Mayr, mathematics and the study of evolution

In 1959 Ernst Mayr challenged the relevance of mathematical models to evolutionary studies and was answered by JBS Haldane in a witty and convincing essay. Fifty years on, I conclude that the importance of mathematics has in fact increased and will continue to do so

Effects of radiation and fallout

https://stars.library.ucf.edu/prism/1821/thumbnail.jp

Special studies of AROD system concepts and designs

Signal processing techniques for range and range rate measurements in airborne range and orbit determinatio

Phase Diagrams of Quasispecies Theory with Recombination and Horizontal Gene Transfer

We consider how transfer of genetic information between individuals influences the phase diagram and mean fitness of both the Eigen and the parallel, or Crow-Kimura, models of evolution. In the absence of genetic transfer, these physical models of evolution consider the replication and point mutation of the genomes of independent individuals in a large population. A phase transition occurs, such that below a critical mutation rate an identifiable quasispecies forms. We generalize these models of quasispecies evolution to include horizontal gene transfer. We show how transfer of genetic information changes the phase diagram and mean fitness and introduces metastability in quasispecies theory, via an analytic field theoretic mapping.Comment: 5 pages, 1 figure, to appear in Physics Review Letter

Frequency-dependent fitness induces multistability in coevolutionary dynamics

Evolution is simultaneously driven by a number of processes such as mutation, competition and random sampling. Understanding which of these processes is dominating the collective evolutionary dynamics in dependence on system properties is a fundamental aim of theoretical research. Recent works quantitatively studied coevolutionary dynamics of competing species with a focus on linearly frequency-dependent interactions, derived from a game-theoretic viewpoint. However, several aspects of evolutionary dynamics, e.g. limited resources, may induce effectively nonlinear frequency dependencies. Here we study the impact of nonlinear frequency dependence on evolutionary dynamics in a model class that covers linear frequency dependence as a special case. We focus on the simplest non-trivial setting of two genotypes and analyze the co-action of nonlinear frequency dependence with asymmetric mutation rates. We find that their co-action may induce novel metastable states as well as stochastic switching dynamics between them. Our results reveal how the different mechanisms of mutation, selection and genetic drift contribute to the dynamics and the emergence of metastable states, suggesting that multistability is a generic feature in systems with frequency-dependent fitness.Comment: 12 pages, 6 figures; J. R. Soc. Interface (2012

Modelling the spread of Wolbachia in spatially heterogeneous environments

The endosymbiont Wolbachia infects a large number of insect species and is capable of rapid spread when introduced into a novel host population. The bacteria spread by manipulating their hosts' reproduction, and their dynamics are influenced by the demographic structure of the host population and patterns of contact between individuals. Reaction–diffusion models of the spatial spread of Wolbachia provide a simple analytical description of their spatial dynamics but do not account for significant details of host population dynamics. We develop a metapopulation model describing the spatial dynamics of Wolbachia in an age-structured host insect population regulated by juvenile density-dependent competition. The model produces similar dynamics to the reaction–diffusion model in the limiting case where the host's habitat quality is spatially homogeneous and Wolbachia has a small effect on host fitness. When habitat quality varies spatially, Wolbachia spread is usually much slower, and the conditions necessary for local invasion are strongly affected by immigration of insects from surrounding regions. Spread is most difficult when variation in habitat quality is spatially correlated. The results show that spatial variation in the density-dependent competition experienced by juvenile host insects can strongly affect the spread of Wolbachia infections, which is important to the use of Wolbachia to control insect vectors of human disease and other pests

Interspecific relationships in the Drosophila mulleri group

The genus Drosophila is particularly adapted to the study of species relationships, since its genetic and ontological possibilities are so well known, and numerous individuals from wild populations are easily available. Various population sizes and densities are represented and hence an unusual opportunity for the study of species differences is offered. Throughout the genus there are numerous subgroups with various cross-fertility relationships, indicating various levels of species differentiation. This work was carried out in connection with a series of similar studies dealing with different groups in the genus Drosophila being done at the University of Texas. In the mulleri group there are two members, representing large dense populations, that occupy the same area, while two other members are geographically isolated from these and from each other. All are related by some degree of cross-fertility so that a study of the isolating mechanisms of these forms makes possible a better knowledge of the nature of genetic relations between speciesEcology, Evolution and Behavio

Random copying in space

Random copying is a simple model for population dynamics in the absence of selection, and has been applied to both biological and cultural evolution. In this work, we investigate the effect that spatial structure has on the dynamics. We focus in particular on how a measure of the diversity in the population changes over time. We show that even when the vast majority of a population's history may be well-described by a spatially-unstructured model, spatial structure may nevertheless affect the expected level of diversity seen at a local scale. We demonstrate this phenomenon explicitly by examining the random copying process on small-world networks, and use our results to comment on the use of simple random-copying models in an empirical context.Comment: 26 pages, 11 figures. Based on invited talk at AHRC CECD Conference on "Cultural Evolution in Spatially Structured Populations" at UCL, September 2010. To appear in ACS - Advances in Complex System