13th International Conference on Membrane Computing - MTA Sztaki

M.A. Martínez-del-Amor, I. Pérez-Hurtado, M. García-Quismondo,
L.F. Macías-Ramos, L. Valencia-Cabrera, A. Romero-Jiménez, C. Graciani,
A. Riscos-Núñez, M.A. Colomer, M.J. Pérez-Jiménez
The species are the following:
• Bearded Vulture (i = 1)
• Pyrenean Chamois (i = 2)
• Female Red Deer (i = 3)
• Male Red Deer (i = 4)
• Fallow Deer (i = 5)
• Roe Deer (i = 6)
• Sheep (i = 7)
Note that although the male red deer and female red deer are the same
species, we consider them as different species. This is because mortality of
male deer is different from the female deer by reason of hunting.
– Σ = ∅.
– Each year in the real ecosystem is simulated by 3 computational steps, so
T = 3 · Y ears, where Y ears is the number of years to simulate.
– R E = ∅.
– µ = [ [ ] 2 ] 1 is the membrane structure and the corresponding initial multisets
are:
• M 1 = { X qi,j
i,j : 1 ≤ i ≤ 7, 0 ≤ j ≤ k i,4 }
• M 2 = { C, B α k∑
1,4
} where α = ⌈ q 1,j · 1.10 · 682⌉
j=1
Value α represents an external contribution of food which is added during
the first year of study so that the Bearded Vulture survives. In the
formula, q 1,j represents the number of bearded vultures that are j years
old, the goal of the constant factor 1.10 is to guarantee enough food for
10% population growth. At present, the population growth is estimated
an average 4%, but this value can reach higher values. Thus, to avoid
problems related with the underestimation of this value the first year we
have overestimated the population growth at 10%. The constant value
682 represents the amount of food needed per year for a Bearded Vulture
pair to survive.
– The set R is defined as follows:
• Reproduction rules for ungulates
Adult males
r 0,i,j ≡ [X i,j ] 1
1−k i,13
−−−→[Yi,j ] 1 : k i,2 ≤ j ≤ k i,4 , 2 ≤ i ≤ 7
Adult females that reproduce
r 1,i,j ≡ [X i,j ] 1
k i,5 k i,13
−−−→[Yi,j , Y i,0 ] 1 : k i,2 ≤ j < k i,3 , 2 ≤ i ≤ 7, i ≠ 3
Red Deer females produce 50% of female and 50% of male springs
r 2,j ≡ [X 3,j ] 1
k 3,5 k 3,13 0.5
−−−→ [Y 3,j Y 3,0 ] 1 : k 3,2 ≤ j < k 3,3
r 3,j ≡ [X 3,j ] 1
k 3,5 k 3,13 0.5
−−−→ [Y 3,j Y 4,0 ] 1 : k 3,2 ≤ j < k 3,3
Fertile adult females that do not reproduce
(1−k i,5 )k i,13
r 4,i,j ≡ [X i,j ] 1 −−−→ [Yi,j ] 1 : k i,2 ≤ j < k i,3 , 2 ≤ i ≤ 7
Not fertile adult females
r 5,i,j ≡ [X i,j ] 1
k i,13
−−−→[Yi,j ] 1 : k i,3 ≤ j ≤ k i,4 , 2 ≤ i ≤ 7
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