Range Expansion Theories Could Shed Light on the Spatial Structure of Intra-tumour Heterogeneity

  • Cindy GidoinEmail author
  • Stephan Peischl
Special Issue: Modelling Biological Evolution: Developing Novel Approaches


Many theoretical studies of range expansions focus on the dynamics of species’ ranges or on causes and consequences of biological invasions. The similarities between biological range expansions and the dynamics of tumour growth have recently become more obvious, highlighting that tumours can be viewed as a population of abnormal cells expanding its range in the body of its host. Here, we discuss the potential of recent theoretical developments in the context of range expansions to shed light on intra-tumour heterogeneity, and to develop novel computational and statistical methods for studying the increasingly available genomic and phenotypic data from tumour cells. We review two spatial eco-evolutionary processes that could lead to a better understanding of the spatial structure of intra-tumour heterogeneity during the development of solid tumours: (1) the increase in dispersal abilities and (2) the accumulation of deleterious mutations at the front of expanding range edges. We first summarize theoretical and empirical evidences for each of these two phenomena and illustrate the eco-evolutionary dynamics of these processes using mathematical models. Secondly, we review evidences that these phenomena could also occur during the spatial expansion of a tumour within hosts. Finally, we discuss promising avenues for future research with the aim of synthesizing insights from clinical and theoretical studies of tumour development and evolutionary biology.


Intra-tumour heterogeneity Expansion load Life-history traits Spread rate 



The ideas that form the foundation of this article were presented by Cindy Gidoin at the conference ‘‘Modelling Biological Evolution 2017: Developing novel approaches”, which took place in Leicester, UK, on 4th–7th April 2017. We thank Dr. Andrey Morozov for organizing the conference, and Dr. Robert Noble and Dr. Philip Gerlee for organizing the symposium “How does spatial structure influence cancer evolution?” and for giving Cindy Gidoin the opportunity to present her work in the symposium.


