Quantifying contributions of climate, geography, and gene flow to divergence: a case study for three North American pines

Long-lived species of trees, especially conifers, often display weak patterns of reproductive isolation, but clear patterns of local adaptation and phenotypic divergence. Discovering the evolutionary history of these patterns is paramount to a generalized understanding of speciation and the processes that confer population persistence versus those that compromise adaptive potential under rapidly changing environments. Forest trees have long generation times and low migratory potential making them especially vulnerable to population fragmentation and reductions of genetic diversity due to insufficient tracking of niche optima and adaptational lags. Within clades of the genus Pinus, evolutionary histories appear to be riddled with hybridization (i.e., interspecific gene flow), periods of isolation, and effective population size changes that co-occur with major shifts in climate. Quantifying the relative contributions of each of these factors to divergence and changes to genetic diversity requires a multidisciplinary approach involving historical species distributional modeling, demographic inference, and associations of genetic structure to climate and geography. This dissertation focuses on identifying drivers of divergence and explaining differing levels of reproductive isolation across three ecologically and economically valuable North American pine species (Pinus pungens, P. rigida, and P. taeda). First, we inferred demographic histories and found the recurrence of interspecific gene flow between P. pungens and P. rigida, as well as population size reductions during the last glacial period, to be important contributors to the mode and tempo of previously documented reproductive isolation between these species. Seasonality and elevation associated with both genetic and distributional differences indicating ecological divergence was also important to the divergences among the three focal species, but the relationship of P. taeda to the other two species remains enigmatic. Next, we illustrate how genomic patterns of differentiation across genic and intergenic regions can explain differing levels of reproductive isolation through pairwise assessments and mapping RADseq contigs to the annotated genome of P. taeda. Finally, in estimating the extent of hybridization and genetic diversity in shared forest stands of P. pungens and P. rigida, we discovered a general lack of hybridization at present and low genetic diversity in southern, trailing edge populations. Striking congruences across results, various methods employed, and work previously performed for the genus Pinus all provide support for emerging hypotheses related to forest tree speciation and biodiversity. This dissertation also presents useful information for forest conservation and management planning. At present, the adaptive potential of P. pungens, a montane pine with highly fragmented populations, is low based on genetic diversity estimates, its current distribution, and restricted levels of interspecific gene flow

NICHE CONSERVATISM OR DIVERGENCE: INSIGHTS INTO THE EVOLUTIONARY HISTORIES OF Pinus taeda, Pinus rigida, AND Pinus pungens

Environmentally related selective pressures and community interactions are well-documented drivers for niche differentiation, as natural selection acts on adaptive traits best fit for survival. Here, we investigated niche evolution between and within Pinus taeda, Pinus rigida, and Pinus pungens and sought to identify which climate variables contributed to species divergence. We also sought to describe niche differentiation across genetic groupings previously identified for P. taeda and P. rigida. Ecological niche models were produced using Maximum Entropy followed by statistical testing based on a measure of niche overlap, Schoener’s D. Both niche conservatism and niche divergence were detected, thus leading us to conclude that directional or disruptive selection drove divergence of the P. taeda lineage from its ancestor with P. rigida and P. pungens, while stabilizing selection was associated with the divergence of P. rigida and P. pungens. The latter implies that factors beyond climate are important drivers of speciation within Pinus

Carbon and Strontium Abundances of Metal-Poor Stars

We present carbon and strontium abundances for 100 metal-poor stars measured from R$\sim$7000 spectra obtained with the Echellette Spectrograph and Imager at the Keck Observatory. Using spectral synthesis of the G-band region, we have derived carbon abundances for stars ranging from [Fe/H]$=-1.3$ to [Fe/H]$=-3.8$. The formal errors are $\sim 0.2$ dex in [C/Fe]. The strontium abundance in these stars was measured using spectral synthesis of the resonance line at 4215 {\AA}. Using these two abundance measurments along with the barium abundances from our previous study of these stars, we show it is possible to identify neutron-capture-rich stars with our spectra. We find, as in other studies, a large scatter in [C/Fe] below [Fe/H]$= -2$. Of the stars with [Fe/H]$<-2$, 9$\pm$4% can be classified as carbon-rich metal-poor stars. The Sr and Ba abundances show that three of the carbon-rich stars are neutron-capture-rich, while two have normal Ba and Sr. This fraction of carbon enhanced stars is consistent with other studies that include this metallicity range.Comment: ApJ, Accepte

