364 POPULATIONS 



at random, or they may be aggregated to Park (1933) pointed out that imago 



a greater or less degree and depart from a flour beetles {Tribolium confusum) are 



random distribution because of this, or, as distributed according to a Poisson series 



is particularly true of certain vertebrates, throughout their flour. This was shown by 



they may be apportioned into special dividing the flour into equal-sized cubes 



areas sometimes called "territories."* It is and counting the beetles in each cube. The 



obvious that the pattern of distribution can observed findings, and their agreement 



vary within the species, its abundance, and with a distribution expected assuming the 



density; with the availabiUty, distribution, Poisson, are shown in Table 25. When the 



and character of the habitat niches; and difference between observed and expected 



with other physical and biotic factors. It frequencies is tested by chi square, it is 



is equally obvious that not enough is shown that the two do not differ signifi- 



known of the quantitative dispersion of cantly from each other (probability = 11 



many forms to state just what the actual per cent). Thus these beetles did not ag- 



pattern is. Further, it seems probable that gregate to any appreciable extent within 



as more knowledge is acquired numerous the flour volume. 



variations in the distribution pattern will Cole (1946) has examined in detail the 



emerge. We present here several examples quantitative distribution of certain forest 



of population dispersion taken from insect floor invertebrates that live, among other 



Table 25. Random Distribution of Flour Beetles in the Medium 



Classes of Cubes Observed Number 



with Respect to of Cubes with Expected Number 



Number of Beetles Their Beetle ( Poisson Distri- 



Found Therein Distribution bution) 



237 246.3 



1 161 147.3 



2 45 44.1 



3 3 8.8 



4 2 1.3 



5 0.2 



studies. These illustrate both random and places, under boards in the interface be- 



aggregated distribution. tween the board and the ground. He was 



The number of organisms vidthin a unit concerned with a series of organisms that 

 area, or volume, of habitat varies from one Dendy (1895) had called the "cryptozoa" 

 unit to the next even when environmental and had defined as "the assemblage of 

 conditions are extremely uniform. Because small terrestrial animals found dwelhng in 

 this number is always an integer, and, by darkness beneath stones, rotten logs, the 

 working with values of 0, 1, 2, 3, 4, 5 bark of trees, and in other similar situa- 

 . . . n organisms per unit, it follows that tions." Dendy further concluded that the 

 the distribution of the units is discontin- cryptozoa should be studied as a unit dis- 

 uous. "If each unit in a given area is tinct from the true soil or subterranean 

 equally exposed to infestation, so that they fauna and from the fauna of other micro- 

 differ from one another entirely at random, habitats, a conclusion supported by Cole's 

 they will agree with the Poisson series" findings. 



(Bhss, 1941). When these quaUfications Cole placed on the forest floor many 



are satisfied and when the dispersion data boards of similar dimensions in various se- 



can be fitted to a Poisson distribution, the lected regions of the woods. At regular in- 



conclusion can be drawn that the organ- tervals, for all seasons and for several years, 



isms are distributed essentially at random. the number of inhabitants was estimated 



It seems probable that in nature a distribu- species by species. Cole was interested in 



tion pattern so simple as this is likely to be analyzing these records from various as- 



the exception rather than the rule. pects. Our interest in this study is that it 



• It is apparent that these are general affords illustrations of patterns of disper- 



categories subject to wide intergradations ex- sions that have been statistically analyzed 



tending as natural populations from quite and are based on large numbers, and that 



simple to extremely complex situations. different groups were considered: i.e.. 



