Environmental Engineering Reference
In-Depth Information
(a)
(b)
(c)
Stabilizes - fluctuating
around carrying capacity
Carrying capacity
Number of
births
Environmental
brakes applied
Added to
population
Exponential
phase
Number
dying
K
0
K
Time
Density
Density
Fig. 7.1 (a) Logistic population growth in which population size increases exponentially at
fi rst but as numbers increase with time the rate of increase fi rst slows down and then
stabilizes around the carrying capacity. The environmental brakes are supplied by density-
dependent factors, such as competition for food or risk of predation, which, at high density,
reduce the per capita birth rate and/or increase the per capita death rate. (b) When time is
replaced by population density on the horizontal axis, the patterns in numbers of births and
deaths at each density can be highlighted. The difference between the birth and death curves
gives us the number of individuals actually added to the population in a unit of time when
the population is at a given density. (If there are more births than deaths a net surplus is
produced.) Largest numbers are added to the population at some intermediate density, when
there are plenty of individuals to produce offspring and density-dependent factors are not yet
fully in operation. As density increases further, the number added per unit time declines
until fi nally the birth and death curves cross. At this point, the number of births is exactly
matched by the number of deaths and the population stabilizes (at K the carrying capacity).
(c) This fi gure shows net recruitment (surplus of births over deaths) per unit time at
different densities. Net recruitment is greatest at some intermediate density (see how the
longest arrows in (b) are at intermediate densities) and declines to zero at K .
rate and dropping its death rate - producing a surplus that can be harvested without further reduc-
ing the population. It is in this sense that the harvest is sustainable.
The maximum sustainable yield (MSY) - putting theory into practice
The ideal harvesting operation takes neither too little nor too much. Consider Figure 7.1c and decide
what would constitute the maximum sustainable harvest. Yes, the maximum is obtained by harvest-
ing at the density where net recruitment is itself maximal - the highest point on the curve. For a
perfect 'logistic' curve this occurs when density is 50% of carrying capacity K . But in real popula-
tions, the shape of the curve is not necessarily symmetrical. In large mammals, for example, the
maximum yield occurs at a density only slightly less than K . However, the maximum sustainable
yield is always at a density that is less than K .
Let's ignore for now some real diffi culties in devising a harvesting strategy, such as how to
determine the precise relationships between net recruitment and density for real populations.
Assuming you know the MSY, how c an you arrange to harvest it without danger to the population?
Two related methods are to take a fi xed quota each year (i.e. the calculated MSY) or to apply a
fi x e d e f f o r t ( i n terms of numbers of exploiters and time spent hunting or fi shing) set so as to achieve
the MSY.
Fixed quota
Harvesting at a fi xed rate (i.e. a fi xed number of individuals removed during a given period of time),
otherwise known as 'taking a fi x e d quota ', is sustainable if the harvesting rate line crosses the net
recruitment curve. When these lines cross, harvesting and recruitment rates are equal and opposite
and the number removed per unit time by the harvester equals the number recruited per unit time
by the population. In Figure 7.2 three different harvesting rates are illustrated (horizontal dotted
lines). The highest of these ( H H ) is to be avoided at all costs. When harvesting rate is greater
than even the maximum recruitment rate, the population is doomed to extinction because more
 
Search WWH ::




Custom Search