We develop an analytical framework for predicting the fitness of hybrid genotypes, based on Fisher’s geometric model. We first show that all of the model parameters have a simple geometrical and biological interpretation. Hybrid fitness decomposes into intrinsic effects of hybridity and heterozygosity, and extrinsic measures of the (local) adaptedness of the parental lines; and all of these correspond to distances in a phenotypic space. We also show how these quantities change over the course of divergence, with convergence to a characteristic pattern of intrinsic isolation. Using individual-based simulations, we then show that the predictions apply to a wide range of population genetic regimes, and divergence conditions, including allopatry and parapatry, local adaptation and drift. We next connect our results to the quantitative genetics of line crosses in variable or patchy environments. This relates the geometrical distances to quantities that can be estimated from cross data, and provides a simple interpretation of the “composite effects” in the quantitative genetics partition. Finally, we develop extensions to the model, involving selectively-induced disequilibria, and variable phenotypic dominance. The geometry of fitness landscapes provides a unifying framework for understanding speciation, and wider patterns of hybrid fitness.

Language diversity is distributed unevenly over the globe. Intriguingly, patterns of language diversity resemble biodiversity patterns, leading to suggestions that similar mechanisms may underlie both linguistic and biological diversification. Here we present the first global analysis of language diversity that compares the relative importance of two key ecological mechanisms – isolation and ecological risk – after correcting for spatial autocorrelation and phylogenetic non-independence. We find significant effects of climate on language diversity, consistent with the ecological risk hypothesis that areas of high year-round productivity lead to more languages by supporting human cultural groups with smaller distributions. Climate has a much stronger effect on language diversity than landscape features, such as altitudinal range and river density, which might contribute to isolation of cultural groups. The association between biodiversity and language diversity appears to be an incidental effect of their covariation with climate, rather than a causal link between the two.

A growing number of studies seek to identify predictors of broad-scale patterns in human cultural diversity, but three sources of non-independence in human cultural variables can bias the results of cross-cultural studies. First, related cultures tend to have many traits in common, regardless of whether those traits are functionally linked. Second, societies in geographical proximity will share many aspects of culture, environment and demography. Third, many cultural traits covary, leading to spurious relationships between traits. Here, we demonstrate tractable methods for dealing with all three sources of bias. We use cross-cultural analyses of proposed associations between human cultural traits and parasite load to illustrate the potential problems of failing to correct for these three forms of statistical non-independence. Associations between parasite stress and sociosexuality, authoritarianism, democracy and language diversity are weak or absent once relatedness and proximity are taken into account, and parasite load has no more power to explain variation in traditionalism, religiosity and collectivism than other measures of biodiversity, climate or population size do. Without correction for statistical non-independence and covariation in cross-cultural analyses, we risk misinterpreting associations between culture and environment.

What role does speaker population size play in shaping rates of language evolution? There has been little consensus on the expected relationship between rates and patterns of language change and speaker population size, with some predicting faster rates of change in smaller populations, and others expecting greater change in larger populations. The growth of comparative databases has allowed population size effects to be investigated across a wide range of language groups, with mixed results. One recent study of a group of Polynesian languages revealed greater rates of word gain in larger populations and greater rates of word loss in smaller populations. However, that test was restricted to 20 closely related languages from small Oceanic islands. Here, we test if this pattern is a general feature of language evolution across a larger and more diverse sample of languages from both continental and island populations. We analyzed comparative language data for 153 pairs of closely-related sister languages from three of the world's largest language families: Austronesian, Indo-European, and Niger-Congo. We find some evidence that rates of word loss are significantly greater in smaller languages for the Indo-European comparisons, but we find no significant patterns in the other two language families. These results suggest either that the influence of population size on rates and patterns of language evolution is not universal, or that it is sufficiently weak that it may be overwhelmed by other influences in some cases. Further investigation, for a greater number of language comparisons and a wider range of language features, may determine which of these explanations holds true.

When divergent populations interbreed, their alleles are brought together in hybrids. In the initial F1 cross, most divergent loci are heterozygous. Therefore, F1 fitness can be influenced by dominance effects that could not have been selected to function well together. We present a systematic study of these F1 dominance effects by introducing variable phenotypic dominance into Fisher's geometric model. We show that dominance often reduces hybrid fitness, which can generate optimal outbreeding followed by a steady decline in F1 fitness, as is often observed. We also show that "lucky" beneficial effects sometimes arise by chance, which might be important when hybrids can access novel environments. We then show that dominance can lead to violations of Haldane's Rule (reduced fitness of the heterogametic F1) but strengthens Darwin's Corollary (F1 fitness differences between cross directions).Taken together, results show that the effects of dominance on hybrid fitness can be surprisingly difficult to isolate, because they often resemble the effects of uniparental inheritance or expression. Nevertheless, we identify a pattern of environment-dependent heterosis that only dominance can explain, and for which there is some suggestive evidence. Our results also show how existing data set upper bounds on the size of dominance effects. These bounds could explain why additive models often provide good predictions for later-generation recombinant hybrids, even when dominance qualitatively changes outcomes for the F1.

Language diversity is distributed unevenly over the globe. Why do some areas have so many different languages and other areas so few? Intriguingly, patterns of language diversity resemble biodiversity patterns, leading to suggestions that similar mechanisms may underlie both linguistic and biological diversification. Here we present the first global analysis of language diversity that identifies the relative importance of two key ecological mechanisms suggested to promote language diversification - isolation and ecological risk - after correcting for spatial autocorrelation and phylogenetic non-independence. We find significant effects of climate on language diversity consistent with the ecological risk hypothesis that areas of high year-round productivity lead to more languages by supporting human cultural groups with smaller distributions. Climate has a much stronger effect on language diversity than landscape features that might contribute to isolation of cultural groups, such as altitudinal variation, river density, or landscape roughness. The association between biodiversity and language diversity appears to be an incidental effect of their covariation with climate, rather than a causal link between the two. While climate and landscape provide strong explanatory signal for variation in language diversity, we identify a number of areas of high unexplained language diversity, with more languages than would be predicted from environmental features alone; notably New Guinea, the Himalayan foothills, West Africa, and Mesoamerica. Additional processes may be at play in generating higher than expected language diversity in these regions.

When divergent populations form hybrids, hybrid fitness can vary with genome composition, current environmental conditions, and the divergence history of the populations. We develop analytical predictions for hybrid fitness, which incorporate all three factors. The predictions are based on Fisher's geometric model, and apply to a wide range of population genetic parameter regimes and divergence conditions, including allopatry and parapatry, local adaptation, and drift. Results show that hybrid fitness can be decomposed into intrinsic effects of admixture and heterozygosity, and extrinsic effects of the (local) adaptedness of the parental lines. Effect sizes are determined by a handful of geometric distances, which have a simple biological interpretation. These distances also reflect the mode and amount of divergence, such that there is convergence toward a characteristic pattern of intrinsic isolation. We next connect our results to the quantitative genetics of line crosses in variable or patchy environments. This means that the geometrical distances can be estimated from cross data, and provides a simple interpretation of the "composite effects." Finally, we develop extensions to the model, involving selectively induced disequilibria, and variable phenotypic dominance. The geometry of fitness landscapes provides a unifying framework for understanding speciation, and wider patterns of hybrid fitness.

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