  1. Adam JA, Maggelakis SA (1990) Diffusion regulated growth characteristics of a spherical prevascular carcinoma. Bull Math Biol 52:549–582. CrossRefzbMATHGoogle Scholar
  2. Alfarouk KO, Ibrahim ME, Gatenby RA, Brown JS (2013) Riparian ecosystems in human cancers. Evol Appl 6:46–53. CrossRefGoogle Scholar
  3. Andor N, Graham TA, Jansen M et al (2015) Pan-cancer analysis of the extent and consequences of intratumor heterogeneity. Nat Med 22:105–113. CrossRefGoogle Scholar
  4. Berthouly-Salazar C, van Rensburg BJ, Le Roux JJ et al (2012) Spatial sorting drives morphological variation in the invasive bird, acridotheris tristis. PLoS ONE 7:1–9. CrossRefGoogle Scholar
  5. Beverton R, Holt S (1957) On the dynamics of exploited fish populations. Fisheries investigation series 2. Ministry of agriculture, Fisheries and Food, LondonGoogle Scholar
  6. Bosshard L, Dupanloup I, Tenaillon O et al (2017) Accumulation of deleterious mutations during bacterial range expansions. Genetics 207:669–684. Google Scholar
  7. Bouin E, Calvez V (2014) Travelling waves for the cane toads equation with bounded traits. Nonlinearity 27:2233–2253. MathSciNetCrossRefzbMATHGoogle Scholar
  8. Bouin E, Henderson C, Ryzhik L (2017) Super-linear spreading in local and non-local cane toads equations. J Math Pures Appl 108:724–750. MathSciNetCrossRefzbMATHGoogle Scholar
  9. Bozic I, Antal T, Ohtsuki H et al (2010) Accumulation of driver and passenger mutations during tumor progression. Proc Natl Acad Sci U S A 107:18545–18550. CrossRefGoogle Scholar
  10. Burton OJ, Phillips BL, Travis JMJ (2010) Trade-offs and the evolution of life-histories during range expansion. Ecol Lett 13:1210–1220. CrossRefGoogle Scholar
  11. Cairns J (1975) Mutation selection and the natural history of cancer. Nature 255:197–200. CrossRefGoogle Scholar
  12. Cote J, Clobert J, Fitze PS (2007) Mother-offspring competition promotes colonization success. Proc Natl Acad Sci U S A 104:9703–9708. CrossRefGoogle Scholar
  13. Cwynar LCLC, MacDonald GMGM (1987) Geographical variation of lodgepole pine in relation to population history. Am Nat 129:463–469. CrossRefGoogle Scholar
  14. Damaghi M, Gillies R (2017) Phenotypic changes of acid adapted cancer cells push them toward aggressiveness in their evolution in the tumor microenvironment. Cell Cycle 16:1739–1743. CrossRefGoogle Scholar
  15. Deforet M, Carmona-Fontaine C, Korolev KS, Xavier JB (2017) A simple rule for the evolution of fast dispersal at the edge of expanding populations. arXiv Preprint arXiv:1711.07955
  16. Edmonds CA, Lillie AS, Cavalli-Sforza LL (2004) Mutations arising in the wave front of an expanding population. Proc Natl Acad Sci U S A 101:975–979. CrossRefGoogle Scholar
  17. Enriquez-Navas PM, Kam Y, Das T et al (2016) Exploiting evolutionary principles to prolong tumor control in preclinical models of breast cancer. Sci Transl Med 8:327ra24. CrossRefGoogle Scholar
  18. Excoffier L, Ray N (2008) Surfing during population expansions promotes genetic revolutions and structuration. Trends Ecol Evol 23:347. CrossRefGoogle Scholar
  19. Fronhofer EA, Altermatt F (2015) Eco-evolutionary feedbacks during experimental range expansions. Nat Commun 6:6844. CrossRefGoogle Scholar
  20. Fronhofer EA, Kubisch A, Hovestadt T, Poethke HJ (2011) Assortative mating counteracts the evolution of dispersal polymorphisms. Evol (N Y) 65:2461–2469. Google Scholar
  21. Fusco D, Gralka M, Anderson A et al (2016) Excess of mutational jackpot events in growing populations due to gene surfing. Nat Commun 7:1–9. Google Scholar
  22. Gatenby RA (2009) A change of strategy in the war on cancer. Nature 459:508–509. CrossRefGoogle Scholar
  23. Gatenby R (2012) Perspective: finding cancer’s first principles. Nature 491:S55. CrossRefGoogle Scholar
  24. Gerlinger M, Swanton C (2010) How Darwinian models inform therapeutic failure initiated by clonal heterogeneity in cancer medicine. Br J Cancer 103:1139–1143. CrossRefGoogle Scholar
  25. Gilbert KJ, Sharp NP, Angert AL et al (2017) Local adaptation interacts with expansion load during range expansion: maladaptation reduces expansion load. Am Nat 189:368–380. CrossRefGoogle Scholar
  26. González-Martínez SC, Ridout K, Pannell JR (2017) Range expansion compromises adaptive evolution in an outcrossing plant. Curr Biol 27:2544–2551. CrossRefGoogle Scholar
  27. Hallatschek O, Nelson DR (2008) Gene surfing in expanding populations. Theor Popul Biol 73:158–170. CrossRefzbMATHGoogle Scholar
  28. Hallatschek O, Nelson DR (2010) Life at the front of an expanding population. Evol (N Y) 64:193–206. Google Scholar
  29. Hallatschek O, Hersen P, Ramanathan S, Nelson DR (2007) Genetic drift at expanding frontiers promotes gene segregation. Proc Natl Acad Sci U S A 104:19926–19930. CrossRefGoogle Scholar
  30. Hanahan D, Weinberg RA (2011) Hallmarks of cancer: the next generation. Cell 144:646–674. CrossRefGoogle Scholar
