Biological Invasions

, Volume 12, Issue 1, pp 219–231 | Cite as

Modelling invasibility in endogenously oscillating tree populations: timing of invasion matters

Original Paper


The timing of introduction of a new species into an ecosystem can be critical in determining the invasibility (i.e. the sensitivity to invasion) of a resident population. Here, we use an individual-based model to test how (1) the type of competition (symmetric versus asymmetric) and (2) seed masting influence the success of invasion by producing oscillatory dynamics in resident tree populations. We focus on a case where two species (one resident, one invader introduced at low density) do not differ in terms of competitive abilities. By varying the time of introduction of the invader, we show that oscillations in the resident population favour invasion, by creating “invasibility windows” during which resource is available for the invader due to transiently depressed resident population density. We discuss this result in the context of current knowledge on forest dynamics and invasions, emphasizing the importance of variability in population dynamics.


Forest model Invasion criteria Species coexistence Oscillations Exploitation competition Stochasticity Individual-based model 



This study was funded by the Natural Sciences and Engineering Research Council of Canada (Madhur Anand and Chris Bauch), Canadian Foundation for Innovation, Ontario Ministry for Research and Innovation, Inter-American Institute for Global Change Research and the Canada Research Chairs Program (Madhur Anand). We also acknowledge two anonymous reviewers for their insightful comments on the manuscript.


