Abstract
In this paper, we review how mate-finding Allee effects enter population dynamical models that consider both sexes, highlight possible limitations of the more widely used “one-sex” models, and outline the links between the different model classes. We further explore interactions between the mate-finding Allee effect and other mechanisms relevant to pest-control strategies: release of natural enemies, sterile male release, and culling. Many of these strategies impose an additional component Allee effect on the population, and we discuss which of them might be efficient in the control of pest species that also suffer from the failure to locate mates. We focus primarily on eradication thresholds; our simple models show that most of the strategies yield similar results, and depending on the costs, one strategy or a combination of several can lead to the most efficient control.
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References
Allen LJS, Fagan JF, Hognas G, Fagerholm H (2005) Population extinction in discrete-time stochastic population models with an Allee effect. J Differ Equ Appl 11:273–293. doi:10.1080/10236190412331335373
Angulo E, Roemer GW, Berec L, Gascoigne J, Courchamp F (2007) Double Allee effects and extinction in the island fox. Conserv Biol 21:1082–1091. doi:10.1111/j.1523-1739.2007.00721.x
Barclay HJ (1984) Pheromone trapping models for pest control: effects of mating patterns and immigration. Res Popul Ecol (Kyoto) 26:303–311. doi:10.1007/BF02515496
Barclay HJ (1992) Combining methods of insect pest control—partitioning mortality and predicting complementarity. Res Popul Ecol (Kyoto) 34:91–107. doi:10.1007/BF02513524
Barclay H, Mackauer M (1980) The sterile insect release method for pest control—a density-dependent model. Environ Entomol 9:810–817
Berec L, Boukal DS (2004) Implications of mate search, mate choice and divorce rate for population dynamics of sexually reproducing species. Oikos 104:122–132. doi:10.1111/j.0030-1299.2004.12753.x
Berec L, Boukal DS, Berec M (2001) Linking the Allee effect, sexual reproduction, and temperature-dependent sex determination via spatial dynamics. Am Nat 157:217–230. doi:10.1086/318626
Berec L, Angulo E, Courchamp F (2007) Multiple Allee effects and population management. Trends Ecol Evol 22:185–191. doi:10.1016/j.tree.2006.12.002
Bessa-Gomes C, Legendre S, Clobert J (2004) Allee effects, mating systems and the extinction risk in populations with two sexes. Ecol Lett 7:802–812. doi:10.1111/j.1461-0248.2004.00632.x
Boukal DS, Berec L (2002) Single-species models of the Allee effect: extinction boundaries, sex ratios and mate encounters. J Theor Biol 218:375–394. doi:10.1006/jtbi.2002.3084
Boukal DS, Sabelis MW, Berec L (2007) How predator functional responses and Allee effects in prey affect the paradox of enrichment and population collapses. Theor Popul Biol 72:136–147. doi:10.1016/j.tpb.2006.12.003
Boukal DS, Berec L, Křivan V (2008) Does sex-selective predation stabilize or destabilize predator-prey dynamics? PLoS ONE 3:e2687. doi:10.1371/journal.pone.0002687
Castillo-Chavez C, Huang W (1995) The logistic equation revisited: the two-sex case. Math Biosci 128:299–316. doi:10.1016/0025-5564(94)00077-D
Courchamp F, Grenfell BT, Clutton-Brock TH (2000) Impact of natural enemies on obligately cooperative breeders. Oikos 91:311–322. doi:10.1034/j.1600-0706.2000.910212.x
