Cliff-edge model of obstetric selection in humans

Successful labor requires the match of the neonatal head and shoulder dimensions with the dimensions of the maternal pelvic inlet, midplane, and outlet. Consider an idealized variable, $D$, that represents the difference between the size of the neonate and the size of the maternal pelvic canal. A negative value indicates a pelvic canal that can accommodate the newborn, whereas fetopelvic disproportion occurs if $D>0$. In practice, this composite quantity cannot be inferred from the usual clinical measurements, but it is conceivable that $D$ can be expressed as a function of a finite set of appropriate morphological measurements.

Neonatal size and maternal pelvic dimensions influence fitness (i.e., reproductive success) of the newborn and the mother in multiple ways. Undoubtedly, relative brain size had increased during human evolution in response to directional selection. Recently, it has also been suggested that the large human brain may be the result of runaway selection for the childcare of infants that are born prematurely because of their large brain (12). It is unclear whether any of this selection still persists after the slight decrease of brain size in the late Pleistocene. However, birth weight, which correlates with brain size at birth, is strongly positively associated with infant survival rate (13) and has also been reported to correlate negatively with the risk of multiple diseases (14). Reducing neonatal brain size by shortening gestation length seems to be equally disadvantageous: Delivery before term clearly increases the likelihood of impaired cognitive function in later life (15, 16). Grabowski and Roseman (17) identified a complex pattern of natural selection that has acted on the pelvis throughout hominin evolution, but no consensus has been reached about the actual benefit of a narrow pelvis for bipedal locomotion (7, 8, 10, 11). However, a narrow pelvic cavity might be advantageous for other reasons as well. During bipedal posture, the inner organs of the peritoneal cavity are vertically aligned with the rectal and urogenital orifices; the pelvic girdle thus supports the inner organs and, secondarily, also the neonate. Whereas in quadruped mammals the pelvic floor muscles are vertically oriented and mostly involved with the motion of the tail, the connective tissue and muscles of the horizontal pelvic floor in humans support the abdominopelvic organs and resist intraabdominal pressure exerted from above (18, 19). Pelvic organ prolapse as well as multiple other pelvic floor disorders and connective tissue defects, such as premature rupture of fetal membranes or cervical insufficiency, are common in human females, especially during pregnancy and after vaginal birth (20–22), suggesting a system very sensitive to perturbations. It has been shown that a wide pelvic cavity increases the probability of disorders: The transverse diameter of the pelvic inlet is correlated with the rate of pelvic floor disorders, including prolapse (23, 24).

In terms of our model, a large neonatal brain and body as well as a narrow maternal pelvic canal both lead to a large value of $D$ and are positively associated with individual fitness (neonatal or maternal). Opposed to that, a large neonate relative to the pelvic canal increases the risk of obstructed labor. It has been shown that Caesarean section rate and maternal morbidity is only weakly related to neonatal head circumference for normal size variation, but beyond a critical value (90th to 95th percentile) obstructed labor and morbidity increase drastically (25–28). In our model, fitness increases with $D$ until it reaches a maximum at $D=0$; beyond this threshold, the neonate does not fit through the mother’s pelvic canal anymore and fitness drops to zero (here the model refers to the situation before the safe availability of Caesarean sections). Individual female fitness, plotted as a function of $D$ (the blue curve in Fig. 1A), has the form of an asymmetric “cliff edge” (29, 30): It increases continually before it drops suddenly. In the simplest version of the model, as presented in Fig. 1A, individual absolute fitness increases linearly with slope ${\beta }_A$ on the left side of the cliff edge. For modern human variation, this linearity is supported by the medical literature cited above. However, the fitness slope may be higher for the offspring than for the mother because of an inherent discrepancy in the optimal amount of fetal provisioning that arises from the effects on future offspring (31); the slope ${\beta }_A$ thus represents the average fitness increase.

The success of labor is not only influenced by $D$ but also by numerous other factors, including flexibility of the pelvic ligaments, orientation of the neonate, and efficiency of uterine contractions (4, 5). However, as long as these factors are statistically independent of the discrepancy between neonatal and maternal dimensions, the selection gradient and evolutionary trajectory of $D$ can be modeled independently of other factors (32, 33).

