FIG. 4-la. b Spoeles-area curves plotted (above) on arithmetic 

 and (below) on logarithmic bases, to illustrate the method of 

 determining sampling area sizes adequate for analysis of com- 

 munity species composition. 



The sizes of "Smallest representative. " 

 "Minimum," and "Fair-sized" areas may be de- 

 termined from a sigmoid curve — of which Fig. 

 4- lb is an example — by the following technique. 



A rectangular sheet of tracing paper is 

 placed over the graph, the bottom edge of the 

 paper coincident with the horizontal axis of the 

 graph. Using the graduations on the log- 

 arithmic scale as a guide, place a mark on the 

 bottom edge of the paper by one of the 

 graduations. To the right of that mark, place 

 another by that scale graduation which is 50 

 times the value of the first (on Fig. 4- lb, if 

 the left mark Is at 2. the right mark should bo at 

 100). The interval between the marks represents 

 a 50-fold Increase in area. From the right mark, 

 draw a vertical line several Inches long. Now 

 place the sheet over the graph in such a way that 

 the bottom edge Is parallel to the horizontal 

 axis of the graph, and the left mark lies on the 

 curve — the vertical line from the right mark 

 should be long enough so that it will continuously 

 Intersect the curve. Keeping the bottom edge of 

 the paper parallel to the horizontal axis of the 

 graph, move the paper in such a way that the 

 left mark traces along the curve. Move the sheet 

 until the vertical line intersects the curve at a 

 point which is twice the value of the point at 

 which the left mark Is resting on the curve, os 

 6o//> vo/ues ore reoc/ off t/ie veriicat scale (on 

 Fig. 4- lb. when the left mark rests on the curve 

 at a point opposite 15 on the vertical scale, and 

 the bottom edge of the tracing paper is hori- 

 zontal to the horizontal axis of the graph, the 

 vertical line intersects the curve at a point 

 opposite 30 on the vertical scale). The point 

 established by the left mark is the value of the 

 "Smallest representative area." and the point 

 established by the perpendicular line Intersect- 

 ing the curve is the value of the "Fair-sized area," 

 OS both values are read m area unifs off the 

 horaonial scale. Find, by measuring, the point 

 on the curve which lies midway between the two 

 points just found — this is the "Minimum area," 

 and its value is read in area units off the hori- 

 zontal scale (after Vestal 1949). 



-ACRES (Units of ' 



Measurement of populations 33 



