subsequent regeneration over untreated plots. In general, coefficients for 

 mechanical and bum site preparation are also larger for shade-intolerant 

 species versus shade-tolerant species. 



The number of years since last disturbance increases the probability of subse- 

 quent species. The rate of increase for plots with spruce budworm defoliation is 

 less than for plots without defoliation for three host species — Douglas-fir, 

 grand fir, and subalpine fir. Spruce budworm defoliation in the 5 years prior 

 to harvest also decreases the probability of subsequent grand fir. 



Residual overstory basal area decreases the probability of subsequent re- 

 generation for every species except western hemlock. And if the species left; 

 in the overstory is the same one being predicted, the probability of subsequent 

 regeneration is significantly increased for all species. 



Probability of Excess regeneration is all regeneration not chosen as best trees on the plot. 



Excess The presence of an excess tree of a species is conditional on a best tree of the 



Regeneration same species being established on the plot. Excess trees are distributed quite 



differently from best trees. Species that become established at high densities 

 have a larger proportion of excess trees than do species that become estab- 

 lished at low densities. For example, grand fir and western hemlock often 

 overstock plots on the Tsuga heterophylla habitat type series. 



A consistently important independent variable increasing the probability of 

 excess regeneration is the same species in the overstory (appendix B, table 14). 

 The largest coefficient is for lodgepole pine and the smallest is for grand fir. 



Heights of Equations predicting heights of regeneration were developed for advance 



Regeneration best trees, subsequent best trees, and excess trees. Various combinations 



and transformations of dependent and independent variables were tried. 

 For advance and subsequent regeneration, the best dependent variable was 

 always the natural log of tree height. Heights of excess trees are determined 

 from Weibull distributions. 



Equations for heights of advance and subsequent best trees use tree age 

 as an independent variable. This necessitates determination of tree age at 

 the end of the Prognosis Model cycle. Weibull equations were developed that 

 represent the distribution of the number of years from harvest to germina- 

 tion of established seedlings. This is a negative value for advance regenera- 

 tion and a positive value for subsequent regeneration. Once "delay to ger- 

 mination" is known, tree age can be calculated. 



Heights of Advance Regeneration — ^Weibull distributions for choosing 

 the delay to germination for advance best trees are given in appendix B, 

 table 15. Delay to germination is dependent on species, residual overstory 

 basal area, and spruce budworm defoliation during the 5 years before har- 

 vest. Age is the number of years from germination to the end of the Prognosis 

 Model cycle. Once tree age is determined, equations given in appendix B are 

 used to predict tree heights. 



A total of 5,648 advance best trees were used to develop the height equa- 

 tions in appendix B, table 16. Age is the single most important predictor of 

 tree height. The coefficient for age is positive for all species; however, these 

 coefficients are not as large as those for subsequent species. This is because 

 the advance trees were suppressed prior to the harvest. 



Amplitude values for regeneration heights given in appendix B, tables 16 

 and 18, are interpreted differently than the amplitude values in probability 

 equations. For tree heights, amplitude is tree height at the optimum aspect 



21 



