When higher carrying capacities lead to faster propagation

10.24072/pcjournal.66 - Peer Community Journal, Volume 1 (2021), article no. e57.

Get full text PDF Peer reviewed and recommended by PCI

Finding general patterns in the expansion of natural populations is a major challenge in ecology and invasion biology. Classical spatio-temporal models predict that the carrying capacity (K) of the environment should have no influence on the speed (v) of an expanding population. We tested the generality of this statement with reaction-diffusion equations, stochastic individual-based models, and microcosms experiments with Trichogramma chilonis wasps. We investigated the dependence between K and v under different assumptions: null model (Fisher-KPP-like assumptions), strong Allee effects, and positive density-dependent dispersal. These approaches led to similar and complementary results. Strong Allee effects, positive density-dependent dispersal and demographic stochasticity in small populations lead to a positive dependence between K and v. A positive correlation between carrying capacity and propagation speed might be more frequent than previously expected, and be the rule when individuals at the edge of a population range are not able to fully drive the expansion.

Published online:
DOI: 10.24072/pcjournal.66
Haond, Marjorie 1; Morel-Journel, Thibaut 2; Lombaert, Eric 1; Vercken, Elodie 1; Mailleret, Ludovic 3, 1; Roques, Lionel 4

1 ISA, Université Côte d'Azur - INRAE - CNRS, 06903 Sophia-Antipolis, France
2 Earth and Life Institute, Biodiversity Research Centre, Université Catholique de Louvain, Louvain-la-Neuve, Belgium
3 Biocore, INRIA, 06902 Sophia Antipolis, France
4 BioSP, INRA, 84000 Avignon, France
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
     author = {Haond, Marjorie and Morel-Journel, Thibaut and Lombaert, Eric and Vercken, Elodie and Mailleret, Ludovic and Roques, Lionel},
     title = {When higher carrying capacities lead to faster propagation},
     journal = {Peer Community Journal},
     eid = {e57},
     publisher = {Peer Community In},
     volume = {1},
     year = {2021},
     doi = {10.24072/pcjournal.66},
     url = {}
AU  - Haond, Marjorie
AU  - Morel-Journel, Thibaut
AU  - Lombaert, Eric
AU  - Vercken, Elodie
AU  - Mailleret, Ludovic
AU  - Roques, Lionel
TI  - When higher carrying capacities lead to faster propagation
JO  - Peer Community Journal
PY  - 2021
DA  - 2021///
VL  - 1
PB  - Peer Community In
UR  -
UR  -
DO  - 10.24072/pcjournal.66
ID  - 10_24072_pcjournal_66
ER  - 
%0 Journal Article
%A Haond, Marjorie
%A Morel-Journel, Thibaut
%A Lombaert, Eric
%A Vercken, Elodie
%A Mailleret, Ludovic
%A Roques, Lionel
%T When higher carrying capacities lead to faster propagation
%J Peer Community Journal
%D 2021
%V 1
%I Peer Community In
%R 10.24072/pcjournal.66
%F 10_24072_pcjournal_66
Haond, Marjorie; Morel-Journel, Thibaut; Lombaert, Eric; Vercken, Elodie; Mailleret, Ludovic; Roques, Lionel. When higher carrying capacities lead to faster propagation. Peer Community Journal, Volume 1 (2021), article  no. e57. doi : 10.24072/pcjournal.66.

Peer reviewed and recommended by PCI : 10.24072/pci.ecology.100004

Conflict of interest of the recommender and peer reviewers:
The recommender in charge of the evaluation of the article and the reviewers declared that they have no conflict of interest (as defined in the code of conduct of PCI) with the authors or with the content of the article.

[1] Altwegg, R.; Collingham, Y. C.; Erni, B.; Huntley, B. Density-dependent dispersal and the speed of range expansions, Diversity and Distributions, Volume 19 (2013) no. 1, pp. 60-68 | DOI

[2] Armstrong, D.; Seddon, P. Directions in reintroduction biology, Trends in Ecology & Evolution, Volume 23 (2008) no. 1, pp. 20-25 | DOI

[3] Aronson, D. G.; Weinberger, H. F. Nonlinear diffusion in population genetics, combustion, and nerve pulse propagation, Lecture Notes in Mathematics, Springer Berlin Heidelberg, Berlin, Heidelberg, 1975, pp. 5-49 | DOI

