Allee Effects, Propagule Pressure and the Probability of Establishment: Risk Analysis for Biological Invasions Paradigms and Perspectives Received: 07 October 2004 Accepted: 23 December 2004 DOI:
Cite this article as: Drake, J.M. & Lodge, D.M. Biol Invasions (2006) 8: 365. doi:10.1007/s10530-004-8122-6 Abstract
Colonization is of longstanding interest in theoretical ecology and biogeography, and in the management of weeds and other invasive species, including insect pests and emerging infectious diseases. Due to accelerating invasion rates and widespread economic costs and environmental damages caused by invasive species, colonization theory has lately become a matter of considerable interest. Here we review the concept of propagule pressure to inquire if colonization theory might provide quantitative tools for risk assessment of biological invasions. By formalizing the concept of propagule pressure in terms of stochastic differential equation models of population growth, we seek a synthesis of invasion biology and theoretical population biology. We focus on two components of propagule pressure that affect the chance of invasion: (1) the number of individuals initially introduced, and (2) the rate of subsequent immigration. We also examine how Allee effects, which are expected to be common in newly introduced populations, may inhibit establishment of introduced propagules. We find that the establishment curve (i.e., the chance of invasion as a function of initial population size), can take a variety of shapes depending on immigration rate, carrying capacity, and the severity of Allee effects. Additionally, Allee effects can cause the stationary distribution of population sizes to be bimodal, which we suggest is a possible explanation for time lags commonly observed between the detection of an introduced population and widespread invasion of the landscape.
Keywords Allee effect biological invasion immigration propagule pressure rescue effect risk analysis risk assessment stochastic differential equation stochastic population growth References Augustin, NH, Mugglestone, MA, Buckland, ST 1996 An autologistic model for the spatial distribution of wildlife Journal of Applied Ecology 33 339 347 Google Scholar Allen, LJS 2003An Introduction to Stochastic Processes with Applications to Biology Pearson Education, Inc. Upper Saddle River, NJ 400 Google Scholar Bailey, NTJ 1964The Elements of Stochastic Processes with Applications to the Natural Sciences Wiley New York 249 Google Scholar Baker, HG 1974 The evolution of weeds Annual Review of Ecology and Systematics 5 1 24 CrossRef Google Scholar Baker, HG, Stebbins, GL 1965The Genetics of Colonizing Species Academic Press New York 588 Google Scholar Bartlett, MS 1960Stochastic Population Models in Ecology and Epidemiology Methuen London 90 Google Scholar Beissinger, SR, McCullough, DR 2002Population Viability Analysis University of Chicago Press Chicago 593 Google Scholar Berggren, A 2001 Colonization success in Roesel’s bush-cricket Metrioptera roeseli: the effects of propagule size Ecology 82 274 280 Google Scholar Boukal, DS, Berec, L 2002 Single-species models of the Allee effect: extinction boundaries, sex ratios and mate encounters Journal of Theoretical Biology 218 375 394 PubMed CrossRef Google Scholar Brook, B, Burgman, MA, Akçakaya, HR, O’Grady, JJ, Frankham, R 2002 Critiques of PVA ask the wrong questions. Throwing the heuristic baby out with the numerical bathwater Conservation Biology 16 262 263 CrossRef Google Scholar Brown, JH, Kodric-Brown, A 1977 Turnover rates in insular biogeography: effect of immigration on extinction Ecology 58 445 449 Google Scholar Chapman, JW, Miller, TW, Coan, EV 2003 Live seafood species as recipes for invasion Conservation Biology 17 1386 1395 Google Scholar Clark, JS 1998 Why trees migrate so fast: confronting theory with dispersal: biology and the paleorecord American Naturalist 152 204 224 CrossRef Google Scholar
Colautti, RI, Grigorovich IA and MacIsaac HJ (in press) Propagule pressure: a null model for biological invasions. Biological Invasions 8(4).
