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UBC Theses and Dissertations

Laboratory studies of competition in two species of cellular slime molds : Dictyostelium discoideum and… McQueen, Donald James 1970

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LABORATORY STUDIES OF COMPETITION OF CELLULAR  I N TWO  SLIME MOLDS; DICTYOSTELIUM  AND  POLYSPHONDYLIUM  -  SPECIES DISCOIDEUM  PALLIDUM  by  DONALD JAMES MCQUEEN B.Sc,  University  of B r i t i s h  Columbia,  1966  M.Sc,  University  of B r i t i s h  Columbia,  1968  A T H E S I S SUBMITTED  IN PARTIAL FULFILMENT  THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in  t h e Department of ZOOLOGY  We  accept  required  this  thesis  as c o n f o r m i n g  to the  standard  THE UNIVERSITY OF B R I T I S H COLUMBIA May,  1970  OF  In p r e s e n t i n g  this thesis  in p a r t i a l  an advanced degree at the U n i v e r s i t y the L i b r a r y  f u l f i l m e n t o f the requirements f o r of B r i t i s h  Columbia,  s h a l l make i t f r e e l y a v a i l a b l e f o r reference  I f u r t h e r agree tha  permission  I agree  that  and study.  f o r e x t e n s i v e copying o f t h i s t h e s i s  f o r s c h o l a r l y purposes may be granted by the Head o f my Department o r by  h i s representatives.  of  t h i s t h e s i s f o r f i n a n c i a l gain  written  permission.  Department o f  ZOOLOGY  The U n i v e r s i t y o f B r i t i s h Vancouver 8, Canada  Date  I t i s understood that  May 2 5 , 1 9 7 0  Columbia  shall  copying o r p u b l i c a t i o n  not be allowed without my  i  ABSTRACT  The competitive  mechanics- o f  s i t u a t i o n and  term i n t e r s p e c i f i c using  two  species  discoideum  and  competition the  some o f  competition of c e l l u l a r  assessed, e x p e r i m e n t a l l y ,  the  consequences of  pallidum.  The  in  e x p l o i t a t i o n and  and  the  p r e d i c t i o n s of  c y c l e of  the  ability D. and  the  to the  competitive  amoeba c o l o n y  expansion.  27°C but  slime  and  the  availability  mold s p e c i e s .  Both species  the  time r e q u i r e d  i r a t e and  form of  engaged  and  to  These rate for  fruiting  interfered with  bodies.  the  and fruitbody  other's  In mixed c u l t u r e s , consumed food  discoideum f r u i t i n g  the  e x p l o i t a t i o n component  f o r spore germination,  amoebae d i v i d e d D.  The  expansion, the  to form f r u i t i n g  discoideum  f o r c e s , the  sub-components which c o n t r i b u t e d  cellular  time required  i n g body p r o d u c t i o n , colony  which  number o f p o t e n t i a l c o m p e t i t o r s  interference.  depended upon a l l o f  form of  linked •  These were: e x p l o i t a t i o n , t o x i c i n t e r f e r e n c e ,  resources,  were: the  and  laboratory.  of  life  of  T h e s e v/ere  modelled mathematically,  e f f e c t of p h y s i c a l f a c t o r s or e x t e r n a l  the  laboratory  mechanics  i n t o component p a r t s .  F i v e major components c o n t r i b u t e d situation.  i n the  long  a components method i n w h i c h  to form a computer model, the  were t e s t e d i n the  interspecific  s l i m e mold; D i c t y o s t e l i u i n  were s t u d i e d u s i n g divided  term  were s t u d i e d  Po.1 y s p h o n d y 1 ium  p r o c e s s was  together  a short  d i d not  between  occur  above  9°  i i  about  24 Co  I n mixed c u l t u r e s ,  and  consumed f o o d b e t w e e n  ing  bodies  d i d n o t form  interference numbers> altered  t h e parameter  contributing  divided  1 8 ° and 3 7 ° C b u t P. p a l l i d u m 24°C.  below about  was m e d i a t e d  Temperature,  P. p a l l i d u m amoebae  by temperature  In both  fruit-  cases  and c o m p e t i t o r  the representative external  force,  v a l u e s o f a l l t h e sub-components  to exploitation  and i n t e r f e r e n c e .  When a l l o f t h e c o m p o n e n t s were a s s e s s e d t h e y incorporated  into  a c o m p u t e r m o d e l w h i c h was u s e d  the  area o c c u p i e d by t h e f r u i t i n g  The  simulation  of  was t e s t e d  324  bodies  were  to predict  o f both  species.  and was a c c u r a t e i n 90.1%  times  the cases. The  long term  experimental  studies o f the conse-  quences o f c o n t i n u e d c o m p e t i t i o n r e v e a l e d t h a t  after  a period  o f c o n t i n u e d c o m p e t i t i o n P. p a l l i d u m o v e r c a m e t h e e f f e c t s o f D. d i s c o i d e u m  inhibition  D. d i s c o i d e u m . to  37°C  24°  and D . d i s c o i d e u m  mixed c u l t u r e s ,  9°  from  after  about  from  9 ° to 27°C.  from  about  from  18°  I n mixed from  9 ° to 24°C.  about In  c o n t i n u e d c o m p e t i t i o n , P. p a l l i d u m  2 0 ° t o 37°C  and D. d i s c o i d e u m  from  about  to 24°C. Apparently  and  fruited  b e f o r e c o m p e t i t i o n , P. p a l l i d u m f r u i t e d  t o 37°C  fruited  i n the presence o f  When grown a l o n e P. p a l l i d u m f r u i t e d  a n d D. d i s c o i d e u m  cultures,  and f r u i t e d  a t t h e same t i m e  P. p a l l i d u m c o n v e r g e d D. d i s c o i d e u m  t o w a r d s D.  discoideum,  increased i t s rate of  r e s o u r c e u s e , and d i v e r g e d away f r o m  P. p a l l i d u m .  The d a t a  iii  suggested  t h a t i n t e r f e r e n c e was r e l a t e d to the p r o d u c t i o n o f  chemicals during the aggregation stage.  I t i s possible  that  a c r a s i n , the c h e m i c a l which a t t r a c t s amoebae t o a g g r e g a t i o n centers i s involved.  E x p e r i m e n t a l evidence  also  suggested  t h a t the change e x p e r i e n c e d by P. p a l l i d u m might have r e s u l t e d from p a r a - s e x u a l i t y . T h i s e n t a i l s the p r o d u c t i o n o f d i p l o i d s p o r e s , the r e c o m b i n a t i o n o f a l l e l e s ,  and chromosome  loss,  a l l o f which tend t o p r o t e c t r e c e s s i v e and l e s s f i t c h a r a c t e r istics.  PREFACE  The  work p r e s e n t e d  towards t h e study cellular  of competition  s l i m e m o l d grown u n d e r  was a n t i c i p a t e d t h a t studied of  over  competitive laboratory existing  and t h a t  c o u l d be s t u d i e d d u r i n g  this  theory  study  to obtain  results  t h e way i n w h i c h  environment, beginning ending  with  spores.  describe  studies.  of f r u i t i n g evidence  A similar  mechanics their  o f spores  bodies  which  i s presented, of information  species express  procedure i s followed  s e c t i o n d e a l i n g with  interfere  with  one a n o t h e r .  during  and  contain diagrams and t o  two s p e c i e s  exploited their  one a n o t h e r .  The r e s u l t s  Since  t h e end o f t h e f i r s t  to simulate environment  of this  link  the develop-  t h e way i n w h i c h t h e  t h e a c t i o n o f t h e v a r i o u s components  a c o m p u t e r m o d e l was c o n s t r u c t e d  at  an o v e r v i e w o f c o m p e t i -  the germination  to follow the build-up  ment o f t h e s e c o n d  with  some o f t h e  t h e way i n w h i c h t h e v a r i o u s p i e c e s o f e v i d e n c e  together.  the  that  t h e two s p e c i e s e x p l o i t  As t h e e x p e r i m e n t a l  have been used  some o f t h e r e s u l t s  s e c t i o n on c o m p e t i t i v e  with  the production  c o u l d be  c o u l d be r e l a t e d t o  t h a t m i g h t be a p p l i c a b l e t o f i e l d first  It  long periods of  I t was a l s o h o p e d  f i n d i n g s from  competitive  describes  to  b e t w e e n two s p e c i e s o f  the mechanics of competition  exposure.  The  two  thesis i s directed  laboratory conditions.  s h o r t time p e r i o d s  competition  tion  i n this  i t was p o s s i b l e mathematically,  t h e way i n w h i c h and i n t e r f e r e d  simulation are presented  s e c t i o n on c o m p e t i t i v e  mechanics.  V  In continued  competition,  ecological and  t h e second r e s u l t s  hypotheses r e l a t i n g  convergence,  some o f t h e d a t a  s e c t i o n which d e a l s  and e c o l o g i c a l  obtained  competitive  divergence  are used  with pressure,  are tested  i n the simulation  model. The first  d i s c u s s i o n i s presented  considers  mold b i o l o g y . of  the  findings relevant to general The s e c o n d  are four  computer programs  deals with  the e c o l o g i c a l  appendices.  In the f i r s t ,  and t h e i r  second c o n t a i n s  referred with  explanatory  slime  aspects  to i n the r e s u l t s  sections.  nine  are presented.  are i n d i r e c t l y  The t h i r d  i s concerned  t h e g e n e r a l i t y and g o o d n e s s o f f i t , o f t h e e q u a t i o n  colonies  expand.  the t e s t s  ability the  write-ups  s e v e r a l f i g u r e s which  w h i c h d e s c r i b e s t h e way i n w h i c h  of  cellular  The  study. There  The  i n two s e c t i o n s .  used  The f o u r t h a p p e n d i x c o n t a i n s to s t a t i s t i c a l l y  of the various  results  amoebae and f r u i t i n g  section.  rate  determine  and l a g e q u a t i o n s  an  body  explanation  the d e s c r i p t i v e developed  in  vi  TABLE OF CONTENTS PAGE Abstract  i  Preface  iv  T a b l e o f Contents  vi  L i s t of Tables  ix  L i s t of F i g u r e s  xi  Acknowledgement  xvi  Introduction  1  The Animals  6  M a t e r i a l s and Methods  14  L a b o r a t o r y Methods  14  Experimental Error  19  Mathematics  21  R e s u l t s S e c t i o n I : Mechanics  of Competition  23  Spore G e r m i n a t i o n  23  Amoeba Colony Expansion  31  The Form o f Colony Expansion  31  The Rate o f Colony Expansion  36  Fruiting  Body Lag  46  Fruiting  Body Formation  50  The Form o f F r u i t i n g  Body Colony Expansion  50  The Rate o f F r u i t i n g  Body Colony Expansion  54  T e s t i n g the E x p l o i t a t i o n Models  60  Summary  65  The E x p l o i t a t i o n - C o m p e t i t i o n S i m u l a t i o n  66  vii  PAGE Interference  73  I n h i b i t i o n o f P. p a l l i d u m  73  C o n f i d e n c e L i m i t s on P. p a l l i d u m I n t e r f e r e n c e  33  I n h i b i t i o n o f D. discoideum  83  The Completed Model  86  T e s t s o f the Model  89  A r e a Occupied by F r u i t i n g Bodies  89  Continued C o m p e t i t i o n  92  Summary  92  R e s u l t s S e c t i o n I I : Consequences o f C o m p e t i t i o n  95  M i x t u r e o f Stock Spores  97  Continued M i x t u r e s  97  Culture Gradient I  99  Culture Gradient I I  101  Culture Gradient I I I  102  C u l t u r e G r a d i e n t IV  103  Changes Between 18° and 24«,5°C  110  Which Competitors Changed  110  Mechanics  112  o f the Change  The Type o f Change  115  C l o n i n g Experiments  117  Changes Between 24° and 26.5°C  118  S i m i l a r i t y o f Resource  119  Use  Germination Lags  121  Colony Expansion Rates  121  Stock Spore Germination Rates  12 7  viii PAGE Stock  Colony Expansion Rates  12 7  Summary  137  Discussion  139  Section  I: Cellular  S l i m e Mold  Biology  139  Inhibition  139  Genetics  143  Section  I I : Ecological  Convergence  Relevance  147  and C o e x i s t e n c e  147  Components o f C o m p e t i t i o n Literature Appendix  149  Cited  157  I - Computer P r o g r a m s  164  Program  I  - Curve F i t t i n g  (Equation  2b)  Program  II  - Form o f C o l o n y E x p a n s i o n ( E q u a t i o n  Program  III  - Calculation  Program  IV  - Curve F i t t i n g  (Equation  3c)  179  Program  V  - Curve F i t t i n g  (Equation  4b)  181  Program  VI  - Exploitation  of Single  Program  VII  - Exploitation  o f Mixed S p e c i e s  Program  VIII  - Inhibition  Program  IX  - Completed  o f Mean S l o p e  Species  o f P. p a l l i d u m Model  165 l c ) 170 172  185 194 198 202  Appendix  I I - Figures  216  Appendix  I I I - Goodness o f F i t o f E q u a t i o n  Appendix  IV - S t a t i s t i c a l S i g n i f i c a n c e (2b), ( 3 c ) , and ( 4 b )  (lc)  228  of Equations  2 33  ix  L I S T OF  TABLES  TABLE I  PAGE A c o m p a r i s o n o f D. d i s c o i d e u m V12 l a g times from c u l t u r e s i n o c u l a t e d w i t h v a r i o u s spore c o n c e n t r a t i o n s .  29  A c o m p a r i s o n o f P. p a l l i d u m l a g t i m e s from c u l t u r e s i n o c u l a t e d with v a r i o u s spore c o n c e n t r a t i o n s ,  30  A c o m p a r i s o n o f D. d i s c o i d e u m V12 g r o w t h i n d e x e s from c u l t u r e s i n o c u l a t e d w i t h v a r i o u s spore c o n c e n t r a t i o n s .  44  A c o m p a r i s o n o f P. p a l l i d u m g r o w t h i n d e x e s from c u l t u r e s i n o c u l a t e d w i t h v a r i o u s spore c o n c e n t r a t i o n s .  45  C h a n g e s i n t h e maximum a r e a o c c u p i e d b y P. p a l l i d u m f r u i t i n g b o d i e s , w i t h c h a n g e s in temperature.  53  A c o m p a r i s o n o f D. d i s c o i d e u m VC4 amoeba' c o l o n y a r e a o b s e r v e d and e s t i m a t e d f r o m Program V I .  61  VII  A c o m p a r i s o n o f P. p a l l i d u m amoeba.: c o l o n y a r e a o b s e r v e d and e s t i m a t e d f r o m P r o g r a m VI.  62  VIII  A c o m p a r i s o n o f D. body a r e a o b s e r v e d Program V I .  63  II  III  IV  V  VI  IX  d i s c o i d e u m VC4 f r u i t i n g and e s t i m a t e d f r o m  A c o m p a r i s o n o f P. p a l l i d u m f r u i t i n g b o d y a r e a o b s e r v e d and e s t i m a t e d f r o m P r o g r a m V I I .  X  A c o m p a r i s o n o f P. p a l l i d u m s p o r e g e r m i n a t i o n l a g s b e f o r e and a f t e r c o m p e t i t i o n .  XI  A c o m p a r i s o n o f D. d i s c o i d e u m spore g e r m i n a t i o n l a g s b e f o r e and a f t e r competition.  XII  XIII  A c o m p a r i s o n o f P. p a l l i d u m s p o r e t i o n l a g s beforehand a f t e r media conditioning.  germina-  A c o m p a r i s o n o f D. d i s c o i d e u m VC4 g e r m i n a t i o n l a g s b e f o r e and a f t e r conditioning.  spore media  64 -^22  12 3  128  129  x  PAGE  TABLE XIV  The for  proportion of v a r i a b i l i t y accounted b y e q u a t i o n s ( 2 b ) , ( 3 c ) , and ( 4 b ) .  L I S T OF FIGURES  I l l u s t r a t i o n o f P. p a l l i d u m b o d y grown a t 24^C.  fruiting  I l l u s t r a t i o n o f P. p a l l i d u m f r u i t i n g grown a t 3 6 ° C . Illustration body.  o f D. d i s c o i d e u m  Illustration of co-fruiting and P. p a l l i d u m .  body  fruiting  D.  Diagram o f temperature g r a d i e n t i n p l a n and s i d e v i e w .  discoideum  apparatus  D. d i s c o i d e u m VC4 g e r m i n a t i o n l a g p l o t t e d against temperature. P. p a l l i d u m s p o r e g e r m i n a t i o n l a g p l o t t e d against temperature. General curve r e l a t i n g l a g and t e m p e r a t u r e .  spore germination  S i m u l a t e d a r e a s c o v e r e d b y amoeba c o l o n i e s a t v a r i o u s i n t e r v a l s o f t i m e and w i t h various values of g i n equation ( l c ) . The s q u a r e r o o t o f a r e a p l o t t e d a g a i n s t time. A c t u a l and p r e d i c t e d l i n e s a r e plotted. The s q u a r e r o o t o f amoeba c o l o n y a r e a i s p l o t t e d a g a i n s t t i m e f o r D. d i s c o i d e u m and P. p a l l i d u m . D. d i s c o i d e u m V12 c o l o n y e x p a n s i o n p l o t t e d against temperature. P. p a l l i d u m c o l o n y e x p a n s i o n against temperature.  rate  D. d i s c o i d e u m VC4 c o l o n y e x p a n s i o n p l o t t e d against temperature. General curve r e l a t i n g and t e m p e r a t u r e .  colony  rate plotted rate  expansion  xii  FIGURE 16 17 18  19  20  21  22 23  24  25  26  27  PAGE D. d i s c o i d e u m VC4 f r u i t i n g against temperature. P. p a l l i d u m f r u i t i n g against temperature.  body  body  lag plotted 48  lag plotted 49  The s q u a r e r o o t o f f r u i t i n g b o d y c o l o n y a r e a p l o t t e d a g a i n s t t i m e f o r D. d i s c o i d e u m and P. p a l l i d u m . D. d i s c o i d e u m VC4 f r u i t i n g b o d y g r o w t h p l o t t e d against temperature.  51  index 56  £• p a l l i d u m f r u i t i n g body e x p a n s i o n r a t e s p l o t t e d against temperature. E q u a t i o n (2c) was u s e d t o f i t t h e l i n e .  57  P. p a l l i d u m f r u i t i n g b o d y e x p a n s i o n r a t e s p l o t t e d against temperature. E q u a t i o n (4b) was u s e d t o f i t t h e l i n e .  59  Components d i a g r a m o f t h e e x p l o i t a t i o n model.  completed  The a r e a o c c u p i e d b y t h e f r u i t i n g b o d i e s and amoebae o f D. d i s c o i d e u m and P. p a l l i d u m a t one day i n t e r v a l s a r e p l o t t e d a g a i n s t time. The d a t a was g e n e r a t e d f r o m P r o g r a m VII. The p r e s e n c e o r a b s e n c e o f D. d i s c o i d e u m and P. p a l l i d u m f r u i t i n g b o d i e s a r e i n d i c a t e d with respect to temperature. Twenty s p o r e c o n c e n t r a t i o n s were u s e d . The p r e s e n c e o r a b s e n c e o f D. d i s c o i d e u m and P. p a l l i d u m f r u i t i n g b o d i e s a r e i n d i c a t e d with respect to temperature. F i v e spore c o n c e n t r a t i o n s were u s e d . P r e s e n c e o r a b s e n c e o f P. p a l l i d u m f r u i t i n g b o d i e s i s i n d i c a t e d w i t h r e s p e c t t o clump s i z e and t e m p e r a t u r e . The p r e s e n c e o r a b s e n c e o f P. p a l l i d u m f r u i t ing bodies i s i n d i c a t e d with r e s p e c t to D. d i s c o i d e u m s p o r e c o n c e n t r a t i o n and temperature.  67 70  7  1  72  75  81  The p r e s e n c e o r a b s e n c e o f D. d i s c o i d e u m f r u i t i n g bodies i s indicated with respect t o D. d i s c o i d e u m s p o r e c o n c e n t r a t i o n and temperature. Components d i a g r a m o u t l i n i n g t h e make-up of Program IX. External force, interference and e x p l o i t a t i o n s u b - c o m p o n e n t s a r e shown. The a r e a o c c u p i e d b y P. p a l l i d u m and D. d i s c o i d e u m f r u i t i n g b o d i e s i s p l o t t e d against temperature. S i x spore concentrat i o n s were u s e d . The a r e a s p r e d i c t e d f r o m P r o g r a m IX and t h e i r 9 5 % c o n f i d e n c e i n t e r v a l s are a l s o d e p i c t e d . A r e a s o c c u p i e d b y D. d i s c o i d e u m and P. p a l l i d u m s t o c k f r u i t i n g b o d i e s a r e p l o t t e d with respect to temperature. G r a d i e n t I - The a r e a o c c u p i e d b y f r u i t i n g b o d i e s from twelve s e r i a l c u l t u r e g r a d i e n t s i s p l o t t e d with respect to temperature. £° p a l l i d u m agar b l o c k e x p e r i m e n t : The a r e a s o c c u p i e d by f r u i t i n g b o d i e s a r e p l o t t e d with respect to temperature. The p r e s e n c e o r a b s e n c e o f P. p a l l i d u m amoebae on a g a r blocks i s noted. D. d i s c o i d e u m ( g r a d i e n t I ) c o l o n y e x p a n s i o n index i s p l o t t e d against temperature. P. p a l l i d u m ( g r a d i e n t I ) c o l o n y e x p a n s i o n index i s p l o t t e d against temperature. D. d i s c o i d e u m ( g r a d i e n t I I ) c o l o n y e x p a n s i o n index i s p l o t t e d against temperature. pallidum (gradient II) colony expansion index i s plotted-.against temperature. The e x p a n s i o n r a t e s o f P. p a l l i d u m s t o c k s which have e x p e r i e n c e d media c o n d i t i o n i n g are p l o t t e d a g a i n s t temperature. The e x p a n s i o n r a t e s o f D. b e f o r e media c o n d i t i o n i n g against temperature.  discoideum VC4 are p l o t t e d  x i v  PAGE  FIGURE 40  The  e x p a n s i o n  a f t e r  m e d i a  a g a i n s t  41  42  r a t e s  D.  c o n d i t i o n i n g  t e m p e r a t u r e .  The amount o f a r c o m p e t i t o r s b e f o i s p l o t t e d a g a i n was o u t p u t from The  o f  e a r e s t Pro  d i s c o i d e u m are  VC4  p l o t t e d  o c c u p i e d by the two and a f t e r c o m p e t i t i o n t e m p e r a t u r e . The d a t a gram VTI.  a r e a  o c c u p i e d  by  a r e a  o c c u p i e d  by  P.  p a l l i d u m  and  P.  p a l l i d u m  and  R' d i s c o i d e u m V12 i s p l o t t e d a g a i n s t tempera t u r e . F i v e spore c o n c e n t r a t i o n s were u s e d . 43  The D.  d i s c o i d e u m  t e m p e r a t u r e . were u s e d . 44  The  area  F i v e  o c c u p i e d  Q° d i s c o i d e u m t e m p e r a t u r e . were u s e d .  45  i s  p l o t t e d  spore  by  P.  by i s  G r a d i e n t  a r e a  II  F i v e  -  a g a i n s t  p a l l i d u m  The  f r u i t i n g b o d i e s from g r a d i e n t s i s p l o t t e d t e m p e r a t u r e .  c o n c e n t r a t i o n s  o c c u p i e d  G r a d i e n t III - The a r e a o c c u p i e d by f r u i t i n g b o d i e s from t e n s e r i a l c u l t u r e g r a d i e n t s i s p l o t t e d w i t h r e s p e c t to t e m p e r a t u r e .  48  G r a d i e n t IV - The a r e a o c c u p i e d by f r u i t i n g b o d i e s from f i v e s e r i a l c u l t u r e g r a d i e n t s i s p l o t t e d w i t h r e s p e c t t o t e m p e r a t u r e . The  areas  o c c u p i e d  by  P.  218  p a l l i d u m  R' d i s c o i d e u m f r u i t i n g b o d i w i t h r e s p e c t t o t e m p e r a t u r e c o m b i n a t i o n s of s p o r e s whic not e x p e r i e n c e d c o n t i n u e d c u s e d .  219  220  by  t w e l v e s e r i a l c u l t u r e w i t h r e s p e c t to  47  49  217  and  P. p a l l i d u m and p l o t t e d a g a i n s t  spore  136  c o n c e n t r a t i o n s  V12 i s p l o t t e d a g a i n s t F i v e spore c o n c e n t r a t i o n s  The a r e a o c c u p i e d D. d i s c o i d e u m V12 t e m p e r a t u r e . were u s e d .  46  V12  133  221  222  223  and  e s are p l o t t e d . V a r i o u s h had and had o m p e t i t i o n were  224  XV  FIGURE 50  51  52  53  54  PAGE The a r e a s o c c u p i e d b y f r u i t i n g b o d i e s a r e p l o t t e d with r e s p e c t t o temperature. Some spores used t o i n o c u l a t e g r a d i e n t s experienced i n t r a s p e c i f i c competition, others d i d not. C l o n i n g e x p e r i m e n t : The a r e a s o c c u p i e d b y f r u i t i n g bodies are p l o t t e d with respect to temperature. The P. p a l l i d u m s p o r e s u s e d i n e a c h g r a d i e n t came f r o m s e p a r a t e clones. D. d i s c o i d e u m a g a r b l o c k e x p e r i m e n t : The areas o c c u p i e d by f r u i t i n g b o d i e s a r e p l o t t e d with respect to temperature. The p r e s e n c e o r a b s e n c e o f D. d i s c o i d e u m amoebae o n t h e a g a r b l o c k s i s n o t e d . The s q u a r e r o o t o f c o l o n y a r e a i s p l o t t e d against time. All. data i s transformed t o f i t t h e l i n e PH = 3 t where A i s a r e a and t i s t i m e . The s q u a r e r o o t o f f r u i t i n g body c o l o n y a r e a i s p l o t t e d a g a i n s t time f o r both R' d i s c o i d e u m ( s o l i d d o t s ) and P. p a l l i d u m (open c i r c l e s ) . A l l data i s transformed to conform t o t h e l i n e d e s c r i b e d by equation ( 7 ) .  225  226  227  2 31  2 32  xvi  ACKNOWLEDGEMENT  I  would  especially  professor,  D r . P.A. L a r k i n ,  criticism,  enthusiasm,  I  am a l s o  and b a c t e r i a  cultures,  comments  the mathematical  photographic Dr.  of constructive  throughout  this  suggestions  components,  t h e f o r m u l a t i o n o f some  and Mr. F . M a u r e r f o r  Dr. J . T . Bonner,  D r . C . L . McLay,  and D r . N . J . W i l i m o v s k y  the manuscript  like  several  made many the manuscript.  t o t h a n k my w i f e , W i n n i e , times  slime  and D r . C.S. M o i l i n g f o r  which I have i n c o r p o r a t e d i n t o  I would  study.  F r a n c i s f o r c u l t u r e s and  and h e l p w i t h  services.  J.D. M c P h a i l ,  Finally,  and s u p p o r t ,  major  i n f o r m a t i o n , D r . K.B. R a p e r f o r c e l l u l a r  manuscript of  t o t h a n k my  who was a s o u r c e  i n d e b t e d t o ; D r . D.W.  technical mold  like  over.  who  typed  1  INTRODUCTION The  process  o f animal  g r e a t many e c o l o g i s t s o v e r yielded  studies.  confusion over  Milne the  the exact  (1957) h a v e d e v o t e d  process  coverage.  involving  i n a certain  that d e f i n i t i o n s  amount  competition.  entire  F o r e x a m p l e , Odum  papers t o  ranged  from  (1959) i n c l u d e s  t h e common u s e o f s p a c e ,  o r waste m a t e r i a l a c t i o n ,  i n t e r e s t has  e x p e r i m e n t a l , and  meaning o f t h e term  s u b j e c t , and h a v e n o t e d to strict  has f a s c i n a t e d a  and t h e i r  I t has a l s o r e s u l t e d  ( 1 9 6 1 ) and B i r c h  broad any  the years;  a l a r g e number o f d e s c r i p t i v e ,  theoretical of  competition  food  and l i g h t ;  o r mutual p r e d a t i o n , o r suscept-  ibility  t o c a r n i v o r e s a n d d i s e a s e . Clements-, a n d S h e l f o r d  provide  a strict  definition.  may b e d e f i n e d i n c l u s i v e l y excess part  o f t h e immediate  o f two o r more The  used for  maintaining  supply  secured  tion for  being  by animals  animals  dissipated  survival.").  operative  sub-divided.  Nicholson  (the competitors  "... and a l l o f t h e g o v e r n i n g  the population.")  competing  demand i n  o f m a t e r i a l o r c o n d i t i o n on t h e  "contest" competition  ("... some, and a t t i m e s the  active  organisms".  requisites  collectively  words: "... t h e p r o c e s s  a s a more o r l e s s  term h a s a l s o been  t h e terms their  In t h e i r  (1939)  contest  requisite  effectively i n  and " s c r a m b l e "  competition  a l l , o f the requisite  takes  secured  by  no p a r t i n s u s t a i n i n g t h e p o p u l a -  by i n d i v i d u a l s  Allee  competition"  i s used  (1954)  which o b t a i n  insufficient  e t a l (1949) have i d e n t i f i e d " c o (beneficial  effect)  and " d i s - o p e r a t i v e  2  competition"  (harmful  The and  effect).  one i d e a t h a t runs  s u b d i v i s i o n s i s t h a t animals  throughout  compete when t h e y  resource  that i s i n short  and  (1954) d i s c u s s t h e i m p o r t a n c e  Park  such  as t e m p e r a t u r e .  exploitation  supply.  Finally,  ( t h e common  interference (thedirect  can  play active  outcomes.  all  by  this  biological  interactions  i n short between  supply)  competitors)  of competitive  study  i n short supply,  and t h e o c c u r r e n c e  the role of  the effects of  of interference, will  Holling  edited  (1963,  process  b y Watt  e n d , t h e c o m p o n e n t s method w i l l  relevance  p r e d a t i o n model,  (1966).  sub-model i s then  The e f f e c t  are involved.  A  o f a component i s  and m o d e l l e d  mathematically.  t o make p r e d i c t i o n s w h i c h  Failure  and s t a r t s  model  t h e c y c l e back  together  as t h e y  i s periodically  The  are tested  o f t h e sub-model i n i t i a t e s  Sub-models a r e l i n k e d  the resulting  o f papers  what a p p e a r t o be e x p e r i m e n t a l l y  used  ment o f t h e component step.  demonstrated  the construction of a  S i x basic steps  experimentally  independently.  be u s e d .  and h a s been d i s c u s s e d i n a s e r i e s  components.  demonstrated  o f t h e method h a s b e e n  1964, 1965) d u r i n g  i s broken i n t o  tractable  and  (1954)  be c o n s i d e r e d . To  The  Nicholson  (1954) p o i n t s o u t t h a t  point f o rthis  f o rresources  factors,  Park  use a  of physical factors,  i n the determination  As a s t a r t i n g  exploitation physical  roles  A l s o , both  use o f a resource  and  a l l the d e f i n i t i o n s  a reassess-  a t the f i r s t  are formulated  tested  against  3  independent  data.  The  use  of  t h e c o m p o n e n t s method i s p o s s i b l e o n l y  b e c a u s e p a s t work on  t h e mechanisms which m e d i a t e  interactions  has  experimental  techniques  1965)  and  the  advanced  field  of  the  at  a different  Kostitzin  nature  1939,  this  Slobodkin  "b",  or  populations  model  MacArthur  i n nature  Levins  and  other) because  (Gause  1934,  Through  the  altered  outcome  to  persist;  (competitor  field  population  (Elton  (1964, 1967)  in  et a l  stable equilibrium irrespective  of  the  depends  number c o n d i t i o n s  under o t h e r s ,  remain untested  assess.  but  of  equilibrium (stability  the  a  Lotka-  slightly  u n d e r some i n i t i a l  are d i f f i c u l t and  i n the  stabilize  unstable  the  progressed  intact.  p r e d i c t i o n s of  stabilize  excludes  demonstrated  and  populations  numbers,  the  the  Studies  r e v e r s e ) have been demonstrated  19 34)  The  n u m b e r s ) and  population  and  1954,  have been o f  L a r k i n 1963).  have remained  the  have  they  around  predictions regarding  B r i a n 1952).  upon i n i t i a l  t h e most p a r t  1961,  of  1961a, b ) .  competition  been c l a r i f i e d  l a b o r a t o r y (Gause  initial  Connell  predictions of exclusion  (both competitor  the  1950,  use  l a b o r a t o r y (Park  have c e n t e r e d  situations  "a" excludes  1946,  the  through  interspecies competition  four original  The  both  For  and  model has  competitive  the  (Ullyett  level.  V o l t e r r a model o f  the  i n both  consequences of continued  theoretical  years  significantly  competitive  and  one  un-  parameters r e q u i r e d Recognizing  this  have r e s t r i c t e d  by  fact,  initial  4  conditions  and t h e o r e t i c a l l y  competition three the  and c o e x i s t e n c e .  populations  compete  2 c a n be e x c l u d e d  m e d i a t e b e t w e e n t h e two. a selective  things.  1 o r 3.  inter-  f o r c e , convergence o r divergence  ared i r e c t i o n s  respect  t o s e l e c t i o n , and c o e x i s t e n c e  i s the  result.  evidence  (Keast  laboratory  study  competition, laboratory  some r a t h e r c i r c u m s t a n t i a l f i e l d  1968, F i c k e n e t al 1968) and a t l e a s t one (Seaton  divergence,  studies  and A n t o n o v i c s  (Miller  relationship  between c o n v e r g e n c e  have been used  should  Since  the hypothesis  i n coexistence.  