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Bulletin of Mathematical Biology

, Volume 78, Issue 11, pp 2165–2185 | Cite as

Expansion Under Climate Change: The Genetic Consequences

  • Jimmy Garnier
  • Mark A. Lewis
Original Article

Abstract

Range expansion and range shifts are crucial population responses to climate change. Genetic consequences are not well understood but are clearly coupled to ecological dynamics that, in turn, are driven by shifting climate conditions. We model a population with a deterministic reaction–diffusion model coupled to a heterogeneous environment that develops in time due to climate change. We decompose the resulting travelling wave solution into neutral genetic components to analyse the spatio-temporal dynamics of its genetic structure. Our analysis shows that range expansions and range shifts under slow climate change preserve genetic diversity. This is because slow climate change creates range boundaries that promote spatial mixing of genetic components. Mathematically, the mixing leads to so-called pushed travelling wave solutions. This mixing phenomenon is not seen in spatially homogeneous environments, where range expansion reduces genetic diversity through gene surfing arising from pulled travelling wave solutions. However, the preservation of diversity is diminished when climate change occurs too quickly. Using diversity indices, we show that fast expansions and range shifts erode genetic diversity more than slow range expansions and range shifts. Our study provides analytical insight into the dynamics of travelling wave solutions in heterogeneous environments.

Keywords

Neutral genetic diversity Range shift Range expansion Climate change Travelling wave Reaction–diffusion model 

Notes

Acknowledgments

MAL gratefully acknowledges a Canada Research Chair, a Killam Research Fellowship, Discovery and Accelerator grants from the Canadian Natural Sciences and Engineering Research Council, and the Natural Science and Engineering Research Council of Canada (Grant No. NET GP 434810-12) to the TRIA Network, with contributions from Alberta Agriculture and Forestry, Foothills Research Institute, Manitoba Conservation and Water Stewardship, Natural Resources Canada - Canadian Forest Service, Northwest Territories Environment and Natural Resources, Ontario Ministry of Natural Resources and Forestry, Saskatchewan Ministry of Environment, West Fraser and Weyerhaeuser. JG gratefully acknowledges the NONLOCAL project from the French National Research Agency (ANR-14-CE25-0013).

