LIBRARY 
 ATE  PLANT  BOARD 
 
 une  1945  BT-223 
 
 UNITED  STATES  DEPARTMENT  OF  AGRICULTURE 
 
 Agricultural  Research  Administration 
 
 Bureau  of  Entomology  and  Plant  Quarantine 
 
 THE  EVIDENCE  REQUIRED  TO  SHOW  SYNERGISTIC  ACTION  GOT  INSECTICIDES 
 AND  A  SHORT  CUT  IN  ANALYSIS 
 
 By  J.  M.  Wadley,  statistical  consultant 
 
 The  purpose  of  this  paper  is  threefold:  (l)  To  restate  definitions 
 of  Joint  action  of  insecticides,  (2)  to  show  what  is  required  for  clear- 
 cut  recognition  of  synergism,  and  (3)  to  indicate  a  workable  short  cut  in 
 analysis. 
 
 Definitions 
 
 Synergism  "between  insecticides  may  he  defined  as  a  Joint  action  of 
 two  materials,  such  that  the  total  effect  is  greater  than  the  sum  of  the 
 two  effects  when  each  is  used  alone.  Cox  (2)  restricts  the  application 
 of  the  term  "synergism"  to  mixtures  of  insecticidal  materials,  each  of 
 which  has  some  toxicity  when  used  alone.  He  thus  excludes  the  case 
 where  a  substance  without  toxicity  of  its  own  improves  the  action  of  an 
 insecticide.  Such  a  substance  is  called  simply  an  activator.  The  proof 
 of  activation  is  less  complex  than  that  of  synergism;  a  significant 
 added  percentage  of  kill  shown  in  replicated  trials  should  be  sufficient. 
 
 To  understand  synergism  it  is  necessary  to  consider  possible  types 
 of  action  of  mixtures  of  poisons.  The  subject  has  been  discussed  clearly 
 by  Bliss  (1)  and  Finney  (3 )  and  touched  upon  by  the  writer  (£) .  Bliss 
 discusses  three  types  of  action  of  two  poisons  in  a  mixture—  Independent 
 Joint  action,  similar  Joint  action,  and  synergistic  action.  Both  Bliss 
 and  Finney  mention  the  possibility  of  negative  synergism,  or  antagonism, 
 and  both  suggest  methods  for  analysis  of  data  on  toxic  action.  The 
 methods  discussed  may  be  extended  to  mixtures  of  more  than  two  poisons. 
 
 Independent  action  can  he  defined  as  action  in  a  different  way  by 
 each  poison,  a  different  physiological  activity  or  vital  system  being 
 affected.  There  may  be  more  or  less  correlation  in  susceptibility, 
 since  the  individuals  susceptible  to  one  action  may  tend  also  to  he 
 susceptible  to  the  other.  If  there  is  a  marked  positive  correlation  of 
 this  sort,  both  poisons  will  tend  to  work  on  the  same  group  of  insects, 
 and  we  will  get  little  or  no  Increase  in  kill  by  the  mixture  over  the 
 mortality  that  would  he  caused  by  the  stronger  Insecticide  used  alone. 
 
 AUG  3 
 
 -  194$ 
 
-  2  - 
 
 If  there  la  little  or  no  correlation,  there  will  he  eons  kill  hy  each 
 substance  and  seme  overlapping,  of  the  sort  Indicated  hy  Ahhott'e 
 f omnia  for  one  mortality  In  the  presence  of  another.  In  that  case 
 the  total  nn  will  he  higher  than  It  vould  he  vlth  correlation.  The 
 possibility  of  negative  correlation,  that  is,  the  individuals  suscep- 
 tible to  one  poison  "being  resistant  to  the  other,  night  also  he  con- 
 sidered. Each  poison  would  kill  the  group  susceptible  to  it  vlth  little 
 or  no  overlapping,  and  the  total  kill  vould  he  still  higher.  This  con- 
 dition seems  unlikely.  Finney  defines  expected  independent  action  vi th- 
 ou t  allowance  for  correlation.  This  is  equivalent  to  the  concept  of 
 Abbott's  formula.  Suppose,  for  Instance,  that  a  certain  concentration 
 of  poison  A  kills  80  percent  and  one  of  B  60  percent.  If  the  two  poi- 
 sons are  independent  In  action,  we  would  expect  a  kill  of  30  percent  ♦  60 
 percent -(60  percent  of  80  percent),  or  92  percent.  It  seems  probable  that 
 some  positive  correlation  often  occurs.  Action  significantly  less  than 
 independent  action  indicates  antagonism. 
 
