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Urban population density distribution: a contribution from the Vancouver case Tse, Ming-Lan 1976

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URBAN POPULATION DENSITY DISTRIBUTION: A CONTRIBUTION FROM THE VANCOUVER CASE By MING-LAN TSE •S.Sc,  THE CHINESE UNIVERSITY OF HONG KONG, 1972  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS In the School of Community & R e g i o n a l P l a n n i n g  We accept t h i s t h e s i s as conforming t o t h e required standard  THE UNIVERSITY OF BRITISH COLUMBIA J a n u a r y , 1976  In p r e s e n t i n g  this  thesis  an advanced degree at the I  Library shall  f u r t h e r agree  for  scholarly  by h i s of  written  thesis  make i t  that permission  for  the requirements  Columbia,  I agree  r e f e r e n c e and  f o r e x t e n s i v e copying o f  this  It  for financial  is understood that gain shall  not  Community & R e g i o n a l  U n i v e r s i t y of B r i t i s h  J a n u a r y , 1976  Columbia  Planning  copying or  for  that  study. thesis  purposes may be granted by the Head of my Department  2075 W e s b r o o k P l a c e V a n c o u v e r , Canada V6T 1W5  Date  freely available  permission.  Department of The  fulfilment of  the U n i v e r s i t y of B r i t i s h  representatives.  this  in p a r t i a l  or  publication  be allowed without my  ii  ABSTRACT C o l i n C l a r k ' s model o f t h e n e g a t i v e  exponential  population  d e n s i t y decay f u n c t i o n i s a p p l i e d t o t h e Vancouver case. model i s c l a i m e d  Though t h e  t o h o l d t r u e f o r a l l p l a c e s a t a l l t i m e s , i t does  not o f f e r s u f f i c i e n t e x p l a n a t i o n s why t h e p r o c e s s i s o c c u r r i n g , n o r does i t pay due r e g a r d s t o t h e t o p o g r a p h i c a l e f f e c t s .  The a p p l i c a t i o n  of t h e model t o t h e east and south s e c t i o n s o f Vancouver may throw some l i g h t t o t h e r a t i o n a l e o f t h e c i t y growth p r o c e s s .  We a r e a b l e  to compare t h e d e n s i t y g r a d i e n t o f t h e e a s t and south due t o t h e d i f f e r e n t t i m i n g o f t r a n s p o r t a t i o n improvement and p h y s i c a l morphology. By examining two s e c t i o n s o f t h e same c i t y we can i s o l a t e t h e e f f e c t of t r a n s p o r t a t i o n on t h e d e n s i t y o f development, s i n c e b o t h s e c t i o n s are s u b j e c t t o t h e same growth p r e s s u r e s . The  d e n s i t y p r o f i l e s o f t h e whole c i t y , and t h e e a s t e r n and  s o u t h e r n s e c t i o n s o f i t ( i n t h e shape o f r i n g , s i n g l e a i r l i n e , and band) a r e p r e p a r e d ; and f o r each p l o t t i n g o f p o p u l a t i o n  sector  density,  two p a r a l l e l r e g r e s s i o n runs a r e made w i t h r e g a r d t o b o t h r a d i a l d i s t a n c e and t r a v e l time.  The model i s t e s t e d a t f o u r p o i n t s i n t i m e ;  and i t s goodness o f f i t i s measured by t h e c o e f f i c i e n t s o f d e t e r m i n a t i o n . The 1.  c o n c l u s i o n s reached a r e as f o l l o w s :  The q u a l i t y o f t h e model i n r e p l i c a t i n g t h e Vancouver  experience  i s s i m i l a r t o t h a t found f o r a wide range o f c i t i e s . 2.  The east and t h e south a r e marked by t h e d i f f e r e n t i a l r a t e s o f d e n s i t y d e c l i n e , which are mainly development takes  place.  due t o t h e date a t w h i c h t h e  The d i s t a n c e parameter measured i n t r a v e l t i m e from the CBD does not g i v e a s i g n i f i c a n t l y b e t t e r f i t t o t h e model than r a d i a l d i s t a n c e from t h e CBD. The c o e f f i c i e n t s o f d e t e r m i n a t i o n suggesting over  o f t h e model d e c l i n e o v e r  v a r i a b l e p a t t e r n of p o p u l a t i o n d e n s i t y w i t h i n t h e c i t y  time.  The imputed c e n t r a l d e n s i t y does n o t show a c o n s i s t e n t over  time,  decline  time.  The s t e e p n e s s o f d e n s i t y d e c l i n e d e c r e a s e s i n t h e c o u r s e o f time.  iv  TABLE OF CONTENTS Chapter I. II.  III.  Page  INTRODUCTION  1  MODELLING THE URBAN POPULATION DENSITY DISTRIBUTION ..  4  A.  Scope o f t h e Study  4  B.  D e s c r i p t i o n o f t h e Model  11  C.  Commentary on C l a r k ' s Model  15  Deficiencies  15  Theoretical J u s t i f i c a t i o n  16  F o o t n o t e s t o Chapter I I  17  ANALYSIS METHODOLOGY  18  A.  Hypotheses I n v e s t i g a t e d  18  B.  Methodology!..  24  0  Measures o f A c c e s s i b i l i t y  24  Data Source  24  Data Weaknesses  25  Manipulation  25  o f Data  . J u s t i f i c a t i o n f o r t h e use o f g r o s s r e s i d e n t i a l d e n s i t y and v a r i o u s g e o g r a p h i c a l F o o t n o t e s t o Chapter I I I IV.  V.  set-ups  27 33  ANALYSIS OF DATA  34  A.  D e s c r i p t i o n o f Graphs  34  B.  Hypotheses D i s c u s s e d  41  CONCLUSION  50  V  Page BIBLIOGRAPHY APPENDIX I :  53 Regression Analysis  60  Footnotes  63  APPENDIX I I : Graphs  64  APPENDIX I I I :  75  APPENDIX I V :  S t a t i s t i c a l Tables Maps  81  vi  ACKNOWLEDGMENTS  Acknowledgments a r e due t o Dr. M. C. P o u l t o n and Mr. H. C h e r n i a c k f o r t h e a d v i c e and s u p e r v i s o n o f t h e s t u d y . express  I wish t o  t o express my g r a t i t u d e to Mr. T. P. M o r r i s , A r c h i t e c t /  P l a n n e r o f t h e C e n t r a l Mortgage and Housing the manuscript  Corporation, f o r reading  and i n t r o d u c i n g me t o u s e f u l s o u r c e s .  I am g r e a t l y  i n d e b t e d to those who h e l p e d i n t y p i n g my t h e s i s and gave me moral support.  CHAPTER I INTRODUCTION C i t i e s have s i m i l a r c h a r a c t e r i s t i c s i n i n t e r n a l s t r u c t u r e . Almost a l l o f them have a c l e a r l y r e c o g n i z a b l e  CBD, w h i c h i s t h e r e g i o n  of h e a v i e s t  and a major employment  center.  c o n c e n t r a t i o n o f economic a c t i v i t y  R e s i d e n t i a l development tends t o f o l l o w a r e g u l a r  pattern.  I t i s most dense i n t h e immediate v i c i n i t y o f t h e CBD, and t h e d e n s i t y d e c l i n e s towards t h e p e r i p h e r y . the p e r i p h e r y  Development tends t o t a k e p l a c e a t  o f t h e c i t y , and so t h e d w e l l i n g s o f t h e i n n e r c i t y  tend  t o be o l d e r than those o f t h e suburbs. C o l i n C l a r k ^ (1951) has produced an e m p i r i c a l l y - b a s e d model t h a t seems t o g e n e r a l i z e t h e r e s i d e n t i a l d e n s i t y p a t t e r n . e f f e c t i v e l y describes  The model  t h e d e n s i t y d i s t r i b u t i o n o f r e s i d e n t i a l deve-  lopment o f N o r t h American and European c i t i e s f o r many d a t e s w i t h i n the past 200 y e a r s .  F u r t h e r , when i t i s a p p l i e d t o t h e same c i t i e s  at s e v e r a l p o i n t s i n t i m e , i t i n d i c a t e s t h a t t h e r e i s a common p a t t e r n t o t h e change i n t h e d e n s i t y d i s t r i b u t i o n t h a t has t a k e n p l a c e i n t h e modern e r a . However, C l a r k ' s model i s p u r e l y d e s c r i p t i v e , and t h e p r o c e s s e s that underly speculate  t h e growth p a t t e r n o f t h e c i t y a r e n o t c l e a r .  We may  t h a t t r a n s p o r t a t i o n f a c t o r s and t h e s e t t i n g o f a c i t y a r e  i m p o r t a n t d e t e r m i n a n t s o f t h e form o f t h e c i t y .  2  I t i s apparent t h a t t r a n s p o r t a t i o n f a c i l i t i e s can i n f l u e n c e urban s p a t i a l s t r u c t u r e by changing t h e r e l a t i v e a c c e s s i b i l i t y o f d i s t a n t and c e n t r a l l o c a t i o n s .  However, t h e demand f o r t r a n s p o r t a t i o n i s i t s e l f  i n f l u e n c e d by s p a t i a l s t r u c t u r e and l a n d u s e . Any change i n t r a f f i c f a c i l i t i e s changes t h e r e l a t i v e a c c e s s i b i l i t y and hence t h e r e l a t i v e a t t r a c t i v e n e s s of various l o c a t i o n s .  On t h e o t h e r hand, t h e uses a t  those v a r i o u s l o c a t i o n s generate t r i p s , and these t r i p s i n t u r n d e f i n e the t r a n s p o r t a t i o n r e q u i r e m e n t s f o r an a r e a . T r a n s p o r t a t i o n can a l s o I n f l u e n c e t h e sequencing o f c i t y growth. The h i s t o r y o f urban development o f almost a l l major c i t i e s i s w e l l marked by v a r i o u s " e r a s " o f t r a n s p o r t t e c h n o l o g y .  F i r s t came t h e  horse-drawn buses or s t r e e t - c a r s ; l a t e r , i n t h e 1880s and 1890s, 2 c a b l e c a r s , e l e c t r i c s u r f a c e c a r s and e l e v a t e d l i n e s .  The s t r e e t c a r s  and t h e r a i l r o a d s a l l o w e d e x t e n s i v e r i b b o n development a l o n g t h e l i n e s of t h e major r a d i a l a r t e r i e s , and t h e subsequent advent o f t h e motorc a r s i n t h e 1920s a l l o w e d t h e space between t h e a r t e r i e s t o be f i l l e d in.  A f t e r World War I I , e x t e n s i v e c o n s t r u c t i o n of highways and e x p r e s s -  ways f a c i l i t i e d t h e use o f p r i v a t e a u t o m o b i l e s .  The i n c r e a s i n g  a v a i l a b i l i t y o f t h e a u t o m o b i l e a l s o a l l o w e d e a s i e r access t o d i s t a n t l o c a t i o n s , causing c i t i e s to "sprawl". As f o r p h y s i c a l morphology, i f a c i t y i s l o c a t e d on an i n f i n i t e f e a t u r e l e s s p l a i n , a c c e s s i b i l i t y t o t h e c i t y c e n t e r tends t o be e q u a l in a l l directions, theoretically at least.  I t i s therefore l i k e l y  t h a t p o p u l a t i o n d e n s i t y would be e q u a l i n every d i r e c t i o n from t h e c i t y center.  I n a s p a t i a l l y r e s t r i c t e d c i t y where growth i n d i f f e r e n t  3  d i r e c t i o n s from t h e c e n t r a l core i s a s s y m m e t r i c a l ,  r e g i o n a l centers  may d e v e l o p t o c l u s t e r urban f u n c t i o n s c l o s e t o r e s i d e n t i a l and t o m i n i m i z e t r a v e l time.  population  I n any event, p o p u l a t i o n d e n s i t y would  not be t h e same f o r a l l p o i n t s a t a g i v e n d i s t a n c e from t h e c e n t e r . The  e f f e c t s o f b o t h t r a n s p o r t a t i o n and p h y s i c a l morphology  on urban form can be observed when t h e c o n s t r u c t i o n o f new t r a n s p o r t a t i o n f a c i l i t i e s eases t r a v e l a c r o s s s u b s t a n t i a l p h y s i c a l b a r r i e r s . T h i s has happened i n Vancouver, a c i t y w i t h a h i g h l y r e s t r i c t e d  site,  where development c o u l d t a k e p l a c e w i t h r e l a t i v e ease o n l y towards the e a s t . R e s i d e n t i a l development was l a r g e l y r e s t r i c t e d t o t h e B u r r a r d P e n i n s u l a by t h e l a c k o f adequate road c r o s s i n g s o f t h e B u r r a r d to  Inlet  t h e n o r t h and t h e F r a s e r R i v e r ( N o r t h Arm) t o t h e south u n t i l w e l l  i n t o t h e 1950s.  However, c o n t i n u o u s  development t o t h e e a s t has been  r e l a t i v e l y u n r e s t r i c t e d by p h y s i c a l o b s t a c l e s . The d i f f e r e n t t i m i n g o f t r a n s p o r t a t i o n improvement i n t h e east and t h e s o u t h has caused c e r t a i n areas i n and around Vancouver t o be a c c e s s i b l e f o r r e s i d e n t i a l development a t d i f f e r e n t t i m e s . consequence, t h e c i t y i s a s s y m m e t r i c a l . hypotheses c o n c e r n i n g examined.  As a  T h i s assymmetry e n a b l e s some  t h e n a t u r e o f t h e c i t y growth p r o c e s s  t o be  Hypotheses on c i t y form, measures o f a c c e s s i b i l i t y  (radial  d i s t a n c e and t r a v e l t i m e ) , and t h e v a l i d i t y o f C l a r k ' s model, w i l l be considered  i n t h i s work.  4  CHAPTER I I MODELLING THE A. I n t h i s s t u d y we distribution.  Scope of the Study s h a l l concentrate  on the r e s i d e n t i a l  density  R e s i d e n t i a l a c t i v i t y i s by f a r the predominant l a n d  use of c i t i e s . as a d e p a r t u r e . the p r e s e n t ,  URBAN POPULATION DENSITY DISTRIBUTION  The  p o p u l a t i o n d e n s i t y f u n c t i o n of C o l i n C l a r k i s t a k e n  C l a r k found t h a t f o r many c i t i e s , i n the p a s t and  p o p u l a t i o n d e n s i t y f a l l s o f f e x p o n e n t i a l l y as  from the c i t y c e n t e r i n c r e a s e s .  