t h e competing  assess  work.  populations  t h e magnitude  By n o t i n g i t might  and t h e d i r e c t i o n  competition,  i s tenuous this  i n t h e l a b o r a t o r y under r e s t r i c t e d  be p o s s i b l e t o t e s t  result  to demonstrate a  between  and c o e x i s t e n c e  need o f f u r t h e r e x p e r i m e n t a l  Drosophila  and c o e x i s t e n c e .  In g e n e r a l , however, t h e l i n k convergence o r divergence,  And t h e r e a r e  1964a, b , 1967) i n w h i c h  and D. s i m u l a n s  conducted  1967) l i n k i n g  and c o e x i s t e n c e .  melanoqaster  by  a phenotype  competition i s  There i s also  can  When 0( i s  situation  o f movement w i t h  In this  2in  When (X i s l a r g e  1 and 3 towards  from  with  i n t h e same way ( (3 ) ,  o r can converge with  2 can diverge  t h a t when  1 and 3 i n t e r a c t  each o t h e r  2 c a n do o n e o f t h r e e  population  end  They demonstrated  so t h a t  same way ( C< ) and w i t h  small  d e r i v e d r e l a t i o n s h i p s between  study  and i n was  conditionsi t  that  competition  t h e changes  experienced  a l s o be p o s s i b l e t o of selective  forces  5  involved,  and to determine some o f the c o n d i t i o n s under  convergence or d i v e r g e n c e might o c c u r .  which  THE The identified in  the  Acrasiales  i n 1880  spore  by  or  Van  "cellular  Tieghem.  by m i t o s i s ,  aggregate  fruiting  to produce The  D.  D.  P.  discoideum  discoideum  They  size,  VC4  are kidney  and  spores  shaped  V12 are  and  pallidum Salvador spores  ellipsoid,  and  pale yellow.  life  cycle  to produce  firs  begins  vegetative  consume b a c t e r i a  and  bodies.  s h a p e , and  VC4  s l i m e m o l d s " were  Their  stage which germinates  amoebae w h i c h d i v i d e  and  ANIMALS  c o l o u r o f P. spores  about  pallidum  are d i f f e r e n t .  18 /j l o n g and  have a d i s t i n c t i v e are about  Salvado  half  (  8 ja w i d e .  green-gold  this  ,  size,  hue  7  The is  size  difference  typically  P. p a l l i d u m  suggests  "diploid" Salvador  most c a s e s ,  strain  are very  amoebae, w h i c h (Bonner  93 different bacteria (19 37)  similar.  produce  produce  a number o f f i l o s e  (Singh  r a t h e r than  support  bacteria  strain  mitosis  and when f o o d becomes s c a r c e a s u b s t a n c e  is  by f o u n d e r  produced  This  themselves.  substance  along which of  the c e l l s  phosphodiesterase The  species occurs  i n pulses  (Shafter  which breaks  In the case  streams produce  other  producing gradient  by t h e p r o d u c t i o n down.  procedure  vary  o f D„ d i s c o i d e u m , amoebae f o r m  the aggregation  s t r o n g l y t o one  from  aggregation loosely center  advances t h e streams  and t h e amoebae a d h e r e  aggregating  center  the acrasin  f l o w i n g towards  As a g g r e g a t i o n  attracts  the chemical  i s shortened  and t h e a g g r e g a t i n g  streams  1956).  more d e n s e  move,  exact mechanics o f t h i s  to species.  integrated  The  I n D. d i s c o i d e u m  which has  largely unidentified)  amoebae w h i c h move t o w a r d s t h e a g g r e g a t i o n acrasin  like  T h e amoebae d i v i d e b y  (and which r e m a i n s cells.  Raper  f o r laboratory  of cellular  acrasin  some  growth.  culture  been c a l l e d  at least  1946) a l t h o u g h  were t h e most s u i t a b l e s l i m e molds.  pseudopods"  o f consuming  t h a t Gram-negative, non-slimy  Escherichia coli  amoebae, w h i c h  Both' s p e c i e s  of bacteria  appear t o i n h i b i t  found  the spores  The amoebae a r e c a p a b l e  strains  strain  i s "haploid".  are small "with  1967).  VC4  and h a s 14 chromosomes w h i l e t h e  Upon g e r m i n a t i o n in  t h a t t h e D. d i s c o i d e u m  become  another.  a mass o f amoebae o r  8  pseudoplasmodium which m i g r a t e s . amoebae b e g i n t o d i f f e r e n t i a t e cells. but  During  t o form  N o t s o much i s known a b o u t  i t has been observed migrate  D. d i s c o i d e u m .  K o n i j n e t a l (1969) a l s o  Following differentiate  i n response  stock  about  20% o f the c e l l s  stock  cells  behind.  build  of this  to light  as they  a c h e m i c a l t o break  that  do i n  down  the c e l l s  and s p o r e c e l l s .  are involved  study  reports that  the aggregation stage  t o form  and p r e - s t o c k  a g g r e g a t i o n i n P. p a l l i d u m ,  during the course  p a l l i d u m does n o t produce  process the  pre-spore  pseudoplasmodia  £•  this  I n D.  acrasin.  begin to discoideum  i n stock formation.  up t h e s t o c k w i t h t h e s p o r e  When s t o c k f o r m a t i o n i s c o m p l e t e  cells  The  following  t h e spores  are at  t h e t o p o f t h e s t o c k , i n t h e c a s e o f D. d i s c o i d e u m , o r distributed  at intervals  P. p a l l i d u m . easily  T h e two s p e c i e s u s e d  distinguished  fruiting  along the stock, i n the case o f  bodies  i n the present  at the f r u i t i n g  are d i s t i n c t  body s t a g e .  when f o r m e d  1) b u t become d i s o r g a n i z e d a t h i g h e r  (Fig.  2).  over  i t s entire  fruiting bodies  strains  (Fig.  growth range produce  from  about  well  (Fig. 3).  temperatures  remain  much t h e same  When m i x e d , t h e c o -  o r g a n i z e d and d i s t i n c t  s l i m e mold  species react  characteristics.  4.0 t o 7.8 ( C a v e n d e r  (Whittingham  bodies  24°C  fruiting  4).  Cellular environmental  fruiting  P. p a l l i d u m  a t about  (Fig.  D. d i s c o i d e u m  study are  and R a p e r  Their  to several  pH t o l e r a n c e r a n g e s  1963) and h u m i d i t y  1957) a n d l i g h t  (Bonner  1950)  are  9  important defined  i n some c a s e s .  temperature  f r o m 9.0°  to  ness of reason closely  P.  the  P.  pallidum  medium and  s t r a i n s u s e d had  with  pallidum i s also  amount o f  a s i m p l e medium was  used  D.  well  discoideum  from  18.0°  to  growing 37.5°  greatly influenced food and  available.  food  by  For  richthis  concentration  was  controlled. Finally,  very  two  tolerances  2 6 . 5 ° and  centigrade.  The  the  much a m y s t e r y .  genetics  of  the  It i s generally  chromosome amoebae a r e  diploid  and  Acrasiales  are  assumed t h a t  that  still  14  7 chromosome  amoebae  i  are  haploid.  are  diploid  contain  on  and  that  and  aggregation  (1962) r e p o r t  to  are  haploid  diploids.  amoebae c o a l e s c e form  agreed that  from  meiosis  does not  s u c c e s s when t r y i n g t o  recombination tion  w h i c h has  and not  14  al  that  comm.) times  chromosomes  a population  Sussman the  It is  could generally  (1956) met  occurrence  (1961) r e p o r t e d  repeated.-  others  (pers.  lose  chromosomes.  occur.  some s t r a i n s  i n a thousand  that  demonstrate  Sussman e t been  and  d i p l o i d s which  7 to  that  Loomis  a b o u t one  s u b s e q u e n t m i t o t i c d i v i s i o n s so  h a v e members w i t h  no  al  others  both h a p l o i d s  adds t h a t during  Sussman e t  one  with  of recombina-  Figure  £• p a l l i d u m  1  f r u i t i n g body grown at 24°  centigrade.  ,  0.25mm  r  Figure  2  p a l l i d u m f r u i t i n g body grown at 36  centigrade.  0.25mm  Figure  D.  discoideum  fruiting  bodies  3  grown a t 2 0  centigrade.  Figure  D. d i s c o i d e u m and P. 23.0° centigrade.  4  pallidum  co-fruiting  at  about  i  C  0 . 2 5 mm  14  MATERIALS AND METHODS Laboratory  Methods The  bacteria  (Escherichia  s o u r c e were o b t a i n e d f r o m Bacteriology, tained  Agar,  5 g of yeast extract,  dextrose. water  T h e medium  15 g o f D i f c o - B a c t o  5 g of triptose,  T h e c o n s t i t u e n t s were d i s s o l v e d  and 1 g o f  i n 100 c c o f c o l d  T h e medium was a u t o c l a v e d f o r 20 m i n u t e s  square i n c h  and 25 7 ° F ,  and p o u r e d  into  dishes.  V/hen t h e a g a r h a d s e t , b a c t e r i a  surface  and a l l o w e d t o grow f o r two d a y s  t h e n removed f r o m 0.6  main-  a n d t h e s o l u t i o n made up t o 1000 c c w i t h b o i l i n g  water. per  T h e y were  transfers.  1000 c c o f w a t e r ,  as a f o o d  Department o f  of Wisconsin.  o f bi-weekly s e r i a l  u s e d was p r e p a r e d f r o m  281) u s e d  D r . K.B. R a p e r ,  The U n i v e r s i t y  by a s e r i e s  coli  placed  and 4.4 m l o f s t e r i l e  i n a 5 cc syringe  cellular  heating  cellular  were s t r e a k e d o n t h e a t room  d i s t i l l e d water  was  dishes.  s l i m e m o l d medium was p r e p a r e d b y f o r 15  T h e h a y was t h e n r e m o v e d , 20 g o f D i f c o - B a c t o A g a r ,  and  1 g o f d e x t r o s e were a d d e d , t h e s o l u t i o n  for  20 m i n u t e s  was  poured  depending  temperature,  A mixture of  5 g o f h a y i n 1000 c c o f d i s t i l l e d w a t e r  minutes.  petri  a n d was t h e n r e a d y f o r u s e i n t h e  s l i m e mold c u l t u r e The  a t 15 pounds  sterile  the surface with a spatula.  ml o f b a c t e r i a  distilled  a t 15 p o u n d s p e r s q u a r e i n c h  into  sterile  growth  upon t h e e x p e r i m e n t  were t h e n p l a c e d  chambers  was a u t o c l a v e d and 2 57°F, and  ( t h e t y p e o f chamber  being conducted).  i n a refrigerator  a t about  The chambers  4°C f o r seven  days.  15  The  c h a m b e r s were t h e n  allowed then  to  achieve  removed  from  the r e f r i g e r a t o r  room t e m p e r a t u r e .  The  bacterial  and food  was  added. 2 For  dish, The  0.2  ml  of  every  2000 mm  t h e g r o w t h s u r f a c e and t h e chamber  allowed in  to  s u r f a c e a r e a on  s o l u t i o n was  was  a t a 45°  s i t f o r two  spread  angle.  hours  The  procedure  produced  homogeneous " l a w n " o f During experimental  are mentioned here the  agar  was  added.  s u r f a c e by  c h a m b e r s were  absorbed  revolv-  then  the  by  of  moisture  the  surface covered  agar. with  a  bacteria.  the  set-ups  the  d u r i n g which time  a dry  culture  p l a c e d i n the c e n t e r  over  t h e b a c t e r i a l - w a t e r s o l u t i o n was  This  the  standard bacterial-water solution  alequot of b a c t e r i a l  ing  of  course  of  the  were u s e d .  and  any  study  The  several  t h r e e major  minor changes  different variations  are d e s c r i b e d with  results. Method  species  from  1 was  used  p o i n t source  t o grow s i n g l e  inoculations.  s p e c i e s and  The  culture  mixed  chambers 2  were 60  mm  surface  area.  mold 0.2  plastic  agar, ml  from stock  of  The  allowed  petri  d i s h e s were h a l f t o s i t f o r one  standard food  either  dishes with  filled  solution.  suspended i n water,  clumps,  and  counted  Cellular  usually  s i x or eight  counts  covered  agitated  were made.  The  mm slime  with  s l i m e mold  the f r u i t i n g  u s i n g a haemocytometer.  2000  with c e l l u l a r  week, and  s p e c i e s were p i c k e d f r o m  cultures,  approximately  spores  bodies  of  to break  up  At  four  least  mean s p o r e  and  number  16  p e r ml  of spore  diluted of  to the  spores  solution  the  suspended  i n .001 dish.  ml  dissecting  a colony.  species  from  were 60  mm  d i s h was  The  observed  and  A known number  produce  under  a  amoebae  the colony  at  binocular  two  t o grow s i n g l e  s p e c i e s and  The  culture  filled  as i n M e t h o d  1,  and  s p e c i e s were made u p .  were t h e n m i x e d w i t h to the  used  placed i n a refrigerator  were c o u n t e d  of the  with  s u r f a c e o f the p l a t e  spores  were d i s p e r s e d o v e r  The  plates  were i n c u b a t e d and  mixed  chambers  cellular  f o r one  week.  appropriate The  spore  the b a c t e r i a - w a t e r s o l u t i o n  way  b o d i e s was  was  then p l a c e d i n the  a r e a c o v e r e d by  d i s h e s w h i c h were h a l f  s l i m e m o l d medium and  mixtures  solution  p l a c e d i n an i n c u b a t o r  many p o i n t s o f i n o c u l a t i o n .  petri  spores  the  microscope. M e t h o d 2 was  mixtures  which  was  i n t h e u s u a l manner.  In  the s u r f a c e o f the growth the  appearance  of  this  plate.  fruiting  noted. Method  over  o f w a t e r was  The  v a r i o u s p e r i o d s o f t i m e was  added  and  s p o r e s were a l l o w e d t o g e r m i n a t e  v/hich p r o d u c e d  The  calculated,  a p p r o p r i a t e spore c o n c e n t r a t i o n .  c e n t e r o f the p e t r i and  was  a continuous  3 was  used  temperature  were l o n g s t a i n l e s s  steel  t o grow m i x e d range.  troughs  The  species cultures culture  with glass  lids  chambers and c o n t a i n -  2 ing  about  and  p l a c e d i n the r e f r i g e r a t o r .  with  the  11,000 mm  1.2  ml  t h e n p l a c e d on  surface area.  Spore  alequot of b a c t e r i a l a temperature  T h e y were f i l l e d mixtures  food.  g r a d i e n t and  The  were  with  agar  added  c h a m b e r s were  allowed  to incubate  17  for  7 o r 14 d a y s .  A t t h e end o f t h e I n c u b a t i o n p e r i o d t h e  a r e a c o v e r e d b y " f r u i t i n g - b o d i e s "was n o t e d . M o s t o f t h e i n c u b a t i o n was c o n d u c t e d gradient pound  d e v i c e w h i c h was c o n s t r u c t e d f o r t h i s  aluminum b l o c k h e a t e d  was i n s u l a t e d in  small holes i n the insulation  gradient  was h e a t e d  circulator  cooling  study.  next  to the block  g r a d i e n t s were u s e d .  temperature  e n d was m a i n t a i n e d  (Fig.  temperature i  to within  b y a PARMETIC  w a t e r i n a 100 1 v a t and c o n t r o l l e d  with  a  HONEYWELL  m o d e l T6 75 A1011, c a p a b l e o f 0 . 1 ° c e n t i g r a d e  accuracy.  The s e c o n d a r y  g r a d i e n t h a d t h e same c o l d  b u t t h e h o t e n d was m a i n t a i n e d  arrangements, by  changing  monitored  water  u s i n g a HAAKE  ED UNITHERM w h i c h was a c c u r a t e t o w i t h i n  0.01°C.  .004°  compressor,  thermostat  control  5).  The m a i n  b y a HAAKE m o d e l FS c o n s t a n t  the cold  A 200  C u l t u r e d i s h e s were p l a c e d  capable of c o n t r o l l i n g  centigrade;  temperature  a t one e n d and c o o l e d a t t h e o t h e r ,  with poly-urethane.  Two t e m p e r a t u r e  in a  model  For both  t h e g r a d i e n t c o u l d be s h o r t e n e d o r l e n g t h e n e d  water temperature  at either  end.  and r e c o r d e d c o n t i n u o u s l y a t s e v e n  Temperature positions  was  along  the  l e n g t h o f t h e g r a d i e n t s u s i n g a Y S I TELETHERMOMETER and  YSI  MODEL 80  RECORDER.  Throughout used. and  I t was m a i n t a i n e d  a t 29°C from  maintained fers  t h e s t u d y one s t r a i n  with  a t 34°C f r o m  May 1969 t o A p r i l a series  and c a r e was t a k e n  o f P. p a l l i d u m was  April  19 70.  1968 t o May 1969,  C u l t u r e s were  o f weekly o r bi-weekly t o mix t h e s p o r e s  from  serial each  trans-  replicate  Fiqure 5  P l a n (top) and s i d e (bottom) view o f the temperature g r a d i e n t c o n s t r u c t e d f o r t h i s study. The l e t t e r "a" r e p r e s e n t s p e t r i d i s h chambers, "b" r e p r e s e n t s the c u l t u r e g r a d i e n t chamber, " c " r e p r e s e n t s the c o l d water l i n e , "d" r e p r e s e n t s the hot water l i n e , "e" r e p r e s e n t s the aluminum b l o c k i n s i d e view, and " f " the urathane i n s u l a t i o n . A l l measurements are i n inches.  19  before  establishing  maintained as c h e c k s  f o r experiments  discoideum  February D.  1969  1968  was  was  to A p r i l  maintained  for  a short period  was  lyophilized  from  o f D. from  as  at 20°C. March  D.  1968  to avoid further  from  to simulate outputs  failure.  kept  discoideum  DF  from was  The  used  VC4  Throughout  d a t a from  stock the  one  stock  has  the  proceeding  another.  Error  The  e x p e r i m e n t a l methods o u t l i n e d  pages i n v o l v e d  several  throughout  the  study.  The  temperature  0.5°C f o r t h e  first  sources of e r r o r  year  increased  to at l e a s t  mentioned  i n the r e s u l t s  otherwise The  w h i c h were c o n s t a n t  e q u i p m e n t was  and  after  - 0.3°C.  on  accurate to  improvement,  within  accuracy  Whenever a t e m p e r a t u r e  section  a 0.3°C v a r i a t i o n  was  is  i s implied  stated.  medium u s e d  k e p t homogeneous b y from  and  used.  to  an i n c u b a t o r  stock l o s s .  not been used  years  time  were  1968  t o J u n e 1968.  and  unless  discoideum  a replacement  s t u d y s t o c k s have been i d e n t i f i e d  Experimental  lengths of  February  d e s t r o y e d by  used  1970  s t o c k s were  i n progress.  when i t was VC4  Separate  for varied  separate strains  V12  discoideum  March  stock c u l t u r e s .  at other temperatures  Three R'  new  for cellular  using the  same h a y  t h e b e g i n n i n g t o end  o f the  s l i m e mold growth for a period study.  The  of  two  hay  was  was  20  kept  i n a sealed p l a s t i c  bag a t a l l times  and a l t h o u g h  was a b r e a k d o w n o f c h l o r o p h y l no o t h e r o b s e r v a b l e  there  changes  occurred. The out  the study.  strain  During  t h e two y e a r  may h a v e u n d e r g o n e  mutational Dr.  b a c t e r i a were grown a t room t e m p e r a t u r e  changes.  experiment  I n an a t t e m p t  occasions  spreads,  t o guard  against  and p i c k e d up 281 p l a q u e s  checked The  during  bacterial  visual  checks  with  there probably  were  When s p o r e s  some a r e a s  were m i x e d  prior  Confidence  every  when t h e work  that  limits  i n most c a s e s  c o n s i d e r i n g t h e work attained.  calculated  spore  suggested  The c a s e s that  However, suggested  thicker, i n a. s t a n d a r d  the b a c t e r i a spreading.  distribution  on t h e agar  to inoculation  haemocytometer.  discovered  with  non-homogeneous  t h e y were d i s t r i b u t e d  mean c o u n t  source  microscope  the bacteria  and s p r e a d  t h e r e was no way t o c h e c k e x a c t  Spore counts  281 f o o d  where t h e lawn was  t o spread  t o o were s u b j e c t t o p o s s i b l e  assumed t h a t  o f 1969).  i n thickness.  a binocular dissecting  e v e n t h o u g h c a r e was t a k e n  accuracy  on two  " l a w n " on t h e s u r f a c e o f t h e c u l t u r e  was assumed t o be homogeneous  results  281 s t o c k )  the study p e r i o d .  dishes  way.  this,  ( d u r i n g t h e summer o f 1968 and t h e s p r i n g  C e l l u l a r ' s l i m e mold g r o w t h on t h e E . c o l i was a l s o  period the  some m e d i a c o n d i t i o n i n g o r  D, F r a n c i s (who was a l s o u s i n g t h e E . c o l i  made d i l u t e  through-  they Since  i t was  s u r f a c e randomly.  were made u s i n g a  ( 9 5 % ) were c a l c u l a t e d f o r  first  b e g a n , b u t i t was  s i x counts  yielded  involved i n counting i n which c o n f i d e n c e  t h e mean c o u n t  soon  optimum and t h e limits  were  may d e v i a t e f r o m t h e  21  actual in  count  by  as much as 20%.  proportion to  was  But  the r e c i p r o c a l  since accuracy increases  of the  number o f c o u n t s  this  deemed a c c e p t a b l e .  Mathematics A mathematical could of  description  have been a c h i e v e d by  the process  nomial  actually  i n mathematical  equation  to the  was  made t o i m p l e m e n t  attempt  met  with  amoebae and  success  fruiting  the d e s c r i p t i o n temperature,  P.  equations  the  former  and  mechanics, these with  and  were n o t  (Program  (2b)  strictly  and  a l l cases  feeding mechanics. independently,  Rather  their  total  All  o f the parameters  i n the  and  measurable i n b i o l o g i c a l  form  of  during numbers,  VIII).  the  expansion The  undoubtedly  than  dispersal treat  effect  T h i s meant t h a t  equations  an  This  mechanistic.  were n o t m e c h a n i s t i c , n o r were t h e y  In  a poly-  between c o m p e t i t o r  lag equations  respect to temperature.  gathered,  In  p r o b a b l y i n v o l v e d enzyme k i n e t i c s ,  processes  equations  fitting  approach.  m e c h a n i s m s i n v o l v e d i n t h e s e p r o c e s s e s were complex  mechanics  ( e q u a t i o n l c ) and  pallidum inhibition  ( 3 c , 4b)  the  d u r i n g the d e s c r i p t i o n o f the  body e x p a n s i o n  However, t h e rate  o r by  relationship.  of the r e l a t i o n s h i p  and  sub-component  describing  terms,  observed  attempt  o f each  the  was  each  of  considered  l a g and  rate  deterministic.  were b o t h  meaningful  terms.  a l l c a s e s , once the  appropriate equations  experimental  d a t a had  were f o r m u l a t e d .  The  been  best  22  s e t o f parameter v a l u e s was then chosen by an i t e r a t i v e fitting of  procedure and by the c a l c u l a t i o n o f t h e sum o f squares  the d e v i a t i o n s between the observed and c a l c u l a t e d  ships.  The d e s c r i p t i v e  power of t h e r e l a t i o n s h i p  t h i s procedure was then t e s t e d coefficient.  by c a l c u l a t i n g  relation-  chosen by  the c o r r e l a t i o n  23  RESULTS SECTION MECHANICS OF  conducted and of  the  Before  any  i t was  important  r a t e s at which,  food  and  space  literature, s l i m e mold to  and  but  by  I t was  observation, that  went f r o m  spore,  life  use  of food  action  cycle.  space,  i n which,  the  the  cellular  I t was  used  up  also  food  depended upon a l l t h e o t h e r  stages  the  t o v e g e t a t i v e amoebae,  body, t o s p o r e .  a l l the  resources  known f r o m  Therefore, to d e s c r i b e adequately  and  were  t h e way  s p e c i e s consumed  i n separate c u l t u r e s .  cycle  their  the  i n the  life  known  and  steps i n the r a t e  of  c y c l e had  to  investigated.  Spore  Germination When s p o r e s  presence time  of b a c t e r i a l  to germinate  called  the  that  as t h e  also  changed.  collected in  two  o n l y t h e v e g e t a t i v e amoebae a c t u a l l y  space,  be  competitive experiments  the  confirmed  life  COMPETITION  to d e s c r i b e both  aggregation, to f r u i t i n g  that  be  actual  I  the  time (Fig.  and  spore  were p l a c e d on food they produce  To  an  s p e c i e s by agar  r e q u i r e d f o r spore 6)  and  P.  lag. the  q u a n t i f y these  f o r both  center of  changed  pallidum  surface i n the  T h i s time I t was  spore  period of p e r i o d might  further  petri  germination. ( F i g . 7)  observed  germination  observations, data  placing  filled  agar  required a certain  amoebae.  germination  temperature  an  lag  were  a known number o f dish The  and  observing  d a t a f o r D.  suggested  that  the  spores the  discoideum germination  Figure  6  T h e t i m e n e c e s s a r y f o r D. d i s c o i d e u m vC4 s p o r e germination i s p l o t t e d against temperature i n d e g r e e s c e n t i g r a d e . The p o i n t s a r e d a t a , t h e l i n e i s f i t t e d f r o m e q u a t i o n ( 2 b ) . T„ = 2 7 . 5 , T_ = 9.0, T = 2 3 . 0 , K = 1.60137, C = 4 . 7 4 4 0 3 . L ' o ' '  Figure  7  T h e t i m e n e c e s s a r y f o r P. p a l l i d u m s p o r e g e r m i n a t i o n i s p l o t t e d a g a i n s t temperature i n degrees c e n t i grade. The p o i n t s a r e d a t a , t h e l i n e i s f i t t e d f r o m e q u a t i o n (2b)„ T = 37.0, T = 18.0, T = 31.0, K = 0.81132, C = 2.59356.  C O >< Q  LU  <  2  or LU  O  2  -j  '  '  i  '  i  J  I  1  I  I  I  I  I  1  1  1  1  L_  1  10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28  TEMPERATURE °C  o  C O> <. Q  1  1  V  \ \ \  -  UJ  1  \ oo \ \  o  o  ° v °\ \  O  S  \  Xo  o o <$>  1  o °X.^ oo  °  z  °  —  -  '  o oo'o~~~$-08-~  cr LU  O  •  •  •  •  1  L  L  1  1  1  1  1  1  L  1  1  1  1  L  18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38  TEMPERATURE °C  25  time  d e c r e a s e d as t e m p e r a t u r e  some optimum increases  temperature  r e a c h e d a minimum a t  and t h e n i n c r e a s e d  with  further  i n temperature. These  tions  increased,  which  o b s e r v a t i o n s form  the basis  o f t h r e e assump-  must b e met b y any e q u a t i o n w h i c h  relationship  between  l a g and t e m p e r a t u r e .  ( 1 ) t h e s p o r e s do n o t g e r m i n a t e (2) s p o r e s do n o t g e r m i n a t e  below  describes the  The a s s u m p t i o n s a r e :  some t e m p e r a t u r e  a b o v e some t e m p e r a t u r e  T , T  T^,  ( 3 ) t h e g e r m i n a t i o n t i m e i s o p t i m i z e d a t some optimum temperature ^  T . o  The  assumptions  of  minus i n f i n i t y  T  (Fig. 8).  q  curve and  L  and T  The absence  implies  that  at T  that  T  o  demand t h a t H  t h e c u r v e s have a s l o p e  and h a v e a s l o p e o f z e r o a t  o f any o t h e r r e s t r i c t i o n s  may o c c u r a n y w h e r e b e t w e e n T^ and T  t h e c u r v e may move t o a n y p o s i t i o n A family  assumptions  on t h e  o f c u r v e s which  on t h e time  incorporates  i s r e p r e s e n t e d by t h e f o l l o w i n g  H  axis.  the three  equation:  T - T ^  - K  dT  "  K  (-l)T^  + T'-T  H  ° + T •T  - T «  L  H  T  '  where d L / d T i s t h e r a t e  o f change o f g e r m i n a t i o n time  respect  T i s temperature,  t o temperature,  optimum,  i s temperature  low ( b e l o w  occurs),  T^ i s t e m p e r a t u r e  occurs),  and K i s a c o n s t a n t .  high  (above This  T  Q  which which  (2a)  L  with  i s temperature no g e r m i n a t i o n no g e r m i n a t i o n  e q u a t i o n may be  integrated  Figure  8  A r e p r e s e n t a t i v e curve from the f a m i l y o f w h i c h h a v e i n f i n i t e s l o p e s a t T (A) and T a slope of zero at T (C).  curves ( B ) , and  TIME •-»>  o -  m m XI  > H C  J3  m O  o  :—i  OF r\> — r  GERMINATION GO  1  ^ r~  27  by  making  use  of  the  following identities  x-q  xdx X  X  =  ax  quadratic.  +  bx  +  and  | x | - 2a |.  dx X  p  and  q  roots  the  following  log  1  2a  c  1947)  X - £  dx X  where  (Dwight  where  The  integration  yields  log  |(-1)T  (T  are  of  the  general  equation:  L  =  K  [(-.5  T  +  H  [  T  L  T  T  i s the  a  which  contain upon data.  up  two  Lmin  of  T  "best and  There  take  -  are  unknown  constants  and  T  + T )  H  T  , and  T  -  T  T  -  T  T  -  T  T  -  L  L  germination other  It  assumptions no  unknown  sources K  and  remain  of  C.  +  -  C  C  i s  a  defined that  i s based  upon  variables, error.  once  for  of  (2a). is  not  realistic only  or  The  these  constant  follow,  contains  constant  | )  L  were  But  L  (2b)  and  and  T  R  H  a l l those  f i t " .  T •  H T.  lag  terms  and  -  L  log  log  equation,  facts  variables.  H  A l l the  curve  biological  H  -  spore  This just  1  2  integration.  T  -  L  K • T  where  +  2  measurable  variables  equation  depend f i t to  does  directly a  set  of  28  To the  o f the program  procedure  i s presented The  line  X I V  The  line  the  variation  fitted  curve  between  It  l a g and  a descriptive  in  this  section  6 7 ) .  description  The  deals spores  (AMOEBAE  was  tion IBM C to  was  of i n i t i a l  Lag time  germination.  (Table  I)  spore  and t h e  and t h e i n i t i a l  against  f o r both  (Table  first  c o n c e n t r a t i o n on l a g  area  Y = C + BX approximated  a n d P. p a l l i d u m  a germination l a g  are formed.  was r e g r e s s e d  The r e s u l t s  stages  1 to 4 i n Figure 22  P a i r e d and r e p l i c a t e d  1 1 3 0 r e g r e s s i o n package)  i n the equation  of  The i n f o r m a t i o n c o n s i d e r e d  a t several temperatures,  varied.  0.025  the f i r s t  (TEMP) m e d i a t e d  PRESENT)  also considered.  were grown  f o r 8 8 %o f  t o the acceptance  (SPORE) e x p e r i e n c e  group  effect  0 . 0 2 5 .  of the relationship  w i t h components  i s temperature  The  a t o( =  coefficient =  a t 0(  accounts  building  components model.  o f amoebae  fitting  temperature.  (GERM L A G ) w h i c h  times  leads  i s possible to begin  of  (page  This  complete  VC4 data  and t h e c o r r e l a t i o n  and i s a l s o " s i g n i f i c a n t "  as an a d e q u a t e  spore  discoideum  pallidum data  IV).  A  of the curve  i s "significant"  to the P.  (Table X I V - Appendix the  t o t h e D.  IV)  - Appendix  I.  Program  I.  i n Appendix  fitted  of equation (2b)  ability  and a d e s c r i p t i o n  7 5 %o f t h e v a r i a t i o n  explains (Table  the descriptive  ( F i g . 6 , F i g . 7 ) were f i t u s i n g  data  listing  test  II)  D.  cultures concentra-  (using the standard so t h a t t h e c o n s t a n t the l a g time  due  discoideum V 1 2  suggest  that  initial  29  TABLE I  Do d i s c o i d e u m V12. A c o m p a r i s o n o f t h e l a g t i m e s f o r c u l t u r e s i n o c u l a t e d with v a r i e d spore concentrations. Actual lags are compared t o l a g s c a l c u l a t e d by r e g r e s s i o n .  TEMPERATURE  INOCULUM CON. SPORES PER ml  REGRESSED LAG  18.2  20000 5000  1.27 0.89  19.5  32000 80000  1.43 1.12  20.7  32000 80000  0.65 0.52  21.9  32000 80000  0.82 0.65  21.9  20000 5000  . 0.94 0.94  23.4  20000 5000  0.91 0.67  5% CON LIMIT  ACTUAL LAG  + +  1.55  + + + + + + + +  + +  0.28 20.07  0.34 0.44  1.15  0.46 0.70  1.00  2.29 0.22  0.95  0.18 0.33  0.95  0.74 0.58  1.10  30  TABLE I I  P„ p a l l i d u m . A comparison o f the l a g times f o r c u l t u r e s i n o c u l a t e d with v a r i e d spore c o n c e n t r a t i o n s . Actual lags a r e compared t o t h e l a g s c a l c u l a t e d by r e g r e s s i o n .  TEMPERATURE  INOCULUM CON. SPORES PER ml  REGRESSED LAG  5% CON. LIMITS  ACTUAL LAG  20.1  100000 50000  3.05 1.96  + 1.03 + 0.31  1.20  20.7  20000 5000  1.88 1.54  + 0.97 + 1.24  1.18  21.9  20000 . 