Courchamp F, Angulo E, Rivalan P, Hall RJ, Signoret L, Bull L, Meinard Y (2006) Rarity value and species extinction: the anthropogenic Allee effect. PLoS Biol 4:e415. doi:10.1371/journal.pbio.0040415
Courchamp F, Berec L, Gascoigne J (2008) Allee effects in ecology and conservation. Oxford University Press, Oxford
Davis HG, Taylor CM, Lambrinos JG, Strong DR (2004) Pollen limitation causes an Allee effect in a wind-pollinated invasive grass (Spartina alterniflora). Proc Natl Acad Sci USA 101:13804–13807. doi:10.1073/pnas.0405230101
Dennis B (1989) Allee effects: population growth, critical density, and the chance of extinction. Nat Resour Model 3:481–538
Dennis B (2002) Allee effects in stochastic populations. Oikos 96:389–401. doi:10.1034/j.1600-0706.2002.960301.x
Deredec A, Courchamp F (2006) Combined impacts of Allee effects and parasitism. Oikos 112:667–679. doi:10.1111/j.0030-1299.2006.14243.x
Du YH, Shi JP (2007) Allee effect and bistability in a spatially heterogeneous predator-prey model. Trans Am Math Soc 359:4557–4593. doi:10.1090/S0002-9947-07-04262-6
Elkinton JS, Parry D, Boettner GH (2006) Implicating an introduced generalist parasitoid in the invasive browntail moth’s enigmatic demise. Ecology 87:2664–2672. doi:10.1890/0012-9658(2006)87[2664:IAIGPI]2.0.CO;2
Engen S, Lande R, Saether BE (2003) Demographic stochasticity and Allee effects in populations with two sexes. Ecology 84:2378–2386. doi:10.1890/02-0123
Fagan WF (1999) Weak influences of initial conditions on metapopulation persistence times. Ecol Appl 9:1430–1438. doi:10.1890/1051-0761(1999)009[1430:WIOICO]2.0.CO;2
Gascoigne JC, Lipcius RN (2004) Allee effects driven by predation. J Appl Ecol 41:801–810. doi:10.1111/j.0021-8901.2004.00944.x
Gascoigne JC, Berec L, Gregory S, Courchamp F (2009) Dangerously few liaisons: a review of mate-finding Allee effects. Popul Ecol. doi:10.1007/s10144-009-0146-4
Hadeler KP (1993) Pair formation models with maturation period. J Math Biol 32:1–15. doi:10.1007/BF00160370
Hadeler KP, Waldstätter R, Wörz-Busekros A (1988) Models for pair formation in bisexual populations. J Math Biol 26:635–649
Hadjiavgousti D, Ichtiaroglou S (2008) Allee effect in a prey–predator system. Chaos Solitons Fractals 36:334–342. doi:10.1016/j.chaos.2006.06.053
Hendrichs J, Robinson AS, Cayol JP, Enkerlin W (2002) Medfly area wide sterile insect technique programmes for prevention, suppression or eradication: the importance of mating behavior studies. Fla Entomol 85:1–13. doi:10.1653/0015-4040(2002)085[0001:MASITP]2.0.CO;2
Hilker FM, Lewis MA, Seno H, Langlais M, Malchow H (2005) Pathogens can slow down or reverse invasion fronts of their hosts. Biol Invasions 7:817–832. doi:10.1007/s10530-005-5215-9
Hopper KR, Roush RT (1993) Mate finding, dispersal, number released, and the success of biological-control introductions. Ecol Entomol 18:321–331. doi:10.1111/j.1365-2311.1993.tb01108.x
Johnson DM, Liebhold AM, Tobin PC, Bjørnstad ON (2006) Allee effects and pulsed invasion by the gypsy moth. Nature 444:361–363. doi:10.1038/nature05242
Keitt TH, Lewis MA, Holt RD (2001) Allee effects, invasion pinning, and species’ borders. Am Nat 157:203–216. doi:10.1086/318633
Kent A, Doncaster CP, Sluckin T (2003) Consequences for predators of rescue and Allee effects on prey. Ecol Model 162:233–245. doi:10.1016/S0304-3800(02)00343-5
Kiørboe T (2006) Sex, sex-ratios, and the dynamics of pelagic copepod populations. Oecologia 148:40–50. doi:10.1007/s00442-005-0346-3
