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Estimation of browse biomass production of Salix SPP. and Betula blandulosa using multiple linear regression Habgood, Helen Leslie 1985

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ESTIMATION  OF BROWSE BIOMASS PRODUCTION OF SAL IX SPP.  AND BETULA  6LAMM LOSA  USING MULTIPLE LINEAR  REGRESSION  By HELEN L E S L I E HABGOOD B.Sc,  Western Washington U n i v e r s i t y ,  A THESIS SUBMITTED  1980  IN PARTIAL FULFILLMENT OF  THE REQIUREMENTS FOR THE DEGREE OF MASTER OF SCIENCE  in THE FACULTY OF GRADUATE Department  We a c c e p t  this  STUDIES  o-f F o r e s t r y  thesis  -to th.e r e q u i r e d  a s con-forming standard  THE UNIVERSITY OF B R I T I S H COLUMBIA S e p t e m b e r , 1985 @  Helen L e s l i e  Habgood  In p r e s e n t i n g  t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of  requirements f o r an advanced degree a t the  the  University  o f B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make it  f r e e l y a v a i l a b l e f o r reference  and  study.  I  further  agree t h a t p e r m i s s i o n f o r e x t e n s i v e copying o f t h i s t h e s i s f o r s c h o l a r l y purposes may department or by h i s or her  be granted by the head o f representatives.  my  It is  understood t h a t copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l gain  s h a l l not be allowed without my  permission.  Department of The  U n i v e r s i t y of B r i t i s h Columbia  1956  Main M a l l  Vancouver, Canada V6T 1Y3  written  ABSTRACT  Browse b i omasa p r o d u c t i o n o-f Saiix glandulosa  on an  a wetland  Based  on  shrub  b i o m a s a and  regression obtained was  the  between  value  required  I t was  f o u r Salix  literature  stem b i o m a s s w i t h  regression relationships  with  More a c c u r a t e p r e d i c t i o n s  general  the approach b e c a u s e of  collection  and  without  taken  equations equations. is limited  and  a density estimate was  applied.  were o b t a i n e d and  preparation.  -  ii -  of  using  biomass equations  b i o m a s s were based  concluded  if site-specific  the c o n s i d e r a b l e time  It  differentiating  equations  I t was  to  combining  to o b t a i n a c c e p t a b l e biomass  s p e c i e s encountered  using s i t e - s p e c i f i c than  pertaining  density estimation, a technique  possible  the s p e c i e s .  data of  the best  i s estimated.  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 s o-f t h e d i m e n s i o n  achieved site  shrub  Betula  Columbia  o-f much o-f t h e  e s t i m a t e s o-f a v e r a g e  that  variables. -for  e x t e n s i v e review  British  and  u s i n g t h e c o r r e c t e d p o i n t d i s t a n c e method  -found  natural  in central  spp.  required for  on  that  pooled the  equations sample  are  TABLE OF CONTENTS  Abstract T a b l e o-f C o n t e n t s List  o-f T a b l e s  List  o-f F i g u r e s  Ac know l o d g e m e n t a 1  INTRODUCTION AND OBJECTIVES  2 2.1 2.2 2.3 2.3.1 2.3.2 2.3.3 2.4 2.4.1 2.4.2 2.5 2.6  LITERATURE REVIEW Introduction R e v i e w o-f s h r u b b i o m a s s e s t i m a t i o n m e t h o d s Regression estimation Developing the regression R e g r e s s i o n models Sampling the p o p u l a t i o n Density sampling Plot sampling P l o t l e s s sampling Biomass p e r u n i t a r e a Conclusion  3 3.1 3.2 3.2.1 3.2.2 3.2.3 3.2.5  STUDY AREA General d e s c r i p t i o n Site descriptions Site 1 Site 4 Site 6 Site 7  4 4. 1 4.2 4.3  F I E L D METHODS Regression equations . Stem d e n s i t y Biomass p e r u n i t a r e a  5 5.1 5.1.1 5.1.2 5.1.3 5.1.4 5.1.5 5.1.6 5.2 5.3  S T A T I S T I C A L METHODS Regression equations Hypothesis 1 Hypothesis 2 Hypothesis 3 Hypothesis 4 Hypothesis 5 Hypothesis 6 Density Biomass p e r u n i t a r e a  i i i i i v v i i viii 1 4 4 ...... S 8 9 •• 1 3 18 • 19 19 20 2 5 28 2 2 3 3 3 3 3  .  3 7 3 7 4 0 41 4 4 4 4 4 4 4 4 4  •  9 9 0 3 4 5 6  3 3 3 5 7 8 9 9 9 5 0  6 6.1  6. 4 . 2 6.5 6.6 6.7 6.8  RESULTS Hypothesis 1 Sal ix Betula Hypothesis 2 Hypothesis 3 Sal ix Betula Hypothesis 4 Sal ix Betula Hypothesis 5 Hypothesis 6 Density Biomass per u n i t  7 7.1 7.2  SYNOPSIS AND ANALYSIS Synapsis Critical analysis  6 . 1 . 1  6.1.2 6.2 6.3 6 . 3 . 1  6.3.2 6.4 6 . 4 . 1  5 2 52 52  57 60 ••• 6 1 61  •  63 6 5  •  65  area  •••  6 7 69 71 72 7 3  •  78 78 80 86  LITERATURE CITED APPENDICES A: S c a t t e r p l o t s o-f Sali'x and Betula data B: ANOVA t a b l e s  /  V -  93 93 106  LIST  OF TABLES  labia  Ease.  4.1  Summary  o-f S a l i x  4.2  Summary  o-f Betula  4.3  Sample s i z e s f o r d e n s i t y , b i o m a s s on s i t e s  5.1  6.1  common  data  common  data  set  3?  set  39  independent v a r i a b l e s and 42  Independent v a r i a b l e s t e s t e d i n development of multiple regression equations Tests  of assumptions  common  of regression  on  44  Salix  regression  55  6.2  Some e x a m p l e s o f p r e d i c t i o n s a n d c o n f i d e n c e i n t e r v a l sf o r S a l i x b a s e d o n t h e common r e g r e s s i o n e q u a t i o n 56  6.3  Tests of assumptions common r e g r e s s i o n  of r e g r e s s i o n  on  58  6.4  Some Betula  6.5  T e s t i n g f o rone equation t o d e s c r i b e four u s i n g r e g r e s s i o n w i t h dummy v a r i a b l e s  6.6  6.7  6.3  6.9  6.10  Betula  examples of p r e d i c t i o n s and confidence intervals f o r b a s e d o n t h e common r e g r e s s i o n e q u a t i o n . . . . . . . . . . 5 9 Salix  species 60  T e s t i n g f o r one e q u a t i o n t o d e s c r i b e S a l i x an a l l s i t e s u s i n g r e g r e s s i o n w i t h dummy v a r i a b l e s  62  T e s t i n g f o r o n e e q u a t i o n t o d e s c r i b e Betula s i t e s u s i n g r e g r e s s i o n w i t h dummy v a r i a b l e s  64  Mean p r e d i c t e d b r o w s e b i o m a s s (grams/stem) paired t tests f o rdifference between p r e d i c t e d and observed biomass of S a l i x C o m p a r i s o n o f mean p r e d i c t e d b r o w s e b i o m a s s and 9 5 % c o n f i d e n c e interval f o r Salix, using three equations Mean p r e d i c t e d b r o w s e b i o m a s s ( g r a m s / s t e m ) paired t tests f o rdifference between p r e d i c t e d a n d o b s e r v e d b i o m a s s o f Betula  -  v -  on a l l  and 66 (grams/stem) - 66 and .- 6 8  labia  6.11  6.12  6.13  6.14  6.15  Eaas  C o m p a r i s o n o-f mean p r e d i c t e d and 9 5 % c o n f i d e n c e intervals using three equations .  browse biomass -for Setula,  68  P a i r e d t t e s t s f o r d i f f e r e n c e between p r e d i c t e d biomass (grams/stem) of f i r s t s e c o n d s t e m o f Setuls on s i t e 4  stem  b i o m a s s and 95% square metre  Betula browse b i o m a s s and in grams per s q u a r e metre  confidence  and 71  Density estimates, probable l i m i t of e r r o r c o n f i d e n c e i n t e r v a l s f o r Salix a n d Bstuia Salix browse in grams p e r  (grams/stem)  and  95% ....  72  limits 74  95%  confidence  limits 74  vi  -  L I S T OF  3.1  3.2  Map o-f B r i t i s h of s t u d y a r e a Locations  FIGURES  Columbia  location 31  o-f s i t e s  -  showing  within  v i i -  study  area  32  ACKNOWLEDGEMENTS  I would his  like  encouragement  t o thank  during the data  and my -former s u p e r v i s o r , encouragement appreciate members,  the contributions  necessary  soil  Barry  kindly  f o r completion  Anna R o b e r t s for  analysis,  throughout  Jim S i b l e y , support  this  and w r i t i n g  o-f my t h v s i a ,  -for h i s s u g g e s t i o n s and  a-f g r a d u a t e  and a s s i s t a n c e  provided  the l o g i s t i c  of the f i e l d with  work.  vegetation  assistance,  the study.  Pitt.  -  assistance  identification, with  density  needed,  Beets,  in Williams  Thanks a r e a l s o  completed.  vitt -  Marty  and f i e l d  Most o f a l l I am g r a t e f u l  have b e e n  also  committee  Branch  and F r a n c i s Schwab  when  I  o-f my o t h e r  John Smith f o r a s s i s t a n c e  never  studies.  and D r . M i c h a e l  for providing distractions would  Marshall, for  o f t h e F i s h and W i l d l i f e  for assistance  Wong f o r c o m p u t i n g  advice  year  D r . J u l i a n Demaerschalk  B . C . , very  analysis  Dr. Peter  Dr. Larry Larson,  d u r i n g my - f i r s t  J i m Young and G o r d W o l f e Lake,  my s u p e r v i s o r ,  due t o A r t Yee  estimation,  for his t o my f i a n c e ,  and w i t h o u t  whose  1.  INTRODUCTION AND  Browse, as  -forage,  This  In  i s an  cattle  (McLean  and w i l d  by  resource.  This  good  Browse  plant  objectives In used  sources  browse  and  measurement developed,  (Pitt  concern  forage  (Beets  was  t o q u a n t i f y browse  for  winter  cattle  input  1981).  o-f - f o r a g e  b u t c a n be  between  reduced  or  o-f t h e  of browse  because from  -for b o t h  biomass.  browse both  plants  herbaceous  occurrence  of  A  of browse  sampling  number range  from  scientists,  simple  of biomass relative  observation of  (Telfer  to  1981),  each  specific  1985). of B r i t i s h  range.  f o r deer  cattle  These  Columbia  some  wetlands  are also  and moose.  and w i l d l i f e  1984, p e r s . production  grazing.  (Telfer  variable  from  ranging  delineation  region  cattle  that  with  and weaknesses  and Schwab  the Cariboo  highly  species.  use con-flicts  different  difficult.  biologists,  strengths  of winter  capacity  arise,  animals  animal  and u n d e r s t a n d i n g  histories  The o f t e n  to accurate  resource  may  management  life  trees.  f o r winter  expressed  Rangeland  problem  and w i l d l i f e  inherent  1979).  source  i s a complex  been  presence  important  by  and d u r i n g t h e  cover  inventory  makes  foresters  snow  inventory  also have  communities  long-lasting i s an  -for many  quantitative  and  methods  component  p l a n t s used  Includes  plants  browse  o-f w o o d y  desert  ungulates  range  physiognomies  range  dietary  o-f h e a v y ,  and w i l d l i - f e stock  leaves  in shrub  browse  eliminated  are  so  Columbia,  domestic  have  and  important  in regions  British  with  the twigs  i s especially  winter  OBJECTIVES  This  comm.).  f o r the area.  -  Wildlife  The purpose  1 -  assist  area  areas  important  managers  a r e competing  i n one wetland would  wetland  have  f o r t h e same of t h i s  that  in defining  study  i s used a  carrying  The  objectives  1.  C r i t i c a l l y review l i t e r a t u r e p e r t a i n i n g to shrub biomass and d e n s i t y e s t i m a t i o n , a s a b a s i s f r o m w h i c h t o s e l e c t appropriate techniques f o r estimation of current annual woody t w i g (browse) p r o d u c t i o n of shrubs within the study area.  2.  Develop simple p r e d i c t browse spp. a n d Setula  3.  Estimate method.  4.  Estimate browse p r o d u c t i o n per square metre 95% c o n f i d e n c e l i m i t s of the estimate.  3.  Provide a critical the study.  After selected theory,  as  browse  the  non-destructive attached  to  as  were  stems  point  measures,  was  the  clearly  determined  of  square  production  per  stem  (from  corrected  point  are  combined  f a r the  be  a  was  the  than  plotless  final  regression)  confidence  by  method).  interval  of  using  basis  distance  density methods,  of  t h e mean  and  provides  browse  multiplying  this  easily  The  individuals,  The  be  plants.  plot  estimate by  i t is  stem  technique  than  in  per  appropriate  of  a  in  was  least  can  on  individual  obtained  distance  limits  define  employed  regression  estimated  efficient  The  techniques  at  to  distance  and  developed  confidence was  point  because,  been  distributions  metre  the  linear  has  t h e most  variance.  per  the  Browse  i t i s more  production  (from  and  method, to  of  technique  equation  regression equations of stems of Saiix the study area.  the corrected  literature,  defined  f o r non-random  approximation  are to:  analysis  efficient,  as  by  estimation  distance  method  compensates an  density  the p r e d i c t i o n . more  study  or m u l t i p l e l i n e a r biomass production gZancfulosa within  regression and  corrected  estimation  this  stem  reviewing  the  once  of  the  stem  respective estimate.  mean density variances  Pursuant regression  t o t h e second  abjective  equations) the f o l l o w i n g  ( i . e . to develop  h y p o t h e s e s were p r o p o s e d and  tested: 1.  R e l a t i o n s h i p s b e t w e e n s h r u b d i m e n s i o n s and b r o w s e b i o m a s s p r o d u c t i o n e x i s t and s i m p l e o r m u l t i p l e l i n e a r r e g r e s s i o n e q u a t i o n s may be d e v e l o p e d t o p r e d i c t b r o w s e b i o m a s s production.  2.  A single, f o u r Salix  3.  T h e common production  4.  The a c t u a l b r o w s e b i o m a s s on s i t e s (measured f r o m a d o u b l e sample) i s not s i g n i f i c a n t l y d i f f e r e n t ( a t t h e 0.05 s i g n i f i c a n c e l e v e l ) f r o m t h e p r e d i c t e d b i o m a s s .  5.  T h e r e i s no s i g n i f i c a n t d i f f e r e n c e ( a t t h e 0.05 s i g n i f i c a n c e l e v e l ) i n t h e a c t u a l (measured) biomass b e t w e e n t h e f i r s t stem and t h e s e c o n d stem e n c o u n t e r e d .  6.  T h e r e i s no s i g n i f i c a n t d i f f e r e n c e ( a t t h e 0.05 s i g n i f i c a n c e l e v e l ) i n t h e p r e d i c t e d biomass between t h e f i r s t and s e c o n d stem e n c o u n t e r e d .  No h y p o t h e s e s production  per unit  common r e g r e s s i o n e q u a t i o n w i l l species i n the area.  d e s c r i b e the  regression equations w i l l adequately predict on s p e c i f i c s i t e s w i t h i n t h e w e t l a n d .  about  stem  density  a r e a were t e s t e d  t h e a c c u r a c y o f t h e stem  or the t o t a l  because  density estimate.  there  browse  was no c h e c k on  2.  LITERATURE REVIEW  2.1  Introduction The  to  usual purpose  quantify  browse a v a i l a b l e  and  Hutchings  and  Kosco  Telfer  1966,  1982),  Telfer  or  Other  purposes  1981)  or  and  Ohmann  current 1966,  annual  Blair  relate  i t to the  diameter  1963)  also  defined  limited depth  and  1974).  and  palatable (Coady  species  vertically  distance) this  would  Telfer  By  Cairns  twigs  raise  varies (Peek  the  b r e a k i n g stems,  1978).  or p r e f e r r e d ,  Not and  (eg. B a s i l e Other  1969a) o r a v e r a g e  height varies also  and  Bartolome  browse  (eg.  Urness  1981).  (Dean  et a l . studies  i t i s defined  1978).  as b r o w s i n g  o t h e r w i s e be beyond  definitions  shrub  e t a l . 1971). a n i m a l s can  only  lower  of  reach  preference varies  and  are  a  snow  availability)  can browse  (Krefting  a l l browse s p e c i e s  species  r e a c h up  species  deer  1963)  B r o w s e must  with animal limit  the  Hutchings  (Shafer  with both  moose and  their  and  as  et a l .  twigs 1966,  equally  among a n i m a l  species  1974). Sampling  difficult of  animal  that  Basile  1979).  Bergstrom  (Telfer  1978,  accumulation  generally  l e a v e s and  t w i g , which  (snow c o v e r may  (Telfer that  largest  of  (eg.  components f o r e c o l o g i c a l  Harrington  Bobek and  of a browsed  (Shafer be  of  Bergstrom  Provenza  of f u e l  of browse v a r y l  growth  1971,  1977,  of biomass  1977,  Definitions  Marsden  production is  livestock  the u t i l i z a t i o n  assessment  quantification  and/or  1969a, Bobek and  and  include  shrub biomass  to w i l d l i f e  to quantify  1969a, F e r g u s o n  (Origal  for assessing  because  b r o w s e on  f o r browse p r o d u c t i o n and/or of  the o f t e n  the plant  and  highly  variable  utilization spatial  of the s h r u b s themselves. - 4 -  is  distribution Browse o f t e n  is  not  d i s t i n g u i s h a b l e i n a uniform  o-f v e r y  many s m a l l  way  discrete parts  Some o f t h e m e t h o d s u s e d modifications  of techniques  This  review  will  used  to estimate  estimation. Pitt  2.2  developed  and w i l l  personal  separate use  of p l a n t based  estimated clipped method bias, and  Include  (Shafer  1969).  and S c h m a u t z  training  The method  1963) and l o s e s e f f i c i e n c y  double sampling.  and  (Shepherd weight  The c o r r e c t i o n f a c t o r  in the corner  may a l s o be e x p r e s s e d  estimator - 5 -  on  i s to  plots is  which i s  Problems with the  consistency to apply  personal (Hutchings  to shrubs  1962).  estimation  was d e r i v e d  on e s t i m a t e d  by a r a t i o  plot,  inevitable  a p o r t i o n o f t h e same p l o t s f o r w h i c h  r e g r e s s i n g a c t u a l weight  estimates  A modification  period,  observer  are corrected  from  1969).  isdifficult  Wilm e t a l . (1944) m o d i f i e d  weighing  by P e c h a n e c and  The e s t i m a t e s  in the central  in maintaining  (1979) and  b i o m a s s by s p e c i e s a r e  where p r o d u c t i o n  (Hutchings  the extensive  and d i f f i c u l t y  Schmautz  developed  of f o r a g e  as a p e r c e n t a g e of t h a t  and w e i g h e d  on r e g r e s s i o n  methods  a r e c l i p p e d and w e i g h e d . plots,  been  techniques f o r  b i a s by u s e o f a r e g r e s s i o n d e v e l o p e d  of f i v e  have  browse.  e s t i m a t i o n method  ocular estimates  p l o t s which  clusters  concentrate  i s also referred to Rutherford's  made on p l o t s by p r a c t i s e d o b s e r v e r s . for  vegetation.  d e s c r i b e a number o f m e t h o d s w h i c h  o f a v a i l a b l e and u t i l i z e d  (1937),  1979).  f o r herbaceous  Review o f shrub biomass e s t i m a t i o n  Pickford  and i t c o n s i s t s  f o r shrub biomass e s t i m a t i o n a r e  (1985) r e v i e w s  In t h e w e i g h t  -field,  (Rutherford  shrub production,  The r e a d e r  and Schwab's  estimation  briefly  i n the  to incorporate  by c l i p p i n g and  estimates  weight. (Blair  were made  The r e l a t i o n s h i p 1959, F r a n c i s e t  al.  1979,  Ahmed e t a l . 1983),  variance.  Francis  underestimation, plant  water  material  within  Bergstrom  1978,  quadrats  (Blair  1977, and  Harlow i s not  Shafer  shrubs be  1971,  than  situations  randomly by  rank. with  method  toward  the v a r i a b i l i t y  in  An  and  local and  From  and  but  Blair costly  and  Harlow  destructive,  Pickford effort  The  where f o r a g e g r o w t h  1937,  is  i s applied  1977).  random  Feduccia  and  and  when t h e method  1972,  (Bobek  and  enormous s a m p l i n g  weigh,  be  within  the f i r s t  to  method  may  I s more  not  better  for  sets  visually  s e t , the h i g h e s t r a n k i n g  and  -  suited  s e t , the second t h e number o f  with equal  Clutter  -  highest clipped  random  1972).  than  of  each  sampling  It will  quadrats.  the e s t i m a t e  quadrat  representation  i s more p r e c i s e located  6  more  s e t the quadrats are  of as s t r a t i f i e d  bias  considerably  quadrats  In t h e end,  (Dell  be  of  the second  thought  may  A number o f  each  t h e mean w h i c h  do  and  variation.  s o on.  as s t r a t a  e s t i m a t e of  a l l -forage  or s y s t e m a t i c a l l y  (Pechanec  ( M c l n t y r e 1932)  weighed, from  efficiency  tendency  random  1971,  plots  same number o f c o m p l e t e l y r a n d o m l y reduce  the  growth.  random c l i p high  on  i s laborious,  situations  set sampling  method may  the ranks  as  1970)  Alcaniz  e q u a l s t h e number o f s e t s ,  The  unbiased  and  f o r permanent  shrub  quadrat,  quadrats  The  located,  and  increase  overall  limits  Phillips  Dzieciolowskl  biomass.  clipped  ranking  Halls  i n range  with  to  Involves c l i p p i n g  f o r reasonable precision  efficient  is  and  R u t h e r f o r d 1979).  Ranked  ranked  w e i g h method  Krefting  homogeneous t h a n  an  in precision  pre-defined height  (Bobek and  tends  Increases.  1977).  more u s e f u l  are  a decline  and  suitable  1963,  required  and  clip  this  e t a l . (1979) n o t e d  content  The  but  g i v e an  clipping  Ranking  ( M c l n t y r e 19S2,  the  errors Dell  and  Clutter  1972).  variability  i s low  The  advantage  relative  to  o-f t h i s  large  method  scale  i s lost  variability  if  local  (Mclntyre  1932). Shafer's count each of  of  species.  dry  The  browsing  speed  and  workers  average  species, exact  quadrats,  weight  precision  Bergstrom  then  found  1978,  accurately  by  this  Parker  count  questionable  of  to determine  and  (Jensen  Morton and  a l l twigs within  terms  of p r e d e t e r m i n e d  Then mass p e r portion  of  regression. per  unit.  likely  cover  the  unit  samples,  cover  i s very  method  was  difficult  a procedure and  The  was  to  the  other  (Bobek  insensitive  a quadrat  and  to very  ability  heavy  to  considered  Smith  Urness  their  l e n g t h s measured.  their  residual  units  be  e s t i m a t e d , by  (Anderson by  and  clipping  unit  calculated  s p e c i e s i s cover  developed  f o r herbaceous  to apply to has  been  In t h e  In  quantified  the f a l l ,  spring,  l e n g t h s a r e measured  1982).  weighing by  a  linear  units  times  mass  v e g e t a t i o n and  shrubs.  " b e f o r e " and  1962).  species,  Kothmann and  f o r any  involving  1944,  c o v e r may  w i t h mass p e r  Browse u t i l i z a t i o n method,  q u e s t i o n e d by  1977).  i s determined  Standing crop The  converted  Shafer himself.  Herbaceous s t a n d i n g crop in  weight.  Shafer'3 claims to  and  Scotter  are  twig  the counts  for  f o r twigs  twigs  the average  f o r dense browse 1978)  twig weight  i s determined  h a v e been  laborious  converting a  average  and  twig weight. method  on  of unbrowsed  a l l twigs are counted  i t too  browse u t i l i z a t i o n  diameter  a sample  diameter  u s i n g the average  who  i s based  o f b r o w s e u s i n g an  at that  random  method  to a weight  a given shrub  clipped On  twigs  (1963) t w i g c o u n t  and  - 7 -  by  "after"  the twig surveys  length (Aldous  twigs a r e tagged  following  winter  and  browsing,  percent u t i l i z a t i o n  is  computed.  