 S<m4i«y  joint  effect  is  produced  hy  two  or  more  poisons  acting 
 similarly,  and  affecting  the  same  organs  or  processes  in  the  individual. 
 It  implies  that  one  insecticide  could  he  substituted  for  the  other  at  a 
 constant  rate.  If  this  rate  is  known,  equivalence  can  also  he  determined. 
 It  is  recognised  that  the  soundest  method  of  comparing  two  insecticides 
 is  to  compare  concentrations  needed  for  a  given  effect,  and  thie  method 
 has  a  special  application  here. 
 
 Suppose,  for  instance,  that  a  concentration  of  1  un5t  of  insecti- 
 cide A  is  required  to  give  50  percent  kill  of  an  Insect  species,  and 
 that  2  units  of  insectioide  B  are  required  for  the  same  result.  Than  A 
 is  twice  am  effective  as  B.  A  mixture  of  l/2  unit  of  A  and  1  unit  of 
 B  vlll  produce  the  same  result  am  either  1  unit  of  A  o-  2  of  B,  if 
 similar  Joint  effect  occurs.  If  action  is  independent,  there  vlll  he 
 some  overlapping,  and  the  mixture  vlll  have  somewhat  less  effect.  On 
 the  basis  of  similar  Joint  effect,  1  unit  of  A  and  1  of  B  will  he 
 equivalent  to  1  l/2  units  of  A  alone. 
 
 It  can  readily  be  shown,  by  the  nature  of  dosage -mortality  curves 
 involved  and  the  alopea  they  usually  show,  that  similar  Joint  effect 
 is  greater  than  Independent  effect,  either  with  or  without  correlation. 
 The  greatest  effect  of  a  mixture,  which  could  be  predicted  from  indi- 
 vidual action  of  its  ingredients,  would  be  similar  Joint  effect.  If 
 the  effect  of  the  combination  can  be  shown  to  exceed  eignif icantly  the 
 action  expected  from  similar  Joint  effect,  synergism  is  strongly  in- 
 dicated. 
 
 The  Determination  of  Synergism 
 
 The  determination  of  synergism  will  require  (1)  dome  estimate  of 
 similar  Joint  effect  Inferred  from  the  action  of  each  Ingredient  used 
 alone,  and  (2)  the  determination  of  significance  of  superiority  In  re- 
 sults, if  any,  over  this  similar  effect. 
 
 To  estimate  the  similar  Joint  effect  we  need  dosage  -mortality 
 curves  for  each  poison  alone,  so  that  equivalence  *t  a  given  mortality 
 can  be  calculated  by  Interpolation.  The  log-prol.it  t*ansf<rmatic^  is 
 
-  3  - 
 
 convenient  for  this  purpose,  sine*  It  usually  gives  linearity  between 
 kO  and  95  percent  mortality,  and  since  special  log-probability  paper 
 can  be  obtained  for  rapid  graphic  interpolation.  As  a  natter  of  fact, 
 between  25  and  70  percent  the  untransformed  dosage-mortality  curre  is 
 near  enough  linearity  for  rough  Interpolation,  but  abore  70  percent 
 the  transformation  is  an  improvement.  When  the  estimate  of  equiv- 
 alence has  been  obtained,  the  concentration  of  the  mixture  can  be 
 calculated  in  terms  of  either  constituent,  and  expected  similar  Joint 
 effect  can  be  read  off  the  dosage -mortality  curre  for  the  constituent 
 chosen.  This  predicted  effect  can  be  compared  with  the  actual.  It 
 is  desirable  also  to  have  a  dosage-mortality  curve  for  different  con- 
 centrations of  a  mixture  of  given  proportions.  This  is  not  essential, 
 however,  for  preliminary  determination,  if  one  concentration  that 
 will  cause  mortality  between  50  and  90  percent  is  available.  Results 
 with  this  one  concentration  of  a  mixture,  if  adequately  replicated, 
 may  be  compared  with  calculated  Joint  effect  derived  from  well- 
 determined  dosage -mortality  curves  of  Individual  materials.  The  com- 
 parison Involves  the  determination  of  significance,  the  second  step 
 mentioned.  Significance  is  basically  determined  from  consistency. 
 Finney (j)  discusses  methods  of  determination  of  significance;  the 
 author,  in  the  next  section,  suggests  a  simple  method. 
 
