Species Spreading due to Environmental Hostility, Dispersal Adaptation and Allee Effects
A phenomenological model for species spreading which incorporates the Allee effect, a species- maximum attainable growth rate, collective dispersal rate and dispersal adaptability is presented. This builds on a well-established reaction-diffusion model for spatial spreading of invading organisms. The model is phrased in terms of the “hostility" (which quantifies the Allee threshold in relation to environmental sustainability) and dispersal adaptability (which measures how a species is able to adapt its migratory response to environmental conditions). The species- invading/retreating speed and the sharpness of the invading boundary are explicitly characterised in terms of the fundamental parameters, and analysed in detail.
[1] R. Fisher, "The wave of advance of advantageous genes," Annals of
Eugenics, vol. 7, pp. 355-369, 1937.
[2] J. Skellam, "Random dispersal in theoretical populations," Biometrika,
vol. 38, pp. 196-218, 1951.
[3] W. Gurney and R. Nisbet, Ecological dynamics. Oxford University
Press, 1998.
[4] J. Murray, Mathematical Biology. Springer-Verlag, 1993.
[5] M. Lewis and P. Kareiva, "Allee dynamics and the spread of invading
organisms," Theoretical Population Biology, vol. 43, pp. 141-158, 1993.
[6] S. Petrovskii and B.-L. Li, "An exactly solvable model of population
dynamics with density-dependent migrations and the Allee effect,"
Mathematical Biosciences, vol. 186, pp. 79-91, 2003.
[7] R. Almeida, S. Delphim, and M. da S. Costa, "A numerical model to
solve single-species invasion problems with Allee effects," Ecological
Modelling, vol. 192, pp. 601-617, 2006.
[8] W. Morris and G. Dwyer, "Population consequences of constitutive
and inducible plant resistance: herbivore spatial spread," American
Naturalist, vol. 149, pp. 1071-1090, 1997.
[9] G. Dwyer and W. Morris, "Resource-dependent dispersal and the speed
of biological invasions," American Naturalist, vol. 167, pp. 165-176,
2006.
[10] C. Taylor, H. Davis, J. Civille, F. Grevstad, and A. Hastings, "Consequences
of an Allee effect in the invasion of a Pacific estuary by spartina
alterniflora," Ecology, vol. 85, pp. 3254-3266, 2004.
[11] W. Allee, The social life of animals. New York: Norton, 1938.
[12] P. Stephens, W. Sutherland, and R. Freckelton, "What is the Allee
effect?" Oikos, vol. 87, pp. 185-190, 1999.
[13] P. Stephens and W. Sutherland, "Consequences of the Allee effect for
behaviour, ecology and conservation," Trends in Ecology and Evolution,
vol. 14, 1999.
[14] F. Courchamp, T. Clutton-Brock, and B. Grenfell, "Inverse density
dependence and the Allee effect," Trends in Ecology and Evolution,
vol. 14, pp. 405-410, 1999.
[15] D. Johnson, A. Liebhold, P. Tobin, and O. Bjornstad, "Allee effects and
pulsed invasion by the gyspy moth," Nature, vol. 444, pp. 361-363,
2006.
[16] J. Berger, "Persistence of different-sized populations: an empirical
assessment of rapid extinctions in bighorn sheep," Conservation Biology,
vol. 4, pp. 91-98, 1990.
[17] F. Courchamp and D. MacDonald, "Crucial importance of pack size in
the African wild dog lycaon pictus," Animal Conservation, vol. 4, pp.
169-174, 2001.
[18] M. Groom, "Allee effects limit population viability of an annual plant,"
American Naturalist, vol. 151, pp. 487-496, 1998.
[19] B. Lamont, P. Klinkhamer, and E. Witkowski, "Population fragmentation
may reduce fertility to zero in Banksia-Goodii: a demonstration of the
Allee effect," Oecologia, vol. 94, pp. 446-450, 1993.
[20] E. Angulo, E. Roemer, L. Berec, J. Gascoigne, and F. Courchamp,
"Double Allee effects and extinction in the island fox," Conservation
Biology, vol. 21, pp. 1082-1091, 2007.
[21] H. Davis, C. Taylor, J. Civille, and D. Strong, "An Allee effect at the
front of a plant invasion: Spartina in a Pacific estuary," Journal of
Ecology, vol. 92, pp. 321-327, 2004.
[22] S. Balasuriya and G. Gottwald, "Wavepeed in reaction-diffusion systems,
with applications to chemotaxis and population pressure," Journal of
Mathematical Biology, 2009, in press, doi: 10.1007/s00285-009-0305-4.
[23] S. Fretwell, Populations in a Seasonal Environment. Princeton, New
Jersey: Princeton University Press, 1972.
[24] W. Gurney and R. Nisbet, "The regulation of inhomogeneous population,"
Journal of Theoretical Biology, vol. 52, pp. 441-457, 1975.
[25] N. Shigesada, K. Kawasaki, and E. Teramoto, "Spatial segregation of
interacting species," Journal of Theoretical Biology, vol. 79, pp. 83-99,
1979.
[26] D. Morris and J. Diffendorfer, "Reciprocating dispersal by habitatselecting
white-footed mice," Oikos, vol. 107, pp. 549-558, 2004.
[27] Wolfram Research Inc., Mathematica, 5th ed. Champaign, Illinois:
Wolfram Research, Inc., 2005.
[1] R. Fisher, "The wave of advance of advantageous genes," Annals of
Eugenics, vol. 7, pp. 355-369, 1937.
