3 Density is stabilized by the removal each year of a constant proportion of the
population, provided that proportion is lower than the intrinsic rate of increase rm.
4 The level at which a population is stabilized by removing a constant proportion
of the population each year can be at any density above the threshold of extinction.
5 If animals are removed at an annual rate greater than rmthe population will decline
to extinction.
These simple rules can be sharpened for those populations whose pattern of popula-
tion growth is approximated by a logistic curve (Caughley 1977b). In general they
will serve for populations of large mammals (i.e. low rm) feeding on vegetation that
recovers rapidly from grazing.
1 When the constant number Cremoved each year is less than the MSY of rmK/4,
the population is stabilized at a size of
N =[rm+√(r^2 m− 4 Crm/K)]/(2rm/K)where Kis the ecological carrying-capacity density, corresponding to the asymptote
of the logistic curve.
2 When a constant proportion of the population is removed each year at a rate less
than rm, the population is stabilized at a size of:
N=K−(KH/rm)where His the instantaneous rate of removal.
3 If a constant number of animals greater than rmK/4 is removed each year, the
population will eventually become extinct.Examples of eradication
Even with large mammals the proportion of the population that has to be culled each
year to eradicate a population is substantial: 90% of the feral goats in Egmont National
Park, New Zealand, had to be culled annually to achieve eradication in 12 years; if
only 50% had been culled eradication would have taken over 50 years, if at all (Forsyth
et al. 2003).
By far the most common examples of the eradication of pest species are found in the
Pacific islands, New Zealand, and Australia, because these places have been subject
to the invasion of exotic vertebrates. An important review of these is provided by
Veitch and Clout (2002). Many islands were deliberately seeded with pigs, goats, and
rabbits by sailors in the 1700s to provide a food source in case of shipwreck. These
populations increased rapidly, changed the vegetation, and indirectly caused the extinc-
tion of many birds. Possums were introduced to New Zealand for commercial harvesting
in the 1800s. Shipwrecks and ordinary landings resulted in the inadvertent intro-
duction of rats and mice to most islands, and snakes to Guam and Mauritius. Control
of rats was the motive for introducing cats (e.g. on Marion Island) and mongooses
(e.g. Mauritius, some Hawaiian and Caribbean islands). Control of rabbits in New
Zealand was the reason for introducing stoats (Mustella erminea) and ferrets (M.furo).
All these predators increased rapidly and exterminated much of the native fauna.
In recent decades there has been much effort to eradicate these exotics and repair
the ecosystems (see papers in Veitch and Clout 2002). Cats were successfully
removed from islands off Mexico, the British West Indies, Marion Island off South