In contrast to the highly asymmetric fitness function, the dimensions of the head and the pelvis tend to be approximately symmetrically distributed (34–36). The difference, $D$, between birth-relevant neonatal and maternal dimensions can thus be considered a polygenic and symmetrically distributed trait. Importantly, $D$ is affected both by maternal and neonatal genes, where half of the alleles affecting neonatal size are of paternal origin and therefore independent of the alleles that influence the mother’s pelvis. If neonatal size and pelvic canal size vary independently, their variances sum up to that of $D$ (Materials and Methods). Whereas both head size at birth and pelvic dimensions show considerable genetic variation (34, 37), gestational age at birth is heavily influenced by environmental factors (38–40). Heritability of gestation length has been estimated to be only 0.3 (41), where about two-thirds of this genetic variation are of maternal origin and one-third is of fetal origin (42). Furthermore, female pelvic remodeling extends into late adulthood (43, 44); the dimensions of the pelvic canal thus are also influenced by the mother’s age. For those reasons, phenotypic variation of $D$ is large, highly polygenic, and has a strong environmental component. Recombination between maternal and paternal alleles—in addition to the environmental effects—is likely to maintain an approximately symmetric and wide trait distribution, despite the asymmetric fitness function.

The mean population fitness (i.e., the average number of offspring per individual in the population) is given by the integral of the product of the fitness function and the trait distribution of $D$. For the cliff-edged fitness function introduced above, Fig. 1B shows the mean population fitness for a range of mean phenotypes, ${\mu }_D$, assuming constant standard deviation (SD), ${\sigma }_D$. Such a plot is referred to as an adaptive landscape (45, 46). It has been shown that in the standard case of adaptive evolution toward a single fitness maximum the population mean of a quantitative trait approaches the fitness peak, that is, the population moves uphill on the adaptive landscape (32, 45).

In these standard models, the fitness distribution is symmetric, and the trait mean that maximizes the population mean fitness thus is equivalent to the trait value with maximal individual fitness. This differs from the evolutionary scenario with an asymmetric fitness function. The symmetric phenotype distribution cannot match the cliff-edged fitness distribution well: The population optimum is shifted toward the flatter shoulder of the individual fitness curve (30, 47, 48). The mean of $D$ that maximizes population fitness thus deviates from the individual fitness maximum at $D=0$ (Fig. 1B). This also leads to the—seemingly paradoxical—situation where the optimal trait distribution involves a fraction of individuals falling beyond the “fitness edge,” that is, with zero fitness (the red area in Fig. 1A). In other words, as long as the size of the neonate relative to that of the maternal pelvic canal is positively associated with reproductive success (increasing fitness for $D<0$), the population will evolve a distribution of $D$ that implies a constant fraction of individuals subject to fetopelvic disproportion.

The larger the slope of the fitness function on the flat shoulder, that is for $D<0$, the faster will the trait distribution evolve toward the fitness edge and the closer toward the edge will the optimal population mean lie. This results in an increase of the fraction of individuals with $D>0$ (Fig. 2A). In other words, the model predicts a higher rate of obstructed labor if the strength of selection for a large neonate, a narrow pelvis, or both is increased. The fraction of individuals with $D>0$ for a given selection pressure can only be reduced by reducing phenotypic variation, the dispersion of $D$. The wider the phenotype distribution, the larger the number of individuals affected by obstructed labor (Fig. 2A; see also ref. 48). In other words, for a population with a mean phenotype close to the edge, the fitness function imposes a stabilizing selection gradient on $D$. But in the case of obstetric evolution the variation of the composite trait $D$, with its complex genetic structure and strong environmental component, cannot easily be reduced by stabilizing selection on either maternal or fetal dimensions separately. However, positive correlation between fetal size and maternal pelvis dimensions can reduce the variance of $D$ (Materials and Methods). Indeed, neonatal head size and maternal pelvis shape have been found to covary (36), presumably via pleiotropic genetic effects. Furthermore, size and weight of the newborn are correlated with maternal stature and pregnancy weight (39, 49, 50). This correlation is partly driven by the genes shared between the mother and the fetus (51), but the fetus also develops under the influence of the maternal environment. For example, data from in vitro fertilizations with egg donation have shown a correlation of infant birth weight and head circumference with the height of the genetically unrelated mother (52). Although this integration of neonatal and maternal dimensions may have evolved as an adaptation to the specific obstetric selection scenario, there is still independent variation: The discrepancy, $D$, varies considerably more than fetal and maternal dimensions separately.