 To  determine  the  equivalence,  similar  slopes  in  both  dosage- 
 mortality  curves  must  be  assumed.  This  la  a  fairly  safe  assumption  for 
 poisons  of  similar  Joint  effect.  In  limited  experimence  slopes  are 
 not  likely  to  differ  significantly,  and  a  common  slope  uay  be  derived 
 and  used.  If  slopes  really  differ,  equivalence  will  vary  at  different 
 points.  This  condition  may  occur  and  add  to  complexity  in  some  cases 
 where  action  Is  independent;  it  seems  unlikely  that  synergism  will  be 
 found  under  such  conditions. 
 
 Finney  (£)  gives  a  good  exposition  of  methods  of  calculation, 
 using  data  from  an  article  by  Martin  (k)   in  the  same  Journal.  Finney 
 illustrates  the  calculation  of  equivalence  from  log-probit  dosage- 
 mortality  curves  for  a  mixture  for  each  ingredient,  with  common  slope, 
 and  the  statement  of  concentration  of  a  mixture  in  terms  of  one  of 
 the  substances  Involved.  A  dosage-mortality  equation  can  then  be 
 written  for  the  mixture,  using  the  equation  for  that  ingredient  in 
 terms  of  which  the  mixture  is  stated.  The  dosage  giving  50  percent 
 mortality  (LJ>.  50),  or  any  other  mortality  level  desired  for  com- 
 parison, can  be  readily  calculated.  Finney  (£)  outlines  a  chi -square 
 test  to  compare  the  actual  effect  of  a  mixture  with  that  expected  from 
 either  Independent  or  similar  Joint  effect.  He  also  cites  a  rather 
 complex  formula  for  standard  error  of  difference  of  L.  D .  50  of  a 
 mixture  from  predicted  L.  D.  50  on  a  Joint-action  basis.  Calculations 
 are  based  on  statistical  methods  developed  for  probit  analysis. 
 
.  k  - 
 
 Short -Out  Procedures 
 
 Much  time  may  he  saved  in  getting  a  preliminary  determination  of 
 equivalence  hy  short-cut  methods,  using  log-prohahlllty  paper  and 
 graphic  determinations.  For  example,  ve  may  take  the  date,  of  Martin 
 used  hy  Finney  on  the  effects  of  rotenone  and  deguelin  on  an  aphid, 
 Maorosiphoniella  sanhorni  (Gill) .  Some  results  obtained  over  a  range 
 of  toxicity  suited  to  the  problems  are  tabulated  as  follows: 
 
 Rotenone 
 
 Deguelin 
 
 Concentrat 
 
 ion 
 
 Mortality 
 Percent 
 
 : 
 : 
 
 Concentration 
 Mg. /liter 
 
 Mortality 
 
 Mg. /liter 
 
 Percent 
 
 3.8 
 
 33.3 
 
 . 
 
 10.1 
 
 37.5 
 
 5.1 
 
 52.2 
 
 • 
 
 20.2 
 
 70.8 
 
 7.7 
 
 85.7 
 
 • 
 
 30.3 
 
 95.9 
 
 10.2 
 
 88.0 
 
 : 
 
 ko.k 
 
 9^.0 
 
 The  data  given  above  are  plotted  on  log-probability  paper  (fig.  1), 
 and  eye-fitted  lines  are  drawn.  A  reading  taken  from  these  lines  at 
 50  percent  shows  that  13.2  units  of  dc~j:olin  are  required  to  equal  k.Q 
 of  rotenone,  or  that  deguelin  is  about  O.36  as  toxic  as  rotenone.  At 
 the  90  -  percent  level  9.7  units  of  rotenone  appear  to  equal  28.0  of 
 deguelin,  giving  deguelin  an  equivalence  of  0.35.  The  average  is  0.355 
 (Finney's  computed  value  is  O.37-). 
 
 According  to  Martin,  the  mixture  of  rotenone  and  deguelin  gave  the 
 results  shown  in  table  1. 
 
 Table  1.— The  actual  and  the  Interpolated  mortality  obtained  vith 
 a  mixture  of  rotenone  and  deguelin  of  given  concentrations 
 
 Rotenone      :  Deguelin      :  Rotenone 
 concentration  :  concentration  :  equivalent 
 :  t 
 
 1/: 
 
 Mortality 
 
 Actual 
 
 Interpolated  Zt 
 
 2/ 
 
 Mg. /liter 
 
 1.0 
 2.0 
 3.0 
 k.O 
 
 Mg. /liter 
 
 k.l 
 
 8.1 
 
 12.2 
 
 16.3 
 
 Percent 
 
 Percent 
 
 2.5 
 
 V.9 
 7.3 
 9.8 
 
 1*7.8  i  11.2 
 58.7  i  5.0 
 79.2  ±  10.2 
 93.5  =t  2.9 
 
 51 
 78 
 90 
 
 l/  Rotenone  +  0.355  deguelin, 
 2/  See  fig.  1. 
 
