More samples are required for measuring attack density and gallery lengths for the 

 smaller size sample than for the larger size. For measurements of brood density, the required 

 number of samples decreases as sample size increases. Combining north and south samples at 

 d.b.h. generally effected an increase of number of trees needed (table 8). 



Table 8. --The number of trees required to be sampled for a 20-percent SME at 2/3 probability 

 level based upon summed north and south bottom samples (rectangular samples only) 



Density 



; Plot 





Sample size 





: 1/10 sq.ft. : 



1/4 sq.ft. 



1/2 sq.ft. : 



Proportional 



Attack 



Teton 



9.13 



3.36 



2.42 



3.13 



density 



Wasatch 



7.76 



4.22 



3.63 



3.08 



Gallery 



Teton 



6.40 



5.71 



5. 56 



4.67 



density 



Wasatch 



2.46 



2.63 



2.20 



2.12 



Brood 



Teton 



8.19 



9.93 



8.16 



7.56 



density 



Wasatch 



54.06 



66.94 



67.84 



55.36 



THE SAMPLING PLAN 



The principal object of any sampling procedure is to secure a sample which, subject to 

 physical limitations, will reproduce the characteristics of the population as closely as possible. 

 The simplest and most certain way to achieve this goal is for the sample to be drawn at random. 

 However, selection at random, subject to restrictions that do not introduce bias- -called 

 systematic random sampling- -is permissible. 



Sampling can be limited to the breast -height region within an infested tree and satisfy the 

 requirements of efficiency and reliability in reproducing the characteristics of the population. 

 In adhering to the principles of systematic random sampling, the sampling universe was defined 

 as that subpopulation within a zone 1 foot above and 1 foot below breast height of infested trees. 



This zone was divided into four quadrants: north, east, south, and west. If the 1/10 sq. 

 ft. sample is used, the zone can be divided into six levels of 4 inches each- -three above and 

 three below breast height; this produces 24 sample loci. If the 1/4 sq. ft. sample is used, the 

 zone can be divided into four levels of 6 inches each, producing 16 loci. Prior to sampling, 

 two loci were selected at random and sampled without replacement . 



The important advantage of this plan is that an estimate of within-tree variance can be 

 computed to determine the statistical distribution; the within-tree error can be treated as error 

 attributable to replication; additional degrees of freedom result- -one an attribute of replication 

 error and the other distributed to the error term or interactions, thus increasing experimental 

 precision. This particular two -sample technique will be used in the future work on the popula- 

 tion dynamics of the mountain pine beetle in lodgepole pine to determine the type of distribution, 

 and to provide the basis for conversion to normality, when necessary. This plan should be a 

 step toward the development of more effective sampling techniques . 



13 