He goes so f a r as to say:  f a l l i n g o f f of d e n s i t y i s an e x p o n e n t i a l  in  distance "That the  f u n c t i o n , appears to be  true 3  f o r a l l times and a l l p l a c e s s t u d i e d , from Los A n g e l e s t o Budapest". For the r e l a t i o n s h i p between d e n s i t y and d i s t a n c e i n C l a r k ' s model to h o l d t r u e , the d e n s i t y p r o f i l e should a l l d i r e c t i o n s i n i n h a b i t e d p a r t s of the c i t y as b o d i e s of w a t e r ) a r e p r e s e n t ,  i d e a l l y be the same i n where no " h o l e s "  t h i s would r e s u l t i n a c i r c u l a r c i t y ,  w i t h the C e n t r a l B u s i n e s s D i s t r i c t (CBD)  at i t s c e n t e r .  C l a r k found t h a t r e s i d e n t i a l p o p u l a t i o n i n c r e a s e of d i s t a n c e from the c i t y c e n t e r , and t h i s d e c l i n e becomes l e s s over time.  density declines  with  t h a t the steepness of  He argues t h a t t r a n s p o r t a t i o n  improvement i s r e s p o n s i b l e f o r t h i s d e c l i n e over time. p r i m a r y r e a s o n s f o r t h i s d e n s i t y p r o f i l e and are not c l e a r .  (such  However, the  i t s change t h r o u g h time  We w i l l use e v i d e n c e from the Vancouver case to improve  our g e n e r a l u n d e r s t a n d i n g of t h i s m a t t e r .  5  S p e c i f i c a l l y , the aims of the study can be o u t l i n e d as: 1)  To t e s t the v a l i d i t y of C l a r k ' s model f o r Vancouver The  repeated  c o n f i r m a t i o n of the v a l i d i t y of the  negative  e x p o n e n t i a l f u n c t i o n of p o p u l a t i o n d e n s i t y d i s t r i b u t i o n has i m p l i c a t i o n s f o r the p l a n n i n g of m e t r o p o l i t a n r e g i o n s .  important  I t has been  found t h a t the i n d i v i d u a l c h o i c e of r e s i d e n t i a l l o c a t i o n s conforms c o l l e c t i v e l y t o the r e g u a l r p a t t e r n .  The n e g a t i v e  exponential  "law"  of mass b e h a v i o u r i s not a r e s u l t of e x t e r n a l l y imposed p h y s i c a l 4 p l a n n i n g , or l e g a l or a d m i n i s t r a t i v e c o n s t r a i n t s .  "The  observed  b e h a v i o u r i s c h a r a c t e r i s t i c o f urban s o c i e t i e s r e s p o n d i n g to f o r c e s and  subject to c o n s t r a i n t s t h a t , although  p e r c e i v e d , are n o n e t h e l e s s  they are not  extremely strong".  consciously  Should t h i s " n a t u r a l "  p a t t e r n of p o p u l a t i o n d e n s i t y decay be the case i n Vancouver, i t must be t a k e n i n t o account i n p l a n n i n g p o l i c i e s .  However, i t i s  f i r s t to v e r i f y t h a t i t does i n f a c t h o l d f o r Vancouver.  The  important city  i s u n u s u a l when compared w i t h o t h e r c i t i e s i n t h a t i t i s e s s e n t i a l l y elongated  i n shape and h i g h l y r e s t r i c t e d i n s i t e .  I t i s necessary  to observe the e f f e c t of p h y s i c a l morphology and the r e s t r i c t i o n on development on t h e a p p l i c a b i l i t y of the model. C i t i e s t h a t a r e l o c a t e d on s i t e s t h a t are not u n d u l y r e s t r i c t e d show many s i m i l a r i t i e s of form. r e s t r i c t e d s i t e and  Vancouver has developed on a h i g h l y  from i t s shape i t would appear to be e x c e p t i o n a l .  The  s l o p e of the d e n s i t y d e c l i n e s h o u l d be d i f f e r e n t i n the east and the s o u t h .  But  6  if  i t . ' i s the same i n every d i r e c t i o n a t one p o i n t i n time, we can  say  t h a t Vancouver  i s not so d i f f e r e n t  from o t h e r c i t i e s .  2)  To observe t h e l o n g - r u n t r e n d s on urban form I t i s n e c e s s a r y t o c o n s i d e r whether t h e l o n g - r u n t r e n d s i n  the  development  o f urban form a r e i n f a c t changing.  C l a r k ' s model, the urban form would d e c l i n e i n imputed  i n time change,  As i n d i c a t e d i n showing  a relative  c e n t r a l d e n s i t y and a r e l a t i v e i n c r e a s e i n suburban  population density.  I t i s to be expected t h a t t h e i n t r o d u c t i o n of  p l a n n i n g p o l i c i e s and c o n t r o l s w i l l a f f e c t  the p a t t e r n o f f u t u r e  lopment  t o some degree.  changes  i n the l o n g - r u n t r e n d f o r t h e type of h o u s i n g c o n s t r u c t e d ,  (a)  F u t u r e urban form would  deve-  a l s o be a f f e c t e d by  Housing Trends: A h o u s i n g survey conducted i n 1972 i n Vancouver  suggests t h a t  6 t h e r e w i l l be more p r e f e r e n c e f o r s m a l l e r u n i t s i n the f u t u r e .  The  N a t i o n a l Housing A c t (NHA) f i n a n c e s more m u l t i p l e d w e l l i n g s (apartments 7  and row housings) than s i n g l e f a m i l y h o u s i n g .  The c o s t of l a n d has  g been i n c r e a s i n g s h a r p l y s i n c e e a r l y 1972.  Other economic  factors  a l s o d i s c o u r a g e p e o p l e from owning s i n g l e detached h o u s i n g . the  Further,  " a s s i s t e d home ownership programme" o f the Canadian Housing and 9  Mortgage C o r p o r a t i o n f i n a n c e s condomium u n i t s .  Ownership  of s i n g l e  detached d w e l l i n g s i s becoming r e l a t i v e l y more expensive as compared w i t h m u l t i p l e housing u n i t s , and as a r e s u l t , apartments a r e more popular. areas.  One r e s u l t  i s the emergence of h i g h d e n s i t y l i v i n g  Townhouses and apartment  i n suburban  complexes now c o e x i s t w i t h q u a r t e r -  a c r e l o t s on t h e f r i n g e s of the c i t y .  T h i s suggests suburban  deve-  lopment i n t h e f u t u r e a t d e n s i t i e s g r e a t e r than has been t h e case i n the l a s t two decades. (b)  The L i v a b l e Region Growth S t r a t e g y : The major p l a n n i n g p o l i c y documented f o r m e t r o p o l i t a n Vancouver  i s t h e s o - c a l l e d L i v a b l e Region P l a n .  T h i s p l a n has s u b s t a n t i a l  c a t i o n s f o r the f u t u r e a p p l i c a b i l i t y of the model.  impli-  The major p r o p o s a l s  adopted by t h e P o l i c y a r e : (1)  The c r e a t i o n o f f o u r r e g i o n a l c e n t e r s a l l t o t h e e a s t and s o u t h -  east of the CBD:  The r e g i o n a l c e n t e r s a r e t o be l o c a t e d i n Burnaby,  New W e s t m i n s t e r , S u r r e y , and t h e N o r t h - e a s t  Sector (the exact  of t h i s f o u r t h a r e a i s as y e t t o be d e t e r m i n e d ) .  location  These would a c t as  f o c i f o r the g e n e r a l l y f o r m l e s s , s c a t t e r e d development t o the e a s t o f Vancouver.  They would h e l p the suburban communities r e a c h a b a l a n c e  o f employment and employable r e s i d e n t s . (2)  P r o t e c t i o n of a g r i c u l t u r a l land:  The h o u s i n g s t o c k would be  expanded p r i m a r i l y w i t h i n the p r e s e n t l y u r b a n i z e d a r e a by and redevelopment.  infilling  The n e t r e s u l t o f t h i s p o l i c y i s t h a t d e n s i t i e s  would be somewhat h i g h e r i n t h e u r b a n i z e d p o r t i o n s of t h e o u t l y i n g m u n i c i p a l i t i e s than would o t h e r w i s e be the case. (3)  A l i g h t r a p i d t r a n s i t system c o n n e c t i n g the r e g i o n a l c e n t e r s and  downtown Vancouver:  T h i s would put t h e r e g i o n a l c e n t e r s on a more  e q u a l f o o t i n g w i t h the p r e s e n t CBD i n q u a l i t y o f s e r v i c e s - a n d a c c e s s i b l e opportunities. I f these p o l i c i e s a r e implemented, s e v e r a l consequences can be e n v i s i o n e d .  There would be an i n c r e a s e i n suburban p o p u l a t i o n  8  d e n s i t i e s , a l e s s u n i f o r m p a t t e r n o f d e n s i t i e s f o r suburbs a t s i m i l a r d i s t a n c e s from t h e CBD, a c o m p a r a t i v e l y l e s s dominant CBD than b e f o r e , and improvement i n a c c e s s i b i l i t y t o s e r v i c e a c t i v i t e s and some o f t h e CBD-type f u n c t i o n s i n t h e r e g i o n a l c e n t e r s w h i c h may a l t e r t h e l o c a t i o n p r e f e r e n c e s of i n d i v i d u a l s . In sum, t h e r e a l r e a d y appear t o be t r e n d s towards h i g h e r d e n s i t i e s i n t h e u r b a n i z e d areas o f t h e o u t l y i n g suburbs, and these t r e n d s w i l l f u r t h e r be e n f o r c e d by t h e L i v a b l e Region P o l i c y . I t i s d o u b t f u l whether t h e p r o j e c t e d d e n s i t y p a t t e r n t o be adopted by the L i v a b l e Region P l a n f i t s C l a r k ' s n e g a t i v e e x p o n e n t i a l c u r v e , and i f C l a r k ' s model r e p r e s e n t s a b e h a v i o r a l "law", then t h e P l a n might be more s u c c e s s f u l i f i t were c o n s i s t e n t w i t h t h i s 3)  "law".  To study the e f f e c t of t r a n s p o r t a t i o n improvement The s i t e o f t h e c i t y poses s i g n i f i c a n t b a r r i e r s t o commuting,  which have i n the p a s t r e s t r i c t e d t r a v e l t o t h e n o r t h and t h e s o u t h . There a r e s t i l l r e l a t i v e l y few c r o s s i n g s o f t h e major w a t e r b a r r i e r s , and these a r e i n f a c t t h e p l a c e s where Vancouver e x p e r i e n c e s at  peak-commuting h o u r s . The  connected  CBD i t s e l f i s c l o s e by t h e B u r r a r d I n l e t W a t e r f r o n t and i s  t o the n o r t h e r n suburbs by two b r i d g e s :  to  the e a s t o f t h e CBD ( t h e Second N a r r o w s ) ,  to  t h e west ( t h e F i r s t Narrows).  a major b a r r i e r . to  congestion  one a few m i l e s  and t h e o t h e r a few m i l e s  To t h e s o u t h , t h e F r a s e r R i v e r i s  The F r a s e r R i v e r reaches t i d e w a t e r a c r o s s a d e l t a  the s o u t h of t h e B u r r a r d P e n i n s u l a .  A few major b r i d g e s and one  t u n n e l have been c o n s t r u c t e d i n t h e l a s t 20 y e a r s t o improve a c c e s s  9  to t h e south.  N e v e r t h e l e s s , t h e F r a s e r remains a s u b s t a n t i a l b a r r i e r .  T r a n s p o r t o b v i o u s l y i s a v e r y important lopment, a l t h o u g h  i t s exact r o l e i s d i f f i c u l t  the m u l t i p l i c i t y o f o t h e r f a c t o r s .  f a c t o r i n urban deve-  t o i s o l a t e because o f  I n Vancouver, improvements i n  t r a n s p o r t a t i o n such as the b r i d g e s and highway programs of the 50s and  60s g e n e r a l l y preceded  t r a n s p o r t a t i o n through  r e s i d e n t i a l spread.  A l s o , improvements i n  the n a t u r a l b a r r i e r s i n the east and the south  have o c c u r r e d a t d i f f e r e n t  times.  Because o f t h i s , we a r e a b l e to  examine the e f f e c t o f t r a n s p o r t a t i o n on the d e n s i t y o f development i n comparison t o o t h e r e x p l a n a t i o n s o f the d e n s i t y p r o f i l e , ;.such as .the-date at wnich^development' takes ' p l a c e t ^ ' ' 1  Among the most important G r a n v i l l e Street Bridge, Tunnel  t  a  k  e  s  P - l a  e  p r o j e c t s l e a d i n g south were the new  1954; Oak S t r e e t B r i d g e , 1957; Deas I s l a n d  ( l a t e r named George Massey T u n n e l ) , 1959; Vancouver-Blaine  Freeway, 1962, through border;  : n t  and Knight  Richmond, D e l t a and Surrey t o the U n i t e d  States  S t r e e t B r i d g e , 1974.  To the east and the s o u t h - e a s t , t h e F r a s e r and i t s t r i b u t a r i e s are s i g n i f i c a n t b a r r i e r s t o t r a v e l i n t h e o u t e r suburbs o f Vancouver and beyond. Pitt  B r i d g e s were b u i l t  R i v e r i n 1957.  at R o s d a l e - A g a s s i z  i n 1956, and a t  The former p r o v i d e d much b e t t e r i n t e r - c o n n e c t i o n s  between the n o r t h and south banks of the F r a s e r R i v e r and p e r m i t t e d east-west  through  traffic  t o use the Lougheed Highway as an a l t e r n a t e  r o u t e t o the Trans-Canada Highway, through and Langley,  both opened i n 1964.  ^  Burnaby, Coquitlam,  Surrey  S i n c e the t r a v e l r e s t r a i n t s of the v a r i o u s s e c t i o n s of the were eased at d i f f e r e n t  city  t i m e s , we would expect the r a t e of p o p u l a t i o n  d e n s i t y d e c l i n e t o the south t o be d i f f e r e n t  from t h a t t o the e a s t .  T h i s s h o u l d be the case when the d i s t a n c e parameter i n the model i s measured i n terms of t r a v e l time or r a d i a l d i s t a n c e . l o c a t i o n a l d e c i s i o n s o f households may than t o the  However, the  be more r e s p o n s i v e t o the former  latter.  