Cook, WC 1931 Notes on predicting the probable future distribution of introduced insects Ecology 12 245 147 Google Scholar Courchamp, F, Clutton-brock, T, Grenfell, B 1999 Inverse density-dependence and the Allee effect Trends in Ecology and Evolution 14 405 410 PubMed CrossRef Google Scholar Dennis, B 1989 Allee effects: population growth, critical density, and the chance of extinction Natural Resources Modelling 3 481 538 Google Scholar Dennis, B 2002 Allee effects in stochastic populations Oikos 96 389 401 CrossRef Google Scholar Dennis, B, Munholland, PL, Scott, JM 1991 Estimation of growth and extinction parameters for endangered species Ecological Monographs 61 115 143 Google Scholar Drake, JM 2004 Allee effects and the risk of biological invasion Risk Analysis 24 795 802 PubMed CrossRef Google Scholar Drake, JM 2003 The paradox of the parasites: implications for biological invasion Biology Letters 270 S133 S135 CrossRef Google Scholar Drake, JM, Bossenbroek, J 2004 The potential distribution of zebra mussels in the United States BioScience 54 931 941 Google Scholar Duncan, RP, Blackburn, TM, Veltman, CJ 1999 Determinants of geographical range sizes: a test using introduced New Zealand birds Journal of Animal Ecology 68 963 975 CrossRef Google Scholar Elton, CS 2000The Ecology of Invasions by Animals and Plants University of Chicago Press Chicago 196 Google Scholar
Environmental Protection Agency (1998) Guidelines for Ecological Risk Assessment. Washington, DC: EPA/630/R095/002F
Feller, W 1939 Die Grundlagen der Volterraschen Theorie des Kampfes ums Dasein in wahrscheinlichkeits theoretischen Behandlung Acta Biotheoretica 5 1 40 CrossRef Google Scholar Fieberg, J, Ellner, SP 2000 When is it meaningful to estimate an extinction probability? Ecology 81 2040 2047 Google Scholar Gardiner, CW 1985Handbook of Stochastic Methods for Physics, Chemistry, and the Natural Sciences2 Springer New York 442 Google Scholar Gjullin, CM 1931 Probable distribution of the Mediterranean fruit fly ( Ceratitis Capitata Weid.) in the United States Ecology 12 248 258 Google Scholar Goel, NS, Richter-Dyn, N 1974Stochastic Models in Biology Academic Press New York Google Scholar Gollasch, S, Leppäkoski, E 1999Initial risk assessment of alien species in Nordic coastal waters Nordic Council of Ministers Copenhangen 124 Google Scholar Grevstad, FS 1999a Experimental invasions using biological control introductions: the influence of release size on the chance of population establishment Biological Invasions 1 313 232 CrossRef Google Scholar Grevstad, F 1999b Factors influencing the chance of population establishment: implications for release strategies in biocontrol Ecological Applications 9 1439 1447 Google Scholar Groves, RH, Panetta, FR, Virtue, JG 2001Weed Risk Assessment CSIRO Publishing Collingwood, Victoria, Australia 256 Google Scholar Groom, M 1998 Allee effects limit population viability of an annual plant American Naturalist 151 487 496 CrossRef Google Scholar Haccou, P, Iwasa, Y 1996 Establishment probability in fluctuating environments: a branching process model Theoretical Population Biology 50 254 280 PubMed CrossRef Google Scholar Hayes, K 1997A Review of Ecological Risk Assessment Methodologies CSIRO Marine Research Technical Report Number 13 Collingwood, Victoria, Australia 113 Google Scholar Henson, SM, King, AA, Costantino, RF, Cushing, JM, Dennis, B, Desharnais, RA 2003 Explaining and predicting patterns in stochastic population systems Proceedings of the Royal Society of London B 270 1549 1553 Google Scholar Kammen, DM, Hassenzahl, DM 1999Should We Risk It? Princeton University Press Princeton 424 Google Scholar Kendall, DG 1949 Stochastic processes and population growth Journal of the Royal Statistical Society B 11 230 264 Google Scholar Kolar, CS, Lodge, DM 2001 Progress in invasion biology: predicting invaders Trends in Ecology & Evolution 16 199 204 Google Scholar Kolar, CS, Lodge, DM 2002 Ecological predictions and risk assessments for alien species Science 298 1233 1236 PubMed CrossRef Google Scholar Lande, R, Orzack, SH 1988 Extinction dynamics of age-structured populations in a fluctuating environment Proceedings of the National Academy of Sciences USA 85 7418 7421 Google Scholar Lande, R, Engen, S, Sæther, BE 2003Stochastic Population Dynamics in Ecology and Conservation Oxford University Press Oxford, UK 224 Google Scholar Levine, JM, D’Antonio, CM 2003 Forecasting biological invasions with increasing international trade Conservation Biology 17 322 326 CrossRef Google Scholar
Lewis MA and Kareiva P (1993) Allee dynamics and the spread of invading organisms Theoretical Population Biology 43: 141–158
