Mutability Driven Phase Transitions in a Neutral Phenotype Evolution Model Adam David Scott Department of Physics & Astronomy University of Missouri at St. Louis Evolution – Snowbird, UT 23 June 2013

Acknowledgements Dr. Sonya Bahar Dawn King McDonnell Foundation Complex Systems Grant UMSL Department of Physics & Astronomy

Model variant Directed percolation – Critical exponents Complex behaviors Overview

Model ONLY phenotypic evolution – No genetics & no physical space – 2D Continuous with absorbing boundaries Asexual Branching & coalescing random walks – Reaction-diffusion process Clustering – sympatric Mutability – Maximum possible offspring mutation from parent – Control parameter Dawn’s: Random death percentage for each organism Control parameter is random death percentage THIS: Random death percentage of population Control parameter is mutability

Model: Clustering Phenetic species – Speciation by phenotypes Cluster seeds – Reference Nearest neighbor Second nearest neighbor Closed sets of cluster seeds

Generations Mutability

Phase Transitions: Order Parameters Results from: Scott et al. (Europhysics Letters, in press)

Directed Percolation Critical Exponents (Henkel, Hinrichsen, Lübeck)

Other Exponents

μ α Density Decay Rate

More Evidence: Times to Extinction

Complex Behaviors Similar behaviors at multiple levels – Organisms undergo clustering transition – Species (clusters of organisms) do too! Cluster centroid  cluster center of “mass”

R measure of clustering Clark & Evans 1954 Organism coordinates Centroid coordinates Aggregated, R<1 Purely Random, R=1 Uniform, R> Results from: Scott et al. (Europhysics Letters, in press)

Reaction-Diffusion at Multiple Levels Organisms coalesce: – A+B  A Species coalesce: – Merge with one or more species, A+B+C  A’

Multiple levels of selection Fitness selection on organisms – Therefore on species Potential selection on clusters – Directed Percolation Fewer species interactions Species density – Isotropic Percolation Phenotype range Samir Okasha, Evolution and the Levels of Selection

Conclusions Phenotype evolution – Neutral & non-neutral: Dees & Bahar, PLoS ONE 2010 – Sympatric Complex dynamics – Mutability driven maximum possible phenotypic variation – Multiple levels – Two transitions  Absorbing State Extinction Surviving AggregatedSpanning

Thank you! Absorbing State Extinction Surviving AggregatedSpanning Henkel, Hinrichsen, Lübeck, Non-Equilibrium Phase Transitions: Vol 1: Absorbing Phase Transitions, 2009 Scott, King, Marić, Bahar, “Clustering and Phase Transitions on a Neutral Landscape”, Europhysics Letters, in press Okasha, Samir, Evolution and the Levels of Selection, 2006

Directed Percolation Density Decay Rate