The long-lasting legacy of reproduction: lifetime reproductive success shapes expected genetic contributions of humans after 10 generations

1. Introduction

Fitness is a fundamental concept in evolutionary biology concerned with how natural selection acts on, for example, genes or phenotypes [1]. To measure how selection acts on either of these units of selection, studies often measure their association with a proxy for fitness. One such proxy is lifetime reproductive success (LRS)—the total number of offspring an individual produces over the course of its lifetime [2]—which captures the realized ability of an individual to contribute genes to the next generation, relative to conspecifics with different genetic or phenotypic variants.

LRS's strength as a proxy for individual fitness stems from (i) not confounding the effects of selection acting on parents and offspring [3–5] and (ii) requiring tracking only one generation of individuals. LRS is therefore one of the most widely used fitness proxies for the estimation of the strength and direction of natural selection in both free-living and captive populations [6]. However, we have little understanding of the extent to which LRS predicts the genetic contributions of individuals beyond initial generations [7] and how this compares to other fitness proxies (but see [8]), or in other words, which part(s) of an individual's life history are the key determinants of these long-term genetic contributions.

An individual's expected genetic contributions (IGC)—the proportional contribution of an individual to the gene pool at a specific point in time—is expected to stabilize over generations and enable the estimation of the genetic contributions over far longer periods [7,9,10]. Assuming, among others, random mating, non-overlapping generations, negligible inbreeding and stable population size, stabilization is predicted to occur after approximately 10 generations in a population of 1000 individuals, but longer in larger populations or if any of these assumptions are violated [7,9,11]. Largely in line with these theoretical predictions, three studies of wild vertebrate populations found IGC to be relatively stable after around eight generations [7,10,12] (though other studies have measured expected genetic contributions over shorter periods; e.g. [13]). They also found that LRS may predict variation in IGC, but the amount of variation explained varied greatly among studies (less than 1–48%; electronic supplementary material, table S1) [7,12,14]. The latter is expected as an individual's realized genetic contribution is the ultimate outcome of many factors (e.g. selection, migration, environmental stochasticity and genetic drift), all of which we expect to vary among study systems. For example, we expect LRS to be a poor predictor of IGC if long-term stochastic processes override an initial adaptive response to selection.

The degree to which LRS predicts IGC may also vary with aspects of a species's or population's life history. For example, given a similar number of generations, we could expect the correlation between LRS and IGC to be lower in species that are long-lived and reproduce over longer time periods, as due to the longer time span there is a greater likelihood that they are exposed to either stochastic mortality events (e.g. a disease outbreak) or changes in selection pressures (e.g. the appearance of a new predator, as in a study by Alif et al. [12]). However, thus far only species with relatively short generation times (e.g. approx. 2–4 years [7,10,12,14]) have been examined. This is at least partly for practical reasons: estimating IGC and demonstrating their stabilization in longer lived species requires individual-based data across longer time periods, which are generally more difficult to obtain.

Human genealogical data, which typically spans centuries rather than decades, provide a powerful opportunity to examine the extent to which LRS predicts long-term genetic contributions in a long-lived species with relatively long generation times. Furthermore, by comparing the predictive power of LRS to other fitness proxies, such as lifespan and the number of grandchildren, we can identify key determinants of variation in IGC. For example, annual survival is considered to be a particularly important driver of within-generation changes to the gene pool (e.g. [15]) in humans. Furthermore, lifespan is associated with increased reproductive success [16]. Hence we would expect lifespan to predict IGC, albeit probably with less accuracy than LRS as it does not directly measure reproductive output. The predictive power of LRS is also likely to vary depending on if it is conditioned on offspring survival until a certain age: in pre-demographic transition humans, infant mortality was high [17,18]. Therefore, measuring LRS as the number of offspring surviving to adulthood and not only the number born should better predict IGC. Finally, variation in both the survival and reproduction of an individual and their offspring are ultimately captured by an individual's number of grandoffspring [19], which is expected to provide a more precise predictor of IGC than LRS. Quantifying the differences in the predictive power of lifespan, number of (surviving) offspring and the number of grandoffspring will give insight into the relative importance of parental and offspring survival and reproduction in shaping IGC in humans.

