Number of 

 Species per 

 Stocked Plot 



Probability of 



Advance 



Regeneration 



The distribution of trees per plot is the important variable to reproduce, 

 rather than the mean. Predictions of mean values with linear regression 

 would not properly simulate the natural occurrence of regeneration because 

 the categories with the highest probability of occurrence would seldom be 

 predicted. Another method that simulates the distribution of the number of 

 trees per plot is used. 



A two-step analysis was used to develop a Weibull cumulative density 

 distribution equation. First, the data were categorized as follows: 



4 Habitat type series (Pseudotsuga menziesii, Abies grandis, 

 Thuja/Tsuga, and Abies lasiocarpa) 



X 4 Aspects (north ± 45 degrees, east, south, and west) 



X 3 Time periods (2-7 years since last disturbance, 8-12 years, 

 13-20 years) 



X 2 Budworm defoliation histories (0-2 years, >3 years). 



Of the possible 96 categories, 73 had adequate data (>25 plots). A Weibull 

 equation was developed for each category, yielding 73 estimates of B and C for 

 equation 2. Averages of variables by category were also calculated — average 

 aspect, average slope, and so on. 



The second step in the analyses used linear regression to estimate Weibull 

 parameters B and C as a function of site conditions. The resulting equations 

 are shown in appendix B, table 10. Slope, aspect, elevation, habitat type series, 

 number of years without budworm defoliation, and number of years with 

 budworm defoliation are important predictors of the B parameter. For the 

 C parameter, important predictors are elevation, number of years without 

 budworm defoliation, and number of years with budworm defoliation. 



It is necessary to predict the number of species on stocked plots because all 

 species do not occur on a given Vsoo-acre plot. This distribution has a reversed 

 J-shape as shown in figure 11. The highest percentage is for 1 species, fol- 

 lowed in decreasing order by 2, 3, 4, 5, 6, and 7 species. Seven species on a 

 Vaoo-acre plot occurred only once. Separate equations were developed to pre- 

 dict the probability of 1, 2, 3, 4, 5, and 6 species on stocked plots. Coefficients 

 are given in appendix B, table 11. 



Prediction of the number of species on a stocked plot is conditional on the 

 number of trees on the plot. For example, one tree on the plot could only 

 result in one species on the plot; two trees, two or fewer species; three trees, 

 three or fewer species; and so on. 



Advance regeneration is defined as best trees that germinated more than 

 3 years prior to the year of harvest. Advance regeneration is commonly found 

 beneath the canopy of mature stands in the Northern Rocky Mountains. Many 

 of these trees survive harvest, site preparation, and the sudden exposure to 

 more sunlight. Advance regeneration was included in the model as a sepa- 

 rate class of regeneration so that future refinements to the Prognosis Model 

 can account for growth response to release, important disease interactions 

 with suppressed regeneration, and so on. Equations to predict the probabil- 

 ity of advance regeneration were developed by species; coefficients are given 

 in appendix B, table 12. 



The occurrence of advance regeneration is related to shade tolerance of 

 the species. Shade-intolerant species have lower probabilities than shade- 

 tolerant species. Occurrence is also related to the relationship of species to 



19 



