﻿24 
  Gleason: 
  Some 
  applications 
  of 
  the 
  quadrat 
  method 
  

  

  to 
  be 
  representative 
  of 
  the 
  whole 
  association, 
  of 
  sufficient 
  number 
  

   to 
  permit 
  drawing 
  logical 
  conclusions, 
  and 
  of 
  a 
  size 
  suitable 
  to 
  the 
  

   character 
  of 
  the 
  vegetation 
  concerned- 
  Several 
  ecologists 
  have 
  

   devised 
  statistical 
  methods 
  toward 
  this 
  end, 
  which 
  have 
  been 
  

   more 
  or 
  less 
  successful. 
  One 
  of 
  the 
  earliest 
  was 
  Drude 
  (1890), 
  

   who 
  described 
  plants 
  as 
  social, 
  gregarious, 
  copious, 
  or 
  rare, 
  de- 
  

   pending 
  on 
  their 
  number, 
  their 
  distribution, 
  and 
  their 
  grouping. 
  

   He 
  also 
  proposed 
  the 
  determination 
  of 
  the 
  frequence 
  of 
  plants 
  on 
  a 
  

   large 
  scale 
  by 
  dividing 
  an 
  area 
  into 
  quadrats 
  of 
  100 
  square 
  kilo- 
  

   meters. 
  Pound 
  and 
  Clements 
  (1898, 
  1900) 
  adopted 
  the 
  same 
  

   terminology 
  in 
  their 
  first 
  studies 
  on 
  the 
  subject, 
  but 
  determined 
  

   abundance 
  within 
  a 
  single 
  association 
  by 
  actual 
  counts 
  of 
  the 
  

   number 
  of 
  individuals 
  in 
  a 
  quadrat 
  5 
  meters 
  square, 
  and 
  investi- 
  

   gated, 
  enough 
  quadrats 
  to 
  warrant 
  them 
  in 
  drawing 
  averages. 
  It 
  

   is 
  obvious, 
  however, 
  that 
  averages 
  from 
  figures 
  obtained 
  in 
  this 
  

   way 
  are 
  not 
  entirely 
  trustworthy, 
  since 
  some 
  species 
  are 
  mutually 
  

   exclusive, 
  while 
  the 
  averages 
  might 
  indicate 
  that 
  they 
  normally 
  

   grew 
  together. 
  Jaccard 
  (1901) 
  adopted 
  the 
  study 
  of 
  several 
  

   adjacent 
  quadrats 
  as 
  a 
  method 
  in 
  his 
  study 
  of 
  alpine 
  vegetation, 
  

   and 
  developed 
  the 
  idea 
  of 
  the 
  frequency 
  index 
  and 
  the 
  community 
  

   coefficient. 
  His 
  results 
  are, 
  however, 
  probably 
  somewhat 
  faulty, 
  

   inasmuch 
  as 
  he 
  used 
  few 
  quadrats 
  in 
  any 
  one 
  association 
  and 
  lo- 
  

   cated 
  them 
  adjacent 
  to 
  one 
  another. 
  Harper 
  (191 
  7 
  and 
  several 
  

   other 
  articles) 
  has 
  also 
  attempted 
  a 
  statistical 
  expression 
  of 
  car- 
  

   window 
  observations, 
  which 
  corresponds 
  to 
  some 
  extent 
  to 
  the 
  fre- 
  

   quency 
  Index 
  as 
  here 
  used. 
  Raunkiaer 
  (1909) 
  used 
  essentially 
  

   the 
  same 
  method 
  described 
  here. 
  

  

  The 
  present 
  writer 
  first 
  attempted 
  the 
  use 
  of 
  statistical 
  methods 
  

   to 
  determine 
  and 
  express 
  the 
  structure 
  of 
  vegetation 
  in 
  1903 
  

   (1907). 
  He 
  improved 
  his 
  method 
  somewhat 
  in 
  1908 
  (1910) 
  and 
  

   adapted 
  it 
  to 
  class 
  work 
  with 
  students 
  in 
  1910. 
  In 
  the 
  summer 
  

   of 
  191 
  1 
  he 
  began 
  the 
  intensive 
  study 
  of 
  the 
  quadrat 
  method 
  and 
  

   its 
  applications 
  at 
  the 
  Biological 
  Station 
  of 
  the 
  University 
  of 
  

   Michigan, 
  and 
  during 
  the 
  following 
  four 
  summers 
  obtained 
  a 
  long 
  

   series 
  of 
  data 
  upon 
  which 
  the 
  present 
  paper 
  is 
  based. 
  The 
  

   statistics 
  used 
  in 
  Tables 
  I 
  and 
  H 
  were 
  secured 
  from 
  the 
  aspen 
  

   (Populus 
  tremnloldes 
  and 
  P. 
  grandidentata) 
  association. 
  

  

  In 
  practice, 
  the 
  following 
  method 
  is 
  adopted. 
  The 
  size 
  of 
  the 
  

  

  