[4] Austerlitz, F.; Mariette, S.; Machon, N.; Gouyon, P.-H.; Godelle, B. Effects of Colonization Processes on Genetic Diversity: Differences Between Annual Plants and Tree Species, Genetics, Volume 154 (2000) no. 3, pp. 1309-1321 | DOI

[5] Barton, N. H.; Turelli, M. Spatial Waves of Advance with Bistable Dynamics: Cytoplasmic and Genetic Analogues of Allee Effects, The American Naturalist, Volume 178 (2011) no. 3 | DOI

[6] Belovsky, G. E.; Mellison, C.; Larson, C.; Van Zandt, P. A. Experimental Studies of Extinction Dynamics, Science, Volume 286 (1999) no. 5442, pp. 1175-1177 | DOI

[7] Blackburn, T. M.; Pyšek, P.; Bacher, S.; Carlton, J. T.; Duncan, R. P.; Jarošík, V.; Wilson, J. R.; Richardson, D. M. A proposed unified framework for biological invasions, Trends in Ecology & Evolution, Volume 26 (2011) no. 7, pp. 333-339 | DOI

[8] Bolker, B. M.; Brooks, M. E.; Clark, C. J.; Geange, S. W.; Poulsen, J. R.; Stevens, M. H. H.; White, J.-S. S. Generalized linear mixed models: a practical guide for ecology and evolution, Trends in Ecology & Evolution, Volume 24 (2009) no. 3, pp. 127-135 | DOI

[9] Brunet, E.; Derrida, B. Shift in the velocity of a front due to a cutoff, Physical Review E, Volume 56 (1997) no. 3, pp. 2597-2604 | DOI

[10] Carter, I.; Cross, A.; Douse, A.; Duffy, K.; Etheridge, B.; Grice, P.; Newbery, P.; Orr-Ewing, D.; O’Toole, L.; Simpson, D.; et al. Re-introduction and conservation of the red kite milvus milvus in britain: current threats and prospects for future range expansion In: Birds of Prey in a Changing Environment (2003)

[11] Courchamp, F.; Berec, L.; Gascoigne, J. Allee effects in ecology and conservation, Oxford University Press, Oxford, 2008

[12] Crooks, J. A. Characterizing ecosystem-level consequences of biological invasions: the role of ecosystem engineers, Oikos, Volume 97 (2002) no. 2, pp. 153-166 | DOI

[13] Davis, H. G.; Taylor, C. M.; Civille, J. C.; Strong, D. R. An Allee effect at the front of a plant invasion: Spartina in a Pacific estuary, Journal of Ecology, Volume 92 (2004) no. 2, pp. 321-327 | DOI

[14] Drake, J. M.; Lodge, D. M. Allee Effects, Propagule Pressure and the Probability of Establishment: Risk Analysis for Biological Invasions, Biological Invasions, Volume 8 (2006) no. 2, pp. 365-375 | DOI

[15] Fife, P. C.; McLeod, J. B. The approach of solutions of nonlinear diffusion equations to travelling front solutions, Archive for Rational Mechanics and Analysis, Volume 65 (1977) no. 4, pp. 335-361 | DOI

[16] Gabriel, W.; Bürger, R. Survival of small populations under demographic stochasticity, Theoretical Population Biology, Volume 41 (1992) no. 1, pp. 44-71 | DOI

[17] Gandhi, S. R.; Yurtsev, E. A.; Korolev, K. S.; Gore, J. Range expansions transition from pulled to pushed waves as growth becomes more cooperative in an experimental microbial population, Proceedings of the National Academy of Sciences, Volume 113 (2016) no. 25, pp. 6922-6927 | DOI

[18] Garnier, J.; Lewis, M. A. Expansion Under Climate Change: The Genetic Consequences, Bulletin of Mathematical Biology, Volume 78 (2016) no. 11, pp. 2165-2185 | DOI

[19] Gidoin, C.; Roques, L.; Boivin, T. Linking niche theory to ecological impacts of successful invaders: insights from resource fluctuation-specialist herbivore interactions, Journal of Animal Ecology, Volume 84 (2015) no. 2, pp. 396-406 | DOI

[20] Gilad, E.; von Hardenberg, J.; Provenzale, A.; Shachak, M.; Meron, E. A mathematical model of plants as ecosystem engineers, Journal of Theoretical Biology, Volume 244 (2007) no. 4, pp. 680-691 | DOI

