Fixation dynamics of beneficial alleles in prokaryotic polyploid chromosomes and plasmids

Theoretical population genetics has been mostly developed for sexually reproducing diploid and for monoploid (haploid) organisms, focusing on eukaryotes. The evolution of bacteria and archaea is often studied by models for the allele dynamics in monoploid populations. However, many prokaryotic organisms harbor multicopy replicons -- chromosomes and plasmids -- and theory for the allele dynamics in populations of polyploid prokaryotes remains lacking. Here we present a population genetics model for replicons with multiple copies in the cell. Using this model, we characterize the fixation process of a dominant beneficial mutation at two levels: the phenotype and the genotype. Our results show that, depending on the mode of replication and segregation, the fixation time of mutant phenotypes may precede the genotypic fixation time by many generations; we term this time interval the heterozygosity window. We furthermore derive concise analytical expressions for the occurrence and length of the heterozygosity window, showing that it emerges if the copy number is high and selection strong. Replicon ploidy thus allows for the maintenance of genetic variation following phenotypic adaptation and consequently for reversibility in adaptation to fluctuating environmental conditions.

Molecular Systems Predict Equilibrium Distributions of Phenotype Diversity Available for Selection

Two long-standing challenges in theoretical population genetics and evolution are predicting the distribution of phenotype diversity generated by mutation and available for selection and determining the interaction of mutation, selection, and drift to characterize evolutionary equilibria and dynamics. More fundamental for enabling such predictions is the current inability to causally link population genetic parameters, selection and mutation, to the underlying molecular parameters, kinetic and thermodynamic. Such predictions would also have implications for understanding cryptic genetic variation and the role of phenotypic robustness. Here we provide a new theoretical framework for addressing these challenges. It is built on Systems Design Space methods that relate system phenotypes to genetically-determined parameters and environmentally-determined variables. These methods, based on the foundation of biochemical kinetics and the deconstruction of complex systems into rigorously defined biochemical phenotypes, provide several innovations that automate (1) enumeration of the phenotypic repertoire without knowledge of kinetic parameter values, (2) representation of phenotypic regions and their relationships in a System Design Space, and (3) prediction of values for kinetic parameters, concentrations, fluxes and global tolerances for each phenotype. We now show that these methods also automate prediction of phenotype-specific mutation rate constants and equilibrium distributions of phenotype diversity in populations undergoing steady-state exponential growth. We introduce this theoretical framework in the context of a case study involving a small molecular system, a primordial circadian clock, compare and contrast this framework with other approaches in theoretical population genetics, and discuss experimental challenges for testing predictions.

Generating normal networks via leaf insertion and nearest neighbor interchange

Background Galled trees are studied as a recombination model in theoretical population genetics. This class of phylogenetic networks has been generalized to tree-child networks and other network classes by relaxing a structural condition imposed on galled trees. Although these networks are simple, their topological structures have yet to be fully understood. Results It is well-known that all phylogenetic trees on n taxa can be generated by the insertion of the n-th taxa to each edge of all the phylogenetic trees on n−1 taxa. We prove that all tree-child (resp. normal) networks with k reticulate nodes on n taxa can be uniquely generated via three operations from all the tree-child (resp. normal) networks with k−1 or k reticulate nodes on n−1 taxa. Applying this result to counting rooted phylogenetic networks, we show that there are exactly $\frac {(2n)!}{2^{n} (n-1)!}-2^{n-1} n!$(2n)!2n(n−1)!−2n−1n! binary phylogenetic networks with one reticulate node on n taxa. Conclusions The work makes two contributions to understand normal networks. One is a generalization of an enumeration procedure for phylogenetic trees into one for normal networks. Another is simple formulas for counting normal networks and phylogenetic networks that have only one reticulate node.