6.1 m. However, advancing th e commencement o f b o th p ru n in g and th in n in g tr e a tm e n ts to s ta n d h e i g h t 4 ,6 m y ie ld e d in c r e a s e d amounts o f c lea rw o o d .
I t i s s u g g e s te d t h a t th e fo llo w in g s c h e d u le would n o t be u n re a so n a b le i f th e o b j e c t o f management i s to p ro d u ce s u b s t a n t i a l volumes o f clearw ood:
( i ) e s t a b l i s h 1 $00 stem s p e r h e c t a r e , ( i i ) p rim e 490 stem s p e r h e c t a r e to 2 .4 m a t s ta n d h e ig h t 4 .6 m, ( i i i ) t h i n to 490 stem s p e r h e c t a r e a t s ta n d h e i g h t 4 .6 m, ( i v ) p rim e 370 stem s p e r h e c t a r e to 4*3 o a t s ta n d h e ig h t 7 .6 m, (v ) p ru n e 250 stem s p e r h e c t a r e to 6.1 m a t s ta n d h e ig h t 1 0 .7 m, ( v i ) t h i n to 250 stem s p e r h e c t a r e a t s ta n d h e ig h t 1 0 .7 m. T h is s c h e d u le i s s i m i l a r to t h a t a d v o c a te d b y F e n to n (1972 a ) . I t i s u n l i k e l y to y i e l d th e maximum p o s s i b l e amount o f clearw ood b e c a u se heav y e a r l y th in n in g i n c r e a s e s k n o t t y c o re d ia m e te r and
re d u c e s clearw o o d y i e l d . P r o c e d u re s do e x i s t to e n ab le th e d e te r m in a tio n o f th e s i l v i c u l t u r a l s t r a t e g y w hich w i l l m axim ise clearw ood y i e l d u s in g th e m odel d e s c rib e d i n C h a p te r 4 . Dynamic progracim ing h a s b e e n used b y S c h re u d e r (1971) to d e term in e
s im u lta n e o u s ly th e o p tim a l th in n in g sc h e d u le s and r o t a t i o n le n g th s f o r even aged s t a n d s , and W att (1968) has d e s c r ib e d s im u la tio n
te c h n iq u e s to f i n d th e s e t o f in d e p e n d e n t v a r i a b l e s which w i l l o p tim is e an o b j e c t i v e f u n c t i o n . However, t h e r e was i n s u f f i c i e n t
tim e a v a i l a b l e to e n ab le th e w r i t e r to a tte m p t to u se one o r
99
A STOCHASTIC ANALISIS OP THE YIELD OF CIEARIOOD
I n t r o d u c t i o n
T he a n a l y s e s c a r r i e d o u t i n C h a p t e r 6 a ssu m e d c o n d i t i o n s o f c e r t a i n t y : t h e y assu m ed t h a t t h e o u tco m e p r e d i c t e d b y ■the m o d e l
o c c u r r e d w i t h a p r o b a b i l i t y o f u n i t y * M o st d e c i s i o n - m a k i n g t e c h n i q u e s i n f o r e s t r y h a v e i m p l i c i t l y a ssu m e d c o n d i t i o n s o f c o m p le te c e r t a i n t y ( F l o r a 1 9 6 8 ) . H o w e v e r, m o s t d e c i s i o n s a r e i n f a c t m ade u n d e r c o n d i t i o n s o f u n c e r t a i n t y * M a r ty (1964) t r e a t e d t h e d e c i s i o n t o p r u n e a s e s s e n t i a l l y a d e c i s i o n u n d e r u n c e r t a i n t y . H is a p p r o a c h c o n s i s t e d o f s p e c i f y i n g t h e r a n g e o v e r w h ic h t h e d e t e r m i n a n t s o f t h e p r o f i t a b i l i t y o f p r u n i n g s u c h a s g r o w t h r a t e s , i n t e r e s t r a t e s , p r u n i n g c o s t s a n d c l e a r wood p r i c e s w e re l i k e l y to v a r y , a n d a n a l y s i n g t h e p r o f i t f u n c t i o n w i t h i n t h e s e r a n g e s . T h i s a p p r o a c h h a s t h e d i s a d v a n t a g e t h a t i t i m p l i c i t l y a ssu m e s u n i f o r m p r o b a b i l i t y d i s t r i b u t i o n s f o r t h e d e t e r m i n a n t s o f p r u n i n g p r o f i t a b i l i t y . T h u s t h e b e s t a n d t h e w o r s t o u tc o m e s w e re assu m ed t o o c c u r w i t h a p r o b a b i l i t y e q u a l t o t h a t o f t h e m o s t l i k e l y o u tc o m e . T h i s a s s u m p tio n i s c l e a r l y i n v a l i d * T hom pson (1 9 6 8 ) a l s o c o n s i d e r e d t h e d e c i s i o n t o p r u n e a s a d e c i s i o n u n d e r u n c e r t a i n t y . As s o u r c e s o f u n c e r t a i n t y h e r e c o g n i s e d f u t u r e y i e l d s , f u t u r e p r i c e s an d t h e d i s c o u n t r a t e . He d e f i n e d d i s c r e t e f u t u r e s t a t e s o f n a t u r e f o r t h e s e v a r i a b l e s , a l l o c a t e d s u b j e c t i v e p r o b a b i l i t i e s o f occurrence t o e a c h s t a t e a n d t h e n a p p l i e d B a y e s i a n d e c i s i o n -th e o ry t o c a l c u l a t e t h e p r o f i t a b i l i t y o f p r u n i n g .