  1. Adler FR, Mosquera J (2000) Is space necessary? Interference competition and limits to biodiversity. Ecology 81:3226–3232Google Scholar
  2. Barlow ND, Kean JM (2004) Resource abundance and invasiveness: a simple model. Biol Invasions 6:261–268. doi: 10.1023/B:BINV.0000034590.77961.6e CrossRefGoogle Scholar
  3. Bauer S, Wyszomirski T, Berger U, Hildenbrandt H, Grimm V (2004) Asymmetric competition as a natural outcome of neighbour interactions among plants: results from the field-of-neighbourhood modelling approach. Plant Ecol 170:135–145CrossRefGoogle Scholar
  4. Berntson GM, Wayne PM (2000) Characterizing the size dependence of resource acquisition within crowded plant populations. Ecology 81:1072–1085Google Scholar
  5. Bolker BM, Pacala SW (1999) Spatial moment equations for plant competition: understanding spatial strategies and the advantages of short dispersal. Am Nat 153:575–602. doi: 10.1086/303199 CrossRefGoogle Scholar
  6. Bolker BM, Pacala SW, Neuhauser C (2003) Spatial dynamics in model plant communities: what do we really know? Am Nat 162:135–148. doi: 10.1086/376575 CrossRefPubMedGoogle Scholar
  7. Boulant N, Kunstler G, Rambal S, Lepart J (2008) Seed supply, drought, and grazing determine spatio-temporal patterns of recruitment for native and introduced invasive pines in grasslands. Divers Distrib 14:862–874. doi: 10.1111/j.1472-4642.2008.00494.x CrossRefGoogle Scholar
  8. Bousquet F, Bakam I, Proton H, Le Page C (1998) Cormas: common-pool resources and multi-agent systems. Lect Notes Artif Intell 1416:826–838Google Scholar
  9. Caplat P, Anand M, Bauch C (2008) Symmetric competition causes population oscillations in an individual-based model of forest dynamics. Ecol Model 211:491–500. doi: 10.1016/j.ecolmodel.2007.10.002 CrossRefGoogle Scholar
  10. Charret IC, Louzada JNC, Costa AT (2007) Individual-based model for coevolving competing populations. Phys Stat Mech Appl 385:249–254CrossRefGoogle Scholar
  11. Chesson P (2000) General theory of competitive coexistence in spatially-varying environments. Theor Popul Biol 58:211–237. doi: 10.1006/tpbi.2000.1486 CrossRefPubMedGoogle Scholar
  12. Cosner C, Lazer AC (1984) Stable coexistence states in the Volterra–Lotka competition model with diffusion. SIAM J Appl Math 44:1112–1132. doi: 10.1137/0144080 CrossRefGoogle Scholar
  13. Davis MA, Grime JP, Thompson K (2000) Fluctuating resources in plant communities: a general theory of invasibility. J Ecol 88:528–534. doi: 10.1046/j.1365-2745.2000.00473.x CrossRefGoogle Scholar
  14. Debain S, Chadoeuf J, Curt T, Kunstler G, Lepart J (2007) Comparing effective dispersal in expanding population of Pinus sylvestris and Pinus nigra in calcareous grassland. Can J For Res 37:103–115. doi: 10.1139/X06-265 CrossRefGoogle Scholar
  15. Drake JM, Drury KLS, Lodge DM, Blukacz A, Yan ND, Dwyer G (2006) Demographic stochasticity, environmental variability, and windows of invasion risk for Bythotrephes longimanus in North America. Biol Invasions 8:843–861. doi: 10.1007/s10530-005-4205-2 CrossRefGoogle Scholar
  16. Durrett R, Levin S (1998) Spatial aspects of interspecific competition. Theor Popul Biol 53:30–43. doi: 10.1006/tpbi.1997.1338 CrossRefPubMedGoogle Scholar
  17. Eppstein MJ, Molofsky J (2007) Invasiveness in plant communities with feedbacks. Ecol Lett 10:253–263. doi: 10.1111/j.1461-0248.2007.01017.x CrossRefPubMedGoogle Scholar
  18. Frey BR, Ashton MS, McKenna JJ, Ellum D, Finkral A (2007) Topographic and temporal patterns in tree seedling establishment, growth, and survival among masting species of southern New England mixed-deciduous forests. For Ecol Manag 245:54–63. doi: 10.1016/j.foreco.2007.03.069 CrossRefGoogle Scholar
  19. Geritz SAH, Kisdi E, Meszena G, Metz JAJ (1998) Evolutionarily singular strategies and the adaptive growth and branching of the evolutionary tree. Evol Ecol 12:35–57. doi: 10.1023/A:1006554906681 CrossRefGoogle Scholar
  20. Greenman JV, Benton TG, Boots M, White AR (2005) The evolution of oscillatory behavior in age-structured species. Am Nat 166:68–78. doi: 10.1086/430640 CrossRefPubMedGoogle Scholar
