APPENDIX G 



DEVELOPMENT OF RECRUITMENT MODELS 



Prior Findings 



Natural regeneration is the process in which an adequate supply of viable seed is produced, 

 dispersed over the area, germinated, and then survives to produce a full stocking of established 

 seedlin.gs. The amount of seed a tree produces depends upon tree size, vigor, level of competi- 

 tive stress, and presence of cone-damaging agents (Larson and Schubert 1970; Schubert 1974) as 

 well as environmental factors. Schubert (1974) concluded that good cone crop years occur at 

 intervals of 3 to 4 years. The amount of viable seed is positively correlated with size of 

 cone crop (Larson and Schubert 1970; Schubert 1974) . 



Seed is disseminated in the fall and generation occurs the following summer (Schubert 

 1974) . Germination follows adequate rainfall and, if this takes place too late in the season 

 or fails to take place at all, mortality rates can be extremely high (Pearson 1950; Schubert 

 1974). Second-year seedlings are also highly susceptible to drought. Therefore, successful 

 regeneration requires adequate rainfall in two consecutive years (Meagher 1950) . Seedling 

 survival is also heavily influenced by the amounts of competing vegetation (Pearson 1942, 

 1950; Schubert 1974) . 



The ingrowth rate, therefore, should be influenced by the potential of the stand to 

 produce cones, which is positively correlated with tree size (Larson and Schubert 1970), by 

 the level of competition, and by the time since the last good seedling year. .Another factor 

 that might influence the ingrowth rate is the structure of the competition. For example, an 

 even-aged stand and an uneven-aged stand could have the same potential for producing cones and 

 the same overall level of competition, but because the diameter structures of the two stands 

 are different, the ingroirth rates might differ. (The same total basal area spread over many 

 diameter classes in the uneven-aged stand may produce a different level of competition on a 

 given diameter class from the same total basal area concentrated in a narrow range of diameter 

 classes in an even-aged stand.) 



The only whole-stand ingrowth models found in the literature were the two tried by Moser 

 (1972, 1974) and one reported by Ek (1974). Moser's differential equations were of the form: 



d( Ingrowth) /dt = i^ie^^QMD (Moser 1972) 



and 



RA 



d(Ingrowth)/dt = + (2) (Moser 1974) 



where 



QMD = quadratic mean stand diameter 

 BA - total stand basal area. 



Integrating these functions over the time interval tg to (tg + 5) provides a means for con- 

 verting these differential forms to equations that represent ingrowth in any 5 -year growth 

 period. The integrated equations are: 



77 



