# Competitive Exclusion in a Discrete Stage-Structured Two Species Model

Mathematical Modelling of Natural Phenomena (2009)

- Volume: 4, Issue: 6, page 156-175
- ISSN: 0973-5348

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topAckleh, A. S., and Zhang, P.. "Competitive Exclusion in a Discrete Stage-Structured Two Species Model." Mathematical Modelling of Natural Phenomena 4.6 (2009): 156-175. <http://eudml.org/doc/222295>.

@article{Ackleh2009,

abstract = {
We develop a stage-structured model that
describes the dynamics of two competing species each of which have sexual
and clonal reproduction. This is typical of many plants including irises.
We first analyze the dynamical behavior of a single species model. We show
that when the inherent net reproductive number is smaller than one then the
population will go to extinction and if it is larger than one then
an interior equilibrium exists and it is globally asymptotically
stable. Then we analyze the two-species model and establish
conditions on the reproduction and survivorship rates that lead to competitive exclusion. We show that
the winner species is the one that attains higher density at which its net reproductive number equals unity.
Numerical results corroborating the theoretical ones are also presented.
},

author = {Ackleh, A. S., Zhang, P.},

journal = {Mathematical Modelling of Natural Phenomena},

keywords = {stage-structured model; net
reproductive number; competitive exclusion; net reproductive number},

language = {eng},

month = {11},

number = {6},

pages = {156-175},

publisher = {EDP Sciences},

title = {Competitive Exclusion in a Discrete Stage-Structured Two Species Model},

url = {http://eudml.org/doc/222295},

volume = {4},

year = {2009},

}

TY - JOUR

AU - Ackleh, A. S.

AU - Zhang, P.

TI - Competitive Exclusion in a Discrete Stage-Structured Two Species Model

JO - Mathematical Modelling of Natural Phenomena

DA - 2009/11//

PB - EDP Sciences

VL - 4

IS - 6

SP - 156

EP - 175

AB -
We develop a stage-structured model that
describes the dynamics of two competing species each of which have sexual
and clonal reproduction. This is typical of many plants including irises.
We first analyze the dynamical behavior of a single species model. We show
that when the inherent net reproductive number is smaller than one then the
population will go to extinction and if it is larger than one then
an interior equilibrium exists and it is globally asymptotically
stable. Then we analyze the two-species model and establish
conditions on the reproduction and survivorship rates that lead to competitive exclusion. We show that
the winner species is the one that attains higher density at which its net reproductive number equals unity.
Numerical results corroborating the theoretical ones are also presented.

LA - eng

KW - stage-structured model; net
reproductive number; competitive exclusion; net reproductive number

UR - http://eudml.org/doc/222295

ER -

## References

top- A.S. Ackleh, P. DeLeenheer. Discrete three-stage population model: persistence and global stability results.J. Biol. Dyn., 2 (2008), 415–427.
- L.J.S. Allen. Introduction to mathematical biology. New Jersey. Prentice Hall, 2007.
- R.J.H. Beverton, S.J. Holt. On the dynamics of exploited fish populations. London. Fishery Investigations Series 2(19), Ministry of Agriculture, Fisheries and Food, 1957.
- H. Caswell. Matrix population models. 2nd Edition. Sunderland. Sinauer, 2001.
- J.M. Cushing. An introduction to structured population dynamics. Philadelphia. SIAM, 1998.
- J. M. Cushing, S. Levarge, N. Chitnis, S. M. Henson. Some discrete competition models and the competitive exclusion principle.J. Diff. Equa. Appl., 10 (2004), 1139-1151.
- J.M. Cushing, Z.Yicang. The net reproductive value and stability in matrix population models.Nat. Res. Mod., 8 (1994), 297–333.
- S. Elaydi. An introduction to difference equations. 3rd Edition. New York. Springer, 2005.
- S.B. Hsu, H.L. Smith, P. Waltman. Competitive exclusion and coexistence for competitive systems on ordered banach spaces. Trans. Amer. Math. Soci., 348(1996), 4083–4094.
- S. Pathikonda, A.S. Ackleh, K.H. Hasenstein, S. Mopper. Invasion, disturbance, and competition: modeling the fate of coastal plant populations. J. Cons. Biol., 23(2009), 164–173.
- W. Sutherland. Biological flora of the British Isles: Iris pseudacorus L. J. Eco., 78(1990), 833–848.
- W. Sutherland, D. Walton. The changes in morphology and demography of Iris pseudacorus L. at different heights on a saltmarsh. Func. Eco., 4(1990), 655–659.
- M. Tobler, P.V. Zandt, K. Hasenstein, S. Mopper. Above and belowground allocation in the wetland perennial, Iris hexagona: effects of population, salinity, and vertebrate florivory. Wetlands., 26(2006), 803–812.
- P. Viosca, Jr. The iries of southeastern Louisiana: a taxonomic and ecological interpretation. J. Amer. Iris. Soc., 57(1935), 3–56.

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