1. 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

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

3. Model variant Directed percolation – Critical exponents Complex behaviors Overview

4. 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

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

6. Generations Mutability

7. Phase Transitions: Order Parameters Results from: Scott et al. (Europhysics Letters, in press) 0.340.38 0.340.38

8. Directed Percolation Critical Exponents (Henkel, Hinrichsen, Lübeck)

9. Other Exponents

10. 0.3100.3150.320 0.325 0.330 0.335 0.340 μ0.3100.3150.3200.3250.330 α3.4893.3262.5891.7730.462 Density Decay Rate

11. More Evidence: Times to Extinction

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

13. R measure of clustering Clark & Evans 1954 Organism coordinates Centroid coordinates Aggregated, R<1 Purely Random, R=1 Uniform, R>1 0.34 0.38 Results from: Scott et al. (Europhysics Letters, in press) 0.34 0.38

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

15. 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

16. 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

17. 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

18. Directed Percolation Density Decay Rate