ACTUAL OR EMPIRICAL DENSITY OF STOCKING 413 



316. Methods of Determining Actual or Empirical Density of 

 Stocking. For even-aged, pure stands, but one variable is present 

 in addition to site quality, that of the density of stocking. As this 

 variable is the result, first, of the intrusion of small areas of unstocked 

 land into the timbered area, which it may not pay to exclude in mapping 

 (§ 306) and second, of the uninterrupted play of natural agencies of 

 destruction operating on stands which are themselves originally the 

 result of chance at the time of reproduction, the problem is to arrive 

 at an average yield per acre which expresses not so much the capacity 

 of the site as the accidental product of these various conditions. This 

 average will in all cases be less than the standard or normal yields for 

 the same area, sometimes by as much as 50 per cent. Evidently the 

 determination of site quality is but the first step in predicting the yields 

 of existing stands from such a standard table, and without correction 

 these predictions may range from 50 to 100 per cent too high except 

 on small tracts, such as plantations or managed forests, whose density 

 factor is known to coincide closely with the yield table. 



Use of Empirical Yield Tables. There are two methods of over- 

 coming this difficulty. The first is an attempt to arrive directly at 

 the average yields based on age for the larger area, or to make an empir- 

 ical yield table (§ 303) which will reflect the degree of stocking present. 

 This applies the principle used in timber estimating in determining the 

 volume of the average acre (§ 209). But the operation is more dif- 

 ficult, as it involves the separation of the entire area into stands based 

 on age, whose area is known, and the combining of these data into a 

 yield table subnormal in character and representing a purely arbitrary 

 percentage of standard yields. In the preparation of such a table, the 

 curves of yield are affected by the varying per cents of stocking of dif- 

 ferent age classes and areas so that practically the entire area must be 

 analyzed to obtain the true average, and then the table will be incorrect 

 in its prediction of yield for any specific age class or stand which differs 

 from this arbitrary average stocking. The table will be correct only 

 for the tract on which it is made since empirical density varies with 

 every forest and block. Empirical yield tables on this basis have the 

 same drawbacks as volume tables for defective trees which express 

 the net contents only (§ 151). 



Use of Normal Yield Tables by Reduction. The better plan, and 

 the one which will probably be universally used, is to depend upon a 

 standard normal yield table (just as upon a volume table for sound 

 trees only) and to ascertain the relation or percentage of deduction from 

 this table, which applies to the specific stand or larger area for which 

 yield is desired. For even-aged stands, the application of the yield 