5000  2.43 1.86  + 1.90 + 0.39  1.10  22.6  100000 50000  1.34 1.56  + 0.56 + 0.58  1.02  25.5  100000 50000  1.08 1.29  + 0.47 + 0.24  0.80  28.7  100000 50000  1.16 0.61  + 0.42 + 0.52  0.75  31  concentration noted that  that  does n o t  the  alter  lags generated  were a c t u a l l y  measured  These d a t a agree Bonner that  l a g time.  (1960) and  i n this  and  way  findings  Ceccarini  dropped  inhibition.  from  about  In t h e i r  99%  a t low  be  also  with  with  those  equation  of Russell  (1967) who  o n l y v e r y h i g h c o n c e n t r a t i o n s o f D.  some s p o r e  agree  approximated  with the  C o h e n and  I t might  (2b).  and  observed  discoideum  work g e r m i n a t i o n  caused  success  c o n c e n t r a t i o n s t o about  70%  at  2 spore  c o n c e n t r a t i o n s o f 2000 s p o r e s  work c o n c e n t r a t i o n s v a r i e d  from  p e r mm  about  .  0.1  to  In the 3.0  present  spores  per  2 mm  , and  therefore l i t t l e  Amoeba C o l o n y  the  disperse,  processes  this  rather  modelled  The  and  the  form  the  amoebae b e g i n  the  dishes  amoebae f r o n t  the food.  Rather  i t s component  of colony expansion  to these moved  than  parts,  divide  both  were a s s e s s e d  and  component.  Form o f C o l o n y  colony  expected.  In the c u l t u r e  t o g e t h e r as  complex p r o c e s s i n t o  as one  filled  food.  lawn r e m o v i n g  Expansion  When s p o r e s agar  use  were o b s e r v e d  the b a c t e r i a l  rate  spores germinate  and  over  the  was  Expansion  After divide,  inhibition  petri  dish  were p l a c e d a t one i n the presence  expanded i n a r e l a t i v e l y  uniform  point  i n a 20  of bacteria, circle  x 60  the  away f r o m  the  mm  32  point of inoculation. areas  The amoebae d i v i d e d and moved i n t o  new  so t h a t the a r e a covered by the e n t i r e c o l o n y grew  slowly at f i r s t  and then i n c r e a s e d u n t i l the r a t e o f a c q u i s i -  t i o n became almost  constant  ( i f t h e a r e a became i n f i n i t e l y  l a r g e the r a t e o f a c q u i s i t i o n would become c o n s t a n t , the growth e s s e n t i a l l y would be along a s t r a i g h t Horn (1969) has observed constant.  line  because front),  t h a t movement along a f r o n t i s  As t h e amoebae moved over t h e s u r f a c e o f the agar  they consumed a l l the f o o d , thereby i n v a s i o n by o t h e r c e l l u l a r  s e c u r i n g t h a t area from  s l i m e mold s p e c i e s .  These o b s e r v a t i o n s suggested  t h a t i t was o n l y t h e  amoebae on t h e p e r i m e t e r of the c o l o n y which expanded the colony.  In mathematical terms, t h e r a t e o f i n c r e a s e i n the  a r e a covered by a c o l o n y i s p r o p o r t i o n a l t o t h e c i r c u m f e r e n c e o f the c o l o n y .  This i s :  |£  = g •2-TT.  r  (  l  a  )  where dA/dt i s t h e r a t e o f change o f a r e a c o v e r e d , g i s a 2 c o n s t a n t , and r i s t h e r a d i u s o f t h e c o l o n y .  Since  TT •  r  h.  equals Area this  (denoted by A ) , then r = (A/TT ) „  substitution into ^  Incorporating  (la): =  fg • 2 • "rr] -  r e a r r a n g i n g and i n t e g r a t i n g :  ( /vr)^ A  (lb)  Figure 9  Areas c o v e r e d by c e l l u l a r s l i m e mold c u l t u r e s growing from p o i n t s o u r c e s as c a l c u l a t e d by Program I I and e q u a t i o n ( I d ) . Both the time and a r e a u n i t s are arbitrary.  300 • f (g) = I O O  Q L U  DC UJ 2 0 0  / f (g) = 0 - 5 0  g o <  < <  9  100 • ' f (g) = 0 - 3 0  •  y  JL.  2  4  6  8  L  J  _  J  L  10 12 14 16 18 TIME  34  The was  relation  examined u s i n g Program  (Fig.  9)  was  compared  mold c u l t u r e s . slowly area  The  at f i r s t ,  acquisition  process by  between A  t o the  actual  and  then  tending  ( l c ) and  plotted this  a g a i n s t time,  hypothesis,  established of  18.9  root of  10-A).  10-A)  straight passed  The  passed  line  through  germination accounted  the  0.0  V12  at a  two  a straight  the  the x - a x i s at  ( F i g . 10-B)  To  test  data  1.0  very  against  observation  points  days,  but  equation  suggesting  time,  line  reaffirmed this  through  (lc) i s  temperature  yielded  When p l o t t e d along  If  result.  same s l o p e p r e d i c t e d by  days  generated  c u l t u r e s were  inoculation  l a g d e s c r i b e d i n the previous  the (lc)  that the  section  must  spore be  for. The  equation  (2b)  can  be  then  of  through  general  equation  should  experiment  line  This  possible.  from  discoideum  work h a s  straight  i s also  line  area d i d f a l l  Subsequent  many t i m e s . (Fig.  a straight  T h i s simple  rate of  9.  calculated  a p o i n t source  the  family of curves  pieces of information.  square  (Fig.  with  area  slime  areas  with  l a g can equal  be  i n c o r p o r a t e d by  a f u n c t i o n of  substituted  into  g  output  their  a constant.  comparison  s e v e r a l D.  - 0.2°C.  important the  moved q u i c k l y ,  the  the  growth of c e l l u l a r  drawn i n F i g u r e  r o o t of the  I ) , and  c u l t u r e s expanded  towards  A quantitative square  t at various values of  (Appendix actual  i s w e l l d e s c r i b e d by  equation  the  II  and  letting  temperature  ( l c ) to  yield:  the  L(T).  lag This  Figure  10  Fig.lO-A: The s q u a r e r o o t s o f t h e a r e a s c o v e r e d byf o u r c u l t u r e s o f D. d i s c o i d e u m V12 a r e p l o t t e d a g a i n s t time i n days. The r e g r e s s i o n l i n e o b t a i n e d i s Y = -3.73 + 3.61X.  Fig.lO-B: The s q u a r e r o o t s o f t h e a r e a s g e n e r a t e d b y e q u a t i o n ( l c ) w i t h g = 3.61 a r e p l o t t e d t o f o r m l i n e one. L i n e two i s t h e a c t u a l r e g r e s s i o n l i n e d e p i c t e d i n F i g . 9-A.  36  A  The  Rate  o f Amoeba C o l o n y  Both in  the rate  In view  To  the constant g i n equation  quantify  temperatures  (1) T h e r e  the  root  are p l o t t e d  o f a r e a and t i m e . 11.  space  available.  the  400 - 500 c u l t u r e s  straight  only  4 or 5 data points).  (Fig.  To p r o v e  A straight  line  each  this  because culture  be due t o a line to  h y p o t h e s i s was  were t r a n s f o r m e d and  relationship  resulted  the i n d i v i d u a l  and e q u a t i o n ( l c ) a r e v a l a d .  Program I I I (Appendix  various  that  I I I ) demonstrating that  S i n c e many c u l t u r e s  individual  from  that  to f i t a straight  d a t a f r o m many t e m p e r a t u r e s  observations  between  a l l the food  be a r g u e d  observed might  ( i t i s not d i f f i c u l t  53 - A p p e n d i x  relationship  were a v a i l a b l e  relationships  together.  grown  Two o b s e r v a t i o n s  s p e c i e s used  r u n , but i t might  of data  plotted  line  were  T h e s e o b s e r v a t i o n s were made i n 100% o f  lack  incorrect  cultures  Representative cultures  (2) Both  of data points  line  i n temperature.  g(T).  relationship,  was a s t r a i g h t  i n Figure  s m a l l number  o f temperature this  and  the  show v a r i a t i o n s  ( I d ) must be  r a n g i n g from 9° t o 37.5°C.  were made:  a  Expansion  o f colony expansion with v a r i a t i o n s  to a function  square  (Id)  2  D. d i s c o i d e u m a n d P. p a l l i d u m  of this,  modified  at  = [ l . 7 7 2 8 g ( t - L ( T ) ) + c]  t  cultures,  temperature  were r u n a t e a c h  I ) was u s e d t o group  intervals,  to calculate  temperature, the slopes o f  t h e d a t a t o f o r m mean s l o p e s a t and t o p l o t  the individual  Fiqure  The s t r a i g h t root of area demonstrated a t 2 4 . 5 ° and 30.5OC.  11  l i n e r e l a t i o n s h i p between the square ( m e a s u r e d i n cm^) and t i m e i s f o r D. d i s c o i d e u m vC4 ( t o p ) grown f o r P. p a l l i d u m ( b o t t o m ) grown a t  1  2  3  4  5  TIME-DAYS  j  1  i  2  1  3  4  TIME - DAYS  5  38  slopes  and mean  slopes.  The s l o p e  data  obtained  was t h e n p l o t t e d a g a i n s t D. d i s c o i d e u m  V12  around large  increased  temperature  with  increased  due t o u n r e c o g n i z e d despite  discovered,  that  i t was i m p o s s i b l e  because the stock  food  pansion three  rate  conditions:  (1) t h a t  some low t e m p e r a t u r e T^, zero  a t some h i g h  colony  expansion  conditions rate  decreases, the  slope  T.-  T . H  l i m i t s (95%) rather  o f e r r o r was again  media c o n d i t i o n i n g .  data  The e q u a t i o n  an e q u a t i o n  was  ex-  h a d t o meet  t h e r a t e o f e x p a n s i o n be  T^,  (3) t h a t  the rate of  a t some optimum  An e x a m p l e o f a c u r v e  i s presented  i s zero.  with  t o do t h e e x p e r i m e n t s  (2) t h a t  be o p t i m i z e d L  a  t h e r a t e o f e x p a n s i o n be z e r o a t  temperature  b e t w e e n T^ a n d T .  reached  t h e r e l a t i o n s h i p between c o l o n y  and t e m p e r a t u r e .  colony  contamination.  the source  had e x p e r i e n c e d  to describe  the rate of  p o i n t s were  On t h e b a s i s o f t h e f o r e g o i n g formulated  from  and d e c r e a s e d  data  bacterial  the fact  that  The c o n f i d e n c e  P. p a l l i d u m  procedure  ( F i g . 1 3 ) , and  temperature,  temperature,  increases.  the i n d i v i d u a l  However,  The d a t a  ( F i g . 14) s u g g e s t e d  maximum a t some optimum further  temperature.  ( F i g . 1 2 ) , P. p a l l i d u m  D. d i s c o i d e u m VC4 expansion  from t h e above  i n Figure  15.  From  this  point  reaching  zero  at T = T . q  t h a t meets  At T  the slope  temperature  T  Q  these  the expansion  ( F i g . 15) g r a d u a l l y  As T i n c r e a s e s  d e c r e a s e s r a p i d l y becoming n e g a t i v e l y  beyond  i n f i n i t e at  T  Q  F i q u r e 12  T h e r e l a t i o n s h i p b e t w e e n g r o w t h i n d e c and t e m p e r a t u r e f o r D. d i s c o i d e u m V 1 2 . T h e p o i n t s a r e mean d a t a p o i n t s ± 5% c o n f i d e n c e l i m i t s o n t h e means. T h e g r o w t h i n d e x h a s no u n i t s , t e m p e r a t u r e i s m e a s u r e d i n d e g r e e s c e n t i g r a d e . The d o t t e d l i n e i s t h e l i n e of b e s t f i t from e q u a t i o n (3c) w i t h T = 26.5°, T, = 13.0O, T = 2 2 . 5 ° , Gmax = 4.5, K = 0.97009, and C = 2.99964. Q  F i q u r e 13 The r e l a t i o n s h i p b e t w e e n g r o w t h i n d e x and t e m p e r a t u r e f o r P. p a l l i d u m . T h e p o i n t s a r e mean d a t a p o i n t s - 5% c o n f i d e n c e l i m i t s o n t h e means. The growth i n d e x h a s no u n i t s , t e m p e r a t u r e i s m e a s u r e d i n d e g r e e s centigrade. The d o t t e d l i n e i s t h e l i n e o f b e s t f i t from e q u a t i o n (3c) w i t h T = 37.0, T = 18.0, T = 30.0, Gmax = 8.3, K = 1.71712 and C = - 4 . 7 7 0 3 4 . H  q  L  10 • 9 8 -  12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 TEMPERATURE  10 9 V°- —  8 x  1N N  7  „ 1  LU  |  6  i  5  il !  oc  0  '1  1  £«•  O  t- - - -  1 3 2  1  £  i  bJL,  J  I  1  i  I  I  1  L  _i  L  i  i  19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 TEMPERATURE  a  Figure  14  The r e l a t i o n s h i p b e t w e e n g r o w t h i n d e x and t e m p e r a t u r e f o r D. d i s c o i d e u m VC4. T h e p o i n t s a r e mean d a t a points i 5% c o n f i d e n c e l i m i t s o n t h e means. The g r o w t h i n d e x h a s no u n i t s , t e m p e r a t u r e i s m e a s u r e d i n d e g r e e s c e n t i g r a d e . The d o t t e d l i n e i s t h e l i n e of b e s t f i t from e q u a t i o n (3c) with T = 2 7.5°, 7 T = 9.0°, T = 2 1 . 5 ° , Gmax = 4.6, K = 0.80084, and G = 0.79554. H  L  Q  GROWTH ro  m m  > H C  J3  m  co  J>  cn  INDEX o>  T  -^i  00  CO  r  T  41  One  e q u a t i o n which r e p r e s e n t s  and  which  fulfils  the  following:  the  three  requirements  T  dG dT  where dG/dT i s t h e respect  to  must be  integrated  rate  temperature,  dG  =  by  =  of  K  o  T  -  T  -  T  change o f  and  the  T  K  T  =  [log  This  equation  dT - T  T  (3b)  identities  .  1  log  =  i j  [x  Integrating  IT  a c q u i s i t i o n with  H  following  ^  = a + bx„  above i s  (3a)  K i s a constant.  dT -  T  f*  where X  response  parts:  K«T  (1947) g i v e s  type of  stated  area  H Dwight  this  - T I ]  (2b)  [K • (T  of  integration:  I X i  -  alog  I X I  i t i s found  - T  ]  that:  )] - K •  T  + K • T  +  (3c) where G i s t h e But hypothetical.  rate this  of  area  equation  I t must be  a c q u i s i t i o n and and  C is a  i t s assumptions  proven that  are  i t describes  constant. only the  C  Fiqure  15  One o f a f a m i l y o f c u r v e s d e s i g n e d t o d e s c r i b e t h e r e l a t i o n s h i p between t h e r a t e o f c o l o n y e x p a n s i o n and t e m p e r a t u r e . A t T L and T the r a t e i s zero and T t h e r a t e i s optimum. H  0  GROWTH  RATE  43  relationship  b e t w e e n area, a c q u i s i t i o n  To  test  the d e s c r i p t i v e  Program IV (Appendix  I ) was u s e d  family  d e s c r i b e d by  fitted  t o t h e D. d i s c o i d e u m  of  the v a r i a t i o n .  (Fig. the  (3c) t o each  The l i n e  ability  D. d i s c o i d e u m  VC4 d a t a  A l lthree  equation  ( 3 c ) was With  V12 d a t a fitted  IV).  accepted  and  colony  t o t h e P. p a l l i d u m The l i n e  a t c*  The d e s c r i p t i v e  space  (COLONY  (AMOEBAE  i n the form  = 0.025  power o f  account rate.  dependent.  c a n be  After  the f i r s t  PRESENT) t h e y  place of g i n equation  A  t  begin  This  and t h e amount o f f o o d and  calculated. equation  (ld)  dependence o f t h e c o l o n y  When g ( T ) ( a s u m m a r i z e d  and  A t any p o i n t i n t i m e t h e  i s a l s o p o s s i b l e t o modify  f o r the temperature  (ld)  d e s c r i b e d by e q u a t i o n ( l d )  S I Z E ) i s known  (FOOD-SPACE) u s e d It  f i t t e d to  5, 6 and 7 t o t h e c o m p o n e n t s  (page 6 7 ) .  the spores  i s temperature  data  i n a l l cases.  i n F i g u r e 22  the colony  size  line  ( F i g . 12) e x p l a i n s 9 4 %  a t t h e r a t e d e s c r i b e d by ( 3 c ) (COLONY E X P . ) .  process  in  The  t h e i n f o r m a t i o n p r o v i d e d by e q u a t i o n s  amoebae emerge f r o m expand  from t h e  ( F i g . 14) e x p l a i n s 9 5 % o f t h e  ( 3 c ) i t was p o s s i b l e t o add s t e p s model o u t l i n e d  o f e q u a t i o n (3c)  set of data.  are " s i g n i f i c a n t "  (Table XIV - Appendix  temperature.  t o f i t one c u r v e  13) e x p l a i n s 5 6 % o f t h e v a r i a t i o n .  variation.  to  and  form  of equation  + c]  2  expansion  (3c)).'is s e t  ( l d ) the f o l l o w i n g equation  = [1.7728 g ( T ) ( t - L ( T ) )  to  results:  (le)  TABLE I I I D. d i s c o i d e u m V12 - a c o m p a r i s o n o f g r o w t h i n d e x e s f r o m c u l t u r e s i n o c u l a t e d with v a r i o u s spore c o n c e n t r a t i o n s .  TEMPERATURE  SPORE CON NUM/ML  MEAN GROWTH INDEX  5% CON LIMIT  17.0  32 80  000 000  2.82 2.66  + 0.22 + 0.69  18.2  32 80 20 5  000 000 000 000  3.16 3.63 3.79 2.33  + 0.76 + 0.46 + 0.34 + 3.44  19.5  32 80  000 000  3.54 2.79  + 0.45 + 0.45  20.7  32 80  000 000  4.12 4.23  + 0.97 + 0.78  21.9  32 80 20 5  000 000 000 000  4.92 5.05 4.89 4.83  + 3.88 + 0.38 + 0.35 + 0.64  23.4  32 80 20 5  000 000 000 000  4.17 4.26 4.70 4.20  + 0.37 + 0.29 + 1.37 + 0.87  24.8  32 80  000 000  2.89 2.80  + 0.31 + 0.25  TABLE I V  H° p a l l i d u m - a c o m p a r i s o n o f growth i n d e x e s from c u l t u r e s i n o c u l a t e d w i t h v a r i o u s spore c o n c e n t r a t i o n s .  TEMPERATURE  SPORE CON NUM/ML  MEAN GROWTH INDEX  20.1  100 000 50 000  3.50 2.74  20.7  20 000 5 000  4.16 2.96  21.9  20 000 5 000  5.33 4.72  25.5  100 000 50 000  7.10 5.60  28.7  100 000 50 000  8.66 7.67  5% CON LIMIT + 2.26 +  0.33  + 2.10 +  1.83  + 5.60 +  0.95  + 2.61 +  0.98  + 3.16 +  0.74  46  where g ( T ) i s c o l o n y The alters  tions,  plates with  limits.  Fruiting  concentration  v a r i o u s spore covered  mold c o l o n y  concentra-  by t h e  t h e mean g r o w t h was  f o r D. d i s c o i d e u m  V12  (Table I V ) .  spore  this  p o i n t the development o f a c e l l u l a r  has been c o n s i d e r e d from  germination  development  the spore  to the colony  stage.  and d i s p e r s e u s i n g up f o o d  amoebae i n t h e c e n t e r o f t h e c o l o n y  find  area without  food.  produced  and  body p r o d u c t i o n b e g i n s .  fruiting  a p e r i o d o f time lag.  A c r a s i n i s then  T h i s p e r i o d o f time  and t h e t i m e  through  through  the  B u t , as t h e and s p a c e , t h e  themselves and  i n an  aggregation  These processes  t h a t m i g h t be r e f e r r e d  slime  stage,  l a g t o t h e amoebae s t a g e ,  of a colony,  amoebae r e p r o d u c e  lag  was  Body L a g To  body  This test  No g r o w t h i n h i b i t i o n  a t the c o n c e n t r a t i o n s used,  I I I ) and P. p a l l i d u m  temperature.  be t e s t e d .  Program I I I t o c a l c u l a t e  - 5% c o n f i d e n c e  (Table  also  spore  and r e c o r d i n g t h e a r e a s  and u s i n g  detected  r a t e mediated by  that i n i t i a l  r a t e must  by i n o c u l a t i n g  observing  colony,  the  hypothesis  the expansion  conducted  index  expansion  require  t o as t h e f r u i t i n g  i n c l u d e s the spore  required f o r aggregation  after  germination  t h e amoebae  appearTo  q u a n t i f y the r e l a t i o n s h i p  body  l a g and t e m p e r a t u r e ,  agar  filled  and b a c t e r i a  between t h e f r u i t i n g  d a t a was c o l l e c t e d covered  petri  by  inoculating  dishes with  a known  47  number o f s p o r e s , i n c u b a t i n g noting first and  at various temperatures,  t h e time between i n o c u l a t i o n fruiting  ( F i g . 16)  P. p a l l i d u m ( F i g . 17) t h e l a g d e c r e a s e d w i t h  increased  increased  reached  F o r both  and t h e f o r m a t i o n o f t h e  D. d i s c o i d e u m VC4  temperature  body.  a minimum  with f u r t h e r It  appeared  a t some optimum t e m p e r a t u r e  temperature that  applicable that  to the f r u i t i n g  the assumptions  the curve r e l a t i n g  infinitely  s l o p e a t T^  zero  Q  describes  pertaining  Program The  this  body L  test  relating  16).  OC = 0.025  I ) was u s e d  fruiting  In both  body  (temperature  body  l a g and  and t h a t  t h e s l o p e be  E q u a t i o n (2b)  to f i t a line  to the data.  l a g and t e m p e r a t u r e f o r variability  IV).  " s i g n i f i c a n t " at Equation  the r e l a t i o n s h i p  (2b) a p p a r e n t l y  between  fruiting  temperature. new i n f o r m a t i o n c a n be u s e d  components model t h r o u g h (Fig.  l o w ) and an  power o f e q u a t i o n ( 2 b )  c a s e s t h e f i t was  to describe  This  22, page  have  f o r P. p a l l i d u m e x p l a i n e d 9 7 % o f t h e  ( T a b l e XIV - Appendix  c a n be u s e d  demand  l a g and t e m p e r a t u r e  optimum) ( F i g . 8 ) .  the d e s c r i p t i v e  The l i n e  variation.  be  assumptions  D. d i s c o i d e u m VC4 e x p l a i n e d 9 6 % o f t h e t o t a l (Fig.  also  t o the  relationship.  I (Appendix  line  fruiting  These  (temperature high)  (temperature  To  lag.  negative slope at T  infinite at T  body  and  increases.  model c o n s t r u c t e d f o r t h e g e r m i n a t i o n l a g might  an  and  67)„  the addition  After  the f i r s t  t o expand t h e  o f s t e p s 8 and 9 amoebae a r e p r e s e n t  Figure  16  T h e t i m e n e c e s s a r y f o r D. d i s c o i d e u m f r u i t i n g b o d y f o r m a t i o n i s p l o t t e d a g a i n s t temperature measured i n degrees c e n t i g r a d e . The b l a c k d o t s a r e d a t a p o i n t s , t h e d o t t e d l i n e i s f i t t e d from e q u a t i o n ( 2 b ) . T = 27.5, T = 9.0, T = 24.0, K = 2.47681, C = 7.62542. H  L  10  11  12  13  14  15  16  17  18 19 20 21  TEMPERATURE  22 23 24 25 26 27  Figure  17  T h e t i m e f o r P. p a l l i d u m f r u i t i n g b o d y f o r m a t i o n i s p l o t t e d a g a i n s t temperature measured i n degrees centigrade. The o p e n c i r c l e s a r e d a t a p o i n t s , t h e d o t t e d l i n e i s f i t t e d f r o m e q u a t i o n ( 2 b ) . T^ = 37. T = 18.0, T = 30.0, K = 1.28527, C = 3.76145. L  Q  4  \  \  > < a  <  2 r  1  o - - o_  r  o  _ _  O  o  J  19  20 21  I  l_  <5"  L  —  ~~ o- —  Jl  o—  I  '  o  o— o —  o  »  22 2 3 24 2 5 26 27 2 8 29 30 31 T E M P E R A T U R E  "O  32 3 3 34  35 3 6  50  there  i s a temperature  the f i r s t  Fruiting  fruiting  Body  dependent  bodies  lag period  are produced  ( F . B . LAG)  (F.B.  PRESENT).  Formation  Once t h e f i r s t  fruiting  b o d i e s have formed  number i n c r e a s e s as more amoebae a g g r e g a t e . which t h i s it  occurs  The  process  occurs  (the r a t e ) ,  Form o f F r u i t i n g  Fruiting  Body C o l o n y  expansion  I t appeared  be  related  test  was  resulted  this  (Fig.  18).  times  and  found. each the  D.  and  straight straight  because line lines  case  at which  the  and  o n l y a few  relationship resulted  from  rate  might  as i t was form  of  f o r the  colony  The  square  straight  VC4  were grown a t  line  ( F i g . 18)  line  root  of  and  a lack  area  P. p a l l i d u m  several  hundred were  d a t a p o i n t s were u s e d be  was  relationships  relationships  i t might  a  body c o l o n y a r e a  were r e p e a t e d  straight  and  equation ( l d ) .  of time.  discoideum  i n every case  just  the f r u i t i n g  These experiments  But,  in  area occupied  expansion  hypothesis cultures  a g a i n s t time  f o r both  rate  slowly at f i r s t  as t h e  that  In t h i s  at various i n t e r v a l s  then p l o t t e d  rates  d e s c r i b e d by  number o f t e m p e r a t u r e s noted  expand  to perimeter s i z e  s h o u l d be  the  t h e way  Expansion  possible  amoeba c o l o n y e x p a n s i o n .  To  and  Both  the  must be d e s c r i b e d .  increases.  expansion  (the form),  body c o l o n i e s  then increase t h e i r  directly  before  for  hypothesized  of data.  To  test  that  Figure  18  The s t r a i g h t l i n e r e l a t i o n s h i p between the square r o o t o f a r e a (measured i n cm^) and time i s demonstrated f o r D« discoideum VC4 (top) and P. p a l l i d u m (bottom). The temperatures a t which t h e s e c u l t u r e s were grown are noted on the graph.  this  hypothesis,  fruiting gether ship  - Appendix  a g a i n s t time ( l c ) can  Two ments.  (1) D.  area occupied  (Fig.  by  the  they  apparently  u s e d up  retraced  their  case  o f P.  a l l of back  the  pallidum food  to the  to t h i s  both  Dr.  expressed  by  the  found  t h a t P. of  (the data  on  experi-  a l l of  and  (2)  expanding  long  amoeba c o l o n i e s the  amoebae  p l a t e and the  then  p l a t e where  formed.  pallidum  The and  has  P.  pallidum f r u i t i n g  bodies  a percentage  of  t h e maximum a r e a  occupied  When 40  fruiting  are g i v e n  the mean).  as  t h e mean - t h e  Also,  t h e r e was  a t t a i n e d by  at which  this  P.  myself.  e x p e r i m e n t s were r u n bodies  no  occupied  by  the  95%  amoeba  the  -  was 0.85  colony  confidence  pallidum over  may  i t  14.08  significant  s p e c i e s grew  the  the  by  t h e maximum a r e a o c c u p i e d  temperature  P.  that  these  covered  body c o l o n y of  and  ( p e r s . comm.) and  pallidum  maximum a r e a  from  center of  strain  area  relationship.  Salvador the  relation-  root of  line,  to-  Raper  amoeba c o l o n i e s .  percent  around  as  the  pallidum  plotted  ( F i g . 18),  a r e a u s e d by  maximum a r e a o c c u p i e d  be  of  the  route  by  bodies  P.  line  square  body c o l o n i e s stopped  i s peculiar  been observed  straight  resulted  fruiting  and  and  to d e s c r i b e t h i s  large disorganized f r u i t i n g  response  VC4  a straight  amoeba c o l o n y  occupied In the  A  that the  observations  discoideum  18).  the  used  pallidum f r u i t i n g  before  The  III).  does y i e l d  be  other  discoideum  were t r a n s f o r m e d  r e s u l t e d , demonstrating  equation  one  f r o m D.  body e x p a n s i o n s  ( F i g . 54  plotted  P.  data  limit  change i n full  (Table V).  range A l l of  TABLE V T h e c h a n g e i n maximum a r e a w i t h  temperature  TEMPERATURE  MEAN AREA  NUM. REP.  f o r P. p a l l i d u m .  9 5 % CON L I M I T  20.5  3  41.0  - 17.2  21.5  5  38.3  22.5  4  t  39.3  23.5  4  40.5  i i  24.5  4  38.5  - 11.6  25.5  5  38.2  - 12.0  27.5  5  38.5  -  8.3  28.5  6  41.8  i  9.6  29.5  5  39.0  - 11.2  30.5  7  44.7  -  31.5  5  45.5  32.5  4  44.2  t  33.5  6  35.5  5  H 2 0  5.7 16.1  7.0  i  7.1 16.2  54.1  -  5.3  44.5  - 11.3  54  the  95%  confidence  mean c a l c u l a t e d did  not  P.  f o r 33.5°,  change w i t h In  cover  limits,  14.08% o f ( l c ) can  the be  both.  The  Rate o f F r u i t i n g B o t h D.  discoideum  the r a t e of f r u i t i n g  in  temperature.  n o t i n g the  intervals  of  quantify this  time.  mean s l o p e s - 9 5 %  both the  D.  limited  to  of colony  while about Equation  expansion  Expansion P.  p a l l i d u m show expansion  constant  with  g i n the  variations variations "form"  t o become a f u n c t i o n o f  Program  confidence  discoideum  temperature,  intervals.  ( F i g . 19)  body e x p a n s i o n  were  bodies  The  collected  at v a r i o u s  I ) was  temperature,  were p l o t t e d  VC4  reached  fruiting  data  I I I (Appendix  r e s p e c t to  intervals  fruiting  relationship  a r e a o c c u p i e d by  group the d a t a with  confidence  area  g(T).  To by  modified  the  body c o l o n i e s  amoeba c o l o n y  form  and  the  that  amoeba c o l o n y .  body c o l o n y  Therefore,  ( l c ) must be  temperature  the  Body C o l o n y  in  equation  by  to d e s c r i b e the  for  fruiting  the  around  V).  body c o l o n i e s a r e  area covered  used  by  interval  suggesting  (Table  discoideum  area covered  pallidum fruiting  the  overlapped,  temperature  summary, D.  a l l of the  excepting  and  used to  calculate  mean s l o p e s  against temperature. and  P.  to  pallidum  rate increased with  a maximum a t some optimum  and For  ( F i g . 20) increased temperature  55  and  decreased  equation between be  equation  to this test  to d e s c r i b e the and  (Appendix  curve  t h e f i t was  ( T a b l e XIV Equation  increases  P.  infinity  pallidum data  increases  - Appendix  between T view  L  that  a t T^,  remains  and  special  body f o r m a t i o n .  dG dT  criteria S u c h an  "significant"  decreases  to temperature,  However,  of colony  rapidly  by  P.  a  to the  expansion  constant  t o z e r o a t T^.  e q u a t i o n was  imposed  reaches  developed  pallidum  In  which  fruiting  equation i s :  (-l)T  rate  at  rate  rapidly  approximately  T  = K  w h e r e dG/dT i s t h e respect  a new  the  = 0.025.  a t CX  the expansion  the r a t e  decreases  of  IV).  and  suggests  and T^,  f o r 69%  with i n c r e a s e d temperature,  of these f i n d i n g s ,  meets the  not  a t some h i g h t e m p e r a t u r e .  rapidly  also  For  "significant"  maximum a t t e m p e r a t u r e - o p t i m u m , negative  I).  accounted  ( 3 c ) demands t h a t  gradually  relationship  temperature, might  p a l l i d u m ( F i g . 2 0 ) t h e f i t was  (A = 0 . 0 2 5  Apparently  h y p o t h e s i s c u r v e s were f i t f r o m  the f i t t e d  and  increase.  situation.  this  VC4  variation  P.  used  (3c) u s i n g Program IV  discoideum  For  temperature  amoeba c o l o n y e x p a n s i o n  applicable  total  further  ( 3 c ) , w h i c h was  To  D.  with  o  + T •. T  "  H  + T  T  L  — T •T -  H  L  o f change o f c o l o n y e x p a n s i o n T i s temperature,  T  is  (4a)  with  temperature  Fiqure  19  D. d i s c o i d e u m VC4; f r u i t i n g b o d y e x p a n s i o n r a t e s w i t h respect to temperature. T h e p o i n t s a r e mean d a t a p o i n t s - 5% c o n f i d e n c e l i m i t s on t h e means. The g r o w t h i n d e x h a s no u n i t s , t e m p e r a t u r e i s m e a s u r e d i n degrees c e n t i g r a d e . The d o t t e d l i n e i s t h e l i n e o f b e s t f i t from e q u a t i o n (2c) w i t h T = 27.5, T = 9.0, T = 21.0, Gmax = 4.4, K = 0.86318, and C = -0.65368. H  L  Q  GROWTH ro  GO  4^ —  INDEX  01  g——r*  1  ro co L  m "0  5) _ L  m .33  -NI  H  00  r \  t—®—\  c m  \ \  CD  t • ©—i  ro o  i  ro  i 1—©—i  1  ro ro ro  co  ro J>  ro ro CD ro  I-  '  0)  . ->l  00  CO  57  GROWTH INDEX ro co J> cn CD ->J \ v CD IO O IO  ro ro  CO  ro J>  ro cn m ro TJ  rn 0)  \ \  ID  > ro —1  c  ZO  ro  m 00  ro  CD CO  O CO CO  ro  CO Co CO  co cn co CD  K H  J—0—3  00  CD  58  optimum, T  i s temperature  L  low, T  i s temperature  H  h i g h , and  K i s a constant. Using this  equation  two i d e n t i t i e s  of integration  (Dwight  1947)  c a n be i n t e g r a t e d t o y i e l d :  G = -K [ ( - . 5 l o g I ( - l ) T  2  + T(T  H  + T ) - T L  H  " T^ I )  -  (4b)  T  1  - T  H  *  T - T log  L  where G i s t h e e x p a n s i o n  T - T  coefficient  H  and C i s a c o n s t a n t o f  integration. This  equation  Program V (Appendix total  variation  I).  The l i n e  and t h e f i t was  ( T a b l e XIV - Appendix accepted  was f i t t o t h e d a t a  IV).  accounted  f o r 75% o f t h e  "significant"  Therefore,  as an a d e q u a t e d e s c r i p t i o n  b e t w e e n P. p a l l i d u m f r u i t i n g  ( F i g . 21) u s i n g  a t 0\  equation  = 0.025  ( 4 b ) was  of the r e l a t i o n s h i p  body e x p a n s i o n  r a t e and t e m p e r -  ature. The incorporated as  steps  information considered i n this into  t h e components d i a g r a m  10, 11, 12 and 1 3 .  are formed  After  c a n be  ( F i g . 