Organisation at Population Level 31
• For N = K, the variation of population size becomes zero; the population is stabilized
• For N > K, the size of N decreases until N = K
Therefore, the value of K is the maximum size of the population which can
survive in a given environment. It is called carrying capacity of the environment, and its value is defined every moment by the current limiting factor
(Chapter 4, Section 4.2), because it is the manifestation of its action in the
particular situation. Potential elimination of the limiting factor would lead
to exponential increase and a possible population boom. In the case of a new
limiting factor emergence, the system returns to a self-limiting increase but
with a different carrying capacity. With the occurrence either of a change in
natural conditions or an appropriate human interference over the course of
time, a succession of limiting factors and corresponding carrying capacities
will appear.
The integration of the logistic model (for stable K) gives:
N
K
K N
e
rt
= + (
) −
−
1
1
0
The logistic model gives, in many cases, a satisfactory description of
the population variations encountered in nature. Such an example is the
increase of unicellular organisms with a small life span and great reproduction speed. However, in most cases of natural populations the variation is
more complex and difficult to interpret. Nevertheless, the logistic model, as
also the exponential one, has many applications in population dynamics.
0
t
N
K
Figure 3.6 Logistic increase. (From Hadjibiros 2007. Ecology. Ecosystems and Environmental
Protection, 3rd edition. Symmetria, Athens. With permission.)
• For N = K, the variation of population size becomes zero; the population is stabilized
• For N > K, the size of N decreases until N = K
Therefore, the value of K is the maximum size of the population which can
survive in a given environment. It is called carrying capacity of the environment, and its value is defined every moment by the current limiting factor
(Chapter 4, Section 4.2), because it is the manifestation of its action in the
particular situation. Potential elimination of the limiting factor would lead
to exponential increase and a possible population boom. In the case of a new
limiting factor emergence, the system returns to a self-limiting increase but
with a different carrying capacity. With the occurrence either of a change in
natural conditions or an appropriate human interference over the course of
time, a succession of limiting factors and corresponding carrying capacities
will appear.
The integration of the logistic model (for stable K) gives:
N
K
K N
e
rt
= + (
) −
−
1
1
0
The logistic model gives, in many cases, a satisfactory description of
the population variations encountered in nature. Such an example is the
increase of unicellular organisms with a small life span and great reproduction speed. However, in most cases of natural populations the variation is
more complex and difficult to interpret. Nevertheless, the logistic model, as
also the exponential one, has many applications in population dynamics.
0
t
N
K
Figure 3.6 Logistic increase. (From Hadjibiros 2007. Ecology. Ecosystems and Environmental
Protection, 3rd edition. Symmetria, Athens. With permission.)