AICME II abstracts
Demography and Dispersal: Integrating Spatial ...
Diomar Cristina Mistro1 , Luiz Alberto D´ıaz Rodrigues2 and Andr´eia Beatriz Schmid3 . Previous models for annual plant dispersion [1, 2, 4] have not take into account the germination of seedbank. Based on the integro-difference model developed by Andersen [2] and the difference model developed by Edelstein-Keshet [3], we formulate an integro-difference equation model for an annual plant population, of which a proportion of seeds remains dormant for two years, i. e., annual plant population with a seed bank. The non-dimensional model takes the form St+1 (x) = A
Ω
k(x − y)Ut (y)dy + AB
Z
Ω
k(x − y)Ut−1 (y)dy
(1)
and Ut+1 (x) = St+1 (x) exp (−St+1 (x)) ,
(2)
where St (x) is the non-dimensional seedling density at the position x in generation t after the dispersion of seeds of the previous two generations of t (x) plants and Ut (x) = Pa/b , describes the non-dimensional density of adults after the density-dependence acts on the seedlings of generation t. The parameters βσ(1 − α) , (3) A = aασγ and B= α describes the density of one year old seeds that survive the winter and germinate and, the ratio of the two years old seeds and the one year’s that germinate, respectively.
References [1] E.J.Allen, L.J.S. Allen and G. Xiaoning, 1996, Dispersal and Competition Models for Plants, Journal of Mathematical Biology, 34: 455481. [2] M. Andersen, Properties of Some Density-Dependent Integrodifference Equation Population Models, 1991, Mathematical Biosciences, 104: 135-157. [3] L. Edelstein-Keshet, ”Mathematical Models in Biology”, Random House, New York, 1988. [4] D.R. Hart and R.H. Gardner, 1997, A Spatial Model for the Spread of Invading Organisms Subject to Competition, Journal of Mathematical Biology, 35: 935-948. [5] D.C. Mistro, L.A.D. Rodrigues, and A.B. Schmid, 2003, An Integrodifference Equation Model for Annual Plant with Seed Bank Dispersion. Preprint.
1
Departamento de Matem´ atica, Universidade Federal de Santa Maria, Campus Camobi, CEP 97105-900, Santa Maria, Brasil (e-mail:
[email protected]). 2 Departamento de Matem´ atica, Universidade Federal de Santa Maria, Campus Camobi, CEP 97105-900, Santa Maria, Brasil (e-mail:
[email protected]). 3 Bolsista de Inicia¸c˜ ao Cient´ıfica - FAPERGS (e-mail:
[email protected]).
04-Mis-a
AICME II abstracts
We show [5] that the seed bank is fundamental in the dynamics of annual plants, it can exert both a damping (stabilizing) effect and a destabilizing effect, depending on the parameters A and B. We determine numerically the regions of the parameters where the model predicts stable, cyclical and chaotic asymptotic behavior. We also show that, in homogeneous habitat, the seed bank doesn’t influence the speed of invasion of new regions.
An Annual Plant with Seed Bank Dispersal Model
Z
Demography and Dispersal: Integrating Spatial ...
04-Mis-b