The simplest version of the cliff-edge model as presented in Fig. 1 (linear fitness increase and normally distributed $D$) has a single parameter only: ${\beta }_{A\sigma }$, the absolute fitness increase per SD of $D$ (Materials and Methods). When ${\beta }_{A\sigma }$ is divided by the population mean fitness, the resulting parameter expresses the increase of relative fitness per SD of $D$, which equals the well-known standardized directional selection gradient, ${\beta }_{\sigma }$ (53). This relationship allows us to infer the directional selection gradient on $D$ for a given rate of fetopelvic disproportion. For example, a population with a 4.5% rate of disproportion at its population optimum (evolutionary steady state) implies ${\beta }_{A\sigma }=0.1$ units increase of absolute fitness per SD of $D$ and ${\beta }_{\sigma }=0.12$ (Fig. 2A; see Materials and Methods for more details). Considering the wide range of reported incidences, disproportion rates of 2 to 6% translate into absolute fitness slopes of 0.05 to 0.13 and standardized selection gradients of 0.06 to 0.16. Studies of numerous morphological and life-history traits in animals have shown that standardized selection gradients typically are rather modest (median 0.15, mean 0.2 of absolute values) but with a long tail of larger values (54–56). According to our model, the current rates of fetopelvic disproportion thus suggest the persistence of moderate directional selection on $D$ toward larger size of the neonate relative to that of the maternal pelvic canal. However, it is not clear from our model whether selection is acting on the neonate, on the maternal pelvic canal, or on both.

The cliff-edge fitness function in Fig. 1 can also be described as consisting of two opposing directional selection regimes: linear selection with slope ${\beta }_A$ favoring larger $D$, and truncation selection favoring smaller $D$ with the threshold at $D=0$, where truncation selection is known to be the most efficient form of selection (57, 58). At the evolutionary steady state, that is, for the mean phenotype with maximal population fitness, these two directional selection gradients cancel. If phenotypic variance stays constant, the remaining stabilizing selection gradient leads to a constant fraction of cases with fetopelvic disproportion, which equals the tail of the phenotype distribution beyond the fitness threshold.

Selection on birth-relevant pelvic dimensions may not necessarily originate only from obstetrics. Due to the developmental and structural integration of the pelvis, other selection regimes, including thermoregulation (59–61), can have an indirect effect on the pelvic canal (17, 33, 62). The directional selection gradient on $D$ may also comprise effects other than actual selection, such as plastic responses to environmental changes. The balance between maternal and fetal interests depends on the environment in which it is negotiated; it may be disrupted if the environment changes (16, 63). For example, mothers born and raised in third-world countries tend to have short stature and narrow pelvic dimensions; they experience marked risk of cephalopelvic disproportion and shoulder dystocia after migrating as adults to the United States, where a change to a high-protein diet putatively causes an increase in birth size (64). Similarly, the unequally strong investment in the fetal brain, which is maintained even under maternal starvation, protects the fetus under conditions of food scarcity. However, when nutritional conditions change substantially, as they did in the last century, this overproportional investment in the fetus may lead to a mismatch of neonatal brain size and maternal pelvic dimensions.

