Few previous studies of the impact of body fatness and WHR have been conducted in African populations. In contrast to our data, 82.5% of the variance in attractiveness was explained by BMI and only 7.5% by WHR in South African Zulus ( Tovée et al., 2006 ), which suggested African populations do not differ from Caucasians and Asians. In contrast, we found much lower % explained variation by body fat and a much greater role for WHR in all four of the African populations in our sample. In fact, in the sample from Nigeria, WHR was more significant than BMI in the multiple regression analyses. The greater role for WHR in the four African populations is consistent with previous studies that have suggested a preference for a more extreme low WHR in African populations ( Furnham, Moutafi & Baguma, 2002 ) and a preference for a lower WHR among African Americans compared to US Caucasians ( Freedman et al., 2007 ; Freedman et al., 2004 ). The reason why WHR may play a greater role in African populations is presently unclear. One potential factor maybe the role of the buttocks in assessments of physical attractiveness among Africans ( Marlowe, Apicella & Reed, 2005 ) and African Americans ( Cunningham et al., 1995 ). This ethnic difference is apparent in the differences in ethnic ideals with respect to buttock augmentation surgery ( Roberts et al., 2006 ) in which Asians prefer very small and African Americans very large buttocks. This difference may accentuate the importance of WHR in attractiveness ratings by African populations.

Evolutionary aspects and optimal BMI

Many previous studies have set the observations that raters prefer women with given WHRs and BMIs into a post hoc evolutionary context by suggesting that BMI and WHR are honest signals of both health and fertility (Bigaard et al., 2004; Singh, 1995a; Wass et al., 1997). Few studies, however, have attempted to rigorously test this suggestion by comparing the actual pattern of variation in attractiveness, as a function of fatness or WHR, to that expected a priori on the basis of epidemiological data on the relationships between fatness, health and fertility. We attempted to fill this gap by constructing a mathematical model relating fatness to future mortality risk (incorporating both health and fertility effects) using data from several large epidemiological studies that have related BMI to all cause mortality in Caucasians (Whitlock et al., 2009), Asians (Zheng et al., 2011) and African Americans (Cohen et al., 2014; Cohen et al., 2012; Flegal et al., 2013) and BMI at age 20 to future reproductive success in over 33,000 females Caucasians (Jacobsen et al., 2013). Factoring these two effects into the model suggested the optimal female BMI should be around 22.4 to 23.2. A limitation of our study is that we could not find data on the link of mortality to BMI for Africans living in Africa, for which we substituted data on African Americans, and we could only find fecundity data based on a large sample size for Caucasians. The similarity of the mortality patterns between Caucasians, Asians and African Americans (Fig. 1A), however, lends some confidence that ethnic effects on these relationships are relatively small and the derived optima are probably appropriate for the populations we studied. An additional potential factor is that body fat stores may provide a resource base to ensure survival during periods of famine (the thrifty gene hypothesis). Using a previous mathematical model relating famine survival to fat storage (Speakman & Westerterp, 2013) we predicted that if famine mitigation was also important the optimum BMI might rise slightly to between 24.0 and 24.8 but the shape of the curve relating attractiveness to body fatness would be more steeply negative at lower levels of body fatness (Fig. 1D).

This predicted peak relationship between body fatness and physical attractiveness with a maximum attractiveness around a BMI of 22.4 to 24.8 was not supported by the data we collected in any population. Over the range of BMIs that we studied (19 to 40) there was a negative linear between attractiveness and BMI (Fig. S2). This range was adequate to detect a peak, if such existed, at the position we predicted. In none of the populations over this BMI range was there any indication of a peak in the relationship (as judged by the significance of adding additional polynomial terms to the regression model). Similar to our data, a linear negative relationship between BMI and physical attractiveness was observed previously over the BMI range 18 to 26 (Swami & Tovée, 2007), and a linear negative relationship was observed between attractiveness and body fatness over a range from 20 to 35% body fat (Smith, Cornelissen & Tovée, 2007). Using the same image set as used here Faries & Bartholomew (2012) also reported a linear negative relationship between attractiveness and BMI rated by US college students of mixed ethnicity.