  21. Grime JP (1977) Evidence for the existence of three primary strategies in plants and its relevance to ecological and evolutionary theory. Am Nat 111:1169–1194. doi: 10.1086/283244 CrossRefGoogle Scholar
  22. Grimm V, Wissel C (2004) The intrinsic mean time to extinction: a unifying approach to analysing persistence and viability of populations. Oikos 105:501–511. doi: 10.1111/j.0030-1299.2004.12606.x CrossRefGoogle Scholar
  23. Higgins SI, Richardson DM (1996) A review of models of alien plant spread. Ecol Model 87:249–265. doi: 10.1016/0304-3800(95)00022-4 CrossRefGoogle Scholar
  24. Higgins SI, Pickett STA, Bond WJ (2000) Predicting extinction risks for plants: environmental stochasticity can save declining populations. Trends Ecol Evol 15:516–520. doi: 10.1016/S0169-5347(00)01993-5 CrossRefPubMedGoogle Scholar
  25. Higgins SI, Cain ML (2002) Spatially realistic plant metapopulation models and the colonization-competition trade-off. J Ecol 90:616–626CrossRefGoogle Scholar
  26. Hurtt GC, Pacala SW (1995) The consequences of recruitment limitation—reconciling chance, history and competitive differences between plants. J Theor Biol 176:1–12. doi: 10.1006/jtbi.1995.0170 CrossRefGoogle Scholar
  27. Keane RE, Austin M, Field C, Huth A, Lexer MJ, Peters D, Solomon A, Wyckoff P (2001) Tree mortality in gap models: application to climate change. Clim Change 51:509–540. doi: 10.1023/A:1012539409854 CrossRefGoogle Scholar
  28. Keeley JE, Bond WJ (1999) Mast flowering and semelparity in bamboos: the bamboo fire cycle hypothesis. Am Nat 154:383–391. doi: 10.1086/303243 CrossRefPubMedGoogle Scholar
  29. Kinezaki N, Kawasaki K, Shigesada N (2006) Spatial dynamics of invasion in sinusoidally varying environments. Popul Ecol 48:263–270. doi: 10.1007/s10144-006-0263-2 CrossRefGoogle Scholar
  30. Kobe RK, Pacala SW, Silander JA, Canham CD (1995) Juvenile tree survivorship as a component of shade tolerance. Ecol Appl 5:517–532. doi: 10.2307/1942040 CrossRefGoogle Scholar
  31. Küster EC, Kuhn I, Bruelheide H, Klotz S (2008) Trait interactions help explain plant invasion success in the German flora. J Ecol 96:860–868. doi: 10.1111/j.1365-2745.2008.01406.x CrossRefGoogle Scholar
  32. Laird RA, Schamp BS (2006) Competitive intransitivity promotes species coexistence. Am Nat 168:182–193. doi: 10.1086/506259 CrossRefPubMedGoogle Scholar
  33. Lamontagne JM, Boutin S (2007) Local-scale synchrony and variability in mast seed production patterns of Picea glauca. J Ecol 95:991–1000. doi: 10.1111/j.1365-2745.2007.01266.x CrossRefGoogle Scholar
  34. Lonsdale WM (1999) Global patterns of plant invasions and the concept of invasibility. Ecology 80:1522–1536CrossRefGoogle Scholar
  35. Mack RN, Simberloff D, Lonsdale WM, Evans H, Clout M, Bazzaz FA (2000) Biotic invasions: causes, epidemiology, global consequences, and control. Ecol Appl 10:689–710. doi: 10.1890/1051-0761(2000)010[0689:BICEGC]2.0.CO;2 CrossRefGoogle Scholar
  36. Maunder M (1992) Plant reintroduction—an overview. Biodivers Conserv 1:51–61. doi: 10.1007/BF00700250 CrossRefGoogle Scholar
  37. Moravie MA, Robert A (2003) A model to assess relationships between forest dynamics and spatial structure. J Veg Sci 14:823–834. doi: 10.1658/1100-9233(2003)014[0823:AMTARB]2.0.CO;2 CrossRefGoogle Scholar
  38. Muko S, Iwasa Y (2008) Spatial heterogeneity of mortality and temporal fluctuation in fertility promote coexistence but not vice versa: a random-community approach. J Theor Biol 253:593–600. doi: 10.1016/j.jtbi.2008.04.008 CrossRefPubMedGoogle Scholar
  39. Myster RW (1993) Tree invasion and establishment in old fields at Hutcheson-memorial-forest. Bot Rev 59:251–272. doi: 10.1007/BF02857418 CrossRefGoogle Scholar
  40. Namba T, Takahashi S (1993) Competitive coexistence in a seasonally fluctuating environment II. Multiple stable states and invasion success. Theor Popul Biol 44:374–402. doi: 10.1006/tpbi.1993.1033 CrossRefGoogle Scholar
