Biology Reference
In-Depth Information
C
1.0
A
B
3.74
x
3.63
3.84
0
3.50
3.58
3.66
3.74
3.82
3.90
r
Figure 1.3. Fuzzy chaos modelling. In such models it is assumed that a metapopulation
consists of subpopulations differing in reproductive rates. The degree of chaos
depends on the number of subpopulations, the range of their reproductive rates, and
the initial size of the metapopulation. In the example illustrated here, the initial
population size x
0
¼
10
2
, the number of subpopulations
¼
1000, and the range of
reproductive values r
¼
10
2
. Note that the chaotic band has contracted compared
with Figure
1.2
, but there is still chaos and at various values of r there are bifurcations
indicating more than one widely diverging point of equilibrium.
is the narrower the more subpopulations are there (Figure
1.3
). However,
chaos still occurs and conditions are largely unpredictable, partly due to the
fact that bifurcations with more than one equilibrium point arise at certain
values of r.
In conclusion, the last two sections have shown that sometimes there is
evidence for long-lasting equilibrium conditions (or long-lasting relative
constancy in population size) in certain populations. However, severe and
apparently irregular fluctuations in population size are common among
plants and animals, although reasons for such fluctuations are in many
cases little understood. Both in populations and metapopulations, envir-
onmental disruptions are important in causing nonequilibrium, although
nonequilibrium can arise even in the absence of disturbances.
Defining the problem
We can use the excellent discussion of Rosenzweig (
1995
) as a starting
point for defining the problem discussed in this topic. His discussion of