22, p a g e 67)  the f i r s t  ( F . B . PRESENT) t h e c o l o n y  section  expands  fruiting  bodies  ( F . B . EXP) w i t h  Figure  21  P. p a l l i d u m f r u i t i n g b o d y e x p a n s i o n r a t e s w i t h r e s p e c t to temperature. The p o i n t s a r e mean d a t a p o i n t s - 5% c o n f i d e n c e l i m i t s o n t h e means. The growth i n d e x has no u n i t s , t e m p e r a t u r e i s m e a s u r e d i n d e g r e e s c e n t i grade. The d o t t e d l i n e i s t h e l i n e o f b e s t f i t from e q u a t i o n ( 4 b ) w i t h Tu = 37.5, T 18.0, T = 31.0, K = 0.78172, and C = 0.97552. L  GROWTH INDEX ro co 4^ cn o) -NI T "  1  CO  ro o ro  ro ro ro oo  ro m  w oi  ro ro ro oo ro co co o co co ro co co co J>  co co CD  &-0—8  1  T  1  1  OO 1  CO 1"  60  the rate in  time  of expansion the  mediated  a r e a o c c u p i e d by  ( F . B , AREA) and  by  temperature.  fruiting  i t i s possible  At  any  point  b o d i e s i s known  to c o n v e r t area to  spore 2  numbers  ( S . PER  47000 -  18000 s p o r e s  -  AREA).  62000 s p o r e s  then produce thirteenth fruiting of  the  new  component  bodies.  the  D.  by  Appendix  D.  and  amoebae, P.  14.08% o f t h e  data.  Data VC4  difference  the p r e d i c t e d  mm  =  2  The  =  300000 spores  situation.  area covered bodies  can  can  The by  cover  fruiting  a r e a o c c u p i e d by  amoebae.  100%  Models  used  and  of  space  a t any  taken  point  up  a cellular  s l i m e mold  to  were c o l l e c t e d  amoebae and  Data  the  VI  they colony.  tested -  independent at eleven  i n every case  ( a t the 95%  by  that  m o d e l s was  s p e c i e s (Program  the output  which  i n time.  proven  power o f t h e two  (Table VI).  models  i t must be  the growth o f both comparing  mm  pallidum  body c o l o n i e s  predictive  discoideum  significant  the  fruiting  t h e amount o f f o o d  I ) and  experimental for  the  mimic t h e e x p a n s i o n  simulating  limits  discoideum  fruiting  The  p a l l i d u m , 6.4  6.4  confidence l i m i t ) .  (LIMIT),  t h e s e m o d e l s c a n be  actually  VC4,  s p e c i e s h a v e b e e n d e s c r i b e d by  predict  amoebae and  f o r P.  Exploitation  Both  discoideum  amoebae i n a f o o d r e n e w e d  a r e a o c c u p i e d by  Testing  Before  and  (mean - 9 5 %  b o d i e s can occupy  should  F o r D.  temperatures  t h e r e was  l e v e l ) between were c o l l e c t e d  the  no  observed  at eleven  TABLE V I  D. d i s c o i d e u m VC4 amoebae. The o u t p u t from Program VI i s compared w i t h i n d e p e n d e n t l y c o l l e c t e d a r e a d a t a . A star i n d i c a t e s a s i g n i f i c a n t d i f f e r e n c e ( 9 5 % l e v e l ) between t h e d a t a and t h e o u t p u t .  TEMP.  TIME  REP. NO.  9 5 % CON AROUND MEAN AREA  14.5  5.0  6  138.4  15.5  4.0  6  95.9  16.5  4.0  6  84.5  17.5  4.0  6  153.5  18.5  4.0  6  181.4  19.5  4.0  7  203.2  20.5  3.3  6  115.3  21.5  3.3  6  131.0  22.5  3.3  6  124.0  23.5  3.3  5  73.7  24.5  4.0  4  110.7  -  -  -  -  168.2 135.3  PREDICTED AREA 120 97  184.4  126  217.4  158  2 39.2  190  263.6  218  196.6  151  214.6  160  233.2  146  185.8  142  197.7  169  TABLE V I I P_o p a l l i d u m amoebae. The o u t p u t f r o m P r o g r a m V I i s c o m p a r e d with independently c o l l e c t e d data. A star indicates a s i g n i f i c a n t d i f f e r e n c e ( 9 5 % l e v e l ) b e t w e e n t h e o u t p u t and the data.  TEMP.  TIME  REP. NO.  9 5 % CON AROUND MEAN AREA  18.5  5.0  6  26  19.5  3.9  7  23  20.5  3.9  6  34  21.5  3.9  9  95  22.5  3.9  3  134.8  23.5  3.3  5  124.7  24.5  3.2  4  154.4  25.5  3.2  3  159.4  27.5  3.0  4  223.4  28.5  2.3  6  162.1  29.5  2.4  3  21.4  30.5  2.2  5  98.1  32.5  2.2  4  235.2  33.5  2.2  7  136.7  PREDICTED AREA  --  67  10.6  62  25.4  -  107  57.1  178  102.7  257.8  160.8  -  212.4  154  -  275.5  192  285.2  243  294.5  294  201.8  173  289.9  209  272.2  176  261.7  167*  230.6  146  -  -  -  TABLE  VIII  D. d i s c o i d e u m VC4 f r u i t i n g b o d y . The o u t p u t from Program VI i s compared w i t h i n d e p e n d e n t l y c o l l e c t e d a r e a d a t a . A star i n d i c a t e s a s i g n i f i c a n t d i f f e r e n c e ( 9 5 % l e v e l ) between t h e o u t p u t and t h e d a t a .  TEMP.  TIME  REP. NO.  9 5 % CON AROUND MEAN AREA  14.5  4.8  6  17.3  15.5  4.8  6  25.6  16.5  4.8  6  28.2  17.5  5.0  6  78.6  18.5  5.0  6  106.4  19.5  4.1  7  77.8  20.5  4.1  6  48.4  21.5  4.1  6  130.7  22.5  4.1  6  74.8  23.5  4.1  5  64.3  24.5  4.0  4  0.0  -  PREDICTED AREA  22.3  20.5  43.9  37.7  60.4  60  123.0  99  185.2  130  107.8  79  113.5  93  160.2  101*  167.4  99  163.6  83 '  72.6  49  TABLE  IX  P. p a l l i d u m f r u i t i n g b o d y . The o u t p u t from Program VI i s compared w i t h i n d e p e n d e n t l y c o l l e c t e d a r e a d a t a . A star i n d i c a t e s a s i g n i f i c a n t d i f f e r e n c e ( 9 5 % l e v e l ) between t h e o u t p u t a n d t h e data*.  TEMP.  TIME  REP. MO.  9 5 % CON AROUND MEAN AREA,  19.5  5.0  3  11.8  20.5  3.7  5  13.9  21.5  3.8  5  19.9  22.5  3.9  4  33.5  24.5  3.2  3  24.8  25.5  3.2  3  13.6  27.5  3.2  3  37.7  28.5  3.2  5  37.4  29.5  3.2  3  13.0  30.5  3.2  7  37.7  32.5  3.3  6  36.7  -—  PREDICTED AREA  26.8  32*  20.4  19  30.8  30  44.9  41  57.1  32  70.3  36  46.5  41  52.1  43  57.6  44  51.6  44  53.8  45  65  temperatures of  the  the  eleven  observed  collected and  f o r D. cases and  discoideum t h e r e was  the  between the  of  no  predicted  at fourteen  i n twelve  VC4  the  temperatures  and  the  ing  i n ten of eleven  between the  observed  These data two rate  exploitation of colony  m o d e l s do  expansion  temperature  Summary:  Exploitation  cellular  steps:  disperse, fruiting  and  pallidum  (Table  the  no d i f f e r e n c e  IX).  contention the  form  species over  the  that  and  the  the  entire  life  c y c l e i s composed o f  g e r m i n a t e t o p r o d u c e amoebae w h i c h consume f o o d ,  bodies  fruit-  used.  s l i m e mold  spores  amoebae,  (Table V I I I ) . ' Data  d e s c r i b e both  f o r both  were  no d i f f e r e n c e  t h e r e was  predicted  seem t o s u p p o r t  range of  (1) The  the  Data  f o r P.  cases  i n ten  d i f f e r e n c e between  t h e r e was  temperatures  and  and  f o r P_. p a l l i d u m  predicted  at eleven  and  significant  fourteen cases  observed  bodies  (Table V I I ) .  were c o l l e c t e d bodies  fruiting  form,  and  the  the  amoebae  fruiting  five divide,  aggregate, bodies  contain  spores o (2)  Since  food  step i n the of (3)  But if all  i s the life  resource  i n short supply,  cycle i s directly  only  this  r e l e v a n t to the  study  exploitation. the any the  rate of  food  more t h a n  one  steps  were  use  depends upon a l l t h e  generation modelled.  i s considered,  other  steps  therefore  66  (4) The ion  spore  germination  l a g s were b o t h  d e s c r i b e d by (5) The  form  colony the  of  r a t e of  both  rates  the  expansion  was  body  and  product-  were  and  fruiting  equation  directly  body  ( l c ) because  p r o p o r t i o n a l to  the  colony.  amoeba and  fruiting  dependent.  s p e c i e s , and  body c o l o n y  Amoebae c o l o n y D.  were d e s c r i b e d by  fruiting  fruiting  dependent  d e s c r i b e d by  r a t e of expansion  temperature for  was  the  (2b).  amoeba c o l o n y  of  and  temperature  equation  expansion  perimeter (6) The  lags,  body e x p a n s i o n  discoideum equation  expansion  expansion  fruiting  (3c).  P.  was  rates  body  expansion  pallidum  r a t e s were d e s c r i b e d by  equation  (4b). (7) The  c o m p o n e n t s were l i n k e d  exploitation  The  The  model p r o v e d  of  cases.  Exploitation If  exploit  their  the  two  to  two  species w i l l  do  accurate  i n at  be  least  case:  together,  to p r e d i c t  only  compete f o r f o o d  possible to predict  derived exploitation models f a i l  90%  Simulation  (in this  when p u t  form  independent  s p e c i e s , when grown t o g e t h e r ,  environment  space) i t should  exploitation  t o be  - Competition  and  independently  ( F i g . 22)  m o d e l s w h i c h were t e s t e d a g a i n s t  data. the  together  on  models.  e x a c t l y what  the b a s i s of I f the  the outsome o f  the  two a  the  real  Figure  22  Diagramatic r e p r e s e n t a t i o n of the e x p l o i t a t i o n m o d e l s i m u l a t e d i n P r o g r a m V I I . The a b b r e v i a t i o n s are e x p l a i n e d i n the t e x t .  P  EXTERNAL FORCE 2  SPORE  S. PER AREA FOOD SPACE  FOOD SPACE  F . B ,  EXP-  68  competitive  situation  competitors  are  then  directly  A competitive s p e c i e s i n the independent (Appendix  i t must be  interfering situation  l a b o r a t o r y was  simulated  Figure  22  illustrates  f o u r c o m p o n e n t s were i d e n t i f i e d  The  "SUM"  component  sums t h e  species.  I t outputs  species.  This  food  and  tion  t o two  been  results  of the  P.  pallidum  and  discoideum  amount o f  bodies  be the  able  sections.  components  and  the model p r e d i c t s  should  be  ( F i g . 23). capable  P,  3 7 . 5 ° C P.  areas  and  occupied  only  amoebae  and  t h a t f r o m 9.0°  using  only  fruiting  bodies  grow  food increases  Beyond  species  ( F i g . 2 3).  to  to  both  temperature  becomes f i t ) .  fruit  able  to 26,5°C  and  the  i s the  by  temperature,  species  18,1°  f i t as  pallidum  t o consume f o o d  the  of growing  pallidum  any  ab-  temperature.  From  becomes l e s s  simula-  presence or  s p a c e u s e d by  (1)  discoideum  various  and  level  should, be  to  food  at  time  t o w a r d s 2 6 , 5 ° C and up  All  competition  the  any  discoideum  and  D.  (1)  at  consume f o o d  species  "LIMIT"  exploitation  sence of  and  system used.  used.  levels:  1 8 . 0 ° C D.  VII  both  a t two  At  two  "TOTAL FOOD-SPACE" u s e d by  assessed  fruiting  the  "COLONY EXPANSION" c o m p o n e n t s when a l l t h e  s p a c e has  the  joining  mold  both  be  (2)  slime  i n previous  can  and  another.  i n Program  the  and  the  s p a c e u s e d by  quantity inputs  the  The  the  food  one  by  e x p l o i t a t i o n models t o g e t h e r  I).  stop  with  that  for cellular  but  which  assumed  At and  26.5°C  that level  should (2)  amoebae  of  both 2.4  species hours  were o u t p u t  together.  absence  level with  of  spores.  as  the  Tests  (level  were c o n d u c t e d  1) b y  Both  species  25).  These data  above 24.3°C  and  P.  pallidum  concentration.  such t h a t o n l y detected.  plates  but  the  since  the  amoebae s t a g e ,  circumvented  discoideum  and  P.  of high In  does not and  I t should  presence or  two  given  the  of  two  presence  between  and  P.  be  numbers  18.0°  and  plate.  short,  completely two  D.  species  fruits  (Fig.  noted  24  V12  of intial  that  the  fruiting  data bodies  ori n o n - f r u i t i n g b o d y  are  i n d i s t i n g u i s h a b l e at to determine  This  which  shortcoming be  was  presented  later.  model p r e d i c t s t h a t  should  discoideum  26.5  discoideum  absence of  present  species  pallidum  pallidum spore  D.  or  covered  probability  be  experiments which w i l l  2 6.5°C when i n f a c t 24.3°C  the  i t i s impossible  any  by  that  i t i s enough t o know t h a t t h e  tions  the  b e l o w 2 4 . 3 ° C d e p e n d s upon t h e  Amoebae may  amoebae o c c u p y  R'  fruit  also indicated that  fruiting  Now  at  the  exploitation-competition simulation predicted  pallidum  the  growing  inoculating bacteria  d i d not  £•  is  at i n t e r v a l s  s i n g l e d r o p s o f w a t e r c o n t a i n i n g known  never f r u i t s  are  simulation  p r e d i c t i o n s were t e s t e d b y  species  Fig.  the  ( F i g . 23). The  plates  by  V12  fruit  between  never f r u i t s  below 24.0°C o n l y  both  18.0°  and  above  under  condi-  concentration. the  e x p l o i t a t i o n - competition  describe  the  must d i r e c t l y  competitive interfere  model  interaction, with  one  another.  Figure 2 3  Output from t h e e x p l o i t a t i o n - c o m p e t i t i o n model. The r e s u l t s o v e r f i v e s u c c e s s i v e d a y s a r e shown. A r e a c o v e r e d ( p r o p o r t i o n a l t o t h e amount o f f o o d u s e d ) i s p l o t t e d on t h e y - a x i s . Temperature along the x - a x i s . Four q u a n t i t i e s are represented: (1)  A r e a c o v e r e d b y D. d i s c o i d e u m (solid line).  (2) A r e a c o v e r e d b y D. d i s c o i d e u m bodies (dotted l i n e ) .  amoebae fruiting  (3)  A r e a c o v e r e d b y P. p a l l i d u m (dashed line).  amoebae  (4)  A r e a c o v e r e d b y P. p a l l i d u m f r u i t i n g b o d i e s ( d o t t e d and d a s h e d l i n e ) .  COVEIRED  20  15  30  25  35  / //  DAY 4  / \ / \ / V //\\ / \ •'** ' \  O Oi  AREA  1  1  ^  .—«-•''  20  15  1  1290  30  25  / \\ / / \\ // \ /  DAY 5  ^ \  35  -  A  /' \\''\  /  645  '  i . ...  15  20  • A _.. 1  25  TEMPERATURE  30  s  1—i  35  Figure  24  T h e p r e s e n c e o r a b s e n c e o f D. d i s c o i d e u m and £• p a l l i d u m f r u i t i n g b o d i e s i s noted w i t h r e s p e c t t o (1) t e m p e r a t u r e - x - a x i s , (2) r e l a t i v e s p o r e c o n c e n t r a t i o n - y - a x i s , (3) a b s o l u t e s p o r e concentration,, A black dot i n d i c a t e s that S° d i s c o i d e u m V12 f r u i t e d a t any t e m p e r a t u r e and r e l a t i v e c o n c e n t r a t i o n . An o p e n c i r c l e i n d i c a t e s t h a t P. p a l l i d u m f r u i t e d . The f i g u r e i s d i v i d e d i n t o f o u r s e c t i o n s t o denote the v a r i o u s absolute s p o r e c o n c e n t r a t i o n s u s e d : ( a ) 8800 s p o r e s p e r p l a t e , (b) 4400 s p o r e s p e r p l a t e , ( c ) 2200 s p o r e s p e r p l a t e , ( d ) 1100 s p o r e s p e r p l a t e . An e x a m p l e : I f a c u l t u r e were s e t up w i t h a t o t a l s p o r e c o n c e n t r a t i o n o f 8800 ( p a r t a ) , and t h i s t o t a l was composed o f 4400 D. d i s c o i d e u m V12 and 4400 P. p a l l i d u m ( 5 / 5 7 , and i f t h i s c u l t u r e were grown a t 2 2.3° t h e n o n l y D. d i s c o i d e u m V12 w o u l d fruit.  OJ CD  «  *  CD  cn  CH  JL  "T  ro O  s  °  90  • •  ro ro ro  •o oo  »o  of  Concentration  oo  ©  osO»  OO?  o / Os oo/ O G  OJ  CD  CD  P. p a ! I i d u m cn  CM  "©  T  ~  of D d i s c o i d e u m  / Concentration — CO  CD —  4oi  cn  cw  ro _» O 9  ro  ro  ro  -u.  ©.  to  o  o oo  oo  •  ••  e  oo  •  ••  O  ••  o  ••  p»  m  OJ  TJ m  ro  >  ro  za H  cr m  cops 9  -,o£'  o»  O  09  -tJo o  oo oo o o  OJ  ro  o  ro  o  o  o o  a OSD3  OsOa  b~~""6~"""o"  01  ro s>  oo  ro  0#  e$  Oo  Oo  OsOv'OO  O  O  ••' o«  ro  OJoo  ro  o  DO  ro  ro 65  ro -j  ro  ro CD  oo  ro  ro co  ro co  ,'0©Oo o  •C  •O OoQ* •  O  So  OO  OO  OO  O  o  o  o  o  o  o  —  © CD  ro  OJ ro  to  •  • . o«  o  o  o  o  o  ro  Iff  °o°  °o°  °§  b o  o  o  C O  o  % o  ro ro co  OJ  O  OJ  ••  o  oi  O  CO  OJ  8  ro oo  CD  cn  ro ro  ro ro • ' oo  ro  CD  ro O  o  so ro _ ro  OJ  TT  C0  O  OJ  OJ  o o  Figure  25  The p r e s e n c e o r a b s e n c e o f D. d i s c o i d e u m V12 and £• p a l l i d u m f r u i t i n g b o d i e s i s n o t e d w i t h r e s p e c t t o Til t e m p e r a t u r e - x - a x i s , ( 2 ) r e l a t i v e s p o r e c o n c e n t r a t i o n , (3) a b s o l u t e s p o r e c o n c e n t r a t i o n . A b l a c k d o t d e n o t e s t h a t D. d i s c o i d e u m V12 fruited. An o p e n c i r c l e d e n o t e s t h a t P. p a l l i d u m fruited. The f i g u r e i s d i v i d e d i n t o f i v e p a r t s to denote the v a r i o u s spore c o n c e n t r a t i o n s used: ( a ) 6 5 0 0 , ( b ) 8 0 0 0 , ( c ) 5 0 0 0 , ( d ) 4 4 0 0 , ( e ) 2000 spores per p l a t e .  If.  -  19  20  21  22  19  20  21  22  19  20  21  22  © O  19  20  21  19  20  21  22  8  O  0  o  J—  23  8  24  1  8  25  26  25  26  J_  TEMPERATURE  \ \  °C  I  27  L  27  l  »  28  29  30  31  J  28  29  -A. 30  31  73  Interference  The outcome  ( F i g . 23)  suggests of  discrepancy  Interference point  are  known:  2 6°  as  (2)  the  f o r food  must be  the  and  probability  spore  range  D.  and,  D.  24.3°C.  distinct  P.  pallidum  These  Inhibition  of At  two  P. the  V12  t o 24°C, from  P.  between  of  at P.  any  pallidum. At  process 18°  and  D.  at  discoideum  (4)  P.  over  i n the  be  spores.  lower V12 most  of  pallidum  ( F i g . 24,  i t can  temperature  pallidum  occurred  fruiting  observations  mechanics  process.  from f r u i t i n g  24.3° t o 26.0°C  types V12  18°  25)  simulation predicted,  fruiting  pallidum  from  these  discoideum  (2)  P.  from  fruit  fruiting  (3)  and  interference  concentration  ( F i g . 24),  discoideum  extending  two  pallidum  Fig.  e x p l a i n the  i n the  the  d i d not  number i n c r e a s e d  From  (1)  initial  prevented  of  competitive  ( F i g . 24,  discoideum  - competition P.  lower temperatures  prevented  that  species  of  range extending  cannot  b e t w e e n D.  exploitation  apparently the  alone  p l a y i n g some p a r t  (1) b o t h  the  simulated  a c t u a l outcome  four c h a r a c t e r i s t i c s  d e p e n d e d upon t h e As  the  that exploitation  competition  this  and  between the  temperature  25).  hypothesized  of i n t e r f e r e n c e occur:  interferes interferes  processes  with with  P. D.  p a l l i d u m below discoideum  were t r e a t e d  V12  24°C above  separately.  pallidum outset  i t can  be  stated that  P.  pallidum  is  i n h i b i t e d f o r  t h i s  at  the  statement  ( F i g .  33),  o f  d i s c o i d e u m  D.  and  f r u i t i n g  but  d i v i d e  w i l l  and  are  Presumably  p r o c e s s ,  p o s s i b l y  o f  c o n c e n t r a t i o n P.  p a l l i d u m  and  can  c o n c e n t r a t i o n  clump  f o r m a t i o n .  c l u m p " 2  must  s p o r e s  c u l t u r e  t h i s  d i s h  c o n t a i n i n g  to  from  i n f l u e n c e  1000 the  do  o f  to  a  i n  h y p o t h e s i z e d  t h a t  s m a l l  The  g r e a t e r  i n  to  the  i s  t o It  .001  ml  b a c t e r i a to  use  5000 o f  and  water D.  s p o r e s  f o o d  the  i n  clumps  p a l l i d u m o f  the  and  an  a r e a  o f  term  " s p o r e  when  p l a c e d  p l a t e ) ,  0  spore  t h a t  d i s c o i d e u m per  of  P.  o b s e r v e d  of  p r e s e n c e  d i s c o i d e u m  t e s t e d ,  was  the  D.  l i k e l i h o o d  be  i n h i b i t o r  p a l l i d u m  overcome  h i g h e r  f o o d  t h i s  c h e m i c a l  f r u i t  presenc  f r u i t i n g  w i t h  P.  a b l e  l a t e r  consume  h i g h  be  e v i d e n c e  the  produce  i n t e r f e r e s  a b l e  d e f i n e d .  suspended  ( c o n c e n t r a t e d a b l e  be  to  i n  o f  h y p o t h e s i s  f i r s t  were  i s  b o d i e s . the  amoebae  p r o d u c t i o n  The  p r e s e n t e d  g e r m i n a t e  aggregate  c o n d i t i o n s  might  spore  do  v e g e t a t i v e  the  be  f r u i t i n g  If  s p o r e s  to  s t a g e .  l o g i c a l l y  d i s c o i d e u m  under  i t  f o r m a t i o n  more  p a l l i d u m  s p o r e s  p r o d u c e  D.  w i t h  P.  d i s c o i d e u m  D.  the  u n a b l e  b o d i e s .  S i n c e  be  p a l l i d u m  P.  but  body  on  a  spores they  about  were  16  to  2 2 2  mm  .  In  a r e a  p e r i o d  o f  f o o d  f o r  time  depending  P.  a  t h i s  p a l l i d u m  f r u i t i n g .  and  upon used  D. at  the the  d i s c o i d e u m l e a s t  t h r e e  t e m p e r a t u r e , f o o d  was  u n a b l e  d a y s . D.  p r e v e n t i n g  to  use  E v e n t u a l l y ,  d i s c o i d e u m P.  p a l l i d u m  the the  overcame from  Figure  26  The r e l a t i o n s h i p between P. p a l l i d u m clump s i z e and temperature. S i n g l e b l a c k dots denote the o c c u r r e n c e o f D. discoideum V C 4 f r u i t i n g b o d i e s only. Open c i r c l e s denote the o c c u r r e n c e o f b o t h P. p a l l i d u m and D. discoideum V C 4 f r u i t i n g b o d i e s . The l i n e i s f i l l e d by eye and the shaded a r e a denotes o t h e r p o s i t i o n s t h a t the l i n e c o u l d have t a k e n . In a l l c a s e s the p l a t e s were i n o c u l a t e d w i t h a random spread of 1000 D. discoideum V C 4 s p o r e s . A p p r o p r i a t e numbers of P. p a l l i d u m spores were i n o c u l a t e d i n .001 ml of water.  LU  21  22 23 TEMPERATURE  24  25  76  I n v i e w o f t h e s e d a t a a "clump o f s p o r e s "  could  2 be  t h e s p o r e s o c c u p y i n g e a c h 19 mm  of  a petri  of  the surface  dish.  were p o s s i b l e  Each clump a r e a c o n s t i t u t e s  a r e a o f a 60 mm p e t r i to divide  s p o r e s i n each c o u l d This Program V I I I 100  a r e a u n i t on t h e s u r f a c e  a petri  dish.  about  Therefore, i f i t  d i s h i n t o 100 s e c t i o n s t h e  r e p r e s e n t one "clump".  p r o c e d u r e was f o l l o w e d  i n the f i r s t  clump c o n t a i n i n g  the greatest  number o f P. p a l l i d u m  number o f s p o r e s was i d e n t i f i e d .  hypothesis stated  D. d i s c o i d e u m o n l y To  surface  that only  t h e l a r g e s t c l u m p was o f i n t e r e s t . (1) F o r l a c k o f any  o f a 60 mm p e t r i  d i s h t h e y were d i s t r i b u t e d a t  ( 3 ) The p l a t e i s d i v i d e d  any s p o r e c o n c e n t r a t i o n  spore  information  i t i s assumed t h a t when s p o r e s a r e s p r e a d o n  u n i t s or spheres o f i n f l u e n c e .  size will  Because  one clump o f a p a r t i c u l a r  ( 2 ) A random d i s t r i b u t i o n f u n c t i o n m i m i c s  occurrence.  for  a plate  t o overcome t h e i n h i b i t o r y e f f e c t o f  recapitulate:  to the contrary  random.  spores used t o i n o c u l a t e  as t h e  t h e s i z e o f t h e maximum c l u m p i n c r e a s e d .  s i z e w o u l d be r e q u i r e d  the  into  t h e s p o r e s were s p r e a d a t random, and t h e  F r o m t h e o u t p u t o f P r o g r a m V I I I i t was f o u n d t h a t  the  section of  ( A p p e n d i x I ) w h e r e a p l a t e was d i v i d e d  equal sections,  increased  l/100th  this  i n t o 100 e q u a l  ( 4 ) T h e maximum c l u m p  i s calculated.  (5) This  area size clump  be t h e " a v a i l a b l e " clump s i z e f o r any p a r t i c u l a r  concentration. This  information  i s summarized i n a components  77  diagram  page 8 7 ) by  ( F i g . 29,  t h e number o f P. area controlled  p a l l i d u m spores by  a r e a of the p l a t e poisson  a s p o r e clump (TOTAL AREA);  distribution  area units,  and  the  area unit  CLUMP  SIZE).  (AVAILABLE  Having  fruiting  temperature  found  the  .001  find  the  and  the  the  spores  clump  at  the  total  a into  random,  spores  size" size  discoideum  for  any  necessary  grown a t  any  D.  found  discoideum  area indicates  were  the  plates  were i n c u b a t e d a t v a r i o u s  b o d i e s were n o t e d  after  seven  that  occurred at  difficult  to judge  unable  i n F i g u r e 26  and  days  as t h e c o n c e n t r a t i o n o f P. p a l l i d u m  t o the nature  p a l l i d u m was  line  were  p a l l i d u m spores onto  covered  pallidum  ( F i g . 26). i t was  spores  inoculated  plates  bacteria  o f P.  atures  Due  size"  o r absence  increased fruiting  boundary  o f D.  the presence  fruiting  I t was  w h i c h P.  and  of  the p l a t e  p a l l i d u m t h e clump  The  spores  at  size  (SPHERE I N F ) ,  Where  a l l a c t as i n p u t s t o  w a t e r and  suspensions.  J2° d i s c o i d e u m  technique  the  V a r i o u s numbers o f P.  temperatures  growth.  (SPORE P P ) ,  " n e c e s s a r y clump  in distilled  ml  4.  must be d e r i v e d .  established.  in  and  "available  d i s h e s c o n t a i n i n g 1000  suspended  2,  c o n t a i n i n g t h e most  i n the presence  To petri  3,  distributes  s p o r e c o n c e n t r a t i o n o f P. for  1,  (POISSON) w h i c h d i v i d e s  appropriate chooses  steps  was  other possible  lower  and  of t h i s  fitted  by  positions  temper-  experimental  the p r e c i s e  to f r u i t .  lower  temperature  T h e r e f o r e , the eye  and  the  that  the  line  shaded could  '  78  have the  assumed. line  area  on  In F i g u r e  i s the the  left  area  26  the  area  i n w h i c h P.  i s the  area  on  the  pallidum  i n w h i c h P.  right  can  side  fruit.  pallidum  of The  cannot  fruit. The lines the  s e c t i o n of In  The  terms o f  information array  inputs which  to  (PP  as  the  i s summarized  pallidum  the  it  study.  The  sources  of  evidence  be  ( F i g . 29, 5,  6,  using  the  page  and  7.  size  (TEMP), a c t  necessary  87)  and as  clump  size  assumed  that  SIZE). been  assumption variation  D.  i s probably  not  i s so  that  methods e m p l o y e d  statement  discoideum  small in  comes f r o m  this two  data.  distributions pallidum  equal  This  into  I)„  i s independent of  for this  Data, s o u r c e  P.  temperature  s e c t i o n i t has  ability  detected  components  (NECESSARY CLUMP  c o r r e c t , however, the  c a n n o t be  incorporated  (Appendix  s e l e c t s the  background c o n c e n t r a t i o n . absolutely  and  straight  r e l a t i o n s h i p b e t w e e n clump  foregoing  fruiting  array  by  DATA I N P U T ) , and  fruiting  In  an  three  components d i a g r a m  a f u n c t i o n which  allows  i s composed o f  Program V I I I  d e s c r i b i n g the  temperature  P.  line  w h i c h were d e s c r i b e d  second  this  boundary  1:  of various  spores.  numbers o f  hypothesized  P. that  P l a t e s were e s t a b l i s h e d w i t h numbers o f  D.  I f experimental pallidum i f D.  spores  discoideum  sets are  discoideum  V12  inoculated  random and  with  compared i t c o u l d  background  is  important  79  t h e n P. p a l l i d u m atures  should  be a b l e  on t h e p l a t e s w i t h  concentrations.  to f r u i t  low D. d i s c o i d e u m  Comparisons  are  EXPERIMENTAL SET NO,. 1 PP CON  LOWEST PP. F . B .  24.3°  Figure  21.8°  Figure 1862  798  One s t a r  i n t h e extreme  tion  alters  24.3°  P. p a l l i d u m ' s  tion.  ability  out of four  fruiting  25.0°  2394  Figure  45-e  1600  14400  hand  refuted the hypothesis  was r e f u t e d t h r e e P. p a l l i d u m  right  column  24.3°  *  23.0°  *  i n d i c a t e s that the  t h a t D. d i s c o i d e u m to fruit.  times,  *  44-e  266  24.3°  44-b  comparison  1862  Figure  466  24.3°  44-d  798  43-d  200  600  Figure  66  43-c  66  42-a  600  table:  LOWEST PP. F . B .  Dd. CON  Figure  10  Figure  background  made i n t h e :f o l l o w i n g  PP CON  42-a  90  temper-  EXPERIMENTAL SET NO. 2  Dd. CON  Figure  a t lower  The  suggesting  concentr  hypothesis that  i s i n d e p e n d e n t o f D. d i s c o i d e u m  concentr  80  D a t a S o u r c e 2: that was P.  Do  discoideum  c o n d u c t e d by pallidum  a  slightly  ground  background  test  a l t e r e d P.  of  the  pallidum  establishing plates containing  spores  concentrations.  A more d i r e c t  and  P.  six different  pallidum  lower temperature  decreased.  But  this  D.  hypothesis  fruiting 1000  discoideum  VC4  might have been  able  ( P i g . 27)  discoideum  trend  was  as  D.  very  to  fruit  at  back-  weak i t i t e x i s t e d  at a l l . In b o t h c a s e s in  P.  D.  discoideum  that  pallidum  the  fruiting  the  data  ability  concentration.  boundary  line  i t i s apparent  smaller  than the  experimental b e t w e e n P.  ( F i g . 26)  that  be  the  experimental  show any  respect  fruiting  may  be  to  trend,  the and  Therefore, of  and  any  D.  trend  fact the  as much  i f i t exists,  inclusion ability  with  by  real  changes i n  imprecise  inaccurate  error.  method p r e c l u d e s  pallidum  with  to  When c o n s i d e r e d  t e m p e r a t u r e m e a s u r e m e n t s may 0.3°C,  failed  as  is  the  interaction  discoideum  concentration. Returning section and  i t has  spore  or out  been  under  any  concentration  size"  P.  using  pallidum the  are  i t should  will  finished  and  the  interference  "necessary  clump  be  temperature  possible to  and  link  make a d e c i s i o n a b o u t  fruit.  size"  calculable quantities.  conditions of  q u a n t i t i e s together not  main body o f  shown t h a t b o t h  " a v a i l a b l e clump  Therefore,  two  to the  T h i s p r o c e d u r e was  version of  Program  VIII  P.  pallidum  these whether carried  (Appendix I ) .  Figure  27  P. p a l l i d u m c o n c e n t r a t e d a t 1000 spores per p l a t e was grown w i t h D, d i s c o i d e u m c o n c e n t r a t e d a t 200, 1000, 2000, 3000, 4000, and 5000 s p o r e s p e r p l a t e . Temperature i n degrees c e n t i g r a d e i s measured a l o n g t h e x - a x i s and D, d i s c o i d e u m s p o r e c o n c e n t r a t i o n i s measured a l o n g the y - a x i s . An open c i r c l e d e n o t e s t h e p r e s e n c e o f P. p a l l i d u m f r u i t i n g b o d i e s i n a c u l t u r e d i s h , and a b l a c k d o t r e p r e s e n t s a d i s h i n w h i c h P„ p a l l i d u m f r u i t i n g b o d i e s d i d n o t a p p e a r . T h e l i m i t l i n e £ 95% c o n f i d e n c e l i m i t i s drawn from Program V I I I ,  82  The i n t e r a c t i v e c o m p o n e n t s diagram  also  added t o t h e components  ( F i g . 2 9 , p a g e '87) a s s t e p s 8 and 9.  function If  were  compares  the available  then f r u i t i n g  the available clump  T h e COMPARISON  and n e c e s s a r y  clump  sizes.  s i z e e x c e e d s t h e n e c e s s a r y clump  occurs.  I f n o t , t h e n P. p a l l i d u m  size  does n o t  fruit. The p r e d i c t i v e using  the data i n Figures  Figure the  a b i l i t y o f t h i s m o d e l was  2 7.  model  lists  In the figures fails  to predict  the results  FIGURE NUMBER  42, 4 3 , 44 ( A p p e n d i x a star  appears  t h e outcome.  I I ) and  at points  where  The f o l l o w i n g  o f comparing expected with  NUMBER CULTURES RUN  tested  observed.  NUMBER FAILURES  % FAILURE  Fig.  42  45  3  6.6%  Fig.  43  39  1  2.5%  Fig.  44  45  3  6.6%  Fig.  27  115  6  5.2%  244  13  5.3%  TOTAL  Out o f t h e 244 c u l t u r e s correct  outcome  acceptable.  r u n t h em o d e l  5.3% o f t h e t i m e .  table  f a i l e d to  predict the  These r e s u l t s a r e  83  Confidence  L i m i t s o n P. P a l l i d u m I n t e r f e r e n c e  Since a poisson confidence  the available  distribution limits  clump  size  t o each e s t i m a t e .  F o r clump  10 a s t a n d a r d  used  ( R i c k e r 1936) b u t f o r e s t i m a t e s  by  (Stevens  1942) was u s e d .  were u s e d  spores  p a l l i d u m growth a t 22.7°C  limit  around  corresponding  temperatures a r e used  maximum a v a i l a b l e spores,and producing  Inhibition  clump  fruiting  o f D.  to establish  about  was  10 a c o r r e c t e d i s exemplified  size  was  calculated  allows  The 9 5 % c o n f i d e n c e  a culture from  Therefore, dish the  10.7 t o 28.4  a t w h i c h P. p a l l i d u m m i g h t varies  from  22.6° t o 23.0°  begin (Fig.27).  Discoideum i n w h i c h D. d i s c o i d e u m  t h a t D. d i s c o i d e u m  up t o a b o u t 2 6 . 5 ° C .  mixed with  intervals  and 2 2 „ 6 ° C .  V12 was c a p a b l e  a b o u t 2 6 ° C and t h a t D. d i s c o i d e u m  growing  larger  o f 18 i s 10.7 t o 28.4 and t h e  s i z e might vary  bodies  Experiments indicated  clump  sizes  1000 P. p a l l i d u m  p e r clump  a r e 2 3°  t h e temperature  than  example  (Fig. 26).  t h e mean e s t i m a t e  when 1000 s p o r e s  to  In t h i s  Eighteen  less  The p r o c e d u r e  and t h e a v a i l a b l e  t o b e 18 s p o r e s . £•  table of poisson confidence  t h e d a t a i n F i g u r e 2 7.  spores  using  i t i s p o s s i b l e t o a t t a c h 95%  than  table  i s calculated  was grown  alone  o f g r o w i n g up  VC4 was c a p a b l e o f  B u t when D. d i s c o i d e u m  V12 was  P. p a l l i d u m i t s g r o w t h was a l w a y s t e r m i n a t e d a t  24.3°C  (Figs.  24, 25, and 41, 42, 43, 44 - A p p e n d i x I I ) .  84  Apparently,  there  concentration  was  and  D.  no  discoideum  C h a n g e s i n D. discoideum  fruiting  As  the  to  2000 s p o r e s  interaction  spore c o n c e n t r a t i o n  occurred  per  expressed  by  following  T  =  A b o v e 2000 s p o r e s  per  average, unable  can  be  can  fruit  Program the  i s the  IX  to  components  D.  foregoing  (Appendix  discoideum  selection ability  D.  per  plate  fruiting be  2000  discoideum  above 23.9°C.  =  23.9°  (5)  VC4  was,  on  This relationship  I)  11,  and  information as  a t w h i c h D.  12.  was  a subroutine,  The  ( F i g . 29,  (6)  discoideum  spore c o n c e n t r a t i o n  and  was  p a g e 87)  temperature (SPORE DD)  SELECTION) w h i c h  discoideum.  incorporated  into  added  to  as  relationships described  (DATA I N P U T ) , t h e  (DD  ; C )> 2000  concentration.  representation  function  o f D.  at which  ; C ^  maximum t e m p e r a t u r e  The  above e q u a t i o n s  spores  as:  C i s spore  10,  pallidum.  r e l a t i o n s h i p can  ( F i g . 28)  fruit  and  diagramatic  This  P.  altered  equation:  plate  Tp  where Tp  f r o m 200  2 3 . 9 ° - C/1800  the  expressed  presence of  temperature  ( F i g . 28).  the  p  i n the  spore  ability.  spore c o n c e n t r a t i o n  increased  p l a t e the  increased  fruiting  discoideum ability  b e t w e e n P_. p a l l i d u m  (TEMP), a l l feed  regulates  the  by  and into  the the a  fruiting  Figure  28  T h e f r u i t i n g a b i l i t y o f D. d i s c o i d e u m grown i n t h e p r e s e n c e o f 1000 P. p a l l i d u m s p o r e s i s p l o t t e d w i t h r e s p e c t t o t e m p e r a t u r e and D. d i s c o i d e u m s p o r e concentration. A b l a c k dot r e p r e s e n t s the presence o f D. d i s c o i d e u m f r u i t i n g b o d i e s i n a c u l t u r e d i s h . An o p e n c i r c l e r e p r e s e n t s a c u l t u r e d i s h w i t h no D. d i s c o i d e u m f r u i t i n g b o d i e s . The l i m i t i n g line i s f i t by e y e and 0.3°C t e m p e r a t u r e i n t e r v a l s h a v e b e e n e s t a b l i s h e d on e i t h e r s i d e o f t h e l i n e .  © Q  O  e  0  OO  aaapRstansgBBioEC  O  8  0  O  ©  CO  o  0  cc  o  ©  @  LU  O -z.  o o LU LX  O QCO  0  ©  ©  ©  ©  le || 1 I at I I I o »  e  o  _ )9oo8c^.8 8888 0080 8 8  I  o o  / /  o  '8  08  o  w  O  OO  O  23  24  TEMPERATURE  o -2.  —1—  " T "  22  O  25  26  86  equations  The  lines  (5)  and  However, t h e there in  measured reason  error  and  an  the  section,  than  P.  and  P.  pallidum  pallidum section,  and  an  the  appears i n F i g u r e From t h e  of  (1)  model,  the  size  (6)  limits. because  i s also  temperature  much as  by  impossible  must be  error to  error  - 0.3°C.  For  used  was-  this  to  i s unable  describe  to  fruit  28).  rate  of  the  f o r m e d by  P.  competition  an  section,  external  force  exploitation a D.  discoideum  section.  These  i n Program  IX  A components r e p r e s e n t a t i o n  s e v e r a l q u a n t i t i e s can  the  number o f pallidum.  of  29.  fruiting (5)  between  must i n c l u d e  germination  spores produced,  bodies,  the  linked together  I - Program I X ) .  ( 3 ) the  there  I t was  interference  (Appendix  are:  and  (Fig.  model d e s c r i b i n g  components have been  model  confidence  discoideum  pallidum  described  i s imprecise  a line  a b o v e w h i c h D.  and  Model  a P.  interference  use,  line  data but  rather  presence of  discoideum  These  the  h a v e b e e n as  interval  Completed  four  have 95%  temperature.  i n the  could  The D.  not  p o s i t i o n i n g of  temperature  The  do  measurement o f  measure the  in  (6)  28  u n d o u b t e d l y i s some d a t a e r r o r  the  the  drawn i n F i g u r e  rates,  (2)  the  body f o r m a t i o n ,  presence or  be  rate of  food  ( 4 ) the  number  absence of  a v a i l a b l e clumps o f  predicted.  the  fruiting necessary  Fiqure  29  F l o w d i a g r a m d e s c r i b i n g t h e way i n w h i c h t h e components d e s c r i b i n g l a b o r a t o r y c o m p e t i t i o n o f D. d i s c o i d e u m and P. p a l l i d u m a r e l i n k e d together. The t e r m s a r e e x p l a i n e d i n t h e text. P r o g r a m IX i n c l u d e s a l l o f t h e i n f o r m a t i o n summarized here.  i  EXTERNAL FORCE  INTERFERENCE  POISSON  AVAILABLE CLUMP SIZE  8  TOTAL AREA  COMPARISON j  PP DATA INPUT  NECESSARY CLUMP SIZE  TEMP  10 DATA INPUT  YES NO  88  E s t i m a t e s o f t h e e r r o r a t t a c h e d t o each o f t h e s e outcomes c a n a l s o be made.  I n a p r e v i o u s s e c t i o n i t was  d e m o n s t r a t e d t h a t 9 5 % c o n f i d e n c e l i m i t s c o u l d be e s t a b l i s h e d around t h e t e m p e r a t u r e  a t w h i c h P. p a l l i d u m f r u i t e d .  e r r o r i n t h e estimate o f the temperature s h o u l d f r u i t has a l s o been c o n s i d e r e d .  The  a t w h i c h D„ Finally,  discoideum  i t i s also  p o s s i b l e t o e s t i m a t e t h e e r r o r a t t a c h e d t o t h e model's p r e d i c t i o n s o f f o o d use and a r e a c o v e r e d by f r u i t i n g  bodies.  These q u a n t i t i e s depend upon many s o u r c e s o f e r r o r such a s : (1) e r r o r i n t e m p e r a t u r e tion  measurement,  (2) e r r o r i n g e r m i n a -  t i m e s , (3) e r r o r i n c o l o n y e x p a n s i o n ,  (4) e r r o r i n  f r u i t i n g body l a g t i m e , (5) e r r o r i n f r u i t i n g body r a t e s , and (6) e r r o r i n spore c o u n t s .  expansion  With t h e e x c e p t i o n  o f t h e s p o r e c o u n t e r r o r , i t has been i m p o s s i b l e t o do any more t h a n assume t h a t t h e e r r o r s a t t a c h e d t o each o f t h e s e components i s random. , S i n c e a l l o f t h e s e components t o g e t h e r p r o d u c e a p r e d i c t i o n o f t h e amount o f a r e a o c c u p i e d by f r u i t i n g b o d i e s a t any time i t c a n be assumed from t h e theorem f o r t h e a d d i t i o n o f P o i s s o n 1965) t h a t t h e e r r o r a t t a c h e d t o t h i s i s a l s o randomly  distributions(Brownlee and s i m i l a r  predictions  distributed.  T h e r e f o r e 9 5 % c o n f i d e n c e l i m i t s from a P o i s s o n distribution  may be p l a c e d around s i m u l a t e d p r e d i c t i o n s o f  s p o r e number, a r e a o c c u p i e d by f r u i t i n g b o d i e s , and f o o d u s e .  89  T e s t s o f the Area  Model  Occupied  by F r u i t i n g  Bodies  Several predictions one  that  the  relative  fruiting used.  upon t h e most c o m p o n e n t s  a r e a s c o v e r e d by  bodies  For t h i s  model has using  calls  after  the  were m o n i t o r e d ,  and  a r e a s o c c u p i e d by  of  temperatures  in  P.  and  space  and  species.  Method  Temperature  Experiments  fruiting  and  concentration  The a series  and  were c o n d u c t e d  c h a n g e i n D.  t h e maximum f r u i t i n g  d a t a from  of f i g u r e s  p a l l i d u m and  results  w i t h each  With  ( F i g . 30-A-F), D.  discoideum  of these tests  one  II  a r e a were  of the  two  at a  range  each  change  temper-  discoideum  temperature  these experiments  the  growth  and  bodies  spore c o n c e n t r a t i o n s .  been  established  when a l l t h e f o o d the  has  i n testing  C u l t u r e s were  of  P. p a l l i d u m  p a l l i d u m c o n c e n t r a t i o n t h e minimum f r u i t i n g  a t u r e changed,  The  area.  employed.  s p e c i e s were n o t e d .  P.  a l l o f t h e f o o d and  been i n t h i s  the  i s the p r e d i c t i o n  discoideum  known s p o r e numbers o f b o t h  progress  of  D.  the model, but  r e a s o n most o f t h e e m p h a s i s  ( m e t h o d s s e c t i o n ) was  used,  a r e made by  spore  changed.  are presented i n  figure  f o r each  pair  spore c o n c e n t r a t i o n v a l u e s .  a r e summarized  as  follows:  Figure  30  T h e a c t u a l a n d t h e o r e t i c a l a r e a s c o v e r e d b y D. discoideum a n d P. p a l l i d u m f r u i t i n g b o d i e s a f t e r a l l t h e a v a i l a b l e f o o d and space has been used. Area occupied i s measured a l o n g t h e y - a x i s and t e m p e r a t u r e on t h e x - a x i s . The s o l i d l i n e f o r D. d i s c o i d e u m and t h e d o t t e d line f o r P. p a l l i d u m a r e p r e d i c t e d b y t h e c o m p l e t e d m o d e l ( F i g . 20) (Program I X ) . A p p r o p r i a t e 9 5 % c o n f i d e n c e l i m i t s around the p r e d i c t i o n s are i n d i c a t e d with shaded areas. The f i g u r e on t h e f i r s t page i n c l u d e s a l l o f t h e a r e a o c c u p i e d b y t h e two s p e c i e s . From t h i s t h e c o n f i d e n c e l i m i t s c a n be viewed i n proper p e r s p e c t i v e . The r e m a i n i n g s i x pages o f s e c t i o n s which data p o i n t s were conducted at several d and one f i g u r e h a s b e e n a l l  FIGURE  NUMBER  SPORE D.  30-A 30-B 30-C 30-D 30-E 30-F  f i g u r e s a r e b l o w - u p s of'..the appear. The e x p e r i m e n t s i f f e r e n t spore concentrations o t t e d t o each c o n c e n t r a t i o n .  CONCENTRATION  DISCOIDEUM  3000 4000 2000 3000 4000 5000  P.  ,  PALLIDUM  1500 1000 1000 3000 4000 5000  TEMPERATURE  TEMPERATURE  TEMPERATURE  21  22  2 3  TEMPERATURE  24  21  22  23  T E M P E R A T U R E  24  TEMPERATURE  0  REPLICATE NUMBER  FIGURE  NUMBER OF FAILURES  %  FAILURE  30-A  62  5  8.0%  30-B  36  9  25.0%  30-C  38  2  5.2%  30-D  50  1  2.0%  30-E  66  7  10.6%  30-F  72  8  11.1%  TOTAL  324  Close of  be  a r e o f the type  D. d i s c o i d e u m explained  minimum clumps all on  inspection of the figure  the failures  and  i s too high.  by t h e f a c t  fruiting  a r e l a r g e r than  the concentration  great  enough t o a t t r a c t  in  area  occupied  o n l y o n e o r two a v a i l a b l e  Unfortunately,  there  clump  size.  Therefore,  s e c t i o n o f t h e p l a t e must  centers. gradient  Iti sdifficult from one c e n t e r  converge  to b e l i e v e w o u l d be  a l l amoebae, a n d t h e r e f o r e , some  by f r u i t i n g  an o v e r - e s t i m a t e  i s t o o low  These f i n d i n g s can p o s s i b l y  amoebae m i g h t be u n a b l e t o f i n d the  where P. p a l l i d u m  the necessary  every  o n e o r two f r u i t i n g  i n d i c a t e s t h a t many  that at temperatures c l o s e t o the  temperature,  t h e amoebae f r o m  that  9.9%  32  a fruiting  bodies.  o f P. p a l l i d u m  This  fruiting  center  and add t o  situation body  results  area.  i s no l e g i t i m a t e way t o i n c o r p o r a t e  hypothesis  into  t h e model u n t i l  more i s known a b o u t t h e  attractive  a r e a o f a c r a s i n i n mixed c u l t u r e s .  this  92  Continued  Competition Since  contains once  such  should food two  from  t h e a v e r a g e P. p a l l i d u m  100 t o 10000 s p o r e s  a fruiting  be a b l e  culture dishes spores  g o n e and f r u i t i n g were p l a c e d second  transfer short  face dishes  replaced.  this  that  and 4000  When t h e f o o d  the completed  new b a c t e r i a c o v e r e d  were a l l o w e d  t o grow and a f a c e  dish.  where  hypothesis  4000 D. d i s c o i d e u m  t o face with  The r e s u l t s  was  dishes dishes. to face  of this  a r e as f o l l o w s :  AREA P. P A L L .  AREA D. D I S C .  1  8, 12  292, 288  2  10, 11  290, 289  3  10, 13  290, 287  P. p a l l i d u m  Also  To t e s t  had formed  TIME PERIOD  and  i n a situation  were grown a t 2 3 . 5 ° C .  was made t o a t h i r d  experiment  t h e model p r e d i c t s  itself  containing  bodies  body  f o r m s anywhere a b o v e 2 2 . 5 ° C i t  to perpetuate  i s constantly being  P. p a l l i d u m  The  body  fruiting  continued  to f r u i t  P. p a l l i d u m  fruited  the f i r s t  throughout  d i d not gain  time  as e x p e c t e d  t h e e n t i r e time  o r l o s e any a r e a  sequence.  during the  sequence.  Summary -  Interference  (1) T h e p r e d i c t i o n s made b y t h e e x p l o i t a t i o n m o d e l d i d n o t agree with  the results  o f e x p e r i m e n t s i n w h i c h t h e two  93  species  (2)  P. p a l l i d u m about  (3)  were  grown  together.  interfered  with  Interference  D. d i s c o i d e u m  was o c c u r r i n g .  fruiting  above  24°C.  D. d i s c o i d e u m  interfered  with  P. p a l l i d u m  fruiting  below about 24°C. (4) T h e f r u i t i n g clump of  size.  spores  60 mm  petri  depended upon  "clump" was d e f i n e d  l/100th  maximum  a s t h e number  o f the surface  area  o f a.  dish.  size  dependent  o f P. p a l l i d u m  The term  occupying  (5) T h e clump  (6)  ability  necessary  f o rfruiting  and was a s s e s s e d  T h e maximum clump  size  spore c o n c e n t r a t i o n  was  temperature  experimentally.  a v a i l a b l e f o r any P.  was c a r - l c u l a t e d u s i n g  a  pallidum Poisson  distribution. (7)  When  " a v a i l a b l e clump  fruiting  occurred.  described (8)  D. d i s c o i d e u m  exceeded 'necessary  The model  i n Program V I I I  temperature  (9)  size"  fruiting  f o rthis  model  completed  size"  process i s  (Appendix I ) .  ability  changed with  and s p o r e c o n c e n t r a t i o n  T h e two i n t e r f e r e n c e m o d e l s were tion  clump  (Fig.  respect to 28).  linked to the e x p l o i t a -  ( F i g . 29) ( P r o g r a m IX - A p p e n d i x I ) a n d t h e m o d e l was t e s t e d .  94  (10) A t o t a l o f 324 p r e d i c t e d c u l t u r e the model which proved cases.  areas were used to t e s t  a c c u r a t e i n 90 l% o  o f the  test  95  RESULTS SECTION I I CONSEQUENCES OF COMPETITION  The deals  only  model c o n s t r u c t e d  with  cellular  time i n t e r v a l s . of  competition  i n the preceding  s l i m e mold  No a t t e m p t  over  short  was made t o p r e d i c t t h e r e s u l t s  c o n t i n u i n g f o r long  such p r e d i c t i o n s c o u l d o n l y  competition  section  periods  o f time,  because  b e made i f t h e o r g a n i s m s d i d n o t  change i n r e s p o n s e t o c o m p e t i t i v e  pressure.  other  e t a l , 1968, M i l l e r  studies  suggest  that  organisms  (Keast this  like  1968, F i c k e n  i s unlikely,  the c e l l u l a r  In view o f t h i s competitive was h o p e d describe  situations  that  slime  information,  o f these  a series  o f long  experiments  the r e s u l t s might  knowledge o f the s e l e c t i v e  term It  would  and P. p a l l i d u m  might  a l s o add t o o u r  f o r c e s i n v o l v e d i n t h e maintenance  e x c l u s i o n , o r the development o f c o e x i s t e n c e . . The c o m p e t i t i v e  two it  simple  were c o n t r i v e d i n t h e l a b o r a t o r y .  the r e s u l t s  and t h a t  with  1967)  molds.  a n y c h a n g e s t h a t D. d i s c o i d e u m  experience,  of  particularly  The r e s u l t s o f  species  excluded  impossible  this  situation  one a n o t h e r  t o compete refuges  f o r long  alone,  gradient  extending  D. d i s c o i d e u m  between  from  was a b l e  making  To remedy  b y g r o w i n g t h e two  w h i c h were p l a c e d about  that the  1 8 ° and 2 6°C,  time p e r i o d s .  were p r o v i d e d  species i n long c u l t u r e dishes ature  model demonstrated  15°C t o 30°C.  t o consume f o o d  on a temperWhen  and f r u i t  grown from  96  about  9°C t o 2 6°C.  1 1 1 1 1 1 1 D. discoideum 1 1 i 1 1 1 1 15°  20°  When grown a l o n e , between  about  25°  30°  P . p a l l i d u m c o u l d consume f o o d  18° and 3 7 ° C  and f r u i t  0  P. P a l l i d u m 15°  Therefore  20°  25°  the laboratory design  provided  30°  refuges  f o r both  species. If  divergence,  were t o o c c u r ,  an a r e a o f c o n f l i c t  above diagrams i n d i c a t e together between  they  convergence o r continued  both  c o u l d compete f o r t h e f o o d  an a t t e m p t  as p o s s i b l e ,  respect  save  t h e agar  and o n l y one b a c t e r i a l  an e n v i r o n temperature.  s u r f a c e was as  s p e c i e s was u s e d as  source. Under t h e s e  the  and space  was made t o p r o d u c e  e n v i r o n m e n t was t w o - d i m e n s i o n a l ,  a food  The  t h a t i f t h e two s p e c i e s were grown  ment t h a t was homogeneous i n e v e r y  flat  be p r o v i d e d .  1 8 ° and 2 6 ° C . Finally,  The  should  exclusion  animals  might both  c o n d i t i o n s i t was h y p o t h e s i z e d converge  t o use the resource  that at the  97  same r a t e , might for  and t h e r e b y e n s u r e  increase i t s rate  coexistence; or that  one s p e c i e s  o f r e s o u r c e use making i t i m p o s s i b l e  t h e o t h e r t o compete, t h e r e b y  ensuring competitive  exclusion.  Mixture  of Stock  Spores  A fifty-fifty from  the stock c u l t u r e s  periodically  fruit  together.  (Fig.  31-A, B, C ) .  26.5°C  In every case  portion  i s summarized  1  D.  1 15  Continued  In both  1  1  1  1  1  directly  culture gradients  over  which  this  t h e two s p e c i e s d i d n o t  V12 f r u i t e d  D. d i s c o i d e u m  ( F i g . 31-D,. E ) .  information  to establish  t h e two y e a r p e r i o d  D. d i s c o i d e u m  the remaining  o f spores coming  was u s e d  throughout  s t u d y was c o n d u c t e d .  over  mixture  up t o a b o u t  DF f r u i t e d  cases  up t o a b o u t  P. p a l l i d u m  of the culture  1  fruited  gradient.  i n the following  24.5°C  This  diagram:  P. p a l l i d u m  discoideum 1 1 1 1 1 1 20  25  30  Mixtures It  was h y p o t h e s i z e d t h a t  i f t h e two c o m p e t i t o r s  w e r e t o c o n t i n u e t o compete i n t h e homogeneous c u l t u r e gradients  they might Since  competition  converge  and c o e x i s t .  i t was i m p o s s i b l e t o p r o m o t e c o n t i n u e d  by s i m p l y  leaving  t h e two s p e c i e s i n t h e same  Figure  31  C u l t u r e g r a d i e n t drawings demonstrating the area o c c u p i e d by f r u i t i n g b o d i e s o f b o t h s p e c i e s . The s p o r e s u s e d came f r o m s t o c k c u l t u r e s . The vertically s h a d e d a r e a s were c o v e r e d w i t h D . d i s c o i d e u m f r u i t i n g b o d i e s , t h e h o r i z o n t a l l y s h a d e d a r e a s w i t h P. p a l l i d u m f r u i t i n g bodies. The u n s h a d e d a r e a s h a d no f r u i t i n g bodies. F o r g r a d i e n t s A, B, and C D. d i s c o i d e u m V12 was u s e d . F o r g r a d i e n t s D and E D. d i s c o i d e u m DF was u s e d .  99  culture  g r a d i e n t , b e c a u s e t h e m e d i a s o o n became f o u l e d  waste p r o d u c t s was  continued  and by  was  g o n e and  fruiting  this  establish gradient  left  was  s o o n u s e d up;  transfer two  then  harvested  to e s t a b l i s h  replicate  by  the  two  The  i n each o f  the  the  Since  series  first  food  spore  and  and  competitors  the  The  spores  a third,  c u l t u r e experiments.  were e n c o u n t e r e d  then  a t random  culture gradient.  were u s e d  competition  technique.  weeks, u n t i l  finished,  g r a d i e n t was a new  was  f o r about  changes e x p e r i e n c e d four  food  a serial  gradient  from  the  with  production  used from  was  to the  so o n .  second  The  were o b s e r v e d  in  minor d i f f e r e n c e s  t h e y must be  considered  separately.  Culture  Gradient  I  Culture gradient I and  completed  gradient in  this  one  were n o t trough  was  d u r i n g March used  t h a t was  species.  the  spores  a t random. closest  This practice  established during July  1969.  to e s t a b l i s h  case,  chosen  was  spore  the next  used  progeny of  i n the  t o make t h e  series, serial  T h e y came f r o m t h e  to the was  The  area occupied  not  by  f o l l o w e d i n the  area the  1968  each but  transfer of  the  other  other  gradient  experiments. The the  area from  occupy  this  data  indicated  about  area  15°  t o 24.5  throughout  o t h e r hand, o c c u p i e d  the  t h a t D.  the  area  discoideum  - 2 5 . 5 ° C and series.  extending  P. from  V12  occupied  continued pallidum, 24  - 25°C  to on to  the  Figure  32  C u l t u r e g r a d i e n t I : g r a d i e n t drawings demonstrating t h e changes i n f r u i t i n g a b i l i t y e x h i b i t e d by £• p a l l i d u m d u r i n g c o n t i n u e d c o m p e t i t i o n . The h o r i z o n t a l l y s h a d e d a r e a s were o c c u p i e d by P. p a l l i d u m f r u i t i n g b o d i e s , t h e v e r t i c a l l y s h a d e d a r e a b y D. d i s c o i d e u m f r u i t i n g b o d i e s . The a r e a s s h a d e d w i t h h o r i z o n t a l and v e r t i c a l l i n e s were o c c u p i e d by f r u i t i n g b o d i e s o f b o t h s p e c i e s . The u n s h a d e d a r e a s were u n o c c u p i e d . Temperature i s marked a t i n t e r v a l s under each d i a g r a m .  101  30°C d u r i n g  the f i r s t  few c u l t u r e s b u t w i t h  competition  P, p a l l i d u m e x t e n d e d  continued  i t s r a n g e down t o a b o u t  20°C  ( F i g . 32). To were u n a b l e  summarize: b e f o r e to co-fruit.  P. p a l l i d u m b e g a n D. d i s c o i d e u m always capable it  was o n l y  it  from d o i n g  After  to f r u i t  V12.  competition  competition  b e t w e e n 2 0 ° and 2 4 ° C ,  I t should  of fruiting  continued  t h e two s p e c i e s  be n o t e d  i n this  a r e a when grown  This interference factor  o v e r c o m e b y some c h a n g e r e s u l t i n g  with  t h a t P. p a l l i d u m  t h e i n t e r f e r e n c e b y D. d i s c o i d e u m so.  along  that  was  was  alone, prevented  apparently  from c o n t i n u e d  competition.  Culture Gradient I I Culture gradient and  finished  continuance except from  d u r i n g May 1969.  the entire  fruiting  S e p t e m b e r 1968  I t s establishment  and  was e x a c t l y t h e same a s t h a t o f c u l t u r e g r a d i e n t I  that the spores  As  I I was b e g u n d u r i n g  used  ffruiting  t o make t h e s e r i a l  area  and were c h o s e n  t r a n s f e r s came a t random.  i n c u l t u r e g r a d i e n t I t h e two s p e c i e s b e g a n b y  i n separate  areas  but after  P. p a l l i d u m b e g a n t o c o - f r u i t  with  continued  competition  D. d i s c o i d e u m .  in  c u l t u r e g r a d i e n t I I was n o t as e x t e n s i v e  as  i t was i n c u l t u r e g r a d i e n t I ( F i g . 46 - A p p e n d i x  real  e x p l a n a t i o n c a n be g i v e n  selection  i n culture gradient  f o rthis,  Co-fruiting  n o r as r e g u l a r  except  II).  No  t h a t the spore,  I I was n o t a s p r e c i s e a s t h a t  102  employed as  i n I,  q u i c k l y or As  that  D.  and as  therefore,  surely.  the  inhibitor  Finally, gradient up  I-G  caused two  the  final  outcome o f  Culture  the  Gradient  This  the  of  was this  however: those  during  ( F i g . 47  used  a r e a was  D.  discoideum  are  short  P.  at the  stages  of  II  suggest  and  26°C  pallidum  fruiting.  discoideum  term  occur.  - Appendix  equipment  I I I was  September  e x a c t l y as  - Appendix  and  fruiting  same  time  failure during  shift  II)  which  the  was  first  enough  that  incubation  to  the  determine  situation.  established during  May  1969.  results  they  II).  (2) The  which has  The  general  were f o r t h e  T h e r e were two  D.  a higher  the  differences  s p o r e number  discoideum  strain  temperature  1969  preceding  were o n l y h a l f as w i d e  experiments, but  identical. DF  ( F i g . 46  temperature  culture dishes  i n other  to  hand  i t from  entire competitive  experiment  (1) The  other  occurred  III  completed  gradients  25°  outcome, s u g g e s t i n g  first  Culture gradient and  between  an  gradient  competitive  during  fruit  were r u n  experienced  i n the  of  the  II-E  did  results  b o t h d e p i c t D.  incubation.  temperatures the  and  a shift  days o f  alter  gradient  Both g r a d i e n t s  1968)  On  have  I the  that prevented  ( F i g . 32)  to 26°C.  (October  unable to  entire series.  overcame the  not  However, c o - f r u i t i n g  i n culture gradient  d i s c o i d e u m was  through  s e l e c t i o n may  as relative  was  tolerance  than  103  either  VC4 o r V12.  D. d i s c o i d e u m preliminary  DF t o grow up t o a b o u t  cultures  Despite different,  occurred.  Culture  the f a c t  that  t h e D. d i s c o i d e u m  were t h e same.  P. p a l l i d u m was  discoideum,  2 6°C as i t d i d i n t h e  ( F i g . 30-D, E ) .  the r e s u l t s  competition £°  This higher tolerance allowed  and a f t e r  unable  to c o - f r u i t  d i d not alter  the spores  gradient  IV.  that  gradient results  The d a t a f r o m  could result  to  ability.  extending  from  i n co-fruiting.  1 8 ° t o 2 6 ° C was  D. d i s c o i d e u m  V12  cultures  2 4 ° C , and P. p a l l i d u m c u l t u r e s spores  that  came f r o m  i n a l l combinations  percent of cultures  s p e c i e s was  then  serial  transfers,  second  time.  periods.  to  establish  a long  temperature  B u t w h e t h e r t h e same  unknown. were grown  To a n s w e r  yielding  fruiting  36°C.  were  were grown a t 2 4 ° C . bodies  from  both  T h e s t o c k s were m a i n t a i n e d  and m i x t u r e s  and c o m p a r i s o n s  was  diagram  by  were made a  continued f o r nine may  this  a t 1 8 ° C and  stock cultures  and t h e m i x t u r e s  This procedure  within the  were grown a t 2 4 ° C and  these four  calculated.  The f o l l o w i n g  used  the t h r e e p r e v i o u s g r a d i e n t s has  c o u l d be a c h i e v e d a t any o n e t e m p e r a t u r e  question  The  i t sfruiting  were e v e n t u a l l y u s e d  shown t h a t c o n t i n u e d c o m p e t i t i o n o v e r  mixed  co-fruiting  e l a b o r a t e e x p e r i m e n t a l d e s i g n was  generate  The  with  Gradient IV  A rather  range  was  Before continued  continued competition  D. d i s c o i d e u m  strain  help to expalin  time t h e method:  104  TEMPERATURE  TIME  18  n ~ Dd  24  v  stock  REMARKS 36^  v  Dd  stock-  -PP  stock  rrPp  ]=5fe»Dd s t o c k " _=»PP  /  :Dd  'Dd  stock  (1)  mix-  H<2)  mix«  stock  •Dd  stock  •PP  stock  (1)  mix'  (2)  mix-  (3)  mix>  -  a l l stocks continued  -  ( 1 ) mix i s Dd s t o c k 24 and PP s t o c k 24°  -  ( 2 ) mix i s Dd s t o c k 1 8 ° and PP s t o c k 3 6 °  -  _ZPp  stock  s t o c k s were s e t up  stock  stock  a l l stocks continued (1) mix i s Dd s t o c k 2 4 ° , and PP s t o c k 2 4 ° (2) mix i s Dd s t o c k 1 8 ° and PP s t o c k 3 6 ° •P  p  stock  ( 3 ) mix i s f r o m number ( 1 ) mix  105  From the mixtures  t h e p r e v i o u s work i t was a p p a r e n t  would produce  homogeneous m i x t u r e s circumvent  this  fruiting  bodies o f both  o f s p o r e s were u s e d  problem  t h e mix c u l t u r e s  m a k i n g two s m a l l h o l e s i n t h e a g a r , 1 t o 2 mm and  apart,  D. d i s c o i d e u m  incubated  tables  summarizes  was n o t e d .  the findings.  species i f  as t h e i n o c u l u m .  To  were e s t a b l i s h e d by-  were p l a c e d i n o n e h o l e  spores i n the other.  absence o f c o - f r u i t i n g  none o f  5 mm i n d i a m e t e r and  P. p a l l i d u m s p o r e s  a t 24°C f o r 4 t o 7 days,  that  The m i x t u r e s  were  and t h e p r e s e n c e o r The f o l l o w i n g  series of  I t s h o u l d be n o t e d  mix  ( 1 ) = Dd s t o c k 2 4 ° + PP s t o c k 2 4 °  mix  ( 2 ) = Dd s t o c k  mix  (3) = o u t p u t o f mix (3) from  that:  1 8 ° + PP s t o c k 1 8 ° time t - 1  TIME 2 - TEMPERATURE 2 4 . 0 ° - 0 . 5 ° MIX  NUMBER  REPLICATE  %  CO-FRUIT 100%  TIME MIX  3 - TEMPERATURE 2 3.6° NUMBER  - 0.6° REPLICATE  %  CO-FRUIT  1  4  25%  2  4  75%  3  4  100%  106  TIME 4 - TEMPERATURE 2 3.0 MIX  NUMBER  - 0.0° REPLICATE  % CO-FRUIT  1  4  100%  2  4  100%  3  4  100%  TIME 5 - TEMPERATURE 2 2 . 