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Intensification and infection mortality of dwarf mistletoe in two stands of western hemlock Wilford, Edward Harry 1982

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INTENSIFICATION AND INFECTION MORTALITY OF DWARF MISTLETOE IN TWO STANDS OF WESTERN HEMLOCK by EDWARD HARRY WILFORD B . S c , The U n i v e r s i t y of B r i t i s h Columbia, 1978 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n THE DEPARTMENT OF FORESTRY We accept t h i s t h e s i s as conforming to the req u i r e d standard. THE UNIVERSITY OF BRITISH COLUMBIA October 1981 (c) Edward Harry W i l f o r d , 1981 In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y a v a i l a b l e f o r reference and study. I further agree that permission for extensive copying of t h i s thesis for s c h o l a r l y purposes may be granted by the head of my department or by h i s or her representatives. It i s understood that copying or pu b l i c a t i o n of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of f^Q y g ^ f V The University of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 D a t e ffcf, Z 6 ) /?8/ ABSTRACT The number, height and age of western hemlock dwarf m i s t l e t o e (Arceuthobium tsugense (Rosendahl) G.N. Jones) i n f e c t i o n s were recorded i n two western hemlock (Tsuga h e t e r o p h y l l a (Raf.) Sarg.) stands (44 and 130 years old) l o c a t e d on s i m i l a r s i t e s on the U n i v e r s i t y of B r i t i s h Columbia Research Forest at Maple Ridge, B.C.. The r a p i d decrease i n numbers of i n f e c t i o n s w i t h i n f e c t i o n age was shown t o be l a r g e l y due to i n f e c t i o n m o r t a l i t y . The r a t e of i n t e n s i f i c a t i o n of the disease expressed as "doubling time" was estimated to be 40 or more years i n both stands. A l s o estimated was a ra t e of v e r t i c a l spread of .15 metres per year. The r e s u l t s d i f f e r e d markedly from those of other s t u d i e s i n s i m i l a r stands, which g e n e r a l l y p r e d i c t "doubling times" of 2 t o 4 years and v e r t i c a l spread r a t e s of up to .5 metres per year. - i i -CONTENTS Page ABSTRACT i CONTENTS . i i LIST OF TABLES i i i LIST OF ILLUSTRATIONS i v ACKNOWLEDGEMENTS v INTRODUCTION 1 1.0 LITERATURE REVIEW 4 2.0 METHODS 7 7 2.1 Stand S e l e c t i o n  2.2 P l o t Establishment 7 2.3 V e r t i c a l Rate of Spread C a l c u l a t i o n 1° 2.4 V e r t i c a l Height Growth C a l c u l a t i o n 10 2.5 Male:Female I n f e c t i o n R a t i o Determination 10 3.0 RESULTS AND DISCUSSION 12 3.1 Rate of I n t e n s i f i c a t i o n 12 3.2 V e r t i c a l Rate of Spread C a l c u l a t i o n 27 3.3 Male:Female I n f e c t i o n R a t i o Determination 30 4.0 CONCLUSIONS 31 LITERATURE CITED 33 APPENDICES 3 5 I . Immature Stand Data . 35 I I . Mature Stand Data 36 I I I . Group Regression Analyses 37 TABLES TITLE Sample p l o t measurements f o r immature and mature dwarf m i s t l e t o e i n f e c t e d western hemlock stands at the U n i v e r s i t y o f B r i t i s h Columbia Research F o r e s t , 1979. Sample p l o t r e s u l t s f o r immature and mature dwarf m i s t l e t o e i n f e c t e d western hemlock stands at the U n i v e r s i t y of B r i t i s h Columbia Research F o r e s t , 1979. Comparison of equations, i n f e c t i o n t o t a l s and doubling times f o r the immature and mature dwarf m i s t l e t o e i n f e c t e d western hemlock stands during the 1962-1975 p e r i o d . Group r e g r e s s i o n analyses of the i n t e n s i f i c a t i o n r a t e of dwarf m i s t l e t o e i n immature and mature dwarf m i s t l e t o e i n f e c t e d western hemlock stands during the 1962-1975 p e r i o d . Comparison of l o g a r i t h m i c and p r o b a b i l i t y equations f o r the p r e d i c t i o n of numbers of dwarf m i s t l e t o e i n f e c t i o n s i n the mature dwarf m i s t l e t o e i n f e c t e d western hemlock stand. - i v -ILLUSTRATIONS FIGURE TITLE PAGE 1. The l o c a t i o n and h i s t o r y of the immature and mature 8 dwarf m i s t l e t o e i n f e c t e d western hemlock stands i n the U n i v e r s i t y of B r i t i s h Columbia Research F o r e s t , Maple Ridge, B.C., Canada, L a t i t u d e 49 15', Longitude 122°33'. 2. The number of l i v e dwarf m i s t l e t o e i n f e c t i o n s per 14 p l o t versus i n f e c t i o n age f o r the mature western hemlock stand. 3. The number of l i v e dwarf m i s t l e t o e i n f e c t i o n s per 15 p l o t versus i n f e c t i o n age f o r the immature western hemlock stand. 4. The number of l i v e (o) and dead (.) dwarf m i s t l e t o e 1 7 i n f e c t i o n s per p l o t versus i n f e c t i o n height above ground i n three metre c l a s s e s f o r the immature western hemlock stand. 5. The l o g of the number of dwarf m i s t l e t o e i n f e c t i o n s 21 per metre squared of p l o t area f o r the immature (.) and mature (o) western hemlock stands versus i n f e c t i o n age (-3 years) f o r the 1962-1975 p e r i o d . 6. The number of l i v e (o) and dead (.) dwarf m i s t l e t o e 23 i n f e c t i o n s per p l o t versus i n f e c t i o n height above ground i n three metre c l a s s e s f o r the mature western hemlock stand. 7. The average host height (o) and the height of the 2 8 advancing f r o n t of the p a r a s i t e (.) versus stand age i n the immature western hemlock stand. 