References

  1. Arenas M, Ray N, Currat M, Excoffier L (2012) Consequences of range contractions and range shifts on molecular diversity. Mol Biol Evol 29(1):207–218CrossRefGoogle Scholar
  2. Balanyá J (2006) Global genetic change tracks global climate warming in drosophila subobscura. Science 313(5794):1773–1775CrossRefGoogle Scholar
  3. Barton N, Etheridge A, Kelleher J, Véber A (2013) Genetic hitchhiking in spatially extended populations. Theor Popul Biol 87:75–89CrossRefzbMATHGoogle Scholar
  4. Barton NH, Etheridge AM (2011) The relation between reproductive value and genetic contribution. Genetics 188(4):953–973CrossRefGoogle Scholar
  5. Battisti A, Stastny M, Netherer S, Robinet C, Schopf A, Roques A, Larsson S (2005) Expansion of geographic range in the pine processionary moth caused by increased winter temperatures. Ecol Appl 15(6):2084–2096CrossRefGoogle Scholar
  6. Berestycki H, Rossi L (2008) Reaction-diffusion equations for population dynamics with forced speed I—the case of the whole space. Discrete Contin Dyn Syst 21(1):41–67MathSciNetCrossRefzbMATHGoogle Scholar
  7. Berestycki H, Diekmann O, Nagelkerke CJ, Zegeling PA (2009) Can a species keep pace with a shifting climate? Bull Math Biol 71(2):399–429MathSciNetCrossRefzbMATHGoogle Scholar
  8. Berger WH, Parker FL (1970) Diversity of planktonic foraminifera in deep-sea sediments. Science 168:1345–1347CrossRefGoogle Scholar
  9. Bonnefon O, Coville J, Garnier J, Hamel F, Roques L (2014) The spatio-temporal dynamics of neutral genetic diversity. Ecol Complex 20:282–292CrossRefGoogle Scholar
  10. Breed G, Stichter S, Crone EE (2013) Climate-driven changes in northeastern US butterfly communities. Nat Clim Change 3:142–145CrossRefGoogle Scholar
  11. Brown JH, Stevens GC, Kaufman DM (1996) The geographic range: size, shape, boundaries, and internal structure. Annu Rev Ecol Evol Syst 27(1):597–623CrossRefGoogle Scholar
  12. Burton OJ, Phillips BL, Travis JMJ (2010) Trade-offs and the evolution of life-histories during range expansion. Ecol Lett 13(10):1210–1220CrossRefGoogle Scholar
  13. Cwynar LC, Mac Donald GM (1987) Geographical variation of lodgepole pine in relation to population history. Am Nat 129:463–469CrossRefGoogle Scholar
  14. Dai Q, Zhan X, Lu B, Fu J, Wang Q, Qi D (2014) Spatial genetic structure patterns of phenotype-limited and boundary-limited expanding populations: a simulation study. PLoS One 9(1):e85778CrossRefGoogle Scholar
  15. Durrett R, Wai-Tong F (2016) Genealogies in expanding populations. Ann Appl Probab. arXiv:1507.00918v2
  16. Edmonds CA, Lillie AS, Cavalli-Sforza LL (2004) Mutations arising in the wave front of an expanding population. Proc Natl Acad Sci USA 101(4):975–979CrossRefGoogle Scholar
  17. Estoup A, Beaumont M, Sennedot F, Moritz C, Cornuet JM (2004) Genetic analysis of complex demographic scenarios: spatially expanding populations of the cane toad, bufo marinus. Evolution 58(9):2021–2036CrossRefGoogle Scholar
  18. Excoffier L, Ray N (2008) Surfing during population expansions promotes genetic revolutions and structuration. Trends Ecol Evol 23(7):347–351CrossRefGoogle Scholar
  19. Excoffier L, Foll M, Petit RJ (2009) Genetic consequences of range expansions. Annu Rev Ecol Evol Syst 40(1):481–501CrossRefGoogle Scholar
  20. Field CB, Barros VR, Dokken DJ, Mach KJ, Mastrandrea MD, Bilir TE, Chatterjee M, Ebi KL, Estradaa YO, Genova RC, Girma B, Kissel ES, Levy AN, MacCracken S, Mastrandrea PR, White LL (eds) (2014) Climate change 2014: impacts, adaptation, and vulnerability. Part A: global and sectoral aspects. Contribution of working group II to the fifth assessment report of the intergovernmental panel on climate change. Cambridge University Press, CambridgeGoogle Scholar
  21. Garnier J, Giletti T, Hamel F, Roques L (2012) Inside dynamics of pulled and pushed fronts. J Math Pures Appl 11:173–188MathSciNetzbMATHGoogle Scholar
  22. Goodsman D, Cooke B, Coltman DW, Lewis MA (2014) The genetic signature of rapid range expansions: dispersal, growth and invasion speed. Theor Popul Biol 98:1–10CrossRefzbMATHGoogle Scholar
