Colonization times in Moran process on graphs

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F25%3A10504424" target="_blank" >RIV/00216208:11320/25:10504424 - isvavai.cz</a>

Result on the web

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=heJU3QrUdV" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=heJU3QrUdV</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1371/journal.pcbi.1012868" target="_blank" >10.1371/journal.pcbi.1012868</a>

Result language

angličtina

Original language name

Colonization times in Moran process on graphs

Original language description

Moran Birth-death process is a standard stochastic process that is used to model natural selection in spatially structured populations. A newly occurring mutation that invades a population of residents can either fixate on the whole population or it can go extinct due to random drift. The duration of the process depends not only on the total population size n, but also on the spatial structure of the population. In this work, we consider the Moran process with a single type of individuals who invade and colonize an otherwise empty environment. Mathematically, this corresponds to the setting where the residents have zero reproduction rate, thus they never reproduce. The spatial structure is represented by a graph. We present two main contributions. First, in contrast to the Moran process in which residents do reproduce, we show that the colonization time is always at most a polynomial function of the population size n. Namely, we show that colonization always takes at most 12n3-12n2 expected steps, and for each n, we identify the slowest graph where it takes exactly that many steps. Moreover, we establish a stronger bound of roughly n2.5 steps for undirected graphs and an even stronger bound of roughly n2 steps for so-called regular graphs. Second, we discuss various complications that one faces when attempting to measure fixation times and colonization times in spatially structured populations, and we propose to measure the real duration of the process, rather than counting the steps of the classic Moran process.

Czech name

—

Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project

—

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2025

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

PLoS Computational Biology

ISSN

1553-734X

e-ISSN

1553-7358

Volume of the periodical

21

Issue of the periodical within the volume

5

Country of publishing house

US - UNITED STATES

Number of pages

12

Pages from-to

e1012868

UT code for WoS article

001481670600002

EID of the result in the Scopus database

2-s2.0-105004710081