Matrix Analyzing Models
ESM 211 Nov. 8, 2006
Projecting the model
Semipalmated Sandpiper in Manitoba Three age classes Initial age distribution (#/ha):
23.5 N(0) 14.2 7.3
Projection matrix:
A 0.02115 0.074 0.0846 0.563 0 0 0 0.563 0.563
Iterate the model:
N(t 1) AN (t )
15
20
0
5
10
1 2 3
N
0
5
10 Year
15
20
N 1 e-03
0 5 10 15 1 2 3 20 Year
1 e-02
1 e-01
1 e+00
1 e+01
Asymptotic growth rate
When population reaches stable age (or size or stage) distribution then all classes grow (or decline) at the same rate: N(t 1) 1N(t )
lambda_1 = Class 1 2 3 0.6389479 Reproductive value 1 1.097332 1.113922
Stable distribution 0.11886...
Analyzing matrix models 06