Owing to the remarkable progress of molecular techniques, heterozygosity-fitness correlations (HFCs) have become a popular tool to study the impact of inbreeding in natural populations. However, their underlying mechanisms are often hotly debated. Here we argue that these "debates" rely on verbal arguments with no basis in existing theory and inappropriate statistical testing, and that it is time to reconcile HFC with its historical and theoretical fundaments. We show that available data are quantitatively and qualitatively consistent with inbreeding-based theory. HFC can be used to estimate the impact of inbreeding in populations, although such estimates are bound to be imprecise, especially when inbreeding is weak. Contrary to common belief, linkage disequilibrium is not an alternative to inbreeding, but rather comes with some forms of inbreeding, and is not restricted to closely linked loci. Finally, the contribution of local chromosomal effects to HFC, while predicted by inbreeding theory, is expected to be small, and has rarely if ever proven statistically significant using adequate tests. We provide guidelines to safely interpret and quantify HFCs, and present how HFCs can be used to quantify inbreeding load and unravel the structure of natural populations.

Genomic scans of multiple populations often reveal marker loci with greatly increased differentiation between populations. Often this differentiation coincides in space with contrasts in ecological factors, forming a genetic-environment association (GEA). GEAs imply a role for local adaptation, and so it is tempting to conclude that the strongly differentiated markers are themselves under ecologically based divergent selection, or are closely linked to loci under such selection. Here, we highlight an alternative and neglected explanation: intrinsic (i.e. environment-independent) pre-or post-zygotic genetic incompatibilities rather than local adaptation can be responsible for increased differentiation. Intrinsic genetic incompatibilities create endogenous barriers to gene flow, also known as tension zones, whose location can shift over time. However, tension zones have a tendency to become trapped by, and therefore to coincide with, exogenous barriers due to ecological selection. This coupling of endogenous and exogenous barriers can occur easily in spatially subdivided populations, even if the loci involved are unlinked. The result is that local adaptation explains where genetic breaks are positioned, but not necessarily their existence, which can be best explained by endogenous incompatibilities. More precisely, we show that (i) the coupling of endogenous and exogenous barriers can easily occur even when ecological selection is weak; (ii) when environmental heterogeneity is fine-grained, GEAs can emerge at incompatibility loci, but only locally, in places where habitats and gene pools are sufficiently intermingled to maintain linkage disequilibria between genetic incompatibilities, local-adaptation genes and neutral loci. Furthermore, the association between the locally adapted and intrinsically incompatible alleles (i.e. the sign of linkage disequilibrium between endogenous and exogenous loci) is arbitrary and can form in either direction. Reviewing results from the literature, we find that many predictions of our model are supported, including endogenous genetic barriers that coincide with environmental boundaries, local GEA in mosaic hybrid zones, and inverted or modified GEAs at distant locations. We argue that endogenous genetic barriers are often more likely than local adaptation to explain the majority of Fst-outlying loci observed in genome scan approaches -even when these are correlated to environmental variables.

Geneticists have been interested in inbreeding and inbreeding depression since the time of Darwin. Two alternative approaches that can be used to measure how inbred an individual is involve the use of pedigree records to estimate inbreeding coefficients or molecular markers to measure multilocus heterozygosity. However, the relationship between inbreeding coefficient and heterozygosity has only rarely been investigated. In this paper, a framework to predict the relationship between the two variables is presented. In addition, microsatellite genotypes at 138 loci spanning all 26 autosomes of the sheep genome were used to investigate the relationship between inbreeding coefficient and multilocus heterozygosity. Multilocus heterozygosity was only weakly correlated with inbreeding coefficient, and heterozygosity was not positively correlated between markers more often than expected by chance. Inbreeding coefficient, but not multilocus heterozygosity, detected evidence of inbreeding depression for morphological traits. The relevance of these findings to the causes of heterozygosity-fitness correlations is discussed and predictions for other wild and captive populations are presented.

Genotypic frequencies at codominant marker loci in population samples convey information on mating systems. A classical way to extract this information is to measure heterozygote deficiencies ( F IS ) and obtain the selfing rate s from F IS = = = = s /(2 − − − − s ), assuming inbreeding equilibrium. A major drawback is that heterozygote deficiencies are often present without selfing, owing largely to technical artefacts such as null alleles or partial dominance. We show here that, in the absence of gametic disequilibrium, the multilocus structure can be used to derive estimates of s independent of F IS and free of technical biases. Their statistical power and precision are comparable to those of F IS , although they are sensitive to certain types of gametic disequilibria, a bias shared with progeny-array methods but not F IS . We analyse four real data sets spanning a range of mating systems . In two examples, we obtain s = = = = 0 despite positive F IS , strongly suggesting that the latter are artefactual. In the remaining examples, all estimates are consistent. All the computations have been implemented in a open-access and userfriendly software called RMES (robust multilocus estimate of selfing) available at http:// ftp.cefe.cnrs.fr, and can be used on any multilocus data. Being able to extract the reliable information from imperfect data, our method opens the way to make use of the ever-growing number of published population genetic studies, in addition to the more demanding progenyarray approaches, to investigate selfing rates.

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Heterozygosity-fitness correlations (HFC) have been studied in various organisms for more than two decades, but they are not universal. Although their detectability is limited by several factors (null alleles, inaccuracy of the phenotypic description of fitness, small sample sizes) the correlations appear intrinsically weak and often inconsistent across samples. Determining the origins of HFC is therefore a complex task. However, this issue might soon be resolved provided clear hypotheses and definitions are used (especially, if the problem of the neutrality of allozyme variation is not identified with the related issue of HFC), as well as new empirical (molecular markers) & theoretical (statistical models) tools.

Handicap models of sexual selection predict that male sexual ornaments have strong condition-dependent expression and this allows females to evaluate male genetic quality. A number of previous experiments have demonstrated heightened condition-dependence of sexual ornaments in response to environmental stress. Here we show that genetic variation underlies the response to environmental stress (variable food quality) of a sexual ornament (male eye span) in the stalk-eyed fly Cyrtodiopsis dalmanni. Some male genotypes develop large eye span under all conditions, whereas other genotypes progressively reduce eye span as conditions deteriorate. Several non-sexual traits (female eye span, male and female wing length) also show genetic variation in condition-dependent expression, but their genetic response is entirely explained by scaling with body size. In contrast, the male sexual ornament still reveals genetic variation in the response to environmental stress after accounting for differences in body size. These results strongly support the hypothesis that female mate choice yields genetic benefits for offspring.