5 ° - 0 . 5 ° MIX  NUMBER  REPLICATE  1  4  100%  2  3  100%  3  3  100%  By t h i s difference cultures agar  time  c o u l d be found  holes.  the f r u i t i n g  intermingling  index  bodies  Therefore,  however, t h a t  A culture  were  little  i n some  o f t h e two s p e c i e s were  f o r every p a i r that  very  u s i n g s m a l l and s e p a r a t e  I t was r e a l l y  was o f i n t e r e s t ,  i n d e x was e s t a b l i s h e d . the mixing  bodies  w i t h one a n o t h e r . that  that  b e t w e e n t h e t h r e e t y p e s o f mix  I t had been o b s e r v e d ,  inter-dispersed  fruiting  i t h a d become c l e a r  when t h e y were e s t a b l i s h e d  instances  of  % CO-FRUIT  t h e degree  and t h e r e f o r e ,  a mixing  was awarded o n e p o i n t o n  o f P. p a l l i d u m a n d D. d i s c o i d e u m  s e p a r a t e d b y n o t more t h a n  i f a D. d i s c o i d e u m  actually  fruiting  five  mm.  b o d y grew i n t h e m i d d l e  107  of  a "forest"  mixing  o f P. p a l l i d u m  index o f four.  adjacent  t o P.  fruiting  One p o i n t  bodies,  f o r each o f t h e f o u r  point  on t h e mixing  tables  percentage o f t h e c u l t u r e which had a mixing more.  sides  pallidum.  From t h i s  or  i t would have a  T h e mean i n d e x  - one s t a n d a r d  register the  i n d e x o f one  deviation  i s also  given.  TIME 6 - TEMPERATURE MIX NUMBER  MIX  % WITH INDEX  8  6%  none  -  INDEX 1.6 -  3.0  -  none  7 - TEMPERATURE 24.5° - 0.5° NUMBER  REPLICATE  % WITH INDEX  INDEX  1 2  none  —  _  none  -  -  3  11  2 3%  2.0 - 4.4  TIME 8 - TEMPERATURE MIX  0.2°  REPLICATE  3 2 1  TIME  2 3.2° -  22.7° i 1.2°  REPLICATE  % WITH INDEX  1 2  8  40%  1.8 - 1.8  8  0.0%  o.o i 0.0  3  24  40%  5.1 i 9.1  NUMBER  INDEX  108  TIME 9 - TEMPERATURE 2 3.5° - 0 , 5 ° MIX NUMBER  REPLICATE  1  8  12%  2  8  0%  3  18  22%  Mixture-type index  and u s u a l l y  the highest percentage  no way t o s u p p o r t  continued  mixing  experimental To r e c t i f y  suspending  inoculating  or refute  situation  - 0.0  2.0 i 4.1  o f mixing,  but there  the hypothesis  t h e mix c u l t u r e s  t h e two t y p e s o f s p o r e s  the cultures  with  i  MIX NUMBER 3  T I M E 11 - TEMPERATURE 2 2 . 0 ° i  3  0.0  u s e d was s i m p l y n o t s e n s i t i v e  TIME: 10 - TEMPERATURE 2 1 . 0 °  MIX NUMBER  0.9 - 1.8  i n c r e a s e d t h e chance o f c o - f r u i t i n g .  method  this  INDEX  3 c o n s i s t e n t l y had t h e g r e a t e s t mixing  was s t i l l  by  % WITH INDEX  were  that The  enough.  established  t o g e t h e r i n water and  the suspension.  1.0° REPLICATE  % MIXING  16  43.6%  1.0° REPLICATE 6  %  MIXING 100%  109  TIME 12 MIX NUMBER  REPLICATE  % WITH INDEX  INDEX  100%  25  TEMPERATURE 2 1 . 5 ° ' i 0 . 7 ° 1  3  TEMPERATURE 2 3 , 6 ° - 0 . 7 ° 3  6  TEMPERATURE  8 3 %  24.4°  2 3 -16.8  -0.6° 8 3%  The cultures  appeared  instance, period  mix c u l t u r e s  particularly  To ability  inhibition of one  culture  o f P. p a l l i d u m  temperatures temperature  during  t h e spores from gradient  IV.  every time  t i m e p e r i o d 12  In gradient IV  and c o n t i n u e d t h r o u g h o u t  ( F i g . 48 - A p p e n d i x I I ) .  summarize; t h i s  does  i n almost  the selection  occurred immediately  the experiment  the  after  this point  to establish  co-fruiting  came f r o m p r e v i o u s m i x  t o be a b l e t o c o - f r u i t  10. To prove  were, u s e d  3 that  9.8 — 6.3  experiment  demonstrated  that  t o o v e r c o m e D. d i s c o i d e u m  n o t d e p e n d upon g r o w t h  o v e r t h e wide  range  provided i n thegradient but can occur at i n t h eo v e r l a p range o f 18° t o 25°C.  110  It nothing  m i g h t be  t o do  with  ky  £•  pallidum.  to  temperatures  acclimation  hypothesized  the change i n f r u i t i n g  One  or both  was  t e s t e d i n the  t h a t were u s e d  grown a t  18°C  (D.  no  co-fruiting  The  temperature  (22.0° - 2.0°)  before  being  overlap enough  to cause At  suggests  ( F i g . 31A,  i n the  B,  first  I I were for In  culture  to e s t a b l i s h  C)  these  the  were grown a t  gradients.  temperature  p o i n t i n the  study  alone  unanswered:  (1) w h i c h  mechanics of  the  Which C o m p e t i t o r  And  But  room  alone  Again was  no  not  data  strongly  necessary  and  three questions  s p e c i e s changed?  change?  C h a n g e s Between 1 8 °  the  i s both  to cause c o - f r u i t i n g .  competition  The  co-fruiting.  this  With  co-fruiting.  f o r a minimum o f f o u r months  Therefore,  that competition  sufficient  this  g r a d i e n t s were e s t a b l i s h e d .  used t o e s t a b l i s h  occurred.  and  (P. p a l l i d u m )  c u l t u r e s t h a t were u s e d  gradients  acclimated  g r a d i e n t s I and  34°C  occurred  preliminary  undergone  f o l l o w i n g manner.  d i s c o i d e u m ) and the  had  (20°C t o 2 4 ° C ) ,  to e s t a b l i s h  a b o u t f o u r months b e f o r e  gradient.  range  m i g h t h a v e b e e n enough t o c a u s e  cultures  cases  ability  s p e c i e s might have  i n the middle  This hypothesis  both  that competition  (2) what a r e  (3) what k i n d o f c h a n g e  remain the  occurred?  24°  Changed?  the  caused  data  available  something  i t was  known o n l y  that  to happen which r e s u l t e d  in  Ill  co-fruiting. of  These r e s u l t s  t h r e e ways:  ing  P.  pallidum,  inhibition have  (1)  from  D.  discoideum  ( 2 ) P. D.  c o u l d have stopped  inhibit-  p a l l i d u m c o u l d have overcome  discoideum,  or  (3) both  one  the  competitors could  changed. To  reasonable  find  which o f t h e s e hypotheses  the f o l l o w i n g  D.  discoideum was  grown  pallidum  D.  discoideum  P.  where  designed:  gradient  A  gradient  B  (changed) with  pallidum (stock)  stock c u l t u r e s  and  co-fruiting  gradients.  "changed" denotes  co-fruiting  then  A and  D.  that  had  cultures  discoideum  B resulted  not  experienced  w h i c h came  I f gradient A resulted  p a l l i d u m must h a v e c h a n g e d .  gradients  t h e most  (stock)  grown  " s t o c k " denotes  P.  was  was  (changed)  competition  then  experiment  with  P.  was  in  c o u l d have been o b t a i n e d i n  in  co-fruiting,  I f gradient B  resulted  must h a v e c h a n g e d .  in co-fruiting  from  I f both  t h e n b o t h must  have  changed. The times ing  and  experiment  i n every case  ( F i g . 49  - Appendix  outlined  a b o v e was  replicated  only gradient A resulted II).  in  four  co-fruit-  I t i s s a f e t o assume t h a t  only  112  pallidum  changed.  In a l l p r o b a b i l i t y  some way,  a b l e t o o v e r c o m e D„  Mechanics  of the  Change  Having  found  that  p r e s s u r e by overcoming of  D.  discoideum  this  point  were n o t  indicated  found  competition  and  that  one  applicable.  have g e r m i n a t e d  amoebae may unable  to produce  following  the three hypotheses i n t h e u s u a l way  dispersal also  appears:  (3) b o t h  was with  of spores o f both  length  the  fruiting  experiment  covered with a b a c t e r i a  down t h e  after  an  was  correct.  species.  o f the g r a d i e n t .  stopped would  (1) P. p a l l i d u m (2) t h e  spores  t h e amoebae  the  spores  amoebae may  may  and  have  been  bodies. designed to f i n d  A culture  a bacteria  lawn,  extended  have been  amoebae b u t  to reproduce, or  to aggregate  discoideum before  to germinate,  to produce  to  bodies  above d e s c r i p t i o n  have a c t e d n o r m a l l y but  The  s e t up  the  about  A l l o f t h e work up  three stages are:  have been unable  have been unable  of  The  presence  t o know s o m e t h i n g  pallidum could  o f t h r e e s t a g e s and  s p o r e s might might  P.  to competitive  pallidum fruiting  t h e y were f o u n d  at  be  P.  i n t h e p r e s e n c e o f D.  of competition.  still  effect.  in  ability.  t o grow i n t h e  desirable  only that  period any  pallidum reacted  i t s inability  the nature o f the i n h i b i t o r y  s p e c i e s was,  discoideum i n h i b i t o r y  P.  i t w o u l d be  this  lawn  gradient  and  was  a random  Small blocks of  were p l a c e d a t In p l a n view  which  the  agar,  intervals gradient  113  o  agar  block-  o  o  o  o 25  20  15 and  o  30  i n s i d e view:  -agar  20  15  The  agar  presence around  I f P. o f D.  and  at  P.  p a l l i d u m was  P.»  discoideum  found  block.  the  temperature in  the  amoebae were m o v i n g  top o f  C)  found (stars  Therefore, each  agar  down t h e  after incubation  block  and  length of  d e n o t e b l o c k s on  These data  incubated the  which  s t r o n g l y suggest  P.  the  pallidum at the  that fruiting  stage.  above 25°C, t h e  agar  B,  a check  and  on  were g e r m i n a t i n g  i f the  able to i n h i b i t  top of the  undivided,  incubated  blocks.  the  found).  was  formation  on  from  ( F i g . 33-A,  As  agar  p a l l i d u m was  R°  body  and  30  i t s h o u l d have been p o s s i b l e t o f i n d  the  taken  36.0°C.  gradient  discoideum  top of  smear was  then  pallidum spores  dividing  amoebae on a  25  b l o c k g r a d i e n t was  gradient.  block  against the hypothesis agar  culture one  The  with  blocks migrated  down f r o m  g r a d i e n t s were r u n aluminum  dividers  foil  t h a t the  the  in pairs,  dividers  amoebae  one  between  were s e a l e d i n p l a c e w i t h  area  each  silicone  Figure  33  C u l t u r e g r a d i e n t drawings demonstrating the a b i l i t y °f £ ° p a l l i d u m t o f r u i t b e l o w a b o u t 2 4 ° C . Horizonta l l y s h a d e d a r e a s were o c c u p i e d by P. p a l l i d u m f r u i t i n g bodies. V e r t i c a l l y shaded a r e a s by D. d i s c o i d e u m . V e r t i c a l l y and h o r i z o n t a l l y s h a d e d a r e a s by b o t h s p e c i e s . Unshaded a r e a s by n e i t h e r . The c i r c l e s r e p r e s e n t t h e a g a r b l o c k s i n p l a n v i e w . The d i v i d e r s b e t w e e n b l o c k s a r e shown i n A DIV, B DIV AND C DIV. The s t a r s o v e r t h e b l o c k s d e n o t e b l o c k s on w h i c h P. p a l l i d u m was f o u n d . Temperature i s measured i n degrees c e n t i g r a d e along the x - a x i s .  115  grease. on  top  In of  the  the To  to  stop  P.  fruiting, all  divided gradients  agar b l o c k s  but  the  discoideum  The  Type o f  remains  that  the  the  species  was  hypothesized  or  manner.  pallidum  (changed)  £•  pallidum  (stock)  At  the  same t i m e D.  d o n e i t was At The  the  able  aggregating  and  f o r food  inhibitor  at  used  D.  an  (from  and  the  discoideum  not  In  the  point  the k i n d of  pallidum  could  V12  the  first  by  I ) was  mixed  V12  have  (stock) but P.  ( i t was  when t h i s pallidum  ( c h a n g e d ) was  f o l l o w i n g diagram e x p l a i n s the  design.  un-  field  two set  50:50  grown a t  from g r a d i e n t  at change  experimental  c u l t u r e d i s h was  mixture  pallidum  to narrow the  gradient  known t h a t o n l y  same t i m e P.  P.  attempt  discoideum  discoideum  and  a d a p t i v e l y , o r i n some o t h e r  In  P.  D.  on  were i d e n t i f i e d ,  e x p e r i m e n t s were c o n d u c t e d .  make t h e  type  t h a t changed,  considered.  genetically,  50:50 w i t h  i n some way,  amoebae c o m p e t e  The  DIV).  unknown.  change o c c u r r e d  took p l a c e  changed  was,  C  found  Change  Since which  still  B DIV,  amoebae f r o m  species of  n o n - l e t h a l temperatures.  D.  DIV,  discoideum  vegetative  two  p a l l i d u m was  ( F i g . 33-A  s u m m a r i z e : D.  pallidum  P.  with  27°C.  I was  mixed  unnecessary experiment had  to was  changed).  grown by  itself.  116  PP  (change)  Dd Dd  (change) (stock)  O  O  o  o  0  PP PP  o o  **o  • co-fruit-*  O  "-no-  O  O  (change) (stock)  Q  co-fruit  O -co-fruit  O  O  O  _^co-f ruit  During  O  time p e r i o d  1 the  first  p l a t e of  was  allowed  t o grow u n t i l a l l f r u i t i n g s t o p p e d  one  week).  The  for  t i m e p e r i o d 2,  and  so  a culture gradient  was  e s t a b l i s h e d with  (PP  c h a n g e ) and  occurred. to  occur  The  lines  line  3  experiments.  i n the  Second, the strains  B,  lost  change  the  change  of  3  + PP  information  output  of  no  3  line  1  Co-fruiting  co-fruiting  II).  of  plates  time p e r i o d  stock).  stock)  continued  When l i n e 2  was  co-fruiting  - Appendix I I ) . are  their  interspecific  c u l t u r e s c o n t a i n i n g both their  s e t up  y i e l d e d by  this  cultures containing only  to maintain  absence of  the  and  ( F i g . 50-D  of  line  (a p e r i o d  used to  end  + Dd  C - Appendix  F i r s t , the  ( c h a n g e d ) were a b l e  At  were c o n t i n u e d  (PP  kinds  on.  (Dd  i n time p e r i o d Two  even  p r o g e n y were t h e n  line 2  ( F i g . 50-A,  mixed with occurred  spore  each  P.  co-fruiting competitive  of  pallidum  ability pressure.  ( c h a n g e d ) and  a b i l i t y to produce c o - f r u i t i n g  set  (stock) spores,  117  suggesting  that  competitive  the  (changed) stock  not  experience  adaptive £•  one  pallidum  an  ability The  not  that  stability  possible  favoured  intraspecific  prove, I f the  t h a t P. change  the  pallidum  were  cultures containing all,  of  change  suggests,  have been  only  their  absence o f i n t e r s p e c i f i c  really  during  One this  type  test  their  selective  but  does  genetic.  during  the  most  or  ability  one  For  the  that  separate  several  been gene  genotypes  competition. s t r a i g h t f o r w a r d methods o f s o l v i n g out In  i n v o l v e s the f o r each  individual the  case  pallidum  spores  of  no  Despite  ten t e s t s  clones  and  and  cellular problems,  establishment  clone.  a maximum o f P.  and  population's  c l o n i n g procedure presents  mixed c u l t u r e g r a d i e n t  are  example:  o r more c o - f r u i t i n g  to c o - f r u i t .  procedure  decided  followed.  (2)  of problem i s to clone  testing  occurring there  mutant might have o c c u r r e d  competition,  of  s l i m e molds the  ten  was  p a t h w a y s w h i c h m i g h t be  w h i c h were f a v o u r e d  using  not  l o s e some, o r  of  p o o l might have c o n t a i n e d  was  the  c h a n g e may  selection  (1) A c o - f r u i t i n g  it  an  Experiments If  the  do  change.  that  i n the  the  but  adaptive  might expect  pressure.  Cloning  suggest,  (changed) would  co-fruiting  prove,  at  disadvantage.  These data did  was  of this  w o u l d be a standard  a  but  separate difficulty  conducted stock  118  Do  discoideum The  culture. fifth  and D. discoideum  test  resulted' i n c o - f r u i t i n g  by P. p a l l i d u m  ( F i g . 51 - Appendix I I ) s u g g e s t i n g t h a t the  stock p o p u l a t i o n o f P. p a l l i d u m c o n t a i n e d spores w i t h c o fruiting  ability.  statistical  T h i s experiment  does not a l l o w any  s i g n i f i c a n c e t o be a t t a c h e d t o the e v i d e n c e .  A p p a r e n t l y , however., the a b i l i t y t o c o - f r u i t  was  contained  w i t h i n the s t o c k gene p o o l .  Changes Between 24.0° And  26.5°C  When grown alone D. discoideum was f o o d and space, and f r u i t i n g  between 24° and 2 6.5°C.  when grown w i t h P. p a l l i d u m , f r u i t i n g o observed  above 24  t o 25 C.  a b i l i t y over t h i s The  b o d i e s were not  A f t e r c o n t i n u e d p e r i o d s of was  unable t o improve i t s  s h o r t temperature  range.  l a c k o f improvement i n f r u i t i n g  u n e x p l a i n e d , but i t was  ability is  observed t h a t beyond 24.5°C the  expansion r a t e o f D. discoideum V12 z e r o at 2 6.4°C ( F i g , 12).  dropped  r a p i d l y t o become  T h i s put D. discoideum at a v e r y  severe competitive disadvantage i n t h i s  a r e a , so t h a t  changes t h a t would have to o c c u r would undoubtedly  D e s p i t e the f a c t still  t h a t no change was  the  involve  changes i n growth r a t e , as w e l l as changes i n f r u i t i n g  was  But,  o  c o m p e t i t i o n D. discoideum V12 fruiting  capable of using  ability.  observed i t  important t o a s c e r t a i n the p o i n t at which  1  R°  discoideum  P.  p a l l i d u m the i n h i b i t i o n  stage, To  inhibited.  f o r P.  inoculated  p a l l i d u m were e m p l o y e d .  agar  of  agar b l o c k s  the  the  consumed  i n c u b a t e d at 20°C.  food, but To  from was  ( F i g . 52-A,  spores germinated  test  that  and  amoebae were s t i l l o f D.  unimportant  due  occurs,  t h e mechanism i n v o l v e d  Similarity  of Resource The  pressure  I I ) and  on  found  agar on a l l  II) suggesting and  culture gradient  D.  above 2 5 ° C .  discoideum While  i s probably  appears  span t o be  the  relatively  over which i t the  same  as  inhibition.  Use  f o r e g o i n g d a t a have i n d i c a t e d  selected-for  and  occur.  a divided  pallidum  was  amoebae were m o v i n g  small temperature  i n P.  was  amoebae d i v i d e d  fruiting  t h e mechanism:, i n v o l v e d  gradient  tops o f the  C - Appendix  growing  discoideum t o the  the  aggregation d i d not  found  those  incubated.  B,  ( F i g . 52-C-DIV - A p p e n d i x  inhibition  from  the hypothesis that  stage  a g a r b l o c k s were s e t  discoideum  the  like  discoideum  D.  the g r a d i e n t a r e a below 24°C, used  tests  t h e g r a d i e n t was  i n c u b a t i o n s m e a r s were t a k e n and  D.  spore  aggregation  A culture  Bacteria covered  s u r f a c e and  blocks  of  c o u l d have o c c u r r e d a t the  w i t h e q u a l numbers o f b o t h  top of the  that  as i n t h e c a s e  between t h e s e p o s s i b i l i t i e s ,  pallidum spores.  After  Just  t h e v e g e t a t i v e amoebae s t a g e , o r t h e  distinguish  used  P.  was  P.  that  pallidum individuals  competitive  that  were  able  120  to  co-fruit  occurrence species £°  with  were u n a b l e  But  of  that  P.  the  precluded  the  acquisition  and  i t was one  of co-fruiting  successfully  ability  however, c o n t i n u e d  use  respect to resource  e x a c t l y the  competition selection  same r a t e .  i t m i g h t be  with the  resources,  In  they  i n the  determining  might  or  use  attempt cellular  t h a t one  the germination  use  the  chances 18°  and  (3) one  and  l a g s and  the  types  of  These  resource might  at  increase  other. paths the  were a s s e s s e d  the c o l o n y  resource  alternate  situation,  The  divergent  the  three  which of these  s l i m e mold  competition.  the  only  continued  use  competitor  to exclude to f i n d  of  could  might o c c u r .  diverge  r a t e s o f resource-.use  of continued  during  might converge u s i n g  same r a t e ,  an  Therefore,  respect to resource  r a t e of resource  period  the  were  o r where irhey u s e d  expected  competitors  (2)  the  followed  since  coexistence  with  its  for  c o e x i s t between  where t h e c o m p e t i t o r s  exactly  the  production of f u r t h e r generations.  come a b o u t i n s i t u a t i o n s  are:; (1)  When  impossible  generation  This  increased. Logically,  at  24.5°C.  coexistence possible.  to c o - f r u i t  pallidum could  2 4 ° C was  between 20°  t o p r o d u c e more t h a n  spores  with  discoideum  makes c o n t i n u e d  pallidum  lack  D.  were  components  after  a  components i n v o l v e d  expansion  rates.  are  121  Germination  Lags  For collected culture data  after  pallidum  and  n o t i n g the  measurements o f began  ence b e f o r e  and  discoideum  before  and  method.  considered  confidence  Colony  was  Expansion  second  rates.  expansion  were m e a s u r e d  Two  i n D.  and  expansion  rates of resource For  the  the  both  regression I I were  after at the  continued 95%  level  P.  use  component c a p a b l e are  be  the  pallidum the r a t e s of  of  competition  noted:  ( F i g . 35)  and  (1)  the  colony  II  I  and  (measurements L i n both  post-competitive  gradient  of  colony  separately for culture gradient  p r o g e n y o f g r a d i e n t s J , K,  points should  from g r a d i e n t I  discoideum  most i m p o r t a n t  a period of continued  w e r e made on  collected  and  differ-  Rates  altering  after  was by  before  XI).  directly  II  change b e f o r e  detected  (Table  The  No  compared  For  f r o m c u l t u r e g r a d i e n t s I and  together.  competition  competition  were  lines  significant  (Table X).  lag data  expansion  lag collected no  was  from  regression  These d a t a  T h e r e was  competition  continued  data  competition,  germination  ( F i g . 7).  lag data  regressing culture  ( F i g . 10).  germination  after  Again  continued  I I , by  spore  after  V12  germination  p o i n t s at which the  the x - a x i s  competition  D.  Salvador,  a period of  g r a d i e n t s I and  intercepted with  P.  ( F i g . 37)  cases). data  are  very  122  TABLE X  P. p a l l i d u m S a l v a d o r ( f r o m g r a d i e n t s I a n d I I ) s p o r e g e r m i n a t i o n l a g s b e f o r e ( s t o c k s ) and a f t e r ( c h a n g e ) c o n t i n u e d competition. R e p l i c a t i o n i s shown f r o m . t h e c h a n g e d c u l t u r e s and 9 5 % c o n f i d e n c e i n t e r v a l s a r o u n d t h e c h a n g e mean a r e given. S t o c k l a g s come f r o m F i g u r e 7.  TEMPERATURE  REPLICATE  GERM LAG CHANGE  9 5 % CON CHANGE  GERM LAG STOCK  22.5  4  1.17  0.60-1.74  1.05  23.5  12  1.02  0.79-1.25  0.94  24.5  11  1.05  0.88-1.22  0.88  25.5  10  0.95  0.68-1.22  0.84  26.5  12  0.84  0.69-0.99  0.78  27.5  13  0.73  0.61-0.85  0.75  28.5  12  0.67  0.46-0.88  0.71  29.5  8  0.60  0.36-0.83  0.70  TABLE X I D. d i s c o i d e u m V12 ( f r o m g r a d i e n t s o n e and two) s p o r e g e r m i n a t i o n l a g s b e f o r e ( s t o c k ) and a f t e r ( c h a n g e ) c o n t i n u e d competition. R e p l i c a t i o n i s l i s t e d f o r t h e change c u l t u r e s and c o n f i d e n c e i n t e r v a l a r o u n d t h e c h a n g e mean a r e g i v e n .  TEMP  REP  GERM LAG CHANGE  18.5  7  0.75  19.5  7  20.5  9 5 % CON CHANGE  REP  GERM LAG STOCK  9 5 % CON STOCK  0.37-1.14  4  0.72  0.20-1.24  0.57  0.32-0.82  5  0.70  0.18-1.21  9  0.56  0.36-0.77  21.5  8  0.51  0.32-0.69  5  0.58  0.19-0.96  22.5  10  0.51  0.37-0.65  23.5  5  0.58  0.34-0.81  24.5  3  0.73  0.44-1.02  7  0.58  0.28-0.88  124  similar.  T h i s was e x p e c t e d  replicates, different  (2) t h e p o s t - c o m p e t i t i v e  from For  were  b e c a u s e t h e two g r a d i e n t s a r e  the pre-competitive D. d i s c o i d e u m  data  data  i s not s i g n i f i c a n t l y  ( F i g . 13).  the rates of colony  a l s o measured s e p a r a t e l y f o r g r a d i e n t  expansion  I and I I , and  m e a s u r e m e n t s were a l s o made on g r a d i e n t s J , K, L . there  a r e two p o i n t s w h i c h  competitive are  data  culture  ( F i g . 12) a r e v e r y  they  were  a t a much g r e a t e r r a t e  different.  and t h e Both  data  hypothesis  alone.  germination cultures  after  competition  before. that rates of resource  response t o competition  these  data  g r a d i e n t s y i e l d e d o r g a n i s m s w h i c h were a b l e t o  The in  (1) t h e p o s t -  and ( 2 ) t h e p o s t - c o m p e t i t i v e  data  expand t h e c o l o n y than  be n o t i c e d :  f o r g r a d i e n t s I ( F i g . 34) and I I ( F i g . 36)  not d i f f e r e n t ,  pre-competitive  should  Here t o o  A search  c a n n o t be t e s t e d on t h e b a s i s o f must b e made f o r c h a n g e s i n  r a t e s and r a t e s o f c o l o n y  which never  use changed  experienced  expansion  competition  of stock  b u t which  were  grown f o r t h e same l e n g t h o f t i m e t h a t t h e c o m p e t i t i o n e x periments in  were r u n .  r a t e s o f food  were t h e r e s u l t not  related  It i s entirely  use experienced  possible that  changes  i n the c o m p e t i t i v e c u l t u r e s  o f m e d i a c o n d i t i o n i n g o r some o t h e r  to competition  at a l l .  cause  Fiqure  34  Do d i s c o i d e u m c u l t u r e g r a d i e n t I e x p a n s i o n r a t e s w i t h respect to temperature. Growth i n d e x h a s no u n i t s , temperature i s measured i n degrees c e n t i g r a d e . The d o t t e d l i n e i s t h e l i n e o f b e s t f i t from t h e familyd e s c r i b e d b y e q u a t i o n ( 2 c ) . T h e p o i n t s a r e means - 9 5 % c o n f i d e n c e l i m i t s o n t h e means. T ^ = 2 7.5, T 13.0, T' = 23.25, K = 1.16758, C = 4.79121, Gmax = 6.2. L  s  q  F i q u r e 35  P. pallidum c u l t u r e gradient I expansion r a t e s with respect-to temperature. Growth i n d e x h a s no u n i t s , temperature i s measured i n degrees c e n t i g r a d e . The dotted l i n e i s t h e l i n e o f b e s t f i t from the f a m i l y d e s c r i b e d b y e q u a t i o n ( 2 c ) T h e p o i n t s a r e means - 9 5 % c o n f i d e n c e l i m i t s o n t h e means. T^ = 37.5, T = 18.0, T = 30.0, K = 1.73781, C = - 4 . 8 2 7 8 1 , Gmax = 8.4. L  0  10  9 8  x  7  LU  i -  |  6  i  5  h-  cr  e> 3 2 h  1  1 JL.  _i  l_  12 13 14 15 16  i  17 18  i • • • _i 1 a i i_ 19 20 21 22 23 24 25 26 27 28 29  TEMPERATURE  10  V  9 8  x  .5-  7  LU  i  I  r5  6  5  ,1"  4  cr O  3 2 1  •  i  19 20 21  '  L.  I  I  1  1  U  _J  1_  22 23 24 25 26 27 28 29 30 31 TEMPERATURE  -I  I I SI  32 33 34 1 35 36  Fiqure  36  Do d i s c o i d e u m c u l t u r e g r a d i e n t I I e x p a n s i o n r a t e s w i t h respect t o temperature. G r o w t h i n d e x h a s no u n i t s , temperature i s measured i n degrees c e n t i g r a d e . The d o t t e d l i n e i s t h e l i n e o f b e s t f i t from t h e f a m i l y d e s c r i b e d b y e q u a t i o n ( 2 c ) . T h e p o i n t s a r e means £ 9 5 % c o n f i d e n c e l i m i t s o n t h e means. T = 27.5, T = 13.0, T = 2 3 . 0 , K = 1.22500, C = 3.02126, Gmax = 5.8. H  L  Q  Fiqure  37  P. p a l l i d u m c u l t u r e g r a d i e n t I I e x p a n s i o n r a t e s w i t h respect t o temperature. Growth i n d e x h a s no u n i t s , t e m p e r a t u r e i s measured i n degrees c e n t i g r a d e . The d o t t e d l i n e i s t h e l i n e o f b e s t f i t from t h e f a m i l y d e s c r i b e d b y e q u a t i o n ( 2 c ) . T h e p o i n t s a r e means - 9 5 % c o n f i d e n c e l i m i t s on t h e means. T y = 37.5, T = 18.0, T = 30.4, K = 1.53059, C = -2.4335, Gmax = 8.0. L  0  10  9 8 x  7  LU |  6  f  ir  x 5 |4 cc  5  o 3  1  2 1  -i  fi  i  l _  _l  _ J  I  I  L.  •  i  a  i  1_  12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 TEMPERATURE  19 20 21 22 23 24 25 26 27 28 29 30 31  TEMPERATURE  32 33 34 35 3 6  12 7  Stock  Spore Germination For  Rates  P. p a l l i d u m t h e s p o r e  measured d u r i n g October were t h e n and  maintained  the spore  by a s e r i e s  the r e g r e s s i o n method.  £°  that  i t was  VC4  occurred  was  presented  culture  As a p a r t i a l  changes e x p e r i e n c e d  b y t h e V12  time  For  1969  experienced  meant have  D.  discoideum through  1970.  t h e changes  Despite  that  do p a r a l l e l  The d a t a from  the  these  by the stock  cultures.  Rates  o f 1968  ( F i g . 38).  was  t h a t no c h a n g e i n s p o r e  P. p a l l i d u m t h e c o l o n y  measured i n October  This  problem  probably  stock.  germination  Expansion  that  1969 and r u n  different  (Table XIII) i n d i c a t e s  Sltock C o l o n y  an,equip-  i n t h e absence o f c o m p e t i t i v e  p e r i o d o f time  was  (Table X I I ) .  stock  lost.  using  significant  Due t o  which ended i n F e b r u a r y was  transfers  f o r changes t h a t might  experiments  June  experienced  remedy t o t h i s  that the s t r a i n during this  t h a t no  problems.  e s t a b l i s h e d i n August transfers  serial  calculated  indicates  g r a d i e n t s I a n d I I was  i n the stock  s t o c k was  fact  were a g a i n  time  impossible to test  12 b i - w e e k l y the  The c u l t u r e s  i n t h e s p r i n g o f 1969 t h e V12  to establish  pressure.  times  germination  used  occurred  o f 1968.  of bi-weekly  The d a t a  discoideum  ment f a i l u r e  r a t e s were  and November  germination  change i n spore  germination  expansion  ( F i g . 13) and a g a i n  A visual  comparison  r a t e s were during  o f t h e two  figures  128  TABLE X I I  P. p a l l i d u m S a l v a d o r : c o m p a r i s o n o f s t o c k g e r m i n a t i o n l a g s b e f o r e a n d a f t e r an e x t e n d e d p e r i o d o f i n t r a s p e c i f i c g r o w t h . Replication i s listed f o r cultures tested after a period of g r o w t h and 9 5 % c o n f i d e n c e l i m i t s a r o u n d t h e " a f t e r " means are g i v e n .  TEMPERATURE  REPLICATE  GERM LAG AFTER  9 5 % CON AFTER  MEAN BEFORE  18.5  7  2.08  1.89-2.28  2.30  19.5  6  1.75  1.30-2.19  1.62  20.5  5  1.72  0.98-2.45  1.30  21.5  8  1.17  0.90-1.44  1.15  22.5  8  0.98  0.71-1.25  1.05  23.5  7  1.01  0.83-1.19  0.94  24.5  6  1.03  0.72-1.34  0.88  25.5  9  0.84  0.67-1.01  0.84  27.5  7  0.91  0.65-1.17  0.75  28.5  11  0.69  0.53-0.85  0.71  29.5  7  0.57  0.32-0.85  0.70  30.5  13  0.60  0.36-0.77  0.70  129  TABLE  D. ext l i s i n t  d i en t e e r  X I I I  s c o i d e u m VC4: comparison o f stock g e r m i n a t i o n lags a f t e r ded p e r i o d s of i n t r a s p e c i f i c g r o w t h . R e p l i c a t i o n i s d f o r c u l t u r e s t e s t e d a f t e r growth and 95% c o n f i d e n c e v a l s around the " a f t e r " means are g i v e n .  TEMPERATURE  REPLICATE  GERM  AFTER  LAG  95%  CON  AFTER  MEAN  BEFORE  15.9  3  1.60  0.86-2.33  1.43  17.9  9  1.40  1.18-1.61  1.18  18.8  5  0.98  0 . 6 2 - 1 . 3 3  1.10  19.4  4  1.00  0.77-1.22  1.04  20.1  4  1.20  0.67-1.72 .  1.02  21.0  4  1.10  0.97-1.22  1.00  22.5  8  0.98  0 . 9 0 - 1 . 0 7  0.98  23.5  3  0.90  0.40-1.39  0.96  24.1  3  1.20  0 . 9 5 - 1 . 4 4  0.98  25.0  3  1.20  0 . 9 5 - 1 . 4 4  1.03  Fiqure  38  £• p a l l i d u m amoebae e x p a n s i o n r a t e s w i t h r e s p e c t t o temperature. The s p o r e s u s e d h a d e x p e r i e n c e d m e d i a conditioning. Growth i n d e x i s measured w i t h o u t u n i t s , temperature i s measured i n degrees c e n t i g r a d e . T h e p o i n t s a r e mean d a t a p o i n t s - 9 5 % c o n f i d e n c e l i m i t s on t h e means. The d o t t e d l i n e i s t h e l i n e o f b e s t f i t from e q u a t i o n (2c) w i t h T = 41.0, T T = 18.0, T = 31.0, Gmax = 7.6, K = 1.62709, C = - 1 3 . 5 9 4 2 3 . H  Q  GROWTH ro  co  1  T  CD  ro o ro ro ro ro co ro  m m  w ro  \  ^  INDEX  01  O)  oo  -si  r  T  r  KH  \  \ N  N  KH  \  KH  N S  KH \  K H  \  \ \ \  KH \  > ro  H  c  JD  m  ro oo ro , CD  co o co /  CO  ro co CO CO CO 01 CO 0)  h-OH  /  I  / h-O-l  CD  O  131  suggests  that the rates of colony  slightly  but the 95% confidence  points  used  impossible rates  to e s t a b l i s h to find  of colony  stock  was u s e d  occurred  intervals curves  any s i g n i f i c a n t  expansion  growth i n stock Since  these  expansion  before  around t h e data  statistical  and a f t e r  t h e D. d i s c o i d e u m a s an i n d i c a t o r  pressure.  during February  significantly  rate o f colony  than  "before"  some o t h e r its  transfers.  The r a t e s o f c o l o n y  (95% l e v e l ) over  expansion  factor  "after"  t h e VC4 have  Colony  1968 ( F i g . 39)  1970 ( F i g . 40) a f t e r  ( F i g . 39).  unknown  was l o s t ,  o f changes t h a t might  and  The  a long period o f  V12 s t o c k  r a t e s were measured d u r i n g August  changed  differencei n  cultures.  expansion  12 b i - w e e k l y  decreased  o v e r l a p , making i t  i n t h e absence o f c o m p e t i t i v e  again  may h a v e  a series of expansion  t h e s i x month p e r i o d .  ( F i g . 40) was g r e a t e r  E v i d e n t l y media c o n d i t i o n i n g o r allowed  D. d i s c o i d e u m  to increase  rate o f resource use. The  pressure  alone  changes t h a t d i d occur a r e summarized  P. PALLIDUM  due t o c o m p e t i t i v e  i n the following table.  BEFORE  AFTER  No  Yes  Co-fruiting 19°  t o 24.5°  Spore  germination  Same  Same  Colony  expansion  Same  Same  Fiqure  39  2° d i s c o i d e u m VC4 e x p a n s i o n r a t e s w i t h r e s p e c t t o temperature. The s p o r e s used had n o t e x p e r i e n c e d media c o n d i t i o n i n g . Growth i n d e x h a s no u n i t s , temperature i s measured i n degrees c e n t i g r a d e . The d o t t e d l i n e i s t h e l i n e o f b e s t f i t from t h e f a m i l y d e s c r i b e d by e q u a t i o n ( 2 c ) . The p o i n t s a r e means - 9 5 % c o n f i d e n c e l i m i t s on t h e means. T = 27.5, T = 9.0, T = 22.25, K = 0.63277, C = 2.01331, Gmax = 4 . 2 . H  L  Q  G R O W T H INDEX ro \  T—~T  J>  co  cn  —i——i  r  \  \ \  co ai  \  V  4  V  \r-©H \  \ \  m  O)  m  \  J3  >  c  I O I \  TJ  \  CO  \ \  \  J3  CD  m  ro o  ro ro ro ro  CO  ro -p* ro cn ro 0)  ro  r f H  I  CO  O)  T  CD  Figure  40  D. d i s c o i d e u m VC4 e x p a n s i o n r a t e s w i t h r e s p e c t t o temperature. The s p o r e s used had e x p e r i e n c e d media conditioning. G r o w t h i n d e x h a s no u n i t s , t e m p e r a t u r e i s measured i n degrees c e n t i g r a d e . The d o t t e d l i n e i s t h e l i n e o f b e s t f i t from t h e familyd e s c r i b e d b y e q u a t i o n ( 2 c ) . T h e p o i n t s a r e means - 9 5 % c o n f i d e n c e l i m i t s on t h e means. T = 27.0, T = 9.0, T = 22.0, K = 0.90973, C = 3.22786, Gmax = 6.0. H  L  Q  GROWTH INDEX _ L  \  ro  co  -P*  T  1  r  cn  CD  -NJ  r  i  \  ro L  CO __L  -p* Ol m  CD  m  no > —i ez  ID m  oo K  CD  ro o ro ro ro ro co  r © i  ro J>  ro ov ro CD  ro  jl, i.n  in /  I" © j I 1  Q  n  |  00  CD  O  134  DISCOIDEUM  AFTER  BEFORE  Co-fruiting  No  No  Same  Same  24.5° t o 26.5° Spore  germination  Colony  expansion  Lower  Possibly* Higher  S i n c e t h e V12 s t o c k c o u l d n o t b e t e s t e d i t i s i m p o s s i b l e to be e x a c t l y s u r e t h a t t h e c o l o n y e x p a n s i o n r a t e d i d not change i n response t o c o m p e t i t i v e p r e s s u r e . T h e VC4 d a t a d o e s s u g g e s t t h a t t h e c h a n g e t h a t was o b s e r v e d was not caused by c o m p e t i t i o n .  In fruiting of  food  tested  summary, c o m p e t i t i v e  ability  o f P. p a l l i d u m  u s e i n D. d i s c o i d e u m . remained u n a l t e r e d .  pressure  changed  theco-  and p o s s i b l y a l t e r e d A l l the other  But these  the rate  parameters  two c h a n g e s  alone are  enough t o g r e a t l y i n f l u e n c e t h e outcome o f c o m p e t i t i o n b e t w e e n t h e two s p e c i e s . This  c a n be d e m o n s t r a t e d  parameter values tition. rates  The output  o f resource  competition spore  derived before  (Fig.  competition  and a f t e r  after  situation  i n time  But, i f t h e  to e s t a b l i s h  p e r i o d two, o n l y  t o use the resource  41-C), w h i l e both  continued  ( F i g . 41-B).  p e r i o d one were u s e d  compe-  p e r i o d one t h e  u s e were more s i m i l a r b e f o r e  progeny o f time  would be a v a i l a b l e  Program V I I w i t h  i n d i c a t e s t h a t i n time  ( F i g . 41-A) t h a n  new c o m p e t i t i v e  using  before  s p e c i e s would u s e f o o d  D.  a discoideum  competition after  competition,  135  because the (Fig.  co-fruiting  41-D).  Logically  e v e n t u a l l y be  excluded  as  D.  q u i c k l y as  suggested  P.  pallidum  i t would  t h a t o n c e P.  D.  discoideum  persist  even i n the  pallidum i n areas  face  of  spores  pallidum  i t s inability  the  |  inhibit  seem t h a t P.  because of  discoideum but  could produce  would  t o use  food  i n t e r f e r e n c e experiments  becomes e s t a b l i s h e d i t c o u l d of high  spore  considerable  concentration  and  exploitation  pressure. These of  simple. this  due In  to convergence  the  work, P.  case  from  P.  pallidum  conditioning  of the  pallidum  when i t became a b l e  one  the o r i g i n a l  cellular  to c o - f r u i t ,  i n response  pressure.  use  and/or divergence,  converged  s l i m e mold towards  and  D.  to e i t h e r  Both o f  these  D„  hypothesis or  are  cotoo  species  used  discoideum  discoideum competitive  diverged or  changes worked  media against  another. I n t i m e p e r i o d one  resource  use  competition  had and  diverged t h a t P.  competition b e c a u s e P. the  i t appeared  during  pallidum  However, i n t i m e p e r i o d two  use  that  e x c l u s i o n on.the b a s i s of unequal resource  existence  in  f i n d i n g s suggest  the  were more c o n v e r g e n t pallidum  resource.  was  able  the  the  period of  would  s o o n be  rates of than  that  were  of  extended excluded.  resource  they  rates  use  after  before,  to produce progeny which  could  Figure  41  A c o m p a r i s o n o f t h e amount o f r e s o u r c e u s e d by c o m p e t i t o r s b e f o r e and a f t e r c o m p e t i t i o n . Percent o f t h e t o t a l r e s o u r c e a v a i l a b l e i s found on t h e y - a x i s , temperature on t h e x - a x i s . The shaded a r e a r e p r e s e n t s t h e a m o u n t o f r e s o u r c e u s e d b y D. discoideum, t h e u n s h a d e d a r e a t h e amount o f r e s o u r c e u s e d by P. p a l l i d u m . The p r o g e n y o f time p e r i o d one were used t o e s t a b l i s h the competitive s i t u a t i o n of time p e r i o d two.  n I I y I llllllllH  19  21  137  Summary - C o n t i n u e d (1)  Stock from  spores about  bodies  up  Competition  grown i n c u l t u r e  15° to  to  g r a d i e n t s which  30°C p r o d u c e d  a b o u t 2 4 ° C and  P.  D,  discoideum  pallidum  extended fruiting  fruiting  bodies  beyondo  (2)  After its  periods  fruiting  change,  (3)  a b i l i t y but discoideum  pallidum  fruited  P.  pallidum  o v e r c a m e D,  D,  between  force (6)  P.  food  (7)  from  24°C  and  2 6°C.  alone  was  both  pallidum  about  stopped  i n this  and  f r u i t i n g body  inhibi-  pallidum  inhibition  and  sufficient  and  before  fruiting  competed  the  for  competition  body p r o d u c t i o n  was  area,  Apparently  the  that  co-fruit  competition.  no  change,  t o 24°C, but  change,P. p a l l i d u m  24°C  changed  20°C,  amoebae a l w a y s r e p r o d u c e d  about 20°  experienced  a necessary to  pallidum  0  24°  induced  could  to  about  o v e r c o m e P.  t o c a u s e P.  pallidum  up  discoideum and  P,  discoideum  d i d not  between about (5) C o m p e t i t i o n  down t o  about 20°  discoideum  D.  competition  fruited  P.  tion (4)  D„  of continued  P.  pallidum and  gene p o o l  these  contained  were s e l e c t e d  for  genotypes by  138  (8)  P, p a l l i d u m s p o r e expansion  germination  l a g s and amoebae  r a t e s d i d n o t change i n r e s p o n s e  colony  to continued  competition.  (9)  D. d i s c o i d e u m but  the colony  competition. responsible (10)  V12  spore  expansion  readily  l a g s d i d not change,  rates increased during  (Competition  alone  continued  may n o t h a v e b e e n  f o r the change).  The s i m u l a t i o n model co-exist  germination  with after  suggested  D. d i s c o i d e u m continued  t h a t P. p a l l i d u m c o u l d  between  competition  2 0 ° and 2 4 ° C more than  before.  139  DISCUSSION The e x p e r i m e n t s r e p o r t e d h e r e w e r e c o n d u c t e d i n an a t t e m p t t o d e s c r i b e t h e way i n w h i c h two s p e c i e s o f c e l l u l a r s l i m e mold compete i n t h e l a b o r a t o r y ; t o t e s t hypotheses r e l a t i n g  competition, covergence or  and  c o e x i s t e n c e ; and t o d e v i s e  for  approaching  in  the f i e l d .  optimistic areas,  some o f t h e divergence,  a preliminary general  c o m p e t i t i v e p r o b l e m s i n t h e l a b o r a t o r y and The r e s u l t s h a v e i n d i c a t e d t h a t i t was  The work a l s o t o u c h e d o n some a s p e c t s  laboratories.  of cellular conducted  These f i n d i n g s a r e c o n s i d e r e d i n  s e c t i o n o n e o f t h e d i s c u s s i o n , w h i l e t h e more o r i e n t e d work i s d i s c u s s e d  Section I : Cellular  these  information  s l i m e m o l d b i o l o g y w h i c h a r e r e l e v a n t t o work b e i n g i n other  overly  t o hope f o r an i m m e d i a t e s o l u t i o n i n any o f  b u t i t h a s b e e n p o s s i b l e t o add a l i t t l e  t o each.  method  ecologically  i n t h e second s e c t i o n .  Slime Mold  Biology  Inhibition During  the study  i t was o b s e r v e d  m o l d c o m p e t i t i o n was c o m p o s e d o f b o t h i n t e r f e r e n c e component.  Since  that c e l l u l a r  an e x p l o i t a t i o n  t h e e n v i r o n m e n t was  slime  and an  simple i t  was p o s s i b l e t o d e s c r i b e t h e m a j o r c o m p o n e n t s i n v o l v e d i n t h e e x p l o i t a t i o n of food the  amount o f f o o d  two c o m p e t i t o r s  and s p a c e a c c u r a t e l y e n o u g h t o s i m u l a t e  and s p a c e u s e d a t a n y t i m e .  B u t , when t h e  were grown t o g e t h e r , t h e y i n t e r f e r e d w i t h  one  140  another's  ability  to produce  fruiting  bodies.  The  components  t h a t were i d e n t i f i e d  were d i f f i c u l t  the  inhibitory  substance  c o u l d n o t be  suggested  that  actual  The actions  took  fruiting  results place.  inhibited  by D.  P.  discoideum  observations  and P.  Ceccarini violaceum  from  ammonia and species,  D.  one  Dodd  carbon  fruiting  that  Thorn  discoideum D.  which  The  was  P. p a l l i d u m  which  was  Similar  ( 1 9 4 1 ) who  fruiting,  purpureum  and  found Cohen  prevented  nature of the  body Bonner  cultures  was  in petri  surfaces,  total  run.  these chemicals  inhibition  three classes  observed  of  body f o r m a t i o n might Bonner  and  inhibitor  s p a c i n g was and  linked  Hoffman  d i s h e s w h i c h had  In view  found  that  i n some  found  purpureum  agar  on  findings  that  or  the top  resulted:'.in f o u r o f  of these  study.  studied  to the p r o d u c t i o n  are r e s p o n s i b l e f o r the i n this  responsible.  (1963)  (1963) a l s o  c o n f r o n t e d w i t h D.  inhibition  chemicals be  Hoffman  d i o x i d e p r o d u c t i o n and  mucoroides  discoideum  seven  of at l e a s t  ( 1 9 6 2 ) and  these gases.  bottom  aggregating.  during f r u i t i n g  and  when D.  P. p a l l i d u m  unknown.  produced  of  D.  R a p e r and  (1967) r e p o r t e d t h a t  Any  Bonner  inhibited  inhibitory  spore c o n c e n t r a t i o n .  h a v e b e e n made b y  violaceum i n h i b i t e d  remains  separate  a b o v e some t e m p e r a t u r e ,  discoideum  because  identified.  p a l l i d u m s p o r e c o n c e n t r a t i o n , and  d e p e n d e n t upon D.  P.  discoideum  to assess  b o d y f o r m a t i o n b e l o w some t e m p e r a t u r e ,  determined  that  D.  two  interference  and  the  i t i s possible  interspecific  141  A observed been  by  second Russrell  s t u d i e d by  Cohen  class and  Snyder  (1967) and  Bonner  C o h e n and  Ceccarini  (1967).  i s , Polysphondylium  violaceum  This  intraspecifically  fruiting  direct  link  appears  Cohen  body i n h i b i t i o n . (Bonner  of C e c c a r i n i  At  ing  body  cellular  during formed. did  not  germination. at  the  o f D.  purpureum. the  again there  inhibitory and  was  chemical  interspecific  time,  cellular  to b e l i e v e  germination  that  that  slime the  i n the  fruit-  w i t h i n the  fruit-  head. A.third  Thorn  study, but  the present  spore  observed  also observed  Cohen i s o n l y e f f e c t i v e  b o d y , where i t p r e v e n t s  and  They  and  v e r y much l i k e  p e r s . comm.) t e n d  and  Ceccarini  inhibited  (1967) i s o l a t e d  ing  by  t o be  first  subsequently  i n the presence  i n the p r e s e n t  and  was  spore  They  between the i n t r a s p e c i f i c  mold b i o l o g i s t s chemical  to f r u i t  inhibition  which C e c c a r i n i fruiting  s p e c i e s were n o t  unable  phenomena o b s e r v e d no  inhibited  Dictyostelium species.  was  has  (1966),  That  P.  (1960) and  Ceccarini  a chemical  s t a g e by  chemical  and  that  spore  of i n h i b i t o r y  general class  s l i m e mold  s p e c i e s m i g h t be  (1941) o b s e r v e d  aggregation but  that  one  ( 1 9 4 7 ) showed t h a t gradients of  the  a chemical  ( 1 9 6 8 ) h a v e shown t h a t  the  time  fruiting  Raper  w h i c h he AMP  were f o r m i n g  called  acrasin.  attracts  bodies  s p e c i e s , however,  even i n mixed c u l t u r e s .  aggregations  cyclic  produced  responsible.  Polysphondylium  another,  products  D i c t y o s t e l i u m s p e c i e s mixed  s e p a r a t e d by  D i c t y o s t e l i u m and approach  of chemical  D.  Bonner  along Konijn et a l  discoideum  and  142  P. p a l l i d u m . species  produce  produces (Chang while  Konijn  cyclic  AMP and t h a t  phosphodiesterase  1968).  Cyclic  5'AMP i s i n e r t  More r e c e n t work chemicals produced used  (1969) h a s shown t h a t b o t h  also  which c o n v e r t s c y c l i c  (Bonner  p e r s . comm.) s u g g e s t s acrasin  i n most c e l l u l a r  and t h a t  such  s l i m e mold  a l l of this  and e f f e c t s  work s e v e r a l  AMP i s p r o d u c e d  ( 4 ) D. d i s c o i d e u m down c y c l i c  unknown and t h e s e m i g h t  that  of fruiting  interfere produced  that  most  bodies.  the acrasin  AMP i s p r o d u c e d b y  produces  Some f a c t s  I t i s possible,  produced  a small chemicals  are also  b y P. p a l l i d u m .  produced  f o r example,  b y D. d i s c o i d e u m  might  I t i s also  b y D. d i s c o i d e u m  with the production o r the reception  might  of the acrasin  b y P. p a l l i d u m . Since  and  by  hold the key t o i n t e r s p e c i f i c  down t h e a c r a s i n p r o d u c e d  possible  food  (1) c y c l i c  AMP and ( 5 ) o t h e r  of acrasin.  the phosphodiesterase  break  the bacterial  (2) c y c l i c  a l s o have t h e a t t r i b u t e s  other  AMP i s  c a n be made:  a n d P. p a l l i d u m , ( 3 ) c y c l i c  inhibition  that  of acrasin  D. d i s c o i d e u m  which breaks  ability.  points regarding the  acrasin,  many o t h e r o r g a n i s m s ,  acrasin,  work.  AMP a c t s l i k e  protein  like  cyclic  as E . c o l i  also AMP t o 5'AMP  with respect t o a t t r a c t i v e  b y many o r g a n i s m s  production  D. d i s c o i d e u m  AMP a c t s as an a t t r a c t a n t  act like  From  o f t h e above  the i n t e r s p e c i f i c  inhibition  observed  here,  i n the other studies,occurs at the aggregation stage, the likely  hypothesis i s that  the substances  produced  during  143  a g g r e g a t i o n a c t as i n t e r s p e c i f i c a g g r e g a t i o n  inhibitors,  A c r a s i n and c h e m i c a l s which break i t down are most abundant a t t h i s p e r i o d i n the l i f e c y c l e o f c e l l u l a r s l i m e molds, t h e r e f o r e , must be t h e most l i k e l y c a n d i d a t e s . P. p a l l i d u m a c r a s i n i s i s o l a t e d , phosphodiesterase any d e f i n i t e  and  However, u n t i l  and u n t i l i t s r e s p o n s e  to  i s c h a r a c t e r i z e d , i t i s i m p o s s i b l e t o make  statements.  Genetics The D. d i s c o i d e u m  r e s u l t s o f t h i s s t u d y a l s o suggested was  that  a b l e t o i n h i b i t P. p a l l i d u m f r u i t i n g b e f o r e  c o m p e t i t i o n , but a f t e r a p e r i o d of continued  competition  P. p a l l i d u m overcame t h e i n h i b i t i o n and began t o f r u i t i n the presence  o f D. d i s c o i d e u m .  A p p a r e n t l y the change  was  g e n e t i c r a t h e r t h a n a c c l i m a t i v e and the gene p o o l o f s t o c k P. p a l l i d u m S a l v a d o r c o n t a i n e d s p o r e s w i t h  co-fruiting  abilities. These c o n c l u s i o n s a r e d i f f i c u l t t o a c c e p t when c o n s i d e r e d a l o n g w i t h two o t h e r p i e c e s o f i n f o r m a t i o n . (1) G l i v e ( 1 9 6 3 ) , Sussman and Sussman ( 1 9 6 3 ) , Huffman O l i v e (1964) and Huffman (1967) a l l c o n c l u d e d no m e i o s i s i n c e l l u l a r s l i m e molds.  (2) The  that there i s data from t h i s  s t u d y i n d i c a t e s t h a t when s t o c k P. p a l l i d u m and  co-fruiting  P. p a l l i d u m a r e mixed and grown f o r a p p r o x i m a t e l y t i o n s a t 2 7°C The  and  120  c o - f r u i t i n g P. p a l l i d u m can no l o n g e r be d a t a makes i t appear t h a t t h e c o - f r u i t i n g  generadetected. strain  144  is  less  f i t than  specific almost found to  the  stock  c o m p e t i t i o n the  completely  disappears.  the c o - f r u i t i n g The  recent  best  genetical  and  co-fruiting  i n a stock c u l t u r e .  s e e how  strain,  Yet  strain  difficult  strains  are p r o t e c t e d .  i t is  d i l e m m a comes f r o m  c e l l u l a r slime molds.  strains  have observed  Huffman cell  aggregate  t o form  and  and  in  Sinha the  Loomis  (1967),  and and  Ashworth  (1969) s t a t e diploid  Huffman  Ashworth  and  (1969)  times.  that  fusions  cell  version of  these  from  two  fusion  haploid occurs  These o b s e r v a t i o n s p l u s  1958)  g e n e r a l mechanism can  (1969).  and  unstable  Ashworth  reports that  p a r a - s e x u a l i t y (Pontecorvo  Ashworth  and  L o o m i s and  o f g e n e t i c marker experiments  The  and  some  Sussman  (1957),  Sinha  f r u i t i n g bodies.  ( p e r s . comm. 1970)  modified  Ross  was  f u s i o n s as t h e v e g e t a t i v e amoebae  once i n a thousand  that  Wilson  f o r m a t i o n o f one  results  or  meiosis  diploid  (1964),  completely  Without  (1963) r e p o r t t h a t h a p l o i d , d i p l o i d  Olive  intra-  spore  Sussman  exist.  during  a co-fruiting  answer t o t h i s  work on  that  a diagram  had  presented  cells. about  the  place.  s u m m a r i z e d by by  result  l e d to the c o n c l u s i o n  takes  be  (1968),  Sinha  and  a  145  haploid n = 7  s t r a i n xy cell fusion  • heteroc aryon (xy)  haploid n = 7  strain  + (XY)  XY  nuclear fusion heterozygotic spore n = 14  heterozygotic myxamoebae n = 14  XY  haploidization aneuploid spore  aneuploid myxamoebae n = 7+1, 2, 3, 4, 5 o r 6  (|-), ( ^ ) , (2EZ), o r 'XY  X  haploidization haploid spores n = 7  w h e r e x/X a n d y/Y a r e two u n l i n k e d  haploid myxamoebae ( x y ) , ( X Y ) , ( x Y ) , o r (Xy)  genes.  146  The istics can  diagram demonstrates  c a n be h i d d e n b y d o m i n a n t s  be p r o t e c t e d .  Since  the average  (haploid)  than  P. p a l l i d u m  stock  co-fruit  that  that  specific  selected  tion,  This  a  mask  fruiting  genetic  prediction P. p a l l i d u m the  time.  the necessary and be  l o s s , r e s u l t s i n an e x t r e m e l y  the f a c t  that meiosis  makes i t p o s s i b l e  variability  that  individual co-  cells  level,  provided  that  cultures. and i t s  i n P. p a l l i d u m  i n s i t u a t i o n s where c o m p e t i t i o n  T h e s e two s p e c i e s  time,  are necessary f o r  para-sexuality  occurs  and D. d i s c o i d e u m  variable  c u l t u r e , and a t t h e same  i n mixed  supposition  recombina-  does n o t o c c u r .  to find  number o f c o - f r u i t i n g  that  and l e s s  the p e r i o d i c f u s i o n of c e l l s ,  to take place The  i s determined by a  cultures  a t t r i b u t e at the population  significant  dent  i n the stock  spores i n the stock this  Salvador to  competition.  general,  variability  fruiting to  o f P. p a l l i d u m  It  c u l t u r e s b u t more f i t i n t h e i n t e r -  be p r o t e c t e d  despite  i n this  m i g h t be i n v o l v e d .  Because o f p a r a - s e x u a l i t y  and chromosome  population  (diploid)  i n the  some o f w h i c h may b e r e c e s s i v e  f o r during In  larger  f o r t h e work p r e s e n t e d  the a b i l i t y  cultures. could  character-  less f i t alleles  considerably  para-sexuality  i n the i n t r a s p e c i f i c  alleles  and t h a t  i n t h e p r e s e n c e o f D. d i s c o i d e u m  number o f a l l e l e s , fit  recessive  have been o b s e r v e d  c u l t u r e used  paper, i t appears seems p o s s i b l e  spores  that  should  co-fruit  have been found  leads  atten-  to the  i s continuous, almost a l l  together  i n their  147  natural and  h a b i t a t by Cavender  Horn  could  (1969).  fruit  indicates  from  pallidum  Section  species  T h e P. p a l l i d u m  strain  and t h e i n f o r m a t i o n a v a i l a b l e competition  from  In the laboratory D. discoideum  and  inhibited  Coexistence  effects  of continued  o f some c o n t r o v e r s y  Grinnell  (quoted  (1934),  resource  competition  1959 and R o s s  the theory  states that  use i s d i v e r g e n t .  considerable  competition  animals This  to morphological  1958),  of competitive coexist only  linked  and e c o l o g i c a l  ( J o h a n n e s and L a r k i n 1961, F i c k e n  and  continued  divergence 1967),  On t h e o t h e r  competition  hand,  work  result  i n convergence i n t h e form o f mimicry Moynihan  territoriality  their  a  recent  or morphological  that continued  later  when  e t a l 1967, K e a s t  i n turn resulted i n coexistence.  time.  exclusion  axiom h a s p r o m p t e d  number o f s t u d i e s w h i c h h a v e  suggests  have been t h e  f o r a considerable period of  i n Udvardy  advanced  which b a s i c a l l y  which  t h e two  (1965),  fruiting.  The  Gause  Salvador  and Raper  I I : E c o l o g i c a l Relevance  Convergence  center  that  i n the laboratory.  that i t never experienced  D. d i s c o i d e u m . £°  And H o r n d e m o n s t r a t e d  together  u s e d h e r e came  (1963), Cavender  might  also (1968),  and b e h a v i o r a l i n t e r f e r e n c e r e l a t e d t o  Cody  (1969).  Miller  (1964) h a s a l s o  shown  148  that  ecological  existence beetle  and  convergence i n f r u i t  Park  and  competition  Lloyd  lasting  homogeneous l a b o r a t o r y In  correct  i n many s i t u a t i o n s .  predictive  hypothesis  may  the  cellular  the  e n v i r o n m e n t was food,  against these  and  the  food  existing  But  too  the  flour  small  coexistence  work p r e s e n t e d  simple  hypothesis  t o h a v e any  exare  both  here  real  s p e c i e s e a c h had  no  coexistence,  a refuge  I t was  Two  co-fruiting  so  to  and  changes d i d and  source  guard  assumed t h a t  ability  that  alternate  convergence could occur  i n coexistence. gained  of convergent  e x p e r i m e n t s were d e s i g n e d  extinction.  tv/o s p e c i e s d i d end f o r the  to resource rates  always able where i t was point  in  co-  under that  this  occur;  D„  discoideum  faster.  but  different  instances of  axiom o f c o m p e t i t i v e  of convergent  and  use.  d i d they They used  co-fruiting  and  They d i d n ' t  converge  completely the  at a r e a l  at  least  one  disadvantage  Coexistence  occurred  P.  fruiting from  co-  diverge  same r e s o u r c e  c o e x i s t e d o n l y because  to produce  of view.  up  wrong r e a s o n s .  t h e r e f o r e c o e x i s t , nor  respect  the  homogeneous o f f e r i n g  conditions only  The  and  the  two  immediate  pallidum  used  be  s l i m e mold  would r e s u l t P.  in  value. Following  of  result  environments.  and  that both  can  f o r several years  clusion  suggests  (1955) l i s t  a l l probability the  flies  an  with at  pallidum  was  b o d y i n an  area  exploitative  because the  advantage  149  gained  f r o m i n t e r f e r e n c e was  from e x p l o i t a t i o n , . and of  i t s opposite resource  use,  Park the  outcome of  definition or  Because G r i n n e l l ' s  (Miller this  1964)  result  (1954) has  - this  being  knowledge, r a t h e r than any  stated that  To  second  feedbacks  situations. there  are  Since for  five  with  about the  investigation  that empirical  is  necessary,  respect  to  the  and  this  study  to i d e n t i f y  was  the  study  analyze  basic  a p p l i c a b l e t o most  s l i m e mold  to  has  the  components  competitive suggested  that  b a s i c components i n v o l v e d . primary  demonstrated  resource,  add  either.  competition.  cellular  some r e s o u r c e  space.  prediction  i s inherent i n  I would  rates  p r e d i c t e d by  "no  reached  consideration i s exploitation  i t i s g e n e r a l l y accepted  species and  be  objective of  something o t h e r  until  this  w h i c h m i g h t be The  The  be  with  term)  Competition  mechanics of c o m p e t i t i o n and  (Udvardy's  concerned  abstract deduction,  consequences of continued  A  disadvantage  a matter f o r e m p i r i c a l  c o n c l u s i o n s can  Components o f  c o u l d not  the  axiom  are only  sustained competition  abstract deduction."  before  g r e a t e r than  than  life  t h a t o r g a n i s m s must itself,  i s exploitated. this  p o i n t by  Their interaction because resource  was  u s e d by  competition The  cellular  competing mediated one  (Park compete  cannot slime  f o r both  through  competitor  1954).  occur mold  food  the could  not  150  be u s e d b y t h e o t h e r . represented  where  as:  and C2  limited  S y m b o l i c a l l y t h e p r o c e s s c a n be  are competitors  by o t h e r c o m p o n e n t s , situations  component  s l i m e mold  food  on  eaten  i n which e x p l o i t a t i o n  involved.  140 grams  this  o f meat t h e y  interfered  certain  temperatures, produced  responsible. come, c h a n g i n g expressed  where  with  one  (1950)  interacted  sericata  I t was  only because the  the e x p l o i t a t i o n  found  observed  the  two  ability that  and f r u i t i n g  alters rates,  that  fruiting  hypothesized  during aggregation  Since interference  were  by t h e o t h e r .  another's  and i t was  reports  observed  c o m p e t i t i v e component  i s interference.  species  complicated  the o n l y c o m p e t i t i v e  and L u c i l i a  b y one c o u l d n o t be e a t e n  study  chemicals  was  was  literature  F o r example, U l l y e t t  The o t h e r i m p o r t a n t in  situation  b u t t h e r e have been  t h a t when C h r y s o m y i a c h l o r o p y q a placed  R i s the  resource. The c e l l u l a r  of  1 and 2 and where  at  the were  the c o m p e t i t i v e i t may  be  out-  symbolically  as:  t h e two c o m p e t i t o r s  directly  alter  exploitation  rates.  151  The  cellular  interfere  slime  m o l d work s u g g e s t e d  by p r o d u c i n g  t o x i c chemicals,,  h a v e b e e n made b y Grummer and B e y e r flax  i s i n h i b i t e d by c h e m i c a l s  Camelina. the  i n Larrea.  respect  that  behavioral  (1961) p r o v i d e s inhibition.  slime  T. confusum  Park  slime  mold  other b u t were O r i a n s and  authors  have with  interference  (1965) r e p o r t e d  food also  that  a t e b o t h i t s own pupae and t h e pupae  could  important  In this  case  and i t was f o u n d always exclude  above about 24°C t h e r e v e r s e i n t e r f e r e n c e became i m p o r t a n t force  as any f o r c e s o u t s i d e t h e  were v e r y  situation.  force,  2 2 ° C D. d i s c o i d e u m  External  other  a t 2 0 ° C and 7 0 % RH.  was t h e e x t e r n a l  also.  study.  numerous  a l t e r s e x p l o i t a t i o n f o r both  of the competitors,  cellular  that  to explain  interference, particularly  External forces, defined control  mold  And c a n n i b a l i s t i c o r p r e d a t o r y  castaneum  Two  and numerous o t h e r  exploitation rates.  Tribolium of  (1954),  to t e r r i t o r i a l i t y ,  space.  