M7116 Maticové populační modely
Populace s interní variabilitou - bifurkační diagramy
18.5.2015
Leslieho model s plodností závislou na velikosti populace
f Tlx
n2 j (í + 1) =
\n3 '
( 0     g(N(t)) bg(N(t))
0.3 0 0 V 0        0.5 0
/ ni n2 I (í)
\ri3
N = m + ri2 + 7i3,   ô'(^V) = i?e
0.005AT
Leslieho model s plodností závislou na velikosti populace
f Tlx
n2 I (í + 1) =
\n3
( 0     g(N(t)) bg(N(t))
0.3 0 0 V 0        0.5 0
N = m + ri2 + 7i3,   ô'(^V) = ite'
0.005AT
o
o o
o m
o o H
o m
Ä = 3
1 o
I
20
—r~
30
40
50
60
Leslieho model s plodností závislou na velikosti populace
/ Tli
T12 J (t+1) =
( 0    g(N(t)) Sg(N(ť))
0.3 0 0 V 0        0.5 0
N = m + ri2 + n3,   g(iV) = i?e
0.005AT
o o
(M
O O O
O O
00
O
o
CD
O O
O O
I   I   I   I   I  I  I I
I   I   I   I   I   I   I   I I
R =15
"T" 10
20
30 t
40
50
60
Leslieho model s plodností závislou na velikosti populace
nA / 0    g(N(t)) 5g(N(t))\
n2   (í +1) =   0.3        0 0 m) \ 0       0.5 0 y
(t).
7V = ni+n2+n3,   g(N) = Re
-0.005ÍV
O O
Ä = 45
t
Leslieho model s plodností závislou na velikosti populace
f Tlx
n2 I (í + 1) =
\n3
( 0     g(N(t)) bg(N(t))
0.3 0 0 V 0        0.5 0
N = m + ri2 + 7i3,   ô'(^V) = ite'
0.005AT
o o o m
o o o o
o o o m
R = 250
"n 1 o
i
20
—r~
30
40
50
60
t
Leslieho model s plodností závislou na velikosti populace
f Tlx
n2 I (í + 1) =
\n3
( 0     g(N(t)) bg(N(t))
0.3 0 0 V 0        0.5 0
N = m + ri2 + 7i3,   ô'(^V) = ite'
0.005AT
o
§ H m
o o o o
o o o m
50
100
150
200
250
R
Model kanibalismu
L(t + 1) = bA(t) exp {-ceaA(t) - ceiL(ť)} P(t + l) = (l-fJn)L(t)
A(t + 1) = exp {-cpaA(t)} P(t) + (1 - /ia)A(í)
L, P, A ... množství larev, kukel a dospělců
b ... počet vajíček jedné dospělé samice za projekční interval
in, /jLa ■ ■ ■ přirozená úmrtnost larev a dospělců
cea, cez, cpa ... „míry kanibalismu"
Model kanibalismu
L{t + 1) = bA(ť) exp {-ceaA{ť) - celL(t)} P(í + 1) = (l-fn)L(t)
A(t + 1) = exp {-cPaA(í)} P(t) + (1 - /Xa)A(í)
6 — 50, /JLl — 0.5, /Xa — 0.3, Cea = 0, Cpa = 0, CeZ
o o o
o o
00
< a:
o o
CD
O O
o
o -
Model kanibalismu
L(t + 1) = bA(t) exp {-ceaA(ť) - celL(t)} P(í + 1) = (l-w)L(t)
A(t + 1) = exp {-cpaA{t)} P(t) + (1 - iia)A{b)
b — 50, fll — 0.5, /ia = 0.3, cea = 5, cpa — 0, cez G [0,10]
larvae
2 4 6 8
c_el
pupae
2 4 6 8 10
c_el
adults
0 2 4 6 8 10
Model kanibalismu
L(t + 1) = bA(t) exp {-ceaA(t) - ceZL(í)} P(í + 1) = (l-fii)L(t)
A(t + 1) = exp {-cpaA(t)} P(t) + (1 - Ha)A(t)
b — 50, /iř — 0.5, [la — 0.3, Cea = 5, Cpa = 0, Cel = 0
larvae
0 20 40 60
t
pupae
0-
20 40
t
adults
0 20 40 60
t
Model kanibalismu
L{t + 1) = bA(t) exp {-ceaA(t) - ceZL(í)} P(t + l) = (l-/xi)L(t)
A(t + 1) = exp {-cpaA(t)} P(í) + (1 - Ma)A(t)
6 — 50, /iř — 0.5, /ia — 0.3, Cea — 5, Cpa — 0, Cel — 1
larvae
20
40
"T"
60
"T"
80
100
pupae
o
o o
20
40
60
80
100
adults
CO
o
~r~
20
I
40
I
60
"T"
80
100
Model kanibalismu
L(t + 1) = bA(t) exp {-ceaA(t) - ceiL(ť)}
p{t +1) = (i - m)L(t)
A(t + 1) = exp {-cpaA(í)} P(í) + (1 - /ia)A(í)
b — 50, /iř — 0.5, IIa — 0.3, Cea — 5, Cpa = 0, Cel — 1
co o
o
o o
larvae
100
200
300
400
500
pupae
o
o
o o
T
T"
100
200 300 t
400
500
adults
o
d
o
100
200
300
400
500
t
Model kanibalismu
L(t + 1) = bA(t) exp {-ceaA(ť) - celL(t)}
P(t+l) = (l-fJLi)L(t)
A(t + 1) = exp {-cpaA(í)} P(í) + (1 - Ha)A(t)
b — 50, 111 — 0.5, /ia — 0.3, Cea = 5, Cpa = 0,
Cel — 2
Model kanibalismu
L(t + 1) = bA(t) exp {-ceaA(t) - ceZL(í)} P(í + 1) = (l-fii)L(t)
A(t + 1) = exp {-cpaA(t)} P(t) + (1 - Ha)A(t)
b — 50, /ij — 0.5, [la — 0.3, Cea = 5, Cpa = 0, Cel = 6
o c\i
larvae
20
40
60
pupae
"T"
20
40
60
adults
o
20
40
60
Model kanibalismu
L(t + 1) = bA(t) exp {-ceaA(t) - ceZL(í)} P(í + 1) = (l-fii)L(t)
A(t + 1) = exp {-cpaA(t)} P(t) + (1 - Ha)A(t)
b — 50, /ij — 0.5, [la — 0.3, Cea = 5, Cpa = 0, Cel = 8
larvae
0-
0 20 40
t
adults
<
b _l—i-1-1 r
0 20 40 60