Specialized nursery pollination mutualisms as evolutionary traps stabilized by antagonistic traits.

We examine the conditions for the transition from antagonism to mutualism between plants and their specialists nursery pollinators in a reference case which is the Trollius europaeus-Chiastocheta interaction. The mechanistic model we developed shows that a specialization of T. europaeus on Chiastocheta could be the result of an attempt to escape over-exploitation by closing its flower. The pressure for such an escape increases with the parasite's frequency and its pollination efficiency but decreases in the presence of alternative pollinators. The resulting specialization is a priori an unstable one, leading either to strong evolutionary oscillations, or to evolutionary suicide due to over-exploitation of the plants. It becomes stable if the plants develop a defense mechanism to regulate their parasite's population size and limit seed-exploitation. The development of a counter-measure by the latter can destabilize the mutualism depending on the costs linked to such a trait. On the other hand, we find that a specialization on a purely mutualistic basis would require a preexisting high diversity of flower-opening within the population.

Solvable models of neighbor-dependent substitution processes.

We prove that a wide class of Markov models of neighbor-dependent substitution processes on the integer line is solvable. This class contains some models of nucleotidic substitutions recently introduced and studied empirically by molecular biologists. We show that the polynucleotidic frequencies at equilibrium solve some finite-size linear systems. This provides, for the first time up to our knowledge, explicit and algebraic formulas for the stationary frequencies of non-degenerate neighbor-dependent models of DNA substitutions. Furthermore, we show that the dynamics of these stochastic processes and their distribution at equilibrium exhibit some stringent, rather unexpected, independence properties. For example, nucleotidic sites at distance at least three evolve independently, and all the sites, when encoded as purines and pyrimidines, evolve independently.

A markovian approach for the prediction of mouse isochores.

Hidden Markov models (HMMs) are effective tools to detect series of statistically homogeneous structures, but they are not well suited to analyse complex structures. For example, the duration of stay in a state of a HMM must follow a geometric law. Numerous other methodological difficulties are encountered when using HMMs to segregate genes from transposons or retroviruses, or to determine the isochore classes of genes. The aim of this paper is to analyse these methodological difficulties, and to suggest new tools for the exploration of genome data. We show that HMMs can be used to analyse complex gene structures with bell-shaped length distribution by using convolution of geometric distributions. Thus, we have introduced macros-states to model the distributions of the lengths of the regions. Our study shows that simple HMM could be used to model the isochore organisation of the mouse genome. This potential use of markovian models to help in data exploration has been underestimated until now.

In silico segmentations of lentivirus envelope sequences.

BACKGROUND: The gene encoding the envelope of lentiviruses exhibits a considerable plasticity, particularly the region which encodes the surface (SU) glycoprotein. Interestingly, mutations do not appear uniformly along the sequence of SU, but they are clustered in restricted areas, called variable (V) regions, which are interspersed with relatively more stable regions, called constant (C) regions. We look for specific signatures of C/V regions, using hidden Markov models constructed with SU sequences of the equine, human, small ruminant and simian lentiviruses. RESULTS: Our models yield clear and accurate delimitations of the C/V regions, when the test set and the training set were made up of sequences of the same lentivirus, but also when they were made up of sequences of different lentiviruses. Interestingly, the models predicted the different regions of lentiviruses such as the bovine and feline lentiviruses, not used in the training set. Models based on composite training sets produce accurate segmentations of sequences of all these lentiviruses. CONCLUSION: Our results suggest that each C/V region has a specific statistical oligonucleotide composition, and that the C (respectively V) regions of one of these lentiviruses are statistically more similar to the C (respectively V) regions of the other lentiviruses, than to the V (respectively C) regions of the same lentivirus.

A computational prediction of isochores based on hidden Markov models.

Mammalian genomes are organised into a mosaic of regions (in general more than 300 kb in length), with differing, relatively homogeneous G+C contents. The G+C content is the basic characteristic of isochores, but they have also been associated with many other biological properties. For instance, the genes are more compact and their density is highest in G+C rich isochores. Various ways of locating isochores in the human genome have been developed, but such methods use only the base composition of the DNA sequences. The present paper proposes a new method, based on a hidden Markov model, which takes into account several of the biological properties associated with the isochore structure of a genome. This method leads to good segmentation of the human genome into isochores, and also permits a new analysis of the known heterogeneity of G+C rich isochores: most (60%) of the G+C poor genes embedded in G+C rich isochores have UTR sequences characteristic of G+C rich genes. This genomic feature is discussed in the context of both evolution and genome function.

Mutation-replication statistics of polymerase chain reactions.

The variability of the products of polymerase chain reactions, due to mutations and to incomplete replications, can have important clinical consequences. Sun (1995) and Weiss and von Haeseler (1995) modeled these errors by a branching process and introduced estimators of the mutation rate and of the efficiency of the reaction based, for example, on the empirical distribution of the mutations of a random sequence. This distribution involves a noncanonical branching Markov chain which, although easy to describe, is not analytically tractable except in the infinite-population limit. These authors for the infinite-target limit, and Wang et al. (2000) for finite targets, solved the infinite-population limit. In this paper, we provide bounds of the difference between the finite-target finite-population case and its finite-target infinite-population approximation. The bounds are explicit functions of the efficiency of the reaction, the mutation rate per site and per cycle, the size of the target, the number of cycles, and the size of the initial population. They concern every moment and, what might be more surprising, the histogram itself of the distributions. The bounds for the moments exhibit a phase transition at the value 1 - 1/N = 3/4 of the mutation rate per site and per cycle, where N = 4 is the number of letters in the encoding alphabet of DNA and RNA. Of course, in biological contexts, the mutation rates are much smaller than 3/4.