﻿26 
  Gleasox: 
  

  

  QUADRAT 
  

  

  the 
  counts. 
  

  

  be 
  

  

  For 
  example, 
  during 
  five 
  years 
  experience 
  in 
  the 
  aspen 
  association 
  

  

  Mich 
  

  

  have 
  been 
  counted 
  by 
  the 
  writer 
  or 
  his 
  students, 
  Cypripedium 
  

   acatde, 
  a 
  plant 
  of 
  great 
  rarity 
  in 
  this 
  habitat, 
  has 
  appeared 
  but 
  once 
  

   in 
  the 
  quadrats. 
  These 
  rarer 
  ones, 
  while 
  of 
  the 
  greatest 
  interest 
  

   to 
  the 
  systematist 
  or 
  the 
  phytogeographer 
  in 
  their 
  relation 
  to 
  

   plant 
  distribution 
  in 
  general, 
  as 
  emphasized 
  so 
  interestingly 
  by 
  

   Fernald 
  (1919), 
  and 
  to 
  the 
  ecologist 
  through 
  the 
  evidence 
  which 
  

   they 
  frequently 
  offer 
  concerning 
  the 
  past 
  or 
  future 
  development 
  

   of 
  the 
  association, 
  are 
  nevertheless 
  of 
  negligible 
  value 
  In 
  formu- 
  

   lating 
  a 
  verbal 
  description 
  of 
  the 
  association. 
  But 
  the 
  important 
  

   species 
  all 
  do 
  occur, 
  provided 
  the 
  number 
  and 
  location 
  of 
  the 
  

   quadrats 
  has 
  been 
  properly 
  chosen 
  with 
  reference 
  to 
  the 
  size 
  and 
  

   character 
  of 
  the 
  association, 
  as 
  the 
  writer 
  has 
  demonstrated 
  fre- 
  

   quently 
  in 
  his 
  own 
  work. 
  

  

  If 
  the 
  whole 
  association 
  were 
  included 
  in 
  a 
  single 
  quadrat, 
  

   the 
  frequency 
  index 
  of 
  each 
  species 
  would 
  be 
  100 
  and 
  would 
  give 
  

   no 
  idea 
  of 
  the 
  comparative 
  value 
  of 
  the 
  species. 
  In 
  general, 
  if 
  the 
  

   quadrats 
  are 
  too 
  large, 
  the 
  frequency 
  indices 
  are 
  also 
  large 
  and 
  

   tend 
  to 
  approximate 
  near 
  ^100. 
  Conversely, 
  if 
  they 
  are 
  too 
  small 
  

  

  while 
  the 
  number 
  of 
  omitted 
  species 
  tends 
  to 
  become 
  large 
  and 
  

  

  may 
  even 
  include 
  some 
  of 
  the 
  more 
  important 
  ones. 
  The 
  optimum 
  

  

  size 
  is- 
  one 
  in 
  which 
  there 
  Is 
  a 
  wide 
  divergence 
  in 
  the 
  indices, 
  from 
  

  

  I 
  to 
  90 
  or 
  even 
  more, 
  so 
  that 
  the 
  variation 
  is 
  an 
  indication 
  of 
  the 
  

  

  relative 
  importance 
  of 
  the 
  species. 
  This 
  is 
  illustrated 
  In 
  the 
  first 
  

  

  three 
  columns 
  of 
  figures 
  In 
  Table 
  I,* 
  of 
  which 
  the 
  second 
  column, 
  

  

  based 
  on 
  quadrats 
  two 
  meters 
  square, 
  presents 
  probably 
  the 
  best 
  

   series 
  of 
  indices. 
  

  

  * 
  The 
  frequency 
  indices 
  given 
  in 
  Table 
  I 
  are 
  not 
  considered 
  typical 
  of 
  the 
  aspen 
  

   assocmtioni 
  n 
  general. 
  The 
  association 
  consists 
  of 
  a 
  sparse 
  growth 
  of 
  two 
  species 
  of 
  

   aspen 
  and 
  the 
  paper 
  birch, 
  alternating 
  with 
  treeless 
  areas 
  dominated 
  by 
  bracken 
  fern. 
  

   The 
  240 
  quadrats 
  counted 
  for 
  this 
  paper 
  were 
  located 
  entirely 
  within 
  a 
  treeless 
  area, 
  

   and 
  do 
  not 
  take 
  account 
  of 
  the 
  conspicuous 
  difference 
  encountered 
  in 
  the 
  shade, 
  

   where 
  MeUmpyrum 
  lineare 
  and 
  Diervilla 
  Lonicera 
  are 
  both 
  abundant. 
  Neither 
  do 
  

   they 
  cover 
  an 
  extent 
  wide 
  enough 
  to 
  give 
  a 
  fair 
  representation 
  of 
  the 
  treeless 
  areas 
  

   m 
  general, 
  snnce 
  these 
  omit 
  completely 
  such 
  relatively 
  common 
  species 
  as 
  Vaccinium 
  

   canadense. 
  Pamcum 
  depauperatum. 
  Oryzopsis 
  pungens. 
  and 
  Convolvulus 
  spithamaeus. 
  

  

  