LAW OF DIMINISHING NUMBERS 



319 



which would otherwise continue to ascend sharply. This influence 

 of age and maturity upon individual trees which survive is due to loss 

 of vitality, but the same effect is observed in all the remaining trees 

 which are suppressed during the growth of the stand and ultimately 

 die because the space needed for their normal expansion is appropriated 

 by more vigorous trees. 



A forest or stand represents an area of land stocked with trees. 

 The number of trees which can grow and thrive upon the acre is in 

 inverse ratio to the size of crown spread and space required by the 

 individual tree. As trees increase in size their numbers will be reduced. 

 The enormous number of seedlings which may spring up on an acre 

 is merely a guarantee that a few will survive to maturity. The curve 

 of diminishing numbers which 

 is characteristic of all species 

 and classes of timber, drops 

 very rapidly in the first few 

 years, and more gradually later 

 on. Numbers diminish most 

 rapidly during the period of 

 rapid height growth and crown 

 expansion. When trees have 

 reached their mature heights, 

 their numbers have been re- 

 duced to a point where the 

 further diminution is a much 

 slower process. 



The cause of reduction is 

 at first failure to survive the 

 juvenile period because of un- 

 favorable climatic or soil factors 



and competition with other vegetation, followed by suppression due 

 to the competition of older trees or of trees of the same age which have 

 attained dominance by some advantage at the start. The crown is 

 restricted in size and spread, is finally overtopped, and the tree dies. 



This process is accompanied by a change in the rate of diameter 

 growth for the trees whose crowns and growing space are restricted 

 in the struggle. Consequently the dominant trees maintain at all 

 times the most rapid rate of diameter and volume growth, while others 

 which at a given period have not yet lost their dominance and still 

 show a rapid rate of growth, will later on, with the closing of the crowns 

 and crowding of the tree, show a falling off in growth, sometimes quite 

 sudden in character. The prediction of the future growth of any single 

 tree is therefore impossible without knowing whether the tree will main- 



10 20 30 



40 60 60 70 

 Age, years 



80 90 100 



Fig. 65. — Number of trees per acre at dif-^ 

 ferent ages in fully stocked stands of 

 white pine. From Table XLVIII. 