[21] Giometto, A.; Rinaldo, A.; Carrara, F.; Altermatt, F. Emerging predictable features of replicated biological invasion fronts, Proceedings of the National Academy of Sciences, Volume 111 (2014) no. 1, pp. 297-301 | DOI

[22] Griffen, B. D.; Drake, J. M. Effects of habitat quality and size on extinction in experimental populations, Proceedings of the Royal Society B: Biological Sciences, Volume 275 (2008) no. 1648, pp. 2251-2256 | DOI

[23] Hadeler, K. P.; Rothe, F. Travelling fronts in nonlinear diffusion equations, Journal Of Mathematical Biology, Volume 2 (1975) no. 3, pp. 251-263 | DOI

[24] Hastings, A.; Cuddington, K.; Davies, K. F.; Dugaw, C. J.; Elmendorf, S.; Freestone, A.; Harrison, S.; Holland, M.; Lambrinos, J.; Malvadkar, U.; Melbourne, B. A.; Moore, K.; Taylor, C.; Thomson, D. The spatial spread of invasions: new developments in theory and evidence, Ecology Letters, Volume 8 (2005) no. 1, pp. 91-101 | DOI

[25] Hayward, M. W.; Somers, M. Reintroduction of Top-Order Predators, Wiley-Blackwell, Oxford, UK, 2009 | DOI

[26] Holmes, E. E. Are Diffusion Models too Simple? A Comparison with Telegraph Models of Invasion, The American Naturalist, Volume 142 (1993) no. 5, pp. 779-795 | DOI

[27] Hornocker, M.; Negri, S.; Rabinowitz, A. Cougar, University of Chicago Press, 2009 | DOI

[28] Hui, C.; Krug, R. M.; Richardson, D. M. Modelling spread in invasion ecology: a synthesis In: Fifty Years of Invasion Ecology (2011), pp. 329-343

[29] Hulme, P. E. Trade, transport and trouble: managing invasive species pathways in an era of globalization, Journal of Applied Ecology, Volume 46 (2009) no. 1, pp. 10-18 | DOI

[30] Hurford, A.; Hebblewhite, M.; Lewis, M. A. A spatially explicit model for an Allee effect: Why wolves recolonize so slowly in Greater Yellowstone, Theoretical Population Biology, Volume 70 (2006) no. 3, pp. 244-254 | DOI

[31] Kanarek, A. R.; Lamberson, R. H.; Black, J. M. An individual-based model for traditional foraging behavior: investigating effects of environmental fluctuation, Natural Resource Modeling, Volume 21 (2008) no. 1, pp. 93-116 | DOI

[32] Keitt, T. H.; Lewis, M. A.; Holt, R. D. Allee Effects, Invasion Pinning, and Species’ Borders, The American Naturalist, Volume 157 (2001) no. 2, pp. 203-216 | DOI

[33] Keller, R. P.; Geist, J.; Jeschke, J. M.; Kühn, I. Invasive species in Europe: ecology, status, and policy, Environmental Sciences Europe, Volume 23 (2011) no. 1 | DOI

[34] van Kleunen, M.; Schlaepfer, D. R.; Glaettli, M.; Fischer, M. Preadapted for invasiveness: do species traits or their plastic response to shading differ between invasive and non-invasive plant species in their native range?, Journal of Biogeography, Volume 38 (2011) no. 7, pp. 1294-1304 | DOI

[35] Kramer-Schadt, S.; Revilla, E.; Wiegand, T. Lynx reintroductions in fragmented landscapes of Germany: Projects with a future or misunderstood wildlife conservation?, Biological Conservation, Volume 125 (2005) no. 2, pp. 169-182 | DOI

[36] Lande, R. Risks of Population Extinction from Demographic and Environmental Stochasticity and Random Catastrophes, The American Naturalist, Volume 142 (1993) no. 6, pp. 911-927 | DOI

[37] Lewis, M.; Kareiva, P. Allee Dynamics and the Spread of Invading Organisms, Theoretical Population Biology, Volume 43 (1993) no. 2, pp. 141-158 | DOI

[38] Liebhold, A. M.; Halverson, J. A.; Elmes, G. A. Gypsy Moth Invasion in North America: A Quantitative Analysis, Journal of Biogeography, Volume 19 (1992) no. 5 | DOI