Quantum graphs with singular two-particle interactions

We construct quantum models of two particles on a compact metric graph with singular two-particle interactions. The Hamiltonians are self-adjoint realisations of Laplacians acting on functions defined on pairs of edges in such a way that the interaction is provided by boundary conditions. In order to find such Hamiltonians closed and semi-bounded quadratic forms are constructed, from which the associated self-adjoint operators are extracted. We provide a general characterisation of such operators and, furthermore, produce certain classes of examples. We then consider identical particles and project to the bosonic and fermionic subspaces. Finally, we show that the operators possess purely discrete spectra and that the eigenvalues are distributed following an appropriate Weyl asymptotic law

NGC 2419, M92, and the Age Gradient in the Galactic Halo

The WFPC2 camera on HST has been used to obtain deep main sequence photometry of the low-metallicity ([Fe/H]=-2.14), outer-halo globular cluster NGC 2419. A differential fit of the NGC 2419 CMD to that of the similarly metal-poor \ standard cluster M92 shows that they have virtually identical principal sequences and thus the same age to well within 1 Gyr. Since other low-metallicity clusters throughout the Milky Way halo have this same age to within the 1-Gyr precision of the differential age technique, we conclude that the earliest star (or globular cluster) formation began at essentially the same time everywhere in the Galactic halo throughout a region now almost 200 kpc in diameter. Thus for the metal-poorest clusters in the halo there is no detectable age gradient with Galactocentric distance. To estimate the absolute age of NGC 2419 and M92, we fit newly computed isochrones transformed through model-atmosphere calculations to the (M_V,V-I) plane, with assumed distance scales that represent the range currently debated in the literature. Unconstrained isochrone fits give M_V(RR) = 0.55 \pm 0.06 and a resulting age of 14 to 15 Gyr. Incorporating the full effects of helium diffusion would further reduce this estimate by about 1 Gyr. A distance scale as bright as M_V(RR) = 0.15 for [Fe/H] = -2, as has recently been reported, would leave several serious problems which have no obvious solution in the context of current stellar models.Comment: 32 pages, aastex, 9 postscript figures; accepted for publication in AJ, September 1997. Also available by e-mail from [email protected]

Intermediate statistics for a system with symplectic symmetry: the Dirac rose graph

We study the spectral statistics of the Dirac operator on a rose-shaped graph---a graph with a single vertex and all bonds connected at both ends to the vertex. We formulate a secular equation that generically determines the eigenvalues of the Dirac rose graph, which is seen to generalise the secular equation for a star graph with Neumann boundary conditions. We derive approximations to the spectral pair correlation function at large and small values of spectral spacings, in the limit as the number of bonds approaches infinity, and compare these predictions with results of numerical calculations. Our results represent the first example of intermediate statistics from the symplectic symmetry class.Comment: 26 pages, references adde

Level spacings and periodic orbits

Starting from a semiclassical quantization condition based on the trace formula, we derive a periodic-orbit formula for the distribution of spacings of eigenvalues with k intermediate levels. Numerical tests verify the validity of this representation for the nearest-neighbor level spacing (k=0). In a second part, we present an asymptotic evaluation for large spacings, where consistency with random matrix theory is achieved for large k. We also discuss the relation with the method of Bogomolny and Keating [Phys. Rev. Lett. 77 (1996) 1472] for two-point correlations.Comment: 4 pages, 2 figures; major revisions in the second part, range of validity of asymptotic evaluation clarifie

The Selberg trace formula for Dirac operators

We examine spectra of Dirac operators on compact hyperbolic surfaces. Particular attention is devoted to symmetry considerations, leading to non-trivial multiplicities of eigenvalues. The relation to spectra of Maass-Laplace operators is also exploited. Our main result is a Selberg trace formula for Dirac operators on hyperbolic surfaces