Bird Ecology and Conservation A Handbook of Techniques

where Ntis the population size at time t, htis the harvest rate for the same time
period,rmaxis the maximum growth rate, and Kis the carrying capacity. This
model underlies the results of Caughley (1977:178–181) and is a simplified ver-
sion (with

1) of the generalized logistic model used by Taylor and DeMaster
(1993), Wade (1998), and Taylor et al. (2000).
Imagine harvesting at a fixed rate, ht
h(where the rate is relative to the popu-
lation size), for an indefinite period of time. The population size will converge to
and maintain an equilibrium value, Neq(h) that is a function of the fixed harvest
rate (provided rmaxis not too large, in which case cyclical or chaotic results can be
obtained (May 1976)). The equilibrium population size is given by:

(13.2)

(see Runge and Johnson 2002 for calculation methods); that is, the equilibrium
population size decreases linearly from K(whenh
0) to 0 (when h rmax)
(Figure 13.1a).

Neq(h)
K

rmaxh

rmax 

306 |Exploitation

0

K/2

Harvest rate

Equilibrium

N

0 rmax/2 rmax

Harvest rate

0 rmax/2 rmax

Annual harvest

(a) K (b)

Fig. 13.1Maximum sustained harvest from a logistic model. (a) Equilibrium
population size as a function of a fixed harvest rate. (b) Annual sustained harvest as a
function of a fixed harvest rate. The maximum sustained yield is achieved by harvest at
a rate of rmax/2, which achieves an equilibrium population size of K/2.