-  5  - 
 
 By  using  the  "rotenone  equivalent"  as  concentration,  the  expected 
 Joint  effect  can  he  read  off  from  the  eye-fitted  rotenone  line.  For 
 instance,  vith  equivalent  of  7.3  the  expected  kill  Is  read  as  78  per- 
 cent. It  vill  he  shown  at  each  point  that  the  actual  Is  somevhat 
 greater  than  the  estimated  effect,  hut  the  estimated  effect  comes  within 
 1  or  2  standard  errors  of  the  actual.  More  exact  calculation  will 
 gire  a  little  better  results.  The  estimated,  as  well  as  the  actual, 
 ralues  have  calculable  standard  errors,  which  decreases  the  tendency 
 to  significant  differences;  on  the  other  hand,  the  fact  that  all  dif- 
 ferences are  in  the  same  direction  will  Increase  this  tendency.  The 
 conclusions  of  Finney  are  the  same  as  hare  been  reached  by  the  shorter 
 method  in  a  few  minutes  work.  The  mixture  tends  to  produce  an  effect 
 exceeding  Joint  action,  but  this  tendency  does  not  reach  significance. 
 
 The  other  cases  treated  by  Martin  and  Finney  hare  been  studied  in 
 the  same  way.  Working  as  above,  the  author  calculated  a  rotenone 
 equivalent  of  0.215  for  elliptone,  as  compared  with  Finney's  0.20.  For 
 toxicarol  the  equivalent  calculated  is  0.175,  as  compared  with  Finney's 
 0.16.  The  conclusions  as  to  synergism  arrived  at  by  the  rapid  method 
 were  the  same  as  those  reached  by  Finney  by  the  more  complex  mathe- 
 matical method. 
 
 Dosage-mortality  curves  from  replicated  experiments  would  afford 
 opportunity  for  several  Independent  determinations  of  equivalence,  and 
 of  expected  mortality  from  a  mixture.  The  latter  could  be  used  in 
 calculating  a  standard  error.  Vith  error  estimates  for  both  calculated 
 and  actual  effects,  tl 
 easily  be  calculated. 
 
 Summary 
 
 The  author  defines  the  types  of  Joint  action  of  insecticides  com- 
 bined In  a  mixture.  He  then  shows  that,  in  order  to  prove  the  exis- 
 tence of  synergism,  the  effect  of  the  mixture  must  be  shown  to  be 
 significantly  greater  than  the  maximum  effect  predictable  from  separate 
 actions  of  the  Insecticides.  This  maximum  is  given  by  assumption  of 
 similar  Joint  effect.  Dosage -mortality  curves  for  separate  Ingredients 
 may  be  used  to  estimate  equivalence  and  expected  similar  Joint  effect. 
 Replicated  trials  with  a  mixture  may  be  used  for  comparison  vith  the 
 estimated  effect.  A  much-shortened  graphic  procedure  vill  give  results 
 of  practical  value.  In  many  cases  the  type  of  action  produced  by  a 
 mixture  vill  not  be  exactly  determinable  from  results,  but  a  clear-cut 
 superiority  over  a  calculated  similar  Joint  effect  vill  indicate 
 synergism. 
 
 Literature  Cited 
 
 (1)  Bliss,  C.  I. 
 
 1939.  The  toxicity  of  poisons  applied  Jointly.  Ann.  Appl.  Biol. 
 26:  585-615. 
 
 (2)  Cox,  A.  J. 
 
 19^3.  Terminology  of  insecticides,  fungicides,  and  other  economic 
 poisons.  Jour.  Scon.  Eat.  36:  813-821. 
 
-  6 
 
 (3)  Tinney,  D.  J. 
 
 19H2.  The  analysis  of  toxicity  tests  on  Mixtures  of  poisons, 
 Ann.  Appl.  Biol.  29s  82 -9U. 
 
 (*)  Martin,  J.  T. 
 
 19^2#  The  problem  of  the  eralnation  calculation  of  rotenone- con- 
 taining plants  (Til).  Ann.  Appl.  Biol.  29:  69 -6*1. 
 
 (5)  Wadley,  F.  M. 
 
 19^3.  Statistical  aspects  of  laboratory  tests  of  inseotloides. 
 Aa»r.  Assoc.  Adr.  Sol.  Pub.  20:  177-188. 
 
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