Oldest Varroa tolerant honey bee population provides insight into the origins of the global decline of honey bees

The ecto-parasitic mite Varroa destructor has transformed the previously inconsequential Deformed Wing Virus (DWV) into the most important honey bee viral pathogen responsible for the death of millions of colonies worldwide. Naturally, DWV persists as a low level covert infection transmitted between nest-mates. It has long been speculated that Varroa via immunosuppression of the bees, activate a covert infection into an overt one. Here we show that despite Varroa feeding on a population of 20-40 colonies for over 30 years on the remote island of Fernando de Noronha, Brazil no such activation has occurred and DWV loads have remained at borderline levels of detection. This supports the alternative theory that for a new vector borne viral transmission cycle to start, an outbreak of an overt infection must first occur within the host. Therefore, we predict that this honey bee population is a ticking time-bomb, protected by its isolated position and small population size. This unique association between mite and bee persists due to the evolution of low Varroa reproduction rates. So the population is not adapted to tolerate Varroa and DWV, rather the viral quasi-species has simply not yet evolved the necessary mutations to produce a virulent variant

Varroa destructor reproduction and cell re-capping in mite-resistant Apis mellifera populations

Globalization has facilitated the spread of emerging pests such as the Varroa destructor mite, resulting in the near global distribution of the pest. In South African and Brazilian honey bees, mite-resistant colonies appeared within a decade; in Europe, mite-resistant colonies are rare, but several of these exhibited high levels of “re-capping” behavior. We studied re-capping in Varroa-naïve (UK/Australia) and Varroa-resistant (South Africa and Brazil) populations and found very low and very high levels, respectively, with the resistant populations targeting mite-infested cells. Furthermore, 54% of artificially infested A. m. capensis worker cells were removed after 10 days and 83% of the remaining infested cells were re-capped. Such targeted re-capping of drone cells did not occur. We propose that cell opening is a fundamental trait in mite-resistant populations and that re-capping is an accurate proxy for this behavior

Computing excluded minors for classes of matroids representable over partial fields

We describe an implementation of a computer search for the "small" excluded minors for a class of matroids representable over a partial field. Using these techniques, we enumerate the excluded minors on at most 15 elements for both the class of dyadic matroids, and the class of 2-regular matroids. We conjecture that there are no other excluded minors for the class of 2-regular matroids; whereas, on the other hand, we show that there is a 16-element excluded minor for the class of dyadic matroids.We describe an implementation of a computer search for the "small" excluded minors for a class of matroids representable over a partial field. Using these techniques, we enumerate the excluded minors on at most 15 elements for both the class of dyadic matroids, and the class of 2-regular matroids. We conjecture that there are no other excluded minors for the class of 2-regular matroids; whereas, on the other hand, we show that there is a 16-element excluded minor for the class of dyadic matroids

NN-detachable pairs in 3-connected matroids II: life in XX

Let $M$ be a 3-connected matroid, and let $N$ be a 3-connected minor of $M$. A pair $\{x_1,x_2\} \subseteq E(M)$ is $N$-detachable if one of the matroids $M/x_1/x_2$ or $M \backslash x_1 \backslash x_2$ is both 3-connected and has an $N$-minor. This is the second in a series of three papers where we describe the structures that arise when it is not possible to find an $N$-detachable pair in $M$. In the first paper in the series, we showed that if $M$ has no $N$-detachable pairs, then either $M$ has one of three particular 3-separators that can appear in a matroid with no $N$-detachable pairs, or there is a 3-separating set $X$ with certain strong structural properties. In this paper, we analyse matroids with such a structured set $X$, and prove that they have either an $N$-detachable pair, or one of five particular 3-separators that can appear in a matroid with no $N$-detachable pairs.Comment: 47 pages, 5 figure

Generalized feedback vertex set problems on bounded-treewidth graphs: chordality is the key to single-exponential parameterised algorithms

It has long been known that Feedback Vertex Set can be solved in time 2^O(w log w)n^O(1) on graphs of treewidth w, but it was only recently that this running time was improved to 2^O(w)n^O(1), that is, to single-exponential parameterized by treewidth. We investigate which generalizations of Feedback Vertex Set can be solved in a similar running time. Formally, for a class of graphs P, Bounded P-Block Vertex Deletion asks, given a graph G on n vertices and positive integers k and d, whether G contains a set S of at most k vertices such that each block of G-S has at most d vertices and is in P. Assuming that P is recognizable in polynomial time and satisfies a certain natural hereditary condition, we give a sharp characterization of when single-exponential parameterized algorithms are possible for fixed values of d: - if P consists only of chordal graphs, then the problem can be solved in time 2^O(wd^2) n^{O}(1), - if P contains a graph with an induced cycle of length ell>= 4, then the problem is not solvable in time 2^{o(w log w)} n^O(1)} even for fixed d=ell, unless the ETH fails. We also study a similar problem, called Bounded P-Component Vertex Deletion, where the target graphs have connected components of small size instead of having blocks of small size, and present analogous results