30 PLANT SOCIOLOGY 



percentage of the surface occupied by foreign vegetation or bare ground 

 must be determined. 



Number of Individuals (Abundance) and the Spacing of the 

 Species. — Abundance is intended to express the plentifulness (number 

 of individuals) of each species. The density on a definite area expresses 

 the average spacing of the individuals and hence the average area 

 occupied by each individual of a certain species. 



Often the quantity and density of a species will differ widely in 

 both space and time in different samples of one and the same com- 

 munity. This hinders an exact determination and in many cases 

 greatly reduces the usefulness of averages. 



Determination of Abundance. — In practice it is found that a series of 

 five figures suffices to express the relative plentifulness of the individual 

 species. 



1 = very sparse (very rare); 



2 = sparse (rare). 



3 = not numerous (infrequent); 



4 = numerous (abundant). 



5 = very numerous (very abundant). 



Whatever is lost by this method of estimating as compared with 

 that of counting exactly the species on very small sample areas is 

 gained in the survey of a larger area that has not been arbitrarily 

 chosen and in the saving of time. To give an exact quantitative 

 value to results from one or more very small sample areas, arbitrarily 

 chosen, in spite of all effort to the contrary, is to give the appearance of 

 exact reliability to accidental data, by using precise methods on mate- 

 rial of uncertain and diverse quality. It is very important, however, 

 that the estimate be made on a uniform stand. 



Determination of Spacing and Density. — In order to get accurate 

 numerical results sample plots of definite size must be investigated. 

 If all the individuals of a species were evenly distributed over the entire 

 surface, it would be sufficient to measure the area of the plot A and 

 count the number of individuals w in order to determine the area a 

 occupied by each individual: a = A/n. Similarly, the average distance 

 apart (distance moyenne) of the individuals d may be determined: 

 d = -y/Ajn. If the distance apart of the individuals d be first deter- 

 mined, then from it the area occupied by each individual a may be 

 determined: a = d^. 



In natural plant communities, however, the distribution of indi- 

 viduals is mostly irregular, and the density must be obtained by indirect 

 methods. Sample plots of equal size are taken in various parts of a 

 uniform community, and the number of individuals or shoots of each 