C l a r k ' s model i s t e s t e d w i t h r e s p e c t t o b o t h t r a v e l time  and  r a d i a l d i s t a n c e i n o r d e r t o study the e f f e c t o f the improvement of t r a n s p o r t f a c i l i t i e s on r e s i d e n t i a l spread.  I t i s used i n the  because i t i s " t h e most a p p r o p r i a t e sample d e s c r i p t i v e p r e s e n t i n g the d i s t r i b u t i o n o f r e s i d e n t i a l d e n s i t y " . ^  study  model f o r r e I t involves  m e r e l y two parameters (A and b ) , w h i c h , at f i r s t g l a n c e , i s s i m p l e but a p p e a l i n g .  The  d e n s i t y g r a d i e n t b i s the s i m p l e s t  measure o f the s p a t i a l d i s t r i b u t i o n of a c t i v i t y . indicate  the changes i n c i t y form.  descriptive  I t can be used t o  I t i s e a s i l y computed; and i t  represents a c l e a r l y understood d e s c r i p t i v e  summary about the s p a t i a l 12  a l l o c a t i o n of r e s i d e n t s i n an urban a r e a .  B.  D e s c r i p t i o n o f t h e Model  Since C l a r k provided  a mathematical expression  f o r t h e popu-  l a t i o n d e n s i t y d i s t r i b u t i o n i n 1951, o t h e r a u t h o r s have worked w i t h the model and come up w i t h some o t h e r f o r m u l a t i o n s .  However, i t i s  d o u b t f u l whether o t h e r models have shown an improvement over t h e 13 o r i g i n a l one.  C l a r k ' s model i s : D  = D e " x o  or : Ln D  = Ln D x  b  (1)  x  - bx  This states that density i s a negative from t h e c i t y c e n t e r . Where:  (2)  o  D  q  exponential f u n c t i o n of d i s t a n c e  and b a r e t h e parameters o f t h e e q u a t i o n .  x i s d i s t a n c e from t h e c e n t e r o f c i t y ; D^ i s t h e d e n s i t y o f r e s i d e n t p o p u l a t i o n a t a d i s t a n c e x; D  q  i s t h e e x t r a p o l a t e d o r imputed c e n t r a l p o p u l a t i o n  density;  Ln denotes t h e n a t u r a l l o g a r i t h m ; e i s t h e n a t u r a l l o g a r i t h m i c base; b i s t h e d e n s i t y g r a d i e n t , o r t h e s l o p e o f t h e curve. D  q  i s the r e s i d e n t i a l density  imputed t o t h e c i t y c o r e .  CBD i s m o s t l y n o n - r e s i d e n t i a l , t h i s d e n s i t y r e p r e s e n t s f i g u r e which i s not r e a l i z e d .  Because the a hypothetical  The n o n - r e s i d e n t i a l CBD shows up as a  ( r e s i d e n t i a l ) " d e n s i t y c r a t e r " n o t e x p l i c i t l y t a k e n i n t o account i n C l a r k ' s model.  G r a p h i c a l l y , the model can be r e p r e s e n t e d  Distance center  from the c i t y  C l a r k d e r i v e d two  by:  Distance center  from the  city  g e n e r a l i z a t i o n s from h i s study of 36 American  and European c i t i e s : 1) I n every l a r g e c i t y , e x c l u d i n g the c e n t r a l b u s i n e s s zone, w h i c h has few r e s i d e n t i n h a b i t a n t s , we have d i s t r i c t s of dense popul a t i o n i n the i n t e r i o r , w i t h d e n s i t y f a l l i n g o f f p r o g r e s s i v e l y as we proceed t o the o u t e r suburbs; 2) I n most (but not a l l ) c i t i e s , as t i m e goes on, d e n s i t y tends to f a l l i n the most populous i n n e r suburbs, and t o r i s e i n the o u t e r suburbs, and the whole c i t y tends to "spread i t s e l f o u t " .  At one s t a t i c p o i n t i n t i m e , t h e f a l l - o f f i n d e n s i t y from t h e c i t y center to the periphery f o l l o w s a negative ship with distance.  exponential  relation-  However, d e n s i t y tends t o d e c r e a s e i n t h e i n n e r  suburbs and i n c r e a s e i n t h e o u t e r suburbs w i t h t h e passage of t i m e , and t h i s tendency i s r e f l e c t e d i n t h e parameter b i n t h e model t a k i n g on s m a l l e r v a l u e s over t i m e .  The d e n s i t y g r a d i e n t may a l s o be c a l l e d t h e  " c o e f f i c i e n t o f compactness".  The l a r g e r t h e v a l u e o f b, t h e more  compact the c i t y , and t h e s m a l l e r t h e more s p r a w l e d t h e c i t y .  ^  Clark  argues t h a t b i s l a r g e l y dependent upon t h e c o s t s o f i n t r a u r b a n t r a n s p o r t , o r t h e c o s t o f t r a v e l l i n g i n r e l a t i o n t o t h e average c i t i z e n ' s 16  income.  I n o t h e r words, i t would g e t s m a l l e r when improvements  i n t r a n s p o r t a t i o n a l l o w people e a s i e r a c c e s s t o t h e suburbs. C l a r k used t h e f o l l o w i n g methodology i n h i s work:  First, a  s e r i e s of c o n c e n t r i c r i n g s were drawn a t one m i l e r a d i u s from the c i t y c e n t e r and t h e average d e n s i t y c a l c u l a t e d f o r each r i n g the n e t a r e a e x c l u s i v e o f open spaces.  using  Second, t h e d e n s i t y measure  was t h e n p l o t t e d a g a i n s t the mean d i s t a n c e of t h e r i n g from t h e c e n t e r . (The p o p u l a t i o n and n e t a r e a were o b t a i n e d  f o r census t r a c t s o r s i m i l a r  a d m i n i s t r a t i v e d i v i s i o n s and where t h e c i r c l e s c u t t h e b o u n d a r i e s o f these d i v i s i o n s , apportionments o f p o p u l a t i o n were t o be made). the parameters D  q  Third,  and b were o b t a i n e d by r e g r e s s i o n a n a l y s i s u s i n g the  l o g a r i t h m i c form o f the e q u a t i o n .  Having adopted t h i s method, C l a r k  goes on t o s t a t e t h a t " i t would be b e t t e r t o / p l o t , f o r each t r a c t , t h e recorded  average d e n s i t y a g a i n s t i t s mean d i s t a n c e from t h e c e n t e r o f  the c i t y , as t h i s would e l i m i n a t e t h e e r r o r s due t o t h e apportionment  p r o c e s s , and g i v e a b e t t e r p i c t u r e of t h e s c a t t e r about the r e g r e s s i o n line". study.  T h i s s i m p l e r and more e f f e c t i v e p r o c e d u r e was adopted i n t h i s  C.  Commentary  on C l a r k ' s Model  I n v e r y sweeping terms, t h e model a t b e s t d e s c r i b e s t h e p o p u l a t i o n d e n s i t y d i s t r i b u t i o n i n a snapshot. p r e d i c t i v e , i t has i m p M c a f c i o n s p f o r  Though i t i s not  t h e growth t r e n d o f a c i t y .  I t b r i n g s f o r t h the i s s u e of the f r i c t i o n a l e f f e c t of d i s t a n c e , i . e . , a c c e s s i b i l i t y o r t h e ease o f i n t e r a c t i o n between t h e p l a c e o f r e s i d e n c e and t h e core a r e a , w h i c h i s t h e p r i m a r y c e n t e r o f economic activity.  However, t h e model i s n o t w i t h o u t i t s s h o r t c o m i n g s .  It  i s t h e r e f o r e the i n t e n t of t h i s s e c t i o n to o u t l i n e i t s d e f i c i e n c i e s i n b r i e f , and t o p r o v i d e a t h e o r e t i c a l j u s t i f i c a t i o n t o e x p l a i n t h e r e l a t i o n s h i p between d e n s i t y and d i s t a n c e . Deficiencies Defluiencies The model has been c l a i m e d t o be a p p l i c a b l e t o a l l p l a c e s 1  at a l l t i m e s .  I t i s d e r i v e d p u r e l y from e m p i r i c a l o b s e r v a t i o n s  and i t does not have w i t h i n i t a n y t h i n g t o e x p l a i n why t h e d e n s i t y d i s t r i b u t i o n i s as i t i s o r why i t has changed i n such a c o n s i s t e n t manner over t h e p a s t c e n t u r y .  I t i s apparent t h a t as soon as  p l a n n i n g i n s t i t u t i o n s such as z o n i n g , t a x e s , e t c . , a r e i n t r o d u c e d , o r a d i f f e r e n t s e t o f market f o r c e s a r e i n o p e r a t i o n , o r t h e f a c t o r s a f f e c t i n g the c h o i c e o f r e s i d e n t i a l l o c a t i o n change, C l a r k ' s " l a w " may no l o n g e r a p p l y .  On t h e o t h e r hand, i f t h e " l a w " does a p p l y ,  t h i s shows t h a t t h e " n a t u r a l " f o r c e s may i n f a c t be much s t r o n g e r these  factors.  than  16  Theoretical Justification The  p o p u l a t i o n d e n s i t y decay f u n c t i o n can be e x p l a i n e d i n  economic terms.  I n the a b s t r a c t , i n d i v i d u a l s tend t o base t h e i r  r e s i d e n t i a l l o c a t i o n d e c i s i o n s upon a t r a d e o f f between l a n d c o s t , c o s t of h o u s i n g and t r a n s p o r t or commuting c o s t s .  the  As d i s t a n c e from  the c i t y c e n t e r i n c r e a s e s , l a n d c o s t s tend t o be lower because more l a n d i s a v a i l a b l e , and  t r a n s p o r t a t i o n c o s t s t o a range of  and j o b o p p o r t u n i t i e s are h i g h e r .  activities  As l a n d c o s t s l e s s and l e s s , i t i s  l i k e l y t h a t p e o p l e w i l l consume more of i t ' .  I t i s therefore  logical  to expect t h a t the per c a p i t a consumption of l a n d f o r h o u s i n g w i t h d i s t a n c e from the c i t y T h i s e x p e c t a t i o n was  increases  center. confirmed  by the f i n d i n g s of the  study  done by the Lower M a i n l a n d R e g i o n a l P l a n n i n g Board of B r i t i s h Columbia i n 1963  concerning  v a l u e of Vancouver.  the i n t e n s i t y of l a n d use and I n the main, i t was  i t s associated  found t h a t the c u r v e s of  i n t e n s i t y of l a n d use and l a n d v a l u e a r e downward s l o p i n g . of the r a t i o of o c c u p i e d  land  The  curve  l a n d t o unoccupied l a n d p l o t t i n g a g a i n s t  time-  d i s t a n c e zones i s v e r y steep a t the c e n t e r and becomes f l a t t e n e d  out  at the p e r i p h e r y .  use  at the core and  This i n d i c a t e d that land i s i n high i n t e n s i t y  low i n t e n s i t y use at the p e r i p h e r y .  ^  Footnotes  1. C. C l a r k , "Urban P o p u l a t i o n D e n s i t i e s " , J o u r n a l o f t h e R o y a l S t a t i s t i c a l , S o c i e t y , V o l . CXIV, p a r t I V , 1951 2. Homer H o y t , "The E f f e c t o f t h e A u t o m o b i l e on P a t t e r n s o f Urban Growth", T r a f f i c Q u a r t e r l y , 1963, p. 294 3.  C. C l a r k , op. c i t . , pp. 490-1.  Emphasis i s my own.  4. Rene B u s s i e r e , The S p a t i a l D i s t r i b u t i o n o f Urban P o p u l a t i o n s , t r a n s , by t h e a u t h o r , P a r i s , CRU, 1970, p. 83 5.  I b i d . , p. 83  6. M i c h e l e L i o y , S o c i a l Trends i n G r e a t e r Vancouver, The U n i t e d Way of G r e a t e r Vancouver, March, 1975, p. 73 7.  I b i d . , p. 76  8.  I b i d . , p. 77i  9.  I b i d . , p. 77  10. A l f r e d H. Siemens ( e d . ) , Lower F r a s e r V a l l e y : E v o l u t i o n o f a C u l t u r a l Landscape, B.C. Geog. S e r i e s , No. 9, Dept. o f Geog., T a n t a l u s Research L t d . , Vancouver, CAnada, p. 86 11. Bernard-Andre G e n e s t , " P o p u l a t i o n D i s t r i b u t i o n F u n c t i o n s f o r Urban A r e a s " , V o l . 2 i n a S e r i e s on A i r p o r t L o c a t i o n and P l a n n i n g , R e s e a r c h Rept., R-70-53, Aug. 1970, p. i i 12. Bruce E. N e w l i n g , "The S p a t i a l V a r i a t i o n o f Urban P o p u l a t i o n D e n s i t i e s " , Geog. Review 59, 1969, p. 248 13.  B-A. Genest, op. c i t .  14.  C. C l a r k , op. c i t . , p. 490  15. C. C l a r k , "The L o c a t i o n o f I n d u s t r i e s and P o p u l a t i o n " , Town P l a n n i n g Review 35, p. 211 16.  C. C l a r k , "Urban P o p u l a t i o n D e n s i t i e s " , op. c i t . , p. 491  17. Dynamics o f R e s i d e n t i a l Land S e t t l e m e n t , Lower M a i n l a n d R e g i o n a l P l a n n i n g Board o f B r i t i s h Columbia, Supp. Study 2 t o Land f o r L i v i n g  CHAPTER I I I  ANALYSIS METHODOLOGY A.  Hypotheses I n v e s t i g a t e d  S i x e x p l i c i t hypotheses a r e c o n s i d e r e d . intended  t o explore c e r t a i n determinants  d i r e c t r e l a t i o n t o t h e model D = D e " x o i . e . , Ln D^ = Ln D where:  x  q  b  The hypotheses a r e  o f c i t y growth.  They have  formula:  x  - bx  ( i n t h e form f o r l i n e a r  distance t o the c i t y center d i s t a n c e o r t r a v e l time)  regression)  (whether measured i n r a d i a l  D^ = p o p u l a t i o n d e n s i t y a t d i s t a n c e x Ln D  q  = t h e n a t u r a l l o g o f t h e p o p u l a t i o n d e n s i t y imputed a t t h e c i t y center  b = d e n s i t y g r a d i e n t , o r t h e s l o p e o f t h e curve i n t h e l i n e a r r e g r e s s i o n model  Hypothesis  1:  The d e n s i t y g r a d i e n t b w i l l be l a r g e r f o r t h e South than f o r the East.  Reasons:  1.  The t o p o g r a p h i c a l c o n s t r a i n t s t o t h e south a r e g r e a t e r than t o t h e e a s t .  