APPENDIX 



227 



divided by the area of commercial forest land to determine 

 numbers of trees per acre. Only trees qualifying as 

 growing stock were included in computing stand table 

 projections, but projections of basal area included cull 

 trees as well as growing stock trees. 



Annual average radial growth. — Average annual growth 

 rates by 2-inch diameter classes were obtained from 

 measurements taken on forest survey plots, either on 

 remeasured permanent plots or by measurement of growth 

 of increment cores during the 5- or 10-year period prior to 

 the survey measurements. 



In the updating to January 1, 1963, no modifications of 

 radial growth rates were made in response to changes in 

 density and stand structure. In the long-term projections 

 to the year 2000, however, radial growth rates were 

 changed in response to increasing stand densities. Data 

 from remeasured plots indicated that both radial growth 

 and mortality rates are directly related to basal area 

 density per acre, with average growth rates dropping and 

 mortality rates increasing as stand basal area rises. In 

 the East, for example, radial growth and mortality rates 

 were therefore modified as follows: 



P2 

 MR2 = MR1 — (a-bD-^cD2) 



where: MR2 (or RG) = mortality rate (or radial growth) 

 after one year's growth. 



MR1 = mortality rate at the beginning of the year 



D = two-inch d.b.h. class 



P = 1.000-| (BA)-| (BA)2 



where: BA = basal area density of all live trees 1.0 inches 

 and larger in square feet 



b and c are regression coefficients 



Dividing the b and c coefficients by 2 divides the constrain- 

 ing influence equally between radial growth and mortality. 

 As a matter of computational expediency all of the con- 

 straining influence was assigned to mortality, which 

 eliminated the need to divide by 2 or some other allocating 

 proportion between radial growth and mortality. 



Constraining equations used in the East were as follows: 

 Northern softwoods: 



P = 1.0000-.0003028BA-.0000282BA2 

 Northern hardwoods: 



P= 1.0000- .0004541BA- .0000424BA2 

 South — all species: 



P = 1.0000-.0003531BA-.0000329BA2 



Theoretically the use of pooled radial growth data 

 without converting the weights to logarithms constitutes 

 a potential source of bias. However, several checks 

 indicated that from a practical standpoint the bias was 

 negligible. 



Mortality rates. — For trees over 5.0 inches d.b.h., mortal- 

 ity rates, i.e., the ratio between the number of live trees 

 that die annually and the inventory number of trees at 

 the beginning of the year, were developed from tallies 

 of dead trees at the time of inventories or from reconstruc- 

 tion of remeasured plots. Mortality rates usually were 

 curved to remove irregularities by diameter classes. 



Sapling mortaJity. — For trees under 5.0 inches, mortality 

 rates were not available in many cases and existing 

 measurements were often irregular. Growth and mortal- 

 ity rates for 2- and 4-inch trees were therefore computed 

 using extrapolated radial growth rates and stand-structure 

 quotients extrapolated from trees above 5.0 inches. 

 Since cutting of 2- and 4-inch trees is negligible it was 

 assumed that the difference between growth and average 

 annual change was mortality. Thus the "potential" 

 increase in numbers of 2- or 4-inch trees plus or minus the 

 average annual change in number of such trees between 

 surveys was taken as the best estimate of mortality rates 

 for 2- and 4-inch trees. Where two or more surveys were 

 not available to obtain the average annual change in 

 numbers of 2- and 4-inch trees over time, average annual 

 change was assumed to be zero. This procedure for com- 

 puting mortality of 2- and 4-inch trees was as follows: 



(1) 



(2) 



(3) PI 



INGl 



(4) 



(5) INGR 



Q 

 RG 



(6) q 



Example 



MR=M/INV 



MR = mortality rate 



M = mortality in number of trees 

 INV = inventory in number of trees 

 M = PI-AC 

 PI = potential increase 



AC = average annual change in number of trees 

 between surveys 

 = ING1— ING2 

 = number of trees growing into the 2- or 4-inch 



d.b.h. class (ingrowth) 

 = number of trees growing out of the 2- or 4-inch 



d.b.h. class (outgrowth) 

 = INGRXAINV 

 = ingrowth 

 = ingrowth rate 



= accumulative stand, i.e., number of trees 1.0 

 inches and larger, 3.0 inches and larger, and 

 5.0 inches and larger 

 = antilog of (Log Q X RG) - 1 

 = stand-structure quotient 

 = average annual radial growth 



_^ AINV„ -; 



~ AINV„ 



= 2, 4, 6, etc., d.b.h. classes 



(East Gulf Softwoods) 



ING2 



ING 



ING 

 INGR 



AINV 



DBH 



(1) 



(2) 



(3) 



(4) 



(5) 



(6) 



(7) 



(8) 





AINV 



Q 



LOG Q 



RG 



INGR 



ING 



PI 



AC 



2 



M trees 

 8,522,248 

 4,153,734 

 2,196,199 



2.213 

 2.052 

 1.891 



1 0.34498 

 .31218 

 .27669 



Inches 

 '0.095 

 .104 

 .113 



0.078 

 .078 

 .075 



M trees 

 664,735 

 323,991 

 164,715 



M trees 



340,744 



159,276 



M trees 

 162 705 



4 



56,829 



6 











' Extrapolated from 4- and 6-inch classes. 



MR2= (340,744-162,705)^(8,522,248-4,153,734) = .0408 



MR4= (159,276- 56,829) ^(4,153,734-2, 196,199) = .0523 



