Spatial sorting as the spatial analogue of natural selection

  • Ben L. PhillipsEmail author
  • T. Alex Perkins


Considerable research effort has been spent to understand why most organisms disperse despite the clear costs of doing so. One aspect of dispersal evolution that has received recent attention is a process known as spatial sorting, which has been referred to as the “shy younger sibling” of natural selection. Spatial sorting is the process, whereby variation in dispersal ability is sorted along density clines and will, in nature, often be a transient phenomenon. Despite this transience, spatial sorting is likely a general mechanism behind the evolution of nonzero dispersal rates in spatiotemporally varying environments. While most often transient, spatial sorting is persistent on invasion fronts, where its effect cannot be ignored, causing rapid evolution of traits related to dispersal. Spatial sorting is captured in several elegant models, yet these models require a high level of mathematical sophistication and are not accessible to most evolutionary biologists or their students. Here, we frame spatial sorting in terms of the classic haploid and diploid models of natural selection. We show that, on an invasion front, spatial sorting can be conceptualised precisely as selection operating through space rather than (as with natural selection) time, and that genotypes can be viewed as having both spatial and temporal aspects of fitness. Viewing fitness in this way shows that, on invasion fronts, organisms maximise spatiotemporal fitness, rather than traditional (temporal) fitness. The resultant model is strikingly similar to classic models of natural selection under gene flow. This similarity renders the model easy to understand (and to teach), but also suggests that many established theoretical results around natural selection could apply equally to spatial sorting.


Dispersal evolution Gene flow Natural selection Population genetics Spatial sorting Travelling wave 



The manuscript was improved by thoughtful comments from Stephan Peischl, Susan Frances Bailey, and Frédéric Guillaume.

Funding information

BLP was supported by the Australian Research Council (DP160101730, FT160100198).