101 T h is method i s t h e o r e t i c a l l y sound b u t becomes cumbersome i f a l a r g e
number o f v a r i a b l e s encom passing a w ide ra n g e o f f u t u r e s t a t e s o f n a tu r e a r e in v o lv e d ,
A m ethod which has b e e n w id e ly u sed to a s s i s t d e c i s io n making u n d e r u n c e r t a i n t y i s th e M onte C a rlo m ethod. B a s i c a l l y th e u se o f
th e method in v o lv e s s p e c i f i c a t i o n o f th e p r o b a b i l i t y d i s t r i b u t i o n s o f th e v a r i a b l e s d e te rm in in g th e outcome o f a p r o c e s s . F o r each su ch v a r i a b l e , a random v a lu e from th e d i s t r i b u t i o n i s s e le c te d and u sed i n s u b se q u e n t c a l c u l a t i o n s , i n s t e a d o f th e mean o r m edian v a lu e used i n th e d e t e r m i n i s t i c m odel. By r e p e a t i n g th e s im u la tio n many tim e s , th e p r o b a b i l i t y d i s t r i b u t i o n o f th e outcome c an b e b u i l t up and used to g u id e a d e c i s i o n ,
A good i n t r o d u c t i o n to th e Monte C a r lo m ethod i s g iv e n b y Jo n e s (1 9 7 2 ) and more advanced tr e a tm e n ts have b e e n w r i t t e n b y N ay lo r e t a l (1966) and Churchman e t a l (1957)* Monte C a r lo
s im u la tio n h a s b e e n w id e ly a p p lie d to p ro b lem s in v o lv in g s t o c h a s t i c p r o c e s s e s whose a n a ly t ic a l, s o l u t i o n w ould b e i n t r a c t a b l e , i n f i e l d s
as d i v e r s e as c r i t i c a l p a t h netw ork a n a l y s i s (K ing 1 9 5 3 ), queuing a n a ly s i s f o r th e d e s ig n o f p r o d u c tio n f a c i l i t i e s (T o ch er 196 3 ),
r is k - in v e s t m e n t a n a l y s i s (J o n e s 1972) and n u c le a r p h y s ic s (Meyer 1956), The m ethod h a s b e e n u sed i n f o r e s t r y d e c i s i o n m aking, D a v is (1968) m en tio n ed u se o f Monte C a r lo m ethods i n netw ork a n a ly s is o f
c o n t r o l l e d b u rn in g s c h e d u lin g p ro b le m s, R u d ra (1970)> Newnham e t a l (1970) and 0*Regan e t a l (1 9 6 6 , 1967) have u sed Monte C a r lo methods
The Y ie ld o f ClearwDod as a S to c h a s t i c P r o c e s s
The r e g r e s s i o n s upon w hich th e s im u la tio n m odel d e s c r ib e d i n C h ap ter 4 i s b a s e d d e s c r ib e s t o c h a s t i c p ro c e s s e s « On th e se grounds
a lo n e th e d e c i s i o n to p ru n e to p ro d u ce clearw o o d embodies a d e g re e o f u n c e r t a i n t y . U n c e r ta in ty i s a ls o in tr o d u c e d i n t o th e m odel b e c a u s e a s i l v i c u l t u r a l t r e a t n e n t i s u n l i k e l y to b e a p p lie d e x a c tly as p r e s c r i b e d .
The s o u r c e s o f u n c e r t a i n t y i n th e clearw o o d y i e l d r e s u l t i n g from th e regim e a d v o cated i n C h a p te r 6 a re :