
Mathematical Biosciences and Engineering, 2020, 17(2): 17181742. doi: 10.3934/mbe.2020090.
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Modeling the effects of density dependent emigration, weak Allee effects, and matrix hostility on patchlevel population persistence
1 Department of Biological Sciences, Louisiana State University, Baton Rouge, LA 70803, USA
2 Department of Mathematics and Statistics, University of North Carolina at Greensboro, Greensboro, NC 27412, USA
3 Department of Mathematics and Computer science, University of Auburn Montgomery, Montgomery, AL 36117, USA
Received: , Accepted: , Published:
Keywords: habitat fragmentation; weak Allee effect; patchlevel Allee effect; reaction diffusion model; density dependent emigration
Citation: James T. Cronin, Nalin Fonseka, Jerome Goddard II, Jackson Leonard, Ratnasingham Shivaji. Modeling the effects of density dependent emigration, weak Allee effects, and matrix hostility on patchlevel population persistence. Mathematical Biosciences and Engineering, 2020, 17(2): 17181742. doi: 10.3934/mbe.2020090
References:
 1. W. C. Allee, Animal Aggregations; a Study in General Sociology, University of Chicago Press, Chicago, 1931.
 2. N. Knowlton, Thresholds and multiple stable states in coral reef community dynamics, Integr. Comp. Biol., 32 (1992), 674682.
 3. B. Dennis, Allee effects: Population growth, critical density, and the chance of extinction, Nat. Resour. Modell., 3 (1989), 481538.
 4. M. A. Lewis, P. Kareiva, Allee dynamics and the spread of invading organisms, Theor. Popul. Biol., 43 (1993), 141158.
 5. M. Fischer, M. Hock, M. Paschke, Low genetic variation reduces crosscompatibility and offspring fitness in populations of a narrow endemic plant with a selfincompatibility system, Conserv. Genet., 4 (2003), 325336.
 6. F. Courchamp, L. Berec, J. Gascoigne, Allee Effects in Ecology and Conservation, Oxford University Press, Oxford, 2008.
 7. A. M. Kramer, B. Dennis, A. M. Liebhold, J. M. Drake, The evidence for allee effects, Popul. Ecol., 51 (2009), 341354.
 8. R. M. Sibly, D. Barker, M. C. Denham, J. Hone, M. Pagel, On the regulation of populations of mammals, birds, fish, and insects, Science, 309 (2005), 607610.
 9. J. A. Hutchings, Thresholds for impaired species recovery, Proc. R. Soc. B: Biol. Sci., 282 (2015), 111.
 10. C. M. Taylor, A. Hastings, Allee effects in biological invasions, Ecol. Lett., 8 (2005), 895908.
 11. A. K. Shaw, H. Kokko, M. G. Neubert, Sex difference and allee effects shape the dynamics of sexstructured invasions, J. Animal Ecol., 87 (2018), 3646.
 12. D. M. Johnson, A. M. Liebhold, P. C. Tobin, O. N. Bjrnstad, Allee effects and pulsed invasion by the gypsy moth, Nature, 444 (2006), 361363.
 13. P. C. Tobin, L. Berec, A. M. Liebhold, Exploiting allee effects for managing biological invasions, Ecol. Lett., 14 (2011), 615624.
 14. J. C. Blackwood, L. Berec, T. Yamanaka, R. S. EpanchinNiell, A. Hastings, A. M. Liebhold, Bioeconomic synergy between tactics for insect eradication in the presence of allee effects, Proc. R. Soc. B: Biol. Sci., 279 (2012), 28072815.
 15. R. R. Regoes, D. Ebert, S. Bonhoeffer, Dosedependent infection rates of parasites produce the allee effect in epidemiology, Proc. R. Soc. London. Ser. B: Biol. Sci., 269 (2002), 271279.
 16. A. Deredec, F. Courchamp, Combined impacts of allee effects and parasitism, Oikos, 112 (2006), 667679.
 17. F. Hilker, M. Langlais, H. Malchow, The allee effect and infectious diseases: Extinction, multistability, and the (dis)appearance of oscillations, Am. Nat., 173 (2009), 7288.
 18. K. S. Korolev, J. B. Xavier, J. Gore, Turning ecology and evolution against cancer, Nat. Rev. Cancer, 14 (2014), 110.
 19. L. Sewalt, K. Harley, P. van Heijster, S. Balasuriya, Influences of allee effects in the spreading of malignant tumours, J. Theor. Biol., 394 (2016), 7792.
 20. M. A. Pires, S. M. DuarteQueirs, Optimal dispersal in ecological dynamics with allee effect in metapopulations, PLoS One, 14 (2019), 115.
 21. C. E. Brassil, Mean time to extinction of a metapopulation with an allee effect, Ecol. Modell., 143 (2001), 916.
 22. P. Amarasekare, Allee effects in metapopulation dynamics, Am. Nat., 152 (1998), 298302.
 23. S. R. Zhou, G. Wang, Alleelike effects in metapopulation dynamics, Math. Biosci., 189 (2004), 103113.
 24. S. Petrovskii, A. Morozov, B. L. Li, Regimes of biological invasion in a predatorprey system with the allee effect, Bull. Math. Biol., 67 (2005), 637661.