The f o r m e r i s c l e a r l y marked by  w a t e r b o d i e s , i . e . , t h e n o r t h and south arms o f t h e Fraser R i v e r ; w h i l e the east i s not c h a r a c t e r i z e d by any major b a r r i e r i n t h e l a n d s c a p e .  19  2.  Development to the s o u t h has been r e l a t i v e l y s l o w e r than t o t h e e a s t .  If residential building  d e n s i t y i s p r i m a r i l y a f u n c t i o n o f the time of c o n s t r u c t i o n f o r new  p e r i p h e r a l development, and  the  lower d e n s i t y i s a s s o c i a t e d w i t h l a t e r development, t h e n the s l o w e r spread o f the u r b a n a r e a t o the s o u t h w i l l be a s s o c i a t e d w i t h a l a r g e r b v a l u e when d e n s i t y i s measured a g a i n s t t r a v e l time.  I f , on  the o t h e r hand, t r a n s p o r t i s the dominant f a c t o r i n e x p l a i n i n g d e n s i t y d i s t r i b u t i o n , then the b v a l u e to Hypothesis  2:  the s o u t h s h o u l d be s i m i l a r t o t h a t t o the e a s t .  There w i l l be a s i g n i f i c a n t d i s c o n t i n u i t y i n the s c a t t e r i n g o f d a t a p o i n t s a t about s i x m i l e s from the c i t y c e n t e r , where the n o r t h arm of the F r a s e r River i s located.  Reasons:  Only i n the  50s-.did h i g h - c a p a c i t y b r i d g e s over  the  F r a s e r R i v e r improve t r a n s p o r t a t i o n l i n k s to t h e south.  P o p u l a t i o n d e n s i t y s h o u l d be h i g h e r between  the c i t y c o r e and the n o r t h arm o f the F r a s e r R i v e r than f u r t h e r south.  R e s i d e n t i a l spread s o u t h of t h e  r i v e r s t a r t e d a t a l a t e r d a t e , and s h o u l d be marked by a lower d e n s i t y .  There s h o u l d thus be a sharp b r e a k  i n the s c a t t e r i n g of d a t a p o i n t s . due  to:  (1)  T h i s b r e a k c o u l d be  The f a c t t h a t d e n s i t y depends on  date of development.  the  The l a t e development s o u t h o f  20  the r i v e r would then be r e s p o n s i b l e f o r t h e b r e a k i n d e n s i t y a t t h a t p o i n t ; o r (2) t o t h e f a c t t h a t d e n s i t y responds t o t r a v e l  time and t h e d e t o u r s and  d e l a y s due t o t h e few r i v e r c r o s s i n g s may cause a sharp l e a p i n average t r a v e l time over a s h o r t i n c r e a s e i n r a d i a l d i s t a n c e from t h e c e n t e r .  Evidence f o r the  former e x p l a n a t i o n would be c o n t i n u e d break when d e n s i t y i s c o n s i d e r e d  existence of a  as a f u n c t i o n o f  t r a v e l time as w e l l as r a d i a l d i s t a n c e .  For the l a t t e r  t o h o l d t r u e , t h e d i s c o n t i n u i t y should be conspicuous o n l y when d e n s i t y i s a f u n c t i o n o f r a d i a l  distance.  When d i s t a n c e i s measured i n terms o f t r a v e l  time,  t h e r e s h o u l d n o t be a sharp d i s c o n t i n u i t y , and t h e residential  d e n s i t y should be r e p r e s e n t e d  by a smoother  profile. H y p o t h e s i s 3:  x measured i n t r a v e l time w i l l g i v e a b e t t e r f i t (as 2 e v i d e n c e d by a h i g h e r R ) t o t h e d a t a than x measured in radial  Reasons:  distance.  I t seems r e a s o n a b l e t o assume t h a t r e s i d e n t i a l  location  d e c i s i o n s a r e made on t h e r e l a t e d bases o f a c c e s s i b i l i t y and  travel costs.  Housing demand i s d i r e c t l y r e l a t e d  to a c c e s s i b i l i t y and i n v e r s e l y r e l a t e d t o t r a v e l Since t r a v e l  costs.  time i s p r o b a b l y a b e t t e r measure o f t r a v e l  c o s t and o f a c c e s s i b i l i t y than r a d i a l d i s t a n c e , i t s h o u l d be a b e t t e r p r e d i c t o r o f d e n s i t y .  21  H y p o t h e s i s 4: Reasons:  R 1.  f o r the model should  d e c l i n e over time.  Decline  i n the r e l a t i v e dominance of the GBD:  CBD  been the major employment c e n t e r .  has  The  Since  the j o u r n e y to work i s the most r e c u r r e n t t r a v e l movement of a l l the d a i l y t r i p s , r e s i d e n c e s be l o c a t e d around the CBD.  tend  I t i s o f t e n assumed  t h a t r e s i d e n t i a l l o c a t i o n i s the r e s u l t of  the  attempt to minimize the l e n g t h of the j o u r n e y work, and curred.  therefore  to  the c o s t s of work t r a v e l i n -  However, the CBD  importance as a c e n t e r a t t r a c t o r of t r i p s .  to  has  declined i n r e l a t i v e  of economic a c t i v i t y  It follows that  residential  l o c a t i o n d e c i s i o n s are l e s s i n f l u e n c e d by ease of access to the CBD, connected w i t h the CBD  and  other  and  the  factors  not  w i l l be more i n f l u e n t i a l  i n d e t e r m i n i n g the d e n s i t y at which development takes 2.  place.  R i s e of m o b i l i t y i n a l l d i r e c t i o n s :  The  a v a i l a b i l i t y of p r i v a t e automobiles has personal  t r a v e l from dependence on the  t r a n s i t network. centers  Decline  freed primary  Residences, workplaces and  can be l o c a t e d away from the major  portation -'''3.  increasing  shopping  trans-  routes.  i n the r e l a t i v e importance of  c o s t through time:  Transportation  has  transportation tended  to  22  become a l e s s and l e s s s i g n i f i c a n t  f a c t o r i n determining  p e r s o n a l c h o i c e o f the type and l o c a t i o n o f r e s i d e n c e . T h i s may be due to r i s i n g m o b i l i t y caused by the i n c r e a s i n g use o f automobiles, t h e d e c e n t r a l i z a t i o n o f employment, shopping and r e c r e a t i o n a l  opportunities,  and t h e marked i n c r e a s e i n the c o s t of a v a i l a b l e modation i n r e c e n t y e a r s .  These f a c t o r s have a c t e d t o  reduce t h e t r a n s p o r t a t i o n c o s t s a v i n g s p o s s i b l e s e l e c t i n g one l o c a t i o n over  acco-  from  another.  A d e c l i n e i n the importance  of a c c e s s i b i l i t y  to the CBD and the q u a l i t y o f t r a n s p o r t a t i o n i n g e n e r a l i n l o c a t i o n d e c i s i o n s should l e a d t o a d e n s i t y p a t t e r n l e s s and l e s s i n f l u e n c e d by these f a c t o r s . result  T h i s would  i n a d e n s i t y d i s t r i b u t i o n l e s s conforming t o  C l a r k ' s "law", which would be evidenced by more d i s p e r s e d p a t t e r n o f d a t a i n the model. a lower R  Thus, we would  over time.  H y p o t h e s i s 5:  A should d e c l i n e over time f o r Vancouver.  Hypothesis 6:  b should d e c l i n e over time f o r Vancouver.  Reasons:  1.  C l a r k ' s e m p i r i c a l f i n d i n g s show t h a t these two parameters  2.  expect  d e c l i n e through time f o r many c i t i e s .  I n Vancouver,  as i n a l l major c i t i e s ,  f a c i l i t i e s have improved sequence,  over time.  transportation  As a con-  d i s t a n t i i l o c a t i o n s have become more a c c e s s i b l e  r e l a t i v e to c e n t r a l l o c a t i o n s , and so p e o p l e have tended t o s e t t l e i n p l a c e s o t h e r than the c e n t r a l a r e a .  Greater  e f f i c i e n c y i n t r a n s p o r t a t i o n has  caused  a d e c l i n e i n t h e r e l a t i v e importance of t r a n s p o r t c o s t as compared t o o t h e r l o c a t i o n a l c o n s i d e r a t i o n s , as w e l l as the r e l a t i v e advantage  o f one l o c a t i o n  over another i n v a r i o u s s e c t i o n s of t h e c i t y .  24  B.  In t h i s The  source  Methodology  s e c t i o n we s h a l l focus on t h e procedure o f t h e study.  of data and i t s p o s s i b l e weaknesses, t h e method o f a g g r e -  g a t i n g t h e data and i t s j u s t i f i c a t i o n w i l l be d i s c u s s e d  i n turn.  Measures o f A c c e s s i b i l i t y The and  u n i t of observation  study  i s t h e census  tract,  d i s t a n c e i n t h e model i s taken from t h e census t r a c t ' c e n t r o i d  to t h e c i t y c o r e . logical, and  for this  However, d i s t a n c e may be e i t h e r s p a t i a l o r psychorV  so measurement i s made w i t h r e s p e c t  travel  time.  to b o t h r a d i a l  distance  ( S i n c e t h e dominant mode o f t r a n s p o r t a t i o n i n  Vancouver i s t h e auto, " t r a v e l  t i m e " i s measured by automobile  travel  t ime.) Data Source The model i n v o l v e s two v a r i a b l e s : " distance  ( r a d i a l d i s t a n c e or t r a v e l  time).  by t a k i n g t h e t o t a l p o p u l a t i o n count.'of t o t a l area. represents  p o p u l a t i o n d e n s i t y and The former i s c a l c u l a t e d  a census t r a c t  I t should be borne i n mind t h a t t h e v a l u e t h e gross r e s i d e n t i a l  d i v i d e d by i t s obtained  d e n s i t y of t h e census t r a c t .  The  d i s t a n c e "as t h e crow f l i e s " from t h e c i t y c e n t e r i s taken from t h e census t r a c t map.  The census s t a t i s t i c s o f 1956,  census t r a c t maps o f 1961  1961,  1966 and 1971,  ( f o r s t a t i s t i c s o f 1956 and 1961)  and t h e  and 1971  (for  ( f o r s t a t i s t i c s of 1966 c i t y c e n t e r f o r 1966 Map  o f 1968  Map  o f 1961.  and 1971)  and 1971  and t h a t f o r 1956  1  are used.  The d r i v i n g time from the  i s t a k e n from the T r a v e l Time I s o l i n e s and 1961  i s t a k e n from the T r a v e l Time  2  Data Weaknesses The d a t a used have some weaknesses: census t r a c t s v a r y c o n s i d e r a b l y .  F i r s t , the s i z e s o f the  They a r e s m a l l a t the c i t y c e n t e r ,  but become l a r g e towards the p e r i p h e r y .  Second, measurement of r a d i a l  d i s t a n c e i s made from t h e c i t y c e n t e r to the c e n t r o i d of t h e census t r a c t concerned. determined  However, the l o c a t i o n of census t r a c t c e n t r o i d s are  by i n t u i t i v e judgment.  Third, i n this'study research i s  not done t o l o c a t e the e x a c t c i t y c e n t e r .  I t i s taken t o be  G r a n v i l l e - G e o r g i a i n t e r s e c t i o n , which i s g e n e r a l l y agreed " h i g h - v a l u e c o r n e r " or the c e n t e r of the CBD.  the  to be  the  There has been debate  on the method o f l o c a t i n g the c i t y c e n t e r e x a c t l y .  However, i t has  been shown by Genest t h a t the e x a c t c e n t e r does not  significantly  3• a f f e c t t h e q u a l i t y o f the model . , and the s e a r c h f o r i t i s t h e r e f o r e not a w o r t h w h i l e u n d e r t a k i n g .  F o u r t h , the t r a v e l time from the c e n t e r  t o the census t r a c t i s an a p p r o x i m a t i o n , s i n c e t r a v e l - t i m e study were not always the same as the census y e a r s .  years  A l s o , we assume t h a t  t h e r e were no major changes i n t h e road network i n the census y e a r s from w h i c h the r e s p e c t i v e T r a v e l Time maps a r e adopted. M a n i p u l a t i o n o f Data A n a l y s e s are made f o r f o u r g e o g r a p h i c a l set-ups  (rings,  lines,  p i e - s l i c e s , and b a n d s ) , two measures of d i s t a n c e ( r a d i a l d i s t a n c e and  t r a v e l t i m e ) and f o u r p o i n t s i n time (1956, 1961, 1966 and 1971). l a t i o n d e n s i t y o f t h e f o u r types o f g e o g r a p h i c a l set-ups  Popu-  a r e aggregated  as f o l l o w s : 1)  Rings:  The whole m e t r o p o l i t a n a r e a o f G r e a t e r Vancouver i s d i v i d e d  i n t o r i n g s a t each m i l e from t h e c i t y c e n t e r  (Diagram 1 ) .  Population  d e n s i t y f o r each r i n g i s p l o t t e d a g a i n s t t h e d i s t a n c e o f t h e i n n e r r i n g boundary and a g a i n s t t r a v e l time from t h e c e n t e r .  (The r i n g boundary  i s used i n t h e study r a t h e r than t h e mean d i s t a n c e o f each r i n g as suggested by C l a r k , s i n c e t h e d i s t a n c e between t h e s u c c e s s i v e  intervals  of t h e r i n g boundary and t h e mean d i s t a n c e o f each r i n g i s e q u a l . ) P o p u l a t i o n d e n s i t y o f each r i n g i s found by a g g r e g a t i n g  the population  counts o f a l l t h e census t r a c t s t h a t f a l l w i t h i n t h e l i m i t , d i v i d e d by t h e i r t o t a l areas. 1971 2)  D e n s i t y p l o t t i n g o f r i n g s i s done f o r 1966 and  only. Lines:  S t r a i g h t l i n e s a r e drawn from t h e c e n t e r towards e a s t  and s o u t h t o t h e p e r i p h e r y  (Diagram 2 ) .  The l i n e s so drawn a r e a l o n g  Broadway and G r a n v i l l e S t r e e t s , w h i c h a r e two o f t h e major arteries  i n Vancouver.  primary  The r a d i a l d i s t a n c e f o r each t r a c t t h a t  falls  on t h e l i n e s i s taken from t h e c e n t r o i d o f t h e t r a c t t o t h e c i t y  center,  and p o p u l a t i o n d e n s i t y i s p l o t t e d a g a i n s t t h i s r a d i a l d i s t a n c e .  It is  also plotted against t r a v e l 3)  Pie slices:  time.  S e c t o r s a r e drawn a l o n g H a s t i n g s  and G r a n v i l l e a t some  a n g l e a t t h e c e n t e r t o i n c l u d e a c o n s i d e r a b l e p o r t i o n o f t h e metrop o l i t a n a r e a i n t h e e a s t and s o u t h d i r e c t i o n s (Diagram 3 ) .  Density,  p l o t t i n g i s done f o r each i n d i v i d u a l census t r a c t a g a i n s t d i s t a n c e and  27  t r a v e l time from the t r a c t c e n t r o i d t o the c i t y c e n t e r . 4)  Bands:  Bands are drawn a l o n g H a s t i n g s and G r a n v i l l e :  band between H a s t i n g s and Broadway, and with G r a n v i l l e troid  i n the middle  (2)  (Diagram 4 ) .  (1)  one band of one-mile Any  width  census t r a c t whose cen-  f a l l s w i t h i n the boundary o f the band i s i n c l u d e d ; and  plotting  one  the same  i s done as f o r m e r l y . S i n c e an o b j e c t i v e of the study i s t o observe  the changes i n  r e s i d e n t i a l spread b e f o r e and a f t e r the c o n s t r u c t i o n of the b r i d g e s and highways, the census years of 1956 as c l o s e s t  and  1961,  which are c o n s i d e r e d  to the dates of the c o n s t r u c t i o n , are chosen.  computed f o r these y e a r s can be compared w i t h . t h o s e years.  In t h i s way,  we  The  statistics  of the l a t e r  can see the changes i n the r e s i d e n t i a l  census  spread  over t ime. I t i s apparent IV", Map  from the Census T r a c t Map  (See Appendix  1) t h a t a g r e a t number of the t r a c t s have undergone r e d i s t r i c t i n g s  and boundary changes through 1971  of 1961  (See Appendix IV, Map  census t r a c t s had  The  Census  2) shows a more r e f i n e d  the same boundaries  s u b d i v i d e d i n 1966. Granville  the decade.  i n 1956  and  T r a c t Map  breakdown. 1961;  of The  and they were  P i e - s l i c e s e c t o r s and bands along H a s t i n g s  are drawn on the Census T r a c t Map  that f a l l w i t h i n the boundary a r e  of 1961.  The  census  and tracts  taken.  J u s t i f i c a t i o n . " f o r the use aft.gross r e s i d e n t i a l d e n s i t y and v a r i o u s geographical  set-ups  The g r o s s r e s i d e n t i a l d e n s i t y measure i s much s i m p l e r than t h a t of the o t h e r l a n d use d a t a , such as the net r e s i d e n t i a l d e n s i t y  28  or f l o o r - s p a c e d e n s i t y , and i s used "because t h e d a t a a r e more r e a d i l y  \  a v a i l a b l e , and t h e q u a l i t y i s s u f f i c i e n t l y c l o s e t o t h a t o f n e t r e s i d e n t i a l 4 density. The use o f l i n e s , s e c t o r s , and bands has a f a i r l y s t r a i g h t - f o r w a r d rationale.  A r e l a t i v e l y s m a l l sample  i s i n v o l v e d i n t h e use of l i n e s ,  w h i c h may a c c i d e n t a l l y pass t h r o u g h t h e r e g i o n a l c e n t e r s o f h i g h popul a t i o n d e n s i t y and t h e r e f o r e b i a s e s t h e r e s u l t s .  However, t h e l i n e V  may s e r v e as a y a r d s t i c k a g a i n s t t h e improvement, o r l a c k t h e r e o f , of the s t a t i s t i c s computed i n t h e l a r g e r samples used i n t h e case of p i e - s l i c e s e c t o r s and bands. The p i e - s l i c e s e c t o r s and bands e n l a r g e t h e sample, and more a c c u r a t e e s t i m a t e s o f t h e parameters would presumably be o b t a i n e d . The p i e - s l i c e s e c t o r i n c l u d e s i n i t s sample an a p p r o x i m a t e l y  equal  number o f t r a c t s a t t h e c e n t e r and a t t h e p e r i p h e r y , s i n c e t h e t r a c t s at t h e c e n t e r a r e s m a l l , and those i n t h e o u t l y i n g a r e a s l a r g e r .  The  use o f s e c t o r s may average out t h e e f f e c t s o f t h e c o n t r i b u t i o n of high population concentrations to the density gradient.  The t h e o r e t i c a l  c e n t r a l d e n s i t y i s , f o r t h e p i e - s l i c e s e c t o r s and l i n e s , a v a l u e obtained f o r a point at the center.  On t h e o t h e r hand, bands would i n c l u d e  r e l a t i v e l y more t r a c t s a t t h e c e n t e r and fewer a t t h e p e r i p h e r y .  The c e n t r a l  d e n s i t y e s t i m a t e i s then found n o t f o r a s i n g l e p o i n t , b u t f o r a band o f some w i d t h . I t i s i n t e r e s t i n g t o f i n d hhw. t h e v a r i o u s g e o g r a p h i c a l s e t ups would g i v e an e s t i m a t e o f t h e c e n t r a l d e n s i t y and how t h e d e n s i t y g r a d i e n t i n t h e model d i f f e r s a c c o r d i n g t o t h e u s e of t h e s e set-ups.  geographical  29  30  Footnotes 1.  T r a v e l Time Map, GVRD, Summer 1968  2. Dynamics o f R e s i d e n t i a l Land S e t t l e m e n t , Lower M a i n l a n d R e g i o n a l P l a n n i n g Board o f B.C., Supp. Study 2 t o Land f o r L i v i n g , 1963 3. 4.  B-A. Genest, op. c i t . , p. 14 Ibid.  34  CHAPTER IV  ANALYSIS OF DATA  A.  The model we  employed i n the study i s e m p i r i c a l by n a t u r e  s t a t i s t i c a l by d e s i g n ; (For a g e n e r a l  D e s c r i p t i o n of Graphs  and  the method of a n a l y s i s i s by  simple  and  regression.  d e s c r i p t i o n of r e g r e s s i o n a n a l y s i s , see Appendix  I.)  Computation of r e g r e s s i o n a n a l y s i s f o r the study i s by means of the SPSS ( S t a t i s t i c a l Package f o r the S o c i a l S c i e n c e s ) package of the U n i v e r s i t y of B r i t i s h  Columbia.  computer  '(;Eor^graphs, see Appendix t l )  Graphs 1 & 2 The  graphs of 1966  scatter points. to Ring 5.  and  Population  1971  show a f l u c t u a t i n g p a t t e r n  d e n s i t y d e c l i n e s g r a d u a l l y from Ring 1  These r i n g s i n c o r p o r a t e m o s t l y t r a c t s of the C i t y of  Vancouver, the d e n s i t y o f which a r e c o m p a r a t i v e l y  higher  than  r e s t of the o t h e r m u n i c i p a l i t i e s , i n d i c a t i n g a " c r e s t " at the The  of  r i n g which i s next h i g h e s t  the center.  i n d e n s i t y i s composed of census t r a c t s  of Coquitlam, Richmond, and New  Westminster  t h r e e major urban  centers.  Graphs 3 & 4 Density  p l o t t i n g of 1966  t r a v e l time from the c i t y metropolitan  center.  r e g i o n are i n c l u d e d  and  1971  i s made w i t h r e s p e c t  to  the  A l l the census t r a c t s of the whole (151  observations).  Graphs 5 & 6 The  graphs r e p r e s e n t  along H a s t i n g s  the d e n s i t y p l o t t i n g of census t r a c t s  to the east of the r e g i o n .  A sample of 12 census t r a c t s  35  i s considered.  D e n s i t y i s h i g h e s t a t the c e n t e r ; Burnaby has a r e l a t i v e l y  h i g h e r d e n s i t y i n one o f t h e t r a c t s w i t h i n i t s m u n i c i p a l i t y . f l u c t u a t e s i n P o r t Moody, P o r t C o q u i t l a m  The d e n s i t y  and C o q u i t l a m .  I n g e n e r a l , d e n s i t y d e c l i n e s w i t h d i s t a n c e from t h e c e n t e r , but not u n i f o r m l y .  There i s a sharp d i s c o n t i n u i t y a t some census t r a c t s  i n t h e Burnaby m u n i c i p a l i t y , w h i c h may be due t o t h e v a c a n t  developable  l a n d o f t h e Burnaby Park. Graphs 7 & 8 Three c l u s t e r s o f d a t a p o i n t s a r e apparent from t h e graphs f o r the s o u t h e r l y p o r t i o n o f t h e r e g i o n .  The census t r a c t s a t t h e c e n t e r  undoubtedly occupy t h e h i g h e s t d e n s i t y w i t h t h a t o f Richmond next i n magnitude and D e l t a s t i l l n e x t .  Richmond has been growing a t a sub-  s t a n t i a l and steady pace i n p o p u l a t i o n and i n d u s t r y i n t h e p a s t decade. D e l t a has r e c e n t l y e x p e r i e n c e d  t h e f a s t e s t growth among t h e m u n i c i p a l i t i e s  i n Canada, y e t i t b e l o n g s t o t h e l o w e s t d e n s i t y c a t e g o r y Vancouver.  i n metropolitan  D e l t a i s made up o f f i v e g e o g r a p h i c a l l y d i s t i n c t  areas:  the r e s i d e n t i a l communities o f South D e l t a (Tsawwassen), Ladner and N o r t h D e l t a , t h e a g r i c u l t u r a l l a n d s , and t h e A n n a c i s I s l a n d i n d u s t r i a l . 2 estate. Graphs 9 - 1 2 These graphs show t h e d e n s i t y p l o t t i n g a g a i n s t t r a v e l t i m e i n the e a s t and south d i r e c t i o n s f o r b o t h census y e a r s Approximately  t h e same p a t t e r n o f d i s p e r s i o n o f d a t a p o i n t s i s d e p i c t e d  when compared t o t h e c o r r e s p o n d i n g distance.  1966 and 1971.  density p l o t t i n g against  radial  Graphs 13 & 14 The  graphs show t h e d e n s i t y p l o t t i n g o f t h e census t r a c t s  of t h e p i e - s l i c e a l o n g Hasings a g a i n s t r a d i a l d i s t a n c e . The d a t a p o i n t s a r e c l u s t e r e d about t h e r e g r e s s i o n l i n e . No sharp d i s c o n t i n u i t y i s apparent i n Burnaby.  A census t r a c t i n P o r t C o q u i t l a m a t  some 17 m i l e s from t h e c i t y c e n t e r r e c o r d s t h e lowest  density.  The  d a t a p o i n t s become more d i s p e r s e d from 1966 t o 1971 as e v i d e n c e d 2 by t h e d e c r e a s i n g  R .  Graphs 15 & 16 The  p i e - s l i c e s e c t o r o f t h e south i s w e l l marked by t h r e e  c l u s t e r s o f p o i n t s f o r t h e year 1966.  There i s some d i s c o n t i n u i t y  i n t h e s c a t t e r i n g o f d a t a p o i n t s a t about s i x m i l e s from t h e c e n t e r . The  sampled census t r a c t s i n Richmond and D e l t a have r e l a t i v e l y low  density.  However, d e n s i t y i n c r e a s e s c o n s i d e r a b l y i n D e l t a from 1966  t o 1971. Graphs 17 & 18 The way i n w h i c h t h e c l o u d of d a t a p o i n t s i s s c a t t e r e d f o r the p i e - s l i c e s e c t o r a l o n g H a s t i n g s  u s i n g t r a v e l time as a parameter  i s more o r l e s s t h e same as compared t o t h a t when r a d i a l i s used.  distance  The d a t a p o i n t s a r e c l u s t e r e d r e l a t i v e l y c l o s e t o the r e g r e -  s s i o n l i n e f o r 1966. They become more d i s p e r s e d t h r o u g h t h e y e a r s . The  sampled census t r a c t s o f P o r t C o q u i t l a m a t about 50 m i n u t e s '  d r i v i n g time from t h e c e n t e r r e c o r d s  the lowest  density.  Graphs 19 & 20 There i s more compact s c a t t e r i n g o f d a t a p o i n t s f o r t h e p i e s l i c e s e c t o r i n the south.  No d i s c o n t i n u i t y i s apparent i n t h e  37  r e g r e s s i o n l i n e a t about 20 t o 25 m i n u t e s ' d r i v i n g time from t h e c e n t e r , where t h e n o r t h arm o f t h e F r a s e r R i v e r i s l o c a t e d .  Two  census t r a c t s i n Richmond r e c o r d r e l a t i v e l y low d e n s i t y . Graphs 21 $ 22 The p l o t t i n g o f r e s i d e n t i a l d e n s i t y i n t h e band between Hastings  and Broadway a g a i n s t r a d i a l d i s t a n c e i n v o l v e s 19 o b s e r v a t i o n s .  The number o f census t r a c t s i n c l u d e d i n t h e band i s o b v i o u s l y l e s s than t h a t o f t h e p i e - s l i c e s e c t o r .  As seen from t h e s c a t t e r i n g  of d a t a p o i n t s , t h e d e n s i t y p a t t e r n has changed c o n s i d e r a b l y over the y e a r s a t 10 m i l e s from t h e c e n t e r t o t h e p e r i p h e r y .  The d e n s i t y  of t h e census t r a c t s of C o q u i t l a m ,  Coquitlam  F o r t Moody, and P o r t 2  i s h i g h e r i n 1971 than i n 1961. The R  o b t a i n e d i s l o w e r than i t s  corresponding  p i e - s l i c e s e c t o r v a l u e u s i n g r a d i a l d i s t a n c e as  a parameter.  The d a t a p o i n t s a l s o show more d i s p e r s i o n over time.  Graphs 23 $ 24 The  graphs o f t h e band t o t h e south f o r b o t h y e a r s show a 2 continuous f a l l - o f f o f d e n s i t y a g a i n s t r a d i a l d i s t a n c e . The R value f o r both years are i n s i g n i f i c a n t . Graphs 25 $ 26 2 The R  v a l u e s drop o f f c o n s i d e r a b l y from 1966 t o 1971 f o r  the band t o t h e east u s i n g t r a v e l time as a parameter. i n c r e a s e s a t some 20 m i n u t e s ' d r i v i n g to t h e p e r i p h e r y .  Density  time from t h e c e n t e r outwards  One census t r a c t i n each o f Burnaby and P o r t  C o q u i t l a m has v e r y low d e n s i t y .  The Burnaby t r a c t c o n t a i n s v a c a n t  38  'land around C e n t r a l Park.  The  d a t a p o i n t s a l s o show a c o n s i s t e n t 2  p a t t e r n of i n c r e a s i n g d i s p e r s i o n o v e r time.  The R  f o r the  u s i n g t r a v e l time as a parameter i s h i g h e r than the  regression  corresponding  value using r a d i a l distance. Graphs 27 & 28 2  For the band t o the s o u t h , the R  values  are v e r y much h i g h e r  when the model i s r e g r e s s e d upon t r a v e l ' i t i m e than.>when r a d i a l "is used.  distance  Two c l u s t e r s of data p o i n t s are apparents i n the graphs.  D e n s i t y i s h i g h e s t around the c i t y c o r e from 2 t o 8 m i n u t e s ' time from the Genter.  The  driving  second b u n d l e of d a t a p o i n t s , r e l a t i v e l y  lower i n d e n s i t y , c o n s i s t s of t r a c t s t h a t are 15 t o 22 m i n u t e s from the c e n t e r , w h i c h c o r r e s p o n d s to about 4 m i l e s i n r a d i a l d i s t a n c e . The  d e n s i t y p a t t e r n shows g r e a t v a r i a b i l i t y .  I t fluctuates  consider-  a b l y ; t h e r e are d a t a p o i n t s t h a t have d i f f e r e n t l e v e l s of d e n s i t y at the same t r a v e l time from the  center.  Graphs 29 & 30 The p i e - s l i c e s e c t o r a l o n g H a s t i n g s 1961  f o r the y e a r s 1956 and 2  a l s o show a c o n s i s t e n t p a t t e r n of d e c r e a s i n g R  values  through 2  time.  I t i s a r e l a t i v e l y b e t t e r f i t f o r the former y e a r (R =  0.80); 2  however, the l a t t e r y e a r a l s o g i v e s some support f o r the model (R = 0.55).  The  sampled census t r a c t s show h i g h e r d e n s i t y around the  c o r e , d r o p p i n g o f f w i t h d i s t a n c e from the c e n t e r .  city  A t r a c t i n Burnaby  at about 9 m i l e s from the core drops o f f i n d e n s i t y t h r o u g h the w h i l e Port Coquitlam increases i n d e n s i t y considerably.  The  years,  data  39  p o i n t s a r e c l u s t e r e d about t h e r e g r e s s i o n l i n e from t h e core t o about seven m i l e s o u t , and become more d i s p e r s e d towards t h e p e r i phery. Graphs 31 & 32 SomeaaiLscoMinui'tyii'h' thetsGateteringiof d a t a a p o i n t s .. i s d e p i c t e d a t t h e n o r t h arm o f t h e F r a s e r f o r the p i e - s l i c e s e c t o r along G r a n v i l l e .  A t r a c t a t about 11 m i l e s from t h e c e n t e r  falls  2 off  i n d e n s i t y n o t i c e a b l y from 1956 t o 1961.  decrease through  The R  values  slightly  time.  Graphs 33 & 34 The d e n s i t y p l o t t i n g f o r t h e band t o t h e e a s t f o r b o t h y e a r s 1956 and 1961 show a r e g u l a r r e l a t i o n s h i p betweeen d e n s i t y and d i s t a n c e .  Data p o i n t s a r e r e l a t i v e l y more d i s p e r s e d u i n Burnaby, 2  Coquitlam  and P o r t C o q u i t l a m .  R  decreases  over  time.  Graphs 35 & 36 For t h e band t o t h e s o u t h , t h e graphs show t h a t t h e r e i s a sharp break i n t h e s c a t t e r i n g of d a t a p o i n t s a t t h e n o r t h s o f t h e F r a s e r f o r t h e y e a r s 1956 and 1961.  A census t r a c t a t t h e  p e r i p h e r y almost doubles i n d e n s i t y through t h e census y e a r s . The R  2  v a l u e i s h i g h e r f o r 1956 (0.64) than f o r 1961 (0.46).  Graphs 37 & 38 When t h e l o g d e n s i t y i s p l o t t e d a g a i n s t t r a v e l time f o r t h e p i e - s l i c e s e c t o r a l o n g H a s t i n g s , d e n s i t y drops o f f c o n s i d e r a b l y i n the census t r a c t s from 19 t o 27 m i n u t e s ' d r i v i n g time from t h e c e n t e r . I t i s f a i r t o say t h a t t h e r e i s more v a c a n t d e v e l o p a b l e naby, w h i c h s h o u l d account f o r t h e low average d e n s i t y . z.  :  * t t o ;_!>- d a f a  s  .1° <»v;/  land i n BurThe model  i s a 'good f i t to t h e data, as evidenced between the l o g o f d e n s i t y and t r a v e l  by a c o n s i s t e n t r e l a t i o n s h i p  time.  Graphs 39 & 40 These graphs show t h e p l o t t i n g o f l o g of. d e n s i t y a g a i n s t time f o r t h e p i e - s l i c e s e c t o r t o t h e south.  Density  travel  drops o f f f o r  the census t r a c t s a t the immediate v i c i n i t y of t h e water b o d i e s ,  continues  2 to decrease i n Richmond, but r i s e s a g a i n i n S t e v e s t o n . 1956 and 1961 a r e lower than t h e i r c o r r e s p o n d i n g i s regressed  The R 's f o r  v a l u e s when t h e model  upon r a d i a l d i s t a n c e , a f i n d i n g c o n t r a r y t o e x p e c t a t i o n .  Graphs 41 & 42 In t h e band to t h e east f o r 1956 and 1961, the graph u s i n g time shows r o u g h l y distance.  t h e same p a t t e r n o f s c a t t e r as t h a t u s i n g  travel  radial  Data p o i n t s f l u c t u a t e c o n s i d e r a b l y a t about 25 t o 45 minutes'  2 time from the c e n t e r .  The model a l s o shows a d e c r e a s i n g  R  over time.  Graphs 43 & 44 The the south  graphs of d e n s i t y a g a i n s t t r a v e l time f o r t h e band t o  show t h a t d e n s i t y drops o f f c o n t i n u o u s l y  from t h e c i t y  center  2 outwards.  R  decreases through time; i t i s 0.57 and 0.43 f o r 1956 and  1961 r e s p e c t i v e l y .  B.  Hypotheses D i s c u s s e d  Hypothesis 1 R e s i d e n t i a l d e n s i t y to t h e south of t h e CBD f a l l s more s t e e p l y than t h a t t o the e a s t . Results: For the h y p o t h e s i s t o he confirmed,  the b v a l u e i n the model  -bx (D e ) f o r the cases c o n s i d e r e d i n the south s h o u l d be l a r g e r o f o r the east. were computed.  than  Data was a n a l y z e d f o r f o u r census y e a r s and t h e b v a l u e s These a r e l i s t e d  i n Table  (1) a l o n g w i t h the r e l e v a n t  2 R  and the A v a l u e s o b t a i n e d from the r e g r e s s i o n e q u a t i o n s .  Tab"le (1) A & b and t h e r e l e v a n t R v a l u e s o f the model f o r v a r i o u s g e o g r a p h i c a l set-ups of the f o u r census y e a r s u s i n g r a d i a l d i s t a n c e ; and t h e i r c o r r e s p o n d i n g v a l u e s f o r t r a v e l time i n p a r e n t h e s i s Geographical set-ups  1956 _  _  S e c t o r , S.  9.94927 (10/7,697,6)  0.11472 (0.13485)  0.67279 (0.57734)  S e c t o r , E.  9.49519 (10.38463)  0.06640 (0.09815)  0.55393 (0.77662)  Band, S.  9.82152 (10.25926)  0.10423 (0.10467)  0.64310 (0.57180)  Band, E.  9.63216 (10.15263)  0.08405 (0.09559)  0.83600 (0.73655)  10.33737 (11.35954)  0.11730 (0.14123)  0.63460 (0.48898)  S e c t o r , E.  9.73567 (10.21197)  0.07428 (0.08117)  0.80048 (0.71855)  Band, S.  9.63519 £ (9.97566)  0.07486 (0.07699)  0.45852 (0.42761)  Band, E.  9.58201 (9.99301)  0.06982 (0.07835)  0.77033 (0.66084)  1961 S e c t o r , S.  1966 L i n e , S.  9.66111 (10.24456)  0.28895 (0.09650)  0.54199 (0.45645)  L i n e , E.  9.84693 (10.35397)  0.24061 (0.08934)  0.71590 (0.70386)  S e c t o r , S.  9.85094 (10.65679)  0.25702 (0.09359)  0.43456 (0.48201)  S e c t o r , E.  9.84228 (10.40791)  0.22191 (0.08326)  0.66800 (0.65105)  Band, S.  9.54759 (10.57283)  0.16530 (0.08065)  0.17092 (0.59724)  Band, E.  9.38258 (9.84140)  0.14716 (0.05737)  0.62008 (0.65125)  L i n e , S.  9.44072 (9.92064)  0.23078 (0.07769)  0.40133 (0.34340)  L i n e , E.  9.45773 (9.82351)  0.18097 (0.06660)  0.58316 (0.56324)  S e c t o r , S.  8.95351 (10.37837)  0.08114 (0.07684)  0.35411 (0.39530)  S e c t o r , E.  9.59935 (10.24331)  0.17807 (0.06994)  0.51984 (0.55583)  Band, S.  9.62282 (10.63269)  0.17242 (0.08287)  0.18107 (0.52402)  Band, E.  9.28304 (9.64117)  0.10425 (0.04143)  0.43038 (0.43859)  1971  The h y p o t h e s i s i s g e n e r a l l y c o n f i r m e d .  I n a l l h u t one case  ( S e c t o r , S., 1971), t h e b v a l u e t o t h e s o u t h i s l a r g e r than t o t h e e a s t by 10 t o 50 p e r c e n t .  The c o e f f i c i e n t s of d e t e r m i n a t i o n o b t a i n e d  f o r over 50 p e r c e n t of the v a r i a b i l i t y f o r 13 cases out o f 20.  account Since the  b v a l u e s f o r t h e s o u t h a r e g e n e r a l l y l a r g e r than f o r t h e e a s t , we  suggest  t h a t t h e d i f f e r e n c e i n d e n s i t y i n v a r i o u s d i r e c t i o n s o f t h e c i t y i s due m a i n l y t o t h e age o f r e s i d e n t i a l a c t i v i t y r a t h e r than t o t h e t r a n s p o r t factor.  43  Hypothesis 2 There w i l l be a sharp d i s c o n t i n u i t y i n t h e s c a t t e r i n g o f d a t a p o i n t s a t s i x m i l e s south o f t h e c i t y c e n t e r where t h e n o r t h arm o f t h e Fraser River i s located. Results:  The h y p o t h e s i s i s n o t e n t i r e l y c o n f i r m e d , s i n c e t h e s c a t t e r i n g of d a t a p o i n t s i s s e n s i t i v e t o t h e way they a r e a g g r e g a t e d ;  i . e . , different  g e o g r a p h i c a l s e t - u p s may show d i f f e r e n t p a t t e r n s o f the d i s p e r s i o n o f d a t a p o i n t s even f o r t h e same s e c t i o n o f t h e c i t y .  However, when  d i s t a n c e i s measured i n terms o f t r a v e l t i m e , t h e r e i s almost no d i s continuity.  (For r a d i a l d i s t a n c e , see graphs 7, 8, 1 5 , 16, 23, 24, 31,  32, 35, 36; and f o r t r a v e l t i m e , see graphs 1 1 , 1 2 , 19, 20, 27, 28, 39, 40, 43, 44>)  44  Hypothesis 3 T r a v e l time would g i v e a b e t t e r f i t to the model than radial  distance.  Results: The h y p o t h e s i s  i s not confirmed,  s i n c e o n l y 7 out o f 20  2 cases used.  (35.0 p e r c e n t )  have R  The r e s u l t s a r e l i s t e d  higher  than when r a d i a l d i s t a n c e i s  i n Table  (2) a l o n g w i t h  ponding A and b v a l u e s . Ttib']?e!_(?2) R f o r the model when r e g r e s s e d distance 2 Geographical R ( T r a v e l time) set-ups V  2  1956 S e c t o r , S. S e c t o r , E. Band, S.  *  upon t r a v e l time and r a d i a l 2 R (Radial distance)  0.57734  0.67279  0.77662  0.55393  0.57180  0.64310  0.73655  0.83600  0.48898  0.63460  0.71855  0.80048  0.42761  0.45852  0.66084  0.77033  0.45645  0.54199  0.70386  0.71590  0.48201  0.43456  Band, E. 1961 S e c t o r , S. S e c t o r , E. Band, S. Band, E. 1966 L i n e , S. L i n e , E. S e c t o r , S. S e c t o r , E. sector,^:  the c o r r e s -  0.65105  0.66800  Band, S i '  0.59724  u.aoauu  Band, E.  0.62125  0;17092 0.62008  1971 L i n e , S.  0.34340  0;40133  L i n e , E.  0.56324  0.58316  S e c t o r , S.  0,39530  0.35411  distance  S e c t o r , E.  0.55583  0.51984  Band, S. *  0.39530  0.35411  Band, E. *  0.43859  0.43038 2  The g e o g r a p h i c a l  set-ups w i t h a s t e r i s k s have R  higher f o r  the model when i t i s r e g r e s s e d upon, t r a v e l time t h a n a g a i n s t distance.  radial  Hypothesis  4  2 R  i n t h e model s h o u l d d e c l i n e oyer  time.  Results: 2 There i s a c o n s i s t e n t p a t t e r n t h a t t h e R e q u a t i o n decreases  over t h e y e a r s .  f o r the l o g - l i n e a r  As t h e graphs r e v e a l e d t o u s , t h e  d a t a p o i n t s become more d i s p e r s e d through time.  T h i s p a t t e r n would  be f u r t h e r d i s p e r s e d by t h e c r e a t i o n o f t h e r e g i o n a l c e n t e r s i n t h e 2 future.  The R. v a l u e s o f v a r i o u s g e o g r a p h i c a l set-ups of t h e f o u r  census y e a r s a r e p r e s e n t e d  i n T a b l e (3) when x i n t h e model i s  measured i n terms o f r a d i a l d i s t a n c e , and i n T a b l e measured i n terms o f t r a v e l GT ae bo lg er a p(h3i)c:a lR ; «set-ups  (4) when x i s  time.  2 f o r t h e model when r e g r e s s i n g upon r a d i a l d i s t a n c e 1956 1961 1966 1971  East Line  0.71590  0.58316  Sector  0.80048  0.55393  0.66800  0.51984  Band  0.83600  0.77033  0.62008  0.43038  8182'/  0.6621P  0-5679?  Average South Line  0.54199  0.40133  Sector  0.67279  0.63460  0.43456  0.35411  Band  0.64310  0.45852  0.17092  0.18107  •0.65795-  0 54656  0.38249  / " a / a r e  47  T a b l e ( 4 ) : :R Geographical set-up  2  f o r t h e model when r e g r e s s i n g upon t r a v e l 1956  1961  time  1966  1971  0.70386  0.56324  East Line Sector  0.77662  0.71825  0.65105  0.55583  Band  0.73655  0.66084  0.65125  0.43859  . f,. 75659  0.68969  6587:.  Average_  "w  -:~  South Line  0.45645  0.34340  Sector  0.57734  0.48898  0.48201  0.39530  Band  0.57180  0.42761  0.59724  0.52402  . veragec.  0„574 ./-  0.4582S.  