2026-10-12T11:44:42Z https://api.figshare.com/v2/oai

oai:figshare.com:article/34036334 2026-09-30T17:50:07Z category_12 category_24 category_272 category_39 category_734 category_811 category_106 category_132 portal_5 item_type_6 month_year_09_2026

<p>Proofs and derivations.</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>Contains all technical tools and detailed proofs supporting the results in the main text, including: the potential function and optional stopping machinery for neutral evolution; the additivity of the fixation probability; the proof that the unbiased () fixation probability is 1/<i>N</i> from any starting location; the proof that the two pure processes cannot both exceed 1/<i>N</i>; the explicit bidegreed fixation probability formula and the sensitivity analysis; the neutral fixation time bounds for the unbiased and bidegreed cases; the constant selection technical tools; the combined derivation of the star fixation probabilities (general <i>r</i> > 0, specializing to neutral evolution); the cycle fixation probability formula; the weak and strong selection fixation time bounds; and the fully polynomial randomized approximation schemes for computing the fixation probability.</p> <p>(PDF)</p> 2026-09-30T18:07:02Z Text Journal contribution 10.1371/journal.pcbi.1014829.s001 https://figshare.com/articles/journal_contribution/_p_Proofs_and_derivations_p_/34036334 CC BY 4.0