Natural selection is usually studied between mutants that differ in reproductive rate, but are subject to the same population structure. Here we explore how natural selection acts on mutants that have the same reproductive rate, but different population structures. In our framework, population structure is given by a graph that specifies where offspring can disperse. The invading mutant disperses offspring on a different graph than the resident wild-type. We find that more densely connected dispersal graphs tend to increase the invader's fixation probability, but the exact relationship between structure and fixation probability is subtle. We present three main results. First, we prove that if both invader and resident are on complete dispersal graphs, then removing a single edge in the invader's dispersal graph reduces its fixation probability. Second, we show that for certain island models higher invader's connectivity increases its fixation probability, but the magnitude of the effect depends on the exact layout of the connections. Third, we show that for lattices the effect of different connectivity is comparable to that of different fitness: for large population size, the invader's fixation probability is either constant or exponentially small, depending on whether it is more or less connected than the resident.

Computer Science Institute Charles University Prague Czech Republic

Department of Applied Mathematics University of Washington Seattle WA 98195 USA

Department of Mathematics Harvard University Cambridge MA 02138 USA

Department of Organismic and Evolutionary Biology Harvard University Cambridge MA 02138 USA

Institute of Science and Technology Austria Am Campus 1 3400 Klosterneuburg Austria

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Durrett R. 2008. Probability models for DNA sequence evolution. Berlin, Germany: Springer Science & Business Media.

Nowak MA. 2006. Evolutionary dynamics. Cambridge, MA: Harvard University Press.

Broom M, Rychtář J. 2014. Game-theoretical models in biology. Boca Raton, FL: CRC Press.

Moran P. 1962. The statistical processes of evolutionary theory, 1st edn. Oxford, UK: Clarendon.

Nagylaki T. 1992. Introduction to theoretical population genetics, vol. 142. Berlin, Germany: Springer.

Pollak E. 1966. On the survival of a gene in a subdivided population. J. Appl. Prob. 3, 142-155. (10.2307/3212043) DOI

Nagylaki T. 1980. The strong-migration limit in geographically structured populations. J. Math. Biol. 9, 101-114. (10.1007/BF00275916) PubMed DOI

Whitlock MC, Barton NH. 1997. The effective size of a subdivided population. Genetics 146, 427-441. (10.1093/genetics/146.1.427) PubMed DOI PMC

Durrett R, Levin S. 1994. The importance of being discrete (and spatial). Theor. Popul. Biol. 46, 363-394. (10.1006/tpbi.1994.1032) DOI

Komarova N. 2006. Spatial stochastic models for cancer initiation and progression. Bull. Math. Biol. 68, 1573-1599. (10.1007/s11538-005-9046-8) PubMed DOI

Santos FC, Pacheco JM, Lenaerts T. 2006. Evolutionary dynamics of social dilemmas in structured heterogeneous populations. Proc. Natl Acad. Sci. USA 103, 3490-3494. (10.1073/pnas.0508201103) PubMed DOI PMC

Lieberman E, Hauert C, Nowak MA. 2005. Evolutionary dynamics on graphs. Nature 433, 312-316. (10.1038/nature03204) PubMed DOI

Antal T, Redner S, Sood V. 2006. Evolutionary dynamics on degree-heterogeneous graphs. Phys. Rev. Lett. 96, 188104. (10.1103/PhysRevLett.96.188104) PubMed DOI PMC

Broom M, Rychtář J. 2008. An analysis of the fixation probability of a mutant on special classes of non-directed graphs. Proc. R. Soc. A 464, 2609-2627. (10.1098/rspa.2008.0058) DOI

Díaz J, Goldberg LA, Mertzios GB, Richerby D, Serna M, Spirakis PG. 2014. Approximating fixation probabilities in the generalized Moran process. Algorithmica 69, 78-91. (10.1007/s00453-012-9722-7) DOI

Adlam B, Chatterjee K, Nowak M. 2015. Amplifiers of selection. Proc. R. Soc. A 471, 20150114. (10.1098/rspa.2015.0114) DOI

Monk T. 2018. Martingales and the fixation probability of high-dimensional evolutionary graphs. J. Theor. Biol. 451, 10-18. (10.1016/j.jtbi.2018.04.039) PubMed DOI

Allen B, Lippner G, Chen YT, Fotouhi B, Momeni N, Yau ST, Nowak MA. 2017. Evolutionary dynamics on any population structure. Nature 544, 227-230. (10.1038/nature21723) PubMed DOI

Venkateswaran VR, Gokhale CS. 2019. Evolutionary dynamics of complex multiple games. Proc. R. Soc. B 286, 20190900. (10.1098/rspb.2019.0900) PubMed DOI PMC

Santos FC, Pacheco JM. 2005. Scale-free networks provide a unifying framework for the emergence of cooperation. Phys. Rev. Lett. 95, 098104. (10.1103/PhysRevLett.95.098104) PubMed DOI

Keeling MJ, Rohani P. 2011. Modeling infectious diseases in humans and animals. Princeton, NJ: Princeton University Press.