Klassen W, Curtis CF (2005) History of the sterile insect technique. In: Dyck VA, Hendrichs J, Robinson AS (eds) Sterile insect technique. Principles and practice in area-wide integrated pest management. Springer, Dordrecht, pp 3–36
Kostitzin VA (1940) Sur la loi logistique es ses generalisations. Acta Biotheor 5:155–159. doi:10.1007/BF01567694
Krafsur ES, Whitten CJ, Novy JE (1987) Screwworm eradication in North and Central America. Parasitol Today 3:131–137. doi:10.1016/0169-4758(87)90196-7
Kuno E (1978) Simple mathematical models to describe the rate of mating in insect populations. Res Popul Ecol (Kyoto) 20:50–60. doi:10.1007/BF02512974
Kuussaari M, Saccheri I, Camara M, Hanski I (1998) Allee effect and population dynamics in the Glanville fritillary butterfly. Oikos 82:384–392. doi:10.2307/3546980
Levitan DR, Sewell MA, Chia FS (1992) How distribution and abundance influence fertilization success in the sea-urchin Strongylocentrotus franciscanus. Ecology 73:248–254. doi:10.2307/1938736
Liebhold A, Bascompte J (2003) The Allee effect, stochastic dynamics and the eradication of alien species. Ecol Lett 6:133–140. doi:10.1046/j.1461-0248.2003.00405.x
Liebhold A, Tobin PC (2008) Population ecology of insect invasions and their management. Annu Rev Entomol 53:387–408. doi:10.1146/annurev.ento.52.110405.091401
McCarthy MA (1997) The Allee effect, finding mates and theoretical models. Ecol Modell 103:99–102. doi:10.1016/S0304-3800(97)00104-X
McNeil JN (1991) Behavioral ecology of pheromone-mediated communication in moths and its importance in the use of pheromone traps. Annu Rev Entomol 36:407–430. doi:10.1146/annurev.en.36.010191.002203
Møller AP, Legendre S (2001) Allee effect, sexual selection and demographic stochasticity. Oikos 92:27–34. doi:10.1034/j.1600-0706.2001.920104.x
Molnár PK, Derocher AE, Lewis MA, Taylor MK (2008) Modelling the mating system of polar bears: a mechanistic approach to the Allee effect. Proc R Soc Lond B Biol Sci 275:217–226. doi:10.1098/rspb.2007.1307
Myers RA, Barrowman NJ, Hutchings JA, Rosenberg AA (1995) Population dynamics of exploited fish stocks at low population levels. Science 269:1106–1108. doi:10.1126/science.269.5227.1106
Myers JH, Savoie A, van Randen E (1998) Eradication and pest management. Annu Rev Entomol 43:471–491. doi:10.1146/annurev.ento.43.1.471
Oostermeijer JGB (2000) Population viability analysis of the rare Gentiana pneumonanthe: importance of genetics, demography, and reproductive biology. In: Young AG, Clarke GM (eds) Genetics demography and viability of fragmented populations. Cambridge University Press, Cambridge, pp 313–334
Petrovskii SV, Morozov AY, Venturino E (2002) Allee effect makes possible patchy invasion in a predator-prey system. Ecol Lett 5:345–352. doi:10.1046/j.1461-0248.2002.00324.x
Petrovskii S, Malchow H, Li BL (2005a) An exact solution of a diffusive predator–prey system. Proc R Soc A Math Phys Eng Sci 461:1029–1053
Petrovskii S, Morozov A, Li BL (2005b) Regimes of biological invasion in a predator–prey system with the Allee effect. Bull Math Biol 67:637–661. doi:10.1016/j.bulm.2004.09.003
Petrovskii SV, Malchow H, Hilker FM, Venturino E (2005c) Patterns of patchy spread in deterministic and stochastic models of biological invasion and biological control. Biol Invasions 7:771–793. doi:10.1007/s10530-005-5217-7
Philip JR (1957) Sociality and sparse populations. Ecology 38:107–111. doi:10.2307/1932132
Rowe S, Hutchings JA, Bekkevold D, Rakitin A (2004) Depensation, probability of fertilization and the mating system of Atlantic cod (Gadus morhua L.). ICES J Mar Sci 61:1144–1150. doi:10.1016/j.icesjms.2004.07.007