Google Scholar Lewontin, RC, Cohen, D 1969 On population growth in a randomly varying environment Proceedings of the National Academy of Sciences USA 62 1056 1060 Google Scholar Liermann, M, Hilborn, R 1997 Depensation in fish stocks: a hierarchic Bayesian meta-analysis Canadian Journal of Fisheries and Aquatic Sciences 54 1976 1984 CrossRef Google Scholar Ludwig, D 1996 The distribution of population survival times American Naturalist 147 506 526 CrossRef Google Scholar Lusk, JJ, Guthery, FS, DeMaso, SJ 2002 A neural network model for predicting Northern Bobwhite abundance in the Rolling Red Plains of Oklahoma Scott, eds. Predicting Species Occurrences: Issues of Accuracy and Scale Island Press Washington, DC, USA 345 356 Google Scholar MacArthur, RH, Wilson, EO 1967The Theory of Island Biogeography Princeton University Press Princeton, NJ 224 Google Scholar Mack, RN, Simberloff, D, Lonsdale, WM, Evans, H, Clout, M, Bazzaz, FA 2000 Biotic invasions: causes, epidemiology, global consequences, and control Ecological Applications 10 689 710 Google Scholar Mangel, M, Tier, C 1993 A simple direct method for finding persistence times of populations and application to conservation problems Proceedings of the National Academy of Sciences USA 90 1083 1086 Google Scholar Matis, JH, Kiffe, TR 2000Stochastic Population Models: A Compartmental Perspective Springer-Verlag New York 202 Google Scholar McCarthy, MA 1997 The Allee effect, finding mates and theoretical models Ecological Modelling 103 99 102 CrossRef Google Scholar McCarthy, MA, Andelman, SJ, Possingham, HP 2003 Reliability of relative predictions in population viability analysis Conservation Biology 17 982 989 CrossRef Google Scholar Morris, WF, Doak, DF 2002Quantitative Conservation Biology: Theory and Practice of Population Viability Analysis Sinauer Sunderland, MA 480 Google Scholar
National Invasive Species Council (2001) Meeting the Invasive Species Challenge:c National Invasive Species Management Plan, 80 pp
National Research Council 1996Stemming the Tide: Controlling Introductions of Nonindigenous Species by Ships’ Ballast Water National Academy Press Washington, DC 141 Google Scholar National Research Council 2002Predicting Invasions of Nonindigenous Plants and Plant Pests National Academy Press Washington, DC 194 Google Scholar Olden, JD, Poff, NL 2003 Toward a mechanistic understanding and prediction of biotic homogenization American Naturalist 162 442 460 PubMed Google Scholar Peterson, AT, Vieglais, DA 2001 Predicting species invasions using ecological niche modeling BioScience 51 363 371 Google Scholar Rand, DA, Wilson, HB 1991 Chaotic stochasticity – a ubiquitous source of unpredictability in epidemics Proceedings of the Royal Society of London Series B 246 179 184 PubMed Google Scholar Reichard, S 2001 The search for patterns that enable prediction of invasion Groves, RH Panetta, FD Virtue, JG eds. Weed Risk Assessment CISRO Publishing Collingwood, Victoria, Australia 10 19 Google Scholar Renshaw, E 1991Modelling Biological Populations in Space and Time Cambridge University Press Cambridge 422 Google Scholar Richter-Dyn, N, Goel, NS 1972 On the extinction of a colonizing species Theoretical Population Biology 3 406 433 PubMed Google Scholar Shaffer, ML 1981 Minimum population sizes for species conservation BioScience 31 131 134 Google Scholar Shigesada, N, Kawasaki, K 1997Biological Invasions: Theory and Practice Oxford University Press Oxford, UK 205 Google Scholar Simberloff, D, Alexander, M 1998 Assessing risks from biological introductions (excluding GMOs) for ecological systems Calow, P eds. Handbook of Environmental Risk Assessment and Management Oxford University Press Oxford 147 176 Google Scholar Soulé, ME 1987Viable Populations for Conservation Cambridge University Press Cambridge 206 Google Scholar Sunstein, CR 2002Risk and Reason Cambridge University Press Cambridge 352 Google Scholar Sutherst, RW 2003 Prediction of species’ geographical ranges Journal of Biogeography 30 1944 1945 CrossRef Google Scholar Tier, C, Hanson, FB 1981 Persistence of density dependent stochastic populations Mathematical Biosciences 53 89 117 CrossRef Google Scholar Tuljapurkar, S 1990Population Dynamics in Variable Environments Springer-Verlag New York 154 Google Scholar Veit, RR, Lewis, MA 1996 Dispersal, population growth and the Allee Effect: dynamics of the House Finch invasion of eastern North America American Naturalist 148 255 274 CrossRef Google Scholar Veltman, CJ, Nee, S, Crawley, MJ 1996 Correlates of introduction success in exotic New Zealand birds American Naturalist 147 542 557 CrossRef Google Scholar Williamson, M 1996Biological Invasions Chapman and Hall London 244 Google Scholar Wilson, EO 2000 On the future of conservation biology Conservation Biology 14 1 3 CrossRef Google Scholar