The number of grandoffspring is not only expected to explain more variation in IGC (i.e. to be a more precise predictor), but it may also be less biased than LRS (i.e. more accurate). For example, LRS may overestimate IGC if there is an offspring quality versus quantity trade-off or sibling competition, causing offspring from larger families to have lower fitness [20]. Conversely, sibling cooperation (e.g. [21]) could cause LRS to underestimate IGC if individuals with many siblings have improved fitness. A first step towards identifying the underlying causes of any bias is testing if LRS systematically over- or underestimates IGC. We can do this by quantifying the relationship between an individual's LRS and the average IGC of their offspring (i.e. of siblings). If this relationship is negative, LRS overestimates the IGC of individuals with high LRS (e.g. due to quality–quantity trade-off or sibling competition), whereas a positive relationship is suggestive of LRS underestimating IGC. This may be the result of e.g. sibling cooperation [21], additive genetic variance in LRS [22] or other parental quality effects (e.g. mediated by socio-economic status) that positively affect both parental reproduction and offspring survival/reproduction.

Here, we quantify the degree to which LRS shapes pedigree-derived estimates of stabilized IGC measured after at least 8, and on average 10, (potential) generations [10] using data from a genealogical archive containing the life histories of humans from two parishes in the canton of Glarus, Switzerland. This dataset spans up to 16 generations, containing individuals born in the sixteenth to the twentieth century. We estimate IGC and infer the number of generations required to reach stabilization. We then use generalized linear mixed models (GLMMs) to examine the degree to which IGC are predicted by four fitness proxies: (i) lifespan, (ii) LRS counting all born offspring (LRS), (iii) LRS counting only offspring surviving to adulthood (LRS_SA) and (iv) the number of grandoffspring. We then compare the predictive power of these four proxies to elucidate the importance of parental and offspring survival and reproduction in shaping IGC, and compare these results to those of previously studied bird species. Finally, we test if LRS provides a biased prediction of IGC by estimating the relationship between an individual's LRS and the average IGC of their offspring.

2. Methods

(c) Stabilization of individual genetic contributions

Although IGC fluctuate over time, they are expected to stabilize and become representative of longer term genetic contributions [9,11,32]. Following previous work [7,12], we evaluated stabilization of IGC by grouping individuals into 10-year birth cohorts and quantifying the Pearson correlation coefficient between IGC to each subsequent year and the final year considered (1990). Ten-year cohorts were used to ensure each cohort had at least two focal individuals, the smallest sample size that allows for the calculation of a correlation coefficient. When the correlation remained above a 0.95 threshold for a period of two generations, IGC were considered to have stabilized. We defined a generation as the mean (± s.e.) parental age at offspring birth, which were 32.2 ± 0.04 and 32.1 ± 0.05 years for Linthal and Elm, respectively.

According to this criterion, IGC had stabilized in 1990 for individuals born before 1718 in Linthal (or after 8.5 generations) and before 1734 in Elm (after 8 generations; figure 1; see electronic supplementary material, figure S2 for a comparison to non-stabilized IGC). Hence, IGC to the year 1990 from 3475 focal individuals (1605 from Linthal and 1870 from Elm) were used for further analyses. The length over which IGC were estimated was at least 274 and 257 years, and on average 10.1 and 9.9 generations (324.81(±0.86) and 319.26 (±0.93) years, for Linthal and Elm, respectively), with the birth years of focal individuals ranging between 1575 and 1734 (electronic supplementary material, figure S3).

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3. Results

(a) Individual genetic contributions

We estimated the IGC for 3475 individuals (1605 from Linthal and 1870 from Elm), born between 1575 and1735, to the individuals making up the gene pool of the parishes of Linthal and Elm in 1990. The probability of an individual's lineage going extinct was high, with 73% of individuals having an IGC of zero to the 1990 population (electronic supplementary material, figure S5a). The majority of extinctions are because an individual did not survive to reproductive age (23.4%), survived until reproductive age but had no offspring (43.5%), had offspring but none survived to adulthood (45.3%) or had surviving offspring but no grandoffspring (52.7%) (electronic supplementary material, figure S5). This leaves approximately 20% of the individual lineage extinctions occurring after individuals had at least one grandchild. Over all individuals included in the analysis, a median of 15.9% of their descendants reproduced and thereby continued the lineage, and 14.6% of the descendants had not yet reproduced but were still alive. This leaves 69.7% of the descendants who failed to continue the lineage, and of these, a median of 40.3%, due to emigration rather than death without reproducing. Individuals whose lineages did not go extinct on average contributed 0.1% of the genetic material present in the population in 1990 (electronic supplementary material, figure S5a), although one male contributed 0.6% of the Linthal gene pool.

