Population Ecology

, Volume 50, Issue 2, pp 215–225 | Cite as

A population facing climate change: joint influences of Allee effects and environmental boundary geometry

  • Lionel RoquesEmail author
  • Alain Roques
  • Henri Berestycki
  • André Kretzschmar
Original Article


As a result of climate change, many populations have to modify their range to follow the suitable areas—their “climate envelope”—often risking extinction. During this migration process, they may face absolute boundaries to dispersal because of external environmental factors. Consequently, not only the position, but also the shape of the climate envelope can be modified. We use a reaction-diffusion model to analyse the effects on population persistence of simultaneous changes in the position and shape of the climate envelope. When the growth term is of logistic type, we show that extinction and persistence are principally conditioned by the species mobility and the speed of climate change, but not by the shape of the climate envelope. However, with a growth term taking an Allee effect into account, we find a high sensitivity to variations in the shape of the climate envelope. In this case, the species which have a high mobility, although they could more easily follow the migration of the climate envelope, would be at risk of extinction when encountering a local narrowing of the boundary geometry. This effect can be attenuated by a progressive opening at the exit of the narrowing into the available space, even though this leads temporarily to a diminished area of the climate envelope.


Biodiversity Climate envelope Conservation Mobility Reaction-diffusion Single species model 



The authors would like to thank the editor and the anonymous referees for their valuable suggestions and insightful comments. The numerical computations were carried out using Comsol Multiphysics®. This study was supported by the French “Agence Nationale de la Recherche” within the project URTICLIM “Anticipation des effets du changement climatique sur l’impact écologique et sanitaire d’insectes forestiers urticants” and by the European Union within the FP 6 Integrated Project ALARM (Assessing LArge-scale environmental Risks for biodiversity with tested Methods) (GOCE-CT-2003-506675).