  31. Henn BM, Botigué LR, Peischl S et al (2016) Distance from sub-Saharan Africa predicts mutational load in diverse human genomes. Proc Natl Acad Sci 113:E440–E449. CrossRefGoogle Scholar
  32. Hoefflin R, Lahrmann B, Warsow G et al (2016) Spatial niche formation but not malignant progression is a driving force for intratumoural heterogeneity. Nat Commun 7:11845. CrossRefGoogle Scholar
  33. Horne SD, Pollick SA, Heng HHQ (2015) Evolutionary mechanism unifies the hallmarks of cancer. Int J Cancer 136:2012–2021. CrossRefGoogle Scholar
  34. Huang F, Peng S, Chen B et al (2015) Rapid evolution of dispersal-related traits during range expansion of an invasive vine Mikania micrantha. Oikos 124:1023–1030. CrossRefGoogle Scholar
  35. Hughes CL, Dytham C, Hill JK (2007) Modelling and analysing evolution of dispersal in populations at expanding range boundaries. Ecol Entomol 32:437–445. CrossRefGoogle Scholar
  36. Ibrahim-Hashim A, Robertson-Tessi M, Enriquez-Navas PM et al (2017) Defining cancer subpopulations by adaptive strategies rather than molecular properties provides novel insights into intratumoral evolution. Cancer Res 77:2242–2254. CrossRefGoogle Scholar
  37. Klopfstein S, Currat M, Excoffier L (2006) The fate of mutations surfing on the wave of a range expansion. Mol Biol Evol 23:482–490. CrossRefGoogle Scholar
  38. Kubisch A, Fronhofer EA, Poethke HJ, Hovestadt T (2013) Kin competition as a major driving force for invasions. Am Nat 181:700–706. CrossRefGoogle Scholar
  39. Lee MSY (2011) Macroevolutionary consequences of “spatial sorting”. Proc Natl Acad Sci 108:E347–E347. CrossRefGoogle Scholar
  40. Lehe R, Hallatschek O, Peliti L (2012) The rate of beneficial mutations surfing on the wave of a range expansion. PLoS Comput Biol 8:e1002447MathSciNetCrossRefGoogle Scholar
  41. Lindström T, Brown GP, Sisson SA et al (2013) Rapid shifts in dispersal behavior on an expanding range edge. Proc Natl Acad Sci U S A 110:13452–13456. CrossRefGoogle Scholar
  42. Ling S, Hu Z, Yang Z et al (2015) Extremely high genetic diversity in a single tumor points to prevalence of non-Darwinian cell evolution. PNAS 112:E6496–E6505. CrossRefGoogle Scholar
  43. Llewelyn J, Phillips BL, Alford RA et al (2010) Locomotor performance in an invasive species: cane toads from the invasion front have greater endurance, but not speed, compared to conspecifics from a long-colonised area. Oecologia 162:343–348. CrossRefGoogle Scholar
  44. Lloyd MC, Cunningham JJ, Bui MM et al (2016) Darwinian dynamics of intratumoral heterogeneity: not solely random mutations but also variable environmental selection forces. Cancer Res 76:3136–3144. CrossRefGoogle Scholar
  45. Lohmueller KE, Indap AR, Schmidt S et al (2008) Proportionally more deleterious genetic variation in European than in African populations. Nature 451:994–997. CrossRefGoogle Scholar
  46. Lombaert E, Estoup A, Facon B et al (2014) Rapid increase in dispersal during range expansion in the invasive ladybird Harmonia axyridis. J Evol Biol 27:508–517. CrossRefGoogle Scholar
  47. Lorenzi T, Venkataraman C, Lorz A, Chaplain MAJ (2018) The role of spatial variations of abiotic factors in mediating intratumour phenotypic heterogeneity. J Theor Biol 451:101–110. MathSciNetCrossRefzbMATHGoogle Scholar
  48. Lynch M, Bürger R, Gabriel W (1993) The mutational meltdown in asexual populations. J Hered 84:339–344CrossRefGoogle Scholar
  49. Marusyk A, Almendro V, Polyak K (2012) Intra-tumour heterogeneity: a looking glass for cancer? Nat Rev Cancer 12:323–334. CrossRefGoogle Scholar
  50. McFarland CD, Korolev KS, Kryukov GV et al (2013) Impact of deleterious passenger mutations on cancer progression. Proc Natl Acad Sci 110:2910–2915. CrossRefGoogle Scholar
  51. McFarland CD, Mirny LA, Korolev KS (2014) Tug-of-war between driver and passenger mutations in cancer and other adaptive processes. Proc Natl Acad Sci U S A 111:15138–15143. CrossRefGoogle Scholar
  52. McFarland C, Yaglom JA, Wojtkowiak JW et al (2017) The damaging effect of passenger mutations on cancer progression. Cancer Res 77:4763–4772. CrossRefGoogle Scholar
  53. Melbourne BA, Hastings A (2009) Highly variable spread rates in replicated biological invasions: fundamental limits to predictability. Science (80-) 325:1536–1539. CrossRefGoogle Scholar
  54. Merlo LMF, Pepper JW, Reid BJ, Maley CC (2006) Cancer as an evolutionary and ecological process. Nat Rev Cancer 6:924–935. CrossRefGoogle Scholar
  55. Milholland B, Dong X, Zhang L et al (2017) Differences between germline and somatic mutation rates in humans and mice. Nat Commun 8:15183. CrossRefGoogle Scholar
  56. Nowell PC (1976) The clonal evolution of tumor cell populations. Science (80-) 194:23–28. CrossRefGoogle Scholar
  57. Ochocki BM, Miller TEX (2017) Rapid evolution of dispersal ability makes biological invasions faster and more variable. Nat Commun 8:14315. CrossRefGoogle Scholar
  58. Pavel AB, Korolev KS (2017) Genetic load makes cancer cells more sensitive to common drugs: evidence from cancer cell line encyclopedia. Sci Rep 7:1–10. CrossRefGoogle Scholar
  59. Peischl S, Excoffier L (2015) Expansion load: recessive mutations and the role of standing genetic variation. Mol Ecol 24:2084–2094. CrossRefGoogle Scholar
  60. Peischl S, Dupanloup I, Kirkpatrick M, Excoffier L (2013) On the accumulation of deleterious mutations during range expansions. Mol Ecol 22:5972–5982. CrossRefGoogle Scholar
  61. Peischl S, Kirkpatrick M, Excoffier L (2015) Expansion load and the evolutionary dynamics of a species range. Am Nat 185:81–93. CrossRefGoogle Scholar
  62. Peischl S, Dupanloup I, Bosshard L, Excoffier L (2016) Genetic surfing in human populations: from genes to genomes. Curr Opin Genet Dev 41:53–61. CrossRefGoogle Scholar
  63. Peischl S, Dupanloup I, Foucal A et al (2018) Relaxed selection during a recent human expansion. Genetics 208:763–777. CrossRefGoogle Scholar
  64. Perkins AT, Phillips BL, Baskett ML, Hastings A (2013) Evolution of dispersal and life history interact to drive accelerating spread of an invasive species. Ecol Lett 16:1079–1087. CrossRefGoogle Scholar
  65. Petrovskii S, Morozov A, Li BL (2008) On a possible origin of the fat-tailed dispersal in population dynamics. Ecol Complex 5:146–150. CrossRefGoogle Scholar
  66. Phillips BL (2009) The evolution of growth rates on an expanding range edge. Biol Lett 5:802–804. CrossRefGoogle Scholar
  67. Phillips BL (2015) Evolutionary processes make invasion speed difficult to predict. Biol Invasions 17:1949–1960. CrossRefGoogle Scholar
  68. Phillips BL, Brown GP, Webb JK, Shine R (2006) Invasion and the evolution of speed in toads. Nature 439:803. CrossRefGoogle Scholar
  69. Phillips BL, Brown GP, Shine R (2010) Life-history evolution in range-shifting populations. Ecology 91:1617–1627. CrossRefGoogle Scholar
  70. Proskuryakov S, Gabai V (2010) Mechanisms of tumor cell necrosis. Curr Pharm Des 16:56–68. CrossRefGoogle Scholar
  71. Rieger H, Welter M (2015) Integrative models of vascular remodeling during tumor growth. Wiley Interdiscip Rev Syst Biol Med 7:113–129. CrossRefGoogle Scholar
  72. Scott J, Marusyk A (2017) Somatic clonal evolution: a selection-centric perspective. Biochim Biophys Acta Rev Cancer 1867:139–150. CrossRefGoogle Scholar
  73. Shine R, Brown GP, Phillips BL (2011) An evolutionary process that assembles phenotypes through space rather than through time. Proc Natl Acad Sci 108:5708–5711. CrossRefGoogle Scholar
  74. Simmons AD, Thomas CD (2004) Changes in dispersal during species’ range expansions. Am Nat 164:378–395. Google Scholar
  75. Sjöblom T, Jones S, Wood LD et al (2006) The consensus coding sequences of human breast and colorectal cancers. Science 314:268–274. CrossRefGoogle Scholar
  76. Thomas CD, Bodsworth EJ, Wilson RJ et al (2001) Ecological and evolutionary processes at expanding range margins. Nature 411:577–581. CrossRefGoogle Scholar
  77. Thomas F, Nesse RM, Gatenby R et al (2016) Evolutionary ecology of organs: a missing link in cancer development? Trends Cancer 2:409–415. CrossRefGoogle Scholar
  78. Travis JMJ, Münkemüller T, Burton OJ et al (2007) Deleterious mutations can surf to high densities on the wave front of an expanding population. Mol Biol Evol 24:2334–2343. CrossRefGoogle Scholar
  79. Trindade S, Sousa A, Gordo I (2012) Antibiotic resistance and stress in the light of Fisher’s model. Evol (N Y) 66:3815–3824. Google Scholar
  80. Van Petegem KHP, Boeye J, Stoks R, Bonte D (2016) Spatial selection and local adaptation jointly shape life-history evolution during range expansion. Am Nat 188:485–498. CrossRefGoogle Scholar
  81. Weinberg RA (2014) Coming full circle—from endless complexity to simplicity and back again. Cell 157:267–271. CrossRefGoogle Scholar
  82. Weiss-Lehman C, Hufbauer RA, Melbourne BA (2017) Rapid trait evolution drives increased speed and variance in experimental range expansions. Nat Commun 8:14303. CrossRefGoogle Scholar
  83. Williams JL, Kendall BE, Levine JM (2016a) Rapid evolution accelerates plant population spread in fragmented experimental landscapes. Science (80-) 353:482–485. CrossRefGoogle Scholar
  84. Williams MJ, Werner B, Barnes CP et al (2016b) Identification of neutral tumor evolution across cancer types. Nat Genet 48:238–244. CrossRefGoogle Scholar

Copyright information

© Society for Mathematical Biology 2018

Authors and Affiliations

  1. 1.UMR CNRS/IRD/UM1 MIVEGECCentre for Ecological and Evolutionary Research on Cancer (CREEC)MontpellierFrance
  2. 2.Interfaculty Bioinformatics UnitUniversity of BernBernSwitzerland
  3. 3.Swiss Institute for BioinformaticsLausanneSwitzerland

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