[39] Mackrill, T. Migratory behaviour and ecology of a trans-saharan migrant raptor, the osprey Pandion haliaetus. Ph. D. thesis, Department of Neuroscience, Psychology and Behaviour. (2017)

[40] Mackrill, T.; Appleton, T.; McIntyre, H.; Wright, J. The Rutland Water Ospreys, A & C Black Publishers, 2013

[41] Matthysen, E. Density-dependent dispersal in birds and mammals, Ecography, Volume 28 (2005) no. 3, pp. 403-416 | DOI

[42] Moravcova, L.; Pyšek, P.; Jarošík, V.; Havlíčková, V.; Zákravskỳ, P.; et al. Reproductive characteristics of neophytes in the Czech Republic: traits of invasive and non-invasive species, Preslia, Volume 82 (2010)

[43] Morel-Journel, T.; Girod, P.; Mailleret, L.; Auguste, A.; Blin, A.; Vercken, E. The highs and lows of dispersal: how connectivity and initial population size jointly shape establishment dynamics in discrete landscapes, Oikos, Volume 125 (2016) no. 6, pp. 769-777 | DOI

[44] Morel-Journel, T.; Hautier, M.; Vercken, E.; Mailleret, L. Clustered or scattered? The impact of habitat quality clustering on establishment and early spread, Ecography, Volume 41 (2018) no. 10, pp. 1675-1683 | DOI

[45] Mortelliti, A.; Amori, G.; Boitani, L. The role of habitat quality in fragmented landscapes: a conceptual overview and prospectus for future research, Oecologia, Volume 163 (2010) no. 2, pp. 535-547 | DOI

[46] Murray, J. D. Mathematical Biology, Interdisciplinary Applied Mathematics, Springer New York, New York, NY, 2002 | DOI

[47] Neubert, M. G.; Caswell, H. Demography and dispersal: calculation and sensitivity analysis of invasion speed for structured populations, Ecology, Volume 81 (2000) no. 6, pp. 1613-1628 | DOI

[48] Newman, W. I. Some exact solutions to a non-linear diffusion problem in population genetics and combustion, Journal of Theoretical Biology, Volume 85 (1980) no. 2, pp. 325-334 | DOI

[49] Okubo, A.; Maini, P. K.; Williamson, M. H.; Murray, J. D. On the spatial spread of the grey squirrel in Britain, Proceedings of the Royal Society of London. B. Biological Sciences, Volume 238 (1989) no. 1291, pp. 113-125 | DOI

[50] Owen, M. How Predation can Slow, Stop or Reverse a Prey Invasion, Bulletin of Mathematical Biology, Volume 63 (2001) no. 4, pp. 655-684 | DOI

[51] Panja, D. Effects of fluctuations on propagating fronts, Physics Reports, Volume 393 (2004) no. 2, pp. 87-174 | DOI

[52] Reay-Jones, F.; Rochat, J.; Goebel, R.; Tabone, E. Functional response of Trichogramma chilonis to Galleria mellonella and Chilo sacchariphagus eggs, Entomologia Experimentalis et Applicata, Volume 118 (2006) no. 3, pp. 229-236 | DOI

[53] Roques, L. Modéles de réaction-diffusion pour l’écologie spatiale, Editions Quae., 2013

[54] Roques, L.; Garnier, J.; Hamel, F.; Klein, E. K. Allee effect promotes diversity in traveling waves of colonization, Proceedings of the National Academy of Sciences, Volume 109 (2012) no. 23, pp. 8828-8833 | DOI

[55] Roques, L.; Hosono, Y.; Bonnefon, O.; Boivin, T. The effect of competition on the neutral intraspecific diversity of invasive species, Journal of Mathematical Biology, Volume 71 (2015) no. 2, pp. 465-489 | DOI

[56] Roques, L.; Roques, A.; Berestycki, H.; Kretzschmar, A. A population facing climate change: joint influences of Allee effects and environmental boundary geometry, Population Ecology, Volume 50 (2008) no. 2, pp. 215-225 | DOI

[57] Schwartz, M. W. Using niche models with climate projections to inform conservation management decisions, Biological Conservation, Volume 155 (2012), pp. 149-156 | DOI