8. The average host height (o) and the height o f the 29 advancing f r o n t of the p a r a s i t e (.) versus stand age i n the mature western hemlock stand. — V — ACKNOWLEDGEMENTS I wish t o express my s i n c e r e thanks t o my p r i n c i p a l a d v i s o r , Dr. B.J. van der Kamp, f o r h i s comments, c r i t i c i s m s , and support throughout the p r o j e c t . I would a l s o l i k e t o thank my committee members, Dr. J.A. McLean and Mr. A.H. Johnson, f o r t h e i r v a l u a b l e c r i t i c i s m s of the t h e s i s . Rosalee Maurice, whose e x c e l l e n t t y p i n g a b i l i t i e s were c a l l e d upon more than once, i s a l s o owed a debt of thanks. My deepest a p p r e c i a t i o n i s reserved f o r my w i f e , Jean, f o r without her patience and understanding t h i s t h e s i s could not have been completed. INTRODUCTION Western hemlock dwarf m i s t l e t o e (Arceuthbbium tsugense (Rosendahl) G.N. Jones ) i s a p a r a s i t i c v a s c u l a r p l a n t found p r i m a r i l y on western hemlock (Tsuga h e t e r b p h y l l a (Raf) Sarg. ). The other known hosts are mountain hemlock (Tsuga mertensiana (Bong.) Carr. ), p a c i f i c s i l v e r f i r (Abies a m a b i l i s (Dougl.) Forbes ), S i t k a spruce ( P i c e a sitcheh'sis (Bong.) Carr.. ), grand f i r (Abies grandis (Dougl.) L i n d l . ), subalpine f i r (Abies  l a s i o c a r p a (Hook.) Nutt. ), white pine (Pinus monticola Dougl.), and Engelman spruce (Picea engelmannii P a r r y ) . A. tsugense, i n what i s thought to be v a r i a n t form, a l s o p a r a s i t i z e s lodgepole pine (Pinus c o n t o r t a v a r . c o n t o r t a Dougl.) (Smith and Wass, 1976). A. tsugense i s found throughout the c o a s t a l range of western hemlock ( c o a s t a l North America) but not the i n t e r i o r where western hemlock grows (Baranyay and Smith, 1972). Understanding the l i f e c y c l e of dwarf m i s t l e t o e i s the key t o any d i s c u s s i o n o f the p a r a s i t e . A. tsugense i s dioecious w i t h the male and female flowers on separate p l a n t s ( i n f e c t i o n s ) . Flowering occurs i n the s p r i n g w i t h the p o l l i n a t i o n mediated by wind or i n s e c t s as occurs with other Arceuthobium species (Hawksworth, 1978). Approximately fourteen months a f t e r p o l l i n a t i o n ( l a t e summer) the seeds are mature and ready f o r d i s p e r s a l . A water powered e x p l o s i v e mechanism f i r e s the seed from the f r u i t w i t h an i n i t i a l v e l o c i t y of 100 k i l o m e t r e s per hour. In s p i t e of the h i g h discharge speed the very low seed mass makes seed f l i g h t dependent on stand d e n s i t y , p l a n t h e i g h t , wind d i r e c t i o n , wind v e l o c i t y and discharge angle. F l i g h t continues u n t i l a t a r g e t (a western hemlock needle i s a very good t a r g e t ) i s h i t , then a s t i c k y substance adheres the seed t o the 2/ . . . - 2 -l a n d i n g s u r f a c e . Rain washes the seed t o the t a r g e t base where the seed germinates the f o l l o w i n g s p r i n g . I n f e c t i o n occurs when the seed r a d i c l e penetrates the bark at the needle base and a p e r e n n i a l endophytic system develops i n the host c o r t e x . One or two years a f t e r i n f e c t i o n a f u s i f o r m s w e l l i n g develops at the p e n e t r a t i o n s i t e . One or two years a f t e r the s w e l l i n g development, shoots appear followed a year l a t e r by flowers t h a t produce more seed. These shoots are r e l a t i v e l y s h o r t - l i v e d . The shoots are not r e q u i r e d f o r the i n f e c t i o n to s u r v i v e as the shoots are v i r t u a l l y unable t o photosynthesize but do produce more seed. The l i f e c y c l e t h e r e -for e takes f o u r t o f i v e years t o complete (Hawksworth 1978). Dwarf m i s t l e t o e as a p a r a s i t e decreases the performance of the host and the g r e a t e r the number of i n f e c t i o n s the g r e a t e r the l o s s (Smith 1969). E f f e c t s of dwarf m i s t l e t o e on western hemlock are v a r i e d and s i g n i f i c a n t . In order of importance the l o s s e s are; reductions i n height and diameter growth, increased m o r t a l i t y of h e a v i l y i n f e c t e d t r e e s , decreased seed p r o d u c t i o n , r e d u c t i o n of wood q u a l i t y and increased s u s c e p t i b i l i t y t o other damaging agents (Buckland and Marples 1952; Smith 1969; Hawksworth 1979). The B r i t i s h Columbia M i n i s t r y of Forests reported western hemlock comprised 41% (12.0 m i l l i o n cubic metres) of the c o a s t a l harvest (Anonymous 1980) and dwarf m i s t l e t o e caused the l o s s of 1.7 m i l l i o n cubic metres (Van S i c k l e and Smith 1978). This study was i n i t i a t e d t o address the f o r e s t management problem of dwarf m i s t l e t o e i n f e c t e d advance regeneration and h i g h l y stocked i n f e c t e d immature stands of western hemlock. The f o r e s t manager i s faced with t h i s disease a f f e c t i n g approximately 15% of h i s (or her) western hemlock stands (Van S i c k l e and Smith 1978) and must have the i n f o r m a t i o n to make e f f i c i e n t 3/ . . . - 3 -d e c i s i o n s . The recommended way to decrease the l o s s e s i s the e r a d i c a t i o n of the i n f e c t e d advance regeneration followed by p l a n t i n g u n i n f e c t e d stock i f r e q u i r e d (Van S i c k l e and Smith 1978). The e r a d i c a t i o n procedure, i n a d d i t i o n to the p l a n t i n g expense, could r e s u l t i n e r o s i o n and brush problems. Spacing i n f e c t e d immature stands has not been recommended because of the p r o l i f e r a t i o n of i n f e c t i o n s of dwarf m i s t l e t o e . However, f a i l i n g t o space dense immature stands prevents maximizing volume on fewer stems over a s h o r t e r r o t a t i o n . The p r e d i c t e d development of the p a r a s i t e i n advanced regeneration and spaced stands i s based on computer models (Bloomberg et a l 1980). Information on the present stand dwarf m i s t l e t o e status i s used to determine the doubling time o f the p a r a s i t e . The doubling times p r e d i c t e d range between two and four years producing huge i n f e c t i o n t o t a l s by r o t a t i o n age (a f o u r year doubling time i s a l s o supported by Richardson and van der Kamp 1972) but these t o t a l s have not been observed and reported. Over-e s t i m a t i n g the r a t e would r e s u l t i n a p r e d i c t i o n of high i n f e c t i o n numbers, a correspondingly high timber loss,and support an e r a d i c a t i o n program. What i s the cause of the i n c o n s i s t e n c y between p r e d i c t e d and observed numbers of i n f e c t i o n s ? The d i f f e r e n c e i s caused by the f a i l u r e of models to f u l l y appreciate the e f f e c t of i n f e c t i o n m o r t a l i t y on i n t e n s i f c a t i o n . Therefore the purpose of t h i s study i s t o examine the e f f e c t of i n f e c t i o n m o r t a l i t y on the development of dwarf m i s t l e t o e i n western hemlock. The two p a r t i c u l a r c h a r a c t e r i s t i c s of the p a r a s i t e s t u d i e d are i n t e n s i f i c a t i o n and v e r t i c a l spread. 4 / - 4 -1.0 LITERATURE REVIEW What i s known about the p o p u l a t i o n dynamics of the p a r a s i t e ? Two areas t h a t have been s t u d i e d are the r a t e s o f v e r t i c a l spread and i n t e n s i -f i c a t i o n . The v e r t i c a l spread r a t e of the p a r a s i t e i s too low to keep pace with the height growth of the host on s i t e s a l l o w i n g western hemlock t o grow < i n excess of 45 centimetres per year. The t r e e ' s g r e a t e r growth rate allows f o r development of a s i g n i f i c a n t p o r t i o n of i n f e c t i o n f r e e upper crown (Richardson and van der Kamp 1972). Scharpf and Parmeter (1976) observed the same phenomenom i n red f i r (Abies magnifica A. Murr.) and white f i r (Abies cdncolor (Gord. and Glendl.) L i n d l . ) . Therefore, advanced regeneration on the b e t t e r s i t e s may be l e f t provided no overhead source of dwarf m i s t l e t o e i s present and the r e s u l t i n g stand i s dense enough t o achieve e a r l y crown c l o s u r e , and i f i t i s not already so h e a v i l y i n f e c t e d t h a t i t w i l l never produce merchantable b o l e s . The i n t e n s i f i c a t i o n of dwarf m i s t l e t o e i n western hemlock advanced regeneration f o l l o w i n g the removal of overstory i n f e c t i o n source was s t u d i e d by Smith (1977). He observed that where advance regeneration was h e a v i l y i n f e c t e d , the i n t e n s i f i c a t i o n r a t e was h i g h due to i n t e r n a l r e i n f e c t i o n . The h e a v i l y i n f e c t e d t r e e s showed a decrease i n growth. The dwarf m i s t l e t o e p o p u l a t i o n i n the l i g h t l y i n f e c t e d t r e e s d i d not i n t e n s i f y r a p i d l y and were not l i k e l y t o show a decrease i n growth. The h e a v i l y i n f e c t e d t r e e s were concentrated w i t h i n three t o f i v e metres of the i n f e c t e d r e s i d u a l t r e e . Smith found an i n i t i a l r a p i d i n c r e a s e i n the i n f e c t i o n t o t a l s per t r e e per year and t h a t e i g h t years a f t e r the overstory removal 5/ . . . - 5 -i n f e c t i o n l e v e l s appeared to be l e v e l l i n g o f f . Smith (1969) observed o l d h e a v i l y i n f e c t e d t r e e s t o have 84% l e s s height growth and 41% l e s s volume growth than l i g h t l y i n f e c t e d t r e e s . However, a c t u a l l o s s e s i n volume or value have yet to be c o r r e l a t e d to numbers of i n f e c t i o n s . I n t e n s i f i c a t i o n and v e r t i c a l spread r a t e s of seve r a l dwarf m i s t l e t o e species on t h e i r r e s p e c t i v e hosts have been observed. Muir (1972) estimated doubling t o occur a f t e r 1.25 years on lodgepole p i n e . Richardson and van der Kamp (1972) found four years t o be the doubling time on western hemlock. I n o c u l a t i o n s on red and white f i r had doubling times which v a r i e d from 3 to over 15 years (Scharpf and Parmeter 1976). A determining f a c t o r i n i n t e n s i f i c a t i o n r a t e s i s the degree of crown c l o s u r e . A very young ( < 10 years) stand's degree o f crown c l o s u r e would be l e s s than t h a t o f a mature stand. Very high r a t e s o f i n t e n s i f i c a t i o n have been observed i n a very young stand by Smith (1977). As crown c l o s u r e i n c r e a s e d , the i n t e n s i f i c a t i o n r a t e decreased markedly. The stand examined by Muir (1972) was a l s o immature. Hawksworth and Lusher (1956) developed a 6-class r a t i n g system f o r dwarf m i s t l e t o e i n f e c t e d lodgepole pine. Ratings were found t o incr e a s e by 1 c l a s s every 10 years. Smith (1969) a l t e r e d the system t o ra t e western hemlock to a 6-class system based only on the i n f e c t i o n s t a tus of the middle t h i r d of the crown. V e r t i c a l spread r a t e s i n open and dense stands of western hemlock of 65 and 30 centimetres per year r e s p e c t i v e l y , (Richardson and van der Kamp 1972) and 7.8 centimetres per year on red and white f i r stand (Scharpf and Parmeter 1976) have been observed. The Richardson and van der Kamp (1972) r a t e s are based on an advancing f r o n t of the p a r a s i t e . The rat e s of the 6/ . . . - 6 -other authors are based on the average height of a l l i n f e c t i o n s each year. The r a t i o of male:female i n f e c t i o n s f o r Arceuthobium species has been found t o be 1:1 f o r species of western United States and Canada. Mexican dwarf m i s t l e t o e species favour the female p l a n t (Hawksworth 1978). Smith (1977) discussed i n f e c t i o n m o r t a l i t y but d i d not inc o r p o r a t e i t i n i n t e n s i f i c a t i o n c a l c u l a t i o n s . 7/ - 7 -2.0 METHODS 2.1 Stand S e l e c t i o n Two stands were s e l e c t e d using the f o l l o w i n g f o u r c r i t e r i a . F i r s t , the s i t e i n d i c e s were to be s i m i l a r . Second, the stands were western hemlock w i t h complete crown c l o s u r e . T h i r d , the mature stand was t o e x h i b i t evidence of e a r l y dwarf m i s t l e t o e development. The f o u r t h c r i t e r i o n was f o r the t e r r a i n t o be l e v e l w i t h sample t r e e s occupying dominant and co-dominant p o s i t i o n s i n the canopy. The stands s e l e c t e d were on the f r i n g e s of two separate f i r e s . The n a t u r a l regeneration was i n f e c t e d from unburned neighbouring stands which were e v e n t u a l l y harvested (younger stand) or burned ( o l d e r stand). The o l d e r stand appeared t o have been rel e a s e d by the f i r e o f 1867. Evidence f o r the i n f e c t i o n h i s t o r y r e l a t i o n s h i p o f the two stands came from two observations. The f i r s t o b s e r v a t i o n was that l a r g e stem i n f e c t i o n s , which r e q u i r e decades f o r development, were present i n the mature stand. The second was t h a t branch stubs, p r e v i o u s l y recorded as dead (Anonymous 1977), were a c t u a l l y l i v e dwarf m i s t l e t o e i n f e c t i o n s of up t o 93 years of age. Some of the undatable trunk i n f e c t i o n s occurred below the 93 year branch i n f e c t i o n s and hence were considered t o be o l d e r . I t was apparent t h a t an overlap i n i n f e c t i o n ages between the two stands e x i s t e d . Figure 1 shows the l o c a t i o n of the two stands and d e t a i l s the h i s t o r y of the area. Study p l o t d e t a i l s are given i n Table 1. 