Environmental Engineering Reference
In-Depth Information
2
δ
3
1.5
2.5
.........
1.0
_____
0.5
2
1.5
1
0.5
σ
R
R
0.25 0.5 0.75
1
1.25 1.5 1.75
2
Figure 4.7. Biodiversity potential as a function of the CV, CV
=
σ
R
/
R
,ofenvi-
ronmental noise, calculated with
β
=
1,
R
gamma distributed with mean,
R
=
3,
and
a
=
0
.
11, i.e.,
P
lim
=
a
/
(
a
+
β
)
=
0
.
1(after
D'Odorico et al.
,
2008
).
species with fitness range
δ
remain unstressed for a sufficient fraction of time to
R
u
−
R
l
),
avoid extinction. If
is an indicator
of the biodiversity that could be sustained in the ecosystem, i.e., of the
potential for
biodiversity
. Larger values of
is the interval width (i.e.,
=
/δ
are associated with a broader range of species
that would be able to have access to environmental conditions favorable to growth
and survival. The exact number of species, of course, depends on a number of other
factors, including the value of
/δ
, the presence of other limiting factors, and the
competitive and facilitative interactions among species. However, with all the other
factors being the same, species biodiversity is expected to increase with
R
/δ
. Thus
/δ
is not exactly the number of species coexisting in the system (as it would be
in the case of nonoverlapping niches) but a measure of the ability of the system to
maintain biodiversity. The biodiversity potential
depends in general on the width
of the fitness window
δ
, the probability distribution of
R
, and the parameters
a
1
,
a
2
,
and
of vegetation dynamics. Notice how when the variance of
R
is zero the process
becomes deterministic with
R
β
.
We can first investigate the effect of noise (i.e., environmental variability) on bio-
diversity in the absence of interspecific interactions. We keep constant the values of
the parameters
a
,
=
R
. In this case the amplitude
tends to 2
δ
β
,and
R
, and study the dependence of biodiversity potential on
the standard deviation
σ
R
of
R
. The results are shown in Fig.
4.7
for different values
of the fitness range
. It is found that environmental noise has two major effects:
(i) with moderate levels of noise intensity (i.e., of CV
δ
) environmental
fluctuations enhance the system's potential for biodiversity with respect to the de-
terministic case
=
σ
R
/
R
=
2
δ
(i.e.,
>
2
δ
); (ii) with relatively large noise intensities,
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