A widespread chromosomal inversion polymorphism contributes to a major life-history transition, local adaptation, and reproductive isolation.

The role of chromosomal inversions in adaptation and speciation is controversial. Historically, inversions were thought to contribute to these processes either by directly causing hybrid sterility or by facilitating the maintenance of co-adapted gene complexes. Because inversions suppress recombination when heterozygous, a recently proposed local adaptation mechanism predicts that they will spread if they capture alleles at multiple loci involved in divergent adaptation to contrasting environments. Many empirical studies have found inversion polymorphisms linked to putatively adaptive phenotypes or distributed along environmental clines. However, direct involvement of an inversion in local adaptation and consequent ecological reproductive isolation has not to our knowledge been demonstrated in nature. In this study, we discovered that a chromosomal inversion polymorphism is geographically widespread, and we test the extent to which it contributes to adaptation and reproductive isolation under natural field conditions. Replicated crosses between the prezygotically reproductively isolated annual and perennial ecotypes of the yellow monkeyflower, Mimulus guttatus, revealed that alternative chromosomal inversion arrangements are associated with life-history divergence over thousands of kilometers across North America. The inversion polymorphism affected adaptive flowering time divergence and other morphological traits in all replicated crosses between four pairs of annual and perennial populations. To determine if the inversion contributes to adaptation and reproductive isolation in natural populations, we conducted a novel reciprocal transplant experiment involving outbred lines, where alternative arrangements of the inversion were reciprocally introgressed into the genetic backgrounds of each ecotype. Our results demonstrate for the first time in nature the contribution of an inversion to adaptation, an annual/perennial life-history shift, and multiple reproductive isolating barriers. These results are consistent with the local adaptation mechanism being responsible for the distribution of the two inversion arrangements across the geographic range of M. guttatus and that locally adaptive inversion effects contribute directly to reproductive isolation. Such a mechanism may be partially responsible for the observation that closely related species often differ by multiple chromosomal rearrangements.

Fermion Mass Generation without Spontaneous Symmetry Breaking

The conventional mechanism of fermion mass generation in the Standard Model involves Spontaneous Symmetry Breaking (SSB). In this thesis, we study an alternate mechanism for the generation of fermion masses that does not require SSB, in the context of lattice field theories. Being inherently strongly coupled, this mechanism requires a non-perturbative approach like the lattice approach.

In order to explore this mechanism, we study a simple lattice model with a four-fermion interaction that has massless fermions at weak couplings and massive fermions at strong couplings, but without any spontaneous symmetry breaking. Prior work on this type of mass generation mechanism in 4D, was done long ago using either mean-field theory or Monte-Carlo calculations on small lattices. In this thesis, we have developed a new computational approach that enables us to perform large scale quantum Monte-Carlo calculations to study the phase structure of this theory. In 4D, our results confirm prior results, but differ in some quantitative details of the phase diagram. In contrast, in 3D, we discover a new second order critical point using calculations on lattices up to size $ 60^3$. Such large scale calculations are unprecedented. The presence of the critical point implies the existence of an alternate mechanism of fermion mass generation without any SSB, that could be of interest in continuum quantum field theory.