Szabó G, Fath G. 2007. Evolutionary games on graphs. Phys. Rep. 446, 97-216. (10.1016/j.physrep.2007.04.004) DOI

Castellano C, Fortunato S, Loreto V. 2009. Statistical physics of social dynamics. Rev. Mod. Phys. 81, 591. (10.1103/RevModPhys.81.591) DOI

Perc M, Gómez-Gardenes J, Szolnoki A, Floría LM, Moreno Y. 2013. Evolutionary dynamics of group interactions on structured populations: a review. J. R. Soc. Interface 10, 20120997. (10.1098/rsif.2012.0997) PubMed DOI PMC

Hadjichrysanthou C, Broom M, Rychtář J. 2011. Evolutionary games on star graphs under various updating rules. Dyn. Games Appl. 1, 386. (10.1007/s13235-011-0022-7) DOI

Mertzios GB, Nikoletseas S, Raptopoulos C, Spirakis PG. 2013. Natural models for evolution on networks. Theor. Comput. Sci. 477, 76-95. (10.1016/j.tcs.2012.11.032) DOI

Galanis A, Göbel A, Goldberg LA, Lapinskas J, Richerby D. 2017. Amplifiers for the Moran process. J. ACM 64, 5. (10.1145/3019609) DOI

Tkadlec J, Pavlogiannis A, Chatterjee K, Nowak MA. 2019. Population structure determines the tradeoff between fixation probability and fixation time. Commun. Biol. 2, 1-8. (10.1038/s42003-019-0373-y) PubMed DOI PMC

Allen B, Sample C, Steinhagen P, Shapiro J, King M, Hedspeth T, Goncalves M. 2021. Fixation probabilities in graph-structured populations under weak selection. PLoS Comput. Biol. 17, e1008695. (10.1371/journal.pcbi.1008695) PubMed DOI PMC

Monk T, Green P, Paulin M. 2014. Martingales and fixation probabilities of evolutionary graphs. Proc. R. Soc. A 470, 20130730. (10.1098/rspa.2013.0730) DOI

Pavlogiannis A, Tkadlec J, Chatterjee K, Nowak MA. 2018. Construction of arbitrarily strong amplifiers of natural selection using evolutionary graph theory. Commun. Biol. 1, 1-8. (10.1038/s42003-018-0078-7) PubMed DOI PMC

Goldberg LA, Lapinskas J, Lengler J, Meier F, Panagiotou K, Pfister P. 2019. Asymptotically optimal amplifiers for the Moran process. Theor. Comput. Sci. 758, 73-93. (10.1016/j.tcs.2018.08.005) DOI

Tkadlec J, Pavlogiannis A, Chatterjee K, Nowak MA. 2021. Fast and strong amplifiers of natural selection. Nat. Commun. 12, 1-6. (10.1038/s41467-021-24271-w) PubMed DOI PMC

Frantz C, Stewart KM, Weaver VM. 2010. The extracellular matrix at a glance. J. Cell Sci. 123, 4195-4200. (10.1242/jcs.023820) PubMed DOI PMC

Hay ED. 2013. Cell biology of extracellular matrix. Berlin, Germany: Springer Science & Business Media.

