Environmental Engineering Reference
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simply cannot compensate for the extra mortality caused by our actions. This is
made clearer in the next example.
Cortes (2002) has explored, using a mathematical modeling approach, the rela-
tionship for 38 shark species between body size, age at which maturity is reached,
generation time and the annual rate of population increase (
is essentially the
multiplier that converts the population size of one generation into the population
size of the next generation. Populations increase when
λ
).
λ
λ
>
1 and decrease when
λ
<
1.
A three-dimensional plot of
against generation time and age at maturity shows
what Cortes calls a 'fast-slow' continuum, with species characterized by early age
at maturity, short generation times and generally high
λ
at the fast end of the spec-
trum (bottom right hand corner of Figure 3.6a). Species at the slow end of the
spectrum displayed the opposite pattern (left of Figure 3.6a) and also tended to be
large bodied (Figure 3.6b). Cortes then assessed the various species' ability to
respond to increased mortality due, for example, to pollution or harvesting. 'Fast'
sharks, such as
Sphyrna tiburo
, could compensate for a 10% increase in mortality
rate by increasing birth rate. On the other hand, particular care must be taken when
considering the state of generally large, slow-growing, long-lived species, such as
Carcharhinus leucas
. Here, even moderate increases in mortality require a level of
compensation in the form of successful reproduction that the species simply cannot
provide.
Skates and rays (Rajidae) provide a graphic illustration of Cortes' warning. Of the
world's 230 species, only four are known to have undergone local extinctions and
signifi cant range reduction (Figure 3.7a-d). These are among the largest of their
group (Figure 3.7e) and Dulvy and Reynolds (2002) propose that seven further
species, each as large or larger than the locally extinct taxa, need to be carefully
monitored in future.
λ
(a)
(b)
1.6
1.6
1.4
1.4
1.2
1.2
λ
λ
40
32
24
40
32
24
1.0
1.0
16
16
0.8
0.8
50
40
8
600
8
30
450
20
300
0
10
0
150
0
0
Fig. 3.6
Mean population growth rates λ of 41 populations from 38 species of shark in relation to (a) age at maturity and
generation time and (b) age at maturity and total body length. Populations increase in size when λ > 1 and decrease when
λ < 1. (After Cortes, 2002.)
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