126 



W. H. DRURY 



ing Humboldt Current water offshore and 

 causes mass mortality in the Peruvian an- 

 chovies (Engraulis ringens) and, as a conse- 

 quence, a die-off among the millions of sea- 

 birds such as Peruvian guanay cormorants 

 (Phalacrocorax bougainvillii) and Peruvian 

 boobies or piquero (Sula variegata) which feed 

 upon them (Murphy 1936) 



Theoretical 

 Considerations 



Can useful generalizations be drawn from 

 these observations on population changes? 

 Can a model be constructed of the forces 

 which drive population changes or of popula- 

 tion-habitat interactions which keep popula- 

 tions from extinction? Some conflicting theo- 

 ries and assumptions of population dynamics 

 are examined and discussed below. 



The Assumption of Population 



Stability and of Closely Attuned 



Density-dependent Mortality 



During the 5 decades before 1970, it was 

 widely accepted that most animal populations 

 were generally stable and saturated before the 

 arrival of the white man. Although a few field 

 biologists vigorously dissented, "establish- 

 ment" ecologists regarded fluctuations as a 

 departure from the norm, and as such, a 

 hazard to the population. Many theorists of 

 both evolution and ecology argued that adap- 

 tations were required to damp fluctuations or 

 the fluctuations would become "random 

 walks" and the population would rapidly be- 

 come extinct. As a consequence, relatively all 

 theoretical models included stability as a cen- 

 tral assumption. 



The basic element of this theoretical com- 

 plex has been the Lotka-Volterra formula for 

 a logistic curve of population growth and sta- 

 bilization. According to this formula it has 

 been reasoned that by establishing the in- 

 herent rate of increase of a population (i.e., its 

 average natality relative to mortality, or r) 

 and by measuring the carrying capacity of the 

 environment (which is the density of the popu- 

 lation at saturation, or K), one can predict the 

 maximally productive population size, and 



maximum rate of production of new indi- 

 viduals (or maximum sustained yield). These 

 assumptions have supplied the theoretical 

 framework for virtually all game management 

 and many fisheries practices. 



Once stability was assumed, a mechanism 

 for maintaining stability was necessary. This 

 mechanism was found in an interaction be- 

 tween the population and the environment, 

 called density-dependent mortality (Nichol- 

 son 1933). The impact of this feedback has 

 been assumed to cause the point of inflection 

 of the "sigmoid curve" and to regulate the 

 density "at equilibrium." 



Populations growing in relatively isolated 

 or closed systems have been observed to fol- 

 low a sigmoid curve toward a steady state. 

 We have data on the growth of several Massa- 

 chusetts gull colonies which show this type of 

 short-period rapid increase followed by a long 

 sequence of shallow oscillations (Drury and 

 Nisbet 1972). But usually observations have 

 been terminated at about the time the popula- 

 tion passed through the point of inflection. 



Lack (1954) accepted the principles formu- 

 lated by Lotka-Volterra and hence viewed 

 Nicholson's (1933) density-dependence as logi- 

 cally necessary. Lack (1948, 1954) argued that 

 reproductive effort (clutch size or litter size 

 times the number of broods) must be as large 

 as the parents can successfully raise to inde- 

 pendence because these biological characteris- 

 tics are directly subject to natural selection. 

 He argued that because reproductive poten- 

 tial is excessive (Darwin 1859), mortality 

 must be density-dependent if a population is 

 to avoid fluctuations. The only adequately 

 density-dependent regulating process he ac- 

 cepted was the population's response to its 

 food supply (Lack 1954). In fact, for many 

 years Lack rejected Kluyver and Tinbergen's 

 (1953) hypothesis that territory could act as a 

 control on population size in birds because, he 

 argued, territories were compressible and 

 therefore allowed wide fluctuations. To his 

 credit, however, Lack eventually acknowl- 

 edged this mistake. 



The first defect in the concept of "carrying 

 capacity" is the idea that populations have 

 "mechanisms" or "institutions" (Wynne- 

 Edwards 1959) by which the population is 

 kept stable at the carrying capacity in a 

 stable habitat. 