[2] J. Skellam, "Random dispersal in theoretical populations," Biometrika,
vol. 38, pp. 196-218, 1951.
[3] W. Gurney and R. Nisbet, Ecological dynamics. Oxford University
Press, 1998.
[4] J. Murray, Mathematical Biology. Springer-Verlag, 1993.
[5] M. Lewis and P. Kareiva, "Allee dynamics and the spread of invading
organisms," Theoretical Population Biology, vol. 43, pp. 141-158, 1993.
[6] S. Petrovskii and B.-L. Li, "An exactly solvable model of population
dynamics with density-dependent migrations and the Allee effect,"
Mathematical Biosciences, vol. 186, pp. 79-91, 2003.
[7] R. Almeida, S. Delphim, and M. da S. Costa, "A numerical model to
solve single-species invasion problems with Allee effects," Ecological
Modelling, vol. 192, pp. 601-617, 2006.
[8] W. Morris and G. Dwyer, "Population consequences of constitutive
and inducible plant resistance: herbivore spatial spread," American
Naturalist, vol. 149, pp. 1071-1090, 1997.
[9] G. Dwyer and W. Morris, "Resource-dependent dispersal and the speed
of biological invasions," American Naturalist, vol. 167, pp. 165-176,
2006.
[10] C. Taylor, H. Davis, J. Civille, F. Grevstad, and A. Hastings, "Consequences
of an Allee effect in the invasion of a Pacific estuary by spartina
alterniflora," Ecology, vol. 85, pp. 3254-3266, 2004.
[11] W. Allee, The social life of animals. New York: Norton, 1938.
[12] P. Stephens, W. Sutherland, and R. Freckelton, "What is the Allee
effect?" Oikos, vol. 87, pp. 185-190, 1999.
[13] P. Stephens and W. Sutherland, "Consequences of the Allee effect for
behaviour, ecology and conservation," Trends in Ecology and Evolution,
vol. 14, 1999.
[14] F. Courchamp, T. Clutton-Brock, and B. Grenfell, "Inverse density
dependence and the Allee effect," Trends in Ecology and Evolution,
vol. 14, pp. 405-410, 1999.
[15] D. Johnson, A. Liebhold, P. Tobin, and O. Bjornstad, "Allee effects and
pulsed invasion by the gyspy moth," Nature, vol. 444, pp. 361-363,
2006.
[16] J. Berger, "Persistence of different-sized populations: an empirical
assessment of rapid extinctions in bighorn sheep," Conservation Biology,
vol. 4, pp. 91-98, 1990.
[17] F. Courchamp and D. MacDonald, "Crucial importance of pack size in
the African wild dog lycaon pictus," Animal Conservation, vol. 4, pp.
169-174, 2001.
[18] M. Groom, "Allee effects limit population viability of an annual plant,"
American Naturalist, vol. 151, pp. 487-496, 1998.
[19] B. Lamont, P. Klinkhamer, and E. Witkowski, "Population fragmentation
may reduce fertility to zero in Banksia-Goodii: a demonstration of the
Allee effect," Oecologia, vol. 94, pp. 446-450, 1993.
[20] E. Angulo, E. Roemer, L. Berec, J. Gascoigne, and F. Courchamp,
"Double Allee effects and extinction in the island fox," Conservation
Biology, vol. 21, pp. 1082-1091, 2007.
[21] H. Davis, C. Taylor, J. Civille, and D. Strong, "An Allee effect at the
front of a plant invasion: Spartina in a Pacific estuary," Journal of
Ecology, vol. 92, pp. 321-327, 2004.
[22] S. Balasuriya and G. Gottwald, "Wavepeed in reaction-diffusion systems,
with applications to chemotaxis and population pressure," Journal of
Mathematical Biology, 2009, in press, doi: 10.1007/s00285-009-0305-4.
[23] S. Fretwell, Populations in a Seasonal Environment. Princeton, New
Jersey: Princeton University Press, 1972.
[24] W. Gurney and R. Nisbet, "The regulation of inhomogeneous population,"
Journal of Theoretical Biology, vol. 52, pp. 441-457, 1975.
[25] N. Shigesada, K. Kawasaki, and E. Teramoto, "Spatial segregation of
interacting species," Journal of Theoretical Biology, vol. 79, pp. 83-99,
1979.
[26] D. Morris and J. Diffendorfer, "Reciprocating dispersal by habitatselecting
white-footed mice," Oikos, vol. 107, pp. 549-558, 2004.
[27] Wolfram Research Inc., Mathematica, 5th ed. Champaign, Illinois:
Wolfram Research, Inc., 2005.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:61437", author = "Sanjeeva Balasuriya", title = "Species Spreading due to Environmental Hostility, Dispersal Adaptation and Allee Effects", abstract = "A phenomenological model for species spreading which incorporates the Allee effect, a species- maximum attainable growth rate, collective dispersal rate and dispersal adaptability is presented. This builds on a well-established reaction-diffusion model for spatial spreading of invading organisms. The model is phrased in terms of the “hostility" (which quantifies the Allee threshold in relation to environmental sustainability) and dispersal adaptability (which measures how a species is able to adapt its migratory response to environmental conditions). The species- invading/retreating speed and the sharpness of the invading boundary are explicitly characterised in terms of the fundamental parameters, and analysed in detail.
", keywords = "Allee effect, dispersal, migration speed, diffusion, invasion.", volume = "4", number = "5", pages = "606-7", }