Lifespan, LRS, LRS_SA and the number of grandoffspring were positively associated with IGC (Beta distribution, pd > 0.975; table 1; figure 2). We also found a negative effect of any of the fitness proxies on the probability of an individuals' lineage going extinct (zero-inflated distribution, pd > 0.975; table 1).

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Table 1. Output from four zero-inflated beta models of IGC with different fitness proxies included: lifespan, LRS, LRS_SA and the number of grandoffspring. Fixed and random effect estimates (posterior distribution median [95% credible intervals] are provided for both the zero-inflated and beta distributions. Significant effects (probability of direction > 0.975) are in italics. Non-significant two-way interactions were removed from the models. Model results with non-significant interactions included are shown in the electronic supplementary material, table S2.

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	lifespan		LRS		LRSSA		number of grandoffspring
	zero inflated	beta	zero inflated	beta	zero inflated	beta	zero inflated	beta
fixed effects
intercept	3.248 [2.882–3.628]	−7.171 [−7.468–−6.880]	2.145 [1.880–2.427]	−7.177 [−7.328–−7.022]	2.219 [1.926–2.521]	−7.264 [−7.418–−7.118]	3.032 [2.623–3.415]	−7.442 [−7.564–−7.322]
[fitness proxy]	−0.054 [−0.059–−0.048]	0.006 [0.002–0.010]	−0.587 [−0.659–−0.515]	0.065 [0.047–0.082]	−0.796 [−0.922–−0.684]	0.098 [0.075–0.119]	−0.591 [−0.711–−0.475]	0.035 [0.031–0.039]
birth parish (Linthal)	−0.037 [−0.351–0.297]	−0.312 [−0.448–−0.162]	0.319 [−0.053–0.718]	−0.403 [−0.535–−0.263]	0.255 [−0.101–0.631]	−0.396 [−0.533–−0.260]	0.220 [−0.323–0.781]	−0.489 [−0.63–−0.349]
sex (male)	−0.154 [−0.371–0.049]	0.079 [−0.029–0.188]	0.138 [−0.111–0.389]	0.050 [−0.057–0.157]	0.115 [−0.125–0.362]	0.063 [−0.045–0.169]	0.141 [−0.241–0.493]	0.057 [−0.047–0.158]
random effects
parish-specific birth cohort (random intercept)	0.217 [0.009–0.626]	0.110 [0.004–0.371]	0.153 [0.006–0.415]	0.069 [0.002–0.212]	0.170 [0.008–0.465]	0.066 [0.002–0.187]	0.281 [0.014–0.759]	0.061 [0.003–0.165]
parish-specific birth cohort × fitness proxy (random slope)	0.006 [0.001–0.014]	0.002 [0.000–0.006]	0.138 [0.069–0.223]	0.011 [0.001–0.031]	0.268 [0.172–0.402]	0.014 [0.001–0.034]	0.269 [0.173–0.402]	0.004 [0–0.009]

IGC (distribution and extinction probability) were dependent upon several other factors. First, individuals born in Linthal had lower IGC, probably because of its larger population size (all models, beta distribution, pd > 0.975; table 1). In line with this, there was no difference in probability of lineage extinction (zero-inflated distribution, pd < 0.975; table 1). There were no interactions between these effects and sex (pd < 0.975; electronic supplementary material, table S2) and no differences between males and females were found (beta and zero-inflated distribution, pd < 0.975; table 1). Further, we found that IGC of individuals varied among birth cohorts (both in their extinction probability and in the non-zero IGC values; see random effects; table 1). There was also variation among birth cohorts in the slope of the relationship between each fitness proxy and IGC, but except for the slope of the relationship between probability of lineage extinction and LRS, LRS_SA and the number of grandoffspring, this variation was small. Finally, a supplementary analysis showed that the proportion of offspring migrating was associated with lower IGC and higher extinction probabilities, but accounting for this did not substantially change the predictive power of the models (electronic supplementary material S2 and table S3).

(c) Is lifetime reproductive success an unbiased estimate of individual genetic contributions?

