Relation of Size of Growth-Study Plots to Inventory- Plot Size 



When small plots (or point -samples with large basal-area factors) are used to 

 sample the irregular spacing of trees that characterizes most forest stands, the 

 estimates of stand density show a wider variation than would occur if larger plots 

 were used. Grosenbaugh and Stover (1957) discuss how small-plot estimates are 

 related to larger, concentric plots through a distribution that has a skewness 

 that changes with density. Jaakkola (1967) suggests that the size of the san^le plot 

 used in stand density studies may affect the magnitude of regression coefficients 

 associated with stand density. Intuitively, there must be some optimum plot size 

 that depends on tree size for explaining the effect of stand density on tree growth. 

 If so, then variable plots should be better for explaining this effect than fixed-area 

 plots if a wide range of tree sizes are to be sampled with the same plot design. In 

 addition, there nust be some optimum basal-area factor for sampling the stand density 

 variable in tree growth studies. Unfortunately, it is also likely that this optimum 

 size will vary by site and species. 



An important feature of this growth prognosis algorithm is that the effect of 

 the bias that may be present in any of the diameter-growth models is compensated by 

 the self- calibration features that scale the median and standard deviation of the 

 residuals in relation to the past performance of the stand as it was actually sampled. 

 If a regression coefficient is too small in absolute magnitude, then the residual 

 variation will be larger, and the scaling of the stochastic nultipliers will modify 

 the estimates accordingly. 



Local variation in stand density is introduced in the same manner. If a sample 

 tree is growing in an area that deviates from the average density, then its con- 

 tribution to the standard deviation of residuals will be large, and the effect will 

 persist in variation of predicted diameter increments. However, the resolution of the 

 overall model will be best if the field inventory plot design and the plot design 

 of the growth studies are as similar as possible and both designs are capable of 

 reflecting local conditions that affect tree growth. 



27 