Stelinski LL, Gut LJ, Haas M, McGhee P, Epstein D (2007) Evaluation of aerosol devices for simultaneous disruption of sex pheromone communication in Cydia pomonella and Grapholita molesta (Lepidoptera : Tortricidae). J Pest Sci 80:225–233. doi:10.1007/s10340-007-0176-7
Stephens PA, Sutherland WJ (1999) Consequences of the Allee effect for behaviour, ecology and conservation. Trends Ecol Evol 14:401–405. doi:10.1016/S0169-5347(99)01684-5
Stephens PA, Frey-Roos F, Arnold W, Sutherland WJ (2002) Model complexity and population predictions. The alpine marmot as a case study. J Anim Ecol 71:343–361. doi:10.1046/j.1365-2656.2002.00605.x
Taylor CM, Hastings A (2004) Finding optimal control strategies for invasive species: a density-structured model for Spartina alterniflora. J Appl Ecol 41:1049–1057. doi:10.1111/j.0021-8901.2004.00979.x
Taylor CM, Hastings A (2005) Allee effects in biological invasions. Ecol Lett 8:895–908. doi:10.1111/j.1461-0248.2005.00787.x
Taylor CM, Davis HG, Civille JC, Grevstad FS, Hastings A (2004) Consequences of an Allee effect in the invasion of a Pacific estuary by Spartina alterniflora. Ecology 85:3254–3266. doi:10.1890/03-0640
Tobin PC, Whitmire SL, Johnson DM, Bjornstad ON, Liebhold AM (2007) Invasion speed is affected by geographical variation in the strength of Allee effects. Ecol Lett 10:36–43. doi:10.1111/j.1461-0248.2006.00991.x
Veit RR, Lewis MA (1996) Dispersal, population growth, and the Allee effect: dynamics of the house finch invasion of eastern North America. Am Nat 148:255–274. doi:10.1086/285924
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
Wang G, Liang XG, Wang FZ (1999) The competitive dynamics of populations subject to an Allee effect. Ecol Model 124:183–192. doi:10.1016/S0304-3800(99)00160-X
Wells H, Strauss EG, Rutter MA, Wells PH (1998) Mate location, population growth and species extinction. Biol Conserv 86:317–324. doi:10.1016/S0006-3207(98)00032-9
Witzgall P, Stelinski L, Gut L, Thomson D (2008) Codling moth management and chemical ecology. Annu Rev Entomol 53:503–522. doi:10.1146/annurev.ento.53.103106.093323
Yamanaka T (2007) Mating disruption or mass trapping? Numerical simulation analysis of a control strategy for lepidopteran pests. Popul Ecol 49:75–86. doi:10.1007/s10144-006-0018-0
Yamanaka T, Liebhold AM (2009) Spatially implicit approaches to understanding the manipulation of mating success for insect invasion management. Popul Ecol. doi:10.1007/s10144-009-0155-3
Zhou SR, Liu YF, Wang G (2005) The stability of predator–prey systems subject to the Allee effects. Theor Popul Biol 67:23–31. doi:10.1016/j.tpb.2004.06.007
Acknowledgments
We thank Erin S. Dunlop, Ane T. Laugen, A. Liebhold, and two anonymous referees for their comments on the manuscript. This research was supported by the Institute of Entomology (project no. Z50070508) and GA AV CR (grant no. KJB600070602). D.S.B. acknowledges support from the EU Research Training Network FishACE (contract no. MRTN-CT-2004-005578) and the EvoFish project funded through Bergen Research Foundation.
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Boukal, D.S., Berec, L. Modelling mate-finding Allee effects and populations dynamics, with applications in pest control. Popul Ecol 51, 445–458 (2009). https://doi.org/10.1007/s10144-009-0154-4
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DOI: https://doi.org/10.1007/s10144-009-0154-4