1999/07/02 by Erik van Nimwegen, James P. Crutchfield, van Nimwegen, Erik +1 · 1 citation
Biochemistry, Genetics and Molecular Biology · Environmental Science · Physics and Astronomy · Social Sciences · #Adaptation and Self-Organizing Systems (nlin.AO) #Ecosystem dynamics and resilience #Evolution and Genetic Dynamics #Evolutionary Game Theory and Cooperation #FOS: Biological sciences #FOS: Physical sciences #Populations and Evolution (q-bio.PE) #adap-org #nlin.AO #q-bio.PE
paper · pdf · doi:10.48550/arxiv.adap-org/9907002
32 pages, 7 figures, 1 table; http://www.santafe.edu/projects/evca/med.ps.gz
arxiv created 1999/07/02 · openalex publication_date 1999/07/02 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We analytically study the dynamics of evolving populations that exhibit metastability on the level of phenotype or fitness. In constant selective environments, such metastable behavior is caused by two qualitatively different mechanisms. One the one hand, populations may become pinned at a local fitness optimum, being separated from higher-fitness genotypes by a \em fitness barrier of low-fitness genotypes. On the other hand, the population may only be metastable on the level of phenotype or fitness while, at the same time, diffusing over \em neutral networks of selectively neutral genotypes. Metastability occurs in this case because the population is separated from higher-fitness genotypes by an \em entropy barrier: The population must explore large portions of these neutral networks before it discovers a rare connection to fitter phenotypes. We derive analytical expressions for the barrier crossing times in both the fitness barrier and entropy barrier regime. In contrast with ``landscape'' evolutionary models, we show that the waiting times to reach higher fitness depend strongly on the width of a fitness barrier and much less on its height. The analysis further shows that crossing entropy barriers is faster by orders of magnitude than fitness barrier crossing. Thus, when populations are trapped in a metastable phenotypic state, they are most likely to escape by crossing an entropy barrier, along a neutral path in genotype space. If no such escape route along a neutral path exists, a population is most likely to cross a fitness barrier where the barrier is \em narrowest, rather than where the barrier is shallowest.