Hence, if there was a peak physical attractiveness, in all ten of the populations we studied the peak was at least as low as BMI = 19 and potentially lower. This was consequently at least 3.5 BMI units below the predictions of the evolutionary model. For an average height woman (1.55m) the difference between the predicted and observed maximum was at least 10 kg of body weight. This is an enormous difference in body weight and based on these data we can clearly reject the evolutionary models, as formulated, based on health, fertility and famine survival. We did not have more extreme body compositions included into the images presented to the raters, and hence there might be a maximum attractiveness at a lower BMI than the lowest BMI in our image set. In fact data from previous studies suggest that there may be a peak in the relationship between BMI and attractiveness (Swami et al., 2006a; Swami & Tovée, 2007; Tovée et al., 2006; Tovee et al., 1999; Tovee et al., 1998) at a BMI around 18 to 20. In all these cases the authors fitted a 3 term polynomial with WHR as an additional term, but in only one study were actual coefficients reported in the publication. Hence it was not possible to explicitly solve the equations to locate the peak. We consequently recoded the data from the plots presented in the figures (using the software package Data-thief) and fitted our own curves to the data and then solved these curves for the maxima by differentiating them and solving them for f′(x) = 0 (Table 4). This reanalysis of previously published data clearly shows that for most populations the maximal physical attractiveness occurred at a BMI between 18.4 and 21.4 (mean of all studies excluding 2b and 4b in Table 4 = 20.152, sd = 1.012, n = 7). The two excluded studies are discussed below. This mean peak attractiveness sits 2.4 to 4.6 BMI units below the prediction (about 9 to 16.5 kg for an average height woman). This estimated peak attractiveness at a BMI at 18.4 to 21.4 is consistent with many other data. For example, the BMIs of Playboy centerfolds and glamour models over the last 50 years are almost all in the range 17 to 20 (Katzmarzyk & Davis, 2001; Tovee et al., 1999; Voracek & Fisher, 2002). Women and men asked to manipulate female 3D computer models to make them maximally attractive make them have BMIs of 18.9 and 18.8 respectively (Crossley, Cornelissen & Tovee, 2012). The biggest outlier in previous studies of attractiveness at low BMI was the observation that in Poland the highest rated attractiveness was at a BMI of 15 (Kościński, 2013), and potentially lower as this was the smallest stimulus in the set presented.

Study x 3 x 2 x Constant r 2 Peak 1 0.0019 −0.1521 3.8397 −26.003 0.732 20.486 2a 0.0016 −0.1421 3.7809 −26.817 0.842 20.185 2b 0.0007 −0.0651 2.0092 −14.419 0.837 28.941 3a 0.0013 −0.1053 2.5562 −15.628 0.784 18.423 3b 0.0016 −0.1369 3.6632 −26.131 0.830 21.431 4a 0.0023 −0.1953 5.1321 −36.786 0.826 20.731 4b 0.0007 −0.0654 1.973 −12.878 0.800 25.633 4c 0.0021 −0.1789 4.6963 −33.44 0.768 20.591 5 0.0018 −0.1503 3.7823 −25.23 0.725 19.215 DOI: 10.7717/peerj.1155/table-4

Why do the data for these modern societies seem to deviate so widely from the evolutionary model predictions about the most attractive level of body fatness? One potential interpretation is that the populations studied here are all exposed to the same western media which promotes a thin female body ideal (Groesz, Levine & Murnen, 2002; Posavac, Posavac & Posavac, 1998). It is difficult however to separate cause and effect. Does media exposure drive people’s perceptions of attractiveness? Or is the ‘thin ideal’ in the media simply reflecting what people already see as attractive? The fact the populations differed significantly in their perceptions of the importance of WHR suggests that in fact their opinions are not all homogenized by exposure to the same western media images of what is attractive. The data were not consistent with the suggestion that people are attracted to averageness in their own population (Kościński, 2012) since the universal preference for low BMI contrasted the much higher and more variable levels of average BMI among the rating populations (Table 1).