  1. Allee WC (1938) The social life of animals. Norton, New YorkGoogle Scholar
  2. Amann H (1976) Supersolution, monotone iteration and stability. J Differ Equ 21:367–377CrossRefGoogle Scholar
  3. Aronson DG, Weinberger HF (1978) Multidimensional nonlinear diffusions arising in population genetics. Adv Math 30:33–76CrossRefGoogle Scholar
  4. Berec L, Angulo E, Courchamp F (2007) Multiple Allee effects and population management. Trends Ecol Evol 22:185–191PubMedCrossRefGoogle Scholar
  5. Berestycki H, Hamel F (2006) Fronts and invasions in general domains. C R Acad Sci Paris Ser I 343:711–716Google Scholar
  6. Berestycki H, Lions P-L (1980) Une méthode locale pour l’éxistence de solutions positives de prolèmes semi-linéaires elliptiques. J Anal Math 38:144–187Google Scholar
  7. Berestycki H, Rossi L (2008) Reaction-diffusion equations for population dynamics with forced speed. I The case of the whole space. Discret Contin Dyn S (in press)Google Scholar
  8. Berestycki H, Hamel F, Roques L (2005) Analysis of the periodically fragmented environment model: I. Species persistence. J Math Biol 51:75–113PubMedCrossRefGoogle Scholar
  9. Cantrell RS, Cosner C (2003) Spatial ecology via reaction-diffusion equations. Series in mathematical and computational biology. Wiley, ChichesterGoogle Scholar
  10. Chapuisat G, Grenier E (2005) Existence and nonexistence of traveling wave solutions for a bistable reaction-diffusion equation in an infinite cylinder whose diameter is suddenly increased. Commun Part Differ Equ 30:1805–1816CrossRefGoogle Scholar
  11. Deasi MN, Nelson DR (2005) A quasispecies on a moving oasis. Theor Popul Biol 67:33–45CrossRefGoogle Scholar
  12. Dennis B (1989) Allee effects: population growth, critical density, and the chance of extinction. Nat Resour Model 3:481–538Google Scholar
  13. Fife PC (1979) Long-time behavior of solutions of bistable non-linear diffusion equations. Arch Ration Mech Anal 70:31–46CrossRefGoogle Scholar
  14. Fisher RA (1937) The wave of advance of advantageous genes. Ann Eugen 7:355–369Google Scholar
  15. Groom MJ (1998) Allee effects limit population viability of an annual plant. Am Nat 151:487–496CrossRefGoogle Scholar
  16. Hilker FM, Lewis MA, Seno H, Langlais M, Malchow H (2005) Pathogens can slow down or reverse invasion fronts of their hosts. Biol Invasions 7:817–832CrossRefGoogle Scholar
  17. Hurford A, Hebblewhite M, Lewis MA (2006) A spatially-explicit model for the Allee effect: why wolves recolonize so slowly in Greater Yellowstone. Theor Popul Biol 70:244–254PubMedCrossRefGoogle Scholar
  18. Intergovernmental Panel on Climate Change (2007) Summary for policymakers. In: Solomon S, Qin D, Manning M, Chen Z, Marquis M, Averyt KB, Tignor M, Miller HL (eds) Climate change 2007: the physical science basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change. Cambridge University Press, Cambridge Google Scholar
  19. Jaeger JAG, Fahrig L (2004) Effects of road fencing on population persistence. Conserv Biol 18:1651–1657CrossRefGoogle Scholar
  20. Keitt TH, Lewis MA, Holt RD (2001) Allee effects, invasion pinning, and species’ borders. Am Nat 157:203–216CrossRefGoogle Scholar
  21. King JR, McCabe PM (2003) On the Fisher-KPP equation with fast nonlinear diffusion. Proc R Soc A Math Phys Eng Sci 459:2529–2546CrossRefGoogle Scholar
  22. Kolmogorov AN, Petrovsky IG, Piskunov NS (1937) Etude de l’équation de la diffusion avec croissance de la quantité de matière et son application à un problème biologique. Bull Univ Etat Moscou Sér Int A1:1–26Google Scholar
  23. Lewis MA, Kareiva P (1993) Allee dynamics and the speed of invading organisms. Theor Popul Biol 43:141–158CrossRefGoogle Scholar
  24. Lutscher F, Lewis MA, McCauley E (2006) Effects of heterogeneity on spread and persistence in rivers. Bull Math Biol 68:2129–2160PubMedCrossRefGoogle Scholar
  25. Matano H, Nakamura K-I, Lou B (2006) Periodic traveling waves in a two-dimensional cylinder with saw-toothed boundary and their homogenization limit. Netw Heterogeneous Media 1:537–568Google Scholar
  26. McCarthy MA (1997) The Allee effect, finding mates and theoretical models. Ecol Model 103:99–102CrossRefGoogle Scholar
  27. Okubo A, Levin SA (2002) Diffusion and ecological problems—modern perspectives, 2nd edn. Springer, HeidelbergGoogle Scholar
  28. Owen MR, Lewis MA (2001) How predation can slow, stop or reverse a prey invasion. Bull Math Biol 63:655–684PubMedCrossRefGoogle Scholar
  29. Pachepsky E, Lutscher F, Nisbet RM, Lewis MA (2005) Persistence, spread and the drift paradox. Theor Popul Biol 67:61–73PubMedCrossRefGoogle Scholar
  30. Parmesan C (2006) Ecological and evolutionary responses to recent climate change. Annu Rev Ecol Evol Syst 37:637–669CrossRefGoogle Scholar
  31. Parmesan C, Yohe G (2003) A globally coherent fingerprint of climate change impacts across natural systems. Nature 421:37–42PubMedCrossRefGoogle Scholar
  32. Potapov A, Lewis MA (2004) Climate and competition: the effect of moving range boundaries on habitat invisibility. Bull Math Biol 66:975–1008PubMedCrossRefGoogle Scholar
  33. Robinet C, Baier P, Pennerstorfer J, Schopf A, Roques A (2007a) Modelling the effects of climate change on the potential feeding activity of Thaumetopoea pityocampa (Den. & Schiff.) (Lep., Notodontidae) in France. Global Ecol Biogeogr 16:460–471CrossRefGoogle Scholar
  34. Robinet C, Liebhold A, Gray D (2007b) Variation in developmental time affects mating success and Allee effects. Oikos 116:1227–1237CrossRefGoogle Scholar
  35. Shi J, Shivaji R (2006) Persistence in diffusion models with weak Allee effect. J Math Biol 52:807–829PubMedCrossRefGoogle Scholar
  36. Shigesada N, Kawasaki K (1997) Biological invasions: theory and practice. (Oxford Series in Ecology and Evolution.) Oxford University Press, OxfordGoogle Scholar
  37. Stephens PA, Sutherland WJ (1999) Consequences of the Allee effect for behaviour, ecology and conservation. Trends Ecol Evol 14:401–405PubMedCrossRefGoogle Scholar
  38. Thomas CD, Cameron A, Green RE, Bakkenes M, Beaumont LJ, Collingham YC, Erasmus BFN, de Siqueira MF, Grainger A, Hannah L, Hughes L, Huntley B, Jaarsveld AS, Midgley GF, Miles L, Ortega-Huerta MA, Peterson AT, Phillips OL, Williams SE (2004) Extinction risk from climate change. Nature 427:145–148PubMedCrossRefGoogle Scholar
  39. Tobin PC, Whitmire SL, Johnson DM, Bjørnstad ON, Liebhold AM (2007) Invasion speed is affected by geographic variation in the strength of Allee effects. Ecol Lett 10:36–43PubMedCrossRefGoogle Scholar
  40. Turchin P (1998) Quantitative analysis of movement: measuring and modeling population redistribution in animals and plants. Sinauer, SunderlandGoogle Scholar
  41. Veit RR, Lewis MA (1996) Dispersal, population growth, and the Allee effect: dynamics of the house finch invasion of eastern North America. Am Nat 148:255–274CrossRefGoogle Scholar
  42. Walther GR, Post E, Convey P, Menzel A, Parmesan C, Beebee TJC, Fromentin J-M, Hoegh-Guldberg O, Bairlein F (2002) Ecological responses to recent climate change. Nature 416:389–395PubMedCrossRefGoogle Scholar

Copyright information

© The Society of Population Ecology and Springer 2008

Authors and Affiliations

  • Lionel Roques
    • 1
    Email author
  • Alain Roques
    • 2
  • Henri Berestycki
    • 3
  • André Kretzschmar
    • 1
  1. 1.Unité Biostatistique et Processus Spatiaux (BioSP)INRAAvignon Cedex 9France
  2. 2.Station de Zoologie ForestièreINRAOlivet CedexFrance
  3. 3.Centre d’Analyse et de Mathématique SocialesEHESSParis Cedex 06France

Personalised recommendations