  23. Hallatschek O, Nelson DR (2008) Gene surfing in expanding populations. Theor Popul Biol 73:158–170CrossRefzbMATHGoogle Scholar
  24. Hallatschek O, Hersen P, Ramanathan S, Nelson DR (2007) Genetic drift at expanding frontiers promotes gene segregation. Proc Natl Acad Sci USA 104(50):19,926–19,930CrossRefGoogle Scholar
  25. Henry RC, Bocedi G, Travis JMJ (2013) Eco-evolutionary dynamics of range shifts: elastic margins and critical thresholds. J Theor Biol 321:1–7MathSciNetCrossRefGoogle Scholar
  26. Hewitt GM (2000) The genetic legacy of the quarternary ice ages. Nature 405:907–913CrossRefGoogle Scholar
  27. Hill JK, Thomas CD, Blakeley DS (1999) Evolution of flight morphology in a butterfly that has recently expanded its geographic range. Oecologia 121(2):165–170CrossRefGoogle Scholar
  28. Hill JK, Hughes CL, Dytham C, Searle JB (2006) Genetic diversity in butterflies: interactive effects of habitat fragmentation and climate-driven range expansion. Biol Lett 2(1):152–154CrossRefGoogle Scholar
  29. Klopfstein S, Currat M, Excoffier L (2006) The fate of mutations surfing on the wave of a range expansion. Mol Biol Evol 23(3):482–490CrossRefGoogle Scholar
  30. Kubisch A, Hovestadt T, Poethke HJ (2010) On the elasticity of range limits during periods of expansion. Ecology 91(10):3094–3099CrossRefGoogle Scholar
  31. Leblois R, Estoup A, Streiff R (2006) Genetics of recent habitat contraction and reduction in population size: does isolation by distance matter? Mol Ecol 15(12):3601–3615CrossRefGoogle Scholar
  32. Leinster T, Cobbold C (2012) Measuring diversity: the importance of species similarity. Ecology 93(3):477–489CrossRefGoogle Scholar
  33. McInerny GJ, Dytham C, Travis JMJ (2007) Range shifting on fragmented landscapes. Ecol Inform 2:1–8CrossRefGoogle Scholar
  34. McInerny GJ, Turner JRG, Wong HY, Travis JMJ, Benton TG (2009) How range shifts induced by climate change affect neutral evolution. Proc R Soc B 276(1661):1527–1534CrossRefGoogle Scholar
  35. Nagylaki T (1975) Conditions for the existence of clines. Genetics 80(3):595–615Google Scholar
  36. Nagylaki T (1980a) Geographical invariance and the strong-migration limit in subdivided populations. J Math Biol 41(2):123–142MathSciNetCrossRefzbMATHGoogle Scholar
  37. Nagylaki T (1980b) The strong-migration limit in geographically structured populations. J Math Biol 9(2):101–114MathSciNetCrossRefzbMATHGoogle Scholar
  38. Nei M, Maruyama T, Chakraborty R (1975) The bottleneck effect and genetic variability in populations. Evolution 29(1):1–10CrossRefGoogle Scholar
  39. Neve G, Pavlicko A, Konvicka M (2009) Loss of genetic diversity through spontaneous colonization in the bog fritillary butterfly Proclossiana eunomia (Lepidoptera: Nymphalidae) in the Czech Republic. Eur J Entomol 106(1):11–19CrossRefGoogle Scholar
  40. Nullmeier J, Hallatschek O (2013) The coalescent in boundary-limited range expansions: the coalescent in boundary-limited range expansions. Evolution 67:1307–1320Google Scholar
  41. Parmesan C (1996) Climate and species’ range. Nature 382:765–766CrossRefGoogle Scholar
  42. Parmesan C (2006) Evolutionary and ecological responses to recent climate change. Annu Rev Ecol Evol 37(8):637–669CrossRefGoogle Scholar
  43. Pearson RG, Dawson TP (2003) Predicting the impacts of climate change on the distribution of species: are bioclimate envelope models useful? Glob Ecol Biogeogr 12(5):361–371CrossRefGoogle Scholar
  44. Pease CP, Lande R, Bull JJ (1989) A model of population growth, dispersal and evolution in a changing environment. Ecology 70:1657–1664CrossRefGoogle Scholar
  45. Perkins TA, 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(8):1079–87CrossRefGoogle Scholar
  46. Peterson AT, Ortega-Huerta MA, Bartley J, Sanchez-Cordero V, Soberon J, Buddemeier RH, Stockwell DRB (2002) Future projections for mexican faunas under global climate change scenarios. Nature 416(6881):626–629CrossRefGoogle Scholar