C51190  (j /• •' "  ;  r  The R 's f o r t h e GVRD when x i s measured i n terms o f r a d i a l d i s t a n c e a r e 0.56914 and 0.51460 f o r 1966 and 1971 r e s p e c t i v e l y ; and when x i s measured i n terms o f t r a v e l t i m e , they a r e 0.43245 and 0.38894. respectively.  Hypotheses 5 & 6 A & b v a l u e s i n the f i t t e d model should d e c l i n e over  time.  Results: There i s not a c o n s i s t e n t p a t t e r n t h a t A v a l u e i n the model d e c l i n e s over time. However, i n almost a decrease as time p r o g r e s s e s .  a l l c a s e s , the b v a l u e  shows  This i n d i c a t e s that population  s i t y g r a d i e n t has become f l a t t e r .  den-  The A and b v a l u e s f o r the v a r i o u s  g e o g r a p h i c a l set-ups at f o u r p o i n t s i n time when the model i s r e g r e s s e d upon r a d i a l d i s t a n c e are to be found  i n Table  ( 1 ) , page 41.  the A and b v a l u e s when the model i s r e g r e s s e d upon t r a v e l they a r e l i s t e d Table  (5)  time,  i n Table (5).  A & b v a l u e s i n the model when r e g r e s s e d upon t r a v e l  Geographical set-ups  A  1956 S e c t o r , S.  10.76976  0.13485  S e c t o r , E.  10.38463  0.09815  Band, S.  10.25926-  0.10467  Band, E.  10.15263  0.09559  S e c t o r , S.  11.35954  0.14123-'"  S e c t o r , E.  10.21197  0.08117  Band, S.  9.97566  0.07699  Band, E.  9.99301  0.07835  1966 L i n e , S.  10.24456  0.09650  L i n e , E.  10.35397  0.08934  S e c t o r , S.  10.65679  0.09359  S e c t o r , E.  10.40791  0.08326  Band, S. '  10.57283  0.08065  9.84140  0.05737  1961  Band, E.  As f o r  time  1971 Line,  S'  L i n e , E. S e c t o r , S. S e c t o r , E. Band, S. Band, E.  9.92064  0.07769  9.82351  0.06660  10.37837  0.07684  10.24331  0.06994  10.63269  0.08287  9.64117  0.04143  The r e l a t i v e i n c r e a s e i n suburban d e n s i t i e s would the b v a l u e .  lower  The r e s u l t s o b t a i n e d a r e comparable t o p r e v i o u s ex-  p e r i e n c e w i t h C l a r k ' s model.  Thus, i t seems f a i r t o c o n c l u d e t h a t  Vancouver i s s i m i l a r to o t h e r major c i t i e s  , a t l e a s t as f a r as t h e  b v a l u e i s c o n c e r n e d , and C l a r k ' s model a p p l i e s t o Vancouver well.  fairly  CHAPTER V CONCLUSION  The a p p l i c a t i o n o f t h e model t o t h e Vancouver case e n a b l e s us to h i g h l i g h t t h e n a t u r e o f t h e c i t y growth p r o c e s s , and t o o f f e r explanations f o r the population density d i s t r i b u t i o n .  I n a capsule, the  f i n d i n g s can be o u t l i n e d as f o l l o w s : J.  The d i f f e r e n t i a l r a t e s o f d e n s i t y d e c l i n e : The model i s found t o a p p l y t o t h e s o u t h and e a s t s e c t i o n s o f  the c i t y a t v a r i o u s p o i n t s i n t i m e . i s l a r g e r than t o t h e e a s t .  However, t h e b v a l u e t o t h e s o u t h  A h i g h e r b v a l u e means t h a t d e n s i t y d e c l i n e s  more s h a r p l y w i t h i n c r e a s i n g d i s t a n c e from t h e c i t y c e n t e r ; and a lower b v a l u e means t h a t d e n s i t y d e c l i n e s more s l o w l y . The d i f f e r e n t b v a l u e s o f b o t h s e c t i o n s o f the c i t y suggest  that  r e s i d e n t i a l d e n s i t y i s more a f u n c t i o n o f t h e age o f development than transport factor.  I n t h e p a s t r e s i d e n t i a l development i n t h e s o u t h h a s  been l a r g e l y r e s t r i c t e d t o t h e B u r r a r d P e n i n s u l a as a r e s u l t o f t h e water b a r r i e r s .  Though improvements i n t r a n s p o r t a t i o n o c c u r r e d i n t h e  l a t e 5 0 s , r e s i d e n t i a l b u i l d i n g a c t i v i t y has n o t been a b l e t o grow f a s t enough t o compensate f o r i t s l a t e s t a r t o f development.  For transport  to be a . r e l a t i v e l y more i m p o r t a n t f a c t o r than t h e time a t w h i c h d e v e l o p ment took p l a c e , t h e b v a l u e t o t h e s o u t h s h o u l d be s i m i l a r t o t h a t towards the e a s t when s e p a r a t i o n from the CBD i s measured i n terms of r a d i a l d i s t a n c e o r t r a v e l time.  I n f a c t t h i s i s n o t t h e case.  The h i g h e r b v a l u e t o t h e s o u t h i s a l s o a s s o c i a t e d w i t h a h i g h e r A v a l u e i n t h e model.  F o r $5 o u t o f 20 cases c o n s i d e r e d , t h e s o u t h has  51  h i g h e r imputed c e n t r a l d e n s i t y than t h e e a s t . A and b v a l u e s f o r t h e s o u t h and  concentrated  higher  i n d i c a t e t h a t d e n s i t y i s more c l u s t e r e d  between t h e c i t y c e n t e r and t h e n o r t h arm o f t h e  F r a s e r R i v e r as a r e s u l t o f t h e t o p o g r a p h i c a l 2.  The r e l a t i v e l y  T r a v e l time v s r a d i a l  restriction.  distance:  D e n s i t y i n the south seems t o respond more t o t r a v e l time than t o r a d i a l d i s t a n c e .  There i s almost no d i s c o n t i n u i t y i n t h e  s c a t t e r i n g o f d a t a p o i n t s i n t h e r e g i o n where t h e n o r t h arm o f t h e F r a s e r R i v e r i s l o c a t e d when t h e model i s r e g r e s s e d  upon t r a v e l  time.  On t h e o t h e r hand, t h e r e i s no c o n c l u s i v e e v i d e n c e t h a t t r a v e l time g i v e s a b e t t e r f i t t o t h e model t h a n r a d i a l d i s t a n c e . 3.  The model as a good The  fit:  f a i r l y good f i t o f t h e model f o r 1966 and 1971 i s i n d i -  c a t i v e o f t h e f a c t t h a t t h e n e g a t i v e e x p o n e n t i a l decay f u n c t i o n c a n d e s c r i b e t h e d e n s i t y d i s t r i b u t i o n even f o r a c i t y w h i c h i s h i g h l y r e s t r i c t e d i n s i t e and e l o n g a t e d  i n shape. However, t h e r e i s e v i d e n c e  t h a t t h e model has d e c l i n e d i n i t s a p p l i c a b i l i t y over t i m e , w h i c h 2 i s r e f l e c t e d by t h e d e c l i n i n g R p e r s e d and random.  values.  Data have become more d i s -  The more d i s p e r s e d p a t t e r n o f d a t a may r e f l e c t  the' appearangfePof nodes "o£^po;p^latiqn cone exit r a t i o n i n some o f t h e o u t l y i n g s  1  m u n i c i p a l i t i e s , such as Burnaby and New W e s t m i n s t e r . 4.  The A and b v a l u e s The  i n t h e model:  A v a l u e has n o t shown a c o n s i s t e n t p a t t e r n o f d e c l i n e  o v e r t h e y e a r s even w i t h i n t h e same g e o g r a p h i c a l The  set-up.  b v a l u e has shown a d e c l i n e as t i m e p r o g r e s s e s .  There  i s a r e l a t i v e i n c r e a s e i n suburban d e n s i t i e s , w h i c h i s a r e s u l t o f the improvement i n t r a n s p o r t a t i o n and t h e r e l a t i v e decrease, i n im-  52  p o r t a n c e i n t r a n s p o r t c o s t as compared w i t h o t h e r l o c a t i o n a l considerations.  As C l a r k says:  "{.There a r e ]  two  f o r development, i f the p o p u l a t i o n i s i n c r e a s i n g .  possibilities  Either transport  c o s t s are reduced, e n a b l i n g the c i t y to spread out, or they cannot be r e d u c e d , i n w h i c h case d e n s i t y has  5.  t o i n c r e a s e at a l l p o i n t s . "  Methodology: There i s no d e c i s i v e e v i d e n c e as to the s u p e r i o r i t y i n the  use of one  geographical  set-up o v e r the o t h e r .  Conceptually,  the  use of s e c t o r s i s b e s t because i t i s a b l e to i n c o r p o r a t e s i m i l a r -numbers of census t r a c t s at d i f f e r e n t d i s t a n c e s from the c e n t e r .  An  e q u a l number of census t r a c t s b o t h at the c e n t e r and a t the i s included i n i t s l i m i t .  The  approximately periphery  s i z e of census t r a c t s u s u a l l y r e f l e c t s  i t s d e n s i t y , i . e . , a s m a l l e r p a r c e l of t r a c t i s u s u a l l y a s s o c i a t e d w i t h a h i g h e r d e n s i t y ; and v i c e v e r s a .  The  s e c t o r would t h e r e f o r e be a more  r e p r e s e n t a t i v e s p a t i a l zone f o r the model t o be t e s t e d .  However, the  use of s e c t o r i s not e n t i r e l y ' e m p i r i c a l l y j u s t i f i e d , s i n c e i n some 2 cases the l i n e s and bands o b t a i n a h i g h e r R . W i t h r e g a r d s t o the goodness of f i t of the model, i t can p o s s i b l y be improved by u s i n g a more d e t a i l e d d a t a b a s e , 1/4 enumeration a r e a , f o r i n s t a n c e . u s i n g net r e s i d e n t i a l d e n s i t y .  mile grid  or  Perhaps i t c o u l d be improved by  BIBLIOGRAPHY BOOKS  A l l p a s s , John, e t a l . , Urban Core and Inner C i t y , U n i v . o f Amsterdam, P r o c . o f t h e I n t e r n a t i o n a l Study Week, Amsterdam, 11-17 S e p t . , 1966, L e i d e n , 1967. Bartholomew, H a r l a n d , Land Uses i n American C i t i e s , H a r v a r d Univ. P r e s s , Cambridge, 1955. B e r r y , B r i a n J.L. & Frank E. H o r t o n , G e o g r a p h i c P e r s p e c t i v e s on Urban Systems, P r e n t i c e - H a l l , N.J., 1970. Bogue, Don J . & HoracerH. Rackhan, The S t r u c t u r e o f t h e M e t r o p o l i t a n Community, A Study o f Dominance and Subdomin-nance, S c h o o l o f Graduate S t u d i e s , U n i v . o f M i c h i g a n , 1950. B u r g e s s , E r n e s t W. & Donald J . Bogue ( e d s . ) , Urban S o c i o l o g y , P h e o n i x Books, U n i v . o f Chicago P r e s s , 1964. B u s s i e r e , Rene, The S p a t i a l D i s t r i b u t i o n o f Urban P o p u l a t i o n s , t r a n s , by t h e a u t h o r , P a r i s , CRU, 1970. C h a p i n , F. S t u a r t , J r . , Urban Land Use P l a n n i n g , U n i v . o f I l l i n o i s , 2nd Ed., 1965. D a v i e s , Owen L. ( e d . ) , S t a t i s t i c a l Methods i n R e s e a r c h and P r o d u c t i o n , . O l i v e r and Boyd, Edingburgi;. 1947. J a c k s o n , John N., The Urban F u t u r e , Univ. o f Birmingham, Urban and R e g i o n a l S t u d i e s , No. 3, George A l l e n & Unwin L t d . , 1972. J o h n s t o n , J . , E c o n o m e t r i c Methods, 2nd. Ed., New Y o r k , McGrawH i l l , 1972. Leahy, W.H., D a v i d L. Mckee & Robert D. Dean, Urban Economics, Theory, Development and P l a n n i n g , The F r e e P r e s s , New Y o r k , 1970.  L i o y , M i c h e l e , S o c i a l Trends o f G r e a t e r Vancouver, The U n i t e d Way o f G r e a t e r Vancouver, March, 1975. M a r t i n , L e s l i e & L i o e l - M a r c h ( e d s . ) , Urban Space and Cambridge Univ. P r e s s , 1972.  Structure,  M i l l s , Edwin S., S t u d i e s i n the S t r u c t u r e o f the Urban Economy, p u b l i s h e d f o r Resources f o r the F u t u r e , I n c . , by the John Hopkins P r e s s , Wash., D . C , 1972. M i l n e r , J.B., R e f l e c t i o n s on Zoning, The Rept. o f the Zoning Study Committee o f the Royal A r c h i t e c t u r a l I n s t i t u t e of Canada, 1964. McLoughlin, J . 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Hemmens, George C., "Experiments i n Urban Form and S t r u c t u r e " , HRR 207, 1967. Hoyt, Homer, "The E f f e c t o f the Automobile on P a t t e r n s of Urban Growth", T r a f f i c Q u a r t e r l y , 1963, pp. 293-301. J u r k a t , E r n e s t H., "Land Use A n a l y s i s and F o r e c a s t i n g i n T r a f f i c P l a n n i n g " , T r a f f i c Q u a r t e r l y 11, 1957, pp. 151-163.  Leven, C h a r l e s L., "Determinants of the S i z e and S p a t i a l Form o f Urban Areas", Reg. Sc. Assoc., P a p e r s , V o l . 22, 1969, pp. 7-28. Leven, "Towards a Theory o f the C i t y " , HRR S p e c i a l Rept., 97;.Land Development Models, Wash., D . C , 1968, pp. 102-111. L e v i n s o n , H.S. & F. Houston Wynn, "Some Aspects o f F u t u r e p o r t a t i o n i n Urban A r e a s " , HRR B u l l 326, 1962, pp. 1-31.  Trans-  MacDonald, Robert, "A C r i t i c a l Growth C y c l e f o r Vancouver, 1900-1914", B.C. S t u d i e s , No. 17, S p r i n g 1973. M i l l s , Edwin S., "Urban D e n s i t y  F u n c t i o n s " , Urban S t u d i e s  7, O c t . 1969.  Muth, R i c h a r d F., "The S p a t i a l S t r u c t u r e o f the Housing Market", R e g i o n a l S c i e n c e Assoc., V o l . 7, 1961. Newling, Bruce E., "Urban Growth and S p a t i a l S t r u c t u r e : Mathematical Models and E m p i r i c a l E v i d e n c e " , The Geog. Review, V o l . L V I , 1966, pp. 213-225. • , "The S p a t i a l V a r i a t i o n o f Urban P o p u l a t i o n D e n s i t i e s " , Geog. Review 59, 1969, pp. 242-252. Pendleton, W i l l i a m C., " R e l a t i o n o f Highway A c c e s s i b i l i t y t o Urban Real E s t a t e V a l u e s " , HRR 16, 1963, pp. 14-23. P u r n e l l , J . S t a n l e y , " P l a n n i n g T r a n s p o r t a t i o n F a c i l i t i e s to Guide Urban Development", T r a f f i c Q u a r t e r l y 20, 1966, pp. 277-287. 