  41. Pacala SW, Tilman D (1994) Limiting similarity in mechanistic and spatial models of plant competition in heterogeneous environments. Am Nat 143:222–257. doi: 10.1086/285602 CrossRefGoogle Scholar
  42. Pacala SW, Weiner J (1991) Effects of competitive asymmetry on a local density model of plant interference. J Theor Biol 149:165–179. doi: 10.1016/S0022-5193(05)80275-9 CrossRefPubMedGoogle Scholar
  43. Pacala SW, Canham CD, Saponara J, Silander JA, Kobe RK, Ribbens E (1996) Forest models defined by field measurements: estimation, error analysis and dynamics. Ecol Monogr 66:1–43. doi: 10.2307/2963479 CrossRefGoogle Scholar
  44. Pham AT, De Grandpré L, Gauthier S, Bergeron Y (2005) Gap dynamics and replacement patterns in gaps of the northeastern boreal forest of Quebec. Can J For Res 34:353–364. doi: 10.1139/x03-265 CrossRefGoogle Scholar
  45. Rademacher C, Neuert C, Grundmann V, Wissel C, Grimm V (2004) Reconstructing spatiotemporal dynamics of Central European natural beech forests: the rule-based forest model BEFORE. For Ecol Manag 194:349–368. doi: 10.1016/j.foreco.2004.02.022 CrossRefGoogle Scholar
  46. Reinhart KO, Maestre FT, Callaway RG (2006) Facilitation and inhibition of seedlings of an invasive tree (Acer platanoides) by different tree species in a mountain ecosystem. Biol Inv 8:231–240. doi: 10.1007/s10530-004-5163-9 Google Scholar
  47. Richardson DM, Pysek P (2006) Plant invasions: merging the concepts of species invasiveness and community invasibility. Prog Phys Geogr 30:409–431. doi: 10.1191/0309133306pp490pr CrossRefGoogle Scholar
  48. Sakai AK, Allendorf FW, Holt JS, Lodge DM, Molofsky J, With KA, Baughman S, Cabin RJ, Cohen JE, Ellstrand NC, McCauley DE, O’Neil P, Parker IM, Thompson JN, Weller SG (2001) The population biology of invasive species. Annu Rev Ecol Syst 32:305–332. doi: 10.1146/annurev.ecolsys.32.081501.114037 CrossRefGoogle Scholar
  49. Sax DF, Stachowicz JJ, Brown JH, Bruno JF, Dawson MN, Gaines SD, Grosberg RK, Hasting SA, Holt RD, Mayfield MM, O’Connor MI, Rice WR (2007) Ecological and evolutionary insights from species invasions. Trends Ecol Evol 22:465–471. doi: 10.1016/j.tree.2007.06.009 CrossRefPubMedGoogle Scholar
  50. Schnurr JL, Ostfeld RS, Canham CD (2002) Direct and indirect effects of masting on rodent populations and tree seed survival. Oikos 96:402–410. doi: 10.1034/j.1600-0706.2002.960302.x CrossRefGoogle Scholar
  51. Schoolmaster DRJ, Snyder RE (2007) Invasibility in a spatiotemporally fluctuating environment is determined by the periodicity of fluctuations and resident turnover rates. Proc R Soc Lond B Biol Sci 274:1429–1435. doi: 10.1098/rspb.2007.0118 CrossRefGoogle Scholar
  52. Snyder RE, Chesson P (2003) Local dispersal can facilitate coexistence in the presence of permanent spatial heterogeneity. Ecol Lett 6:301–309. doi: 10.1046/j.1461-0248.2003.00434.x CrossRefGoogle Scholar
  53. Takenaka A (2006) Dynamics of seedling populations and tree species coexistence in a forest: a simulation study. Ecol Res 21:356–363. doi: 10.1007/s11284-006-0165-y CrossRefGoogle Scholar
  54. Tilman D (1994) Competition and biodiversity in spatially structured habitats. Ecology 75:2–16. doi: 10.2307/1939377 CrossRefGoogle Scholar
  55. Vandermeer J (2006) Oscillating populations and biodiversity maintenance. Bioscience 56:967–975. doi: 10.1641/0006-3568(2006)56[967:OPABM]2.0.CO;2 CrossRefGoogle Scholar
  56. Veltman CJ, Nee S, Crawley MJ (1996) Correlates of introduction success in exotic New Zealand birds. Am Nat 147:542–557. doi: 10.1086/285865 CrossRefGoogle Scholar
  57. Weiner J (1990) Asymmetric competition in plant-populations. Trends Ecol Evol 5:360–364. doi: 10.1016/0169-5347(90)90095-U CrossRefGoogle Scholar
  58. Zeide B (2004) Intrinsic units in growth modelling. Ecol Model 175:249–259. doi: 10.1016/j.ecolmodel.2003.10.017 CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Department of Environmental BiologyUniversity of GuelphGuelphCanada
  2. 2.Department of Mathematics and StatisticsUniversity of GuelphGuelphCanada

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