  1. Balkau B J, Feldman M W (1973) Selection for migration modification. Genetics 74:171–174PubMedPubMedCentralGoogle Scholar
  2. Benichou O, Calvez V, Meunier N, Voituriez R (2012) Front acceleration by dynamic selection in Fisher population waves. Phys Rev E 86:041908CrossRefGoogle Scholar
  3. Bouin E, Calvez V (2014) Travelling waves for the cane toads equation with bounded traits. Nonlinearity 27:2233CrossRefGoogle Scholar
  4. Bouin E, Calvez V, Meunier N et al (2012) Invasion fronts with variable motility: phenotype selection, spatial sorting and wave acceleration. C R Math 350:761–766CrossRefGoogle Scholar
  5. Burgess S C, Baskett M L, Grosberg R K et al (2016) When is dispersal for dispersal? Unifying marine and terrestrial perspectives: when is dispersal for dispersal? Biol Rev 91:867–882. CrossRefGoogle Scholar
  6. Burton O J, Travis J M J, Phillips B L (2010) Trade-offs and the evolution of life-histories during range expansion. Ecol Lett 13:1210–1220. CrossRefGoogle Scholar
  7. Case T J, Taper M L (2000) Interspecific competition, environmental gradients, gene flow, and the coevolution of species’ borders. Am Nat 155:583–605CrossRefGoogle Scholar
  8. Crow J F, Kimura M (1970) An introduction to population genetics theory. Burgess Publishing Company, MinneapolisGoogle Scholar
  9. Cwynar L C, MacDonald G M (1987) Geographical variation of lodgepole pine in relation to population history. Am Nat 129:463. CrossRefGoogle Scholar
  10. Deforet M, Carmona-Fontaine C, Korolev K S, Xavier J B (2017) A simple rule for the evolution of fast dispersal at the edge of expanding populations. arXiv:171107955 [q-bio]
  11. Ellner S P, Schreiber S J (2012) Temporally variable dispersal and demography can accelerate the spread of invading species. Theor Popul Biol 82:283–298CrossRefGoogle Scholar
  12. Fisher R A (1937) The wave advance of advantageous genes. Ann Eugen 7:355–369CrossRefGoogle Scholar
  13. Fronhofer E A, Altermatt F (2015) Eco-evolutionary feedbacks during experimental range expansions. Nat Commun 6:6844. CrossRefGoogle Scholar
  14. Gandon S (1999) Kin competition, the cost of inbreeding and the evolution of dispersal. J Theor Biol 200:345–364. CrossRefGoogle Scholar
  15. Haldane J B S (1924) A mathematical theory of natural and artificial selection—I. Trans Camb Philos Soc 23:19–41Google Scholar
  16. Hamilton W D, May R M (1977) Dispersal in stable habitats. Nature 269:578–581CrossRefGoogle Scholar
  17. Hartl D L, Clark AG, Clark AG (1997) Principles of population genetics. Sinauer Associates, SunderlandGoogle Scholar
  18. Hastings A (1983) Can spatial variation alone lead to selection for dispersal? Theor Popul Biol 24:244–251CrossRefGoogle Scholar
  19. Holt R (1985) Population dynamics in two-patch environments: some anomalous consequences of an optimal habitat distribution. Theor Popul Biol 28:181–208. CrossRefGoogle Scholar
  20. Hughes C L, Dytham C, Hill J K (2003) Evolutionary trade-offs between reproduction and dispersal in populations at expanding range boundaries. Proc R Soc Biol Sci Ser B 270:S147–S150CrossRefGoogle Scholar
  21. Johnson M L, Gaines M S (1990) Evolution of dispersal: theoretical models and empirical tests using birds and mammals. Annu Rev Ecol Syst 21:449–480CrossRefGoogle Scholar
  22. Krug P J, Zimmer R K (2004) Developmental dimorphism: consequences for larval behavior and dispersal potential in a marine gastropod. Biol Bull 207:233–246. CrossRefGoogle Scholar
  23. Lenormand T (2002) Gene flow and the limits to natural selection. Trends Ecol Evol 17:183–189CrossRefGoogle Scholar
  24. Levin S A, Cohen D, Hastings A (1984) Dispersal strategies in patchy environments. Theor Popul Biol 26:165–191. CrossRefGoogle Scholar
  25. 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 27:508–517CrossRefGoogle Scholar
  26. McPeek MA, Holt RD (1992) The evolution of dispersal in spatially and temporally varying environments. Am Nat 140:1010–1027CrossRefGoogle Scholar
  27. Moody M E (1988) The evolution of migration in subdivided populations. I. Haploids. J Theor Biol 131:1–14. CrossRefGoogle Scholar
  28. Nagylaki T (1992) Introduction to theoretical population genetics. Springer, BerlinCrossRefGoogle Scholar
  29. Ochocki B M, Miller T E X (2017) Rapid evolution of dispersal ability makes biological invasions faster and more variable. Nat Commun 8:ncomms14315. CrossRefGoogle Scholar
  30. Olivieri I, Michalakis Y, Gouyon P-H (1995) Metapopulation genetics and the evolution of dispersal. Am Nat 146:202–228CrossRefGoogle Scholar
  31. Otto S P, Day T (2007) A biologist’s guide to mathematical modeling in ecology and evolution. Princeton University Press, PrincetonGoogle Scholar
  32. Peischl S, Gilbert KJ (2018) Evolution of dispersal can rescue populations from expansion load. bioRxiv.
  33. 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
  34. Peischl S, Kirkpatrick M, Excoffier L (2015) Expansion load and the evolutionary dynamics of a species range. American Naturalist, in pressGoogle Scholar
  35. Perkins T A, Phillips B L, Baskett M L, 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
  36. Perkins S E, Boettiger C, Phillips B L (2016) After the games are over: life-history trade-offs drive dispersal attenuation following range expansion. Ecol Evol 6:6425–6434. CrossRefGoogle Scholar
  37. Phillips B L (2015) Evolutionary processes make invasion speed difficult to predict. Biol Invasions 17:1949–1960. CrossRefGoogle Scholar
  38. Phillips B L, Brown G P, Travis J M J, Shine R (2008) Reid’s paradox revisited: the evolution of dispersal in range-shifting populations. Am Nat 172:S34–S48CrossRefGoogle Scholar
  39. Phillips B L, Brown G P, Shine R (2010) Evolutionarily accelerated invasions: the rate of dispersal evolves upwards during range advance of cane toads. J Evol Biol 23:2595–2601. CrossRefGoogle Scholar
  40. 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. CrossRefGoogle Scholar
  41. Shine R, Brown G P, Phillips B L (2011) An evolutionary process that assembles phenotypes through space rather than through time. Proc Natl Acad Sci 108:5708–5711. CrossRefGoogle Scholar
  42. Simmons A D, Thomas C D (2004) Changes in dispersal during species’ range expansions. Am Nat 164:378–395PubMedGoogle Scholar
  43. Skellam J G (1951) Random dispersal in theoretical populations. Biometrika 38:196–218CrossRefGoogle Scholar
  44. Slatkin M, Excoffier L (2012) Serial founder effects during range expansion: a spatial analog of genetic drift. Genetics 191:171–181. CrossRefGoogle Scholar
  45. Travis J M J, Dytham C (2002) Dispersal evolution during invasions. Evol Ecol Res 4:1119–1129Google Scholar
  46. van Ditmarsch D, Boyle K E, Sakhtah H et al (2013) Convergent evolution of hyperswarming leads to impaired biofilm formation in pathogenic bacteria. Cell Rep 4:697–708CrossRefGoogle Scholar
  47. Van Valen L (1971) Group selection and the evolution of dispersal. Evolution 25:591–598CrossRefGoogle Scholar
  48. Weiss-Lehman C, Hufbauer R A, Melbourne B A (2017) Rapid trait evolution drives increased speed and variance in experimental range expansions. Nat Commun 8:ncomms14303. CrossRefGoogle Scholar
  49. Wright S (1931) Evolution in Mendelian populations. Genetics 16:97–159PubMedPubMedCentralGoogle Scholar
  50. Wright S (1940) Breeding structure of populations in relation to speciation. Am Nat 74:232–248. CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.School of BioSciencesUniversity of MelbourneParkvilleAustralia
  2. 2.Department of Biological Sciences and Eck Institute for Global HealthUniversity of Notre DameNotre DameUSA

Personalised recommendations