Results and Discussion To analyze the behavior of FST on a polygenic trait, we started by simulating the action of a polygenic stabilizing selection pressure in a very simple model. Such a model relies on the following simplifying assumptions: (i) each contributing allele has small and relatively equal additive effects, without neither environmental influences nor non-linear effects (dominance, epistasis, etc), (ii) individual fitness is given by a bell-shaped curve where the maximum is achieved by individual owning only a part of the advantageous alleles, (iii) no migration or demographic events affect the populations. Under these simple assumptions, we observed that the set of alleles involved in the phenomenon has a higher mean FST value than those subject to genetic drift only. We thus checked whether the same behavior was observable in the 180 loci influencing adult height. Indeed, more than 80% of its variation within a given population is estimated to be attributable to additive genetic factors of small effects. Moreover, the authors found no evidence that non-additive effects including gene–gene interaction would increase the proportion of the phenotypic variance explained [8]. In the light of this, our simulations seem to reasonable model this scenario and, for this reason, we explicitly searched for an increase in the mean FST value of the 180 variants associated to height. We found in the FST distribution for these variants an overrepresentation of higher values with respect to the genomic background (median = 0.1 vs. 0.086; p = 0.0356, one-tailed Mann- Whitney test; Figure 1). We investigated for potential confounding factors, first of all whether the increase was just due to the presence of outliers. We thus excluded from the initial set of height related variants those falling in the top or in the bottom 5% tail according to the genomic distribution of FST, obtaining a set of 161 SNPs (hereafter denoted as ‘‘core set’’). The number of outliers excluded is compatible with the expected 5% (4% and 5% of the SNPs falling in the top and in the bottom tail, respectively). Moreover, the ‘‘core set’’ still exhibits a significant overrepresentation of high values FST value (median = 0.1 vs. 0.086; p = 0.0232, one-tailed Mann-Whitney test). In a recent paper, Pritchard and Di Rienzo argued that a signature of selection on a polygenic trait should reasonably be small and spread across the loci [12]. Our result is, to some extension, in agreement with this hypothesis. Indeed, the increased FST value is not dominated by few outlier loci, but small and Figure 1. FST density distribution for the genomic background and the height associated variants. Green lines mark the 5th and 95th percentiles of the genomic distribution. doi:10.1371/journal.pone.0027588.g001 Signs of Selection on Human Height distributed. From this point of view, also the low value of statistical significance that we found could be expected. On the other hand, if we consider height either under a stabilizing selective pressure or a worldwide distributed sexual selection, the higher mean FST value could seem unexpected. Under these hypotheses, indeed, we expected a result that is opposite to that obtained, even in presence of marginal phenomena of local adaptation. In these conditions, one should expect the majority of the genes having a vanishing FST and some outliers with very high values of FST. But looking at the simulated alleles trajectories over time, a possible explanation could be suggested. In simulations, one can observe that, in different populations, different sets of alleles become prevalent (Figure S1). In particular, the dynamics favors in each population the prevalence of a specific subset of alleles among the large amount of different subset choices all capable to maximize the phenotype under selective pressure. In absence of extraneous forces, the choice of the allele subset for each population is just randomly driven and, hence, it is highly probable to be different for each population. This results in an increase of the mean diversity among the populations. This very simple model resembles the behavior of a well-known statistical mechanics phenomenon denoted as Spontaneous Symmetry Breaking (SSB). This mechanism generally plays a relevant role in system self-organization, and it is common in many fields of Natural Sciences where a system described in a theoretically symmetrical way ends up in a non-symmetrical state. The physics of condensed matter probably provides the most striking examples of SSB phenomena. In a ferromagnet cooled below its critical temperature, as the thermal fluctuations slow down, will become energetically favorable the appearance of domains where all elementary magnets point in the same direction, randomly chosen, and hence breaking the original rotational symmetry. SSB has been widely observed in biological systems. Population genetics also provides examples of SSB even though in this case to lead the breaking are the initial conditions, stochastically modified by events like drift, bottlenecks, etc, and other stochastic events like the born of new mutations. Among the others, we can quote the role of symmetry breaking and coarsening in spatially distributed evolutionary processes relevant for genetic diversity and species formation [13]., and the relevance of symmetry breaking in the long-term evolution of multilocus traits [14]. The symmetry-breaking scenario could represent a simple yet reasonable model of the selection acting on height. But, even though height is basically under stabilizing selection, local adaptive phenomena cannot be excluded. To explicitly explore the pre- sence of local adaptive phenomena, we analyzed how iHS, another marker of selective pressure, is distributed in genetic variants involved in height. iHS is a score specifically oriented to detect recent adaptive phenomena with higher geographical resolution. We found that, in each population, the number of SNPs associated with height having a value of iHS falling in the highest 5% of the genomic distribution is compatible with the expectation (varying from 4-7% across populations; Figure 2). This finding seems to indicate that, even if recent local adaptation phenomena cannot be excluded, their role seems to be marginal. Another hypothesis that we explored was that loci responsible of local adaptive phenomena on different phenotypes, in linkage disequilibrium with height related variants, were responsible of the selective signatures that we found. Under this hypothesis, the increased mean FST value that we attributed to the height associated genes could be the by-product of selective pressures acting on other traits. To test this hypothesis, we extracted height related SNPs that were in linkage disequilibrium (r2.0.8 in at least PLoS ONE | www.plosone.org 2 November 2011 | Volume 6 | Issue 11 | e27588