★ Bjørn Østman
Postdoc
Adami Lab
BEACON Center for the Study of Evolution in Action
Microbiology and Molecular Genetics
Michigan State University
Biomedical and Physical Sciences
567 Wilson Road, room 2228D
East Lansing, MI 48824
Email: ostman@msu.edu
Phone: 517-355-8733



  

Evolutionary Dynamics in Fitness Landscapes

Common to all the models below is that

The distinction between genetic drift and selection is not strong, contrary to what most people imagine (I gather from the debate about the relative strengths of drift vs. selection). Because the population size is always smaller than infinity, and because selection is a stochastic process (a series of random events), genetic drift is always present. The strength of selection depends on the shape of the fitness landscape (the selection coefficients of mutations). The larger the effects of mutations are, the more selection "dominates" over drift. In the case of crossing valleys in the fitness landscape, one could say that the population "drifts" across the valley, even in cases where the valley is not even in fitness.

The color of the individuals is arbitrary and have nothing to do with the scale colors of the fitness landscape.
 
Two-dimensional landscapes
 

Dynamic landscape with two fluctuating peaks. The landscape changes slowly enough that the population can track the peaks. Population size is 2,304. Per-trait mutation rate is 0.5. Mutations cause the organisms to move to a neighboring genotype. Grid-size is 200 by 200 genotypes. Rate of death is 10 percent per update.
2014/3/25

Density-dependent landscape where each individual reduces fitness a tiny amount in an area of 7x7 pixels centered on itself. Population size is 2,304. Per-trait mutation rate is 0.05. Mutations cause the organisms to move to a neighboring genotype. Grid-size is 200 by 200 genotypes. Rate of death is 10 percent per update.
2014/3/25

Survival of the flattest. At first the mutation rate is low (0.05), so it is advantageous for the organisms to sit on the tall peak. Then the mutation rate is increased to 0.5, at which point the mutational load makes the average fitness quite low, and it becomes more advantageous to be on the plateau. Population size is 2,304. Mutations cause the organisms to move to a neighboring genotype. Grid-size is 200 by 200 genotypes. Rate of death is 10 percent per update.
2014/3/25
 

Neutral landscape. Population size is 2,304. Per-trait mutation rate is 0.5. Mutations cause the organisms to move to a neighboring genotype. Grid-size is 200 by 200 genotypes. Rate of death is 10 percent per update.
2013/12/29

Half-holey landscape. Neutral grid is 15x15 genotypes. Holes have 90 percent fitness of neutral grid. Population size is 2,304. Per-trait mutation rate is 0.5. Mutations cause the organisms to move to a neighboring genotype. Grid-size is 200 by 200 genotypes. Rate of death is 10 percent per update.
2013/12/29

Holey landscape. Neutral grid is 15x15 genotypes. Holes have zero fitness. Population size is 2,304. Per-trait mutation rate is 0.5. Mutations cause the organisms to move to a neighboring genotype. Grid-size is 200 by 200 genotypes. Rate of death is 10 percent per update.
2013/12/29
 

Half-holey landscape. Neutral grid consists of ridges every 30 genotypes. Holes have 95 percent fitness of neutral grid. Population size is 2,304. Per-trait mutation rate is 0.5. Mutations cause the organisms to move to a neighboring genotype. Grid-size is 200 by 200 genotypes. Rate of death is 10 percent per update.
2014/1/2

Smooth single-peaked fitness landscape. The peak is a Gaussian. The tail is not neutral, despite its appearance, but actually has a greater relative slope than nearer the peak, which is why the population starts out moving really fast and slows down as it gets closer to the peak. Population size is 2,304. Per-trait mutation rate is 0.5. Mutations cause the organisms to move to a neighboring genotype. Grid-size is 400 by 400 genotypes. Rate of death is 10 percent per update.
2013/11/20

Four Gaussian peaks. Population size is 100. Per-trait mutation rate is 0.2. Mutations cause the trait to change by a Gaussian distributed amount (mean = 0, standard deviation = 0.07). Rate of death is 10 percent per update.
2010/4/14
 
Multi-dimensional genotype-fitness landscapes / fitness graphs
In fitness graphs - networks representing multi-dimensional genotype-fitness landscapes - every genotype is plotted at its fitness vs. the number of mutations away from an arbitrary wild-type. Edges/lines between nodes indicate neighboring genotypes separated by a single mutation. The area of the circles are proportional to the fraction of the population that inhabits each genotype.
 

Aspergillus niger landscape. The population gets stuck on a peak two mutations away from the global peak (the wild-type). Population size is 1,000. Mutation rate is 0.01. Moran process. Mutations can only move an organism between neighboring genotypes. Data is from Franke J, Klözer A, de Visser JAGM, Krug J (2011) Evolutionary Accessibility of Mutational Pathways. PLoS Comput Biol 7(8): e1002134.
2013/8/14

NK landscape. N=20 loci. K=6. Only five loci shown. Moran process (one individual killed and replaced per update). Population size is 1,000. Mutation rate is 0.1.
2013/2/28

NK landscape. N=20 loci. K=6. Only five loci shown. Moran process (one individual killed and replaced per update). Population size is 1,000. Mutation rate is 0.01.
2013/2/28