302 K. STERN 



2. There are no genotype-environment interactions, i.e., no depen- 

 dence of host-parasite relations on the environment, 



3. There is a strong correlation of character expression in different 

 stages of development', i.e., no dependence of resistance on host age. 



Tree breeders might decide whether or not these assumptions hold in 

 a given case. It is of course possible to verify this experimentally, but 

 it takes time and should be combined with basic experiments on the gene- 

 tical, physiological, and biochemical background of resistance and 

 virulence, and the different opportunities of the genetic systems of both 

 host and parasite to make use of genetic variability. 



If resistance is inherited by major genes and if identification of 

 bearers of genes for resistance is possible with sufficient reliability, 

 the older gene-frequency approach from population genetics might be pre- 

 ferred. The proportion of resistant individuals expected after one 

 generation of selection can be easily calculated in such simple cases if 

 it is known whether R-genes are dominant, partially dominant, intermediate, 

 or recessive. The degree of penetrance and expressivity can also be 

 accounted for. But the great unknown quantity here is the probability of 

 emergence of new V-genes on the side of the parasite. This cannot be 

 accounted for in a reasonable way because it is a rare and unpredictable 

 event . 



Genetic gain in a threshold model can also be calculated as usual 

 for purposes of resistance breeding. The same assumptions are to be made 

 as in the case of typical quantitative variation of the character "resis- 

 tance". But the problem here is dependence of threshold values on the 

 environment and/or age rather than dependence of resistance on both 

 complexes. One of the main difficulties still to be solved arises from 

 the fact that we might expect threshold ranges rather than threshold 

 values. This means that resistance against a variety of genotypes of the 

 parasite might fall in a more or less narrow part of the total range of 

 variation of the character that determines the threshold. There might 

 also be a chance for the environment to change the threshold range. 



Resistance is most likely to be a threshold character if its base is 

 of the biochemical kind, for concentration of a biochemical agent is 

 related to its toxicity. One could easily construct quantitative-genetic 

 models making one or more major genes on the host side responsible for 

 the production of a toxic substance, the concentration of which is varied 

 by modifiers. Virulence in' the parasite can be inherited in the same or 

 a similar way. This model would easily account for a situation where 

 resistance is gradual in a certain range and absolute above a threshold 

 point. Mtllder (1953) has shown that situations similar to this are 

 given in both resistance of white pines to Cvonartiwn ribioola J.C. 

 Fisch. ex Rabenh. and of Scotch pine to Pevidermivm pini (Pers.) Lev. 



MAIN ASSUMPTIONS TO BE MADE IF COMBINING ABILITY IN 

 THE GENERAL SENSE IS TO BE USED 



Resistance can also be caused by epistatic gene effects, as, for 

 instance, Wright (1956) already has pointed out. Only a small portion 

 of genetic gain is due to epistatic components of genetic variance when 

 mass selection is applied, and only components of the additive x additive 

 type can be used in mass selection or related procedures. Breeding 



