%0 Book Section %1 statphys23_0614 %A Sumedha, S. %A Martin, O.C. %A Peliti, L. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K computer ecology evolution genealogical modelling networks simulations statphys23 theory topic-10 trees %T Population size effects in evolutionary dynamics on neutral networks. %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=614 %X In evolutionary biology, populations are subject to a number of forces that shape their genetic composition. Amongst these, mutations, selection and drift play a central role. Drift becomes dominant for small populations, while for large populations one reaches a steady state where mutations balance effects of selection. The landscape paradigm provides a relation between genotype/phenotype and fitness, allowing for quantitative studies of evolving populations, while at the same time giving a qualitative picture. We study the dynamics of a population subject to selective pressures, evolving either on RNA neutral networks or on toy fitness landscapes. We discuss the spread and the neutrality of the population in the steady state. Different limits arise depending on whether selection or random drift are dominant. In the presence of strong drift we show that observables depend mainly on $M \mu$, $M$ being the population size and $\mu$ the mutation rate, while corrections to this scaling go as $1/M$: such corrections can be quite large in the presence of selection if there are barriers in the fitness landscape. Also we find that the convergence to the large $M \mu$ limit is linear in $1/M \mu$. Random drift reduces the population spread and thus delays the approach to the large $M$ limit at fixed $\mu$. Lowering the drift would thus allow one to reach the large $M$ limit more easily. Furthermore, one would have a higher mutational robustness of the steady-state population for a given population size; this higher survival probability suggests that biological mechanisms for reducing drift could be selected for in natural populations. (In fact, in numerous eukaryotes there are well documented mechanisms for avoiding inbreeding; this is understandable from an evolutionary perspective because cosanguinity effects in populations are deleterious.) We introduce a protocol that minimizes drift; then observables scale like $1/M$ rather than $1/(M\mu)$, allowing one to determine the large $M$ limit faster when $\mu$ is small; furthermore the genotypic diversity increases from $O(M)$ to $O(M)$.

@incollection{statphys23_0614, abstract = {In evolutionary biology, populations are subject to a number of forces that shape their genetic composition. Amongst these, mutations, selection and drift play a central role. Drift becomes dominant for small populations, while for large populations one reaches a steady state where mutations balance effects of selection. The landscape paradigm provides a relation between genotype/phenotype and fitness, allowing for quantitative studies of evolving populations, while at the same time giving a qualitative picture. We study the dynamics of a population subject to selective pressures, evolving either on RNA neutral networks or on toy fitness landscapes. We discuss the spread and the neutrality of the population in the steady state. Different limits arise depending on whether selection or random drift are dominant. In the presence of strong drift we show that observables depend mainly on $M \mu$, $M$ being the population size and $\mu$ the mutation rate, while corrections to this scaling go as $1/M$: such corrections can be quite large in the presence of selection if there are barriers in the fitness landscape. Also we find that the convergence to the large $M \mu$ limit is linear in $1/M \mu$. Random drift reduces the population spread and thus delays the approach to the large $M$ limit at fixed $\mu$. Lowering the drift would thus allow one to reach the large $M$ limit more easily. Furthermore, one would have a higher mutational robustness of the steady-state population for a given population size; this higher survival probability suggests that biological mechanisms for reducing drift could be selected for in natural populations. (In fact, in numerous eukaryotes there are well documented mechanisms for avoiding inbreeding; this is understandable from an evolutionary perspective because cosanguinity effects in populations are deleterious.) We introduce a protocol that minimizes drift; then observables scale like $1/M$ rather than $1/(M\mu)$, allowing one to determine the large $M$ limit faster when $\mu$ is small; furthermore the genotypic diversity increases from $O(\ln M)$ to $O(M)$.}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Sumedha, S. and Martin, O.C. and Peliti, L.}, biburl = {https://www.bibsonomy.org/bibtex/2097b7a6fd60d93054b9856326fda478b/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {182e1b5e1042fb95c9f528a9aba8568e}, intrahash = {097b7a6fd60d93054b9856326fda478b}, keywords = {computer ecology evolution genealogical modelling networks simulations statphys23 theory topic-10 trees}, month = {9-13 July}, timestamp = {2007-06-20T10:16:25.000+0200}, title = {Population size effects in evolutionary dynamics on neutral networks.}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=614}, year = 2007 }