The per capita IGC of an individual's offspring increased with LRS, but the slope of this relationship was very shallow (pd > 0.975, posterior mode = 0.070, 95% CrI = 0.052–0.089; figure 3). This finding suggests that LRS slightly underestimates IGC in larger family sizes. Furthermore, individuals who lived longer had offspring with higher IGC (pd > 0.975, posterior mode = 0.010, 95% CrI = 0.006–0.014). As before, and likely due to population size differences, mean IGC of offspring was lower for individuals born in Linthal (pd > 0.975, posterior mode = −0.162, 95% CrI = −0.339–0.011) but sex differences showed only trend effects and the offspring of males did not have lower mean IGC (pd = 0.962, posterior mode = −0.066, 95% CrI = −0.173–0.04). No interactions were significant (pd < 0.975; electronic supplementary material, table S4).

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Finally, we found that variance in the mean IGC of offspring was explained by their parents' birth cohort (posterior mode = 0.163, 95% CrI = 0.032–0.306). The parent's birth cohort also affected the slope of relationship between LRS and mean offspring IGC but this variation was relatively small (posterior mode = 0.014, 95% CrI = 0.001–0.038).

4. Discussion

We quantified the extent to which LRS and other fitness proxies predict stabilized IGC measured after approximately 10 generations (321 years), in historical humans from the Swiss Canton of Glarus. We found that LRS predicted 28% of the variation in IGC, showing that reproductive success shapes the long-term genetic contributions of individuals even in a population of a long-lived species with appreciable migration that has experienced large and rapid changes in its environment.

We have shown that different fitness proxies varied in their predictive power of IGC (table 2), allowing us to identify the components of an individual's life history that are most important in determining its IGC. Overall, the model containing the number of grandoffspring explained 57% of variation in IGC, whereas the next best fitness proxy (LRS_SA) explained only 32%, followed by LRS (28%) and lifespan (13%). This is broadly in line with results based on genetic contributions estimated over four generations in nineteenth-century Sweden [40]. The number of grandoffspring explaining most variation was expected, as the number of grandoffspring incorporates the most information about the life history of an individual. However, together with our finding that LRS_SA and LRS explain a similar amount of variation in IGC (28% versus 32%) and that lifespan explains only 13% of the variation in IGC, this suggests that offspring mating and reproduction is a much greater determinant of IGC than survival (of both offspring and the individual themselves), even in a population with substantial childhood mortality (electronic supplementary material, figure S1). The lack of a significant increase in the predictive power of LRS when accounting for infant mortality could be due to the replacement effect that can occur in humans where the death of a child during childhood results in another child being born soon after and the number of children surviving to adulthood to be largely unaffected. Finally, although we found no difference between the sexes, the highest IGC were for multiply-marrying males whose first wives died around the age of menopause, allowing the widowers to remarry a younger female and achieve a LRS (and IGC) greater than males who did not remarry.

Although the number of grandoffspring will naturally be a more precise predictor of IGC than LRS because it is closer in time to our estimates of IGC, and therefore incorporates more of the stochasticity that influences IGC, it is not necessarily the most useful fitness proxy. First, although statistically significant, we found only a weak relationship between an individual's LRS and the average IGC of its offspring, showing that LRS is a relatively unbiased measure of IGC. The fact that the association is positive suggests that the increase in predictive power between LRS and number of grandoffspring is not due to LRS being a biased predictor. Albeit small, the positive relationship between LRS and per capita IGC argues against the existence of an offspring quality–quantity trade-off, which has been previously found in humans [41–43]. Instead it is somewhat suggestive of positive sibling effects, perhaps due to alloparenting [21], or an overriding effect of parental quality and resources (e.g. through socio-economic status) (e.g. [44,45]) or additive genetic variance in LRS [22]. Second, there are practical reasons that limit the utility of the number of grandoffspring as a fitness proxy: Not only is it more sampling intensive, reliably counting the number of grandoffspring may not be feasible if a significant proportion of the population disperses outside of the study site, or offspring cannot be linked to parents once they have reached independence. Third, the number of grandoffspring confounds the fitness of multiple individuals, which can be problematic when estimating the strength of phenotypic selection [3–5]. All things considered, our results therefore strengthen the case for LRS as an evolutionary relevant and relatively unbiased fitness proxy when it comes to the study of selection in humans, assuming our findings are representative for other populations and time periods.

Although at first sight high, our finding that 70% of individual lineages went extinct over the study period is similar to that found in previous studies on pedigreed populations of birds, which reported extinction probabilities of 61–71% (electronic supplementary material, table S1), and comparable with levels of lineage extinction in bighorn sheep [13], and in humans after four generations in Sweden [46]. The main difference between our results and those for the three bird studies [7,12,14] was that when we measured LRS at a later point in the offspring's life (i.e. LRS_SA), the predictive power of LRS for IGC did not increase greatly. This is in contrast with, for example [14], which found that offspring survival was a key determinant of reproductive success. Our results therefore suggest that despite substantial infant mortality, offspring survival to adulthood is a less important determinant of IGC than mating and reproductive success in humans.

