Biology Reference
In-Depth Information
A
500
400
300
200
100
0.3
1
0.2
0.5
0.1
0
0
B
500
400
300
200
100
0.3
1
0.2
0.5
0.1
0
0
Fuzzy Fuzzy each generation randomised. A:
r
x
=
1.6667, B:
r
x
=
2.6667
Figure 3.3. Fuzzy chaos modelling is based on the assumption that populations consist
of subpopulations that are largely separate and differ in their reproductive rates. In this
example, we apply fuzzy chaos modelling to two interacting species. Each species is
assumed to consist of 10 subpopulations with different reproductive rates. The ranges
of the reproductive rates of species x and z, r
x
and r
z
(indicative of the heterogeneity of
the metapopulations) are plotted against alpha and beta (the competition factors of
both species), and the time of extinction in number of generations. The initial
population sizes of species x and z, x
0
and z
0
¼
0.5. The reproductive rate of species z,
r
z
¼
3.7. In A, r
x
¼
1.6667, in B, r
x
¼
2.6667. Stochastic variability over time of both
species r
t
¼
0.01. Extinction of species x is indicated by hollow, of species z by grey,
no extinction by blank. Note that a minor difference in alpha and beta can lead to a
dramatic difference in the outcome of competition. Programs and algorithms for the
programs can be found on www-personal.une.edu.au/
krohde/ (fuzzy/fuzzy chaos,
2 and 3 species competition).
