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.