the fraction of children who signed their marriage certificate is positive and highly significant statistically (columns 5 and 6). Moreover, the literacy of heads of lineages has a highly significant positive effect on the literacy of their children. These results are robust to alternative specifications (Supplementary Section 3).

Table 2 |.

Effect of fecundity (as proxied by PI) on offspring quality

	Marriage rate of children (among survivors to the age of 40 years)		Average marriage age of children		Literacy rate of children
Column number	1	2	3	4	5	6
PI	0.299***	0.232**	−0.430***	−0.339**	.401***	0.337***
	(0.113)	(0.110)	(0.151)	(0.149)	(.090)	(0.091)
Literacy		0.779***		−0.705***		1.305***
		(0.109)		(0.180)		(0.095)
Male		0.365***		−0.720***		0.407***
		(0.120)		(0.161)		(0.098)
Stoppage age fixed effects	No	Yes	No	Yes	No	Yes
Number of observations	3,727	3,727	3,796	3,796	3,448	3,448

This table examines the effect of fecundity (as proxied by PI) on different forms of child quality. Columns 1 and 2 present the results of fractional logit regressions of the marriage rate (among children surviving to the age of 40years) on the fecundity (as proxied by PI) of heads of lineages with at least one child surviving to the age of 40years. Columns 3 and 4 present the results of OLS regressions of the average marriage age of children on the fecundity of heads of lineages (as proxied by PI). Columns 5 and 6 present the results of fractional logit regressions of the literacy rate of children (as inferred from marriage certificate signatures) on the PI of heads of lineages with at least one surviving child with observed literacy status. Birth year and marriage age dummy variables are included as controls in all specifications. Furthermore, the specifications in columns 2, 4 and 6 include dummy variables for gender, stoppage age, literacy (as proxied by marriage certificate signatures) and unknown literacy status. Standard errors (clustered at the level of the firstborn) are reported in parentheses.

^*P<0.10;

^**P<0.05;

^***P<0.01.

For additional information, see Methods and Supplementary Section 3.

Conclusion

Evidence from preindustrial Quebec suggests that the forces of natural selection favoured individuals characterized by moderate fecundity. While higher fecundity was associated with a larger number of children, moderate fecundity maximized the number of descendants after several generations, reflecting the beneficial effect of lower fecundity on various measures of child quality²⁵.

Moreover, the analysis suggests that evolutionary forces decreased the level of fecundity in the population over this period. These findings are consistent with theories of the onset of the demographic transition and the transition of economies from stagnation to modern growth in which natural selection favoured individuals with a larger predisposition towards child quality²⁶, as well as with the predictions of unified growth theory²⁷.

Methods

Data and sample.

The data are based on the demographic history of 471,412 individuals who lived in Quebec during European settlement in the region. The data are based on the reconstructed genealogy of the parish registers of the Saint Lawrence Valley in Quebec²⁸, as provided by Le Programme de Recherche en Démographie Historique at the University of Montreal. It exhaustively covers the Catholic population of European descent who lived in this area from 1608–1799²⁹. Nearly all individuals whose data are included (that is, more than 99.96%) were born after the founding of Quebec City in 1608, and more than 94% of them were born and died in Quebec. Importantly, the data cover all parishes of Quebec, and in light of the negligible inter-provincial migration over this period, the presence of some intra-provincial migration does not prevent tracking of the reproductive success of individuals over several generations.

The sample is restricted to the reproductive success of 3,798 individuals, defined as ‘heads of lineages’. This sample satisfies several criteria. First, the heads of lineages were born in Quebec before the end of 1685 and died in the province. Second, the sample is restricted to individuals whose PI is at least 38 weeks and less than 2 years and 38 weeks^25,30. The use of plausible alternative lower-end cut-offs, such as 36 or 40 weeks, would not affect the qualitative results. Moreover, the upper-end cut-off mitigates the effect of measurement errors that may characterize extreme PIs, as well as the potential confounding impact of underlying biological conditions associated with extreme PIs on reproductive success. Third, the key data for each head of lineage regarding their date of first marriage as well as the birth date of their firstborn received the highest-quality grade by the data provider (see Supplementary Section 4 for additional information on the data).

Statistical model.

The impact of the time from marriage to first birth (that is, PI) of heads of lineages on the number of children, grandchildren, great-grandchildren and great-great-grandchildren is assessed by estimating a series of regression models. The analysis is performed across all 3,798 heads of lineages, regardless of their maternal origins, as well as across siblings, using two-sided statistical tests. Some heads of lineage have no siblings and the identification in the second method is based effectively on variation across 3,348 heads of lineages.

First, the effect of the PI of the head of lineage on the number of children is estimated using the ordinary least squares (OLS) regression model:

$$\ln \left[D_{i,1}\right]={\beta }_{0,1}+{\beta }_{1,1}{\text{PI}}_i+{\mathbf{Z}}_i^{\prime }{\mathbf{b}}_1+{\epsilon }_{i,1}$$

where D_i,1 is the number of children (that is, offspring in generation 1) born to the head of lineage i; PI_i is the PI of the head of lineage i; Z_i is a vector of control variables capturing the characteristics of the head of lineage i (that is, marriage age, birth year, gender, literacy and stoppage age; see Supplementary Section 4) and ε_i,1 is an error term clustered at the level of heads of lineages sharing the same firstborn. The coefficient of interest is β_1,1 and it is predicted to be negative. Namely, the PI of the heads of lineages is predicted to have a negative effect on the number of children. Furthermore, the analysis considers a quadratic specification; however, the impact of the second-order quadratic term of PI on the number of children is insignificantly different from zero.

Second, the effect the PI of the heads of lineages and long-run reproductive success is estimated using the OLS regression model:

$$\ln \left[D_{i,t}\right]={\beta }_{0,t}+{\beta }_{1,t}{\text{PI}}_i+{\beta }_{2,\text{t}}{\text{PI}}_i^2+{{\mathbf{\text{Z}}}^{\prime }}_i{\mathbf{b}}_t+{\epsilon }_{i,t}$$

where D_i,t is the number of descendants that the head of lineage i has in generation t, and t = 2, 3 or 4. The coefficients of interest are β_1,t and β_2,t. If indeed PI has a hump-shaped effect on long-run reproductive success, β_1,t > 0 and β_2,t < 0.

Alternative regression methods suitable for count data are also employed. In particular, Supplementary Table 4 demonstrates that the results are robust to the use of a GLM model with a negative binomial distribution and a logarithmic link function.

Reporting Summary.

Further information on research design is available in the Nature Research Reporting Summary linked to this article.

Data availability

The data that support the findings of this study are available from PRDH at the University of Montreal. Restrictions apply to the availability of these data, which were used under license. They are available from the authors upon reasonable request and with permission of PRDH.

Code availability

The statistical code is available from the authors upon request.