﻿Gleason; 
  Some 
  applications 
  of 
  the 
  quadrat 
  method 
  29 
  

  

  The 
  relative 
  abundance 
  of 
  a 
  species 
  is 
  a 
  fair 
  measure 
  of 
  its 
  

   ability 
  to 
  maintain 
  itself 
  under 
  the 
  conditions 
  of 
  environment 
  and 
  

   competition 
  prevalent 
  within 
  the 
  association. 
  Long-established 
  

   species 
  of 
  an 
  old 
  association 
  have 
  frequently 
  become 
  diffused 
  

   thoroughly 
  over 
  the 
  whole 
  area, 
  and 
  their 
  abundance 
  may 
  be 
  

   determined 
  by 
  counting, 
  but 
  recent 
  immigrants 
  into 
  old 
  associa- 
  

   tions 
  or 
  any 
  species 
  of 
  young 
  associations 
  are 
  not 
  uniformly 
  

   distributed. 
  The 
  number 
  of 
  individuals 
  of 
  such 
  plants 
  is 
  there- 
  

   fore 
  zero 
  in 
  those 
  parts 
  which 
  they 
  have 
  not 
  yet 
  reached 
  and 
  is 
  too 
  

   high 
  to 
  show 
  their 
  relative 
  adjustment 
  in 
  those 
  parts 
  which 
  they 
  

   have 
  reached. 
  

  

  4 
  

  

  But 
  there 
  is 
  a 
  definite 
  relation 
  between 
  the 
  number 
  of 
  individ- 
  

   uals 
  of 
  a 
  species 
  and 
  its 
  frequency 
  index. 
  If 
  only 
  one 
  is 
  present 
  in 
  

   the 
  area 
  covered 
  by 
  the 
  quadrats, 
  the 
  frequency 
  index 
  naturally 
  

   cannot 
  exceed 
  i. 
  If 
  only 
  two 
  are 
  present, 
  it 
  can 
  not 
  exceed 
  2 
  

   and 
  may 
  be 
  only 
  i 
  if 
  both 
  happen 
  to 
  occur 
  in 
  the 
  same 
  quadrat. 
  

   While 
  'it 
  is 
  possible 
  for 
  a 
  species 
  to 
  be 
  represented 
  by 
  a 
  large 
  

   number 
  of 
  individuals 
  all 
  of 
  which 
  occur 
  in 
  a 
  single 
  quadrat 
  only, 
  

   the 
  chance 
  of 
  such 
  a 
  thing 
  actually 
  happening 
  is 
  very 
  small 
  indeed. 
  

   Similarly, 
  while 
  lOO 
  individuals 
  might 
  be 
  so 
  thoroughly 
  distributed 
  

   that 
  they 
  would 
  occur 
  one 
  in 
  each 
  quadrat, 
  there 
  is 
  again 
  very 
  slight 
  

   probability 
  of 
  it. 
  The 
  mathematical 
  possibihties 
  are 
  capable 
  of 
  

   solution 
  according 
  to 
  the 
  laws 
  of 
  probability 
  and 
  chance. 
  If 
  n 
  

   plants 
  are 
  scattered 
  at 
  random 
  over 
  q 
  quadrats, 
  the 
  probability 
  

   of 
  any 
  one 
  quadrat 
  being 
  occupied 
  is 
  expressed 
  by 
  the 
  formula 
  

  

  I 
  — 
  ( 
  I 
  — 
  - 
  ) 
  . 
  Thus 
  for 
  2 
  plants 
  in 
  5 
  quadrats 
  i 
  — 
  ( 
  i 
  

   0.36 
  = 
  FI 
  36, 
  Or 
  for 
  65 
  plants 
  in 
  100 
  quadrats 
  i 
  

  

  100 
  

  

  FI^8, 
  Or, 
  conversely, 
  F/48 
  should 
  indicate 
  a 
  total 
  of 
  65 
  indi- 
  

   viduals 
  within 
  the 
  100 
  quadrats. 
  But 
  since 
  plants 
  are 
  not 
  dis- 
  

   tributed 
  entirelj^ 
  at 
  random, 
  the 
  actual 
  number 
  is 
  therefore 
  always 
  

   greater 
  than 
  indicated 
  by 
  the 
  mathematical 
  formula, 
  which 
  may 
  

  

  be 
  expressed, 
  when 
  q 
  = 
  100, 
  as 
  w 
  = 
  — 
  ; 
  . 
  Thus, 
  Pteris 
  

  

  ^ 
  ' 
  ^ 
  log 
  0.99 
  

  

  agtiilina^ 
  determined 
  by 
  actual 
  count 
  to 
  have 
  an 
  average 
  abun- 
  

   dance 
  of 
  4,400 
  in 
  100 
  quadrats, 
  has 
  FI 
  99, 
  corresponding 
  to 
  a 
  

   theoretical 
  number 
  of 
  only 
  455 
  ijidividuals. 
  Obviously, 
  the 
  

  

  