2026-10-11T21:44:31Z https://api.figshare.com/v2/oai

oai:figshare.com:article/34036355 2026-09-30T17:50:16Z category_12 category_24 category_272 category_39 category_734 category_811 category_106 category_132 portal_5 item_type_1 month_year_09_2026

Fixation probabilities on a star graph with N = 10 vertices when . 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 The plotted range extends below r = 1, that is, to deleterious mutants, for which Theorem 3.11 remains valid. The various curves represent the various values of . The solid lines represent the average of 104 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 3.11. The dotted black line is the fixation probability for a well-mixed population [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1014829#pcbi.1014829.ref034" target="_blank">34</a>]. a, Fixation probabilities as a function of r for starting with a mutant in the center. b, Same as a) except a mutant is initially on a leaf. Note that for none of the values of depicted do the star and well-mixed fixation probabilities agree for all r. In b the curve lies close to, but does not coincide with, the well-mixed curve. The inset in each panel shows the theoretical fixation probability from Theorem 3.11 on the same axes and color scale as the main panel, but for a fine sweep of across [0,1] rather than the five values plotted with simulations, so that the whole continuum of update rules is visible. 2026-09-30T18:07:02Z Image Figure 10.1371/journal.pcbi.1014829.g007 https://figshare.com/articles/figure/_p_Fixation_probabilities_on_a_star_graph_with_i_N_i_10_vertices_when_p_/34036355 CC BY 4.0