2.2 P l o t Establishment The immature p l o t was .01 o f a hectare i n s i z e and contained 6 t r e e s . The mature stand p l o t had 5 t r e e s i n .025 of a hectare. The p l o t t r e e s 8/ . . . LOGGED 1962 LEGEND N-V> CREEK * s = » ROADWAY HISTORY BOUNDARY 9. I T km Figure 1. The location and history of the immature and mature dwarf mistletoe infected western hemlock stands in the University of British Columbia Research Forest, Maple Ridge, B.C., Canada, Latitude 49015', Longitude 122°33'. i 9/ . . . - 9 -T a b l e 1. S a m p l e p l o t m e a s u r e m e n t s f o r i m m a t u r e a n d m a t u r e d w a r f m i s t l e t o e i n f e c t e d w e s t e r n h e m l o c k s t a n d s a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a R e s e a r c h F o r e s t , 1 9 7 9 . C h a r a c t e r i s t i c I m m a t u r e S t a n d M a t u r e S i t e i n d e x (m) 40 40 N u m b e r o f p l o t t r e e s A v e r a g e h e i g h t (m) R a n g e 2 0 . 8 1 9 . 3 - 2 2 . 9 3 8 . 1 3 3 . 8 - 4 6 . 0 A v e r a g e l i v e c r o w n b a s e (m) 3.7 9.2 A v e r a g e t r e e a g e ( y e a r s ) R a n g e 44 n i l 1 3 0 8 1 - 1 6 0 P l o t a r e a ( h a ) .01 . 0 2 5 1 0 / . . . were f e l l e d and examined from ground l e v e l to t e r m i n a l on a branch by branch b a s i s i n the f i e l d . The average age of t r e e s i n the p l o t s was determined by aging a ground l e v e l c r o s s - s e c t i o n of each t r e e and o b t a i n i n g a p l o t average. 2.3 V e r t i c a l Rate of Spread C a l c u l a t i o n The f o u r month (May t o August, 1979) branch by branch search l o c a t e d the dwarf m i s t l e t o e i n f e c t i o n s which were c o l l e c t e d and taken i n f o r l a b examination. The age of i n f e c t i o n s was determined using a technique developed by Scharpf and Parmeter (1966). The procedure c o n s i s t s of c r o s s - s e c t i o n i n g the widest po i n t of the i n f e c t i o n and counting from the f i r s t i r r e g u l a r r i n g out to the cambium. The f i r s t i r r e g u l a r r i n g i s the r e s u l t of the p a r a s i t e causing a b n o r m a l i t i e s i n the p a t t e r n of annual r i n g formation at the time of i n f e c t i o n . 2.4 V e r t i c a l Height Growth of Trees The t r e e s of both p l o t s were sectioned (from ground l e v e l up) at 2-metre i n t e r v a l s and the age of each s e c t i o n was determined to f i n d out when the maximum v e r t i c a l r a t e of growth of the t r e e s s t a r t e d . The height growth of the t r e e s o c c u r r i n g i n the l i n e a r phase was d i v i d e d by the number of years i n the l i n e a r phase and averaged t o o b t a i n a stand value of height growth. The r a t e of growth was compared t o the v e r t i c a l spread r a t e of the p a r a s i t e . 2.5 MaletFemale I n f e c t i o n R a t i o Determination In the l a b o r a t o r y the sex of the i n f e c t i o n s was determined using the c h a r a c t e r i s t i c s of the mature p l a n t s w i t h a d i s s e c t i n g microscope at 10 power. Male flowers contain p o l l e n sacs and have 3 or 4 sepals. Femal flowers have 2 sepals, no p o l l e n sacs, and had mature or immature f r u i t Infections with shoots that could not be i d e n t i f i e d to sex were not included i n the sex r a t i o determination. 12/ . - 12 -3.0 RESULTS AND DISCUSSION The data (see Appendices I and I I ) were analyzed on a stand b a s i s f o r s e v e r a l reasons. F i r s t , the canopies were dense with the i n d i v i d u a l crowns meshed together. The branch overlap would prevent the development o f a s e l f - c o n t a i n e d dwarf m i s t l e t o e p o p u l a t i o n i n any one crown. Second, western hemlock i s managed on an even-aged b a s i s ( c l e a r c u t h a r v e s t i n g ) . Therefore, any volume l o s s e s due t o i n f e c t i o n s would appear on a stand b a s i s . The l a s t 3 years o f i n f e c t i o n data were not used i n c a l c u l a t i o n s because i n f e c t i o n s l e s s than 4 years o l d cannot be detected with c e r t a i n t y . Therefore c a l c u l a t i o n s and f i g u r e s w i t h i n f e c t i o n age are i n f e c t i o n age minus 3. (The sample p l o t observations were presented i n Table 2 ) . 3.1 Rate o f I n t e n s i f i c a t i o n The i n t e n s i f i c a t i o n r a t e i s u s u a l l y estimated from the number and age of i n f e c t i o n s present i n a stand at the time of sample c o l l e c t i o n (Muir 1963; Richardson and van der Kamp 1972). The data were arranged t o show the number of i n f e c t i o n s e s t a b l i s h e d each year over a pe r i o d of time ( u s u a l l y more than a decade) and the r a t e o f increase estimated (Figures 2 and 3 ) . The method assumed t h a t as the p a r a s i t e i n f e c t i o n s were p e r e n n i a l a l l the i n f e c t i o n s e s t a b l i s h e d i n the p e r i o d under study were s t i l l present at sample c o l l e c t i o n . A second assumption was t h a t the number o f new i n f e c t i o n s e s t a b l i s h e d annually was p r o p o r t i o n a l to the number of seeds produced when the crown volume ( t a r g e t area) i n the stand remained constant. Some v a r i a t i o n w i l l be observed each year, l a r g e l y due to weather, but the general p r o p o r t i o n a l increase i n numbers should be described by a l o g a r i t h m i c equation. The equation would r e l a t e number of i n f e c t i o n s (Y) to the 13/ . . . - 13 -Table 2. Sample p l o t r e s u l t s f o r immature and mature dwarf m i s t l e t o e i n f e c t e d western hemlock stands at the U n i v e r s i t y of B r i t i s h Columbia Research F o r e s t , 1979. C h a r a c t e r ! s t i c Stand Immature Mature Number of l i v e i n f e c t i o n s Number of dead i n f e c t i o n s T o t a l number of i n f e c t i o n s Number of l i v e i n f e c t i o n s per u n i t of p l o t area (m 2) Average number of i n f e c t i o n s per t r e e Range Average top i n f e c t i o n height (m) Range Average % l i v e crown f r e e of i n f e c t i o n Male t o female i n f e c t i o n r a t i o Frequency Average r a t e o f current host height growth (m/year) Range Rate o f p a r a s i t e advance (m/year) without m o r t a l i t y Range Rate of p a r a s i t e advance (m/year) w i t h m o r t a l i t y 278 405 683 2.78 46.3 3.78 12.4 10.4-14.0 58.7 18:14 1:0.78 . .54 n i l .49 0.0-1.6 .28 418 93 511 1.64 83.6 10-244 ' 25.4 22.3-28.7 54.5 88:107 1:1.2 .41 .35-.47 .42 0.0-1.2 .19 14/ - 14 -40 36 32 L 28 z 24 o 2 0 I 6 •• • • • • • • • •• • •• • # • •• ••• • • • • • • • ••• • ••• • # ••• ••••• • • • • i • I L. • I I 1 1-J 1 J L. 10 20 30 40 50 60 70 INFECTION A G E , y e a r s - 3 80 90 Figure 2. The number of live dwarf mistletoe infections per plot versus infection age for the mature western hemlock stand. 15/ . . - 15 -36 32 L 28 241 if) z o t-b 20 o z 12 _J i i_ _i i i_ i ' • ' i i i i t 16 18 4 6 8 10 12 14 I N FE CTl ON AGE , yeors -3 Figure 3. The number of l i v e dwarf mistletoe i n f e c t i o n s per p l o t versus i n f e c t i o n age f o r the immature western hemlock stand. 16/ . . . - 16 -i n f e c t i o n age (X) i n the f o l l o w i n g forms; Log Y = a + bX with the doubling time (dt) o f : dt = l o g 2 b The l o g form seems t o describe the young stand (and the f i r s t 14 years of the o l d stand) w e l l . The dependent v a r i a b l e (number of i n f e c t i o n s ) was examined on an area b a s i s (per metre squared) because the study p l o t s were of unequal s i z e . l o g Y = .41434 - .06212X ( l ) r = .957 p e r i o d = 1962 - 1975 Equation 1 i s based on the 238 l i v e i n f e c t i o n s i n the pe r i o d of study found i n the young stand. An a d d i t i o n a l 405 dead (undatable) i n f e c t i o n s were a l s o observed. The dead i n f e c t i o n s were small and b e l i e v e d to be l e s s than 10 years o l d at the time of death. The dead i n f e c t i o n s were below and i n the l i v e crown, and t h e r e f o r e not n e c e s s a r i l y t a b u l a t e d (Figure 4 ) . (Dead branches w i t h dead i n f e c t i o n s c o n t r i b u t e d t o the l i t t e r l a y e r below the p l o t t r e e s but were not counted as part of the 405 dead i n f e c t i o n s . ) The t o t a l number of i n f e c t i o n s e s t a b l i s h e d i n the 44 year o l d p l o t was at l e a s t 683 (405 dead + 278 l i v e ) . For Equation 1 to be c o r r e c t a l l the dead i n f e c t i o n s must be from before or a f t e r the 1962 - 1975 study p e r i o d . Equation 1 i n d i c a t e d only 29 i n f e c t i o n s , not 405, were e s t a b l i s h e d between 1936 and 1962. Moreover, most i n f e c t i o n s e s t a b l i s h e d before 1962 and k i l l e d w i t h i n 10 years would have been l o s t by the c o l l e c t i o n date of 1979. And as the dead i n f e c t i o n s 17/ . . . - 17 -Figure 4. The number of l i v e (o) and dead (.) dwarf mistletoe i n f e c t i o n s per p l o t versus i n f e c t i o n height above ground i n three metre classes f o r the immature western hemlock stand. 18/ - 18 -appeared to be over 3 years o l d , they could not have been e s t a b l i s h e d a f t e r 1976. The presence of dead i n f e c t i o n s , apparently from the pe r i o d between 1962 t o 1975, suggested i n t e n s i f i c a t i o n and m o r t a l i t y occurred c o n c u r r e n t l y . Therefore, Equation 1, based s o l e l y on the l i v e i n f e c t i o n s , i s not represen-t a t i v e of the po p u l a t i o n development. I n f e c t i o n s e s t a b l i s h e d i n 1974 and 1975 were probably a l i v e i n 1979 and i f not a l i v e , the i n f e c t i o n s would be too small to be observed and inc l u d e d i n the 405 dead i n f e c t i o n s . Of the i n f e c t i o n s over 5 years o l d , some would have died and the remaining l i v e i n f e c t i o n s would have decreased at a r a t e p r o p o r t i o n a l to age. I f the number of i n f e c t i o n s e s t a b l i s h e d each year was constant, t a k i n g the number of i n f e c t i o n s found f o r 1975, which was 38, and m u l t i p l y i n g 38 by 14 (the length o f the study p e r i o d 1962 - 1975) , the number of i n f e c t i o n s expected t o have been e s t a b l i s h e d i n the study p e r i o d would be 532. Therefore, accepting 643 (238 l i v e + 405 dead) i n f e c t i o n s as the number e s t a b l i s h e d between 1962 and 1975 the a c t u a l number of i n f e c t i o n s had increased very l i t t l e . Based on the data, Equation 1 does not give the rat e of i n t e n s i f i -c a t i o n but i t does give an i n d i c a t i o n of i n f e c t i o n m o r t a l i t y . The expression: t y = l o g 2  / 2 ~ b gives a h a l f - l i f e of i n f e c t i o n s f o r the immature stand of 4.8 years (Table 3). The mature stand data were then compared to the immature stand data (see Table 1 ). The mature stand had fewer dead and more l i v e i n f e c t i o n s than the immature stand. Fewer dead i n f e c t i o n s could be a r e s u l t of the 19/ . . . Table 3. Comparison o f equations, i n f e c t i o n t o t a l s and doubling times f o r the immature and mature dwarf m i s t l e t o e i n f e c t e d western hemlock stands during the 1962-1975 p e r i o d . Stand Equation A r * Sy.x* I n f e c t i o n Total Doubling Time Immature (1-14 years) Mature (1-14 years) Log Log Y = -.3826 - .06212X Y = -.8291 - .06864X .975 .925 3.26 4.17 238 200 4.8 4.4 * "Because the standard e r r o r of estimate determined from the r e s i d u a l mean square of a l o g a r i t h m i c equation cannot be transformed back t o an a r i t h m e t i c s c a l e without b i a s , the standard e r r o r s o f estimate (Sy.x) of a l l l o g a r i t h i m i c equations were c a l c u l a t e d from observed and estimated values of the dependent v a r i a b l e : + .JE^L „h< — V n-m-l A /S(V-V)^ * Sy.x = + \/ „_m_-\ where y and y = observed and estimated values o f the dependent v a r i a b l e n = number o f observations m = number of independent v a r i a b l e s S i m i l a r l y , an estimated c o e f f i c i e n t of determination ( r ) was obtained d i r e c t l y from: A2 A r = SS t o t a l - SS r e s i d u a l SS t o t a l where SS t o t a l = sum of square of untransformed Y SS r e s i d u a l ^ ( y - y ) 2 " 1 1. Johnstone 1976, pp. 5-7. 