Heterosis via non-linear phenotypic effects
While heterosis has been widely viewed as emerging from non-additive genetic effects (Box 1, Figure 3), recent developments suggest that heterosis could alternatively result from non-linear phenotypic effects. Such outcomes can arise given a non-linear genotype-phenotype map, even when underlying genetic effects are purely additive and do not depend on the genetic background (Lynch & Walsh 1998, Fiévet et al. 2010, 2018) (Fig. 4A). The trait value for a heterozygous individual can then be closer to the value of one of the parents and deviate from the mid-parent value, fulfilling the broad definition of heterosis (Box 1). For instance, Wright’s model of physiological dominance proposes that the physiological activity of enzymes saturates, resulting in a non-linear relationship between enzyme concentration, i.e. the product of additive genetic effects between multiple loci, and the resultant metabolic flux or phenotype (as in Fig. 4A; see also Fiévet et al. 2010). Similarly, as individuals increase linearly in body size, other traits within the organisms may increase logarithmically (i.e. allometric traits). This non-linear increase in trait values with respect to body size changes has been shown to explain up to 75% of heterosis magnitude in two fitness-related traits in Arabidopsis thaliana (Vasseur et al. 2019).
The importance of non-linear relationships in determining heterosis may be far greater, and further highlight the importance of accounting for the ecological divergence between parental lineages when predicting fitness effects of the hybrid offspring (Fig. 2). This is because the relationship between phenotype and fitness is expected to be non-linear, due to effects of stabilizing selection as populations adapt to local conditions and approach the optima (Phillips & Arnold 1989). Moreover, if local conditions vary spatially, adaptation to local conditions may result in patterns of local adaptation, whereby individuals from a focal population have higher fitness in their environment of origin than in a foreign environment (“home vs away”) or individuals from a local population present higher fitness than the ones from foreign populations (“local vs foreign”) (Kawecki & Ebert 2004). In these cases, the non-linearity of the adaptive landscapes and fitness trade-off between environment can lead to dominance reversals (see Connallon & Chenoweth 2019). As such, the shape of the adaptive landscape across environments and the degree of maladaptation presented by immigrant individuals may influence not just differences in fitness between residents and immigrants, but that of the hybrid filial generations (Fig. 2). Reciprocally, estimates of fitness across filial generations and parental environments can reveal the differences between optima in the adaptive landscape across the respective environmental conditions of subpopulations (Fig 4B-C).
These intuitions are highlighted by a series of theoretical studies using Fisher’s geometrical model (Barton 2001, Chevin et al. 2014, Simon et al. 2018, Schneemann et al. 2020), culminating in an extension of genetic effects coefficients (Box 1) that explicitly accounts for the degree of local adaptation (Schneemann et al. 2020). These studies consider a fitness function with additive phenotypic effects and stabilizing selection near the optimum in a fitness landscape which results in a non-linear relationship between the [multi-dimensional] phenotype and fitness. Variations of this model have been shown to make reasonable predictions of heterosis in F1 and recombinant hybrids (Barton 2001, Chevin et al. 2014, Simon et al. 2018, Vasseur et al. 2019) and to match empirical data from inbred line-crosses (Simon et al. 2018).
Moreover, similarly to Dagilis et al. 2019 (previously discussed), these studies present conclusions that are highly relevant to the case of natural dispersal in spatially structured populations. Namely, that expectations for hybrid fitness depend on the relative influence of drift and selection during early stages of lineage diversification (Barton 2001, Chevin et al. 2014, Simon et al. 2018, Schneemann et al. 2020). Specifically, non-adaptive genetic divergence (e.g. with population-level inbreeding) leads to a net benefit of increased heterozygosity (Schneemann et al. 2020), which decays across generations from the maximum value in F1. With adaptive divergence, positive heterosis is also expected for the F1, but due to a net benefit of admixture via transgressive variation (Schneemann et al. 2020). In F2s and backcrosses, however, this benefit can be outweighed by a cost of recombination creating phenotypic variance around the optimum (i.e. segregational variance; Barton 2001, Chevin et al. 2014). When both selection and drift interact, such as in the case of stabilizing selection on phenotype with the evolution of cryptic genetic differentiation between populations (i.e. “system drift”), the intermediate phenotype of F1 hybrids presents higher fitness than the mid-parent value, due to the curvature of the fitness landscape (Barton 2001). However, recombinants incur a cost of admixture due to the breakdown of coadapted gene complexes from the parental lines (Chevin et al. 2014, Schneemann et al. 2020). Predicted hybrid fitness from these models, therefore, also generally align to predictions of the traditional line-cross theory, and nuances are determined by the relative importance of adaptive and non-adaptive processes during the divergence of populations.