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<p>a, Fixation probabilities on an undirected cycle with <i>N</i> = 10 vertices as a function of <i>r</i> for starting with one mutant.</p>
David A. Brewster (17118328)
Yichen Huang (5794106)
Michael Mitzenmacher (25145498)
Martin A. Nowak (24845)
Cell Biology
Evolutionary Biology
Environmental Sciences not elsewhere classified
Ecology
Biological Sciences not elsewhere classified
Mathematical Sciences not elsewhere classified
Science Policy
Infectious Diseases
unweighted undirected graphs
edges denote interactions
graph — compete
evolutionary graph theory
study mixed updating
randomly chosen neighbor
prove exact formulas
div >< p
study fixation probabilities
short fixation times
mixed updating
graph represent
fixation probabilities
neighbors —
evolutionary dynamics
vacancy proportional
two scenarios
time step
reproduction proportional
population structure
offspring replaces
neutral evolution
n </
efficient algorithm
constant selection
complex structures
competitive replacement
chosen uniformly
adjacent vertex
<p>The various curves represent the various values of . The solid lines represent the average of 10<sup>4</sup> simulations of the mixed -updating process, and the surrounding translucent regions are the 95% confidence intervals. The dashed lines are the theoretical fixation probabilities from Theorem 3.10. <b>i)</b> Zoomed in plot of the theoretical curves in the region , normalized by the fixation probability when . At <i>r</i> = 1, the fixation probability is 1/<i>N</i> regardless of . This value is indicated by a dot. The plotted range extends below <i>r</i> = 1, that is, to deleterious mutants, for which Theorem 3.10 remains valid. The fixation probability for the well-mixed population is equivalent to the fixation probability for a cycle under pure Bd updating (drawn in dashed light blue) for all <i>r</i>, by the Isothermal Theorem [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1014829#pcbi.1014829.ref034" target="_blank">34</a>].</p>
2026-09-30T18:07:02Z
Image
Figure
10.1371/journal.pcbi.1014829.g006
https://figshare.com/articles/figure/_p_a_Fixation_probabilities_on_an_undirected_cycle_with_i_N_i_10_vertices_as_a_function_of_i_r_i_for_starting_with_one_mutant_p_/34036352
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