390 FACTORS AFFECTING THE GROWTH OF STANDS 



By increasing the area of the stand, this possible expansion of area becomes less. 

 By reducing the area, the per cent of expansion possible becomes greater, since a 

 greater per cent of the total number of crowns are so placed as to be able to utilize 

 the increased space. The maximum possible expansion occurs when there are but 

 59 trees per acre at 30 years, equally spaced, and unobstructed by older age classes, 

 in which case the area actually utilized by this age class expands 332 per cent or is 

 432 per cent of its original area, and the stand becomes fully stocked at 80 years. 

 This expansion of actual are is shown on the right, in Fig. 82. 



This second process is what takes place in a forest composed of stands of many 

 different ages. In the case of even-aged stands, thinning or removal of trees simply 

 permits the remainder to grow, with no change in area for the class, and the removal 

 of the final crop is followed by reproduction which in turn occupies the entire original 

 area. But with many-aged stands, when the final crop is removed, which takes place 

 on any acre in several different cuttings, the area so released is reproduced only in 

 part. The remainder is absorbed by the crown spread of the intermediate age 

 classes which thus increase their total area in the manner shown by Fig. 82. 



In the illustration, this stand at 30 years occupies but one-fourth of the total 

 area of the 4 acres. The remainder can be occupied by older timber, which in the 

 50-year period is removed as it matures. By assuming this 4 acres to be but a part 

 of a larger area, and to be distributed over the area coinciding with the distribution 

 of the single age class in question, the conditions of a many-aged forest are visualized. 

 This factor of crown expansion and competition between different age classes is the 

 basis of the differences between the increment of many-aged and even-aged stands. 

 It explains suppression, economic age, and increased growth after cutting. The 

 actual amount of expansion and rate of increase due to this factor will be consider- 

 ably less in all instances than the per cents given in table LXI since only a portion 

 of the maximum space required by each tree of the class for expansion is available 

 at all, and but a part of this can be taken from other age classes. Summed up, 

 this factor represents an additional rate of increment to be added to that which an 

 even-aged stand of like volume would show, and caused by the fact that the volume 

 of the age class in the many-aged forest, while occupying only a certain per cent of 

 the area of the forest, is thereby distributed over a much larger area into which its 

 crowns can expand. 



299. Annual Increment of Many-aged Stands. The rate of growth 

 per year based on a unit of area for many-aged forests does not repre- 

 sent production of a single age class, but of the sum of all the age classes 

 on the area, averaged for a long period. If desired for a single age 

 class, this rate or yield per acre should not be based on the area occupied 

 by the timber at maturity divided by the total ages of the trees com- 

 posing this stand, for this would greatly under-estimate the rate of 

 mean annual growth. The error can be expressed and corrected in 

 one of three ways: (1) either the age used as a divisor must be shortened 

 to represent the economic age of dominant trees growing in even-aged 

 stands, or (2) the area occupied by the mature crop must be reduced 

 to represent the average area for the stand during its life, which is 

 practically impossible, or (3) to the yield for the period represented 

 by the total life of the trees in the stand as actually shown by ring 

 counts, must be added the additional yields from other crops of timber 



