On the close relationship between speciation, inbreeding and recessive mutations.

Whilst the principle of adaptive evolution is unanimously recognised as being caused by the process of natural selection favouring the survival and/or reproduction of individuals having acquired new advantageous traits, a consensus has proven much harder to find regarding the actual origin of species. Indeed, since speciation corresponds to the establishment of reproductive barriers, it is difficult to see how it could bring a selective advantage because it amounts to a restriction in the opportunities to breed with as many and/or as diverse partners as possible. In this regard, Darwin himself did not believe that reproductive barriers could be selected for, and today most evolutionary biologists still believe that speciation can only occur through a process of separation allowing two populations to diverge sufficiently to become infertile with one another. I do, however, take the view that, if so much speciation has occurred, and still occurs around us, it cannot be a consequence of passive drift but must result from a selection process, whereby it is advantageous for groups of individuals to reproduce preferentially with one another and reduce their breeding with the rest of the population. 

In this essay, I propose a model whereby new species arise by “budding” from an ancestral stock, via a process of inbreeding among small numbers of individuals, driven by the occurrence of advantageous recessive mutations. Since the phenotypes associated to such mutations can only be retained in the context of inbreeding, it is the pressure of the ancestral stock which will promote additional reproductive barriers, and ultimately result in complete separation of a new species. I thus contend that the phenomenon of speciation would be driven by mutations resulting in the advantageous loss of certain functions, whilst adaptive evolution would correspond to gains of function that would, most of the time be dominant.

A very important further advantage of inbreeding is that it reduces the accumulation of recessive mutations in genomes. A consequence of the model proposed is that the existence of species would correspond to a metastable equilibrium between inbreeding and outbreeding, with excessive inbreeding promoting speciation, and excessive outbreeding resulting in irreversible accumulation of recessive mutations that could ultimately only lead to the species extinction. 
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A comprehensive, self-contained derivation of the one-body density matrices from single-reference excited-state calculation methods using the equation-of-motion formalism

In this contribution we review in a rigorous, yet comprehensive fashion the assessment of the one-body reduced density matrices derived from the most used single-reference excited-state calculation methods in the framework of the equation-of-motion formalism. Those methods are separated into two types: those which involve the coupling of a deexcitation operator to a single-excitation transition operator, and those which do not involve such a coupling. The case of many-body auxiliary wave functions for excited states is also addressed. For each of these approaches we were interested in deriving the elements of the one-body transition and difference density matrices, and to highlight their particular structure. This has been accomplished by applying a decomposition of integrals involving one-determinant quantum electronic states on which two or three pairs of second quantization operators can act. Such a decomposition has been done according to a corollary to Wick's theorem, which is brought in a comprehensive and detailed manner. A comment is also given about the consequences of using the equation-of-motion formulation in this context, and the two types of excited-state calculation methods (with and without coupling excitations to deexcitations) are finally compared from the point of view of the structure of their transition and difference density matrices

Choose Outsiders First: a mean 2-approximation random algorithm for covering problems

A high number of discrete optimization problems, including Vertex Cover, Set Cover or Feedback Vertex Set, can be unified into the class of covering problems. Several of them were shown to be inapproximable by deterministic algorithms. This article proposes a new random approach, called Choose Outsiders First, which consists in selecting randomly ele- ments which are excluded from the cover. We show that this approach leads to random outputs which mean size is at most twice the optimal solution.Comment: 8 pages The paper has been withdrawn due to an error in the proo

Orbifold quantum cohomology of weighted projective spaces

This article is a revised, short and english version of my PhD thesis. First, we show a mirror theorem : the Frobenius manifold associated to the orbifold quantum cohomology of weighted projective space is isomorphic to the one attached to a specific Laurent polynomial. Secondly, we show a reconstruction theorem, that is, we can reconstruct in an algorithmic way the full genus 0 Gromov-Witten potential from the 3-point invariants.Comment: 27 pages, revised and short version of my PhD thesis : math.AG/0510331. Accepted for publication in Journal of Algebraic Geometr