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Jackson, J.N., et a l . , The Impact of Highway Development on Land A Study of S e l e c t e d L o c a l i t i e s i n the G r e a t e r Vancouver A r e a , Research Rept., No. 1, Comm. & Reg. P l a n n i n g , UBC, June 1963. Our F i f t y Years 1890-1940, A b r o c h u r e i s s u e d by the P a c i f i c Coast F i r e Insurance Co., Vancouver, B.C., 1940. VATS, 1968, C i t y o f Vancouver, B r i t i s h  Columbia.  Use,  T e c h n i c a l Rept., P a r t 2: The Urban F r o n t i e r , Lower Mainland R e g i o n a l P l a n n i n g Board o f B r i t i s h Columbia, Supp. Study 4 to Land f o r L i v i n g . Dynamics of R e s i d e n t i a l Land S e t t l e m e n t , Lower Mainland R e g i o n a l P l a n n i n g Board o f B r i t i s h Columbia, Supp. Study 2 to Land f o r L i v i n g . Downtown Vancouver,  Rept.  f o r D i s c u s s i o n , C i t y o f Vancouver,  Sept.  1974.  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Roy, P a t r i c i a E., R a i l w a y s , P o l i t i c i a n s and the Development of the C i t y of Vancouver as a M e t r o p o l i t a n Centre 1886-1929, u n p u b l i s h e d M.A. t h e s i s , Univ. o f T o r o n t o , Oct. 1963,  NEWSPAPERS  Province: 3 A p r i l 29, 1937, " I n d u s t r i a l Expansion Supplement: Vancouver o f the F u t u r e w i l l be World-Famous M e t r o p o l i s " .  Greater  60a  Appendix I :  Regression Analysis  REGRESSION ANALYSIS Regression ing  a n a l y s i s i s concerned w i t h the problem of d e s c r i b -  or e s t i m a t i n g the v a l u e of one v a r i a b l e , c a l l e d the "dependent  v a r i a b l e " , on the b a s i s of one or more o t h e r v a r i a b l e s , c a l l e d "independent v a r i a b l e s " .  I t i s hypothesized  t h a t the  behaviour  observed f o r a dependent v a r i a b l e can be accounted f o r by the independent v^rjuablres..,  The model used i n t h i s work i n v o l v e s two  parameters:  e x t r a p o l a t e d d c e n t r a l d e n s i t y and d e n s i t y g r a d i e n t , w h i c h a r e used t o i n d i c a t e the n e g a t i v e e x p o n e n t i a l d e c l i n e of p o p u l a t i o n d e n s i t y w i t h the i n c r e a s e i n d i s t a n c e .  I t i s important  to n o t e t h a t the  from the d a t a a r e d e r i v e d from a c o n c e p t u a l and p r e t a t i o n o f the s t a t i s t i c a l r e s u l t s ; and from a  theoretical  inferences inter-  statistical  s t a n d p o i n t , t h e r e s h o u l d not be any i m p l i c a t i o n o f c a u s a t i o n , or d i r e c t i o n o f "cause and e f f e c t " i n v o l v e d .  1  The Method of L e a s t Squares i s most o f t e n used i n d e t e r m i n i n g the p r o b a b l e v a l u e s o f the dependent v a r i a b l e from the independent variable(s).  I t r e q u i r e s f i t t i n g a c e n t r a l l i n e , o r the b e s t - f i t t i n g  l i n e , to the d a t a , where the sum of the o b s e r v a t i o n s minimum.  o f squares of the v e r t i c a l d e v i a t i o n s  f o r the dependent v a r i a b l e from the l i n e i s a  I n o t h e r words, the Method of L e a s t Squares g i v e s  minimum e r r o r v a r i a n c e f o r the purpose o f p r e d i c t i n g one  the  property  2 from a knowledge of the o t h e r . identified  by:  The  r e g r e s s i o n e q u a t i o n can  be  y = a + bx + u where:  y i s the dependent v a r i a b l e x i s the independent v a r i a b l e a, b are c o n s t a n t s , which are to be determined from  the  equation u i s the " d i s t u r b a n c e " p o s i t i v e or n e g a t i v e  o r " e r r o r " t e r m , w h i c h may  take  on  values.  Among the many f a c t o r s t h a t c o n t r i b u t e  to the i n s e r t i o n of  the u term, the more i m p o r t a n t ones are the measurement e r r o r  and  s p e c i f i c a t i o n e r r o r ; the l a t t e r means t h a t the a c t u a l phenomena not be f u l l y r e p r e s e n t e d by the expressmond b T h e h s p e e i f i e a t i o n i s i n v e r s e l y r e l a t e d to the number of v a r i a b l e s i n v o l v e d expression,  in  The  assumptions i n v o l v e d  i s a c o n s t a n t and  the  i n the s p e c i f i c a t i o n  of the d i s t u r b a n c e term are h o m o s c e d a s t i c i t y and i s , the v a r i a n c e  error  the  w h i l e the measurement e r r o r i s d i r e c t l y r e l a t e d to  number of v a r i a b l e s .  may  independence, t h a t ,  independent of x, and  the v a l u e s  3 are independent of one  another.  I t i s u s u a l l y a common p r a c t i c e to g i v e a f u l l of the r e l a t i o n s h i p by means of a " s c a t t e r diagram" or relation r e l a t i o n diagram".  The  called a "regression" v a r i a b l e and  other.  "cor-  c e n t r a l l i n e f i t t e d t o the d a t a p o i n t s  line.  The  to i n c r e a s e  is  r e l a t i o n s h i p between the dependent  the independent v a r i a b l e s  tendency f o r one  appraisal  (s) i s e x p r e s s e d by  or d e c r e a s e w i t h an i n c r e a s e  a in  the  For the v a r i a b l e s to be h i g h l y c o r r e l a t e d , a l l the d a t a p o i n t s  are c l u s t e r e d about the r e g r e s s i o n  l i n e , o r n e a r l y so.  O f t e n i n the  case o f n o n - l i n e a r i t y , a t r a n s f o r m a t i o n by way o f l o g a r i t h m , r e c i p r o c a l , o r square r o o t o f one o r b o t h v a r i a b l e s can be made t o 4 eliminate the curvature.  R e f e r r i n g t o t h e model we a p p l i e d , t h e r e  i s a l o g a r i t h m i c t r a n s f o r m a t i o n of the p o p u l a t i o n d e n s i t y at a d i s t a n c e x. ( D ) , and imputed c e n t r a l d e n s i t y ( D ) • x  Q  The e x t e n t o f t h e p r e c i s i o n o f t h e r e g r e s s i o n depends on the f o l l o w i n g f a c o r s : 2)  1)  t h e number o f o b s e r v a t i o n s ; and  t h e e x t e n t o f t h e s c a t t e r about t h e r e g r e s s i o n .  F o r any v a l u e  of y, t h e r e i s a c o r r e s p o n d i n g v a l u e o f x, where y^ = a + b x ^ + u^ y  =a+bx n  n  +u. The d i s c r e p a n c y between t h e t h e o r e t i c a l n /A  v a l u e o f y, denoted by y, and t h e observed v a l u e o f y may be regarded as e r r o r s , t h e measure o f w h i c h i s known as t h e " v a r i a n c e " .  tnotes Donald J . Bogue & Dorothy L. H a r r i s , "Comparative P o p u l a t i o n and Urban Research v i a M u l t i p l e R e g r e s s i o n and C c V a r i a t e A n a l y s i s " , S c r i p p s Foundation f o r Research i n P o p u l a t i o n Problems, 1954, p.7 Owen L. D a v i e s ( e d . ) , S t a t i s t i c a l Methods i n Research and P r o d u c t i o n , O l i v e r and Boyd, E d i n g b u r g , 1947, p. 123 J . J o h n s t o n , E c o n o m e t r i c Methods, M c G r a w - H i l l Book Co., New Y o r k , 2nd Ed., 1972, pp. 8-12 Owen L. D a v i e s , op. c i t . , p. 120  Appendix I I :  Graphs  64b  (3)')  GVRD, T r a v e l Time,  1966  (4)  GVRD, T r a v e l Time, (I;  1971 ot s'  ,65  66  (9)  (11)  L i n e , E a s t ? l T i ? a v e l Time, 1966  L i n e , South, T r a v e l Time, 1966  (10)  (12)  L i n e , East", T r a v e l Time, 1971  L i n e , South, T r a v e l Time, 1971  67  (15)  S e c t o r , South, R a d i a l D i s t a n c e , 1966  (16)  S e c t o r , South, R a d i a l D i s t a n c e , 1971  68  (17)  S e c t o r , E a s t , T r a v e l Time, 1966  (18)  S e c t o r , E a s t , T r a v e l Time 1971  (19)  S e c t o r , South, T r a v e l Time, 1966  (20)  S e c t o r , South, T r a v e l Time, 1971  69  (23)  Band, South, R a d i a l D i s t a n c e , 1966  (24)  Band, South, R a d i a l 1971  Distance  (25)  (27)  Band, E a s t , T r a v e l Time, 1966  Band, South, T r a v e l Time, 1966  (26)  Band, E a s t , T r a v e l Time, 1971  (28)  Band, South, T r a v e l Time, 1971  (31)  S e c t o r , South, R a d i a l D i s t a n c e , 1956  (32)  S e c t o r , South, R a d i a l D i s t a n c e , 1961  72  (33)  Band, E a s t , R a d i a l D i s t a n c e ,  (34)  Band, E a s t , R a d i a l D i s t a n c e , 1961  1956  ]  6 (35)  1 -4-  1 *  —i  1 ^  Band, South, R a d i a l D i s t a n c e , 1956  (36)  Band, South, R A d i a l D i s t a n c e , 1961  73  (39)  S e c t o r , South, T r a v e l Time,> 1956':  (40)  S e c t o r , South, T r a v e l Time, 1961  74  (4,3)  Band, South, T r a v e l Time, 1956  (44)  Band, South, T r a v e l Time, 1961  Appendix I I I :  Statistical  Tables  R e l a t i o n s h i p Between D e n s i t y and R a d i a l o D i s t a n c e From t h e C i t y Centre Geog. S e t „ ups/1966 A b r No. R  Graph  GVRD  9.12414  0.14715  -0.75441  23  0.56914  1  LINE,::"E.  9.84693  0.24061  -0.84611  12  0.71590  5  LINE,"S.  9.66111  0.28895  -0.73620  14  0.54199  7  SECTOR, E. SECTOR SECTOR, S.  9.84228  0.22191  -0.81731  33  0.66800  13  9.85094  0.25702  -0.65921  32  0.43456  15  BAND, E.  9.38258  0.14716  -0.78745  19  0.62008  21  BAND, S.  9.54759  0.16530  -0.41343  21  0.17092  23  R e l a t i o n s h i p Between D e n s i t y and R a d i a l D i s t a n c e From the C i t y Centre Geog.Set2 ups/1971 A b r r No.r R  Graph  GVRD  9.15360  0.13229  -0.71736  23  0.51460  : 2  LINE, E.  9.45773  0.18097  5017,6365  •12-- 763550.58316  6  LINEj, S.  9.44072  0.23078  -0.63350  14  0.40133  8  SECTOR, E.  9.59935  0.17808  -0.72100  33  0.51984  14  SECTOR, S.  8.95351  0.08114  -0.59507  32  0.35411  16  BAND, E.  9.28304  0.10425  -0.65603  19  0.43038  22  BAND, S.  9.62282  0.17242  -0.42552  21  0.18107  24  R e l a t i o n s h i p Between D e n s i t y and T r a v e l Time From t h e C i t y Center Geog. S e t ups/1966  A  b  r  No.  R  Table 3 2  Graph  GVRD  10.41882  0.08161  -0.65761  151  0.43245  3  LINE, E.  10.35397  0.08934  -0.83896  12  0.70386  9  LINE, S.  10.24456  0.09650  -0.67561  14  0.45645  11  SECTOR, E.  10.40791  0.08326  -0.80688  26  0.65105  17  SECTOR, S.  10.65679  0.09359  -0.69427  29  0.48201  19  BAND, E.  9.84140  0.05737  40.78820  21  0.65125  25  BAND, S.  10.57283  0.08065  -0.77282  28  0.59724  27  R e l a t i o n s h i p Between D e n s i t y and T r a v e l Time From t h e C i t y Center Geog. Setups/1971  A  b  r  No.  Table 4 R  2  Graph  10.26468  0.07217  -0.62365  151  0.38894  4  LINE, E.  9.82351  0.06660  -0.75049  12  0.56324  10  LINE, S.  9.92064  0.07769  -0.58600  14  0.34340  12  SECTOR, E.  10.24311  0.06994  -0.74554  26  0.55583  18  SECTOR, S.  10.37837  0.07684  -0.62873  29  0.39530  20  BAND, E.  9.64117  0.04143  -0.66226  21  0.43859  26  BAND, S.  10.63296  0.08287-  -0.72389  28  0.52402  28  GVRD  00  Relationship Geog. S e t ups/1956  Between D e n s i t y and R a d i a l D i s t a n c e From the C i t y Center A  b  r  No.  R  2  Table 5 Graph  SECTOR, E.  9.73567  0.07428  -0.89469  17  0.80048  29  SECTOR, S.  9.94927  0.11472  -0.82024  16  0.67279  32  BAND, E.  9.63216  0.08405  -0.91433  15  0.83600  33  BAND, S.  9.82152  0.10423  -0.80193  15  0.64310  35  R e l a t i o n s h i p Between D e n s i t y and R a d i a l D i s t a n c e From t h e C i t y C e n t e r — - T a b l e 6 Geog. S e t ups/1961  A  b  r  No.  R  2  Graph  SECTOR, E.  9.49519  0.06640  -0.74426  17  0.55393  30  SECTOR, S.  10.33737  0.11730  -0.79662  16  0.63460  31  BAND, E.  9.58201  0.06982  -0.87769  15  0.77033  34  BAND, S.  9.63519  0.07486  -0.67714  15  0.45852  36  R e l a t i o n s h i p Between ' D.e n s i t y and T'r a v e l Time From the C i t y Center Geog. Setups/1956  A  b  r  Table 7 R  No.  Graph  2  SECTOR, E.  10.38463  0.09815  -0.88126  17  0.77662  37  SECTOR, S.  10.76976  0.13485  -0.75983  16  0.57734  39  BAND, E.  10.15263  0.09559  -0.85823  15  0.73655  41  BAND, S.  10.25926  0.10467  -0.75618  15  0.57180  43  R e l a t i o n s h i p Between D e n s i t y and T r a v e l Time From the C i t y Center Geog. S e t ups/1961  A  b  r  No.  Table 8 R  2  Graph  SECTOR, E.  10.21197  0.08117  -0.84767  17  0.71855  8  SECTOR, S.  11.35954  0.14123  -0.69927  16  0.48898  40  BAND, E.  9.99301  0.07835  -0.81292  15  0.66084  42  BAND, S.  9.97566  0.07699  -0.65392  15  0.42761  44  OO  o  Appendix IV:  Maps  Map of Census T r a c t s of M e t r o p o l i t a n Vancouver, 1971  Map  2  METROPOLITAN I  T r a v e l Time I n GVRD Source: Dynamics o f R e s i d e n t i a l Land S e t t l e m e n t , LMRPB o f B.C., 1963 3 M  a  p  VANCOUVER  T r a v e l Time i n GVRD Summer 1968. Source: T r a f f i c Volumes T r a v e l Times, 1967/1968 P l a n n i n g Dept., 'GVRD. Map 4  

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