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We present a new class of metrics for unrooted phylogenetic X-trees inspired by the Gromov-Hausdorff distance for (compact) metric spaces. These metrics can be efficiently computed by linear or quadratic programming. They are robust under NNI operations, too. The local behaviour of the metrics shows that they are different from any previously introduced metrics. The performance of the metrics is briefly analysed on random weighted and unweighted trees as well as random caterpillars.

Generalising a site-based stochastic model due to Royama, Solé et al. and Sumpter et al., we investigate competition in a single species with discrete, non-overlapping generations. We show that the deterministic limit of the dynamics depends on a few easily interpretable parameters only. Further, we discuss qualitative properties and limit sets of the corresponding difference equations, and we relate these to modes of competition. Moreover, a detailed analysis of stochastic effects in some relevant scenarios indicates that the behaviour of the stochastic model is very sensitive to further details of the model.

We analyze the reduction of intrinsic noise caused by transition of a promoter between its active and inactive state in a negatively regulated genetic network, i.e., transcription of the gene is inhibited by its own gene product. To measure the noise attenuation, we compare its behavior to an inducible gene for which activation and deactivation of the gene take place at constant rates. As a model, we choose a hybrid approach in which some of the reaction channels are modeled as discrete events, and other reactions are modeled as continuous processes. Such a model is appropriate for investigations of noise caused by low reactant numbers. By focusing on intrinsic noise originating from the switching behavior of the regulatory system of a particular gene, we model only the transition between two different promoter states as a discrete event. We show that the stationary distributions of the unregulated and the autoregulated system are given as a solution of two coupled ordinary differential equations. Also, beside the distribution densities, the first two central moments are derived in closed analytical forms. We give conditions on the parameters when one or the other system shows lower fluctuations.