Walker C, Mojares E. 2018. Role of extracellular matrix in development and cancer progression. Int. J. Mol. Sci. 19, 3028. (10.3390/ijms19103028) PubMed DOI PMC

Gibson WT, Gibson MC. 2009. Cell topology, geometry, and morphogenesis in proliferating epithelia. Curr. Top. Dev. Biol. 89, 87-114. (10.1016/S0070-2153(09)89004-2) PubMed DOI

Kachalo S, Naveed H, Cao Y, Zhao J, Liang J. 2015. Mechanical model of geometric cell and topological algorithm for cell dynamics from single-cell to formation of monolayered tissues with pattern. PLoS ONE 10, e0126484. (10.1371/journal.pone.0126484) PubMed DOI PMC

Radisky D, Muschler J, Bissell MJ. 2002. Order and disorder: the role of extracellular matrix in epithelial cancer. Cancer Invest. 20, 139-153. (10.1081/CNV-120000374) PubMed DOI PMC

Nelson CM, Bissell MJ. 2006. Of extracellular matrix, scaffolds, and signaling: tissue architecture regulates development, homeostasis, and cancer. Annu. Rev. Cell Dev. Biol. 22, 287-309. (10.1146/annurev.cellbio.22.010305.104315) PubMed DOI PMC

Brauchle E, Kasper J, Daum R, Schierbaum N, Falch C, Kirschniak A, Schäffer TE, Schenke-Layland K. 2018. Biomechanical and biomolecular characterization of extracellular matrix structures in human colon carcinomas. Matrix Biol. 68, 180-193. (10.1016/j.matbio.2018.03.016) PubMed DOI

Guillot C, Lecuit T. 2013. Mechanics of epithelial tissue homeostasis and morphogenesis. Science 340, 1185-1189. (10.1126/science.1235249) PubMed DOI

Chaffer CL, Weinberg RA. 2011. A perspective on cancer cell metastasis. Science 331, 1559-1564. (10.1126/science.1203543) PubMed DOI

Melissourgos T, Nikoletseas SE, Raptopoulos CL, Spirakis PG. 2022. An extension of the Moran process using type-specific connection graphs. J. Comput. Syst. Sci. 124, 77-96. (10.1016/j.jcss.2021.07.007) DOI

Comins HN, Hamilton WD, May RM. 1980. Evolutionarily stable dispersal strategies. J. Theor. Biol. 82, 205-230. (10.1016/0022-5193(80)90099-5) PubMed DOI

Dieckmann U, O’Hara B, Weisser W. 1999. The evolutionary ecology of dispersal. Trends Ecol. Evol. 14, 88-90. (10.1016/S0169-5347(98)01571-7) DOI

Hutson V, Martinez S, Mischaikow K, Vickers GT. 2003. The evolution of dispersal. J. Math. Biol. 47, 483-517. (10.1007/s00285-003-0210-1) PubMed DOI

Levin SA, Muller-Landau HC, Nathan R, Chave J. 2003. The ecology and evolution of seed dispersal: a theoretical perspective. Annu. Rev. Ecol. Evol. Syst. 34, 575-604. (10.1146/annurev.ecolsys.34.011802.132428) DOI

Ronce O. 2007. How does it feel to be like a rolling stone? Ten questions about dispersal evolution. Annu. Rev. Ecol. Evol. Syst. 38, 231-253. (10.1146/annurev.ecolsys.38.091206.095611) DOI

May RM, Nowak MA. 1994. Superinfection, metapopulation dynamics, and the evolution of diversity. J. Theor. Biol. 170, 95-114. (10.1006/jtbi.1994.1171) PubMed DOI

Olivieri I, Michalakis Y, Gouyon PH. 1995. Metapopulation genetics and the evolution of dispersal. Am. Nat. 146, 202-228. (10.1086/285795) DOI

Heino M, Hanski I. 2001. Evolution of migration rate in a spatially realistic metapopulation model. Am. Nat. 157, 495-511. (10.1086/319927) PubMed DOI

Svoboda J, Tkadlec J, Kaveh K, Chatterjee K. 2023. Coexistence times in the Moran process with environmental heterogeneity. Proc. R. Soc. A 479, 20220685. (10.1098/rspa.2022.0685) DOI

Ohtsuki H, Pacheco JM, Nowak MA. 2007. Evolutionary graph theory: breaking the symmetry between interaction and replacement. J. Theor. Biol. 246, 681-694. (10.1016/j.jtbi.2007.01.024) PubMed DOI PMC

Krieger MS, McAvoy A, Nowak MA. 2017. Effects of motion in structured populations. J. R. Soc. Interface 14, 20170509. (10.1098/rsif.2017.0509) PubMed DOI PMC

Herrerías-Azcué F, Pérez-Muñuzuri V, Galla T. 2019. Motion, fixation probability and the choice of an evolutionary process. PLoS Comput. Biol. 15, e1007238. (10.1371/journal.pcbi.1007238) PubMed DOI PMC

