weeks, or if tlic mean length of life of a generation is 

 three weeks, then r = log^ 2/i = 0.2310 per individ- 

 ual per week. 



A number of factors affect the intrinsic growth of 

 a species : number of young at each reproduction, the 

 number of reproductions in a given j)eriod of time, 

 the sex ratio of the species, the age distribution of the 

 |X)pulation, their age at reaching sexual maturity, and 

 so forth. The value of r has been obtained for com- 

 paratively few species (Table 15-7; Edmondson 1946, 

 Odum.1959. Solomon 1953. DeWitt 1954, Olif? 1933, 

 Root 1960). 



In Fig. 10- 11 the logistic curve has been fitted to 

 the annual ecesis of the invertebrate community of the 

 herb and shrub strata of a deciduous forest (raw data 

 from Fig. 9-14). The upper asymptote, K. was ob- 

 tained by averaging the five randomly fluctuating 

 density values for June through October. The value 

 of r was derived from the increase in community size 

 for 28 days in February-March, but different values 

 of r can be substituted in the integrated ec|uation 

 above until a curve is obtained that best fits empirical 

 data. 



The value of r being known, the equation for in- 

 stantaneous growth rate was solved for different parts 

 of the curve to give the following values : March, 1.08 

 individuals per day : April, 3.55 ; May, 2.65 : June, 

 0.59. By plotting intermediate times it appears that 

 the highest growth rate, 3.87, comes about April 24, 

 at the point of inflection of the growth curve, and also 

 at the time of greatest absolute growth. 



r is an important constant, the potential rate of 

 population growth with ecesis taking place on an area, 

 where ideal conditions prevail. Neither such condi- 

 tions nor, by so much, an actual rate equivalent to r 

 are realized in Nature except that r may be infre- 

 quently approximated in the initial phases of growth. 

 The actual rate is best expressed by the instantaneous 

 growth rate. It is necessary to take equivalent stages 

 in the growth curves for making growth rate com- 

 parisons between different populations. The point of 

 inflection is of considerable significance in this regard ; 

 it represents the same equivalent age of populations 

 whether they respectively attain to the asymptote in a 

 matter of hours, days, months, or year. The instanta- 

 neous percentage (jrowth rate 



declines progressively with time. 



In study of the process of population growth there 

 are many advantages to working in the laboratory 

 with populations of a single species held under experi- 

 mental conditions where environmental factors can be 

 closely controlled and varied at will (Park 1941). In 

 such studies, the rate of growth of the flour beetle in 



experimental cultures has been found to vary with tem- 

 l)erature, humidity, and light ; according as whether 

 fresh flour is added each day ; whether competing 

 forms or predators are introduced ; and so on. The 

 final ])oi)ulation density turns out to be the same re- 

 gardless of the number of beetles originally introduced 

 into the flour, but it varies with the volume of the 

 medium and other factors. The accelerating phase of 

 growth is probably induced by fre([uent and successful 

 mating contacts between individuals as po])ulations 

 increase in size. The inhibiting phase of growth is a 

 result of decreasing food supply , accumulation of ex- 

 creta which correlates with reduced fecundity of the 

 adults : lowered rate of metamorphosis of the imma- 

 ture and increased mortality of the larvae , and can- 

 nibalism of the adults on the eggs. 



Under natural conditions logistic growth curves 

 for populations of single species are clearly evident 

 when a species invades a new area that is favorable ; 

 when a species is recovering from a catastrophe or 

 cyclic depression ; and as a species builds up its popu- 

 lation in the spring after the termination of a winter 

 dormancy or migration. The many factors in natural 

 environments that modify rates of population growth 

 and determine the levels at which populations become 

 stabilized at the asymptote will be considered in Chap- 

 ter 16. 



The total community is an aggregation of many 

 species. When a bare area becomes receptive to prop- 

 agation of life, only a few hardy plant species become 

 established at first. These pioneer species react on the 

 habitat by providing humus, food, shelter, and shade, 

 making conditions in which other, more sensitive 

 plant and animal, species can invade and become estab- 

 lished. With many species present, interactions or co- 

 actions between them bring about the establishment 

 of dominance, influence, and complete community or- 

 ganization. The result is a closed community. A com- 

 munity thus fully organized discourages invasion by 

 new species. It persists for the longer or shorter time 

 until there is further change or development of the 

 habitat permitting succession to a new community. 

 Each invasion and ecesis of species to form new com- 

 munities follows the sigmoid or logistic curve. Thus 

 the process of growth and ecesis is much the same 

 whether it is at the level of the individual cell, 

 organism, species population, or the complex com- 

 munity. 



Ecesis of plant communities, as recognized by the 

 species of plant dominants, is often more rapid than 

 ecesis of complete animal communities. For example, 

 some six to eight plant stages may be recognized in 

 the floodplain sere, each stage giving way to the next 

 in an orderly succession (Chapter 8). However, ex- 

 cept for a poor representation of forest-edge species 

 along the banks of the river itself, there is only one 



Dispersal, migration, and ecesis 



161 



