VEGETATIONAL ANALYSIS 45 



for some time to come. Several recent papers summarize ideas and 

 analyze the problem in detail. Their extensive bibliographies will 

 soon lead one to the conclusions of a variety of workers. Cain's 

 publications 43 > 49 have done much to clarify methods of determin- 

 ing sample sizes and numbers both through his own contributions 

 of methods and their applications as well as through his summaries 

 of the literature. Penfound 196 has brought together and analyzed 

 the usefulness of several currently favored procedures. 



Species : area curves have been used in a variety of ways. Orig- 

 inally used by European ecologists to determine the "minimal 

 area" to be recognized as an "association individual" (^ stand), they 

 have been equally useful in arriving at numbers or sizes of plots to 

 be used in sampling individual stands. A characteristic curve will 

 result from plotting the number of species obtained against the 

 area sampled. The accumulated number of species found may be 

 expressed as a percentage of the total or as an absolute number and 

 plotted on the y axis. When the corresponding numbers of plots, 

 or sizes of area sampled, are plotted on the x axis, the curve formed 

 by the joined points will rise abruptly with first increases in area, 

 but will soon level off, and tend to rise only slightly thereafter 

 with increase of sampling area. It is assumed that the added infor- 

 mation represented in the slight rise of the curve is not sufficient 

 to justify the time and effort needed for the extra sampling. There- 

 fore, for this same type of vegetation, the sampling is assumed to 

 be adequate when the size of the sample somewhat exceeds the 

 area plotted against the point at which the curve flattens strongly. 



It is of interest that, when the ratio of the x to the y axis is 

 shifted, it will result in a change in the form of the curve and a 

 consequent shift in the position where the curve tends to flatten. 

 This suggested the desirability of some means other than inspec- 

 tion for determining this point. Cain 46 suggests that, in terms of 

 his experience, sampling is adequate when a 10 percent increase 

 in sample area results in an increase of species equaling 10 percent 

 of the total present. He suggests a mechanical means of determin- 

 ing this point on the curve regardless of the ratio of the x and y 

 axes. When a triangle is placed so that one edge passes through the 

 zero point and the point representing 10 percent of the area and 

 10 percent of the species, the triangle can be pushed upward along 