The  method  i s more a c c u r a t e t h a n  e s t i m a t e s o-f b r o w s i n g Scotter  1977),  surveys  a r e needed  (Basile  Jensen  Urness  percent of  i t i s more  and  utilization  browsing,  advantage browsing  2.3  but  in s i t u a t i o n s  this  method  the shrub. leafy  biomass  (eg.  (eg. T e l f e r  biomass  twig  and/or  The individuals the  1977,  independent  Using  two  to  calculate at the  point  the twig t i p diameter.  one  1969b),  from  and  survey  i s needed  The  after  biomass  Murray  annual  height.  dimensions  total  woody  t w i g biomass  1976),  I t has  is predicted  t i p (eg. T e l f e r  Provenza  and  Urness  i s developed  the p o p u l a t i o n  under  ( d i m e n s i o n s ) and  between  dimensions  or f i n e a s stem  fuel  (eg.  from  biomass  in i n terms  measuring 1970,  of  twig  Ferguson  1981).  by  selecting  s t u d y on  equation  a sample of  which  a r e measured  (biomass)  is fitted  biomass.  - 8 -  and  diameter,  been a p p l i e d  1969a, L y o n  dependent  and  on  ( e g . Peek e t a l . 1 9 7 1 ) ,  measurements such  plant  mathematical  measured  to predict  current  leaf  there i s a  easily  been u s e d  these data, a regression  relationship  only  biomass  twig weight,  regression of  a method  where t h e amount o f b r o w s e consumed,  at t h e browsed  Marsden  and  assumes t h a t  t w i g and  and  studies  diameter  because  and  range.  ( e g . H a r n i s s and  dimensions  length  the  t e c h n i q u e has  utilization  and  left  Dean e t a l . 1981)  canopy  i s that  estimation  Ohmann e t a l . 1976), foliage  diameter  (Jensen  1966).  (1981) d e v e l o p e d  between shrub The  costly  percentage  estimation  Regression relationship  Hutchings  utilization  from measurements of t w i g d i a m e t e r  a n i m a l s have  Regression  o-f h e a v y  l a b o r i o u s and  and  the twig basal  of  twig counts or  The  both  variables.  which  describes  population  the  i s then  sampled input  -Far t h e  into  the  production. has  been  regression equation  No  Developing  random  (Tel-fer  1969b,  or  sampling  Bryant  The an  on  and  each  or  otherwise  t o d e r i v e an  inevitably  results  i n an  unbiased  in reduced  i s a more v a l i d  sample  (Telfer  logarithmic 1979). than  and  within  1969a);  the  upward  classes  values  of  used  achieved.  on  or  b i a s of  twigs  or  1978,  the  the  1977,  volume  range  recommended  the  population  and  good  form  included  Unfortunately,  (Rutherford  lower 1979),  1979).  correlation but  The  yield  data  the  predictions in  - 9  -  the  with (Rutherford  better predictions  a l . 1976).  independent  variables include  in  this  dimensions o c c u r r i n g  produce m i s l e a d i n g  over  Damaged,  be  extrapolation, particularly may  Marks  estimate.  f i t and  1982) .  plant.  plants should  Rutherford  r a n g e of  Sneva  (1970)  t r e e s of  be  Jacobson  Whittaker  vigorous  dimensions w i l l  (Ohmann e t  Some commonly  one  and  r e p r e s e n t a t i v e of  g o o d n e s s of  Cairns  transformations,  Absolute  size  be  and  Lyon  location  relationship.  relationship  reliable  to  b i o m a s s may  a size  Murray  stems.  on  upward  imperfect  (Telfer  only  1979,  shrub based  coefficients  are  equation  determined  (Rittenhouse  to cover  undamaged  to s e l e c t  resulting  as  Kothmann  tendency  poorer  order  so  i s t o be  a  diseased  systematic  estimate  (1973) n o t e d ones,  the  basis.  s e l e c t e d s h r u b s must  unbiased  a l s o be  are  shrub  after  -for d i m e n s i o n s and  selective  (1976) s e l e c t e d o n l y  stratification  i s required  values  regression  (Ohmann e t a l . 1 9 7 6 ) , a l . 1981)  if  the  area  the  t o p r e d i c t t h e mean  d e n s i t y must  a unit  initial  Dean e t  Brown  Shrub  b i o m a s s on  The  v a r i a b l e ( s ) and  d e s t r u c t i v e sampling  developed.  estimate  2.3.1  s e l e c t e d independent  stem  d i a m e t e r measured some a r b i t a r y and  total  and  height  plant  Jacobson  Murray  Often diameter Z  dimensions  (1976) u s e d  plant  Peek  ellipse  height.  cone  developed  f o r four  volume f o r v a r i o u s predict  leaf  include  shrub  ring  branching  widths  Basile  were a b l e  to predict tridentata)  diameter  diameter  stems  twig  by s u b t r a c t i o n .  two r a d i a l  and w e i g h t from  to u t i l i z a t i o n and M a r s d e n  the diameter  f o r each  (1977)  f o r bitterbrush  could  at the be c l i p p e d and  and H u t c h i n g s s u g g e s t e d  10 -  (stems  1973).  and t h e p e r c e n t a g e u t i l i z e d  -  variables  ( B a r t o l o m e and K o s c o  been a p p l i e d  e q u a t i o n s s h o u l d be d e v e l o p e d  (1982)  measurements)  o r d e r stems  The r e m a i n i n g p o r t i o n  Basile  times  a r e a and  predictor  (1966) and F e r g u s o n  before browsing twig.  area f o r both  and J a c o b s o n  ( T a p p e i n e r and J o h n  length  and t h e  crown v o l u m e a s an  common  of second  has a l s o  and crown  diameter  canopy  Harniss  and h e i g h t m e a s u r e m e n t s t o  less  (averaged from  o r i t s l e n g t h measured,  calculated separate  total  (Bobek  Dean e t a l .  (circumference, surface  Other  and H u t c h i n g s  of t h e browsed  weighed  from  estimation  studies.  variables.  volume a s a r e a  Murray  o f f o f t h e p r i m a r y s u p p o r t i n g stem)  Regression  base  basal  plant  species.  variables  and number o f a e r i a l  iPurshia  and c a l c u l a t e d  (1979) c a l c u l a t e d  and t w i g b i o m a s s .  ( D a v i s e t a l . 1972),  1982)  desert  shapes)  a s DxH  d i a m e t e r , crown d e p t h  and c a l c u l a t e d  15 i n d e p e n d e n t  predictor  t h e maximum crown  angles to that,  B r y a n t and Kothmann  inverted  crown  (1970) m e a s u r e d  and a c i r c l e  1978)  1977, M u r r a y and  height times circumference.  denseness.  an  1969b) o r a t  1978).  may be u s e f u l  maximum and minimum  at right  (eg. T e l f e r  and h e i g h t a r e c o m b i n e d  (Crow  (1981) u s e d  diameter  level  ( e g . R i t t e n h o u s e and S n e v a  1978) o r D H  Canopy and  a t ground  (Ohmann e t a l . 1976, Bobek and B e r g s t r o m  height  1982).  Berstrom  either  site,  easily that  but Ferguson  and  Marsden  -felt that  a more g e n e r a l e q u a t i o n would  usually  be  adequate. Provenza blackbrush to  branch  and  Urness  (Coleogyne length  ramosissima),  and  weight  They  diameter  m e a s u r e m e n t s made a t  actually  predicted  browse  length  weight.  or  Tel-fer dry  The  are  combined  The  weight  curve  t h e browsed  lengths, since or weight  t o oven  dry  as  with  diameter  average  used  c o r r e s p o n d i n g t o each s p e c i e s and  twig weights,  tip.  -from  avoided  was  need  o-f p r e d i c t e d  as  total  equations r e l a t i n g a i r  at paint  s p e c i e s o-f t r e e s  o-f b r o w s i n g  i s established  diameter  the  calculated  i n s u r v e y s where c o u n t s  dpb  by  This  -for 22  t h e mean w e i g h t  tallied  diameter  material  utilization  twig weight  with  c o n t a i n s a number o-f  regression  be  an  branch  a proportion  equations could  f o r that  Utilized  length  related  method  t h e amount o-f b r o w s e d  (1969a) d e v e l o p e d  twig diameter  shrubs.  predicted  m e a s u r e any  but  a similar  (where a b r a n c h  twigs).  to  also  (1981) u s e d  of  the  -from  twig  classes,  and  o-f t w i g s  (dpb) .  the  specific  i s computed.  could  also  be  est imated. A potential estimate  utilization  and  dry  oven  closely  or  not  browsed  dpb's m e a s u r e d found one  t h e dpb  an  the browsed early  u s i n g browsed  Freshly of  Species differences  whether (twigs  with  collected  twigs  the f r e s h ,  twigs w i l l  i n the f i e l d  (such as  amount  of  dies  b a c k ) and  in winter  have  longer t o dry)  diameter  decrease  For  example  11  -  a i r dry always  during a  browse  in twigs  time will  of  and  browsing  affect  Potvin  ( f o r a l l s p e c i e s ) of  week's a i r d r y i n g . -  the  to  not  sap  end  d u r i n g browse s u r v e y s .  average  twig diameters  i s t h e d i s c r e p a n c y between  diameters.  approximate  survey.  problem  8%  the  (1981) following  Uniformly in  species that  determined Hutching  by  measuring  have f l a t t e n e d  or  two  diameters  (Ferguson  and  Hutchings  (1966) n o t e d  different  Marsden  1977,  paints  basal  given  distance  an  1977)  above or  Jensen  Urness  be  (Basile  each  1981).  and  other  Basile  and  significant  f o r measurements taken  point  o f measurement  s h o u l d be  specifically  the basal  bud  immediately  from  statistically  The  difficulties  diameters  degrees  and  present  d i a m e t e r s may  minimum  coefficients  the p l a n t .  diameter  Twig  a t 90  s m a l l but  in regression  basal  Marsden  twigs.  a v e r a g i n g maximum and  1966)  differences  t w i g d i a m e t e r s may  scar  defined.  (Lyon  a b o v e t h e bud  1968,  scar  at  f o r twig  I t may  be  Ferguson  a  and  ( J e n s e n and  Urness  1981). Browsing regression  by  production. an  The  subjectively and  only author  variable  heavily  browse  Schwab  browsed,  classes  and  birch  and used  He  d e s i g n a t e d a s 0,  He  suggested  rather  than  t h r e e , and  effects  vary  considerably  the  biomass  browse c o n d i t i o n  used  classes  browse c o n d i t i o n  amount o f  into  three  of  unbrowsed,  1 and  squared  as  2  respectively.  was  using at  very  least  stratification  important  five  based  browse on  condition.  the s e v e r i t y  used  who  (1985).  browse c o n d i t i o n  the v a r i a b l e  Browsing  of  was  growth form  encountered  accounting for variation.  condition  unknown amount o f v a r i a b i l i t y  a shrub's  determined  Schwab f o u n d in  affecting  independent  browsed  i n t r o d u c e s an  to study (Betula  the e f f e c t alba  the c u r r e n t  production,  of b r o w s i n g .  and  of  Clipping  willow  growth (Salfx  both  an  f o r s i x years without  -  12  increased -  species  production.  withstood c l i p p i n g  spp.)  plant  t o s i m u l a t e b r o w s e has  continued browsing  var.papyrifera)  annual  with  of  50%  reduced  production  in  been White  response  to  Mountain  maple  annual other  100%  growth clumps  Rabbitbrush  \Acsr  greater  species  species  30%  was  (Wol-f-f  1978).  Animal  preference  are  on  same e s t i m a t e  Regression Forms o f of  regression, log-log),  curvilinear  others Ponto  by  McKell  shrubs  previous  r e m o v a l o-f  1978).  in  sense  and  winters  degree of  or  total  to  utilization  animal  i n c l u d e an  in  some  Stratification  apparent  Browse  Alaska  c o n s i d e r a t i o n , as  1983).  r e g r e s s i o n models biomass  only  and  by  this  shrub may  vary  species  preference  unpalatable  rarely  may  be  species in  and  range of  shrub linear  will  1979).  for  multiple  (and  linear  i t s linear  13  dimension  farm  of  occurs, and  a b e t t e r f i t to  example, -  size  relationship,  provide  For -  used  linear.  f i t a simple  Rutherford  h a v e been  allometric  weighted  a small  that  include simple  regression equation  1969a,  caused  and  s t i m u l a t e d browse p r o d u c t i o n  quadratic, semi-log,  data  e t a l . 1966).  d e s i r a b l e browse s p e c i e s .  exponential  biological  the  to t i m i n g  and  scouleriana  than  snowberry  effects  (Willard  regrowth  models  shrub  Unless  (Telfer  little as  (Kre-fting  and  1952).  i t s current  clipping  adverse  browse p r e s s u r e  I t makes  estimation  1974,  of  (Aldous  greater  i s another  p r e f e r r e d over  groups based  100%  were s e n s i t i v e  Salix  also  growth  maintained  no  h e a v i l y browsed  years  had  i / i s c i d i f lorus)  g r e a t e s t on  (Coady  2.3.2  or  o-f c u r r e n t g r o w t h  -for two  useful.  years  less  usee in iaides)  considerably  the  to  (Cfirysatftannus  been most  clipping  -for t e n  subjected  than  had  which  o-f d e f o 1 i a t i o n , w i t h  production that  o-f c u r r e n t a n n u a l  spicatun)  clipped  \Synphoricarpos intensity  clipping  Basile  and  a the  data  Hutchings  (1966) were a b l e t o - f i t and  twig weight  were  less  than  o-f a l m o s t  Linear straight  line  observations  mm.  and  i s equal  the standard  assumptions often  variance  as  of  assumptions  linear  then  be  of  the data,  be  so  that  r e g r e s s i o n and  allometric  a biological  model  transformation.  The  ordinary least  equivalent for  solution  on  the  s p r e a d o-f  these  the  normal  relationship  graph  paper  independent  transformed  with  the  variable  some t y p e  least  The  i s staight-forward  However  the  the  a  the r e g r e s s i o n l i n e .  o v e r c o m e by  equation, (Zar  of  1968)  the form  and  biomass e s t i m a t i o n i n i t s l i n e a r i z e d  to  the data -fit  biomass data;  the magnitude of  range  more a p p r o p r i a t e .  the v a r i a n c e or  technique.  by  diameters  of  v a l u e s meet  the  squares  technique  may  Y = B X ,  i s widely  used  used. The  as  that  when p l o t t e d  T h e s e p r o b l e m s may  transformation  equation  requires that  squares  curvilinear  increasing  increases.  and  are often violated  appears  a diameter  regression i s that  least  diameter  (1969a) e n c o u n t e r e d  at a l l p o i n t s along  linear  twig  twig  a curvilinear  relationship,  between  s i n c e most o-f t h e i r  Tel-fer  -found  relationship  regression theory  a d v a n t a g e o-f a using  linear  o-f b i t t e r b r u s h 2.4  40 mm  a  least  log-log  squares  solution,  is applied  form,  achieved InB  Although  model, and  often  lnY »  fitting.  to the a l l o m e t r i c squares  model,  can  a  i t i s not lead  + a  to  shrub  by l o g a r i t h m i c  lnX,  is  compatible  mathematically statistically  equvalent  to biased estimates  (Zar  1968). The unique squares to  least  s e t of (i.e.,  f i t the  squares  parameter £  (Yj  curve  fitting  estimates  - Y.)  l o g a r i t h m i c form  2  technique  which minimizes  i s minimized). £  (lnYj -  14  Using  seeks the  to find  residual  least  lnYj ) * i s m i n i m i z e d , -  the sum  squares which  of  Is  clearly  n o t t h e same a s t h e p r e v i o u s  does suggest homogeneity the  o-f v a r i a n c e  and t h e v a r i a n c e o-f  (Yj - Y > i s r e l a t e d  to the s i z e  o-f X, b u t he c a u t i o n s  b i a s o-f t h e e s t i m a t e .  Converting  the logarithmic estimate  <lnY| ) and i t s v a r i a n c e  normal,  exactly  1972),  normally  medians,  1972).  the geometric  by  not accounting  systematically (Baskerville and  adjustments Olson  with  gives  1974).)  The e s t i m a t e will  1973) .  a t X; i s (Zar  1968,  ;  be t h e  distributions  lognormal,  The b i a s e d  the value effect:  When t h e random e f f e c t  will  they  estimation  bias  and Bunce  of t h e t r u e value be b i a s e d  result  Several  When t h e e f f e c t  a  as  o f t h e Y 's a r e  arithmetic  i f not p e r f e c t l y  (1969) d i s c u s s e d  Y = B X  be skewed  i-f t h e l o g a r i t h m s  an u n d e r e s t i m a t i o n  when  will  of Y , j  have  (Baskerville  a  o f t h e random  -  o f X,  15 -  i s large  element  (£ )  v a r i a b l e (Y)  v a r i a b l e ( X ) , E, h a s a  w h i c h may be s o l v e d  + E, > and an i t e r a t i v e  e^  1976).  and t h e t r a n s f o r m e d  i s independent  of  recommended  o f E, on t h e d e p e n d e n t  Y = E, B X  f  1972, Beauchamp and  1973, Madgwick the effect  of Y  by a f a c t o r  the variance  authors  of t h e independent  l n Y = InB + a l n X + 1 n £  effect:  certainly  o-f InYj  t h e a n t i l o g s o f t h e lnY; 's w i l l  (Munro  to correct this  multiplicative  i s not as simple  f o r t h e skewness of t h e d i s t r i b u t i o n ,  1973, M o u n t f o r d  varies  is  means  and Bunce  t h e model.  will  f  (Otherwise,  1972).  Hafley  units  t h e means o f t h e skewed  serious underestimation  (Mount-ford  on  o-f Y  and i n -fact,  than  be  to original  o-f t h e d e p e n d e n t v a r i a b l e  I-f t h e d i s t r i b u t i o n  distributed  rather  (Baskerville  back  the antil-ogs.  the d i s t r i b u t i o n  Baskerville  when t h e  i s violated  ;  taking  Zar  assumption  the inherent  merely  ( Z a r 1968).  c o n s i d e r i n g the l o g - l o g trans-formation  residuals  about  quantity  by l e a s t  linear  form  squares.  E, h a s an a d d i t i v e  procedure  rather  than t h e  normal  least  s q u a r e s must be u s e d  t o e s t i m a t e the parameters  (Hafley  1969). Zar  <1968) recommended  solving  allometric  log-log  linear  logarithmic  regression  of  transformation.  the i t e r a t i v e  significantly error the  log-log  (Hafley  different  method 1969).  Also,  may  of "search"  converge  minimum.  and  Swank  inversely  determined  on t h e s u r f a c e  t h e sum  until  an e x a m p l e i n  function  and c a n n o t  because  surface  of b i a s  introduced  to the v a r i a n c e  1961). 16 -  to the  statements  cannot  procedure i s  the estimates  not t h e a b s o l u t e  a s t h e number o f  by u s i n g  1980).  a  rather  be a v o i d e d by t h e u s e o f w e i g h t e d  -  of the parameter  the i t e r a t i v e  by i t e r a t i v e  1971, 1973, Crow and L a i d l y  involved  be r e l a t e d  minimum,  problems  iterative  time  f o r a minimum,  becomes more s e r i o u s  proportional  yielded  squares s o l u t i o n of  so p r o b a b i l i t y  1969).  may  iteration  properties  to a local  and o f s o l u t i o n  t h e minimum  on e a c h  (Hafley  transformation,  locate  amount o f c o m p u t a t i o n  o f an e r r o r  -from  using  a standard least  Furthermore,  to the  by r e p e a t e d c o m p u t a t i o n  increases  The  squares,  procedures  the d i s t r i b u t i o n  The p r o b l e m  parameters  the bias  However one d i s a d v a n t a g e o f t h e  i s the large  them.  resorting  e s t i m a t e s and s m a l l e r s t a n d a r d  o f t h e random e l e m e n t ,  be made a b o u t  than  to the a l l o m e t r i c  those from  p r o c e d u r e -for  Zar demonstrated  parameter  e s t i m a t e s a r e not e a s i l y  a sort  residuals  solution  equation.  distribution  iterative  rather  Iterative  t o change.  e s t i m a t e s than  solution  models,  values f o r the parameters  s q u a r e s has c e a s e d  which  an  approximation, in order to avoid  o-f t h e sum o-f t h e s q u a r e d different  using  logarithmic than  least  regressions  (Schreuder  The w e i g h t s s h o u l d be  of the r e s i d u a l s  (Furnival  Crow and L a i d l y (aboveground  shrub  corresponding logically The  X  (1980) -found t h a t  biomass) (basal  both  be e x p r e s s e d a s some f u n c t i o n  and u n w e i g h t e d  non-linear  alternatives  (1973) a l s o estimation  trees  and w e i g h t e d  into  within  each  Choosing  different  when  and  Swank  1971):  distributed that never  (when  or d i f f e r e n t  which  2  linear  that  tested that  more  Schreuder  regression  area.  diameter  and Swank  technique f o r  Schreuder  and Swank  by d i v i d i n g  sampled  classes  and c a l c u l a t e d  c a n be a p e r p l e x i n g types of  numbers o f i n d e p e n d e n t of determination, R , z  of f i t .  It i s valid  i t i s meant  t o be a p p l i e d  i t i s immediately  must  a r e not normally d i s t r i b u t e d ) }  i s meaningful  of other  only  models, variables. h a s been  a r e met  l n X o r X*  i s used  problem,  providing the  variables  d e c r e a s e d by t h e i n c l u s i o n of R  variable.  and f o u n d  1) The i n d e p e n d e n t  these variables  comparison  models.  weighting factors  the c o e f f i c i e n t  under  models,  and recommended  and s u r f a c e  spaced  They  could  m o d e l s were a c c e p t a b l e  to evaluate d i f f e r e n t  t o measure goodness  conditions  model,  t h e " b e s t " model  scales,  of t h e  class.  trying  Conventionally, used  their  three equally  especially  linear  a weighted  of t r e e biomass  the data.  and n o n - l i n e a r  be g i v e n t o a l t e r n a t i v e  1973) d e r i v e d  variance  linear  recommended  to the size  of t h e independent  e s t i m a t e d from  to the log-log  consideration  (1971,  was p r o p o r t i o n a l  o-f Y  d i a m e t e r ) , and s o w e i g h t i n g f a c t o r s  v a r i a n c e was d i r e c t l y  weighted  the variance  (Schreuder  be n o r m a l l y known  and 2)  independent  is  variables,  so  when m o d e l s h a v e t h e same  number o f c o e f f i c i e n t s . Furnival by  comparing  (1961) s u g g e s t e d  an a p p r o a c h  the product of the l i k e l i h o o d s -  17 -  which  e v a l u a t e s models  of the v a l u e s of t h e  dependent <1971,  v a r i a b l e under  1973)  evaluate  and  from  Crow and  weighted The  the  and  the  has  z e r o means and  only  reflect  making of  models  must be is  the  a very  normally  and  before  coefficients  the  Swank  data  2.3.3  Sampling  the  Once t h e variability developed, dimension  on  the  estimated  on  b a s i s of  i t to  models.  the  data  specified  came  model  The  approach  distributed  computed  errors  likelihoods  not  also passible  and  constant  variance,  f o r e v a l u a t i n g a l l types  Crow and  Laidly  ensuring  1980).  t h a t some  A disadvantage affects  1971).  Laidly  Formulae  models are  the  Models  forethought i s that  size  of  the  the  for calculation  given  in Schreuder  of and  (1980).  d i m e n s i o n s most determined  steps  are  m e a s u r e m e n t s and  biomass e s t i m a t e be  shrub  next  Swank  Swank  population  have been the  tool  determined  functions for specific Crow and  The  models.  likelihood  (1971) and  and  that  likelihood.  normality  1971,  (Schreuder  the  and  used  non-linear  independently  analysis,  t o be  and  r e s i d u a l s but  of  likelihood  Swank  the  useful s t a t i s t i c a l and  Schreuder  probability  variance.  to d e f i n i n g meaningful  number o f  the  larger  assumptions  (Schreuder  defined  given  the  constant  linear  more c l o s e l y  the magnitude of  from  this  The  models.  (1980) s u c c e s s f u l l y  indicate  t r u e model,  with  departures  Laidly  model.  assumes e a c h model  different  unweighted,  likelihoods  specified  resembles  the  a per  and  a  to sample  for density unit  stems or  area  important  in accounting  r e g r e s s i o n model the  population  in order  basis.  p l a n t s , depending  for  to a r r i v e  Density on  has  for  been the  at  a  estimation  whether  biomass  will is  f o r stems or p l a n t s .  There  are  a number of  d e n s i t y e s t i m a t i o n methods -  18  -  available  which  a r e d i s c u s s e d i n the next  stratify should  the p a p u l a t i o n , such  estimate density  most c o n v e n i e n t t i m e a s one field to  efficiency.  Although  classes  a l . 1976),  2.4  2.4.1  Plot  All  plants  study the  within be  may  individuals  dimension  law  shrubs,,  one  It i s probably  m e a s u r e m e n t s a t t h e same  be mare c o n v e n i e n t classes),  effort  to assign  more  t o a more p r e c i s e  plants  precise  estimate  (Ohmann  i s worthwhile.  of  the e a s i e s t  size  square either  s h o u l d be  Ellenburg  difficulties of  on  The  of  Quadrat  the study  of a g i v e n s i z e  and  and  within  the of  Bpacing  counts  1974).  in the a p p l i c a t i o n  individuals,  individuals  1968).  counted.  to the s i z e  i n o r d e r t o m a i n t a i n a c c u r a c y of and  are  technique  (Lyon  or s y s t e m a t i c a l l y  related  2)  the boundary first  two  -  line)  problems  and  been used 19  -  quadrat  effects and  3)  require  requires  (Mueller-Dombois  m e t h o d s have o f t e n  of  boundary  t o be made, w h i l e t h e t h i r d  purpose  units  or r e c t a n g u l a r , randomly  used  to understand  dimensional sampling  located  individuals.  decisions the  two  the r e c o g n i t i o n  count  separately.  diameter  lead  and  circular,  be  Three  to  ( e g . stem  density  a r e a . Quadrat  - exclusion  and  to  sampling  (Mueller-Dombois  1)  shrubs  decided  t e c h n i q u e s a r e p r o b a b l y t h e most commonly  may  s h a p e and  has  c o u n t s or measurements t o maximize  the a d d i t i o n a l  estimate plant  Quadrats  tall  strata  i t may  generally  I-f one  sampling  Plot to  so  Density  into  t o make t h e p l a n t  measurements w i l l et  as  f o r each  makes t h e d e n s i t y  dimension  section.  counts  are  (inclusion time  or  required  arbitrary  a clear Ellenburg  as a check  evaluation 1974). or i n  of  comparison Pielou  with  1959,  several  one  Risser  quadrat  o r more p l o t l e s s  methods  and  Boyd  sizes  Zedler  being  1968,  tested  (Cottam  1980),  (Lyon  1968,  et a l .  sometimes  Oldemeyer  1953, with  and  Regelin  1980). Achieving clumped stated  distributions "Quadrat  number o f  data  quadrats  (1968) f o u n d to  a precise  that  may  required no  a s e a r c h of  quadrats  required  acre.  increase  of 95%  nearly  from  in p r e c i s i a n but  little  m  z  quadrat,  and  they  Curtis  confidence  level  U s i n g 20  Regelin  f t by  thousand  1 m  ft  in going  t h e 5 m*  needing  quadrats  efficient  size  close  a considerable  quadrat  a  density  samples c o v e r i n g  (1980) f o u n d a  20  the Lyon  without  s m a l l e r more  improvement  recommended  + 10%,  (1956)  that  technique could estimate shrub  to s e v e r a l  no  and  in  for  to a to a  5 10  shrub  sampling.  Plotless  sampling  Plotless distance between  from  or  d i s t a n c e sampling  t h e measurement  of  or d i s t a n c e s  shrubs. e t a l . (1953) and  d i s t a n c e measures which plant  number o f spacing,  involves  random o r s y s t e m a t i c p o i n t s t o s h r u b s ,  Cottam  per  or  Cottam  sampling  impossible to a t t a i n . "  2 a c r e s , and  and  plot  s t a n d s a r e so v a r i a b l e  in going from  quadrat,  four  400  Oldemeyer  1  2.4.2  difficult.  sample s i z e .  m  density  very  e s t i m a t e by  i s almost  quadrat  large  required  t o one  be  in aggregated  his specifications  a prohibitively  density  (M) w h i c h plants and  can  per be  i s the unit  Cottam  a r e based  reciprocal area.  calculated  N/M by  on of  Curtis  the  -  of  (1956)  i d e a of  density,  is a direct  each  - 20  and  developed  t h e mean  rather  than  indication  the d i f f e r e n t  of  area on  the  plant  methods.  In  the  closest individual  to c l o s e s t p l a n t of  nearest  each times  so t h a t  neighbour  individual  plant;  correct  The  distances  plant  The p o i n t  i s made, and t h i s  centred  distance  u s e s an a n g l e o f  and b i s e c t i n g t h e c l o s e s t  quarter  point,  i s measured;  outside  the angle  method  i n each  uses  four  of which  the point  the average of t h e f o u r  m e t h o d s a l l assume a random d i s t r i b u t i o n  i n the population.  independently  of a l l others,  That  i s , each  and any o b j e c t  c h a n c e o f o c c u r r i n g a t any l o c u s .  equal-sized  sampling  Individuals  per quadrat  u n i t s were would  laid  object  and  I f a number o f  down r a n d o m l y ,  be a P o i s s o n  of the  i s located  has an e q u a l  independent  the frequency  distribution  of  (Cattam e t  1933).  Shrub p o p u l a t i o n s clumped and  from  vTf.  These f o u r  al.  root  \ / M . In  o f t h e mean d i s t a n c e  to the c l o s e s t plant  on t h e s a m p l i n g distance  equals  individuals  point  point  t h e n m u l t i p l i e d by a c o r r e c t i o n f a c t o r t o o b t a i n t h e  distance.  nearest  sampling  half of the square  random p a i r s method  the interplant distance  from  times 2 . 0 0 equals  an e s t i m a t e  on t h e s a m p l i n g  quadrants centred to  equals  mean d i s t a n c e  method  vfT.  centred  i s measured,  which  to i t s c l o s e s t neighbour  1 . 6 7 equals  exclusion  t h e mean d i s t a n c e  i s determined,  t h e mean a r e a ,  the  method,  or aggregated.  artificial  density  Laycock  (Lyon  because  Several compensate  they  1 9 7 5 ,  nan-random  1980,  -  developed  21  -  bunchgrass biased  f o r non-random  O l d e m e y e r and R e g e l i n  distributions.  t o be  1 9 6 8 , Batcheler 1 9 7 1 ,  and Z e d l e r  Boyd  shrub,  methods y i e l d e d  do n o t c o m p e n s a t e  m e t h o d s have been  f o r non-random  i n d i v i d u a l s tend  t h e above f o u r  1 9 6 8 , Risser  and B a t c h e l e r  random;  When t e s t e d w i t h  dot p o p u l a t i o n s  estimates  distribution  are rarely  which  1980).  attempt t o  In t h e w a n d e r i n g  quarter  method along and  Catana  (1963) m e a s u r e d  a meandering  a 90  degree angle  Catana ordered separating density  transect  recombined  determined  inclusion  a l l distance  within  and  o-f  size the  Unfortunately  clump  sequential by  between  -for an  C a t a n a g a v e no  on  distances  compass  successive  i n a -frequency  between clump  o-f c l u m p s and  to p l a n t  a constant  centred  measurements  and  information  plant  distances.  clump  overall  calculation  plants. distribution,  He  densities,  density  bearing  calculated and  estimate.  for variance  of  the  density  e s t imate. Morisita unbiased around  (1937) d e v e l o p e d  density  each  sampling  centred  on  closest  plant  individual  estimates  the  of  point  points  This  degree of  non-randomness p r e s e n t .  Mi  estimates is  given.  earlier  estimate are  Lyon  version  of  the  and  point  of  Batcheler method point  density (1971,  individual neighbour  ( r ) , the p  ( r ) and n  another  not  Batcheler  the  third  then  the  than  the  two  calculation as  for  The  3  i s i n f l u e n c e d by  variance  did  area  quadrants  (M ),  same v a r i a n c e  which  give  estimates:  is greater  i f smaller,  The  to  density  to  that  formula  of  an  correct for  (1975) s u g g e s t e d  using  to c a l c u l a t e v a r i a n c e .  1973)  developed density  distance  distance  from  distance  two  If Mi  the  and  unbiased  measures the  one  1 9 7 9 ) . No  method  Laycock  for obtaining one  (Boyd  (1968) assumed  non-randomness, estimates  from  i s accepted;  averaged  method  equal  q u a d r a n t s combined  of  the  estimates  the  yields  deviation  Ma,  these  into four  quadrant  and  A  order  non-random p o p u l a t i o n s .  i n each  (M )  angle  is divided  i s measured.  quadrants  the  that  from  from  corrected  estimates. the  that  individual - 22  the  -  point plant to  to to  At  point  each  distance  sampling  the c l o s e s t i t s nearest  i t s nearest  neighbour  <<" ).  The plant  basic premise  measurement  of  the  method  <f* ) g i v e s  the  t r u e mean  p  random p o p u l a t i o n , departures first and  and  the  two  clumping  degree of  within  Batcheler limit  (1975) d e v e l o p e d  of  e r r o r " or  density be  i s Student's estimate  considered  (Batcheler density as  the  the  1975)  degree of  (1973) c o n c l u d e d  samples  that  t, A n  PLE,  at  PLE  departure  estimates  are  of  repeated  The  corrected  a maximum s e a r c h  1979).  If used,  R  to f i n d  with which  an  having  in  a very  after  a few  by  large  affects the  ratio  aggregated  a point  takes  not  of  (usually after  formula  the  for  the  farm  non-randomness,  the  standard  limit  of  D  A D  / V^n  The  PLE  broadens  Batcheler  of  the  error,  made, and  measures  the  same members.  (R)  end"  beyond  about  in the  (D).  - 23  -  the  cause  r  as  R  Boyd distance problems  distribution,  p  precision  increases.  becomes  sample),  few  or  1975,  Generally,  PLE/D r a t i o of  1973,  that  with  a prespecified  i s improved  80%  used  d i s t a n c e may  distances  the  be  (Batcheler  estimate  PLE/D)  may  can  the  are  to  the  error"  e r r o r of  estimate  is  aggregation  search  population,  1970).  increases.  density of  correct for  sample p o i n t s ) .  large search  "tail  -for a  / \fr\  d i s t a n c e method  A  the  Bell  uniformity  distance  would  distances  m  level.  total  nearest  c o r r e c t -for  confidence  distance  individual.  in turn  (as d e f i n e d  one  of  r  empirical  i s a reasonable  point  without  and  probable  from  to  r e s p e c t i v e l y ( i . e . clumping,  a n a l o g u e of  i s the  PLE  and  n  which  number  a specified  that  an  = t A D  i s the  point  interplant distance  i s a m e a s u r e of  "empirical and  estimate  provided  and  r  (Batcheler  PLE (where t  The  aggregation,  clumps)  the  additional distances  -from n o n - r a n d o m n e s s . second  "probable  and  i s that  less  and  But precise  Batcheler  (1975) c o n s i s t e n t l y minimum PLE/D) Boyd  was  -found  a l s o most  (1979) k e p t  a r a n g e o-f i n c r e a s i n g with  the changing  smallest not  PLE/D  R  running  t h e PLE/D  criterion.  p  limit),  PLE/D  papulation  (Boyd  For  reason  However  with  species  d i d recommend  d i s t a n c e , s i n c e they  t h e method d i d  i n some c a s e s  more  the actual  error,  (Laycock  However  the angle  found  for single o r d e r method  i t t o be s l i g h t l y method  over  ( O l d e m e y e r and R e g e l i n  Although second  to angle  efficient. in  angle  and  order  in accuracy  order,  but both  limits.  artificial  less  than  be a c l o s e  i t i s much  mare  dot p o p u l a t i o n s ,  (1980) g o t more a c c u r a t e  - 24 -  also  16.7% f o r c o r r e c t e d  and p r e c i s i a n ,  m e t h o d s had  than  1980).  T e s t i n g t h e two m e t h o d s w i t h Boyd  corrected  to estimate  t h e c o r r e c t e d p o i n t d i s t a n c e method may  t h r e e out of f o u r cases  with  order  1975).  more p r e c i s e  using corrected point distance  14.3% f o r a n g l e  be  species  t h e t r u e d e n s i t y w e l l w i t h i n 95% c o n f i d e n c e  distance  the  t h e use of  encompassed  point  by  i s that i f  and B a t c h e l e r  (1980) a d v o c a t e d  (using the p o i n t estimate  were  with  s p e c i e s , d i s t a n c e s must  Their estimates  errors  accurate  n o t optimum  variance).  Average  the  as non-randomness i n c r e a s e d i n  f o r each  d i s t a n c e measures.  B a t c h e l e r ' s method  distances associated  d i s t a n c e s t h a t were  O l d e m e y e r and R e g e l i n  they  m  o f any d i s t a n c e m e a s u r e t e c h n i q u e  s e p a r a t e l y f o r each  point  and  increasing  measured  information  estimate.  overestimated  one d e s i r e s d e n s i t y e s t i m a t e s  over  and r  over  1979).  A disadvantage  quadrats  n  o-f P L E and D, made  the d e n s i t y estimate  f o r search  of o v e r e s t i m a t i o n  this  calculations  Improve r e s u l t s ,  were o b t a i n e d  precise estimate ( i . e .  accurate.  becoming the -final  estimates  the  t h e most  (using the r , r  search  significantly  amount  that  estimates  20% e r r o r  in three  out  of  -four c a s e s .  required  60%  Batcheler both  the  o-f t h e  time  in tests  to varying  time of  angle  needed  natural  corrected  technique Because  it  i s not  d e s i r a b l e to group  be  the  times  the  unit  estimate  estimate  needed  Morisita the  angle  by  angle  low  diversity  order,  sampling  i t may  a greater  number  d e s c r i b e a comp1 e x ' c o m m u n i t y  shrub  s p e c i e s ) , i t may  be  best  be  (where t o use  a  per  stem  (or  plant)  of  shrub  density  and  by  of  stems  able  the  and  fact  a d e n s i t y method order  or  conducive not  method,  unit  that  to exact  given  regression permits  this,  variance  regressions.  shrubs are  seldom  The  randomly  accomodates non-randomness i s distance).  calculation  a formula  -  of  Such  density  variance.  for calculating  authors  - 25  area. a  non-linear  that  a few  per  t h e mean and  corrected point  give but  Linear  expressing data  (or p l a n t s )  t o make a p r e d i c t i o n w i t h  precision.  transformed  (1957) d i d order  than  of  be  of mean s h r u b b i o m a s s p r o d u c t i o n  ( i . e . angle not  density  appears to  area of  i s compounded  measures are  half  estimation.  problems with  and  required  were  will  are  distributed  that  area  but  with  distance  with  unit  confidence  problem  To  i s d e s i r a b l e t o be  associated  o-f t r u e d e n s i t y  per  amount o f there  and  biomass p r o d u c t i o n  estimate  It  Laycock  d i s t a n c e method  for estimating  same t i m e .  for density  Biomass per The  point  a more p r e c i s e e s t i m a t e  in the  2.5  20%  point  i t is faster  points  method  order.  distance  bunchgrass p o p u l a t i o n s  Corrected  of  quadrat  angle  esimates within  with  the  shrub p o p u l a t i o n s . to get  by  corrected point  order.  most p r o m i s i n g  passible  time t r i a l s ,  degrees.  In summary, the  -field  (1975) o b t a i n e d  methods  clumped  In  variance  have a t t e m p t e d  to  for  estimate  it  (Lyon  1968,  "probable o-f t h e  Laycock  limit  and  o-f e r r o r "  confidence  limits  Batcheler (PLE)  1975).  -formula  -for t h e  Batcheler's  i s an  (1975)  empirical  corrected point  approximation  distance  density  e s t imate. Rutherford confidence  limits  encountered log-log  of  i n the  confidence  log-based  relevant  interval and  that  back-transformed  the  upper  the  limit  density  PLE  might  and  reduced  more e f f o r t  biomass per  unit  estimates  must be  accepted  way.  variance  of  resulting  biomass of used  only  Bergstrom  by on  the  an  but  the  the  the  there  log-log  are  questioned  point  transformation,  between by  limit.  the  underestimating For  For  the  no  effort  to  estimate  of  density generally  f o r the  statistical  variance  that  the  r e g r e s s i o n and  because the  when  transformed  density sampling  (1960) f o r m u l a the  used  back-transformed,  a p p e a r s t o be  Goodman's  (1985) who  (Schwab n o t e d  3  discussion  i s assymmetrlc  lower  PLE .  only  corrected  Schwab c o m p r o m i s e d  e r r o r s of but  The  final  exact  validity  e m p i r i c a l PLE  of  the  estimate  was  variance.  other  (1978),  the  expressing  Schwab  the  limits  reallocating  especially  area  by  heterogeneous p l o t s . )  Schwab u s e d  density  on  used  combined,  products,  f o r the  production  area,  variance,  The  and  was  relationship  overestimating he  area.  estimate  simple  variance.  estimate be  the  confidence  i s no  concentrate  used  unit  Because of  around  lower  there  and  the  per  literature  for density.  upper  indicating  of  biomass d a t a  r e g r e s s i o n f o r b r o w s e b i o m a s s and  d i s t a n c e method the  (1979) a l l u d e s t o p r o b l e m s w i t h  example found basis using who  for rarer species.)  regression estimation  combined  a l l s p e c i e s with  involving estimation  regression estimation  quadrat  densities.  They c l a i m e d - 26  -  their  (Twig  method  of  was  by  of  11  Bobek  browse  counts  was  shrub  were  times  more  efficient include 93%  than  time  spent  confidence  plots  needed  required  21  would  interval  plots  of browse of  t h e same d e g r e e  533,  Schwab  an  less  total  individual  77  (1985) u s e d  104  and  three shrub  and  low  31  plots  an  confidence  achieved  distances shrubs  + 20%.  took,  on  analyse  taking  data.  shrubs  70  worthwhile locally area, may  70  each  plot  time  and  of  to develop  time.  efficiency  For  sampling  and  of  the  and  four  90  man-days  the  sampling  i t may  that  study  i s q u e s t i o n a b l e , and  to  a  regressions.  i s planned,  time  by  i s probably  a regression  a single  he  and  hundred  this  to develop area  deciduous  half  efficiency  effort,  i n v e n t o r y o f an  density  regression  material  improved  required  326.  over  Four the  quantify  In g e n e r a l  on  and  abiea)  f o r dimensions  to develop  sampling  (Picas  m>.  and  sampled  c o u l d have  to  coniferous, tall  . + 30%,  the  (Pinus  pine  m x 120  a  method  variable  effort  plotless  man-hours.  the time  a period  the u t i l i t y  The  the  intensive  t o spend  over  be more  field  an  he  achieve  However  aucuparia)  eight  reallocating  r e a s o n a b l e example of If  with  man-days t o c o l l e c t  Although and  interval  average,  not  17 3 m x 5 m  highly  spruce  (Sorbus  groups:  (each  Sampling  were d e s t r u c t i v e l y  equations,  fewer  80%  did To  time.  of s a m p l i n g  plots,  rowan  browse biomass of  achieved  that  sampling  example,  regression  plots  they  equation.  s p e c i e s was  For  for  on  regression  enormous amount  spp.)  however  weighed, w h i l e the r e g r e s s i o n  have r e q u i r e d  deciduous,  weigh!  they c a l c u l a t e d  of p r e c i s i o n .  (Betula  birch  and  w i t h much  would  and  + 20%,  clipped  have r e q u i r e d  silx/estrus)  clip  d e v e l o p i n g the  t o be  distribution  to  traditional  can  be  be used  of a s m a l l  other  methods  suitable. optimum  sampling  measurements, m i n i m i z e  method  should  calculation - 27  -  minimize  time,  and  complexity  maximize  of  accuracy  of  estimation  to a t t a i n  acceptable  much e-f-fort likely  (Rut her-ford  program  the question  efficient precise  regression  quicker  browse  possible  estimation,  and c h e a p e r m e t h o d s  information,  of whether  in a restricted  biomass e s t i m a t i o n  o-f t e n will  research should  be  t h a t would  be  v a l i d one.  this  estimate  dimensions,  with  a sampling  method  and o f f i c e , a known  would  level  estimation  combined  estimation,  provide  with would  of browse  point  appropriate  estimation  provides  acceptable  estimate.  Once t h e r e g r e s s i o n  d i s t a n c e method  technique  because  an e s t i m a t i o n field  time.  would  yield  an e f f i c i e n t  no a c t u a l c o l l e c t i o n  of the l e v e l  felt  f o r these  purposes.  statistically  i s needed.  of the r e g r e s s i o n  The c o r r e c t e d  appropriate  f o r aggregated  density  populations,  provides  i n terms of  and d e n s i t y  biomass per u n i t  - 28 -  method o f  r e l a t i o n s h i p h a s been  of biomass  of browse  be  I t was  distance  o f e r r o r , and i s e f f i c i e n t  The c o m b i n a t i o n an e s t i m a t i o n  scale.  and  a p p e a r e d t o be t h e most  i t i s designed  and w o u l d  b i o m a s s b a s e d on s h r u b  the corrected be most  an a c c u r a t e and  of confidence,  Regression  established  was d e s i r e d  f o r a p p l i c a t i o n on an o p e r a t i o n a l  regression  density  study,  in the f i e l d  appropriate  point  i t i s usually  Conclusion For  that  Because  acceptable  done a t a l l i s a v e r y  2.6  Although  p r e c i s i o n through  i s required.  not p r o v i d e  1979).  area.  estimates  STUDY AREA  3.  3.1  General The  an  description study  a r e a was l o c a t e d  e x t e n s i v e and c o m p l e x  central the  interior  B i g Creek  situated dry  approximately  characterized season  British  drainage,  Sub-Boreal  Spruce  Columbia  In d e p r e s s i o n a l a r e a s  deposits;  The fen,  extreme c o l d  rocky,  gravels, cobbles this  i s overlain  are thin  and t h i c k e r main w e t l a n d  shallow  layer  lodgepole pine forage trees  <Pinus  o r browse occur  (less  tend  to occur  with  the shrub  a region growing  than  15 cm)  morainal of v o l c a n i c  by a  siIty  areas  or mesic  of t h e  organic  i n meadows and  in fens. ecological  associations  1981).  in the area.  contorts)  raised  i n bands a l o n g  a r e sedge f e n ,  There  site  Within  mounds.  the f o r e s t  and s e d g e f e n s o c c u p y i n g  areas. - 29 -  shrub  by v e g e t a t i o n and d e p t h o f are also  The s u r r o u n d i n g  of poor  i n the understory.  on s l i g h t l y  in  It i s i n the  largely  In most  by f i b r i c  (Runka and L e w i s  l a k e s and p o n d s  is  R i v e r , and i s  d e r i v e d from  may be o v e r l a i n  s h r u b - c a r r and meadow, d e f i n e d m a i n l y  the o r g a n i c  Meadow  and a s h o r t  and s t o n e s  or g 1 a c i o 1 a c u s t r i n e veneer.  these  shrub-carrs,  o-f t h e C h i l c o t i n  i s very  origin.  soil  Dick  1979).  of the area  mineral  1400 m),  i n the Fraser Plateau of  o-f B.C. Highway 20.  dryness,  of unsorted  wetland,  (elevation  (SBSa) b i o g e o c l i m a t i c s u b z o n e ,  deposits  glaciofluvial  Meadow  ( F i g u r e 3.1).  30 km s o u t h  by r e l a t i v e  soil  system  a tributary  (Annas and Coupe The  wetland  at Dick  quality,  several  forest with  the wetland  cover i s little  " i s l a n d s " of  The meadows and s h r u b - c a r r s edge and a r o u n d t h e lower  tree  and more  islands,  central  A track  -from t h e e a s t  e d g e and meadows t o a c o r r a l leads  north to a shallow  -follows h i g h e r ground and c a b i n ,  l a k e and a n o t h e r  a b u n d a n c e o-f d r o p p i n g s , c a t t l e the  r o a d and t r a i l ,  the  -forest. Dick  which  includes  Winter o-f  Meadow  -fall  and e a r l y  Cattle  tend  From t h e  t o be c o n c e n t r a t e d a l o n g  i s crown  apart  land  and p a r t  Service  -from a s m a l l  o-f t h e r o a d .  58  The W i n t e r  In 1984, f o u r  -from November  holding  I t i s within the  o r 23,000 ha) i s u s e d  grazing.  o-f 765 head  private  a d m i n i s t e r e d by t h e Range  i n W i l l i a m s Lake.  winter c a t t l e  -for a t o t a l  system.  trail  e d g e s and m i n e r a l meadows b o r d e r i n g  a r e a a p p r o x i m a t e l y 230 km  permits  which  use appears  Range r a n g e management u n i t  (total  wetland  a cattle  i n t h e -forest  the cabin  t h e B.C. F o r e s t  -from w h i c h  a l o n g t h e -forest  Branch  Range  -for l a t e  permitees  in this  unit,  systems  where -forage and b r o w s e a r e a v a i l a b l e .  No d a t a a r e a v a i l a b l e  an w i l d l i - f e  u s e o-f D i c k Meadow b u t - f i e l d  observation  utilization  by moose d u r i n g  indicated  held  1 t o December 3 1 .  t o c o n c e n t r a t e i n t h e open meadows o-f t h e w e t l a n d  a r e common  unit  both  summer and  wi n t e r .  3.2  Site  descriptions  Four associations sites  were  sampled  on  within  the wetland  identified.  Site  t o r e p r e s e n t wetland ( F i g u r e 3.2).  to four,  but the o r i g i n a l methodology  e t a l . (1980); wetland  t o t h e SBSa  subzone. - 30 -  site  numbers were follow  classification  (1984),  seven  t h e number o-f s i t e s  and t e r m i n o l o g y  association  (1981) and R o b e r t s  shrub  (Originally  Due t o t i m e c o n s t r a i n t s  description  Runka and L e w i s  specific  were s e l e c t e d  was r e d u c e d  retained.) Walmsley  sites  the l a t t e r  i s based  of which i s  Figure 3.1.  Map of B r i t i s h Columbia showing l o c a t i o n of study area.  Figure  3,2.  Locations  o-f s i t e s  within  the  study  area.  3.2.1  Site 1 This  Lewis  site  i s predominantly  1981) o r " G r e y - l e a v e d  (Roberts  1984).  decomposed  willow  I t has a t l e a s t  organic  soil  an o r g a n i c  shrub-carr  - moss - s h r u b - c a r r  10 cm o-f m o d e r a t e l y  overlying  mineral  soil.  (Runka and  association"  to well  In p l a c e s , d e p o s i t s  o-f up t o 60 cm o-f o r g a n i c m a t e r i a l w o u l d make t h e c l a s s i - f i c a t i o n shrub  -fen, however  shrub-carr  site  stones The  veneer  occasionally  moisture  i s level regime  permesotrophic The north  overlying  appear  with  eroded  cobbles  ablation  and s t o n e s .  at the surface  a s t r o n g l y mounded  wet  g 1 a c i o 1 a c u s t r i n e or moraine with  a high  T h e s e c o b b l e s and  i n s o r t e d rock surface.  The  t o h y g r i c and t h e n u t r i e n t  "pools". ecological regime i s  to eutrophic.  site  i s l o c a t e d w i t h i n an e x t e n s i v e s h r u b b y along  the o l d drainage  and t o t h e e a s t and west  shrub-carrs, sloping  Shrub cover  to Roberts'  was o n c e a s m a l l  materials are a s i l t y  i s subhygric  and s o u t h  associations dry  Parent  o-f v o l c a n i c o r i g i n  site  similar  i s l o c a t e d i n what p r o b a b l y  channel.  glacio-f l u v i a l content  i s mast  association.  The drainage  the vegetation  i s patchy  cover.  Dominant  percent  cover):  up t o i s l a n d s  with  vegetation  channel  - 33 -  higher  of l o d g e p o l e  i s as f o l l o w s  To t h e  a r e shrub f e n  on s l i g h t l y  some d e n s e a r e a s  area.  pine  ground a r e forest.  and o t h e r s w i t h  (occularly  sparse  estimated, in  shrub  Iayer:  dwarf  shrub  herb  layer:  moss  layer:  Maxlmium  shrub  layer:  height  20% 13% 20% 2% 5% 3% 2% 1% 1% 20%  Salix glauca Betula glandulosa Salix myrtillifolia Arctostaphylos u\/a-ursi Carex aguatillis Calanagrostis strict a Valeriana dioica Fragaria virginiana Achillea millefolium  i s about  1.3 m;  most s h r u b s  are less  than  1 m  tal 1 .  3.2.2  Site  4  This 1981)  i s a fresh  o r a "Scrub  (Roberts  1984).  moderately mineral  shallow  moderately  organic s o i l  mounded  virtually  surface.  regime  Vegetation shrub  (0 t o 3 cm)  overlying  zone  gravels derived  The s i t e  The e c o l o g i c a l  i s nearly moisture  coarse  from  (20 cm)  comprises  site.  layer: shrub l a y e r :  herb  layer:  moss  layer!  ablation  due t o t h e  level regime  the shrub  1 with  layerj  with a i s mesic  Betula Salix  more  willow i s  Dominant v e g e t a t i o n ( i n p e r c e n t  cover).is: shrub dwarf  The  i s mesotrophlc.  Birch  at this  layer of  mineral s o i l .  i s shallow  Lewis  association"  i s more homogeneous t h a n a t S i t e  cover.  absent  shrub-carr  (up t o 40%) o f m a i n l y rooting  (Runka and  (SL t o S) and h a s a h i g h  to parent m a t e r i a l .  the nutrient  uniform  - kinnikinnick  I t has o n l y a v e r y t h i n  The e f f e c t i v e depth  mineral shrub-carr  i s coarse textured  content  moraine.  birch  decomposed  soil  fragment  and  site  glandulosa bracftycarpa  Arctostaphylos uva-urs /(atresia myosuro ides fluf) lenbergia richardsonis Carex praegraciI is  15% 8% i  2% 50% 3% 2%  4% - 34 -  Maximum  shrub  height  i s about  1.5 mj most  shrubs  a r e about  .75 m o r  1 ess. The pine  site  -forest.  3.2.3  Site  site  1984).  decomposed  i s a -fresh m i n e r a l birch There  glacio-f l u v i a l  (50%)  o-f c o b b l e s  high  i s a thin  coarse  moisture  then  into  to the c o r r a l  over  mineral  and c a b i n .  soil.  and s t o n e s ,  over  mounded  regime  vegetational  surface.  i s mesic  site  Site  4 which  6 has g r e a t e r shrub  cover  than  site  ( i npercent  shrub dwarf  Vegetation layer: shrub  with  Betula layer:  regime  layer:  (30 cm) due t o t h e level  shrub  i s permesotrophic. with  This  site  greater  a dry shrub-carr.  a much g r e a t e r w i l l o w  component  caver) i s :  glandulosa  25%  glauca  20%  Salix  brachycarpa  10% uva-urs  myosuroides  i  8% 2%  20%  layer: height  a  The e c o l o g i c a l  Antennari a pulcherrima F ragar i a virginiana Achillea millefolium  moss  with  Salix  /(atresia  content  morainal  and r i c h e r ,  i s also  Arctostaphylas Salix myrtillifolia  herb  clay-loam  i s nearly  moister  Site  4.  a high  " p o o l s " a r e common.  slightly  than  materials are a  with  i s shallow  and t h e n u t r i e n t  appears  diversity  Rock  o-f p o o r l y  Parent  a gravelly  The s i t e  association"  layer  o r g 1 ac i o l a c u s t r i ne v e n e e r  -fragment c o n t e n t .  This  Maximum  lodgepole  (Runka and L e w i s  shrub-carr  (1 t o 7 cm)  The e - f - f e c t i v e r o o t i n g z o n e  moderately  meadow  shrub-carr  - kinnikinnick  organic s a i l  silty  deposit.  a mineral  6  or a "Scrub  (Roberts  into  I t i s b i s e c t e d by t h e r o a d  This 1981)  grades  4% 2% 1%  8% i s 1.5 mi most  slopes very  shrubs  slightly - 35 -  are 1 m t a l l  down t o t h e s o u t h  or  less.  and  grades  into -fen  a narrow  band  o-f o r g a n i c s h r u b - c a r r where  and s m a l l pond.  upward,  i t b o r d e r s on a s e d g e  In t h e o p p o s i t e d i r e c t i o n  b o r d e r i n g a m i n e r a l meadow  i t slopes  slightly  a t t h e e d g e o-f l o d g e p o l e p i n e  •forest.  3.2.4  Site  7  This or  site  "Maccall's willow  with  over  level  intermittent The wetland  Dominant  There  site  plant  -fen (Runka and L e w i s  -fen a s s o c i a t i o n "  decomposed  layer  water  was e n c o u n t e r e d within  1981)  1984),  The s i t e i s  The e c o l o g i c a l  moisture  i s meso- t o i n August  a t 35 cm  the c e n t r a l  and i s s u r r o u n d e d  (Roberts  organic s o i l .  regime  was no s u r f a c e  i s located  system  shrub  mounded m i c r a t o p o g r a p h y .  -frozen  shrub  1984, b u t an  depth.  d r a i n a g e c h a n n e l o-f  by s e d g e -fen a s s o c i a t i o n s .  cover i s : layer:  dwarf s h r u b herb l a y e r : moss l a y e r : Despite  layer:  Salix Betula Salix Salix  arbusculo ides glandulosa mace a. 11 i ana glauca  20% 15% 10% 5%  Salix Carex  myrtilliiolia aquatill is  10% 25% 65%  the implication  appearance  w i t h many s h r u b s clumps  shrub  i s s u b h y d r i c and t h e n u t r i e n t  permesotrophic.  overall  - tall  60 cm o-f m o d e r a t e l y  with severely  regime  the  I s i n a deep m e s i c  i s o f dwarf  barely  (up t o 2 m>  o f t h e name shrubs,  r e a c h i n g 30 cm.  "tall  generally There  shrub less  than  50 cm and  a r e a few t a l l e r  a l o n g t h e edges of t h e shrub f e n .  - 36 -  fen", the  4.  F I E L D METHODS  4.1  Regression  basis,  equations  A decision  was  r a t h e r than  on  defining  a clump.  spp.  Betula  and  selectively representing  the  t o as  specific  sites)  equations. develop  used  clump  range  the and  basis,  stems t a l l e r  of  the  size  study  were u s e d  equations"  in r e g r e s s i o n equations  area,  30  the  were  the  present.  a per  difficu1ty  collected  These d a t a  each  are  shown  of are  from  sites  were used  to  "pooled-site equations".  from  of  Salix  intention  to data  stem  "common" r e g r e s s i o n  specific  and  cm  with  (as o p p o s e d  to develop  t r a n s e c t s on  d a t a were r e c o r d e d  than  variation  "common d a t a s e t "  (Data from  because of  developing regression equations,  throughout  "site-specific  following  a per  glandulosa  from  referred  For  made t o e s t i m a t e b r o w s e b i o m a s s on  stem  collected  The  (abbreviations  in parentheses):  1.  basal  stem d i a m e t e r n e a r e s t 0.1 mm  (DIAM) - m e a s u r e d w i t h d i a l a t 1 cm a b o v e t h e g r o u n d .  2.  stem  l e n g t h (LENGTH) - t h e l e n g t h f r o m t h e b a s e of t h e stem ( a t t h e p o i n t where d i a m e t e r was m e a s u r e d ) t o t h e stem t i p , m e a s u r e d t o t h e n e a r e s t 1 cm.  3.  c a n o p y d e p t h (DEPTH) - t h e d i s t a n c e f r o m stem t i p t o t h e b a s e o f the lowest p r o d u c t i v e branch ( i . e . branch with c u r r e n t annual t w i g g r o w t h ) , m e a s u r e d t o t h e n e a r e s t 1 cm.  4.  c a n o p y w i d t h 1 (WID1) - t h e d i a m e t e r o f t h e c a n o p y p o i n t , m e a s u r e d t o t h e n e a r e s t 1 cm.  5.  c a n o p y w i d t h 2 (WID2) - t h e d i a m e t e r o f t h e c a n o p y a t r i g h t t o c a n o p y w i d t h 1, m e a s u r e d t o t h e n e a r e s t 1 cm.  6.  b r o w s e c o n d i t i o n (BRS) - c l a s s i f i e d i n t o c a t e g o r i e s b a s e d on a c c u i a r e s t i m a t e s o f t h e d e g r e e of b r o w s i n g t h e p r e v i o u s year. ( B e c a u s e t h e s t u d y was done i n J u l y and A u g u s t , t h e r e was no b r o w s i n g o f t h e c u r r e n t y e a r ' s t w i g p r o d u c t i o n . )  - 37  -  calipers  at  the  to  the  widest  angles  0 1 2 3 4 (Hedging growth.) 7.  no b r o w s i n g 1-25% o-f t w i g s browsed 25-50% o-f t w i g s browsed o r s l i g h t h e d g i n g 5 0 - 7 5 % of t w i g s browsed o r m o d e r a t e h e d g i n g 7 5 - 1 0 0 % o-f t w i g s b r o w s e d o r s e v e r e h e d g i n g i s b r o w s i n g o-f t w i g s o l d e r t h a n t h e p r e v i o u s y e a r ' s  b r o w s e b i o m a s s (BIOMASS) t h e oven d r y w e i g h t o-f t h e c u r r e n t y e a r ' s woody t w i g p r o d u c t i o n . C u r r e n t a n n u a l t w i g s were c l i p p e d , t h e l e a v e s removed, and t h e woody m a t e r i a l oven d r i e d a t 5 0 ° C t o a c o n s t a n t w e i g h t ( a t l e a s t 72 h o u r s ) and w e i g h e d an a d i g i t a l b a l a n c e t o 0.01 g. Items  development dependent  1-6  were u s e d  o-f r e g r e s s i o n  variable.  dimension,  browse  as  equations;  T a b l e s 4.1  and  independent v a r i a b l e s  biomass  and  data  item  7,  biomass,  i n the was  the  4.2  summarize  t h e raw  stem  that  were u s e d  in equation  development. Salix  species  o-f o b s e r v a t i o n s Salix  -for e a c h  Salix  arbuscuIoides maccalIi  identified  species  glauca  Salix Salix  were  ana  myrti11iioIia  was: n n n n  = » = »  - 38  73 26 36 25  -  and  recorded.  The  number  Table  4.1.  Summary  Variable  1. 2. 3. 4. 5. 6. 7.  Diameter Length Depth Width 1 Width 2 Browse Biomass  Table  4.2.  N  (mm) (cm) (cm) (cm) (cm) (g)  Summary  V a r i ab1e  1. 2. 3. 4. 5. 6. 7.  D i ameter Length Depth Width 1 Width 2 Browse Biomass  o-f Salix  N  (mm > (cm) (cm) (cm) (cm) (g)  112 112 70 112 112 112 112  data s e t .  M i n i mum  Max imum  3.4 27 10 3 3 0 0.01  23. 1 182 147 69 66 4 7.07  160 160 160 160 160 160 160  of  common  Betula  3landulasa  Mi n imum  - 39 -  8.4125 57.537 39.787 21.037 13.837 1.2562 0.95544  Std.  Dev  3.9765 29.822 24.309 13.641 10.791 1.5057 1.2170  common d a t a s e t .  Max imum  3. 5 27 12 3 2 0 0.01  Mean  14.3 153 130 50 35 4 4.51  Mean  7.7937 65.723 48.057 18.214 11.839 .83929 .71804  Std.  Dev.  2. 7462 29. 301 25. 993 9. 5610 6. 7831 1. 3190 .82277  4.2  Stem  density  To basis,  an  estimate estimate  o-f b i o m a s s p e r distance  individuals.  very  so  density  Density  (Batcheler  review.  t h a n p l o t s and  clumped,  o-f stem  stem.  method  literature  shrub production  In the  1973,  Brie-fly,  corrects this  was  the  -for t h e  study  corrected  on  i s needed estimated  using  discussed  method  uses  as  the  area  an  estimate  corrected  in d e t a i l  distance  in  point the  measures  rather  non-random d i s t r i b u t i o n o-f  area,  i n d i v i d u a l s ( s t e m s ) were  point  distance  each  site,  at  equally  spaced  -follows  distance  closest  -from t h e  h i g h ) was  neighbour  point  recorded,  neighbour  Salix  and  each  to  then  species.  -from t h a t  two  Transect  t y p e o-f w e t l a n d  the  the  were r e c o r d e d .  thus g i v i n g  Betula,  method  was  strongly  considered  to  be  sets lines  association,  avoiding  s i z e and  density  o-f t h e  providing  site.  consecutive  within equal  which to  the  the  to  search  distance  problem  of  - 4 m  30  to  The  that  lines  the  wetland  the  cm  its closest Salix  points.  remeasuring  did -  40  not -  with  given  site,  the  and  the  i s not  i s not  i t was,  occur,  the  on  Points size  -from  distance  species,  was  s t e m s were so a stem  and  critical,  measured  maximum  appropriate  As  a  association.  same stem  the  -for  heterogeneous  points  or  one  traverse  depending  limit,  of  to  varied  between  search  -for a stem between  measurements,  apart,  distance  enough  points.  (over stem  distance  1 cm):  its closest  e d g e s and  s h a p e o-f t h e  were 2 The  i t i s great  to  were e s t a b l i s h e d  the  lines  nearest  -from t h a t  o-f d i s t a n c e  depending  transect  transects,  T h e s e m e a s u r e m e n t s were r e p e a t e d -for  number o-f t r a n s e c t  the  on  stem  Salix  neighbour  The  on  points (to the  distances  vegetation.  that  well  1975),  m e a s u r e m e n t s were c o l l e c t e d as  two  as  unit  suitable. On  on  a biomass per  was  dense  always  encountered  4.3  within  Biomass  per u n i t  Biomass density unit  data  area  described second  of b r o w s e  used  on  stem  described  every  fourth  was  site  dependent 4,  done due  been  smaller  paint,  collected,  the c u r r e n t  dried  T a b l e 4.3 indepependent  and  variables  to a suspected  The  biomass  per  transects  data.  At  browse  were c o l l e c t e d  browse  every condition on  the  weighed.  biomass of t h e Thus  the  f o r which both  almost e n t i r e l y  bias  and  of  Betula,  second stems e n c o u n t e r e d .  in the sampling design,  the o u t s i d e s  of c l u m p s  in that  and may  stems.  shows t h e number o f o b s e r v a t i o n s  variables  and  the  were known.  on b o t h t h e f i r s t  inside  biomass p r o d u c t i o n  a d o u b l e sample  t e n d e d t o be o n e s on than  4.1)  with  Betula.  which c o n s i s t e d  d a t a were c o l l e c t e d  stems  and  Salix  combined  d i m e n s i o n s and  in Section  data set included  and  first  stem  was  methods").  to c o l l e c t  the t r a n s e c t s ,  of each of  stem  On  were a l s o  1-6  independent  Be  an e s t i m a t e  above  site-specific  was  from the s i t e s  "Statistical  At  This  area  ( s e e C h a p t e r 6,  (variables  measured  limit.  data c o l l e c t e d  to y i e l d  point  closest  the search  b i o m a s s on e a c h s i t e ,  tula.  - 41  -  for density, for  Salix  and  have  T a b l e 4.3. b i o m a s s on  Site  Sample sites.  s i z e s -for d e n s i t y ,  Spec i e s  Sa  n = n =  I i x  BetuIs Betu Sal  First  n n  100 100  146  n n  72 72  (1) <2>  and  Biomass  n n  50 50  n n  35 35  i x  n n  200 200  n n  150 150  n n  38 37  ix  n n  195 195  n n  150 149  n n  42 42  Betula  <1)  200 200  Is  BetuIs SaI  Independent Variables  Dens i t y  BetuIs  independent v a r i a b l e s  stems  (2)  Second  stems  - 42  -  (1) (2)  5.  5.1  STATISTICAL  Regression An  equations  initial  decision  was made t o keep  data separate, rather  Betula  describe  both  preference. wildlfe  genera, Separate  or range All  0.05  METHODS  5.1.1  because  Hypothesis  and  one e q u a t i o n t o  o-f s u s p e c t e d  manager  than tests  a combined employed  d i-f-f e r e n c e s  i n animal to a  estimate.  throughout  t h e study used  a  level.  1:  R e l a t i o n s h i p s between  browse biomass p r o d u c t i o n e x i s t regression  develop  Salix  p r o d u c t i o n e s t i m a t e s may be more u s e f u l  statistical  significance  than  the  shrub  d i m e n s i o n s and  and s i m p l e o r m u l t i p l e  e q u a t i o n s may be d e v e l o p e d  to predict  linear  browse  biomass  p r o d u c t i on. Least Betula  package  squares multiple  were d e v e l o p e d (Fox and G u i r e  data c o l l e c t e d regression against  stem  1976),  not from  dimension  curvilinear  with  the study specific  T a b l e 5.1 l i s t s  ( i . e . those  area s p e c i f i c a l l y sites).  increasing  variance  variables  f o r the  B i o m a s s was p l o t t e d  t o examine t h e r e l a t i o n s h i p s ,  t o remove t h e c u r v i 1 i n e a r i t y  variance.  and  statistical  u s i n g t h e common d a t a s e t s  T r a n s f o r m a t i o n s of t h e independent attempt  r e g r e s s i o n s f o r Salix  t h e a i d o f t h e MIDAS  throughout  equations,  each  typically  from  with  linear  which  (see Appendix A ) .  were e x a m i n e d  i n an  and o b t a i n a homogeneous  the v a r i a b l e s  - 43 -  tested.  were  T a b l e 5.1. regression  Independent equations.  variables  tested  i n development  d i a m e t e r (DIAM) length (LENGTH) * c a n o p y d e p t h (DEPTH) * c a n o p y w i d t h 1 (WID1) * canopy width 2 (WID2) * browse (BRS) browse squared (BRS ) browse cubed (BRS ) diameter squared (D ) # diameter squared X length (D L) # (diameter squared X length) squared c i r c u l a r c a n o p y a r e a (AREA C) * e l l i p t i c a l c a n o p y a r e a (AREA E) # c i r c u l a r p l a n t v o l u m e (VOL C) * e l l i p t i c a l p l a n t v o l u m e (VOL E> *  o-f  multiple  2  3  a  Z  #  natural  The  of  circular  canopy  the average  area  o f t h e two  AREA C -  The  elliptical  2  l o g a r i t h m s o-f t h e s e v a r i a b l e s  (AREA C)  was  2  were a l s o  calculated  TT r , where t h e r a d i u s  •formula -for t h e a r e a o-f a c i r c l e , half  ((D )L)  2  width  measurements!  tested  -from  the  was  thus  77  canopy a r e a  (AREA E)  AREA E =( - 2 - )  (WID  was  computed  1 X WID  as  follows:  2)  4 The  circular  and  respectively) stem  elliptical  were computed  plant by  volumes  (VOL  multiplying  C and  VOL  the r e s p e c t i v e  E, areas  by  length. The  natural  untransformed  logarithm  were r e g r e s s e d on  MIDAS " f o r w a r d " and excluded  from  dependent  variable,  the above v a r i a b l e s ,  "backward" p r o c e d u r e  t h e model  i f t h e y were n o t  level. - 44  browse biomass,  -  options.  using  Variables  significant  and i t s  at the  the  were 0.05  Once e q u a t i o n s the  p r e d i c t i o n s were e x a m i n e d  Tests  -for t h e a s s u m p t i o n s  were per-formed 1. prediction  tests  p l o t s o-f t h e r e s i d u a l s a g a i n s t  -for l i n e a r i t y  o-f l i n e a r i t y ,  and h o m o s k e d a s t i c i t y .  equal  variance  Linearity:  Residuals  and d i v i d e d  into  f o r zero  were o r d e r e d  groups  by t h e s i z e  ( f o u r f o r Salix  linear.  mean was made on e a c h  A standard  lack of repeated  lack of f i t t e s t  observations  f o r any g i v e n  of  the  and s i x f o r  had t o be n o n - s i g n i f i c a n t a t t h e 0.0S l e v e l  considered  and n o r m a l i t y  on t h e r e s i d u a l s a s - f o l l o w s :  A t test  Betula).  of  were d e v e l o p e d ,  group.  All t  f o r t h e model  was n o t done value  of  t o be  because  the  independent v a r i a b l e s . 2. and  Equal  a Bartletts 3.  variance. test  Normality  test  f o r normality  5.1.2  Hypothesis  describe  This variables  f o r equal  Dummy v a r i b l e s  D  l  D  2  D  2  D  4  A single  Salix  f o r thefour  if  s p e c i e s 2,  a  1 if  spec i e s 2  a  0 if  species  0 if  1,  a regression using  1973). as f o l l o w s :  1  0 if  will  i n the area.  were a s s i g n e d  species  goodness of f i t  regression equation  (Cunia  3, o r 4  3 or 4  s p e c i e s 1,2 o r 3 - 45 -  above  performed. A Chi sqare  was t e s t e d w i t h species  as d e s c r i b e d  on r e s i d u a l s .  common  species  a  :  variance  was p e r f o r m e d  hypothesis  i  were g r o u p e d  of d i s t r i b u t i o n .  2:  the four  Residuals  dummy  New i n d e p e n d e n t independent such  variables  variable,  by m u l t i p l y i n g  , by t h e c o r r e s p o n d i n g  each  dummy v a r i a b l e ,  D  ,  that D  l  D  l  D  l  D  l  X  1  X  1  X  2  X  4  D  *  2  4  X ^  i-f s p e c i e s  ' *1  = o if species  -  0 i-f s p e c i e s  ™  *  4  variables  i  +  s  P  e  c  2  1, 3 o r 4  i  without  e  s  1,2 o r 3 intercept  and t h e new i n d e p e n d e n t i s equivalent  variable  c a n be o n l y  variable  i s the intercept  new v a r i a b l e To  test  variables.  separate  f o r that  i s the slope  using  t h e dummy  E s s e n t i a l l y s u c h an  equations.  The dummy  species,  f o r that  dummy  and t h e c o e f f i c i e n t f o r  species.  were n o t s i g n i f i c a n t l y d i f f e r e n t ,  was f i t t e d  and d i v i d e d  to obtain  was - f i t t e d ,  0 o r 1, s o t h e c o e f f i c i e n t f o r e a c h  The d i f f e r e n c e  determined  performed  t o -four  i f intercepts  regression  intercept.  freedom  2, 3 o r 4  = 0 i-f s p e c i e s  equation  another  1  i-f s p e c i e s  - *2  A regression  each  were c r e a t e d  with  dummy v a r i a b l e s  in the residual  by t h e d i f f e r e n c e  the difference  but using  o n l y one  sum o f s q u a r e s was  in the residual  mean s q u a r e ,  MS  ^ .  degrees of  An F t e s t was  as f o l l o w s :  MS  res where MS  i s from  the f i r s t  (largest)  equation.  res To  test  i f slopes  were s i g n i f i c a n t l y d i f f e r e n t , a -  46 -  regression  with  dummy v a r i a b l e s was - f i t t e d ,  slope was  coe-f-f i c i e n t  performed.  -for e a c h  To t e s t different,  and  coefficient  one s l o p e  common e q u a t i o n ) ,  MS^f  3.1.3  3:  Hypothesis  predict  production  with  f o r each  T h e common  equations.  site-specific  data  as p r e v i o u s l y  The  Betula, from  and i n t e r c e p t s t o g e t h e r  were  within  set.  tests,  cases  loss  site  were  only  site  data  from  and  sites  into  f o r Salix  s e t was n o t i n c l u d e d ) .  (see S e c t i o n 6.3).  f o r both  genera.  a single and  data  s e t and  Betula  "Site-specific  equations"  the respective s i t e .  In a l l  were o f t h e l o g - l o g f o r m .  regression estimates  were c o r r e c t e d  1,  in precision resulted  were c o m b i n e d  "pooled-site equations"  the equations The  a l l sites  using  sites  differences  together  Salix  f o r both  were d e v e l o p e d  were d e v e l o p e d  with t h e  described.  a d d i t i o n a l equations  data  as well  t o represent  and i n t e r c e p t s and s l o p e s  Therefore,  ( t h e common  sites  forsignificant  on s p e c i f i c  t o devlop  i f one  s e t was c o m b i n e d  Tests  adequately  a regression  to test  predict for specific data  performed.  will  above,  was u s e d  t h e common e q u a t i o n s  used  F test  the  the wetland.  using  from  variable (i.e.  described  sites  T h e common  outcome o f t h e s e  data  one i n t e r c e p t  regression equations  indicated that a s i g n i f i c a n t  Transect  with  and dummy v a r i a b l e s a s s i g n e d  intercepts, slopes,  performed  F test  independent  sites  would  4, 6, 7, and t h e common d a t a in  v a r i a b l e , and a s i m i l a r  was f i t t e d  analagous t o that  regression equation  separate  i n t e r c e p t s b u t o n l y one  c a l c u l a t e d and a s i m i l a r  dummy v a r i a b l e s r e p r e s e n t i n g  common as  slopes  an e q u a t i o n  on s p e c i f i c  In a manner  -four  independent  i f both  significantly  using  f o r the bias  o f mean b i o m a s s p e r stem inherent - 47 -  in logarithmic  on e a c h  transformation.  Each  p r e d i c t i o n o-f l o g Y ^  was b a c k - t r a n s f o r m e d  by  a? 2  taking  t h e a n t i l o g , then  (where a Bunce  was t h e r e g r e s s i o n  2  1973),  estimate  corrected  then  by t h e f a c t o r e  -for b i a s  mean s q u a r e  residual)  ( M o u n t f o r d and  the average of the back-transformed  and c o r r e c t e d  was c a l c u l a t e d . The  variance  calculated  of the estimated  in a similar fashion.  mean p r o d u c t i o n  The v a r i a n c e .  p e r stem  S'  was  , was  2  logY calculated  f o r each  back-transformed and  prediction,  by t a k i n g  logY^  .  to y i e l d  in  original  of  mean p r o d u c t i o n  the variance  units.  Confidence p e r stem Y  sites  5.1.4  using  t h e common,  H y p o t h e s i s 4:  significantly This observation  limits  were a t t a c h e d  i n t h e normal ± t • S£  respective residual) compared  found. with  site,  with  S | , 2  and Betula  on equations.  i s not  biomass.  a paired  t t e s t , where  (measured) b i o m a s s was p a i r e d  each  with i t s  (equivalent  to the  T h e a v e r a g e o f t h e s e d i f f e r e n c e s o r r e s i d u a l s was  zero  using  was  way:  b r o w s e b i o m a s s on s i t e s  the predicted  1  to the estimate  and s i t e - s p e c i f i c  p r e d i c t i o n , and t h e d i f f e r e n c e  where d = Y^ - Y ^ . each  pooled-site  h y p o t h e s i s was t e s t e d of a c t u a l  variances  o f t h e mean b i o m a s s p e r stem,  The a c t u a l  d i f f e r e n t from  was  by t h e f a c t o r &  and c o r r e c t e d  T h e s e c a l c u l a t i o n s were made f o r Salix all  variance  the a n t i l o g , corrected  t h e mean o f t h e s e b a c k - t r a n s f o r m e d  calculated  Each  in the t t e s t :  This  was done f o r Salix  p r e d i c t i o n s from -  t h e common, 48 -  and Betula,  on  p o o l e d - s i t e and  s i t e - s p e c i-f i c  equations.  5.1.5  Hypothesis  actual  b r o w s e b i o m a s s between  encountered  site  the average  5.1.6  4 data,  =  i ( l ) -  Y  of these  Hypothesis  predicted  this  stem  hypothesis  predictions  6:  There  was t e s t e d w i t h  stem  a paired t f i r s t and  computed:  compared  i s no s i g n i f i c a n t  a paired t test  the f i r s t  with  zero.  difference  stem  i n the  and t h e s e c o n d  stem  was u s e d  first  with  site  and s e c o n d  4 data,  where  s t e m s were p a i r e d and  computed: d  average  and t h e s e c o n d  (measured) b i o m a s s f r o m  differences  o f biomass from  difference  in the  Betula.  of  Again  difference  K 2 )  Y  browse biomass between  encountered  The  the f i r s t  s t e m s were p a i r e d and t h e d i f f e r e n c e d  the  i s no s i g n i f i c a n t  where o b s e r v a t i o n s o f a c t u a l  second  and  There  Betula.  of  Using test,  5:  • i(l)" Y  of these  Y  i ( 2 )  differences  done f o r p r e d i c t i o n s f r o m  was compared  with  zero.  T h i s was  t h e common, p o o l e d - s i t e and s i t e - s p e c i f i c  equations.  5.2  Density A computer  1973)  program  f o r a m o d i f i c a t i o n of B a t c h e l e r ' s  c o r r e c t e d p o i n t d i s t a n c e method,  Wildlife density  S e r v i c e , was used on t h e s i t e s .  made, u s i n g s u b s e t s  to estimate  In t h i s  program  of the e n t i r e  data  - 49 -  obtained  Salix  from  and Betula  successive  (1971,  the Canadian stem  iterations are  s e t with p r o g r e s s i v e l y  increasing point the  search  limits  ( t h e maximium d i s t a n c e f r o m  within  which  t o encounter  a stem).  estimate  which  has t h e s m a l l e s t  The p r o g r a m  variability  the transect then  selects  as the best  density  e s t imate. At  each  f o r Salix  separately the  transect point,  than  combined  (Laycock The  treated 1985,  data  pers.  making  s e t Independently.  and B a t c h e l e r  probable  limit  comm.),  in the variance  times  stem  o f two e s t i m a t e s  variance  of the f i n a l  estimate  s =  i s determined  o  where X = e s t i m a t e d Y =° e s t i m a t e d  2  program i s (Smith  i s represented  ? +  each  by P L E . 2  s  final  have v a r i a n c e s , t h e  by c o m b i n i n g  x  Y  t h e two  I960): 2  s  2  y  -  browse p r o d u c t i o n stem  2  x  n(X)  n(Y)  Because t h i s  (Goodman  s  y  x  X y  corrected  which  the f o l l o w i n g formula  o  by t h i s  c a l c u l a t i o n s ( s e e next  density.  i s a product  s  s p e c i e s groups a r e  i n grams p e r s q u a r e m e t r e was c a l c u l a t e d a s  p e r stem  using  i n a bittter  area  estimate  p e r stem  results  d e v i a t i o n of t h e d e n s i t y e s t i m a t e  Browse b i o m a s s p e r u n i t  mean p r o d u c t i o n  (PLE) g i v e n  of the d e n s i t y estimate  Browse b i o m a s s  (The  This  1975).  of e r r o r  therefore  the variance  variances  i t p o s s i b l e to run  when d i s t a n c e m e a s u r e s t o d i f f e r e n t  as the standard  section)  5.3  and Betula,  p r o g r a m on e a c h  estimate  d i s t a n c e m e a s u r e m e n t s were made  n(X)  n(Y)  p e r s t e m , and  density  biomass estimate  and v a r i a n c e  are back-transformed  and  f o r bias.)  The  confidence  limits  of the estimated - 50 -  biomass per square  metre a r e ,  there-fore, XY  +  t •  T h e s e c a l c u l a t i o n s were made -for Salix all  sites,  using  t h e common, p o o l e d - s i t e  - 31 -  and Betula,  and s i t e - s p e c i-f i c  on equations.  6.  RESULTS  6.1  Hypothesis  1:  biomass p r o d u c t i o n equations  independent  o-f Salix  dimension  2) r e v e a l e d  increasing  condition.  logarithms,  and Betula  or m u l t i p l e regression  curvilinear  length,  r e l a t i o n s h i p s with  i n the plot  1976),  A.)  various  of the independent  Using  No  including natural  variables (listed in  squares m u l t i p l e  described  package  linear  common  regressions  data  by l o g - l o g m o d e l s .  Salix  6.1.1  The log  best  equation  developed  f o r Salix  BIOMASS - -6.1708 + . 4 6 4 7 8 ( l o g  was  D») + . 6 8 5 0 9 ( l o g  DEPTH)  + . 4 4 3 3 6 ( l o g WID2) + .10892(BRS) R The  2  » .81697  a n a l y s i s of v a r i a n c e Slightly  using  higher  SE »• .48720  i s given R* v a l u e s  n » 160  i n Appendix  B.  were o b t a i n e d  with  the following v a r i a b l e s : log-D L, z  l o g LENGTH, (R  2  =  1 and  the variance  t h e MIDAS s t a t i s t i c a l  and Betula  t h e r e l a t i o n s h i p s were b e s t  width  o f b r o w s e b i o m a s s on b r o w s e  and d e p e n d e n t  t h e Salix  depth,  variable.  trans-formations,  5.1) were t e s t e d , and l e a s t F o r both  production.  browse biomass a g a i n s t t h e  v a r i a b l e s (diameter,  (See Appendix  were d e v e l o p e d . sets,  linear  d i m e n s i o n s and b r o w s e  t o p r e d i c t browse biomass  was a p p a r e n t  and G u i r e  Table  and s i m p l e  shrub  p r o p o r t i o n a l l y t o the independent  relationship  (Fox  exist  may be d e v e l o p e d  Plots  width  R e l a t i o n s h i p s between  l o g WID2 and BRS  .81904) - 52 -  models  log D ,  l o g VOL E, l o g AREA E and BRS  a  (R* However  the -first  measurements  model  •  .81837)  was s e l e c t e d  in the f i e l d  because  ( i . e . four  i t requires  versus f i v e  -fewer  and f i v e ,  respect i v e l y ) . In errors  linear regression  or r e s i d u a l s :  have a c o n s t a n t model  a valid  incorrect  Confidence  (Draper  The  following  assumptions  of  B a r t l e t t s t e s t s f o r equal  3)  Goodness of f i t t e s t Results  2  -  the f i r s t  passed  square  i s lack of  predict i f t h e model 1  on t h e r e s i d u a l s to t e s t the  variance,  to test f o r linearity using  that  of l i n e a r i t y  d i s t r i b u t i o n of r e s i d u a l s . group  of r e s i d u a l s  of the other from  showed  the untransformed  residuals. The model  the t e s t s f o r equal In t h e t e s t f o r  (n»40) had a v a r i a n c e  two t o  groups.  t h i s model  a marked  data,  groups of r e s i d u a l  i n T a b l e 6.1.  but f a i l e d  should  the test f o r l i n e a r i t y . model  four  distributed  o f t h e t e s t s a r e summarized  and n o r m a l  times  will  n o t be v a l i d  equation  f o r normally  the assumption  transformed from  a  The  1966).  groups of r e s i d u a l s  Predictions model  If there  of  zero,  regression:  2)  three  estimate  regression  t t e s t s on f o u r  variance,  distribution. i f t h e mean  t e s t s were p e r f o r m e d  1)  variance  h a v e a mean o f  these assumptions  intervals will  and S m i t h  by t h e Salix  calculated  meet  a normal  a r e made a b o u t t h e  i s , t h e d a t a a r e n o t l i n e a r , t h e model  inadequately.  did  a r e independent,  and f o l l o w  and meet  i s to provide  that  they  variance,  must be c o r r e c t  residual fit,  that  c e r t a i n assumptions  even  A plot  reduction though  - 53 -  be a c c u r a t e  because the  of t h e r e s i d u a l s  of the  in heteroscadasticity  the assumption  was n o t met.  A weighted  r e g r e s s i o n may  but  i t i s more c o m p l e x  the  non-transformed  every the by  v a l u e of  residuals the  X.  If t h i s  would  not  but  assumptions.  transformation distribution be  will  variables  are  i s t r u e , then  be  normally  unequal  i s reasonable  variance,  t o assume t h a t  normally  in a  distributed  log-transformed  distributed  may  case,  the  homogeneity (although  of  s o l v e some o f  but  would  be  these  linearity  assumption  was  problems of  p r o b l e m s by was  of v a r i a n c e was  the  residuals  aware of  the  i n t u r n c r e a t e new  In t h i s  transformation,  at  model skewed  violating  achieved  improved  was  not  violating other  by  by  met),  but  the  skewed  by  the  transformation.  The  limitations  of  the  predictions derived  user from  equation. B e c a u s e of  intervals examples degrees  difficulty  in g r a p h i c a l l y  o f more t h a n  representing various sizes of browsing  and  units  (Mountford 1.12602.  and  and  underestimate The  the  of  with  two  shrub  the  ( T a b l e 6.2)  limits  1973).  words, correct  several  stems with  different  the  factor  correction  factor  simply  t a k i n g the  antilog  by  a  suggests  e f o r Salix of  log y  lightly  54  that  A h e a v i l y browsed browsed  T h i s s t i m u l a t i o n by -  to  was would  ±  12.6%.  browse biomass p r o d u c t i o n .  p r o d u c e more b r o w s e b i o m a s s t h a n  and  the  shown a r e b a c k t r a n s f o r m e d  The  value  confidence  dimensions,  In a l l c a s e s  common r e g r e s s i o n model  t h e same d i m e n s i o n s .  depicting  p r e d i c t e d browse biomass  c o r r e c t e d f o r b i a s by  Bunce  Salix  interval  confidence  In o t h e r  stimulates  are given,  confidence  predictions original  the  for relationships  associated  of  It  the  transformation.  assumptions,  the  t o compute.  dependent  Transformation  should  have b e t t e r h a n d l e d  -  browsing stem  should  or unbrowsed  browsing  stem  i s supported  by  browse s i m u l a t i o n (Aldous  studies  1952, K r e f t i n g The  on v a r i o u s  species  from  Salix  e t a l . 1966).  confidence interval  around  the p r e d i c t i o n  b e c a u s e o-f t h e b a c k - t r a n s - f o r m a t i o n f r o m width  including  of the c o n f i d e n c e i n t e r v a l  logarithmic  i s skewed  values.  a s a p e r c e n t a g e o f t h e mean  The ranges  a p p r o x i m a t e l y + 7.5% a t t h e means o f t h e l o g a r i t h m s o f t h e  independent values  variables,  t o a p p r o x i m a t e l y + 3 0 % a t t h e maximum  f o r the independent  T a b l e 6.1. regression.  of r e g r e s s i o n  Calculated statistic  1. L i n e a r i t y  variance  3. N o r m a l i t y  on Salix  Critical value  common  Significance a t 0.05 l e v e l  = 0.1707 =-0.6001 = 0.4649 =-0.2172  t = 2.021 t = 2.021 t = 2.021 t = 2.021  N. S. N.S. N.S. N.S.  -x  =  16.9293  x  =  7.815  Sig.  x  =  102.781  x  =  16.919  Sig.  t, t t  2. E q u a l  variables.  T e s t s of assumptions  Test  2  2  observed  - 55 -  2  2  T a b l e 6.2. Some examples o-f p r e d i c t i o n s and c o n f i d e n c e i n t e r v a l s -for based on t h e common r e g r e s s i o n e q u a t i o n .  Satix  DIAM  DEPTH  WID 2  (mm)  (cm)  (cm)  BRS  3. 4 3.4 3.4 3.4 3.4  10. 0 10.0 10.0 10.0 10.0  3.0 3.0 3.0 3.0 3. 0  0 1 2 3 4  6.4 6.4 6. 4  23. 0 23.0 23.0  9.0 9. 0 9.0  7.66 7. 66 7.66  34.0 34.0 34. 0  9.3 9.3 9.3 16. 2 16.2 16.2  +  Predicted Browse Bi amass (g)  93% Confidence I n t e r v a l  0.05797 0.06463 0.07208 0.08038 0.08963  0.04687 0.03344 0.05977 0.06333 0.07072  0 2 4  0.31893 0.39635 0.49307  0.28297 0.35909 0.40717  11.0 11.0 11.0  0 1. 256 * 4  0.30946 0.38416 0.78763  0.43689 0.34169 0.63303  39. 8 39.8 39.8  13.9 13.9 13.9  0 1. 236 ** 4  0.73246 0.36279 1.16331  0.66232 0.79133 0.97314  93.0 93. 0 93.0  40.0 40. 0 40.0  0 2 4  3.61409 4.49371 3.38743  3.01554 3.74661 4.33346  147.0 147.0 147.0 147.0 147. 0  66.0 66.0 66. 0 66. 0 66. 0  0 1 2 3 4  8.39662 9.38586 10.68894 11.91895 13.29050  6.77647 7.62335 3.43833 9.19610 9.90493  23. 23. 23. 23. 23.  1 1 1 1 1  + ++ # #*  Minimum o b s e r v e d v a l u e s of untransformed independent Maximum o b s e r v e d v a l u e s of u n t r a n s f a r m e d v a r i a b l e s Averages of l o g - t r a n s f o r m e d independent v a r i a b l e s Averages of u n t r a n s f o r m e d Independent v a r i a b l e s  ++  - 56 -  -  •-  -  variables  0.07172 0.07820 0.08693 0.09839 0.11339 0.35945 0.43792 0.39709 0.56809 0.62996 0.94995 0.83460 0.94044 1.38779 4.33144 3.38979 7.20425 10.90367 12.03011 13.33978 13.44800 17.33318  Betula  6.1.2  The log  best  a n a l y s i s of Higher  log-log and R  a  =  z  variance R  values  z  and  no  .82516.  For  t tests  and  was  therefore rejected  met  more of  Results  variance,  but  for  the  did  of  met  the  not  pass  3  112 B.  f o r models without  the  using  dependent  <D L) Z  of  the  The  the Z  v a r i a b l e , had  r e s i d u a l s showed  non-1inearity;  in favour  of  .0068697(BRS )  n =  linearity.  of  -  i n Appendix  the  assumptions  l o g - l o g model  .67759  of  suggested  tests  E)  e x a m p l e a model  transformation  Bartletts  was:  Betula  VOL  were o b t a i n e d  and  the  =  i s given  heteroscadasticity  The  SE  However p l o t t i n g  test  for  .66984(log  .67404  transformation.  WID1, =  developed  BIOMASS = -6.8506 + R  The  equation  an  severe  this  was  confirmed  non-transformed  l o g - l o g model,  as  by  model  the  latter  regression. assumptions  assumptions the  test  of  are  shown  linearity  f o r normal  in Table  and  6.3.  equal  distribution  of  residuals. Examples  representing  different  browse  predicted  browse biomass p r o d u c t i o n  interval. have b e e n Betula  was  As  with  1.25805;  Salix  given  of  shrub  in Table  and  6.4  associated  stems with  with  the  confidence  the  p r e d i c t i o n s and  confidence  and  corrected.  correction factor  i . e . the  would  are  sizes  result  bias i n an  The  a s s o c i a t e d with underestimate  the  of  limits for  logarithmic  25.8%  when  taking  ant i 1 a g . Unlike  that  Salix,  backtransfarmed  transformation the  intensities  various  browsing model,  the  Salix  inhibits the  model, the  confidence  the  Betula  production  of  intervals - 57  are -  model  predicts  browse biomass. skewed  in  Like  original  the  units.  This regression i s less  regression.  The w i d t h  approximately variables,  to approximately  interval  Salix ranges  o-f r e g r e s s i o n on  Linearity  variance  Cr i t i c a l v a l ue  t t t t t t  =-0.0257 =-0.0440 = 1.2413 = 1.1180 =-1.5267 = 1.0420 =  10.2104  = 36.87  - 58 -  = = = = = =  2. 093 2. 093 2.093 2.093 2.093 2.201  -from  independent  + 5 3 % a t t h e maximum o b s e r v e d  Calculated statistic  3. N o r m a l i t y  the  + 12.5% a t t h e means o-f t h e trans-formed  Test  2. E q u a l  than  o-f t h e c o n f i d e n c e  T a b l e 6.3. T e s t s o-f a s s u m p t i o n s common r e g r e s s i o n .  1.  precise  values.  Betula  Signi-f i c a n c e a t 0.05 l e v e l  N.S. N.S. N.S. N.S. N.S. N.S.  11.070  N.S.  16.919  Sig.  T a b l e 6.4. Same examples o-f p r e d i c t i o n s and c o n f i d e n c e i n t e r v a l s -for Betula based an t h e common r e g r e s s i o n e q u a t i o n .  VOL E  BRS  (cm ) 3  179. 0 179. 0 179.0 179.0 179.0  Pred i c t e d Browse Biamass (g>  93% C o n f i d e n c e  Interval  0 + 1 2 3 4  0.04302 0.04273 0.04072 0.03374 0.02772  0.02933 0.0293S 0.02S27 0.02474 0.01720  0.06268 0.06214 0.03866 0.05162 0.04468  3899.3 3899.3 3899.3  0 2 4  0.33878 0.32067 0.21826  0.29068 0.27885 0.14897  0.39484 0.36876 0.31978  7619.8 7619.8 7619.8 7619.8  0 1 2.88 * 4  0.33064 0.32701 0.30128 0.34187  0.46283 0.46080 0.44216 0.23240  0.60838 0.60274 0.36830 0.30289  18,967.8 18,967.8 18,967.8 18,967.8  0 0. 769 2 4  0.97748 0.97332 0.92321 0.62975  0.83634 0.83398 0.79598 0.41942  1.14216 1.13641 1.07342 0.94333  80,781.2 80,781.2 80,781.2  0 2 4  2.38009 2.44211 1.66223  2.01315 1.90332 1.04046  3.30668 3.13309 2.63358  0 1 2 3 4 ++  3.97384 3.94663 3.76133 3.30109 2.36017  2.94673 2.92713 2.78238 2.34699 1.34326  5.33896 5.32122 3.08471 4.64305 4.24166  133,937.2 133,937.2 133,937.2 133,937.2 133,937.2  + Minimum o b s e r v e d v a l u e s of Independent v a r i a b l e s ++ Maximlum o b s e r v e d v a l u e s of independent v a r i a b l e s * Averages of t r a n s f o r m e d v a r i a b l e s Averages of non-transformed v a r i a b l e s  - 59 -  6.2  Hypothesis  describe  to  A single  t h e -four Salix Using  with  2:  common r e g r e s s i o n e q u a t i o n  species  t h e common Salix  i n the area. data  dummy v a r i a b l e s r e p r e s e n t i n g  test  will  s e t (n=160>, a r e g r e s s i o n  t h e -four Salix  s p e c i e s was u s e d  t h e -following hypotheses: 1)  i n t e r c e p t s a r e n o t s i g n i - f l e a n t l y di-f-ferent  2) s l o p e s a r e n o t s i g n i - f i c a n t l y 3)  i n t e r c e p t s and s l o p e s  di-f-ferent  together  a r e not signi-f leant l y  d i fferent. In a l l c a s e s level the in  the c a l c u l a t e d F value  ( T a b l e 6.5)  -four s p e c i e s  There-fore, i n the study  p r e c i s i o n by d e v e l o p i n g  was n o t s i g n i f i c a n t  one e q u a t i o n and t h e r e  may be u s e d  would  species-specific  DF  to describe  be no s i g n i f i c a n t  four  Salix  calculated F  critical F  1.  Intercepts a r e not significantly different  (3,140)  0.288  2.67  2.  Slopes a r e not significantly different  (12,140)  0.427  1.82  3.  I n t e r c e p t s and s l o p e s a r e n o t significantly different  (16,140)  0.884  1.74  - 60 -  gain  equations.  T a b l e 6.5. T e s t i n g f o r o n e e q u a t i o n t o d e s c r i b e s p e c i e s u s i n g r e g r e s s i o n w i t h dummy v a r i a b l e s .  Hypothesis  a t t h e 0.05  6.3  Hypothesis  predict  3:  The common  p r o d u c t i o n on s p e c i f i c A r e g r e s s i o n with  used, plus  regression equations  but t h i s those  time  site  sites  will  adequately  w i t h i n the wetland.  dummy v a r i a b l e s  r e p r e s e n t i n g s i t e s was  t h e d a t a s e t c o n s i s t e d o f t h e common  d a t a f o r which  data s e t i s referred  data s e t  b i o m a s s had been m e a s u r e d .  to as " s i t e  99" and a s s i g n e d  T h e common  a dummy  variable  accordingly.  6.3.1  Salix F o r Salix,  no  significant  differences shown  the r e g r e s s i o n s with  differences  indicated  b u t t h e r e were  significant  together, as  i n T a b l e 6.6.  site-specific regression  SITE  in intercepts,  i n s l o p e s , and i n s l o p e s a n d i n t e r c e p t s  Due t o t h e l o s s  all  dummy v a r i a b l e s  equations  analysis l :  Salix  of p r e c i s i o n  data with  of variance tables  data,  pooling  site-specific  The e q u a t i o n s  are given  below;  a r e i n A p p e n d i x B:  SE » .52053  n = 50  l o g BIOMASS = -4.8459 + .52938 (LOG D=» DEPTH) SE = .46465  n = 38  l o g BIOMASS = -7.0869 + . 7 1 6 0 5 ( l o g R* • .77815  In a d d i t i o n t o t h e equation  from  l o g BIOMASS = -6.9076 + 1.7391<log DEPTH)  R" = .48251  S I T E 7:  t h e common  were d e v e l o p e d .  R* = .59908  S I T E 6:  arising  SE = .46334  individual  was d e v e l o p e d u s i n g  DIAM)  those  site  n = 42  equations  d a t a from  - 61 -  + 1.4038<log DEPTH)  sites  a "pooled-site"  1, 6 and 7 f o r  which  b i o m a s s had  excluded.  The  o-f v a r i a n c e log  been m e a s u r e d  i s i n Appendix  R*  -  The  i s given  common d a t a  below  and  the  set  was  analysis  B.  .29389(log  .63201  Interestingly,  The  130).  -6.3720 + . 2 4 0 3 8 ( l o g +  as  =  pooled-site equation  BIOMASS =  variables  <n  this  SE  use  +  WID2) +  .50130  equation  t h e common e q u a t i o n  s i t e - s p e c i f i c equations  =  D»)  but  1.0731(log  .081898(BRS) n =  130  uses  the  with  different  fewer  and  DEPTH)  same  independent coefficients.  i n some c a s e s  different  variables.  T a b l e 6.6. T e s t i n g f o r one e q u a t i o n t o d e s c r i b e Salix a l l s i t e s u s i n g r e g r e s s i o n w i t h dummy v a r i a b l e s .  Hypothesis  DF  on  calculated F  1.  I n t e r c e p t s a r e not significantly different  (3,270)  2.  S l o p e s a r e not significantly different  (12,270)  1.854  *  1.75  3.  I n t e r c e p t s and s l o p e s a r e significantly different  (16,270)  1.905  #  1.67  *  Significant  a t 0.05  not  level  - 62  -  2.050  critical F  2.60  Betula  6.3.2  There slopes, sites, test  was no s i g n i f i c a n t  indicated  by t e s t s  intercepts  Therefore  Betula given SITE  i n Appendix l :  was s i g n i f i c a n t and s l o p e s  site-specific  and a r e shown  below.  a t t h e 0.05 l e v e l  inthe  e q u a t i o n s were d e v e l o p e d f o r of v a r i a n c e  tables are  B.)  SE =» .52652  l o g BIOMASS = -3.4574 R (The s i t e  = .70266  a  n = 50  + 1.3084(log  SE = .62091  4 e q u a t i o n was b a s e d  WID2)  - .2329(BRS)  n =» 35  on f i r s t  stems o n l y . )  6: log  BIOMASS = -8.1241 R  SITE  7:  a .53050  a  a  = .60114  A pooled-site using  only  which  biomass  D L) + .65218(log  SE = .76266  SE = .59433  sites  had b e e n m e a s u r e d ,  1, 4  n = 37  developed  (first  i s shown b e l o w and t h e a n a l y s i s  - 63 -  VOL E)  n = 42  for  stems),  and e x c l u d i n g  B.  WID2)  Z  e q u a t i o n was a l s o  t h o s e d a t a from  equation  Appendix  + .65842(log  l o g BIOMASS = -6.6450 + . 6 1 0 1 7 ( l o g R  The  w i t h dummy v a r i a b l e s f o r  l o g BIOMASS = -6.3201 + . 3 6 7 0 5 ( l o g VOL E)  4:  SITE  nor i n  (Table 6.7).  (Analysis  R* » .43897  SITE  in intercepts,  on t h e r e g r e s s i o n  but the F s t a t i s t i c  combining  difference  Betula,  6 and 7 f o r  t h e common  of v a r i a n c e  data s e t . is  in  log R  a  BIOMASS = -7.2008 + .68993<log « .56112  SE = .67188  n »  VOL  E)  164  T a b l e 6.7. T e s t i n g -for one e q u a t i o n t o d e s c r i b e Betula. a l l s i t e s u s i n g r e g r e s s i o n w i t h dummy v a r i a b l e s .  Hypothesis  DF  on  calculated F  critical F  1. I n t e r c e p t s a r e n o t significantly different  (4,261)  0.260  2.37  2. S l o p e s a r e n o t significantly different  (8,261)  1.405  1.94  2.184 #  1.74  3.  I n t e r c e p t s and s l o p e s a r e n o t significantly different  # Significant  a t 0.05  (13,261)  level  - 64 -  6.4  Hypothesis  significantly  The  the  results  and  from  results  of  b r o w s e b i o m a s s on  sites  i s not  the p r e d i c t e d biomass.  of  the  of  pooled-site equations  F tests  the  paired  t test,  Table  6.8. On  intervals  full  and  ( T a b l e 6.8),  other  equations  i n c r e a s e SSX used  cases!  and  the  much b e t t e r  than  c o n s i d e r i n g the  using  using  the  the  r e g r e s s i o n with  common, s i t e - s p e c i f i c  the  confidence  the  the  and  yet y i e l d s  narrower The  to represent reduce  the  the  t h e more common smal1  i t was  is less  outperformed  size  data,  s t e m s and  the  i s not  accurate  few  -  of  shown i n  than  the  the p a i r e d t than  the  used  that  were  data  the  stems other  resulting of  the  Intervals  the  in  rarer  on  (which two  collection  t h e most a c c u r a t e  pooled-site equation  - 65  by  r a n g e of  while  for  those  indicated  confidence  variance)  equation by  as  full  a percent  used  from  common e q u a t i o n  systematically collected  site-specific  subset  predictions differ  common e q u a t i o n  as  stem,  These p r e d i c t i o n s are  the  pooled-site equations,  and  interval  three equations.  ( T a b l e 6.9).  selected  The  differences  the  shows t h e mean p r e d i c t e d b i o m a s s and  t h e r e f o r e the  tests  many o f  surprising  d a t a s e t , r a t h e r than  a l l sites  site-specific  stems.  6.8  performed  that  c o m p a r e s mean p r e d i c t e d b r o w s e b i o m a s s p e r  t h e mean p r e d i c t e d by  equations  for site  Table  6.9  confidence  purposely  i s not  indicate  equations.  Table  made f r o m  This  the p a i r e d t t e s t s ,  pooled-site  would  the p a i r e d t t e s t s  common e q u a t i o n .  dummy v a r i a b l e s .  of  actual  different  results  site-specific  93%  The  Salix  6.4.1  did  4:  large in a l l  site  1.  T a b l e 6.8. Mean p r e d i c t e d browse biomass (grama/stem) and p a i r e d •for d i f f e r e n c e between p r e d i c t e d and o b s e r v e d biomaas f o r Salix.  Actual b i omasa  Common equat i o n  S i t e - s p e c i f ic equat i on  t tests  Pooled-si te equat i on  Site  1  30  .32440  .60686  2.310*  .54373  0.603  .51396  -0.235  6  38  .43447  .38009  2.897*  .43382  0.017  .49262  0.903  7  42  .39000  .79009  3.973*  .60199  0.261  .60424  0.337  * S i g n i f i c a n t a t 0.03 l e v e l  T a b l e 6.9. Comparison of mean p r e d i c t e d browse biomass (grams/stem) 93% c o n f i d e n c e i n t e r v a l s f o r Salix, using three equations.  Common e q u a t i o n Site  n  Y  Site-specif ic equat i on  + 93% C I (% of mean)  and  Pooled-site equat i on  + 93% C I (% of mean)  + 93% C I (% of mean)  1  100  .38076  ± .20876 ( + 36%)  ,53340  + .21630 ( ± 40%)  .49708  + .21184 ( ± 43%)  6  130  .53107  + .17046 ( ± 31%)  ,43234  ± .17549 ( ± 40%)  .47472  + .17118 < + 36%)  7  130  .37204  + .17067 ( t 30%)  ,44687  + .17332 ( + 39%)  43399  t .17142 < ± 38%)  * Confidence  Interval  - 66 -  6.4.2  Betula  The common by  s i t e - s p e c i-f i c e q u a t i o n s  or p o o l e d - s i t e equations  the paired t tests  test  ( T a b l e 6.10).  s i t e - s p e c i -f i c e q u a t i o n .  Table  6.11 shows  interval  site  a percent  However  either the  i s not s u r p r i s i n g  s e t as i s used  t h e common  as the t  t o develop the  4 was t h e e x c e p t i o n ,  where  On s i t e s  (at the 95% l e v e l )  a s shown  t h e common  1 and 6 t h e r e  b e t w e e n p r e d i c t e d and  and p o o l e d - s i t e e q u a t i o n s .  t h e mean p r e d i c t e d b r o w s e b i o m a s s p r o d u c t i o n , 9 5 % and c o n f i d e n c e  the three equations  complete as  differences  biomass u s i n g both  confidence for  This  g a v e t h e most a c c u r a t e p r e d i c t i o n s .  were s i g n i f i c a n t actual  Site  b e t t e r than  on t h r e e o-f t h e -four s i t e s ,  i s a p p l i e d t o t h e same d a t a  equation  performed  data  interval  on f o u r s i t e s .  sets.  On s i t e  as a percent  These d a t a  a r e based  1, 6 and 7 t h e c o n f i d e n c e  o f t h e mean were s m a l l e s t f o r t h e common  the actual  width  of the confidence  units  a s t h e mean) was n a r r o w e s t  sites  1, 4 and 7, and w i t h  o f t h e mean  with  interval  - 67 -  intervals  equation.  ( i n t h e same  the s i t e - s p e c i f i c  the p o o l e d - s i t e equation  on t h e  equation f o r  for site  6.  T a b l e 6.10. Mean p r e d i c t e d browse biomass (grama/atsm) and p a i r e d t t e s t -for di-f-ference between p r e d i c t e d and o b s e r v e d biomass o-f Betula.  Actual biomass  Common equat i on  S i te-speci-f i c equat ion  Pooled-sit« equat ion  Site  1  SO  .4446  .60213  4.74*  4<1)  33  1.0306  .93732  -0.838  4(2)  33  .96171  .88903  -0.740  6  37  .33865  .36198  3.139*  7  42  .70214  .82911  1.795  • S i g n i f i c a n t a t 0.05 l e v e l (1) F i r s t stems <2) Second  .44873  0.136  .31014  2.092*  1.1291  1.004  .86467  -1.834  1.0073  0.412  .79961  -1.629  .38470  1.267  .49187  3.963*  .70365  0.024  .72802  0.386  stems  T a b l e 6.11. Comparison of mean p r e d i c t e d browse biomass (grams/stem) and 95% c o n f i d e n c e i n t e r v a l s f o r Betula, using three equations.  Site-specif ic equat i o n  Common E q u a t i o n  7  Site  * 95% C I (% of mean)  1  100  .65866  + .22036 < + 33%)  4  72  .98692  + .26031 ( i 26%)  6  150  .37198  + .18029 < ± 31%)  7  149  .74923  + .18043 ( • 24%)  * Confidence  f  .38398  Pooled-si te equation  ± 93% C I (% af mean)  + 95% C I (% of mean)  + .21223 < + 35%)  .33991  + .21991 < + 39%)  ± .25921 ( + 21%)  ,87774  + .23938 ( + 30%)  .37405  + .20900 ( + 36%)  49839  + .17967 ( ± 36%)  ,49812  ± .17683 < + 35%)  .63772  ± .17978 ( + 27%)  1.2219  Interval  - 68 -  6.5  H y p o t h e s i s 3:  browse  There  b i o m a s s between  i s no s i g n i f i c a n t  the f i r s t  stem  difference  and s e c o n d stem  i n the actual encountered of  Betula.  The 0.0824  paired  indicating  confidence  level)  t test  for this  no s i g n i f i c a n t i n the actual  h y p o t h e s i s gave a t v a l u e o f  average d i f f e r e n c e  (at the 95%  biomass of t h e f i r s t  and s e c o n d  stems. The might  be e n t e r i n g  measured (i.e. the  outside  clumps.  a stem  close stem  the transect  the f i r s t  within  a clump  address  inside  o f a clump  Field  t h a n t h o s e on t h e o u t s i d e  question  of a d i f f e r e n c e  biomass clump, and with  differences one c o u l d  a stem  of b i a s between  sample  t test.  i t i s usually clumped point  a s t e m on  nature of the  usually  fell  stems  different  a r e very  from t h e f i r s t  from  were t h a t  and have  o f a clump.  pairs  and i n s i d e  of stems:  inside  a l s o be  stems  s t e m s on t h e  a larger  basal  Unfortunately the h a s n o t been  i n t h e s a m p l i n g method. outside  made  h y p o t h e s i s d i d not r e a l l y  i n biomass p r o d u c t i o n  from the c e n t r e  a paired  This  t e n d e d t o be t a l l e r  has t h e q u e s t i o n  t o be  stem e n c o u n t e r e d  the distance  observations  diameter  nor  bias  t h a n 10 cm) t h e s e c o n d stem w o u l d  are outside  biomass p r o d u c t i o n ?  t h e stem  However, b e c a u s e s t e m s  (typically  o f t h e clump.  the question:  line  that  d i s t a n c e measurement was u s u a l l y  o f a clump.  t o t h e s e c o n d was l e s s to the outside  point)  Due t o t h e s t r o n g l y  area,  Thus  When  as the f i r s t  to the transect  on t h e o u t s i d e  together  close  in  established  o f a clump. study  because of a s u s p i c i o n  t h e s a m p l i n g method.  closest  in this  between  into  isarbitrarily  t h e stem  shrubs  to  h y p o t h e s i s was t e s t e d  stems  the f i r s t  answered,  To t e s t f o r i n t h e same  stem e n c o u n t e r e d  o f t h e clump,  then t e s t  for differences  Some s e t o f r u l e s  to define  the c e n t r a l  - 69 -  stem  would  be needed  statistically  to avoid  personal  significant  the present  sampling  some method  of determining  stem was  was c o n v e n i e n t  bias.  difference  scheme would which  and seemed  I-f i n d e e d  between  have stem  outer  t o measure;  - 70 -  is a  and i n n e r  t o be m o d i f i e d .  a p p r o p r i a t e when  designed.  there  One  selecting  the sampling  stems, needs the f i r s t scheme  6.6  H y p o t h e s i s 6:  predicted  browse  encountered  of  t h e 0.05  equations, however, second on  biomass  t tests  level  stems  between  difference stem  i n the  and s e c o n d  stem  to test  this  i n T a b l e 6.12.  significantly (t=2.025,  hypothesis  using  with  t h e common and  The s i t e - s p e c i f i c  different  n=72)  were n o t  predictions  greater  significant pooled-site  equation d i d ,  f o r the f i r s t  and  b i o m a s s on t h e f i r s t  stem,  the average.  T a b l e 6.12. (grams/stem)  P a i r e d t t e s t s f o r d i f f e r e n c e between o f f i r s t stem and s e c o n d stem o f Betula  1st Equation  n  Common  72  Site-specific  72  Pooled-site  72  *  the f i r s t  for predictions  a s shown give  i s no s i g n i f i c a n t  Betula.  Paired at  There  Significant  a t 0.05  stem Y  2nd stem  predicted on s i t e  Paired  Y  .98692  .85700  1.2219  1.0319  .87774  .77037  level  - 71 -  biomass 4.  t  test:  t  value  t =  1.856  t = 2.025 * t  =-1.779  6.7  Density Betula  sites  had a g r e a t e r  where b o t h  occurred.  the  d e n s i t y o f Salix,  2.1  times.  site  On s i t e  on s i t e  than  Salix  1, Betula  o-f e r r o r  on t h e t h r e e had a b o u t  6 i t was 1.6 t i m e s  The g r e a t e s t d e n s i t y o v e r a l l ,  4, where v i r t u a l l y  limits  density  no Salix  (PLE) and 9 5 % c o n f i d e n c e  times  and on s i t e  42 stems/m , 35  occurred.  1.3  Densities,  intervals  7,  was on probable  a r e shown  i n Table  6.13.  T a b l e 6.13. Intervals  Density  f o r Salix  estimates, and  probable  limit  S A L I X  Site  n  Density (stems/m )  PLE  2  1  200  12.4232  B E T U L A  + 95% CI* (% of mean)  .4513 (  4  6  200  12.4977  +  -  195  6.4230  . 4363  +  .3741 (  # Confidence  . 8843 7. 1%)  <  7  o-f e r r o r and 95% c o n f i d e n c e  Betula.  +  n  200  . 8831 6.3%)  200  1. 123 17.3%)  193  - 72 -  PLE  2  146  interval  Density (stems/m )  16.3130 42.0908  20.0936  + 95% CI <% of mean)  .4392 (  +  . 8608 3.3%)  (  +  1. 383 3.3%)  . 7038  . 4343  . 8516 4.2%)  ( 13.4207  ±  .6164 (  1 . 208 9. 0%)  6.8  Biomass The  simply  estimate  stem  i s determined  equations,  area  o-f b r o w s e b i o m a s s p e r u n i t  area  d e n s i t y by b i o m a s s p e r stem.  i s obtained  t h e -formula g i v e n  interval  per unit  point estimate  by m u l t i p l y i n g  o-f t h i s using  production  by c o m b i n i n g  this  i n t h e normal f a s h i o n .  the confidence  The t h r e e f o r m s o f  and p o o l e d - s i t e , r e s u l t  estimates  o f t h e mean and v a r i a n c e , and t h e r e f o r e l e a d  estimates  of biomass per u n i t  area.  equations  a r e shown i n T a b l e s  6.14 and 6.15.  "Sample"  refer  to the double  The v a r i a n c e  the r e s p e c t i v e variances  i n S e c t i o n 5.35 -from  common, s i t e - s p e c i f i c  Estimates  sampled  i s made  using  in different  to different  the d i f f e r e n t  The c o l u m n s  biomass data  headed  combined  with  dens i t y . One with  i s roughly  ranges  from  interval is  interval  confidence  stem  of combining  t h e v a r i a n c e s of t h e d e n s i t y  t h e b i o m a s s p e r stem e s t i m a t e  confidence the  result  interval between  t o t h e mean.  f o r the r e g r e s s i o n estimate + 25-50%S  reduced  biomass e s t i m a t e s .  the  d e n o m i n a t o r o f Goodman's e q u a t i o n .  square  Note  that  sizes  and  per  metre f o r the d i f f e r e n t  site  minimal  6 there  of biomass per i t mostly  the confidence  + 3-5% o f t h e mean.  used  n(density)  of t h e 95% c o n f i d e n c e  T a b l e s .6.14 and 6.15, i n d i c a t e s Salix  estimate  f o r both  and n ( b i o m a s s ) a r e i n  limits  of estimated  regression equations,  t h a t f o r a l l Betula  on s i t e s  1 and 7.  - 73 -  This  the density  biomass  shown i n  s i t e s and  i s no o v e r l a p p i n g a t a l l on t h e same s i t e ,  o v e r l a p f o r Salix  of the  o f t h e mean,  f o r the density estimates  to approximately  due t o t h e l a r g e s a m p l e  Comparison  i n the s i z e  As a p e r c e n t  +. 4-10%, and f o r t h e c o m b i n e d  has been  largely  relative  i s a reduction  estimate  and  Table  Site  6.14.  broNii blomiii  Smltx  Common BI omasa <g/m > 2  Equation 93% C . L . j t ( H of fl  6.933  7.213  < ± 6.687  6.710 ( 1 3.374  3.674  (  # Confidence  Table  Site  6.13  +  -  7.477  and  93% c o n f i d e n c e  Site-specific  6.631  -  7.064  3.773  VI  3.406  3.231 (  2.870  ±  2.774  2.7%)  ( ±  -  6.916  6. 173  3.974 ( ±  3.381  3. 929  3.732  3.2%) -  metre.  z  < + 4.0X1  2.6%) -  -  square  C ±  2.966  2.916  2.819  3.3%)  < ±  -  6.376  Sample Biomass  93%  <g/m >  I i  6.46  3.14  2  3.3X) -  6.106  3.013  -  ?l  7.77  ( ± 20%) 5.62  4.31  -  6.94  ( ± 24%)  3.0%) -  C.L.^  » of  2.77  3.79  -  4.81  < • 27%)  3.3%)  Llmlti  browse  Batula  Common Biomass  blomaaa  Equation 93% C . L . *  and  93% c o n f i d e n c e  Site-specific  10.743  10.383 ( ±  41.340  40.243 ( i  11.493  11.197 ( ±  10.033  9.846 (  Limits  -  11.107  -  42.837  31.431  11.798  7.317  -  10.264  + 2.1%>  30.137  7.173 < 1  6.685  6.486 (  -  ?)  6.643  in  grams  -  32.724  7.861  -  6.884  metre.  A  9 . 134  8.773 (  36.943  *  33.634 ( ±  10.020  4.6%)  + 3.0%l  square  2  2.3%) -  per  Pooled-site Equation Biomass 93% C . L . (g/ro ) ( • % of Yl  + 3.3%)  ( ±  2.6%)  C.L.^  < + % of  (  3.1%) -  93%  3.949  3.3%)  limits  Equation  Biomass 2  Confidence  6.387  per  Pooled-alte Equation Biomass 93% C . L . <g/m ) I i X o f VI  C.L.^  I • « of  3.6%)  (g/m )  *  93%  2  i n grama  Equation  Biomass <g/m >  limits  8.827  -  9.494  Samp 1e Biomass (g/m ) z  7 . 18  3.9%) -  38.236  43.33  3.3%)  8.621  9.39  9.033  2.3%)  -  8.71  + 21%)  31.93 (  6 . 83  -  3.63 (  9.724 10.316 ( ± 3.0%)  ( ±  93% C . L . < ± % o f Y)  -  54.  + 26%)  4.96  -  8.71  ( ± 27%) 6.33  -  12.  < ± 30%)  This equation for -  to use?  significant  Yj  or  leads  to  the  One  obvious  answer  difference  accurate  the  equation.  cases  equation.  is  on  only  based  the  In most  data  favour  the s i t e - s p e c i f i c  between  t e r m s of  the  three  consistently  masked  when t h e  Therefore, the best  able  rather  would or  be  closer  d  observation of  the  the  i s to zero,  the  comparisons are  are  more the  equation  e x a c t l y the  possibly  Yj  (d =  is for  site-specific  which  test  differences  the s m a l l e s t t v a l u e  that s i t e ,  t h e r e was  equations,  t h e most p r e c i s e .  not  and  a great  t h e r e was  biased  same  in  difference no  one  type  Differences in precision  biomass e s t i m a t e s  accuracy  a practical  having  should  one  p o i n t of  general  to develop  once a s a t i s f a c t o r y  used  on  sites  be  a necessity.  study  sites  the  accuracy  Another equations,  as  were c o l l e c t e d  general  on  of  be  are  t h e main  that  are  combined.  concern  in  selecting  be  a  i t i s much more d e s i r a b l e t o t h a t can  be  equations  equation  has  required.  large scale,  to the  were d e v e l o p e d  -  75  -  developed, if this  equations  was  case,  and  equations for  dozens in  poor. pooled-site  i s that biomass  selectively,  no  method  Unfortunately  site-specific  s y s t e m a t i c a l l y r a t h e r than  site.  general-type  equations  in t h i s  been  Indeed,  site-specific  general  widely applied,  f o r every  a p r o h i b i t v e task.  the  disadvantage  they  specific  Developing would  view,  equation  should  operationally  h u n d r e d s of  this  average  paired t  equation.  than  t o be  of  and  best  equations.  d e n s i t y and  biomass sampling is  types  to develop  Ideally,  the  precision,  equation  From be  t test,  from  in the  In  the  However, b e c a u s e  d a t a used of  i s that The  i s the  to r e t u r n to the  between p r e d i c t i o n  i s c l o s e to zero.  site-specific  was  c o u l d be  ), where t h e e x p e c t a t i o n  residuals  q u e s t i o n : which  with  the  data  result and  that  most  o-f t h e s t e m s c o l l e c t e d  more e - f - f i c i e n t  the sampling  over  representation  1 i ne  better. alternative  better  establish  they  size  i n each  would are  -fill  less  Biomass per o-f  regression  on  d a t a -from  variance random  o-f t h i s  -formula.  The  t h e mean) and  three  regression  e q u a t i o n s would sampling,  square  with  m e t r e was  with  of  the  the  spread  scale.  which be  to  c o u l d be  o-f t h e  because  size  stems,  without  s t e m was  interval  the  based  normal  -for s i m p l e  method  was  and  with  6.15  Goodman's  under  many t i m e s  equations.  of  t h e same amount  the  three  the  wider  the e s t i m a t e s from  superior  only  The  r e g r e s s i o n s ( a v e r a g i n g about  one  use  -for b i o m a s s .  i n most c a s e s e n c o m p a s s e d  t h e r e f o r e be  sampled  the s m a l l e r  larger  estimated  i n the  any  would  collected.  T a b l e s 6.14  Using  This  number o-f  variance calculated  confidence any  by  collected  a r e shown on  i s to  would  individuals  t h e mean p r o d u c t i o n p e r  the combined  The  o-f s t e m s ,  also  calculated  better  good  the s i t e s ,  more o-f t h e be  A  de-fine t h e s l o p e o-f t h e  requirements  and  stems a c t u a l l y  and  to get  on  passed  common, w o u l d  results  than  be  equation  determine  Then  the  quickly,  mean was  "Sample".  t h i s method of  those  and  class.  to - f i l l  equations;  sampling,  heading  classes  small.  e n d s o-f t h e s i z e  o-f s a m p l i n g  Many s m a l l s t e m s would  they  and  t h e v a r i a n c e , and  o-f s i z e  desired  classes  because  at both  method  were e n c o u n t e r e d  classes.  range  r e p r e s e n t a t i o n o-f a l l s i z e s  a number  individuals as  reduce  a regression  size  o-f i n d i v i d u a l s  i n c r e a s e SSX,  ensure  to develop  the e n t i r e  will  An  way  were - f a i r l y  with  +, 25% the  regression  t o random o r s y s t e m a t i c  of e f f o r t ,  because  of  the gain in  prec i sion. An  approximate  breakdown  of - 76  the e f f o r t -  spent  in  collecting  data  and p r e p a r i n g  samples i s :  Common r e g r e s s i o n d a t a : c o l l e c t i n g independent v a r i a b l e and b i o m a s s d a t a ( i n c l u d i n g sample p r e p a r a t i o n ) Site  d a t a : c o l l e c t i n g b i o m a s s -from -four ( i n c l u d i n g sample p r e p a r a t i o n )  Site  the  -field  work b e c a u s e  t w i g growth twigs, this •for  biomass  must be removed  consumed  -from e a c h  bagged,  30 man-days,  t h e common r e g r e s s i o n variables  i s by -far t h e most  o-f t h e s a m p l e p r e p a r a t i o n .  and t h e m a t e r i a l  independent  data  dried  equally (this  on t h i s  stem,  included  material)  15  man-days  12 man-days  t i m e c o n s u m i n g o-f Current  l e a v e s removed  and w e i g h e d .  divided  man-days  sites  d a t a : c o l l e c t i n g d e n s i t y and i n d e p e n d e n t v a r i a b l e d a t a -from -four s i t e s  Collecting  15  between  annual -from t h e  In t h i s  study  the material  used  t i m e -for m e a s u r i n g t h e and t h e m a t e r i a l  collected  -from t h e s i t e s . I-f o n l y and  no s i t e b i o m a s s  would  have been  biomass •for e a c h to  t h e common  d a t a co 1 1 e c t e d ,  36% l e s s .  a t e v e r y -fourth site  collect  regression  With  the total  the sampling  p o i n t ) t h e biomass  was a p p r o x i m a t e l y  density  e q u a t i o n s had been deve1 oped -field regime  variable  used  requirement (collecting  sample p r e p a r a t i o n  1.25 t i m e s g r e a t e r  and i n d e p e n d e n t  time  data.  than  time  the time  used  7.  7.1  SYNOPSIS AND  ANALYSIS  Synopsis Much o-f t h e  shrub d e n s i t y  was  most a p p r o p r i a t e estimation method,  of  method  in Chapter  from  independent  Salix  f o r the  p u r p o s e of  independent  v a r i a b l e and  representing  different  density  wetland  variables  biomass p r o d u c t i o n d i m e n s i o n s and  per  stem  purpose  of  common  equations.  from  four  by  significantly  measured  of  Salix species  linear of  improved  by  equations.  Also,  four  sites  A portion  of  equations and  using  independent browse  characteristics (i.e.  present  on  equation.  73  woody  r e l a t i o n s h i p s between  e q u a t i o n s and  -  annual  Betula.  collected specifically  developing  condition)  biomass.  dependent  the  the  browse  current  regression  shrub  a single regression  for  were c o l l e c t e d on  f o r browse  data  distance  were  shrub a s s o c i a t i o n s .  and  deriving regression  The  and  weight  describe  the  regression  point  glandulosa  b r o w s e c o n d i t i o n ) , f o r S a l i x and  e q u a t i o n s were d e v e l o p e d  described  to  was  that  and  technique.  data  transformations  were d e v e l o p e d  determined  d i m e n s i o n s and  dry  shrub biomass  inventory  deriving regression  squares m u l t i p l e  logarithmic  I t was  corrected  area  stem  (oven  t h e s e s t e m s were a l s o s a m p l e d  natural  the  Betula  study  (several  variable  Least  with  and  the  dependent  growth),  2.  estimation  spp.  thoughout  variables  concerning  o-f b r o w s e b i o m a s s  a p l o t l e s s density  collected  the  reviewed  biomass combined  Stems o f  and  available literature  are  the  for  the  r e f e r r e d to as  study  area  could  P r e d i c t i o n s would  separate -  These  equations.  the  be not  However,  be  •for b o t h  Salix  and B e t u l a , s i g n i f i c a n t l y  specific  sites  were o b t a i n e d  or  by p o o l i n g a l l s i t e  set.  On a l l t h r e e s i t e s  significant common For  differences  equation  Betula,  pooled-site  equation  confidence  intervals  -36%)  those  the  one s i t e ,  sampling  transect  measured  were t h e r e  f o r t h e common  of  point, data There  significant while  the  In g e n e r a l ,  differences t h e 95%  were n a r r o w e r  ( + 30  ( + 21 - 56%) and p o o l e d - s i t e equations  equation  yielded  estimates  less  had a 9 5 %  + 30 - 36%.  i n an a t t e m p t by u s i n g  to determine  the f i r s t  were c o l l e c t e d  from  were no s i g n i f i c a n t  biomass of these  stems,  stem  i f b i a s was e n t e r i n g encountered  the f i r s t differences  n o r were t h e r e  t h e common  equations.  The s i t e - s p e c i f i c  d i d , however,  differences  i n p r e d i c t i o n s between  stems  in the actual  significant  i n p r e d i c t e d biomass u s i n g equation  a t each  and s e c o n d  differences  significiant  sample.  Using  in significant  equations  b u t t h e common  The common  data  were  a double  biomass,  and none f o r S a l i x .  procedure  encountered.  biomass from  f o r the s i t e - s p e c i f i c  interval  there  this  mean b i o m a s s p r e d i c t e d by t h e  f o r Betula resulted  predictions.  On  ocurred,  equations,  from  on two o f f o u r s i t e s .  i n no c a s e  < + 27 - 4 3 % ) ,  confidence  measured  site-specific  equations  p r e d i c t e d and a c t u a l  two o f f o u r s i t e s ,  accurate  i n the S a l i x  equations,  between  equations  and d e r i v i n g  was t h e c a s e  differences  than  by d e v e l o p i n g  where S a l i x  and a c t u a l  this  site-specific  on  data  b e t t e r p r e d i c t i o n s -far  and p o o l e d - s i t e  first  yield and  second  stems. The sites of  corrected point  f o r stem  d i s t a n c e method  density estimates.  the confidence  of the e s t i m a t e  was e m p l o y e d  The method with  - 79 -  g i v e s an  the "probable  on t h e f o u r approximation  limit  of e r r o r "  (PLE). site  On a l l s i t e s  w h i c h was v i r t u a l l y  •four s i t e s . o-f  Betula  Salix  (one was  was e s t i m a t e d  density  using  estimates  the three  the  .  -factor e  backtrans-formed mean b i o m a s s corrected  -forms  was  (common,  i n grams p e r s q u a r e by t h e  p e r stem  estimate  density  was t a k e n  estimates  i n 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 by was t h e mean o-f t h e of the  and  of the p r e d i c t i o n s . of t h e f i n a l  estimate  of browse  by c o m b i n i n g t h e v a r i a n c e s  and t h e d e n s i t y  estimate.  biomass per o f t h e p e r stem  The v a r i a n c e  o f t h e stem  t o be P L E .  browse  38  production  was more p r o d u c t i v e ,  one s i t e  variances  was t h e mean o f t h e b a c k t r a n s f o r m e d  was o b t a i n e d  biomass  Salix  inherent  accompanying  and c o r r e c t e d p r e d i c t i o n s , and t h e v a r i a n c e  variances  square metre  and t h e i r  The mean b i o m a s s p e r stem  The v a r i a n c e  7.2  equation  Browse b i o m a s s  o-f b i o m a s s  -for t h e b i a s  and  interval  p e r stem  by m u l t i p l y i n g t h e p e r stem e s t i m a t e  were c o r r e c t e d  for  and t h e  estimate. All  Betula  Salix,  had a 9 5 % c o n f i d e n c e  biomass p r o d u c t i o n  s i t e - s p e c i-f i c and p o o l e d - s i t e ) . metre  than  + 13%).  and B e t u l a b r o w s e  on e a c h s i t e  density  a l l B e t u l a was a l s o t h e most d e n s e o-f t h e  S i x o-f t h e s e v e n e s t i m a t e s  + 10% o r l e s s  estimated  had a g r e a t e r  where e s t i m a t e s  had 9 5 % c o n f i d e n c e  was on t h e o r d e r  on t h e o r d e r  of 3 t o 8  o f 5 t o 12 g/m  were f r o m 30 t o 50 g / r a . a  intervals  of  z  g/m . 3  except  These  + 2.3 - 5.5% ( T a b l e s  6.14  6.15).  Critical  analysis.  The p r e c i s i a n improved  of t h e r e g r e s s i o n e q u a t i o n s  ( i . e . narrower c o n f i d e n c e  limits)  - 80 -  could  by s a m p l i n g  have  been  greater  numbers o-f l a r g e s t e m s . r a n g e o-f s i z e s  Despite  present,  the attempt  sampling  abundant  smaller  stems.  improved  by d e - f i n i n g s i z e  sampling  to s a t i s f y  to represent  was c o n c e n t r a t e d  Sampling  evenly the  on t h e more  -for t h e r e g r e s s i o n c o u l d  c l a s s e s -for t h e i n d e p e n d e n t  t h e number o f o b s e r v a t i o n s  have  been  v a r i a b l e s and  d e s i r e d f a r each  c1 a s s . The  sample  sizes  (Salix  n=160, B e t u l a  Betula  n=164), b u t c o u l d  equations  were a d e q u a t e f o r t h e common  n=112) and p o o l e d - s i t e e q u a t i o n s have been  ( t h e s m a l l e s t sample s i z e  straightforward  systematic  sampling  could  satisfy  effort size  class  as d i s c u s s e d  of  on t h e a c c u r a c y  t h e common  equations  was b e s t .  regression that  equation  with  was p o o r e s t  This  supports  doubt  equations,  so as t o  a b o v e and i n S e c t i o n 6.8.  was d o u b l e  sampled  f o r biomass as  In g e n e r a l ,  the accuracy  and t h a t o f t h e s i t e - s p e c i f i c the r e s u l t s  of the t e s t s  dummy v a r i a b l e s r e p r e s e n t i n g s i t e s ,  on t h e v a l u e  than  by s a m p l i n g  of the r e g r e s s i o n s .  b e t t e r p r e d i c t i o n s would  casts  data  Rather  n=130,  specific  f o r the s i t e - s p e c i f i c  have been o p t i m i z e d  criteria,  (Salix  f o r the s i t e  was 3 5 ) .  sampling  A p o r t i o n of t h e s i t e a check  greater  regressions  result  o f a common  from  specific  which  using  indicated  e q u a t i o n s , and  regression equation  and  its  resulting predictions. No c h e c k was a v a i l a b l e estimate.  According  d i s t a n c e method  1980)  and n a t u r a l p o p u l a t i o n s is efficient  seems t o be t h e most population  (most  of the d e n s i t y  t o i n v e s t i g a t o r s who have u s e d  point  method  on t h e a c c u r a c y  on a r t i f i c i a l  and y i e l d s  (Batcheler  (Laycock  shrub  estimates.  to use with  p o p u l a t i o n s ) , a s most - 81 -  1973, 1975; Boyd  and B a t c h e l e r  acceptable  a p p r o p r i a t e method  the c o r r e c t e d  other  1.979,  1975), t h e It certainly a very  plotless  clumped methods  do  not  account  for a  tedious  and  to  variability  high  The perfected. density will  would  require a between  problem  estimate".  density  from  as  coefficient well.  program with  of  estimate  varying search  sampling,  there  accurate  better  the  ratio  which  the  in t h i s and  no  way  has  and  found  "best  The  "best  t h e most  i n some c a s e s  the  lowest  PLE/density  ratio.  such  knowing  density  the e s t i m a t e as  was  to  accurate  most The  calculations  with  independent  i f this  is  analagous  that  selects  PLE's,  i s t h a t which  t o be  iterates  been  different  1979).  (1975)  not  i s the  of P L E / d e n s i t y ,  he  study  check,  of  certainly  (Boyd  Batcheler  density estimates  f o r 6 out  corrected  For The  of  multiplying  this  (one  the  minimum  quadrat  in fact  the  + 3  - 5%.  The  and  density estimates  high  relatively  estimate  d e n s i t y sample s i z e s  estimates  had  level  l a r g e sample  of  biomass per  regression estimate  estimate,  accepted  is relatively  allowing a  study  be  a 95%  7 estimates  field,  final  can  satisfactory:  p o i n t d i s t a n c e method  in the  quickly.  density  i s no  were v e r y  conduct  With  due  the  most  estimate. If  results  ratio.  have  limits  i s very  large plots  what a c t u a l l y  limit  (1979) f o u n d  s u p p l i e d f o r use  PLE/density  search  a minimum  d i d not  sampling  and/or  density estimates,  variation),  However Boyd  accurate  i s determining  d e f i n e d by  most p r e c i s e ( i . e . has the  d i s t a n c e method  Different  as  Plot  plots.  v a r y i n g the  estimate"  distribution.  l a r g e sample s i z e  corrected point One  result  non-random  levels  of  of  size  and  were f r o m  of  the  stem  r e d u c t i o n of  to  obtained 150  to  200.  obtained by  the  confidence  both  or  The  fast  metre,  95%  +, 10%  18%).  t o be  biomass per  c o n t r i b u t e d to the -  +  simple  square  sizes  valid,  confidence  was  precision:  l a r g e sample  - 82  of  as  by  stem levels  the r e g r e s s i o n the  confidence  intervals  of  the  final  Regression useful is  method  quick  than  and  e s t i m a t i o n of  because,  from  f o r the  as  once e q u a t i o n s  many o t h e r  methods.  were n e e d e d , stem.  on  average,  Therefore,  h o u r s would single  be  square  f o r an  metre p l o t  limits  estimates shown  which  6.14  However,  of  the  6.3) time  the p r e s e n t  certainly the  study,  was  the  traditional  reduces  the  than clip  approximately  2  stem and  the  d e n s i t y of  prepare clip  and  28  the  the  6.15  and  weigh  required for developing  56  than  than  random  or  confidence those  of  sites.  in S e c t i o n  equations  the  This is  6.8.  (discussed in  regression estimation  equations  a  method.  s a m p l e s on  is discussed  a d v a n t a g e of  each  a browse sample from  much n a r r o w e r  for site-specific  from 2  regression estimate  systematic  and  hours  steras/ra ,  from  need  faster  average  in a l l cases  and  study,  growth  using  very  sampling  t o remove a l l c u r r e n t t w i g  shown by  are  derived only  in Tables  Section  as  6.3  developed,  p r o v i d e s a more p r e c i s e e s t i m a t e  sampling,  limits  In  through  this  r e q u i r e d to c l i p  Regression systematic  For  in Section  is a potentially  have been  regression variables  f o r example.  out  t h e p r e d i c t i o n s a r e more p r e c i s e  m e a s u r i n g browse biomass d i r e c t l y weigh method,  pointed  p l a n t biomass  n o n - d e s t r u c t i v e and  estimates  sampling  estimates,  (primarily  because  sample  p r e p a r a t i on) . When r e g r e s s i o n i s c o m b i n e d the  v a r i a n c e of  the  individual  defined,  the  resulting  variances.  statistically  combined  dependent  variable  a separate  estimate  acceptable  i s used.  way  to c a l c u l a t e  when a The - 83  density  estimate,  i s a combination  However t h e r e d o e s not  t h e mean r e g r e s s i o n p r e d i c t i o n the  with  appear  t o be  of  a well  t h e v a r i a n c e of  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 variances calculated -  in  this  study as  by t h e method  approximations.  PLE  should  3  combined  t h e v a r i a n c e o-f t h e d e n s i t y  develop  o-f t h i s  Even  measured  study  s o , t h e method  a t each  particular  association  a r e a would  devalue  making  t h e e-f-ficiency  such  o-f t h e  dimensions  must  be  generating  o-f a  of t o t a l  production  of shrub  that shrub  p l a n t s , as t h i s  outlined  estimated  in a three dimensional  for predicting  o-f t h e a r e a  a s s o c i a t i o n s on  necessary.  of v a r i a b i l i t y ,  and w e i g h e d ,  n a t u r e o-f  An i n a c c u r a t e e s t i m a t e  two s o u r c e s  by Zamora  in  vegetation often occurs in  (1985) s u g g e s t e d  on i n d i v i d u a l  as t h e wetland  patchy  and p r e c i s e b r o w s e  procedure  are c l i p p e d  o n l y be p r a c t i c a l  i-f many s h r u b  t y p i n g and d e l i n e a t i o n  and Schwab  the sources  variable  negate  the detemination  difficult.  p h o t o g r a p h s would  thus  would  a s t h e work r e q u i r e d t o  a large area  In w e t l a n d s ,  an a c c u r a t e  so c a r e f u l  be m e a s u r e d  limit  would  i s tedious  biomass over  narrow bands o r s t r i p s ,  estimate,  t h a t c a n be o b t a i n e d .  point.  distribution.  Pitt  estimate  Thus t h e  I t would  are applicable, site  regarded  estimate i s  c o u l d p o s e p r o b l e m s due t o t h e v e r y  vegetation  not  area  be  on an o p e r a t i o n a l l e v e l  o-f t h e t e c h n i q u e s .  -for e a c h  Determining  estimate,  method  biomass equations  an e q u a t i o n  method.  aerial  an a p p r o x i m a t i o n .  but un-fortunate 1 y i t i s t h e b e s t  much r e - f i n i n g  i-f g e n e r a l  this  Similarly  v a r i a n c e o-f t h e b i o m a s s p e r u n i t  Application  be  i n S e c t i o n 5.1.2 c a n o n l y  o n l y be c o n s i d e r e d  questionable,  require  described  so t h a t biomass.  recommended  i n which  plot.  Then  the estimate  In o r d e r t o  a double  sampling  canopy volume i s a p o r t i o n of the p l o t s becomes an  A disadvantage - 84 -  should  necessitates a density  of v a r i a b i l i t y .  they  (1981)  biomass  independent  o f t h e method i s  that  separate  variability  in observer,  Pitt estimation should "be  r e g r e s s i o n s would  and  Schwab  i s used,  provide  developed  biomass data  any  shrub  with  independent  variables,  and  either  will  from  a l s o be  plants'  growth  equations. given  area  task  of  form  no  should  not  be  exist  biomass  estimates  or  be  canopy  shrub  universally  will  probably  t o one  volume  need  seriously before  f o r shrub evaluated,  undertaking  involving  dimensions  -  85  -  as  least  be  necessary).  use) of  level  could  new  It (such  alter  the  in  any  a s t r o n g commitment requisite  as  regression  biomass e s t i m a t i o n  the  and  applicable (i.e. site  heavy  and  should  program".  in u t i l i z a t i o n of  and  However, m o d e l s  n e c e s s i t a t e development the  with  inventory  t h a t a change  browsing  and  shrub  i f regression  i n v o l v e much t e d i o u s work, a t  equations  Therefore, should  the  re-flect  b i o m a s s e s t i m a t i o n method  will  considered  a situation  that,  relationships.  visual  likely  species specific  should  the  and  during  to  season.  site/season/species specific  regression,  initially,  neeeded  volume c o r r e l a t e s w e l l  predictive  collected  Clearly,  and  be  (1983) a l s o s u g g e s t e d  shrub  good from  site  likely  field  work.  to  LITERATURE  Ahmed, J . , C D . techniques sampling.  CITED  Bon ham and W.A. Laycock. 1983. C o m p a r i s o n o-f u s e d -for a d j u s t i n g b i o m a s s e s t i m a t e s by d o u b l e J . Range Manage. 3 6 ( 2 ) : 2 1 7 - 2 2 1 .  A n d e r s o n , D.M. and M.M. Kothmann. 1982. A t w o - s t e p t e c h n i q u e -for e s t i m a t i n g s t a n d i n g c r o p o-f h e r b a c e o u s v e g e t a t i o n . J . Range Manage. 3 3 ( 5 ) : 6 7 3 - 6 7 7 . A l d o u s , S.E. 1944. 23:130-136. A l d o u s , S.E. region.  A deer  browse s u r v e y  method.  1932. Deer b r o w s e c l i p p i n g s t u d y J . W i l d l . Manage. 1 0 ( 4 ) : 4 0 1 - 4 0 9 .  J.  i n the  Mammalogy.  lake  states  Annas, R.M. and R. Coupe. 1979. B i o g e o c 1 i m a t i c z o n e s and s u b z o n e s o-f t h e C a r i b o o F o r e s t R e g i o n . B.C. M i n . o-f F o r . , V i c t o r i a , B.C. B a r t o l o m e , J.W. and B.H. K o s c o . 1982. by d e e r b r u s h (Ceanathus integerrimus). 33(5):671-672.  E s t i m a t i n g browse p r o d u c t i o n J . Range Manage.  B a s i l e , J.V. and S.S. H u t c h i n g s . 1966. Twig d i a m e t e r - l e n g t h - w e i g h t r e l a t i o n s of b i t t e r b r u s h . J . Range Manage. 19(l):34-38. B a s k e r v i l l e , G.L. 1972. e s t i m a t i o n of p l a n t Batcheler, point  CL. 1971. and n e a r e s t  Use o f l o g a r i t h m i c r e g r e s s i o n i n t h e biomass. Can. J . F o r . R e s . 2:49-53.  E s t i m a t i o n of d e n s i t y from a sample of j o i n t neighbor d i s t a n c e s . Ecology 52(4):703-709.  Batcheler, C L . 1973. E s t i m a t i n g d e n s i t y and d i s p e r s i o n f r o m t r u n c a t e d or u n r e s t r i c t e d j o i n t p o i n t - d i s t a n c e nearest neighbour distances. P r o c . New Z e a l a n d E c o l . S o c . 20:131-147. Batcheler, C L . 1975. P r o b a b l e l i m i t o f e r r o r o f t h e p o i n t d i s t a n c e - n e i g h b o u r d i s t a n c e e s t i m a t e of d e n s i t y . Proc. Z e a l a n d E c o l . S o c . 22:28-33.  New  B a t c h e l e r , C L . and D.J. B e l l . 1970. Experiments in e s t i m a t i n g d e n s i t y f r o m j o i n t p o i n t and n e a r e s t - n e i g h b o u r d i s t a n c e s a m p l e s . P r o c . New Z e a l a n d E c o l o g i c a l S o c . 17:111-117. Beauchamp, J . J . and J . S . O l s o n . regression estimates after 54(6):1403-1407.  1973. Corrections f o r bias in logarithmic transformation. Ecology  B e e t s , M.L. 1984. P e r s o n a l communication. Wildlife Biologist. B.C. M i n . o f E n v i r . , F i s h and W i l d l . B r a n c h . W i l l i a m s Lake, B.C. Blair,  R.M.  1959.  Weight  techniques -  86  f o r sampling  browse p r o d u c t i o n  on d e e r r a n g e s . Pp 26-31 in: U.S. F o r e s t S e r v i c e . Symposium on T e c h n i q u e s and Methods o-f M e a s u r i n g U n d e r s t o r y V e g e t a t i o n . T i - f t o n , GA. S o u t h e r n F o r . E x p t . S t n . and S o u t h e a s t e r n F o r . E x p t . S t n . , USDA F o r e s t S e r v i c e . 174 p p . B l a i r , R.M. 1971. F o r a g e p r o d u c t i o n a f t e r hardwood c o n t r o l southern pine-hardwood s t a n d . F a r . S c i . 17(3):279-284. B l a i r , R.M. and D.P. F e d u c c i a . 1977. M i d s t o r y deer f o r a g e i n l o b l o l l y p i n e p l a n t a t i o n s . 41(4):677-684. Bobek, B. and R. B e r g s t r o m . estimation in a forest  in a  hardwoods i n h i b i t J . W i l d l . Manage).  1978. A r a p i d method o f b r o w s e b i o m a s s habitat. J . Range Manage. 3 1 ( 6 ) : 4 5 6 - 4 5 8 .  Bobek, B. and R. D z i e c i o 1 o w s k i . 1972. Method o f b r o w s e e s t i m a t i o n in d i f f e r e n t types of f o r e s t s . Acta Theriologica 17(14):171-186. Boyd,  M. 1979. A c o n s i d e r a t i o n o f t h e c o r r e c t e d p o i n t d i s t a n c e method o f v e g e t a t i o n s a m p l i n g . A l b e r t a R e c . and P a r k s , R e s . and S y s t e m s B r . 17 pp.  Boyd,  M. 1980. A c o m p a r i s o n o f f i v e m e t h o d s o f s h r u b s a m p l i n g u s i n g a r t i f i c i a l dot p a p u l a t i o n s . A l b e r t a R e c . and P a r k s , R e s . and S y s t e m s B r . 23 pp.  Brown, J.K. 1976. E s t i m a t i n g s h r u b b i o m a s s f r o m diameters. C a n . J . F o r . R e s . 6:153-158.  basal  stem  B r y a n t , F.C. and M.M. Kothmann. 1979. V a r i b i l i t y i n p r e d i c t i n g e d i b l e b r o w s e f r o m crown v o l u m e . J . Range Manage. 32(2):144-146. C a t a n a , A . J . , J r . 1963. population density.  The w a n d e r i n g q u a r t e r method Ecology 44(2):349-360.  of e s t i m a t i n g  Coady, J.W. 1974. I n t e r i o r moose s t u d i e s . P r o j . P r o g . Rep., V o l . 2. A l a s k a , D e p t . o f F i s h and Game, D i v . o f Game. Fed. A i d i n W i l d l . R e s t o r . , P r o j . W-17-6. C o t t a m , G., J . T . C u r t i s and B.W. H a l e . 1953. Some s a m p l i n g c h a r a c t e r i s t i c s of a p o p u l a t i o n of randomly d i s p e r s e d individuals. Ecology 34(4):741-757. C o t t a m , G. and J . T . C u r t i s . 1956. T h e u s e o f d i s t a n c e m e a s u r e s i n p h y t o s o c i o l o g i c a l sampling. Ecology 37(3):451-460. Crow, T.R. 1978. B i o m a s s and p r o d u c t i o n i n t h r e e c o n t i g u o u s in northern Wisconsin. Ecology 59(2):265-273.  forests  Crow, T.R. and P.R. L a i d l y . 1980. A l t e r n a t i v e m o d e l s f a r e s t i m a t i n g woody p l a n t b i o m a s s . Can. J . F o r . R e s . 10:367-370. Cunia,  T.  1973.  Dummy v a r i a b l e s  and some o f t h e i r  - 87 -  uses i n  regression France.  analysis.  IUFRO P r o c .  o-f J u n e  1973  meeting.  Nancy,  D a v i s , J.B., P.T. T u e l l e r and A.D. Bruner. 1972. Estimating forage p r o d u c t i o n f r o m s h r u b r i n g w i d t h s i n Hot C r e e k V a l l e y , N e v a d a . J . Range Manage. 2 3 ( 3 ) : 3 9 8 - 4 0 2 . Dean, S., J.W. B u r k h a r d t and R.O. Meeuwig. 1981. E s t i m a t i n g twig and f o l i a g e p r o d u c t i o n o f s a g e b r u s h , b i t t e r b r u s h and r a b b i t b r u s h in the Great B a s i n . J . Range Manage. 3 4 ( 3 ) : 2 2 4 - 2 2 7 . Dell,  T.R. order  and J . L . C l u t t e r . 1972. Ranked s e t s a m p l i n g t h e o r y s t a t i s t i c s background. B i o m e t r i c s 28:545-555.  with  D r a p e r , N.R. and H. S m i t h . 1966. Applied regression analysis. W i l e y in S o n s , I n c . New Y o r k . 407 pp. F e r g u s o n , R.B. and M.A. Marsden. b i t t e r b r u s h u t i l i z a t i o n from relations. J . Range Manage. F r a n c i s , R.C, of w e i g h t analysis. Fox,  John  1977. Estimating overwinter twig diameter-length-weight 30(3):231-236.  G.M. Van Dyne and B.K. Williams. 1979. An e v a l u a t i o n e s t i m a t i o n d o u b l e s a m p l i n g a s a method o f b o t a n i c a l J . E n v i r o n . Manage. 8:55-72.  D.J. and K.E. G u i r e . S t a t i s t i c a l Research  1976. D o c u m e n t a t i o n f o r MIDAS. L a b o r a t o r y , Univ. of M i c h i g a n . 203  pp.  F u r n i v a l , G.M. 1961. An i n d e x f o r c o m p a r i n g e q u a t i o n s u s e d c o n s t r u c t i n g volume t a b l e s . F o r . S c i . 7<4>:337-341.  in  G r i g a l , D.F. and L . F . Ohmann. 1977. B i o m a s s e s t i m a t i o n f o r some shrubs from n o r t h e a s t e r n Minnesota. N o r t h C e n t . F o r . Exp. Stn., USDA F o r e s t S e r v i c e , Res. N o t e NC-226. 3 pp. Goodman, L.A. Statist.  1960. Assoc.  H a f l e y , W.L. equation  1969. C a l c u l a t i o n and m i s c a l c u l a t i o n o f t h e a l l o m e t r i c reconsidered. B i o s c i e n c e 19(11):974-983.  H a l l s , L.K. and R. pine-hardwood  On t h e e x a c t v a r i a n c e 55(292):708-713.  Alcaniz. 1971. forest. J. For.  of  products.  Forage y i e l d s 69(l):25-26.  i n an  H a r l o w , R.F. 1977. A technique f o r s u r v e y i n g deer southeast. W i l d l . Soc. B u l l . 5(4):185-191.  J.  Am.  east  forage  Texas  in  the  H a r n i s s , R.O. and R.B. Murray. 1976. Reducing b i a s in dry w e i g h t e s t i m a t e s of b i g s a g e b r u s h . J . Range Manage. 29(5):430-432.  leaf  H a r r i n g t o n , G. 1979. E s t i m a t i o n of a b o v e g r o u n d b i o m a s s of s h r u b s i n a Eucalyptus populnea F. M u e l l . w o o d l a n d by r e g r e s s i o n of mass on t r u n k d i a m e t e r and p l a n t h e i g h t . B o t . 27:135-143.  trees  - 38  -  Aust.  and J.  H u t c h i n g s , S.S. and J . E . S c h m a u t z . 1969. A f i e l d t e s t of the r e l a t i v e weight e s t i m a t e method f o r d e t e r m i n i n g h e r b a g e production. J . Range Manage. 2 2 ( 6 ) : 4 0 8 - 4 1 1 . Jensen, C H . and Q.W. Scotter. 1977. A comparison of twig^-length and b r o w s e d - t w i g methods o f d e t e r m i n i n g b r o w s e u t i l i z a t i o n . J. Range Manage. 30<l):64-67. Jensen, C H . and P . J . U r n e s s . 1981. E s t a b l i s h i n g browse u t i l i z a t i o n from twig d i a m e t e r s . J . Range Manage. 3 4 ( 2 ) : 1 1 3 - 1 1 6 . K r e f t i n g , L.W., M.H. S t e n l u n d and R.K. S e e m u l . 1966. E f f e c t of s i m u l a t e d and n a t u r a l d e e r b r o w s i n g on m o u n t a i n m a p l e . J. W i l d l . Manage. 3 0 ( 3 1 : 4 8 1 - 4 8 8 . K r e f t i n g , L.W. and R.L. P h i l l i p s . 1970. Improving deer h a b i t a t u p p e r M i c h i g a n by c u t t i n g m i x e d - c o n i f e r swamps. J. For. 68:701-704.  in  L a y c o c k , W.A. and C L . B a t c h e l e r . 1975. Comparison of distance-measurement techniques f o r sampling tussock grassland s p e c i e s i n New Z e a l a n d . J . Range Manage. 2 8 ( 3 ) : 2 3 5 - 2 3 9 . Lyon,  L.J. 1968. An s h r u b community.  Lyon,  L.J. 1970. serviceberry  e v a l u a t i o n of d e n s i t y s a m p l i n g methods J . Range Manage. 2 1 ( 1 ) : 1 6 - 2 0 .  L e n g t h - and w e i g h t - d i a m e t e r r e l a t i o n s twigs. J . W i l d l . Manage. 34:456-460.  Madgwick, H.A.I. 1976. Mensuration of f o r e s t biomass. Biomass S t u d i e s . U n i v . of Maine P r e s s , Orono. Pp.  in a  of  In: O s l o 13-27.  M c l n t y r e , O.A. 1932. A method f o r u n b i a s e d s e l e c t i v e s a m p l i n g , u s i n g ranked s e t s . A u s t . J . A g r i c . Res. 3:385-390. McLean, A.M. (ed.) 1979. Range management Columbia. W a y s i d e P r e s s , V e r n o n , B.C.  handbook f o r 104 pp.  British  M o r i s i t a , M. 1957. A new method f o r t h e e s t i m a t i o n o f d e n s i t y by t h e s p a c i n g method a p p l i c a b l e t o n o n - r a n d o m l y d i s t r i b u t e d p o p u l a t i o n s . ( I n J a p a n e s e w i t h E n g l i s h a b s t r a c t and summary). P h y s i o l , and E c o l . ( K y o t o , J a p a n ) . 7(2):134-145. M o u n t f o r d , M.D. and R.G.H. Bunce. 1973. Regression sampling with a l l o m e t r i c a l l y r e l a t e d v a r i a b l e s , with p a r t i c u l a r r e f e r e n c e to production studies. F o r e s t r y 46(2):203-212. M u e l l e r - D o m b o i s , D. and H. E l l e n b u r g . 1974. Aims and m e t h o d s o f vegetation ecology. John W i l e y and S o n s , T o r o n t o . 547 pp. Munro, D.D. 1974. Use o f l o g a r i t h m i c r e g r e s s i o n i n t h e e s t i m a t i o n of p l a n t b i o m a s s ; d i s c u s s i o n . Can. J . F o r . Res. 4:149. Murray,  R.B.  and  M.Q.  Jacobson.  1982. -  85  An -  evaluation  of  dimension  a n a l y s i s -for p r e d i c t i n g 35(4):451-454.  shrub  biomass.  J . Range Manage.  Ohmann, L . F . , D.F. G r i g a l and R.B. Brander. 1976. Biomass e s t i m a t i o n -for -five s h r u b s -from n o r t h e a s t e r n M i n n e s o t a . North C e n t . F o r . Exp. S t n . , USDA F o r e s t S e r v i c e Res. Pap. NC-133. 11 pp. O l d e m e y e r , J . L . and W.L. Regelin. 1980. f o r e s t i m a t i n g d e n s i t y of s h r u b s and W i l d l . Manage. 4 4 ( 3 ) : 6 6 2 - 6 6 6 .  C o m p a r i s o n o-f n i n e m e t h o d s saplings in Alaska. J.  P a r k e r , Q.R. and L.D. M o r t o n . 1978. The e s t i m a t i o n of and i t s u s e by moose on c l e a r c u t s i n N e w f o u n d l a n d . Manage. 3 1 ( 4 ) : 3 0 0 - 3 0 4 .  winter forage J . Range  P e c h a n e c , J . F . and O.D. Pickford. 1937. A weight e s t i m a t e f o r the d e t e r m i n a t i o n of range or p a s t u r e p r o d u c t i o n . S o c . A g r o n . 29:894-904. Peek, J.M. 1970. R e l a t i o n of c a n o p y of t h r e e woody s p e c i e s . Ecology Peek,  production  J.M., L.W. K r e f t i n g and J.C. T a p p e i n e r I I . 1971. V a r i a t i o n i n twig diameter-weight r e l a t i o n s h i p s in northern Minnesota. J. W i l d l . Manage. 35:501-507.  Pielou, of Pitt,  a r e a and v o l u m e t o 51(6):1098-1101.  method J. Am.  E.C. 1959. The u s e o f p o i n t - t o - p l a n t d i s t a n c e s i n t h e the p a t t e r n of p l a n t p o p u l a t i o n s . J . E c o l . 47:607-613.  M.D. shrub For.,  study  and F.E. Schwab. 1985. Q u a n t i t a i v e d e t e r m i n a t i o n s of biomass p r o d u c t i o n : a problem a n a l y s i s . B.C. M i n . o f Range Manage. B r a n c h . ( I n p r e p a r a t i o n . )  P o n t o , F.W. 1983. R e g e n e r a t e d w i l l o w (Salix spp.) utilization in a C a r i b o o wetland system. BCIT F o r e s t R e s o u r c e s C o u r s e no. 45.328. ( A v a i l a b l e a t B.C. M i n . o f E n v i r . , F i s h and W i l d l . Branch, W i l l i a m s Lake, B.C.) P o t v i n , F. twigs.  1981. C o n s t r u c t i n g d r y w e i g h t - d i a m e t e r J . W i l d l . Manage. 4 5 ( 1 ) : 2 7 6 - 2 7 9 .  P r o v e n z a , F.D. and P . J . U r n e s s . 1981. r e l a t i o n s f o r b l a c k b r u s h (Coleogyne J . Range Manage. 3 4 ( 3 ) : 2 1 5 - 2 1 7 . R i s s e r , P.G. quarter  curves  f o r browsed  Diameter-length-weight ramasissima) branches.  and P. H. Z e d l e r . 1968. An e v a l u a t i o n of method. Ecology 49(5):1006-1009.  the  grassland  R l t t e n h o u s e , L.R. and F.A. S n e v a . 1977. A technique f o r estimating big sagebrush production. J . Range Manage. 3 0 ( l ) : 6 8 - 7 0 . R o b e r t s , A. spruce  1984. Guide to wetland ecosystems of a subzone. B.C. M i n . o f F o r . , C a r i b o o  -  °to  -  the s u b - b o r e a l For. Region.  Runka, G.Q. and T, L e w i s . 1981. P r e l i m i n a r y w e t l a n d managers m a n u a l ; C a r i b o o r e s o u r c e management r e g i o n . B.C. Min o-f E n v i r . APD T e c h . Pap. 5. 112 pp. R u t h e r - f o r d , M.C. 1979. P l a n t b a s e d t e c h n i q u e s -for d e t e r m i n i n g a v a i l a b l e browse and b r o w s e u t i l i z a t i o n : a r e v i e w . B o t Rev. 45(2):203-228. S c h r e u d e r , H.T. and W.T. Swank. 1971. A c o m p a r i s o n o-f s e v e r a l s t a t i s t i c a l m o d e l s i n - f o r e s t b i o m a s s and s u r f a c e a r e a estimation. In: F o r e s t Biomass S t u d i e s . U n i v . o-f M a i n e P r e s s , Orono. pp. 125-136. S c h r e u d e r , H.T. and W.T. Swank. 1973. S t a t i s t i c a l considerations in s a m p l i n g b i o m a s s and s u r f a c e a r e a o v e r t i m e f o r a Pirtus stratus L. f o r e s t . I n : IUFR0 B i o m a s s S t u d i e s . U n i v . of Maine P r e s s , Orono. pp. 131-141. Schwab, F.E. 1985. Moose h a b i t a t s e l e c t i o n i n r e l a t i o n t o f o r e s t c u t t i n g p r a c t i c e s in north c e n t r a l B r i t i s h Columbia. PhD. t h e s i s , U n i v . o f B r i t i s h C o l u m b i a , V a n c o u v e r , B.C. (In preparation.) S h a f e r , E.L. 1963. The t w i g - c o u n t method f o r m e a s u r i n g deer browse. J . W i l d l . Manage. 2 7 ( 3 ) : 4 2 8 - 4 3 7 .  hardwood  S h e p h e r d , W.O. 1962. Herbage s a m p l i n g f o r y i e l d : n a t u r a l p a s t u r e s and r a n g e . Pp 102-105 in'. P a s t u r e and r a n g e r e s e a r c h techniques. C o m s t o c k P u b l . A s s o c . , I t h a c a , NY. 242 pp. S m i t h , A.D. and P . J . U r n e s s . 1962. A n a l y s e s of t h e t w i g l e n g t h method o f d e t e r m i n i n g t h e u t i l i z a t i o n o f b r o w s e . Utah D i v . of F i s h and Game B u l l . 62-9. 34 pp. ( c i t e d by J e n s e n and U r n e s s 1981). Smith, J . 1985. P e r s o n a l communication. Biometrician, Canada, C a n a d i a n W i l d l i f e S e r v i c e , Ladner, B.C. T a p p e i n e r , J.C. content of T e l f e r , E.S. species.  I I and H.H. John. hazel undergrowth.  Environment  1973. B i o m a s s and n u t r i e n t E c o l o g y 54(6):1342-1348.  1969a. Twig w e i g h t - d i a m e t e r r e l a t i o n s h i p s J . W i l d l . Manage. 33:317-321.  T e l f e r , E.S. 1969b. plant species.  Weight-diameter r e l a t i o n s h i p s Can. J . B o t . 47:1851-1855.  T e l f e r , E.S. 1974. hare browsing.  V e r t i c a l d i s t r i b u t i o n o f c e r v i d and J . W i l d l . Manage. 3 8 ( 4 ) : 9 4 4 - 9 4 6 .  f o r browse  f o r 22  woody  snowshoe  T e l f e r , E.S. 1981. Browse i n v e n t o r i e s : t e c h n i q u e s and e v a l u a t i o n . Pp. 67-82 in: M i l l e r , F.L. and A. Gunn ( e d s . ) . Symposium on c e n s u s and i n v e n t o r y m e t h o d s f o r p o p u l a t i o n h a b i t a t s . Proc. N.W. W i l d l . Soc. U n i v . Idaho.  T e l - f e r , E.S. and A. C a i r n s . Manage. 4 2 ( 3 ) : 6 3 9 - 6 4 2 .  1978.  Stem  b r e a k a g e by moose.  J . Range  W a l m s l e y , M., G. U t z i g , T. V o i d , D. Moon and J . v a n B a r n e v e Id 1980. D e s c r i b i n g ecosystems in the f i e l d . B.C. M i n . o f and M i n . o f F o r . RAB T e c h . Pap. 2, Land Manage. Rep. 7. pp.  (eds.). Envir. 224  W h i t t a k e r , R.H. and P.L. M a r k s . 1975. Methods o f a s s e s s i n g terrestrial productivity. Pp. 55-118 in'. L i e t h , H. and R.H. Whittaker (eds.). P r i m a r y p r o d u c t i v i t y of t h e b i o s p h e r e . S p r i n g e r - V e r l a g New Y o r k I n c . W i l l a r d , E.E. and C M . McKell. 1978. Response of s h r u b s t o s i m u l a t e d b r o w s i n g . J . W i l d l . Manage. 4 2 ( 3 ) : 5 1 4 - 5 1 9 . Wilm,  H.G., D.F. C o s t e l l o and G.E. K l i p p l e . 1944. Estimating y i e l d by t h e d o u b l e s a m p l i n g method. J . Am. S o c . A g r o n . 36:194-203.  W o l f f , J.O. 1978. B u r n i n g and b r o w s i n g e f f e c t s on w i l l o w interior Alaska. J . W i l d l . Manage. 4 2 ( 1 ) : 1 3 5 - 1 3 9 . Zamora, in Zar,  forage  growth i n  B.A. 1981. An a p p r o a c h t o p l o t s a m p l i n g f o r c a n o p y shrub communities. J . Range Manage. 4 3 ( 2 ) : 1 5 5 - 1 5 6 .  volume  J.H. 1968. C a l c u l a t i o n and m i s c a l c u l a t i o n o f t h e a l l o m e t r i c e q u a t i o n a s a model i n b i o l o g i c a l d a t a . Bioscience 18(12):1118-1120.  - <?2 -  APPENDIX A: SCATTER PLOTS OF SALIX  AND  - 93 -  BETULA  DATA  BIOMASS 7.0700  S.28SS  +  5.S011  +  4.71S7  +  3.1478  *  2.3633  +  .79444  +  •2 *2 2  • ••  .  2  .  "  .3.  * • "2 3'"2'222 • * "'2346 3" • 2' ' 2'445"332 • 2 • .10000 -1* •• 3-4000  5.5889  7.7778  3  . 3  9.9667  Figure A . l . Scatter plot on stem d i a m e t e r (mm).  12.156  o-f Salix  14.344  16.533  browse  - 9* -  18.722  biomass  20.911  (g)  DI AM 23.100  BIOMASS 7.0700  5.5011  •  4.7167  *  3.9322  *  2.3633  *  1.5789  *  .79444  *  •2 • 2" • "  •2 2 * * * • 23222 232 • "3222 236*" 2 2 •238254" « 2 " .10000 -1* •"• 2 7 0 0 0  '„„,,, 44.222  S 1  '  4 4 4  78.667  F i g u r e A.2. Scatter plot on stem l e n g t h (cm).  9 9 8 8 9  o-f Salix  ,13.11  '  3 0 3 3  147.56 '64.78  browse biomass  - 95  -  (g)  LENGTH 182.00  BIOMASS 7.0700 +  5.23S6  *  5.5011  *  4.7167  *  2.3633  +  1.S789  *  .79444  +  •« 2 2"" "2 * "2 442*2 " " • "22243 '222 "• •2*3»2 33523"' • . 10000 - 1 * " 10.00O  25.222  40.444  * * 2 •  55.S67  F i g u r e A.3. Scatter plot on c a n o p y d e p t h (cm).  70.889  o f Salix  86.111  101.33  116.56  browse biomass  - 96  -  131.78  (g)  DEPTH 147.OO  BIOMASS 7.0700  +  6.2856  *  3. 1478  +  2.3633  +  . 79444  *  .  22' * •2 • . 10000  «  - 1*  3  0  2  0  0  0  '2 • «5 •  10 1  0  --2 336 2-X  3  333 3  3  422 344 3  ,  -2* '3  7  S  S  7  ™ 25.000  F i g u r e A.4. S c a t t e r -plot on c a n o p y w i d t h 1 (cm).  3  2  "  3  4  39.667  o-f Salix  browse  - 97  -  7  0  0  0  54.333  biomass  ^'V'"^ nr =o  <g)  BIOMASS 7.0700  6.2856  *  4.7167  *  3.9322  •  3.1478  *.  2.3633  *  1.5789  +  .79444  +  • •  ..  2 •• •2 *• 22 .22  .  2  • 3 54 222 • 65 38 «2* 3 45 66 22. 10000 - 1*" 3.0000  10.000  •  2 • •  .  17.000  24.000  F i g u r e A.5. Scatter plot on c a n o p y w i d t h 2 (cm).  31.000  o-f Salix  38.000 '  browse  - 90  -  45.000  52.000  biomass  59.000  WI02 66.000  BIOMASS 7.0700  2 2 +2 2 +2 3 +3 4 7 +6 X X -1+3  *  2 2 • 4 4 5  • 2 *  3 2  • 5 4  3 4 4  '  * " 3 3 2 BRS 4.0000  Figure A.6. Scatter plot on b r o w s e c o n d i t i o n .  o-f Salix  browse biomass  - 9«? -  (g)  BIOMASS 4.5100  +  4.0100  +•  3.5100  +  3.0100  +  2.5100  +  1 .5100  +  .51000  +  « *2  10000 3  '  5  0  °°  •  2 2  « nrm 7 0 0 0  4  -  «  5  9  0  0  0  8  :  3  0  0  0  7.1000  F i g u r e A. 7. Scatter plot on stem d i a m e t e r (mm).  1  9.5000  o-f Betula  0  -  browse  too  7  0  0  11.900  biomass  13.10o""oiAM 14  (g)  30  BIOMASS •4.5100 +  4.0100 +  3.0100 +  2.5100  +  2.0100  •  1.5100 +  * • - • 2 2 ... ,,.. • 232 • "« 2 2 . 10000 -1 + « * • " 27.000 55.000 41.000 2  3  69.000  F i g u r e A.8. Scatter plot on stem l e n g t h (cm).  83.000  97.0O0  o-f Betula  - 101  111.00  browse  -  125.00  biomass  139.00  <g)  LENGTH 153.00  BIOMASS 4.5100  +  3.5100  +  3.01O0  *  2.0100  +  1.5100  *  1.0100  +  .51000  +  +  • * *»  lOOOO  *2 *  •*  2 • 2  2 •  " " *  - 1+»  1  2  0  0  38.222  0  25.111  F i g u r e A.9. Scatter plot on c a n o p y d e p t h (cm).  64.444 51.333  90.S67 77.556  o f Betula  browse  - I0Z -  116.89 103.78  biomass  DEPTH 130.00  <g>  BIOMASS 4.5100 +  4.0100  *  3.5100 +  2.51O0  *  2.01O0  *  1.5100 +  1.0100  *  2•  * .51000  2  +  . 1O0O0 -1*  * 2 * • 2 2 3' 2 * 2 * 2 • .  * -  3 2 2 2 2  13-444  '8.667  F i g u r e A. 10. Scatter plot on c a n o p y w i d t h 1 (cm).  23.889  29.111  o-f Betula  -  103  34.333  39.556  browse biomass  -  44.778  (g)  WID1 SO.00  BIOMASS 4.5100  3.5100  +  3.0100  +  2.5100  +  2.0100  +  1.5100  *  2 • * 3 2 « 2 2 - » " » 3 2 ' 2 •2 4 « 3 2 . 1000O -1+ 2 2.0000 9.3333 5.S667  13.000  F i g u r e A. 1 1 . Scatter plot on c a n o p y w i d t h 2 (cm).  1G.S67  20.333  o-f Betula  -  104  24.000  browse  -  27.SS7  biomass  31.333  (g)  WID2 35.000  BIOMASS 4.S100  •  4.0100  +  3 .0100 *  2.5100  •  2.0100  *• 3  1.5100  *  1.0100  • 2  2 2 +3 3 3 .51000 +4 3 4 +8 S . 100OO - 1 + 3  2 4 3 . 4 44444  8 8 8 8 9  ,-3333 '  F i g u r e A. 12. Scatter plot on b r o w s e c o n d i t i o n .  1 3 3 3 3  ,  , „2.2222 „  7778  o-f Betula  -  105  2 8 6 6 7  browse  -  3.1111• 3  biomass  5 5 5 6  (g)  8RS i n  APPENDIX B:  -  ANOVA  10S  -  TABLES  Table  B.l.  Source  ANOVA -for S a l i x  DF  Regression  4  164.72  155  Total  159  Source  ANOVA  109  Total  112  B.3.  Source  41.035  36.792  172.92  .23737  Sum o-f s q u a r e s  103.49  DF  51.744  50.045  ANOVA -for S a l i x  site  Mean s q u a r e  F  112.70  .45913  1 regression equation.  Sum a-f s q u a r e s  Mean s q u a r e  1  19.433  19.433  Error  48  13.005  Total  49  Regression  F  201.01  2  Error  Table  Mean s q u a r e  -for B e t u l a common r e g r e s s i o n e q u a t i o n .  DF  Regression  regression equation.  Sum o-f s q u a r e s  Error  T a b l e B.2.  common  -  .27095  107 -  F  71.723  Table  B.4.  Source  ANOVA f o r S a l i x  DF  Regression  site  6 regression equation.  Sum o-f s q u a r e s  1  7.2470  Error  36  7.7723  Total  37  Table  B.5.  Source  ANOVA -for S a l i x  DF  Regression  39  Total  41  Table  B.6.  Source  Regression  ANOVA  square  7.2470  F  33.567  .21590  7 regression equation.  Sum o-f s q u a r e s  2  Error  site  Mean  29.367  Mean  square  14.684  8.3727  F  68.397  .21468  37.740  f o rSalix  DF  pooled-site regression  Sum o-f s q u a r e s  4  53.950  Error  125  31.412  Total  129  -  Mean  equation.  square  13.488 .25130  108 -  F  53.672  Table  B.7.  Source  Regression  ANOVA -for B e t u l a s i t e  DF  Sum o f s q u a r e s  1  10.413  Error  48  13.308  Total  49  23.720  T a b l e B.8.  Source  Regression  ANOVA f o r B e t u l a s i t e  DF  29.154  Error  32  12.337  Total  34  Source  ANOVA f o r B e t u l a s i t e  F  37.557  .27725  4 regression equation.  Mean s q u a r e  14.577  F  37.811  .38552  6 regression equation.  Sum o-f s q u a r e s  Mean s q u a r e  F  2  22.345  11.173  19.209  Error  34  19,776  Total  36  42.121  Regression  DF  Mean s q u a r e  10.413  Sum o-f s q u a r e s  2  T a b l e B.9.  1 regression equation.  -  .58165  10«? -  Table  B.10.  Source  Regression  ANOVA  DF  f o r Betula s i t e  Sum o-f s q u a r e s  1  21.293  Error  40  14.129  Total  41  35.424  Table B . l l .  Source  Regression  ANOVA  DF  7 regression equation.  Mean s q u a r e  21.295  F  60.286  .35323  -for B e t u l a p o o l e d - s i t e r e g r e s s i o n e q u a t i o n .  Sum o-f s q u a r e s  1  93.500  Error  162  73.130  Total  163  93.500 .45142  166.63  -  1IO  Mean s q u a r e  -  F  207.12  

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