Molecular Replicator Dynamics

Template-dependent replication at the molecular level is the basis of reproduction in nature. A detailed understanding of the peculiarities of the chemical reaction kinetics associated with replication processes is therefore an indispensible prerequisite for any understanding of evolution at the molecular level. Networks of interacting self-replicating species can give rise to a wealth of different dynamical phenomena, from competitive exclusion to permanent coexistence, from global stability to multi-stability and chaotic dynamics. Nevertheless, there are some general principles that govern their overall behavior. We focus on the question to what extent the dynamics of replication can explain the accumulation of genetic information that eventually leads to the emergence of the first cell and hence the origin of life as we know it. A large class of ligation-based replication systems, which includes the experimentally available model systems for template directed self-replication, is of particular interest because its dynamics bridges the gap between the survival of a single fittest species to the global coexistence of everthing. In this intermediate regime the selection is weak enough to allow the coexistence of genetically unrelated replicators and strong enough to limit the accumulation of disfunctional mutants

Replicator Dynamics in Protocells

Replicator equations have been studied for three decades as a generic dynamical system modelling replication processes. Here we show how they arise naturally in models of self-replicating polymers and discuss some of their basic properties. We then concentrate on a minimal dynamic model of a protocell by coupling replicating polymers with a growing membrane

The Topology of Evolutionary Biology

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

U7 snRNAs

U7 small nuclear RNA (snRNA) sequences have been described only for a handful of animal species in the past. Here we describe a computational search for functional U7 snRNA genes throughout vertebrates including the upstream sequence elements characteristic for snRNAs transcribed by polymerase II. Based on the results of this search, we discuss the high variability of U7 snRNAs in both sequence and structure, and report on an attempt to find U7 snRNA sequences in basal deuterostomes and non-drosophilids insect genomes based on a combination of sequence, structure, and promoter features. Due to the extremely short sequence and the high variability in both sequence and structure, no unambiguous candidates were found. These results cast doubt on putative U7 homologs in even more distant organisms that are reported in the most recent release of the Rfam database

Evolution of the vertebrate Y RNA cluster

Relatively little is known about the evolutionary histories of most classes of non-protein coding RNAs. Here we consider Y RNAs, a relatively rarely studied group of related pol-III transcripts. A single cluster of functional genes is preserved throughout tetrapod evolution, which however exhibits clade-specific tandem duplications, gene-losses, and rearrangements

Saddles and Barrier in Landscapes of Generalized Search Operators

Barrier trees are a convenient way of representing the structure of complex combinatorial landscapes over graphs. Here we generalize the concept of barrier trees to landscapes defined over general multi-parent search operators based on a suitable notion of topological connectedness that depends explicitly on the search operator. We show that in the case of recombination spaces, path-connectedness coincides with connectedness as defined by the mutation operator alone. In contrast, topological connectedness is more general and depends on the details of the recombination operators as well. Barrier trees can be meaningfully defined for both concepts of connectedness

Abstention in Dynamical Models of Spatial Voting

We consider a model of platform adaptation in spatial voting focussing on the effect of abstention on the stability of the mean voter equilibrium. Two distinct approaches for modeling abstention are explored: (1) voters abstain if party platforms are too similar to each other and (2) voters abstain if both party platforms are far away from their ideal points

Adaptive Platform Dynamics in Multi-Party Spatial Voting

We explore the dynamics of multiple competing political parties under spatial voting. Parties are allowed to modify their positions adaptively in order to gain more votes. The parties in our model are opportunistic, that means they try to maximize their share of votes regardless of any ideological position. Each party makes small corrections to its current platform in order to increase its own utility by means of steepest ascent in the variables under its own control, i.e. by locally optimizing its own platform. We show that in models with more than two parties bifurcations at the trivial equilibrium occur if only the voters are critical enough, that is, if they respond strongly to small changes in relative utilities. A numerical survey in a three-party model yields multiple bifurcations, multi-stability, and stable periodic attractors that arise through Hopf bifurcations. Models with more than two parties can thus differ substantially from the two-party case, where it h..

Replicator Dynamics in Protocells

Replicator equations have been studied for three decades as a generic dynamical system modelling replication processes. Here we show how they arise naturally in models of self-replicating polymers and discuss some of their basic properties. We then concentrate on a minimal dynamic model of a protocell by coupling replicating polymers with a growing membrane