A potential problem with studies such as ours, and all previous studies of the role of BMI or body fatness, based on 2D images or 3D models, is that the people making the ratings are given no instructions about the age of the subjects. Body fatness and BMI are both strongly related to age (Speakman & Westerterp, 2010) as to a lesser extent is WHR (Marlowe, Apicella & Reed, 2005). Hence, individuals rating the images may be using BMI as a proxy to estimate the age of the subjects. Our observers were definitely sensitive to the ages of the individuals in the pictures, despite there being no immediately obvious way they could tell their ages. Were they also using BMI as a cue to the age of the subjects? There was some evidence to support this hypothesis. When individuals matched up the models ages to their pictures, there was a strong association between the estimated age and both BF% and BMI but not to their actual ages (Fig. 5). This suggests that people viewing the images used body fatness to estimate the age of the subjects. In the evolutionary model of the impact of fatness and fertility we assumed that age and BMI were independent. However, fertility is strongly dependent on age, in part because of the declining ovarian reserve as a function of age (Wallace & Kelsey, 2010). However, fertility reaches a peak in the late teens and early 20s because prior to age 20 there is an increased risk of annovulatory cycles. The relationship between infertility and age based on literature data for Caucasians (Henry, 1961; Leridon, 1978; Leridon, 2008; Menken & Larsen, 1986; Pittenger, 1973; Trussell & Wilson, 1985; Vincent, 1950) is shown in Fig. S3 and a 4th order polynomial explained 98.3% of the variation in infertility. The best fit equation was (12) y 5 = 0 . 0052 A 4 − 0 . 6164 A 3 + 27 . 105 A 2 − 514 . 95 A + 3558 . 1 where y 5 is the age related infertility per thousand population, and A is the age. Given the relationship between BMI and estimated age of the subjects (Fig. 5) we can use the derived fitted relationship (13) A = 0 . 027 x 2 + 3 . 1717 x − 30 . 599 where x is the BMI, to derive the expected relationship between BMI and mortality risk if BMI is used only as a proxy for age. Substituting Eq. (13) into Eq. (12) gives (14) y 5 = 0 . 0052 0 . 027 x 2 + 3 . 1717 x − 30 . 599 4 − 0 . 6164 0 . 027 x 2 + 3 . 1717 x − 30 . 599 3 + 27 . 105 0 . 027 x 2 + 3 . 1717 x − 30 . 599 2 − 996 . 68 x + 12495 . 57 Differentiating Eq. (14) gives d y d x = 0 . 0208 0 . 027 x 2 + 3 . 1717 x − 30 . 599 3 − 1 . 8492 0 . 027 x 2 + 3 . 1717 x − 30 . 599 2 + 1 . 4637 x 2 + 171 . 94 x − 2655 . 45 Expanding the brackets and collecting terms gives the 6th order polynomial (15) d y d x = 0 . 000000409 x 6 + 0 . 0001445 x 5 + 0 . 01421 x 4 + 0 . 019753 x 3 − 31 . 793 x 2 + 716 . 18 x − 3790 . 53 . And solving Eq. (15) for f(x) = 0 gives a single root in the range 16 to 50 at x = 17.41. Although, this is significantly lower than the mean peak attractiveness of 20.15 across the studies in Table 4 (one sample t-test = 7.17, p < 0.001), the local minimum at 17.41 is very shallow and there is very little difference over the range from 16 to 21, which encompasses most of the maxima in attractiveness in the studies summarized in Table 4. This analysis suggests that the shape of the relationship between BMI and physical attractiveness may come about primarily because subjects in such experiments use BMI as an indicator of subject age, and then attractiveness is primarily gauged on the evolutionary significance of the estimated age. The strong link of age to fertility results in subjects rating the pictures with BMIs around 20 as most attractive because they would be aged 19 to 22 and hence most fertile. Additional factors such as health relationships to BMI and the role of famine, and indeed the effects of BMI at a fixed age on fertility appear negligible by comparison.

There were 2 exceptions to this pattern of a peak in the range 18 to 19 (Table 4). The hill tribes people of northern Thailand had a maximum attractiveness at BMI = 25.6 (Swami & Tovée, 2007), and the Zulus of South Africa had a maximum attractiveness at BMI = 28.9. In these latter cases the maximum clearly sits much closer to the predictions of the evolutionary model derived here. Although insufficient images and data were available to fit an exact curve it seems likely that similar data with higher BMIs at maximal levels of attractiveness would also be observed among the Hadza of Tanzania (Marlowe & Wetsman, 2001).One hypothesis is that these divergent patterns emerge because these communities do not use BMI as a proxy for age, and the resultant pattern then matches more closely the evolutionary predictions from the model excluding such a link. This may be because in these communities that are all resource poor, body fatness does not increase with age in the same way it does in modern societies (Lawrence et al., 1987; Prentice et al., 1981), and hence low BMI is not an honest signal of youthfulness.