20/ - 20 -g r e a t e r e f f e c t o f wind pruning o f dead branches i n o l d e r , t a l l e r stands. More l i v e i n f e c t i o n s were found i n the mature stand as a r e f l e c t i o n of the in c r e a s e i n i n f e c t i o n s over time. The s i m i l a r i t y o f Figures 2 and 3 prompted f u r t h e r examination. The tr a n s f o r m a t i o n o f the number of i n f e c t i o n s (1-14 years) f o r the mature stand t o an area b a s i s allowed f o r d i r e c t comparison (Figure 5). The l o g a r i t h m i c t r a n s f o r m a t i o n of the number of i n f e c t i o n s c o r r e c t e d f o r p l o t 2 area (m ) preceded r e g r e s s i o n analyses of the data (Table 4 ) . The equations f o r the immature and mature stands (1-14 years) were very s i m i l a r . The s i m i l a r i t y prompted f u r t h e r a n a l y s i s o f the two sets of data. Table 4 presents the r e s u l t s o f F - t e s t s f o r d i f f e r e n c e s o f slopes and l e v e l s of r e g r e s s i o n . No s i g n i f i c a n t d i f f e r e n c e was found between the slopes but the l e v e l s of r e g r e s s i o n were s i g n i f i c a n t l y d i f f e r e n t . Therefore 1 equation could not describe the 2 stands, but 1 doubling time can be used f o r both stands (Figure 5 ). A steady decrease was observed f o r the 15-60 year p e r i o d followed by a f a s t e r r a t e o f i n f e c t i o n l o s s t o only 1 93-year o l d i n f e c t i o n . S i x t y year o l d pl u s i n f e c t i o n s were on l e a f l e s s branch stubs below the l i v e crown (see Figure 6 ) . Presumably, many a d d i t i o n a l i n f e c t i o n s from the 60 year o l d p l u s i n f e c t i o n s were l o s t through branch senescence. Accepting the f i r s t 14 years of data t o represent m o r t a l i t y and t h a t f o l l o w i n g the i n i t i a l p e r i o d of m o r t a l i t y the p o p u l a t i o n was r e l a t i v e l y s t a b l e up t o the 60th year, the rat e of i n t e n s i f i c a t i o n could be estimated f o r the 1-60 year p e r i o d . A l o g a r i t h m i c equation: l o g Y = 1.0534 - .01221X (2) r * = .648 Sy.x* =7.62 produced a doubling time of 24.0 ye a r s . 21/ . . . - 21 -o •2.01 2 4 6 8 10 12 14 INFECTION AGE, years -3 Figure 5. The l o g of the number of dwarf m i s t l e t o e i n f e c t i o n s per metre squared o f p l o t area f o r the immature (.) and mature (o) western hemlock stands versus i n f e c t i o n age f o r the 1962-1975 p e r i o d (-3 y e a r s ) . 22/ - 22 -Table 4. Group r e g r e s s i o n analyses of the i n t e n s i f i c a t i o n r a t e o f dwarf m i s t l e t o e i n the immature and mature dwarf m i s t l e t o e i n f e c t e d western hemlock stands during the 1962-1975 p e r i o d (Appendix I I I ) . Stands Immature Mature I n t e r c e p t Regression c o e f f i c i e n t F -test of d i f f e r e n c e i n slope F - t e s t o f l e v e l s o f r e g r e s s i o n N.S. not s i g n i f i c a n t * s i g n i f i c a n t at the .05 p r o b a b i l i t y l e v e l .41434 .14822 .06212 -.06854 .42027 N.S. 6.09334* 23/ - 23 -I00 r <7.9 8.0- 11.0- 14.0 - 17.0- 20.0" 23.0 26.0 2 9.0 10.9 13.9 16.9 19.9 22.9 25.9 28.9 31,9 HEIGHT, m Figure 6 . The number of live, (o) and dead (.) dwarf mistletoe i n f e c t i o n s per p l o t versus i n f e c t i o n height above ground i n three metre classes f o r the mature western hemlock stand. 24/ - 24 -I n f e c t i o n s t h a t occur on young high order branches are expected t o be l o s t e a r l y (before 10 years) due to branch senescence. I n f e c t i o n s e s t a b l i s h e d on major branch axes are l i k e l y to become brooms and survive f o r a long p e r i o d o f time. As there are more high order f i n e branches than major axes, i f one i n f e c t i o n i s e s t a b l i s h e d on each small branch and on each a x i s , the r e s u l t i s a r a p i d decrease i n the numbers of i n f e c t i o n s f o r any year u n t i l the f i n e branch i n f e c t i o n s are mostly gone and only i n f e c t i o n s at major axes remain. Therefore, the o l d e s t i n f e c t i o n s are found on major branch axes. I f the decrease i n i n f e c t i o n s with time i s due s o l e l y to m o r t a l i t y then Figure 2 represents a l i f e t a b l e from which an equation can be developed t o d e scribe the p r o b a b i l i t y of an i n f e c t i o n s u r v i v i n g another year. The equation developed was: P = 1 I <3> s u r v i v a l ( a g e - 3 ) 1 * 1 2 + 2 Equation 2 d e s c r i b e s the s i t u a t i o n represented by Figure 2 as w e l l as the p r o b a b i l i t y of s u r v i v a l i ncreases as a f u n c t i o n o f i n f e c t i o n age. Equation 3 can be used t o d e r i v e a d i s t r i b u t i o n of numbers of i n f e c t i o n over i n f e c t i o n age as f o l l o w s : S t a r t i n g w i t h 100 i n f e c t i o n s at age 4, the number of i n f e c t i o n s at age 5 would be: n = 100 X 1 -( I ) 1 " 1 2 + 2 = 66.67 and at age 6: n = 66.67 X 1 -( 2 ) 1 ' 1 2 + 2 50.69 • • • 61C • The sum of the number of i n f e c t i o n s from age 1 to 60 i s 940.77. The a c t u a l number of i n f e c t i o n s observed between 1 and 60 was 379. The p r e d i c t e d number of i n f e c t i o n s i s determined by d i v i d i n g the observed i n f e c t i o n t o t a l 25/ . . . - 25 -(379) by the t r i a l number t o t a l 940.77 and m u l t i p l y i n g the dividend by the o r i g i n a l estimate. For example, the p r e d i c t e d number of 1 year o l d i n f e c -t i o n s i s : 1 0 0 X 9§0T77 = 4 0 ' 2 9 and the 2 year o l d i n f e c t i o n s : 66.67 X „ ^ 7 9 = 26.86 . . . etc, 940 .77 In comparison equation 3 i s s i g n i f i c a n t l y b e t t e r than 2 i n d e s c r i b i n g the data of the mature stand (Table 5). This study i n d i c a t e s t h a t the apparent i n c r e a s e i n i n f e c t i o n over time i s a c t u a l l y a decrease due to m o r t a l i t y . Most of the m o r t a l i t y occurs by 14 years of age. While the