The presented model can be extended in various ways (see ref. 48 for a comprehensive mathematical treatment of asymmetric fitness functions). For instance, taking into account that not all cases of fetopelvic disproportion are lethal for the mother, or that she had offspring from earlier pregnancies, slightly increases the rate of affected women. More importantly, the above model (model I) describes only female phenotypes and assumes no genetic correlation between the sexes. However, because neonatal head size and pelvic morphology are controlled by genes that are expressed in both sexes, the traits are expected to coevolve in males and females (65). Both sexes may be subject to similar nonobstetric selective forces, yet obstructed labor primarily affects the mother’s fitness; the father’s lifetime reproductive success is much less influenced by it. We therefore extended the previous model by including both sexes (model II, with a sex ratio of 1/2). We assumed complete genetic correlation (coevolution) between the sexes, and an unconstrained fitness increase for males, whereas female fitness drops to 0 at $D>0$ (Fig. 2B). For a slope of absolute fitness ${\beta }_{A\sigma }=0.1$, the inclusion of males pushes the optimal mean to ${\mu }_D=-1.2{\sigma }_D$, with 11.1% of females experiencing disproportion (note that a constant sexual dimorphism does not influence this rate). Incidences of 2 to 6% correspond to standardized directional selection gradients ranging from 0.02 to 0.07—considerably lower than those for model I. This implies that genetic correlation between the sexes severely aggravates the risk of obstructed labor for women. The biological and social factors determining fitness and genetic correlation in the sexes differ across populations; the actual selection scenarios specific to different populations thus may vary between models I and II.

In industrialized countries, Caesarean sections have minimized maternal mortality due to obstructed labor. Although the obstetric selection pressure has been relaxed, the directional selection on $D$ may persist and induce an evolutionary change. Theory shows that the expected evolutionary change of a mean phenotype resulting from directional selection equals the product of the additive genetic variance (the heritable part of phenotypic variation) and the directional selection gradient (32, 45). Heritabilities of most pelvic dimensions have been reported to range from 0.5 to 0.8; the heritability of biischial breadth (the only birth-relevant dimension reported) is 0.56 (34). A twin study reported a heritability of 0.73 for intracranial volume at gestational week 40 (37), but this estimate does not take into account the plasticity of gestational length. The heritability of intracranial volume at the time of birth may thus be considerably lower (39). As a conservative estimate, let us assume a 3% incidence of fetopelvic disproportion before the availability of Caesarean sections and a heritability of 0.5 for $D$. This implies a standardized selection gradient of ${\beta }_{\sigma }=0.080$ for model I and of ${\beta }_{\sigma }=0.037$ for model II. The predicted average change of $D$ after the emergence of Caesarean sections is 0.040 and 0.018 SDs per generation for the two models, respectively. For the time range that Caesarean sections have been regularly and safely conducted in industrialized countries (since the 1950s and 1960s, i.e., roughly two generations), our model predicts a 20% increase of the incidence of fetopelvic disproportion for model I and a 9% increase for model II. Note that these are predictions about the actual disproportion rate, not Caesarean section rate, which has increased much more rapidly for other reasons; the obstetric literature typically considers the actual disproportion rate constant.

In an attempt to model the evolutionary dynamics underlying the obstetric dilemma, we identified three distinct characteristics of human obstetric selection that jointly produce the high rates of obstructed labor. First, the size of the neonate relative to the birth-relevant dimensions of the maternal pelvis has a highly asymmetric, cliff-edged fitness distribution. Second, the genetic structure of this trait is particularly complex. It involves maternal and paternal genes distributed across two generations and is superimposed by a strong environmental component. This causes a wide and approximately symmetric variation of the discrepancy between fetal and maternal dimensions. Third, obstetric selection affects only the female half of the population, but female and male dimensions are genetically correlated and subject to similar nonobstetric selection. The tight fit of the neonate through the maternal birth canal thus is aggravated by the influence of the genes selected in males.

We demonstrated that due to these three properties weak directional selection favoring large neonates relative to the maternal pelvic dimensions is sufficient to account for the high incidence of fetopelvic disproportion in human populations. Our model does not specify the origin of these selective forces, but we found evidence in the medical literature for a reproductive advantage of both large neonates and women with a narrow pelvis, independent of putative biomechanical advantages. We predict that this weak directional selection has led to a 10 to 20% increase in the rate of fetopelvic disproportion since the regular use of Caesarean sections.

This work was supported by Austrian Science Fund Grant FWF, P 29397-B27 (to P.M.), by a postdoctoral fellowship of the Konrad Lorenz Institute for Evolution and Cognition Research (to B.F.), and March of Dimes Prematurity Research Center Ohio Collaborative Grant 22-FY14-470 (to M.P.).