Thalhauser CJ, Lowengrub JS, Stupack D, Komarova NL. 2010. Selection in spatial stochastic models of cancer: migration as a key modulator of fitness. Biol. Direct 5, 1-17. (10.1186/1745-6150-5-21) PubMed DOI PMC

Manem VS, Kohandel M, Komarova N, Sivaloganathan S. 2014. Spatial invasion dynamics on random and unstructured meshes: implications for heterogeneous tumor populations. J. Theor. Biol. 349, 66-73. (10.1016/j.jtbi.2014.01.009) PubMed DOI PMC

Waclaw B, Bozic I, Pittman ME, Hruban RH, Vogelstein B, Nowak MA. 2015. A spatial model predicts that dispersal and cell turnover limit intratumour heterogeneity. Nature 525, 261-264. (10.1038/nature14971) PubMed DOI PMC

Manem VS, Kaveh K, Kohandel M, Sivaloganathan S. 2015. Modeling invasion dynamics with spatial random-fitness due to micro-environment. PLoS ONE 10, e0140234. (10.1371/journal.pone.0140234) PubMed DOI PMC

Broom M, Hadjichrysanthou C, Rychtář J, Stadler B. 2010. Two results on evolutionary processes on general non-directed graphs. Proc. R. Soc. A 466, 2795-2798. (10.1098/rspa.2010.0067) DOI

Hindersin L, Möller M, Traulsen A, Bauer B. 2016. Exact numerical calculation of fixation probability and time on graphs. Biosystems 150, 87-91. (10.1016/j.biosystems.2016.08.010) PubMed DOI

Möller M, Hindersin L, Traulsen A. 2019. Exploring and mapping the universe of evolutionary graphs identifies structural properties affecting fixation probability and time. Commun. Biol. 2, 1-9. (10.1038/s42003-019-0374-x) PubMed DOI PMC

Pavlogiannis A, Tkadlec J, Chatterjee K, Nowak MA. 2017. Amplification on undirected population structures: comets beat stars. Sci. Rep. 7, 1-8. (10.1038/s41598-017-00107-w) PubMed DOI PMC

McAvoy A, Allen B. 2021. Fixation probabilities in evolutionary dynamics under weak selection. J. Math. Biol. 82, 1-41. (10.1007/s00285-021-01568-4) PubMed DOI

Brendborg J, Karras P, Pavlogiannis A, Rasmussen AU, Tkadlec J. 2022. Fixation maximization in the positional Moran process. In Proc. of the AAAI Conf. on Artificial Intelligence, 28 June, vol. 36, pp. 9304–9312. (10.1609/aaai.v36i9.21160) DOI

Ann Goldberg L, Lapinskas J, Richerby D. 2020. Phase transitions of the Moran process and algorithmic consequences. Random Struct. Algorithms 56, 597-647. (10.1002/rsa.20890) DOI

Alsubaie FS, Khataee H, Neufeld Z. 2023. Modelling of tissue invasion in epithelial monolayers. Life 13, 427. (10.3390/life13020427) PubMed DOI PMC

Kaveh K, Komarova N, Kohandel M. 2014. The duality of spatial death–birth and birth–death processes and limitations of the isothermal theorem. R. Soc. Open Sci. 2, 140465. (10.1098/rsos.140465) PubMed DOI PMC

Hindersin L, Traulsen A. 2015. Most undirected random graphs are amplifiers of selection for birth-death dynamics, but suppressors of selection for death-birth dynamics. PLoS Comput. Biol. 11, e1004437. (10.1371/journal.pcbi.1004437) PubMed DOI PMC

Tkadlec J, Pavlogiannis A, Chatterjee K, Nowak MA. 2020. Limits on amplifiers of natural selection under death-Birth updating. PLoS Comput. Biol. 16, e1007494. (10.1371/journal.pcbi.1007494) PubMed DOI PMC

Durocher L, Karras P, Pavlogiannis A, Tkadlec J. 2022. Invasion dynamics in the biased voter process. arXiv. (http://arxiv.org/abs/2201.08207)

Tkadlec J, Kaveh K, Chatterjee K, Nowak MA. 2023. Evolutionary dynamics of mutants that modify population structure. Figshare. (10.6084/m9.figshare.16910170) PubMed DOI PMC

Colonization times in Moran process on graphs

Amplifiers of selection for the Moran process with both Birth-death and death-Birth updating

Evolutionary dynamics of mutants that modify population structure

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