Deep mtDNA divergences indicate cryptic species in a fig-pollinating wasp

Background: Figs and fig-pollinating wasps are obligate mutualists that have coevolved for ca 90 million years. They have radiated together, but do not show strict cospeciation. In particular, it is now clear that many fig species host two wasp species, so there is more wasp speciation than fig speciation. However, little is known about how fig wasps speciate. Results: We studied variation in 71 fig-pollinating wasps from across the large geographic range of Ficus rubiginosa in Australia. All wasps sampled belong to one morphological species (Pleistodontes imperialis), but we found four deep mtDNA clades that differed from each other by 9–17% nucleotides. As these genetic distances exceed those normally found within species and overlap those (10–26%) found between morphologically distinct Pleistodontes species, they strongly suggest cryptic fig wasp species. mtDNA clade diversity declines from all four present in Northern Queensland to just one in Sydney, near the southern range limit. However, at most sites multiple clades coexist and can be found in the same tree or even the same fig fruit and there is no evidence for parallel sub-division of the host fig species. Both mtDNA data and sequences from two nuclear genes support the monophyly of the "P. imperialis complex" relative to other Pleistodontes species, suggesting that fig wasp divergence has occurred without any host plant shift. Wasps in clade 3 were infected by a single strain (W1) of Wolbachia bacteria, while those in other clades carried a double infection (W2+W3) of two other strains. Conclusion: Our study indicates that cryptic fig-pollinating wasp species have developed on a single host plant species, without the involvement of host plant shifts, or parallel host plant divergence. Despite extensive evidence for coevolution between figs and fig wasps, wasp speciation may not always be linked strongly with fig speciation

Uniformity in Association schemes and Coherent Configurations: Cometric Q-Antipodal Schemes and Linked Systems

2010 Mathematics Subject Classification. Primary 05E30, Secondary 05B25, 05C50, 51E12

Strongly walk-regular graphs

We study a generalization of strongly regular graphs. We call a graph strongly walk-regular if there is an $\ell >1$ such that the number of walks of length $\ell$ from a vertex to another vertex depends only on whether the two vertices are the same, adjacent, or not adjacent. We will show that a strongly walk-regular graph must be an empty graph, a complete graph, a strongly regular graph, a disjoint union of complete bipartite graphs of the same size and isolated vertices, or a regular graph with four eigenvalues. Graphs from the first three families in this list are indeed strongly $\ell$-walk-regular for all $\ell$, whereas the graphs from the fourth family are $\ell$-walk-regular for every odd $\ell$. The case of regular graphs with four eigenvalues is the most interesting (and complicated) one. Such graphs cannot be strongly $\ell$-walk-regular for even $\ell$. We will characterize the case that regular four-eigenvalue graphs are strongly $\ell$-walk-regular for every odd $\ell$, in terms of the eigenvalues. There are several examples of infinite families of such graphs. We will show that every other regular four-eigenvalue graph can be strongly $\ell$-walk-regular for at most one $\ell$. There are several examples of infinite families of such graphs that are strongly 3-walk-regular. It however remains open whether there are any graphs that are strongly $\ell$-walk-regular for only one particular $\ell$ different from 3

“Biodrop” Evaporation and Ring-Stain Deposits:The Significance of DNA Length

Small sessile drops of water containing either long or short strands of DNA (“biodrops”) were deposited on silicon substrates and allowed to evaporate. Initially, the triple line (TL) of both types of droplet remained pinned but later receded. The TL recession mode continued at constant speed until almost the end of drop lifetime for the biodrops with short DNA strands, whereas those containing long DNA strands entered a regime of significantly lower TL recession. We propose a tentative explanation of our observations based on free energy barriers to unpinning and increases in the viscosity of the base liquid due to the presence of DNA molecules. In addition, the structure of DNA deposits after evaporation was investigated by AFM. DNA self-assembly in a series of perpendicular and parallel orientations was observed near the contact line for the long-strand DNA, while, with the short-stranded DNA, smoother ring-stains with some nanostructuring but no striations were evident. At the interior of the deposits, dendritic and faceted crystals were formed from short and long strands, respectively, due to diffusion and nucleation limited processes, respectively. We suggest that the above results related to the biodrop drying and nanostructuring are indicative of the importance of DNA length, i.e., longer DNA chains consisting of linearly bonded shorter, rod-like DNA strands

On almost distance-regular graphs

Distance-regular graphs are a key concept in Algebraic Combinatorics and have given rise to several generalizations, such as association schemes. Motivated by spectral and other algebraic characterizations of distance-regular graphs, we study `almost distance-regular graphs'. We use this name informally for graphs that share some regularity properties that are related to distance in the graph. For example, a known characterization of a distance-regular graph is the invariance of the number of walks of given length between vertices at a given distance, while a graph is called walk-regular if the number of closed walks of given length rooted at any given vertex is a constant. One of the concepts studied here is a generalization of both distance-regularity and walk-regularity called $m$-walk-regularity. Another studied concept is that of $m$-partial distance-regularity or, informally, distance-regularity up to distance $m$. Using eigenvalues of graphs and the predistance polynomials, we discuss and relate these and other concepts of almost distance-regularity, such as their common generalization of $(\ell,m)$-walk-regularity. We introduce the concepts of punctual distance-regularity and punctual walk-regularity as a fundament upon which almost distance-regular graphs are built. We provide examples that are mostly taken from the Foster census, a collection of symmetric cubic graphs. Two problems are posed that are related to the question of when almost distance-regular becomes whole distance-regular. We also give several characterizations of punctually distance-regular graphs that are generalizations of the spectral excess theorem

Self-Similarity in Random Collision Processes

Kinetics of collision processes with linear mixing rules are investigated analytically. The velocity distribution becomes self-similar in the long time limit and the similarity functions have algebraic or stretched exponential tails. The characteristic exponents are roots of transcendental equations and vary continuously with the mixing parameters. In the presence of conservation laws, the velocity distributions become universal.Comment: 4 pages, 4 figure

The reversible polydisperse Parking Lot Model

We use a new version of the reversible Parking Lot Model to study the compaction of vibrated polydisperse media. The particle sizes are distributed according to a truncated power law. We introduce a self-consistent desorption mechanism with a hierarchical initialization of the system. In this way, we approach densities close to unity. The final density depends on the polydispersity of the system as well as on the initialization and will reach a maximum value for a certain exponent in the power law.Comment: 7 pages, Latex, 12 figure

Structure and Magnetization of Two-Dimensional Vortex Arrays in the Presence of Periodic Pinning

Ground-state properties of a two-dimensional system of superconducting vortices in the presence of a periodic array of strong pinning centers are studied analytically and numerically. The ground states of the vortex system at different filling ratios are found using a simple geometric argument under the assumption that the penetration depth is much smaller than the spacing of the pin lattice. The results of this calculation are confirmed by numerical studies in which simulated annealing is used to locate the ground states of the vortex system. The zero-temperature equilibrium magnetization as a function of the applied field is obtained by numerically calculating the energy of the ground state for a large number of closely spaced filling ratios. The results show interesting commensurability effects such as plateaus in the B-H diagram at simple fractional filling ratios.Comment: 12 pages, 19 figures, submitted for publicatio