[58] Seebens, H.; Blackburn, T. M.; Dyer, E. E.; Genovesi, P.; Hulme, P. E.; Jeschke, J. M.; Pagad, S.; Pyšek, P.; Winter, M.; Arianoutsou, M.; Bacher, S.; Blasius, B.; Brundu, G.; Capinha, C.; Celesti-Grapow, L.; Dawson, W.; Dullinger, S.; Fuentes, N.; Jäger, H.; Kartesz, J.; Kenis, M.; Kreft, H.; Kühn, I.; Lenzner, B.; Liebhold, A.; Mosena, A.; Moser, D.; Nishino, M.; Pearman, D.; Pergl, J.; Rabitsch, W.; Rojas-Sandoval, J.; Roques, A.; Rorke, S.; Rossinelli, S.; Roy, H. E.; Scalera, R.; Schindler, S.; Štajerová, K.; Tokarska-Guzik, B.; van Kleunen, M.; Walker, K.; Weigelt, P.; Yamanaka, T.; Essl, F. No saturation in the accumulation of alien species worldwide, Nature Communications, Volume 8 (2017) no. 1 | DOI

[59] Shigesada, N.; Kawasaki, K. Biological Invasions: Theory and Practice, Oxford Series in Ecology and Evolution, Oxford University Press, Oxford, 1997

[60] Silva, T.; Reino, L. M.; Borralho, R. A model for range expansion of an introduced species: the common waxbillEstrilda astrildin Portugal, Diversity and Distributions, Volume 8 (2002) no. 6, pp. 319-326 | DOI

[61] Smith, S. M. Biological Control with Trichogramma: Advances, Successes, and Potential of Their Use, Annual Review of Entomology, Volume 41 (1996) no. 1, pp. 375-406 | DOI

[62] Snyder, R. E. How demographic stochasticity can slow biological invasions, Ecology, Volume 84 (2003) no. 5, pp. 1333-1339 | DOI

[63] Tanaka, H.; Stone, H. A.; Nelson, D. R. Spatial gene drives and pushed genetic waves, Proceedings of the National Academy of Sciences, Volume 114 (2017) no. 32, pp. 8452-8457 | DOI

[64] Taylor, C. M.; Hastings, A. Allee effects in biological invasions, Ecology Letters, Volume 8 (2005) no. 8, pp. 895-908 | DOI

[65] Tobin, P. C.; Berec, L.; Liebhold, A. M. Exploiting Allee effects for managing biological invasions, Ecology Letters, Volume 14 (2011) no. 6, pp. 615-624 | DOI

[66] Travis, J. M.; Mustin, K.; Benton, T. G.; Dytham, C. Accelerating invasion rates result from the evolution of density-dependent dispersal, Journal of Theoretical Biology, Volume 259 (2009) no. 1, pp. 151-158 | DOI

[67] Turchin, P. Quantitative Analysis of Movement: Measuring and Modeling Population Redistribution in Animals and Plants, Sinauer, Sunderland, MA, 1998

[68] van den Bosch, F.; Hengeveld, R.; Metz, J. A. J. Analysing the Velocity of Animal Range Expansion, Journal of Biogeography, Volume 19 (1992) no. 2 | DOI

[69] Vázquez, J. L. The Porous Medium Equation. Mathematical Theory, Oxford Univ Press., 2007

[70] Veit, R. R.; Lewis, M. A. Dispersal, Population Growth, and the Allee Effect: Dynamics of the House Finch Invasion of Eastern North America, The American Naturalist, Volume 148 (1996) no. 2, pp. 255-274 | DOI

[71] Verbruggen, E.; Heijden, M. G. A.; Rillig, M. C.; Kiers, E. T. Mycorrhizal fungal establishment in agricultural soils: factors determining inoculation success, New Phytologist, Volume 197 (2013) no. 4, pp. 1104-1109 | DOI

[72] Vercken, E.; Vincent, F.; Mailleret, L.; Ris, N.; Tabone, E.; Fauvergue, X. Time-lag in extinction dynamics in experimental populations: evidence for a genetic Allee effect?, Journal of Animal Ecology, Volume 82 (2013) no. 3, pp. 621-631 | DOI

[73] Kolmogorov, A. N.; Petrovsky, I. G.; Piskunov, N. S. Étude de l’équation de la diffusion avec croissance de la quantité de matière et son application à un problème biologique, Bull Univ État Moscou, Sér Int A, Volume 1

Cited by Sources: