Population histories of right whales (Cetacea: Eubalaena) Inferred from Mitochondrial Sequence Diversities and Divergences of Their Whale Lice (Amphipoda: Cyamus)

Right whales carry large populations of three ‘whale lice’ (Cyamus ovalis, Cyamus gracilis, Cyamus erraticus) that have no other hosts. We used sequence variation in the mitochondrial COI gene to ask (i) whether cyamid population structures might reveal associations among right whale individuals and subpopulations, (ii) whether the divergences of the three nominally conspecific cyamid species on North Atlantic, North Pacific, and southern right whales (Eubalaena glacialis, Eubalaena japonica, Eubalaena australis) might indicate their times of separation, and (iii) whether the shapes of cyamid gene trees might contain information about changes in the population sizes of right whales. We found high levels of nucleotide diversity but almost no population structure within oceans, indicating large effective population sizes and high rates of transfer between whales and subpopulations. North Atlantic and Southern Ocean populations of all three species are reciprocally monophyletic, and North Pacific C. erraticus is well separated from North Atlantic and southern C. erraticus. Mitochondrial clock calibrations suggest that these divergences occurred around 6 million years ago (Ma), and that the Eubalaena mitochondrial clock is very slow. North Pacific C. ovalis forms a clade inside the southern C. ovalis gene tree, implying that at least one right whale has crossed the equator in the Pacific Ocean within the last 1–2 million years (Myr). Low-frequency polymorphisms are more common than expected under neutrality for populations of constant size, but there is no obvious signal of rapid, interspecifically congruent expansion of the kind that would be expected if North Atlantic or southern right whales had experienced a prolonged population bottleneck within the last 0.5 Myr.

Vanishing of Ext and Tor over complete intersections

Let (R,m) be a local complete intersection, that is, a local ring whose m-adic completion is the quotient of a complete regular local ring by a regular sequence. Let M and N be finitely generated R-modules. This dissertation concerns the vanishing of Tor(M, N) and Ext(M, N). In this context, M satisfies Serre's condition (S_{n}) if and only if M is an nth syzygy. The complexity of M is the least nonnegative integer r such that the nth Betti number of M is bounded by a polynomial of degree r-1 for all sufficiently large n. We use this notion of Serre's condition and complexity to study the vanishing of Tor_{i}(M, N). In particular, building on results of C. Huneke, D. Jorgensen and R. Wiegand [32], and H. Dao [21], we obtain new results showing that good depth properties on the R-modules M, N and MtensorN force the vanishing of Tor_{i}(M, N) for all i>0. We give examples showing that our results are sharp. We also show that if R is a one-dimensional domain and M and MtensorHom(M,R) are torsion-free, then M is free if and only if M has complexity at most one. If R is a hypersurface and Ext^{i}(M, N) has finite length for all i>>0, then the Herbrand difference [18] is defined as length(Ext^{2n}(M, N))-(Ext^{2n-1}(M, N)) for some (equivalently, every) sufficiently large integer n. In joint work with Hailong Dao, we generalize and study the Herbrand difference. Using the Grothendieck group of finitely generated R-modules, we also examined the number of consecutive vanishing of Ext^{i}(M, N) needed to ensure that Ext^{i}(M, N) = 0 for all i>>0. Our results recover and improve on most of the known bounds in the literature, especially when R has dimension two.

A macroscopic kinetic model for DNA polymerase elongation and high-fidelity nucleotide election

The enzymatically catalyzed template-directed extension of ssDNA/primer complex is an impor-tant reaction of extraordinary complexity. The DNA polymerase does not merely facilitate the insertion of dNMP, but it also performs rapid screening of substrates to ensure a high degree of fidelity. Several kinetic studies have determined rate constants and equilibrium constants for the elementary steps that make up the overall pathway. The information is used to develop a macro-scopic kinetic model, using an approach described by Ninio [Ninio J., 1987. Alternative to the steady-state method: derivation of reaction rates from first-passage times and pathway probabili-ties. Proc. Natl. Acad. Sci. U.S.A. 84, 663–667]. The principle idea of the Ninio approach is to track a single template/primer complex over time and to identify the expected behavior. The average time to insert a single nucleotide is a weighted sum of several terms, in-cluding the actual time to insert a nucleotide plus delays due to polymerase detachment from ei-ther the ternary (template-primer-polymerase) or quaternary (+nucleotide) complexes and time delays associated with the identification and ultimate rejection of an incorrect nucleotide from the binding site. The passage times of all events and their probability of occurrence are ex-pressed in terms of the rate constants of the elementary steps of the reaction pathway. The model accounts for variations in the average insertion time with different nucleotides as well as the in-fluence of G+C content of the sequence in the vicinity of the insertion site. Furthermore the model provides estimates of error frequencies. If nucleotide extension is recognized as a compe-tition between successful insertions and time delaying events, it can be described as a binomial process with a probability distribution. The distribution gives the probability to extend a primer/template complex with a certain number of base pairs and in general it maps annealed complexes into extension products.