The amount of variation in IGC explained by LRS measured close to birth (28%) in this study was similar to previous findings for song sparrows and scrub-jays (37% and 32%, respectively), but higher than for house sparrows (0–4%). While the role of migration in the latter island population is likely to be small, the low explanatory power of LRS is potentially due to a population bottleneck that occurred between the timepoint when fitness proxies were measured and when IGC was estimated [12]. This could have caused stochastic mortality resulting in low predictive power of fitness proxies. Another factor explaining different findings across populations is the role of stochasticity in driving variation in LRS itself. LRS is influenced by both environmental and genetic components with the environment contributing most of the variation [47], including in humans [48]. In species where the environment determines less variation in LRS, LRS would be expected to be a greater predictor of IGC [7,8]. Here, we showed that environmental effects were an important factor, with non-negligible variation in IGC being explained by an individual's birth cohort (table 1). Further, as mean LRS values decrease, there is a greater likelihood of lineages going extinct due to stochasticity, drift or dispersal [7,49], which perhaps partially explains the relatively high rates of lineage extinction in this study (70% versus 61–71%; electronic supplementary material, table S1). Although these species also differ in numerous other ways. However, future studies could examine if this phenomenon is detectable across the human fertility transition towards lower LRS. In summary, there are both similarities and differences across study systems, but the small number of species and the lack of different human populations (across cultures) studied limits broader extrapolation.

The majority of the variation in IGC (72%) remained unexplained in the model containing LRS, with migration being a contributing factor to this unexplained variation: First, there were significant levels of both immigration and emigration (electronic supplementary material, figure S1), and both are expected to decouple LRS and IGC. Indeed, the dispersal of descendants of ancestral individuals is a particularly important driver of local lineage extinction. Although migration is also expected to reduce the stabilization times relative to theoretical expectations, we observed stabilization times lower than theory predicts [9]. One explanation for this is that the effective population size (number of breeding individuals) is far lower than the total population size, for example because a significant proportion of individuals did not reproduce (see electronic supplementary material, figures S1 and S5). However, other explanations (e.g. non-random mating according to social class, drift and fluctuating selection) are also possible, and it is clear that we need to further our understanding of the determinants of the time until stabilization of IGC in natural populations. Enumerating the relative contributions of these factors across different systems (or using simulations, e.g. [50]) should be a target of future work.

Although still in its infancy, the use of pedigree data to estimate long-term genetic contributions opens a range of exciting avenues. Building on our work using human genealogical data, and the work on non-human animals by others [7,12,14], future work would benefit from further exploration of the similarities and differences among the different methodologies at our disposal, and between gene-dropping methods [7,12,14] and expected genetic contributions (e.g. [10]; this study) in particular, as the two do not necessarily equate. Furthermore, while our study has highlighted the ability of human genealogical data to provide insight into human evolution [51,52], and the estimation of fitness more broadly, applying these methods to similar data for an array of human populations (see [53] for a review) will allow us to quantify the degree to which these findings hold across cultures, environments and time.

Data accessibility

All data and R scripts necessary for replicating the analysis can be accessed at Dataverse https://doi.org/10.34894/P2ETYZ [54].

The data are provided in the electronic supplementary material [55].

Authors' contributions

E.A.Y.: conceptualization, formal analysis, investigation, methodology, project administration, software, validation, visualization, writing—original draft and writing—review and editing; E.C.: conceptualization, formal analysis, investigation, methodology, software and writing—review and editing; V.L.: conceptualization, investigation, methodology, supervision and writing—review and editing; E.P.: conceptualization, data curation, funding acquisition, investigation, methodology, supervision and writing—review and editing; H.L.D.: conceptualization, funding acquisition, investigation, methodology, supervision and writing—review and editing.

All authors gave final approval for publication and agreed to be held accountable for the work performed therein.

Conflict of interest declaration

We declare we have no competing interests.

Funding

E.A.Y.'s PhD was funded by the University of Groningen, through a Rosalind Franklin Fellowship awarded to H.L.D. Digitization and transcription of the data were funded by the Swiss National Science Foundation (grant no. 31003A_159462). V.L. was funded by the Strategic Research Council of the Academy of Finland (grant nos. 345185 and 345183).