doubling time cannot be derived d i r e c t l y , t h i s study shows the method used by e a r l i e r s t u d i e s to be i n a c c u r a t e . A doubling time of 40 or more years i s suggested by t h i s study. The 40 years p l u s doubling time i s confirmed by the increase i n i n f e c t i o n s per t r e e from the young (46.3) to the o l d (83.6) stand. A doubling time of 4 or 5 years should have r e s u l t e d i n the per t r e e i n f e c t i o n t o t a l many orders of magnitude g r e a t e r than observed. There i s a l s o a decrease i n the i n f e c t i o n s per metre squared of 2.78 t o 1.64 from the immature stand to the mature stand. The model developed by Bloomberg et a l (1980) produces doubling times of 2 to 4 years. While the model does use a m o r t a l i t y equation developed by Smith (1977), the equation was recommended not be e x t r a p o l a t e d beyond 12 years. The model should not be used u n t i l research can develop doubling times a c c u r a t e l y by i n c l u d i n g i n f e c t i o n m o r t a l i t y . 26/ - 26 -Table 5.. Comparison of l o g a r i t h m i c and p r o b a b i l i t y equations f o r the p r e d i c t i o n of numbers of dwarf m i s t l e t o e i n f e c t i o n s i n the mature dwarf m i s t l e t o e i n f e c t e d western hemlock stand. ,. , „ Residual sums Residual mean ^ . Equation d.f. „ „ F = 1.96 ^ of squares of squares .05, 60, 60 (2) Logarithmic 59 1,697.10 28.76 (3) P r o b a b i l i t y 59 248.74 4.22 F value 6.82 27/ - 27 -3.2 V e r t i c a l Spread Rate of Dwarf M i s t l e t o e The r a t e s of v e r t i c a l spread were .49 (range 0 t o 1.6) and .42 (range 0 t o 1.2) metres per year f o r the immature and mature stands r e s p e c t i v e l y (Figures 7 and 8 ) . The height growth r a t e s were .54 and .30 metres per year f o r the immature and mature stands r e s p e c t i v e l y . The growth r a t e of the immature stand was keeping ahead of the p a r a s i t e and the mature stand was not keeping up (Figures 7 and 8 ) . P r o j e c t i n g the v e r t i c a l spread r a t e f o r the immature stand (.49 metres per year) f o r 86 years (to reach the age of the mature stand) the i n f e c t i o n l e v e l i s p r e d i c t e d t o be 42.14 metres, c o n s i d e r a b l y higher than the observed l e v e l o f 25.4 metres and the height of the mature stand (38.1 metres). I t appears that i n f e c t i o n m o r t a l i t y has a f f e c t e d the v e r t i c a l spread r a t e . I f o l d e r i n f e c t i o n s experienced m o r t a l i t y throughout the v e r t i c a l range of normally d i s t r i b u t e d i n f e c t i o n s i n the crown, the highest and lowest o l d e r i n f e c t i o n s have l i k e l y been l o s t while a l l the younger i n f e c t i o n s are l i k e l y s t i l l present. Therefore, the estimate of v e r t i c a l spread i s from the centre of the range of o l d e r i n f e c t i o n s t o the top of the v e r t i c a l range of the l a t e s t i n f e c t i o n s . The data was re-examined. The height of the highest average i n f e c t i o n was d i v i d e d by the stand age (Table 2) and produced v e r t i c a l spread r a t e s of .28 (immature stand) and .19 metres per year (mature stand). A l t e r n a t i v e l y , f o r the i n f e c t i o n l e v e l of the immature stand to reach the l e v e l of the mature stand the r a t e could be only .15 metres per year ( d i f f e r e n c e between the i n f e c t i o n l e v e l s o f the two stands, 12 metres, d i v i d e d by the age d i f f e r e n c e of the stands, 86 y e a r s ) . 28/ . . . - 28 -2 2 . 18 in Qi | I4L x Ixl X 10 • 25 30 35 STAND AGE , years 4 0 45 Figure 7. The average host height (o) and the height of the advancing front of the parasite (.) versus stand age i n the immature western hemlock stand. 29/ - 29 -4 0 r STAND AGE, years Figure 8 . The average host height (o) and the height of the advancing front of the para s i t e ( .') versus stand age i n the mature western hemlock stand. 30/ - 30 -3.3 Male:Female I n f e c t i o n R a t i o Determination The male:female r a t i o s were 1:0.8 or (18:14), and 1:1.2 or (88:107) f o r the immature and mature stands r e s p e c t i v e l y . For both stands the r a t i o s are not s i g n i f i c a n t l y d i f f e r e n t from an equal d i s t r i b u t i o n o f the sexes. The 1:1 d i s t r i b u t i o n supports previous s t u d i e s (Hawksworth 1978). 31/ - 31 -4.0 CONCLUSIONS The i n t e n s i f i c a t i o n and v e r t i c a l spread ra t e s o f dwarf m i s t l e t o e were examined i n 2 stands of western hemlock. The 2 stands were of d i f f e r e n t age but s i m i l a r i n s i t e and i n f e c t i o n h i s t o r y . The standard method of e s t i m a t i n g i n t e n s i f i c a t i o n and v e r t i c a l spread r a t e s , based on the apparent number o f i n f e c t i o n s e s t a b l i s h e d each year over a p e r i o d o f 10 or more years p r i o r t o the sample c o l l e c t i o n date, as used by Muir (1963) and Richardson and van der Kamp (1972), was shown to be i n a p p r o p r i a t e . I n f e c t i o n m o r t a l i t y , ignored i n the standard method, was shown t o be very important i n the p r e d i c t i o n of v e r t i c a l spread and i n t e n s i f i c a t i o n r a t e s of the p a r a s i t e . I n f e c t i o n m o r t a l i t y i s important because the l o s s of i n f e c t i o n s over time prevents the accurate determination of i n t e n s i f i c a t i o n and v e r t i c a l spread r a t e s . I n f e c t i o n m o r t a l i t y produces a decrease i n numbers of i n f e c -t i o n s over time. A d d i t i o n a l l y , i f the same number of i n f e c t i o n s i s e s t a b l i s h e d each year then i n t e n s i f i c a t i o n , as determined by the standard method, i s more c o r r e c t l y an example of i n f e c t i o n h a l f - l i f e . The r e a l doubling time, while not d i r e c t l y determined, i s over 40 years. I n f e c t i o n m o r t a l i t y a l s o a f f e c t s the v e r t i c a l spread rat e c a l c u l a t i o n by reducing the number of o l d e r i n f e c t i o n s . Therefore, assuming the o l d e r i n f e c t i o n s experienced m o r t a l i t y throughout the v e r t i c a l range of normally d