 25. I. D. Jonsen, R. S. Bourchier, J. Roland, Influence of dispersal, stochasticity, and an allee effect on the persistence of weed biocontrol introductions, Ecol. Modell., 203 (2007), 521526.
 26. R. R. Veit, M. A. Lewis, Dispersal, population growth, and the allee effect: Dynamics of the house finch invasion of eastern north america, Am. Nat., 148 (1996), 255274.
 27. O. Kindvall, K. Vessby, S. Berggren, G. Hartman, Individual mobility prevents an allee effect in sparse populations of the bush cricket metrioptera roeseli: An experimental study, Oikos, 81 (1998), 449457.
 28. D. Bonte, L. Lens, J. P. Maelfait, Lack of homeward orientation and increased mobility result in high emigration rates from lowquality fragments in a dune wolf spider, J. Anim. Ecol., 73 (2004), 643650.
 29. P. Amarasekare, The role of densitydependent dispersal in sourcesink dynamics, J. Theor. Biol., 226 (2004), 159168.
 30. D. E. Bowler, T. G. Benton, Causes and consequences of animal dispersal strategies: Relating individual behaviour to spatial dynamics, Biol. Rev., 80 (2005), 205225.
 31. E. Matthysen, Multicausality of Dispersal: A Review, Oxford University Press, United Kingdom, 2012, 318.
 32. R. Harman, J. Goddard, R. Shivaji, J. T. Cronin, Frequency of cccurrence and populationdynamic consequences of different forms of densitydependent emigration, Am. Nat., Forthcoming.
 33. R. S. Cantrell, C. Cosner, Density dependent behavior at habitat boundaries and the allee effect, Bull. Math. Biol., 69 (2007), 23392360.
 34. J. Goddard II, Q. Morris, C. Payne, R. Shivaji, A diffusive logistic equation with ushaped density dependent dispersal on the boundary, Topol. Methods Nonlinear Anal., 53 (2019), 335349.
 35. J. Drake, A. Kramer, Allee effects, Nat. Educ. Knowl., 3 (2011), 2.
 36. J. Shi, R. Shivaji, Persistence in reaction diffusion models with weak allee effect, J. Math. Biol., 52 (2006), 807829.
 37. S. A. Levin, Dispersion and population interactions, Am. Nat., 108 (1974), 207228.
 38. S. A. Levin, The role of theoretical ecology in the description and understanding of populations in heterogeneous environments, Am. Zool., 21 (1981), 865875.
 39. P. C. Fife, Mathematical Aspects of Reacting and Diffusing Systems, SpringerVerlag, 1979.
 40. A. Okubo, Diffusion and Ecological Problems: Mathematical Models, Springer, Berlin, 1980.
 41. J. D. Murray, Mathematical Biology. II, 3rd edition, SpringerVerlag, New York, 2003.
 42. R. S. Cantrell, C. Cosner, Spatial Ecology via ReactionDiffusion Equations, Wiley, Chichester, 2003.
 43. E. E. Holmes, M. A. Lewis, R. R. V. Banks, Partial differential equations in ecology: Spatial interactions and population dynamics, Ecology, 75 (1994), 1729.
 44. J. T. Cronin, J. Goddard II, R. Shivaji, Effects of patch matrixcomposition and individual movement response on population persistence at the patchlevel, Bull. Math. Biol., 81 (2019), 39333975.
 45. R. S. Cantrell, C. Cosner, On the effects of nonlinear boundary conditions in diffusive logistic equations on bounded domains, J. Differ. Eq., 231 (2006), 768804.
 46. N. Foneska, J. Goddard II, Q. Morris, R. Shivaji, B. Son, On the effects of the exterior matrix hostility and a ushaped density dependent dispersal on a diffusive logistic growth model, Discrete Contin. Dyn. Syst. Ser. B, Forthcoming.
 47. J. Goddard II, R. Shivaji, Stability analysis for positive solutions for classes of semilinear elliptic boundaryvalue problems with nonlinear boundary conditions, Proc. R. Soc. Edinburgh, 147 (2017), 10191040.
 48. S. Robinson, M. A. Rivas, Eigencurves for linear elliptic equations, ESAIM Control Optim. Calc. Var. 25 (2019), 4569.
 49. C. V. Pao, Nonlinear Parabolic and Elliptic Equations, Plenum Press, New York, 1992.
 50. J. Goddard II, Q. Morris, S. Robinson, R. Shivaji, An exact bifurcation diagram for a reaction diffusion equation arising in population dynamics, Boundary Value Probl., 170 (2018), 117.
 51. P. A. Stephens, W. J. Sutherland, R. P. Freckleton, What is the allee effect?, Oikos, 87 (1999), 185190.
 52. I. Hanski, Metapopulation Ecology, Oxford University Press, Oxford, 1999.
This article has been cited by:
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