Environmental Engineering Reference
In-Depth Information
0.5
0.4
0.3
0.2
0.1
0
0
20
40
60
Seedling density (m
-2
)
Fig. 2.14
The growing heart of the palm
Euterpe edulis
is cut to provide the
Brazilian delicacy palmito, killing the plant. In order to model the impacts of
harvest, it is important to define the crucial density dependent processes in a
population, achieved in this case by fitting a Beverton-Holt function to
seedling density and survival data.
Source:
Silva Matos
et al
. (1999). Photo © Henrik Balsler
the breeders (for example, through cannibalism or competition for spawning
sites), while the Beverton-Holt function is more appropriate if the density of juve-
niles affects their own mortality rate (for example, through direct competition for
food). The functions can also be applied broadly to any survival or productivity
rate and abundance data. For example, Silva Matos
et al
. (1999) studied the
demography of a harvested palm,
Euterpe edulis
, in the Atlantic forest of Brazil,
finding that the key point of density-dependent regulation was seedling competi-
tion (Figure 2.14). They found this by monitoring the density and survivorship
of seedlings in 100 1 m
2
50 m
2
. A
Beverton-Holt function was fitted to the seedling survival data from the plots,
giving a maximum survival rate estimate (
plots, with densities ranging from 0 to
max
) of 0.486 (SE 0.024), and a rate of
decline (
b
) of 0.307 (SE 0.029).
The most important problem to be aware of in any of these approaches is bias
resulting from observation error. To understand this bias, imagine a series of
abundance estimates taken from an essentially density-independent population.
Whenever census error leads to a mistakenly high observed abundance, the fol-
lowing growth rate estimate will be biased low, leading to a spurious negative cor-
relation between abundance and growth rate and general over-estimation of the
strength of density dependence. The same principle applies to estimates of dens-
ity dependence in survival or productivity. This bias can be corrected if the degree
of observation error is known, either through formal statistical methods based on
sampling or, if no sampling has been used, through repeated surveys of the same
population to measure the error directly. Alternatively, promising simulation
methods that may help are now becoming available. Freckleton
et al
. (2006)
provide a detailed review of this problem and how to deal with it.