i s t r i b u t e d i n f e c t i o n s i n the crowns, the highest and lowest o l d e r i n f e c t i o n s have l i k e l y been l o s t while a l l the younger i n f e c t i o n s are l i k e l y s t i l l present. Therefore, the estimate of v e r t i c a l spread i s from the centre of o l d e r i n f e c t i o n v e r t i c a l ranges to the top of the l a t e s t i n f e c t i o n v e r t i c a l ranges. The data, while not d i r e c t l y determining the 32/ - 32 -r a t e , suggested the v e r t i c a l spread r a t e to be approximately .15 metres per year. The i m p l i c a t i o n of the study i s t h a t on s i t e s where western hemlock grows f a s t e r than 45 centimetres per year, and where no overhead i n f e c t i o n sources are present, i n f e c t e d small r e s i d u a l s ( l e s s than 2 metres) can be kept and i n f e c t e d immature stands can be spaced. The number of new i n f e c t i o n s w i l l i ncrease i n i t i a l l y but w i l l decrease again when crown c l o s u r e occurs. This work i n d i c a t e d continued study i s r e q u i r e d t o o b t a i n a more accurate estimate of i n f e c t i o n m o r t a l i t y f o r computer models t o avoid u n j u s t i f i e d management d e c i s i o n s being made with respect t o western hemlock dwarf m i s t l e t o e c o n t r o l i n c o a s t a l B r i t i s h Columbian f o r e s t s . 33/ - 33 -LITERATURE CITED Anonymous, 1977. Volume and decay manual, F o r e s t r y Inventory D i v i s i o n . B. C. For. Serv., V i c t o r i a , B.C. :122-123. Anonymous, 1980. Report of the M i n i s t r y of F o r e s t s , year ended December 31, 1980. M i n i s t r y of F o r e s t s , V i c t o r i a , B.C. :44. Baranyay, J.A. and R.B. Smith, 1972. Dwarf m i s t l e t o e s i n B r i t i s h Columbia and recommendations f o r t h e i r c o n t r o l . Pac. For. Res. Cen. BC-X-72. Bloomberg, W.J., R.B. Smith, and A. van der Weveld, 1980. A model of spread and i n t e n s i f i c a t i o n of dwarf m i s t l e t o e i n f e c t i o n i n young western hemlock stands. Can. J . For. Res. 10(1):42-52. Buckland, D.C. and E.G. Marples, 1952. Management of western hemlock i n f e c t e d with dwarf m i s t l e t o e . B.C. Lumberman 36(5):50, 51, 136, 138, 140. Freese, F., 1967. Elementary s t a t i s t i c a l methods f o r f o r e s t e r s . A g r i c . Hdbk. 317, U.S. Dept. A g r i c . For. Serv. :68-70. Hawksworth, F.G., 1978. Bases f o r c o n t r o l , b i o l o g i c a l f a c t o r s of dwarf m i s t l e t o e i n r e l a t i o n to c o n t r o l . Proc. symp. dwarf m i s t l e t o e c o n t r o l f o r . man. Berkeley, Ca., U.S. Dept. A g r i c . For. Serv. Gen. Tech. Rep. PSW-31:5-15. 1979. M i s t l e t o e s and t h e i r r o l e i n North American f o r e s t r y . Second symp. on p a r a s i t e weeds. :13-33. and A.A. Lusher, 1956. Dwarf m i s t l e t o e survey and c o n t r o l on the Mescalero Apache Reservation, New Mexico. J . For. 54:384-390. Johnstone, W.D., 1976. V a r i a b l e - d e n s i t y y i e l d t a b l e s f o r n a t u r a l stands of lodgeple pine i n A l b e r t a . Dept. of F i s h e r i e s and Environment, C. F.S., For. Tech. Report 20. pp 6-7. Muir, J.S., 1963. A study of epidemics of lodgepole pine dwarf m i s t l e t o e i n A l b e r t a . B.S.F. Thesis, F a c u l t y of F o r e s t r y , Univ. of B r i t i s h Columbia. 22 pp. Richardson, K.S. and B.J. van der Kamp, 1972. The r a t e o f upward advance and i n t e n s i f i c a t i o n of dwarf m i s t l e t o e on immature western hemlock. Can. J . For. Res. 2(3):313-316. 34/ - 34 -Scharpf, R.F. and J.R. Parmeter, J r . , 1966. Determining the age of dwarf m i s t l e t o e i n f e c t i o n s on red f i r . U.S. Dept. A g r i c . For. Serv. Res. Note PSW-105, 5 p. 1976. P o p u l a t i o n build-up and v e r t i c a l spread of dwarf m i s t l e t o e on young red and white f i r s i n C a l i f o r n i a . U.S. Dept. A g r i c . For. Serv. Res. Pap. PSW-122, 9 p. Smith, R.B., 1969. Assessing dwarf m i s t l e t o e on western hemlock. For. S c i . 15(3):277-285. 1977. Overstory spread and i n t e n s i f i c a t i o n of hemlock dwarf m i s t l e t o e . Can. J . For. Res. 7(4):632-640. and E.F. Wass, 1976. F i e l d e v a l u a t i o n of e c o l o g i c a l d i f f e r e n t i a t i o n of dwarf m i s t l e t o e on shore pine and western hemlock. Can. J . For. Res. 6(2):225-228. Van S i c k l e , G.A. and R.B. Smith, 1978. Dwarf m i s t l e t o e c o n t r o l s i n B r i t i s h Columbia. Proc. symp. dwarf m i s t l e t o e c o n t r o l f o r . man., Berkeley, Ca., U.S. Dept. A g r i c . For. Serv. Gen Tech. Rep. PSW-31:106-122. 35/ APPENDIX I Immature Stand Data I n f e c t i o n Number of Age I n f e c t i o n s 1 1 2 15 3 20 4 38 5 36 6 31 7 22 8 15 9 16 10 11 11 13 12 14 13 15 14 8 15 7 16 7 17 5 18 1 19 1 2 0 1 21 1 36 / . - 36 -APPENDIX I I Mature Stand Data I n f e c t i o n Number of I n f e c t i o n Number of I n f e c t i o n Number of Age I n f e c t i o n s Age I n f e c t i o n s Age I n f e c t i o n s 1 1 26 4 51 4 2 5 27 5 53 2 3 23 28 7 54 3 4 42 29 3 55 3 5 24 30 7 56 4 6 22 31 5 57 3 7 24 32 3 59 3 8 14 33 8 60 4 9 11 34 4 61 3 10 10 35 4 62 3 11 11 36 2 63 3 12 9 37 6 64 2 13 6 38 3 65 2 14 13 39 4 66 3 15 5 40 4 67 2 16 6 41 4 69 1 17 3 42 4 72 2 18 5 43 3 75 2 19 3 44 5 77 1 20 4 45 1 93 1 21 4 46 5 22 8 47 2 23 8 48 3 24 3 49 2 25 5 50 6 37/ - 37 -APPENDIX III Group Regression Analyses (Freese 1967) Line Group 1 Immature Mature df xy x 2 df RESIDUALS SS MS 13 .97105 -14.13348 227.5 12 .09300 2 13 1.25635 -15.61861 227.5 12 .18408 3 Pooled re s i d u a l s 24 .27708 .01154 4 Difference f o r t e s t i n g common slopes 1 .00485 .00485 .42028 N.S. 5 Common 26 2.22739 -29.75208 455.0 25 .28193 .01128 slope 6 Difference f o r t e s t i n g common l e v e l s 1 1.71788 1 .71788 *6.09334 7 Single 27 3.94527 -29.75204 455.0 26 1.99980 regression 2 2 xy y x Residual SS MS Immature -14.1335 .9711 227.5 .0930 Mature -15.6186 1.2564 227.5 .1841 Common slope -29.7521 2.2274 455.0 .2771 .0115 Immature Mature n = 14 Y = -11.54390 + -18.81557 = -30.69568 Y 2 = 26.54390 + 11.05226 = 37.59616 X = 105 + 105 =210 X 2 = 1,015 + 1,015 = 2,030 XY = -103.23428 + -156.73540 = -259.96968 

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