In this paper we present general results on aggregation of variables, specifically as it applies to decomposable (partitionable) dynamical systems. We show that a particular class of transition matrices, namely, those satisfying an equitable partitioning property, are aggregable under appropriate decomposition operators. It is also shown that equitable partitions have a natural application to the description of mutation-selection matrices (fitness landscapes) when their fitness functions have certain symmetries concordant with the neighborhood relationships in the underlying configuration space. We propose that the aggregate variable descriptions of mutation-selection systems offer a potential formal definition of units of selection and evolution.

In this paper, we investigate fitness landscapes (under point mutation and recombination) from the standpoint of whether the induced evolutionary dynamics have a “fast-slow” time scale associated with the differences in relaxation time between local quasi-equilibria and the global equilibrium. This dynamical hevavior has been formally described in the econometrics literature in terms of the spectral properties of the appropriate operator matrices by Simon and Ando (Econometrica 29 (1961) 111), and we use the relations they derive to ask which fitness functions and mutation/recombination operators satisfy these properties. It turns out that quite a wide range of landscapes satisfy the condition (at least trivially) under point mutation given a sufficiently low mutation rate, while the property appears to be difficult to satisfy under genetic recombination. In spite of the fact that Simon-Ando decomposability can be realized over fairly wide range of parameters, it imposes a number of restriction on which landscape partitionings are possible. For these reasons, the Simon-Ando formalism does not appear to be applicable to other forms of decomposition and aggregation of variables that are important in evolutionary systems.

The systematic assessment of rate variations across large datasets requires a systematic approach for summarizing results from individual tests. Often, this is performed by coarse-graining the phylogeny to consider rate variations at the level of sub-claded. In a phylo-geographic setting, however, one is often more interested in other partitions of the data, and in an exploratory mode a pre-specified subdivision of the data is often undesirable. We propose here to arrange rate variation data as the partially ordered set defined by the significant test results.

The phylogenetic position of Xenoturbella bocki has been a matter of controversy since its description in 1949. We sequenced a second complete mitochondrial genome of this species and performed phylogenetic analyses based on the amino acid sequences of all 13 mitochondrial protein-coding genes and on its gene order. Our results confirm the deuterostome relationship of Xenoturbella. However, in contrast to a recently published study (Bourlat et al. in Nature 444:85–88, 2006), our data analysis suggests a more basal branching of Xenoturbella within the deuterostomes, rather than a sister-group relationship to the Ambulacraria (Hemichordata and Echinodermata).

In this paper, we present a method and a corresponding tool called Tarzan for cophylogeny analysis of phylogenetic trees where the nodes are labelled with divergence timing information. The tool can be used for example to infer the common history of hosts and their parasites, of insect-plant relations or symbiotic relationships. Our method does the reconciliation analysis using an event-based concept where each event is assigned a cost and cost minimal solutions are sought. The events that are used by Tarzan are cospeciations, sortings, duplications, and (host) switches. Different from existing tools, Tarzan can handle more complex timing information of the phylogenetic trees for the analysis. This is important because several recent studies of cophylogenetic relationship have shown that timing information can be very important for the correct interpretation of results from cophylogenetic analysis. We present two examples (one host-parasite system and one insect-plant system) that show how divergence timing information can be integrated into reconciliation analysis and how this influences the results.

Central notions in evolutionary biology are intrinsically topological. This claim is maybe most obvious for the discontinuities associated with punctuated equilibria. Recently, a mathematical framework has been developed that derives the concepts of phenotypic characters and homology from the topological structure of the phenotype space. This structure in turn is determined by the genetic operators and their interplay with the properties of the genotype-phenotype map.

Background Coevolutionary systems like hosts and their parasites are commonly used model systems for evolutionary studies. Inferring the coevolutionary history based on given phylogenies of both groups is often done by employing a set of possible types of events that happened during coevolution. Costs are assigned to the different types of events and a reconstruction of the common history with a minimal sum of event costs is sought. Results This paper introduces a new algorithm and a corresponding tool called CoRe-PA, that can be used to infer the common history of coevolutionary systems. The proposed method utilizes an event-based concept for reconciliation analyses where the possible events are cospeciations, sortings, duplications, and (host) switches. All known event-based approaches so far assign costs to each type of cophylogenetic events in order to find a cost-minimal reconstruction. CoRe-PA uses a new parameter-adaptive approach, i.e., no costs have to be assigned to the coevolutionary events in advance. Several biological coevolutionary systems that have already been studied intensely in literature are used to show the performance of CoRe-PA. Conclusion From a biological point of view reasonable cost values for event-based reconciliations can often be estimated only very roughly. CoRe-PA is very useful when it is difficult or impossible to assign exact cost values to different types of coevolutionary events in advance.