  47. Phillips BL (2012) Range shift promotes the formation of stable range edges. J Biogeogr 39(1):153–161CrossRefGoogle Scholar
  48. Pluess AR (2011) Pursuing glacier retreat: genetic structure of a rapidly expanding larix decidua population. Mol Ecol 20(3):473–485CrossRefGoogle Scholar
  49. Potapov AB, Lewis MA (2004) Climate and competition: the effect of moving range boundaries on habitat invasibility. Bull Math Biol 66(5):975–1008MathSciNetCrossRefzbMATHGoogle Scholar
  50. Root TL, Price JT, Hall KR, Schneider SH, Rosenzweig C, Pounds JA (2003) Fingerprints of global warming on wild animals and plants. Nature 421(6918):57–60CrossRefGoogle Scholar
  51. Roques L, Garnier J, Hamel F, Klein E (2012) Allee effect promotes diversity in traveling waves of colonization. Proc Natl Acad Sci USA 109:8828–8833MathSciNetCrossRefGoogle Scholar
  52. Rousselet J, Zhao R, Argal D, Simonato M, Battisti A, Roques A, Kerdelhué C (2010) The role of topography in structuring the demographic history of the pine processionary moth, Thaumetopoea pityocampa (lepidoptera: Notodontidae). J Biogeogr 37:1478–1490Google Scholar
  53. Samarasekera GDN, Bartell NV, Lindgren BS, Cooke JEK, Davis CS, James PMA, Coltman DW, Mock KE, Murray BW (2012) Spatial genetic structure of the mountain pine beetle (Dendroctonus ponderosae) outbreak in western Canada: historical patterns and contemporary dispersal. Mol Ecol 21:2931–2948CrossRefGoogle Scholar
  54. Schippers P, Verboom J, Vos CC, Jochem R (2011) Metapopulation shift and survival of woodland birds under climate change: will species be able to track? Ecography 34(6):909–919CrossRefGoogle Scholar
  55. Schwartz MW, Iverson LR, Prasad AM, Matthews SN, O’Connor RJ (2006) Predicting extinctions as a result of climate change. Ecology 87(7):1611–1615CrossRefGoogle Scholar
  56. Shannon CE (1948) A mathematical theory of communication. Bell Syst Tech J 27:379–423MathSciNetCrossRefzbMATHGoogle Scholar
  57. Simmons AD, Thomas CD (2004) Changes in dispersal during species’ range expansions. Am Nat 164(3):378–395CrossRefGoogle Scholar
  58. Simpson EH (1949) Measurment of diversity. Nature 163:688CrossRefzbMATHGoogle Scholar
  59. Skellam JG (1951) Random dispersal in theoretical populations. Biometrika 38:196–218MathSciNetCrossRefzbMATHGoogle Scholar
  60. Stokes AN (1976) On two types of moving front in quasilinear diffusion. Math Biosci 31:307–315MathSciNetCrossRefzbMATHGoogle Scholar
  61. Travis JMJ (2003) Climate change and habitat destruction: a deadly anthropogenic cocktail. Proc R Soc B 270:467–473CrossRefGoogle Scholar
  62. Travis JMJ, Mustin K, Benton TG, Dytham C (2009) Accelerating invasion rates result from the evolution of density-dependent dispersal. J Theor Biol 259(1):151–158MathSciNetCrossRefGoogle Scholar
  63. Travis JMJ, Delgado M, Bocedi G, Baguette M, Bartoń K, Bonte D, Boulangeat I, Hodgson JA, Kubisch A, Penteriani V, Saastamoinen M, Stevens VM, Bullock JM (2013) Dispersal and species’ responses to climate change. Oikos 122(11):1532–1540CrossRefGoogle Scholar
  64. Walther GR, Post E, Convey P, Menzel A, Parmesan C, Beebee T, Fromentin JM, Hoegh-Guldberg O, Bairlein F (2002) Ecological responses to recent climate change. Nature 416(6879):389–395CrossRefGoogle Scholar
  65. White TA, Perkins SE, Heckel G, Searle JB (2013) Adaptive evolution during an ongoing range expansion: the invasive bank vole (myodes glareolus) in ireland. Mol Ecol 22(11):2971–2985CrossRefGoogle Scholar
  66. Xin J (2000) Front propagation in heterogeneous media. SIAM Rev 42:161–230MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Society for Mathematical Biology 2016

Authors and Affiliations

  1. 1.LAMACNRS – Université Savoie Mont-BlancChambéryFrance
  2. 2.Department of Mathematical and Statistical Sciences, Centre for Mathematical BiologyUniversity of AlbertaEdmontonCanada
  3. 3.Department of Biological SciencesUniversity of AlbertaEdmontonCanada

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