Inconvenient truths in population and speciation genetics point towards a future beyond allele frequencies

In 1999 Whitlock & McCauley (1999) illustrated that FST does not have a simple relationship to migration (4 Nm). For example, in empirical studies of populations, we typically observe a single realization of a combination of processes that include stochasticity and genetic drift so that we do not expect FST to match expectations exactly (Buerkle et al., 2011). Scientists using approximate Bayesian computation to infer evolutionary histories from coalescent simulations have learned to test empirically which statistics calculated for simulated genetic data were correlated with, and therefore informative about, evolutionary parameters of the simulated history (Wegmann et al., 2009; Aeschbacher et al., 2012). In other words, even in simple simulations of populations with migration, we cannot readily predict which measures on the genome will record the differences in evolutionary histories that were simulated. Undeterred, in speciation and landscape genetics, we have often utilized measures of FST as if they were indicative of historical migration, when the reality is much more complex. Ravinet et al. (this volume) provide an extensive and thorough discussion of many of the relevant complexities. The cautionary notes include mutation and recombination, for which we rarely have relevant information in many empirical systems. And even when we have estimates, say for recombination, these are for a particular cross (e.g. an F2 linkage map from a single pair of individuals), or in the context of a particular population. It remains unknown to what extent these estimates predict recombination in wider crosses, such as those following secondary contact and relevant to speciation. Ravinet et al. come to a fairly optimistic conclusion that the obstacles are surmountable and we can make progress in finding barrier loci, and they offer suggestions for the way forward. If in future studies we are mindful of the cautionary notes of Ravinet et al. and others (e.g. Whitlock & McCauley, 1999), then I can share their optimism. For one, we will need to move beyond simply equating transformations of allele frequencies to evolutionary processes, including gene flow or its absence. Despite the extensive treatment of complexities, Ravinet et al. could have gone on and highlighted additional significant considerations that should heighten our scepticism. A fundamental problem for inferring evolutionary processes from population genomic variation is that genome variation typically contains very limited information, particularly if we are considering only allele frequencies. The allele frequencies at variable nucleotides most commonly correspond to one or a few copies of a rare allele, with the remainder of the population possessing the second, common allele (with p 1⁄4 1=2N as the most common frequency among variable sites, 2/2N as the next most common, etc.; Nelson et al., 2012; Lek et al., 2016). Consequently, most of the genome will be uninformative about associations of alleles in genotypes and populations (e.g. FST) or between loci (measures of linkage disequilibrium). The maximum possible value of FST is limited by the allele frequency of the major allele (Jakobsson et al., 2013), and much of the variation across the genome will be shaped by global frequencies (and possible information), rather than population structure. Standardization of these statistics that take into account the maximum possible value of FST (Hedrick, 2005; Meirmans & Hedrick, 2011; Whitlock, 2011) or linkage disequilibrium does nothing to affect the information content of the allele frequency variation. Thus, it is possible that covariation of measures of FST and linkage disequilibrium (Hohenlohe et al., 2012) results in part from the information limits set on each by underlying global allele frequencies, rather than reflecting evolutionary processes. Although FST variation among loci can reflect differences in selection and migration that affect differentiation, it is clear that FST poorly tracks variation in these processes. In the future, our measures of recombination will likely be improved as long reads from DNA sequencing will provide direct observations of gametes and meioses in each parent. Given the very limited information in FST, at most loci, identification of regions of the genome that harbour barrier loci will be facilitated by explicit models of gene flow rather than consideration of differentiation (and islands and other metaphors). These models of gene flow will typically need to be complex (incorporating demography, recombination, mutation, possibly complex migration histories, etc.), and analyses will involve comparison of a large number of alternative possible histories. It seems very possible that model choice that today is regarded as comprehensive, complex or both (e.g. Gutenkunst et al., 2009; Christe et al., 2017) will be unacceptably, overly simplistic in the notso-distant future. Beyond the difficulty of inference based on allele frequencies alone, a further challenge to understanding the genetics of barriers between species comes from the complexity of trait genetics. Reproductive isolation between many species is likely to result from many phenotypes that function in different life stages and Correspondence: C. A. Buerkle, Department of Botany, University of Wyoming, 1000 E. University Ave., 82071 Laramie, WY, USA. e-mail: buerkle@uwyo.edu