alters  observations  ( 1 9 6 0 ) who r e p o r t  appear i n t h e l i t e r a t u r e  i n the c e l l u l a r  (1969), Lack  reported  and  induced  of interference  observed  Horn  Similar  could  washed o u t o f t h e l e a v e s o f  Grummer  examples o f c h e m i c a l l y  not  animals  And t o x i c i n t e r f e r e n c e h a s b e e n i n v o k e d  spacing  classes  that  was t r u e .  that  i n the  temperature below  about  P. p a l l i d u m  while  B e t w e e n 2 2 ° and 2 4 ° C  but temperature  c a n be s y m b o l i c a l l y  controlled  represented  as:  that  152  where E r e p r e s e n t s usually  an  a b i o t i c and  external  can  humidity, hours of t h e y may  a l s o be  fish  remove s e v e r a l  that  Friday  and  fourth  an  important  In  the  colony  thereby  altering  alter  (1969) r e p o r t parasite  the  suggests that  star-  which o r d i n a r i l y (1967)  of Thais  curtail  or  cariosus  competition  evidence  also  time that  has  prevent  f o r space  at  Horn  one  i s resource  (pers.  be  the  very rates  the  amounts o f  food  to  and  play  In  Filter  Griffiths  contagion of  were  that  food  the  concentration,  field  situations  feeding  e x p l o i t a t i o n with  degree of  not  comm.) r e p o r t s  important. of  did  availability.  exploitation.  competitor interference  suggests  "three  of  that  zoo-  changes  in  and  Holling  hosts  alter  rates.  span i s  space i n the  and  ( M u l l i n 1963),  that  attack  e f f e c t of  study  rate  their  Finally,  found  literature  expansion i s p r o p o r t i o n a l  availability  long  pH,  Connell  s i t u a t i o n constant  component c a n  plankton  the  temperature,  and  consideration  a l l times, but  rate of  food  B.  role i n this  laboratory  at  this  species  are  (1966) n o t e d  species  space,  forces  Harbor. A  used  and  by  The  Paine  foreshore  three  Balanus g l a n d u l a  etc.  biotic.  compete f o r n u t r i e n t s  External  exemplified  sunlight,  that  observed  be  force.  that  availability  component i n t h i s  competitor  . . important. species  Potholes  of  of  greatly  study.  availability  Orians  blackbirds  altered  and  Horn  over  But  a  (1969)  compete f o r f o o d  c e n t r a l Washington.  Field  they  and only  153  compete the  a t c e r t a i n t i m e s o f t h e d a y and d u r i n g  year.  In t h i s  situation i t i s possible  does n o t o c c u r because t h e p e r i o d and  regulating mortality occurs  different  periods  of time.  Because  a laboratory  external  forces  possible  to assess  competitive  at other  places  exclusion i s too short, and  during  s i t u a t i o n was u s e d i n w h i c h  i n some d e t a i l I t was  that  of competition  and a v a i l a b i l i t i e s  situation.  one p e r i o d o f  could  b e c o n t r o l l e d i t was  the factors involved  also possible  in a  to determine the  ways i n w h i c h t h e c o m p o n e n t s i n t e r a c t .  EXTERNAL FORCE (TEMPERATURE)  i  1  x COMPETITOR (MOLD) AVAILABILITY  RESOURCE (FOOD) AVAILABILITY  INTERFERENCE (TOXIC)  Exploitation altered  was t h e c e n t e r  i n t e r f e r e n c e by a l t e r i n g  available.  I t , i n turn,  was  of competition  and  t h e number o f c o m p e t i t o r s  a l t e r e d by t h e amount o f b a c t e r i a l  154  food  a v a i l a b l e and  Interference areas ing  altered  of high  the  t h e number o f c o m p e t i t o r s exploitation  affected exploitation  not  altered  by  did  not  directly  dotted  field  above  this  But  and  value  In the  availability  the  these  alter-  general  be  was  (shown  i f i t has  any  g e n e r a l i t y , the  assessed  literature  by  made.  system which  o n l y be  i n the  two.  competitor  links  can  of  the  Ullyett  best  s t u d i e s i n the  (1950),  s p e c i e s of blow f l i e s ;  chloropyqa,  C.  laboratory  data  a l b i c e p s , and  and  by  has  future  component should  field parts  f i t the  Lucilia C.  were.included.  field.  He  considered  d i d not  marginalis. Ullyett  interspecific  situations  a l b i c e p s was the  others  competitive  to L u c i l i a  eating  found  larvae.  Both f i e l d  found  use,  was  but  The  inter-  species of  he  a l l larval  important  extent  the  when  I n most  that this  and  that a l l four  situations,  units.  between  Chrysomyia  l a b o r a t o r y and  only exploitation  i n v o l v e d he by  the  was  competition  sericata,  measure r a t e s o f f o o d  numbers were c o n v e r t e d specific  literature  concerned  species e x p l o i t e d c a r r i o n i n both  with  by  outline.  c o n d u c t e d by  C„  or  study  studies reported  and  in  l a b o r a t o r y the' t e m p e r a t u r e  situations  of  time  i n t e r f e r e n c e but  would almost c e r t a i n l y  real  One  four  in field  lines)  emerged f r o m studies.  change f o o d  but  The  of  competition.  of  feeding  a v a i l a b l e i n time p e r i o d  Temperature  the  inhibiting  density f o r short periods  number o f c o m p e t i t o r s  availability  by  available.  but  when  interfered  predatory  155  interference One  biotic  and two  Temperature adult  depended upon r e s o u r c e abiotic  and h u m i d i t y  dispersal,  and  altered  the  field  was  and  dispersion.  included.  Finally,  competition.  with  i n the winter  situation  was  important.  to quantity,  component  reason  was  little  availability  a potentially  reduced  and  Walk  Food a v a i l a b i l i t y i n  respect  this  and f o r t h i s competitor  also  numbers.  vitripennis  t o two  quality  very  information  restricted  B e c a u s e two o f t h e c o m p e t i t o r s  summer and two competitor  important  mortality.  Unfortunately  to assess  larval  the rates of o v i p o s i t i o n  a p a r a s i t e Mormoniella  C. a l b i c e p s p u p a l  difficult  and  e x t e r n a l f o r c e s were  increased  very  quality  breed  field  i n the  complex  separate  was  four  two  competitor  situations. In found  i n the c e l l u l a r  Ullyett*s included  study  studies. this  species  situation  have been f i t t o c e l l u l a r  author  was  however,  i n various habitats  with  the others,  existence alone.  c o u l d be  The p r e s e n t  were  a l s o found  could  in  be  out t h a t food  mold  field  field work known  the d i s t r i b u t i o n  (Cavender 1963). quality  was  However, very  competition  on w h i c h t h e y  study  suggests  that while  Horn  that since ;  could out-  c o u l d be r e s o l v e d  a t t a i n e d on t h e b a s i s o f f o o d  of  important  s t u d i e d , and he h y p o t h e s i z e d  s p e c i e s had a s e r i e s o f foods  compete  competition  slime  the only  concerned only  s p e c i e s he  data  of  I t would have been b e t t e r i f the  Unfortunately,  the four  most  s l i m e mold  and a l l - o f U l l y e t t ' s  (1969) has p o i n t e d to  a l l o f t h e components  i n the system.  system c o u l d  to  general,  and c o quality  food  quality  156  is  very  important,  some c a s e s  i n t e r f e r e n c e , also determine  competition  on  can  due  be  said  ecology  response to environmental  any  patch  to the  of c e l l u l a r It  of b a c t e r i a .  lack of  s l i m e mold  i s hoped  that  the  factors,  the  outcome  Beyond  information  general  model  developed  feedbacks which  a l s o be  general  e a c h component was model  simulated  s l i m e mold w i t h  involved i n competitive  i n c l u d e d w i t h i n each  i n nature.  During  the  course  a reasonable  between  two  amount o f  however, t h a t the minute mechanics  situation  w o u l d be  The into  e a c h component must d e p e n d upon t h e Studies  of  term r e s u l t s  of  there  general  are  no  the  short  continued  laws which w i l l  make p r e d i c t i o n s a b o u t c o m p e t i t i o n . t o be  a finite  number o f  number o f  selective  moment, i t a p p e a r s solved  by  It is  incorporated  system under  suggests allow  and  of both  of  the  t h a t to  competitors. problems can  these  study. long date  e c o l o g i s t s to  s t r a t e g i e s a v a i l a b l e and  that competitive  this  competition.  However, t h e r e  f o r c e s a c t i n g on  o n - s i t e study  and  term mechanics  competition  cellular  involved i n  instances of  ways i n w h i c h i n f o r m a t i o n i s a s s e s s e d  work  resulting  of  accuracy.  The  should  this  the  species  unlikely,  useful i n other  systems.  of  and  from  components  component  s t u d i e d i n some d e t a i l  competition  natural  species.  and  of information  little  about the  l a b o r a t o r y s t u d i e s i n c l u d e s most o f t h e m a j o r  kinds  in  of  this,  the  are  and  factors.  a  do  seem  finite For  only  the be  157  LITERATURE  CITED  Allee,  W.C., A . E . E m e r s o n , T. P a r k , 0. P a r k , and K „ P . S c h m i d t , 1949. P r i n c i p l e s of Animal Ecology. Philadelphia: W.B. S a u n d e r s C o .  Birch,  L.C.,1957. The m e a n i n g s N a t u r a l i s t . 9 1 : 5-18.  of competition.  Amer.  Bonner,  J . T . , 1947. Evidence f o r the formation of c e l l a g g r e g a t e s by c h e m o t a x i s i n t h e development o f t h e s l i m e mo'ld P i c t y o s t e l i u m d i s c o i d e u m . J . E x p t l . Z o o l . 106: 1-26.  Bonner,  J . T . , 1950. 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E c o l o g y 50: 9 2 2 - 9 2 4 .  APPENDIX  I  COMPUTER PROGRAMS  PAGE //  1  LOG D R I V E 0000 V2  165  JOB  MO 6  CART S P E C 0001 ACTUAL  8K  CART A V A I L 0001 CONFIG  PHY D R I V E 0000  8!<  / / FOR • L I S T SOURCE PROGRAM •ONE WORD I N T E G E R S • I O C S <CARD»1132 P R I N T E R ) REAL KON REAL L M I N I 2 0 ) REAL L A G U O ) DIMENSION T ( 3 0 ) » Q ( 3 0 ) » T T ( 3 0 ) » T O ( 3 0 ) » S Q ( 3 0 ) » A C T ( 3 0 ) TH = TL = I I = JJ = KK = LL = READ(2»1000) ( T ( I ) * Q ( I ) » 1 = 1.11) 10 00 F O R M A T ( 2 F 1 0 # 5) R E A D ( 2 » 2 0 0 0 ) ( T O ( J ) .J = 1 , J J ) . 2000 F0RMATIF10.5) READ(2»3000) (LMIN(K)»K=1»KK) 3000 FORMAT(F10.5) READC2»4000) ( T T ( L ) > AC T ( L ) » L=1» L L ) 4000 FORMATC2F10.5)  DO 1 I = 1 » I I A = (-•5*AL0G({-1.0)*T{I)**2«0 + T(I)#(TH+TL) - TH*TL))1 ( ( (TH+TL ) / 2 . 0 ) » ( 1 . 0 / ( T H - T L ) ) * 1 (ALOG(ABS(T(I) - T H ) / ( T ( I ) - T L ) ) ) ) B = ( ( ( 1 . 0 )/(TH-TL ) 1*AL0G(ABS(T( I ) - T H ) / ( T ( I )-TL) ) )  DO 2 J = 1 *JJ D = ( - . 5 * A L O G < ( - 1 . 0 ) * T O U ) * * 2 . 0 + T0(J)#(TH+TL) - T H * T L ) ) 1 (((TH+TL)/2.0)*<(leO)/(TH-TL))* 1 (ALOG(ABS(T0(J)-TH)/(TO!J)-TL)))) E = ( ! 1.0)/(TH-TL) )*{AL0G(ABS(T0(J)-TH)/(T0U)-TL) ) )  DO 3 K = 1 , K K KON = ( Q ( I ) -LMIN(K))/(A+B*TO(J)-D-E*TO(J)) CON = ( L M I N ( K ) - ( ( Q ( I ) - L M I N ( K ) ) * ( D + E * T O ( J ) ) ) 1 (A+B*T0(J)-D-E*T0(J)))  WRITE(3»200)T!I)»Q(  I)  /  PAGE 200 300 400 500 600 700  100 4 3 2 1  2  166  FORMAT*' TEMP OF POINT USED IS • F 1 0 . 5 WRITE(3*300) TOIJ) FORMAT( • TEMP OPTIMUM IS F10.5) WRITE(3»400) LMIN(K) FORMAT( LAG MIN IS • F 1 0 . 5 ) WRITE O f 5 0 0 ) KON FORMAT( ' K I S F10.5) W R I T E ( 3 » 6 0 0 ) CON FORMAT( ' C I S ' F10.5) WRITE ( 3 > 7 0 0 ) FORMAT( ' TEMP LAG PRE LAG ACT 1  ». AND POINT  IS  1  F10«5!  1  1  1  SUMSQ  SUMSQ = 0 . 0 DO 4 L = 1 i L L L A G ( L ) = KON*( ( - . 5 ) * A L O G ( ( - 1 • 0 ) * T T ( L ) * * 2 . 0 1 (TH*TL))) 1 KON*(((TH+TD/2.0)*<(1.0)/(TH-TL))• 1 ALOG(ABS((TT(L)-TH)/(TT(L)-TL))))+ 1 KON*TO(J)*{(1.0)/(TH-TL)>* 1 ALOGtABSt ( T T ( L ) - T H ) / ( T T ( L ) - T L ) ) ) + C O N SQ(L) = (LAG(L) - ACT(L))**2«0 SUMSQ = SUMSQ + S Q ( L ) WRITE(3»10 0 )TT(L) »LAG(L)»ACT(L)»SUMSQ FORMA T ( 4 F 1 0 . 5 ) CONTINUE CONTINUE CONTINUE CONTINUE CALL EXIT END  '  )  + . ( T T ( L ) * ( T H + TL) ) -  167  PROGRAM I - CURVE F I T T I N G  Program equation  (2b)  complicated  unknowns; L a g C.  the  comparing  the  calculating  Lag  sum  of the  calculated,  and  choosing  2b  T  b  H  log | ( - l ) T  + T  =  L  so  -  H  T  "H 2b  s T  then  the  can  be  equation  T  those  two K  to the  and lag  values,  Q  observed,  d e v i a t i o n between  curve  (T  H  that best  fits  observed the  f o l l o w i n g s t e p s were  + T ) T  log  T  L T  - T.  T  - T,  data. taken.  - T^T | ) "H L T  -  H  T,  H  written  2b  are  that:  -  L = K>a If T  squared  with  T T  there  been f i t t e d and  by  T h i s problem i s  (2b)  minimum  values  + T  2  log  equation  has  terms the  i s b r o k e n up  a = [(-.5  lag data.  (2b)  many p o s s i b l e L a g calculated  described  , which i n t u r n determine  equation  In mathematical  then  T  the  Equation  to f i t curves  that i n equation  minimum, and  trying  2b)  germination  fact  In view of t h i s ,  d a t a by  and  I i s designed  to spore  by  (Equation  + K>T can  as:  o  •b  be  (2c)  + C b r o k e n up  again to  yield:  168  l o g | (-1) T^ + T  [(.-5  d =  T  + T  H  and  H  - T  log L  L  . mm  i s t h e minimum  must o c c u r  at T = T . o solve  Q  H  o  L  7  and L . mm  K  and C.  and T  o  T value  are estimated  into  substitutions  T h e s e K and C and T  some  this  reason  the  available  into  into ( 2 d ) .  then  be  substituted  J  be s o l v e d .  T h e r e i s no way o f into  i s no way o f k n o w i n g t h e b e s t v a l u e s o f L . mm  For  data  i t i s possible to solve f o r v a l u e s may  ( 2 b ) , which can then  J  of  7  i s substituted  k n o w i n g w h i c h d a t a p o i n t s h o u l d be s u b s t i t u t e d there  definition,  and s u b s t i t u t e d  o back  L  (2d)  ( 2 c ) and ( 2 d ) s i m u l t a n e o u s l y  (2c),  made t h e s e  T 0-  H T — T,  l a g v a l u e , which, by  f o r L and i t s c o r r e s p o n d i n g  Having  H  c o u l d b e w r i t t e n as  value '  L  = K • d + K •T • e + C o  where L min .  To  + T ) - T-  L  ( 2 b ) with T = T  equation  H  log  - T H  T  (T  T - T  L T  e =  Q  J  Program T has been designed  d a t a p o i n t s may be t r i e d  ( 2 d ) and and T . o  so t h a t a l l o f  i n combination  L ,_ and T values. min o In g e n e r a l about 2 0 0 c o m b i n a t i o n s  with a l l  the reasonable 3  data values, least  a r e examined b e f o r e  o f squares  method.  a curve  The c u r v e  of T  , L . , and o' mm'  i s chosen by t h e  c h o s e n must h a v e a sum o f  169  squared d e v i a t i o n s which i s i n a " s i n k "  ( i e . the sum  squared d e v i a t i o n s f o r every o t h e r combination of and data i s l a r g e r ) .  L m i n  of >  T 0  >  PAGE  1  MCQUEEN  170  // JOB  MCQUEEN  LOG DRIVE 0000 V2 M06  CART SPEC 0001 ACTUAL  8K  CART AVAIL 0001 CONFIG  PHY DRIVE 0000  8K  // FOR • L I S T SOURCE PROGRAM • IOCS ( TYPEWRITER»1132 PR INTER * KEYBOARD) DIMENSION A ( 2 5 ) Z=1.0 16 WRITE(3,5)Z 5 FORMAT(3H1Z=»F10.5) WRITE(3tl2)  12  3 2 4 13 1 14 15  FORMAT(20X»20H  J  DO 1 J = 1»25 IF(J-1)2»2*3 A!J) = ( M Z*3e 54490 * J ) + GO TO 4 A ( 1 ) = loO CONTINUE WRITE(3»13) J»A(J) FORMAT (20X»I3»7X»F10.5) CONTINUE READ(6»14)Z FORMAT(F6•0) IF (Z)15»15»16 CALL EXIT END .  A)  l)/2)**2  171  PROGRAM  I I - FORM OF COLONY EXPANSION Program  by  a colony  a t any t i m e  area, J i s time, to  t.  The o u t p u t  occupied  ( I d ) , and C h a s b e e n s e t  indicates  the slope of the l i n e ,  t h e growth r a t e o f t h e c o l o n y ,  the p r i n t e r .  the area  I n t h e program n o t a t i o n A ( J ) i s  Z are i n p u t , u s i n g the keyboard via  to calculate  Z i s g i n equation  1.0 a r e a u n i t s .  increases; as  I I i s designed  (Equation l c )  t h a t as Z ( o r g )  w h i c h may be i n t e r p r e t e d also  increases.  Values of  and A ( J ) a n d J a r e o u t p u t  PAGE  1  172  // JOB LOG DRIVE 0000 V2 M O 6  CART SPEC 0001 ACTUAL  8K  CART AVAIL 0001 CONFIG  PHY DRIVE 0000  8K  // FOR • L I S T SOURCE PROGRAM •ONE WORD INTEGERS * I 0 C S ( C A R D » 1132 PRINTER. PLOTTER) DIMENSION A(14)» X ( 5 0 ) , Y ( 5 0 ) . ANS(16)» 1 TABLE(30) . TTEST(50 ) READ(2.900)(TTEST(JJ)»JJ=1»50) 900  901 501  C 3 10 0 2 6  1 5  C • 200 4 16 101  C  '  STORE(8»65).  FORMAT(8F10.5)  READ(2.901)(TABLE(NN)>NN=1.30) FORMAT ( 8 F 1 0 . 5 ) DO 501 I = 1.75 IUSEDfl) = 0 L=0  CARD COUNTER TO GET DATA FOR EACH REGRESSION K=0 READ(2.100)TEMP » T I M,A FORMAT (15F5*0.F4»0) IF(TEMP)2»1>2 IF(K)16.6.16 SAVE = TEMP L = L+1 N=0 K=l GO TO 3 DO 4 1=1.14 IF ( A ( I ) J 3 . 3 . 5 N = N+1. X(N) =TIM Y ! N) = SORT(A ( I ) )  DATA IS WRITTEN OUT HERE WRITE ( 3 . 2 0 0 ) X(N!.Y!N) FORMA T(2 F10•5) CONTINUE GO TO 3' WRITE ( 3 . 1 0 1 ) SAVE FORMAT (//' L= '» F 6 . 2 )  REGRESSION CARRIED OUT AND ANSWERS ARE CALL LREG(X.Y.N.AMS) CALL LREGO(ANS) WRITE ( 3 . 4 0 0 )  WRITTEN  IUSED(65)»  PAGE 40 0 401 402 403 404  332  C  C 11  602 603 525 88 8 5 26 560  173 FORMAT (1H0) WRITE ( 3 . 4 0 1 ) ANS(4) FORMAT ( SUM OF XY = F10.5) WRITE (3»402) ANSt5) FORMAT ( ' SUM OF X SQUARED = ' » F10.5) WRITE (3 .403) ANSI 9) FORMAT ( • SUM OF Y SQUARED = • . F l O o S ) SUMDS = ANS(9) - ( A N S ( 4 ) * * 2 ) / A N S ( 5 > WRITE ( 3 . 4 0 4 ) SUMDS FORMAT ( SUM OF DEVIATION SQUARED OF XY = WRITE(3»832) WRITE(3.S32 ) WRITE(3.832) FORMAT(1H0) 1  1  ALL THE BASIC PLOTTING S T O R E ( l . L ) = ANS(1) STORE(2.L) = ANS(2) STORE(3.L) = ANS(3) STORE(4.L) = ANS(4) STORE(S.L) = ANSI 5) STORE! 6 » D = ANS(9) STORE(7,L) = SUMDS STORE(8»L) = SAVE IF (TEMP)11 .11 .6  1  > F10.5)  INFORMATION IS COLLECTED HERE  THE DATA IS SORTED ACCORDING TO TEMPERATURE DO 600 NN = 1.30 LC = 0 SUMN =0. YMEAN = 0. XMEAN = Oo SUMXY =0. SUMXS =0. SUMYS = 0 » SSUMD = 0. DO 601 LL = l . L IF ( I U S E D ( L D ) 601.602.601 IF (STORE(8»LL) - TABLE(NN)) 603.601.601 IUSED(LL)=1 T = STORE!8.LL) WRITE ( 3 . 5 2 5 ) STORE(8»LL) FORMAT (' STORE(8.LL) IS TEMP = •» F10.5) WRITE ( 3 . 8 8 8 ! FORMAT ( » N YBAR XBAR SUMXY 1 SUMYSQ SUMDXY ' ) WRITE (3 .526) ( STORE ( KK.» LL ) . KK = 1.7) FORMAT ( 7 F 1 0 . 5 ) SLOP = ( S T 0 R E ( 4 . L L ) ) / ( S T O R E ( 5 . L L ) ) WRITE ( 3 . 5 6 0 ) SLOP FORMAT (• SLOP OF SINGLE LINE = . F 1 0 . 5 ) WRITE(3»832) 1  SUMXSQ  PAGE  61  62 88 89 90  75 76 77 78  628  601 22 527 889 528  999 529  174  3  LC = LC +1 I F ( L C - 1) 61,61,62 CALL SCALF (7.0/7.0,10.0/20.0» 0.0,0*0) CALL FGRID(0,0.0.0.0,1.0,7) CALL F G R l D l l f 0 . 0 . 0 . 0 , 1 . 0 , 2 0 ) CALL FCHAR!0.0,0.0,0.07,0.07,1.570796) YE == S T 0 R E ( 2 , L L ) + SLOP*(7.0 - ST0RE(3»LL)J IF (( YE - 20. ) 88,88,89 XE == 7.0 GO TO 90 XE = ( 2 0 . ~ STORE(2,LL) + S L O P * ( S T O R E ( 3 , L L ) ) ) / S L O P YE = 20. CONTINUE XS = (-STORE(2»LL)/SLOP) + STORE(3,LL) IF (XS) 75,76,76 YS = S T O R E ( 2 » L L ) - ( SLOP* STORE(3 i L L ) J ) GO TO 77 YS = 0. GO TO 78 XS = 0. CONTINUE CALL FPLOT (-2 »XS,YS CALL FPLOT (-1,XE,YE) WRITE(7,628) LC FORMAT (12) CALL FPLOT ( 0,0.0,0,0) SUMN = S T O R E ( l , L L ) + SUMM STORE(2,LL) +. YMEAN YMEAN XMEAN S T O R E ( 3 » L L ) + XMEAN SUMXY S T O R E U » L L ) + SUMXY SUMXS STORE(5,LL) + SUMXS SUMYS STORE(6,LL) + SUMYS SSUMD STORE(7,LL) + SSUMD CONTINUE IF (LC) 600,600,22 WRITE(3,527) T IS TEMP = » F10.5) FORMAT ( T WRITE (3,889) SUMXY YMEAN XMEAN SUMXS FORMAT( • SUMN 1SUMYS SSUMD ' ) WRITE(3,528) SUMN, YMEAN, XMEAN» SUMXY, SUMXS, SUMYS, FORMAT(7F10.5) SLOPE = (SUMXY) / (SUMXS) DFREE = (SUMN) - (LC) - 1. ) SSYX - (SSUMD) / (D FREE) SS8 = (SSYX) / (SUMXS) SB = SQRT(SSB) J J = DFREE DEVIA = T T E S T ( J J ) * SB XPLOT = XMEAN/LC YPLOT = YMEAN / LC WRITE (3,999) FORMAT ( SLOPE DEVIA SB SSB DFREE SSYX 1 XPLOT YPLOT WRITE (3,529) SLOPE, DFREE, SSYX, SSB, SB, DEVIA,XPLOT, YPLOT FORMAT(8F9.5) 1  1  1  PAGE  4 WRITE(3»832) W R I T E ( 3 » 83 2) W R I T E ( 3 . 832) WRITE(3»832) YEM = YPLOT + S L O P E * ! 7 . 0 - X P L O T ) IF (YEM - 2 0 . ! 30 , 30 . 3 1 XEM = 7 . 0 GO TO 32 XEM = ( 2 0 . 0 - YPLOT + S L O P E * X P L O T ) / S L O P E YEM = 2 0 . CONTINUE XSM = XPLOT (YPLOT/SLOPE) IF ( X S M ) 3 3 . 3 4 , 3 4 YSM = YMEAN - ( S L O P E * X M E A N ) GO TO 35 YSM = 0 . 0 GO TO 36 XSM = 0 . 0 CONTINUE C A L L FPLOT ( - 2 , X S M , Y S M ! C A L L FPLOT ! - l . X E M . Y E M ) WRITE(7.629) FORMAT( ' MEAN L I N E » ) C A L L FCHAR ( 1 . 0 . 1 9 . 0 . 0 . 1 4 . 0 . 1 4 . 0 . 0 ) WRITE ( 7 . 2 2 3 ) T FORMAT( TEMP = • F 1 0 . 5 ) C A L L FCHAR ( 1 . 0 . 1 8 . 0 , 0 . 1 4 , 0 . 1 4 , 0 . 0 ) WRITE(7.224) SLOPE FORMAT( ' S L O P E = ' F 1 0 . 5 ) C A L L FCHAR ( 1 . 0 , 1 7 . 0 , 0 . 1 4 , 0 . 1 4 . 0 . 0 ) WRITE(7,225) DEVIA FORMAT ( • D E V I A = F10.5) C A L L FCHAR ( 1 . 0 , 1 6 . 0 , 0 . 1 4 , 0 . 1 4 , 0 . 0 ) WRITE(7,226)SUMN FORMAT( SUMN = ' F 1 0 . 5 ) C A L L FPLOT ( 0 , 1 0 . 0 , 0 . 0 ) CONTINUE CALL EXIT END  30 31 32 33 34 35 36  6 29 223  1  224 225  1  226  1  600  F E A T U R E S SUPPORTED ONE WORD I N T E G E R S IOCS CORE REQUIREMENTS FOR COMMON 0 VARIABLES END OF //  XEQ  COMPILATION  1610  PROGRAM  1452  176  PROGRAM  III  -  CALCULATION  Program w h i c h t i m e  ( F i g .  each a t u r e are i s  r e s u l t  III  f r o m  p l o t t i n g  a r e a  the  f i r s t  c u l t u r e  are  c o n s i d e r e d  then  r e a d  and  s u b r o u t i n e s .  and  a  r e g r e s s i o n  are  grouped  p r o c e s s  the  A . r e g r e s s i o n  LREGO  at  s e c t i o n  t h e n  c a l c u l a t e d  r e s u l t i n g  SLOPE  c a l c u l a t e s  In  i s  MEAN  the  mean  o c c u p i e d  s l o p e s by  a  o f  the  c o l o n y  l i n e s  a g a i n s t  1 1 ) .  r e a d .  grown  OF  l i n e  w i t h  from  c u l t u r e s  21.5° e i g h t  r e g r e s s i o n .  are  These  to  o f  y  mean  (3)  x  mean  (4) Ixy  2y  2  (7)  Id .  A f t e r  IBM  20.5°  1130  the  are  of  been  area) and p r o c e s s e d  r e g r e s s i o n  ( i e . are  t e m p e r c u l t u r e  LREG  have  a l l  the  g r o u p e d ,  D u r i n g  o f  d a t a  t h i s  p r i n t e d  l i n e s  l i n e s a l l  t h o s e  g r o u p i n g out  from  p o i n t s  time square  r o o t  (X  o f  (£Y)1  [(SX)  a r e a  /n  X) /n 2  (%Y) /n 2  CE xy)  2  x y  (8) T  r o o t  from  a r e :  (2)  (6)  at  c u l t u r e  square  e a c h ,  i n f o r m a t i o n  number  2  f o r  d a t a  t h a t  c u l t u r e s  e t c . ) .  n  ^x  and  the  f o r  t e m p e r a t u r e  grown  (1)  (5)  the  The  d a t a  s t a n d a r d  a l l  grouped  p i e c e s  (time  o b t a i n e d  r e s p e c t  program  t i m e - a r e a  the  A f t e r  the  s e p a r a t e l y .  l i n e  u s i n g  o f  2  /  x  2  t e m p e r a t u r e a l l  o f  the  r e g r e s s i o n s  f o r  any  p a r t i c u l a r  each  177  temperature  h a v e b e e n c a l c u l a t e d a mean r e g r e s s i o n  calculated. Four  This  i s accomplished  i n t h e f o l l o w i n g manner:  q u a n t i t i e s a r e summed:  2 2  C"cr  2 _ 7 2  <csr 2  2% Y X  c -  temperature  2  = (^xy^  where k i s t h e t o t a l  slope  being  c2 < - 2  ^ c2 ^-  ^-2  _  k  + C§:xy)  2  2  k  ...  CSxy)  number o f r e g r e s s i o n  considered.  With  this  k  lines  f o r the  information  a mean  c a n be c a l c u l a t e d .  _ IdEiiY—  b  SSx  w h e r e b i s t h e mean s l o p e . established  2  A 5% confidence  limit  c a n a l s o be  around b. S  S so  line i s  2  yx  2  b  = %Zd2  yx  = S  /%%x  2  yx  /Zn  - k - 1  2  that: b  " b "  where n i s t h e t o t a l total  S  t  ( S n - k - 1 ) , CX = .05  number o f r e g r e s s i o n  number o f r e g r e s s i o n  lines  points  incorporated  and k i s t h e  t o produce t h e  178  mean r e g r e s s i o n l i n e . space by c a l c u l a t i n g  T h i s mean r e g r e s s i o n l i n e i s p l a c e d i n the mean x and y v a l u e s  so t h a t  k = !>,  V k  i =l  mean x  k =  x./k i =l  mean y  When a l l o f t h e r e g r e s s i o n l i n e s have been grouped and  t h e i r mean r e g r e s s i o n l i n e s c a l c u l a t e d  is called  and each s e t o f l i n e s  plotted.  The p l o t t e r  confidence  t h e i r mean l i n e i s  l i m i t around the mean s l o p e f o r every  index.  routine  a l s o w r i t e s t h e mean s l o p e and t h e 5 %  T h i s s l o p e and 5 % c o n f i d e n c e the growth  along with  the p l o t t e r  interval  temperature.  can then be used as  PAGE / /  1  MCQUEEN  179 MCQUEEN  J O B  LOG D R I V E OOOO V2 MO 6  CART S P E C 0001 ACTUAL  8K  CART A V A I L 0001 CONFIG  PHY D R I V E 0000  8I<  // FOR •ONE WORD I N T E G E R S • L I S T SOURCE PROGRAM •IOCS (CARD. 1132 PRINTER) REAL K DIMENSION G ( 2 0 ) . G D ( 2 0 ) » T ( 2 0 ) , S S Q ( 2 0 ) . Q ( 2 0 ) . T O ( 2 0 ) TL = TH = KK = JJ = I I = READ ( 2 . 5 1 ) (GD< I) >T( I) . 1 = 1 . I I ) 51 FORMAT ( 2 F 1 0 . 5 ) READ(2.200)(TO(J).J=1.JJ) 200 FORMAT ( F 1 0 . 5 ) READ(2.201)(Q(L).L=1.LL) 201 FORMAT(F10.5) DO 2 0 3 J = l . J J A = ( A L O G ( T H - T L ) ) • ( T H - T O ( J ) ) - (TH) + ( TL ) B = ( A L O G ( T H - T O ( J ) ) ) • ( T H - T O ( J ) J - (TH) + ( T O I J I ) DO 2 0 4 L = 1 » L L K=Q(L)/(B-A) C= - A # { Q ( L ) / ( B - A ) ) DO 205 1 = 1 » I I Gd) = (ALOG(TH-T(I)))*K*(TH-TO<J))-K*TH+K*T(I)+C 20 5 CONTINUE S S Q ( l ) = (GD(1) - G ( 1 ) ) * * 2 . DO 2 0 6 I = 2 . 1 1 S S Q ( I ) =SSQ ( I - 1 ) + ( G D ( I ) - G ( I ) ) * * 2 • 206 CONTINUE 1 WRITE ( 3 . 5 ) TO(J) 5 FORMAT ( 4 H 0 T O = . F 1 0 . 5 ) WRITE ( 3 . 2 0 9 ! Q ( L ) 209 FORMAT ( I X » 5 H Q ( I ) = » F 1 0 • 5 ) WRITE ( 3 . 1 0 0 J K 100 FORMAT(3H K = . F 1 0 „ 5 ) WRITE ( 3 . 1 0 D C 101 FORMAT(3H C = . F 1 0 . 5 ) WRITE ( 3 . 1 0 2 ) 102 F O R M A T ( 3 6H T GD G SSQ) WRITE (3 . 1 0 3 ) ( T ( I ) . G D ( I ) . G ( I ) . S S Q ( I ) ,1 = 1 . 1 1 ) 103 FORMAT(4F10.5) 204 CONTINUE 203 CONTINUE 30 CALL EXIT END  180  PROGRAM I V - CURVE F I T T I N G  Program I V f i t s data.  T h i s problem  (  T Q  before  by t h e f a c t  the equation  t h a t two  c a n be f i t .  These  (Gmax) a n d t h e optimum  ) a t w h i c h Gmax o c c u r s .  solution  t o the equation  = T^ and G = 0.0 i n e q u a t i o n  0.0  =  where T  H  log |T  and T  -  H  T  Gmax = l o g | T 3  T  q  a n d Gmax  determine  There  u  may be  ) - K«T  - T ( ' K ( T - T  O  H  ) — K - T „  O  data.  equation  problem  the curve  A l l the reasonable  were c a l c u l a t e d ,  + C o  for T  o  ( K , C) s o a  and Gmax a r e unknown,  was f i t t e d  and c a l c u l a t e d  The  pair  fit  ( s m a l l e s t sum o f s q u a r e d  i t e r a t i v e l y to  Gmax and T v a l u e s were o  a n d Gmax v a l u e s  tried, 7  values o f G at every  a n d t h e sum o f t h e s q u a r e d  between t h e observed Q  + K»T  H  ( 3 c ) was s o l v e d f o r e a c h p a i r ,  of T  + C  found.  overcome t h i s  the  + K * T ^  and two unknowns  However, t h e b e s t v a l u e s ' To  H  I t i s a l s o known t h a t g = gmax  a r e now two e q u a t i o n s  solution  by s e t t i n g  ( 3 c ) so t h a t :  - T  H  c a n be found  ( 2 c ) may a l s o be w r i t t e n :  H  1  |• K (T  a r e known.  L  when T = T so t h a t o  T  index  a n d C. One  T  (3c) t o t h e growth  t h e maximum g r o w t h o f t h e c o l o n y  temperature K  equation  i s complicated  unknowns must b e f o u n d are  ( E q u a t i o n 3c)  values  deviations  o f G was c a l c u l a t e d ,  which y i e l d e d  d e v i a t i o n s ) was  the curve used.  o f best  PAGE //  1  LOG D R I V E 0000 V2  181  JOB  MO6  CART SPEC 0001 ACTUAL  8K  CART A V A I L 0001 CONFIG  PHY  DRIVE  0000  8K  // FOR * L I S T SOURCE PROGRAM *ONE WORD I N T E G E R S *IOCS ( C A R D , 1 1 3 2 P R I N T E R ) REAL KON DIMENSION T ( 3 0 ) , Q ( 3 0 ) , T T ( 3 0 ) , T O ( 3 0 ) , S Q ( 3 0 ) , A C T ( 3 0 ) , G M A X ( 4 0 ) , 1 GRO(40) TL = TH = LL = KK = JJ = I I = READ(2,1000) ( T ( I ) , Q ( I ) , 1=1,11) 1000 FORMA T ( 2 F 1 0 »5 ) R E A D ( 2 , 2 0 0 0 ) ( T O ( J ) ,J = 1 , J J ) 2000 FORMAT(F10.5 ) R E A D ( 2 , 3 0 0 0 ) (GMAX(K),K=1»KK) 3000 FORMAT(F10.5 ) READ(2,4000) (TT(L),ACT(L),L=1,LL) 4000 FORMAT(2F10. 5 J DO 1 I = 1 , 1 T A = ( - . 5 * A L O GJ.( ( - 1 . 0 ) * T ( I ) * * 2 « 0 + T ( I ) * { T H + T L ) - Th'*Tl_))1 (((TH+TL)/2.0)*(1.0/(TH-TL)) * 1 ( A L O G ( A B S < T ! I) - T H ) / ( T ! I ) - T L ) ) ) ) B = (((1.0)/(TH-TL))»ALOG(ABS(T(I)-TH)/(T(I)-TL))) DO 2 J = 1 , J J D = (-.5*ALOG< ( - 1 . 0 ) * T 0 ( J ) * * 2 . 0 + T O ( J ) * ( T H + TL) - T H * T L ) ) 1 (((TH+TL)/2.0)*((1.0)/(TH-TL))* 1 (ALOG(ABS(TO(J)-TH)/(TO(J)-TD))) E = . ( ( 1 . 0 )/(TH-TL) ) * ( A L O G ( A B S ( T O ( J ) - T H ) / ( T O ( J ) - T L ) ) ) DO 3 K = 1 , K K KON = ( Q ( I ) -GMAX(K))/(-A-B*TO(J)+D+E*TO(J)) CON = ( G M A X ( K ) + ( ( Q ( I ) - G M A X ( K ) ) * ( D + E ^ T O ( J ) ) ) / 1 (-A-B*TO(J)+D+E*TO<J))) WRITE(3,200)T(I),Q(I) 200 FORMAT( • TEMP OF P O I N T USED IS * F 1 0 . 5 • AND POINT I S F10.5) WRITE(3,300) TO(J) 300 FORMAT( • TEMP OPTIMUM IS ' F 1 0 . 5 ) W R I T E ( 3 , 4 0 0 ) GMAX(K) 400 FORMAT( GRO MAX I S ' F 1 0 . 5 1 W R I T E ( 3 , 5 0 0 ) KON 500 FORMAT! K IS F10.5) W R I T E ( 3 , 6 0 0 ) CON 60 0 FORMAT( C IS ' F 1 0 . 5 ) WRITE ( 3 , 7 0 0 ) 70 0 FORMAT( TEMP GRO PRE GRO ACT SUMSQ ) SUMSQ = 0 . 0 DO 4 L = 1 , L L 1  1  1  1  1  1  1  PAGE  100 4 3 2 1  2  182  G R O ( L ) =-KON*( ( - . 5 ) * A L O G ( ( - 1 . 0 ) * T T ( L ) * * 2 . 0 + ( T T ( L ) * ( T H + TL )) 1 (TH*TL))) + 1 KON*(((TH+TL)/2.0)*{(1.0)/(TH-TL!)• 1 ALOG(ABS(!TT(L)-TH)/(TT(L)-TL))))1 KON*TO(J)»((1.0)/(TH-TL)}* 1 A L O G ( A B S ( ( T T ( L J - T H ) / ( T T ( L 1 - T L ) ) ) + CON . SQ(L) = (GRO(L) - A C T ( L ) ) * * 2 . 0 SUMSQ = SUMSQ + S Q ( L ) WRITE(3»100)TT(L)»GRO(L)»ACT(L)»SUMSQ FORMAT(4F10•5) CONTINUE CONTINUE CONTINUE CONTINUE CALL EXIT " END  183  PROGRAM V - CURVE F I T T I N G  ( E q u a t i o n 4b)  P r o g r a m V was u s e d described from G  by e q u a t i o n  P. p a l l i d u m .  H  + T  (4b) t o f r u i t i n g  In equation  = -K ["(-.5) l o g  T  t o f i t curves o f the type  | (-1) T  2  (T  H  H  - T  log  L  L  j  T  H  - T  fitting  log  T.  H  + C  T - T,  L  procedure  H  T - T T  The  + T ) - T^» T ^ | ) -  T - T T  i s c o m p l i c a t e d by t h e f a c t  that  t h e r e a r e two unknowns; g r o w t h maximum  turn  determine  These f a c t o r s fitting  K and C.  There  those observed,  deviations  the curve This  in  which i n  t o u s e an i t e r a t i v e  the calculated calculating  between o b s e r v e d  that best f i t s fitting  the following  a =  Q  method u s i n g a l l t h e r e a s o n a b l e c o m b i n a t i o n s o f  values with  ing  and T  i s a l s o o n l y one e q u a t i o n .  h a v e made i t n e c e s s a r y  g r o w t h max a n d T , c o m p a r i n g  squared  data  (4b) where:  + T  L  K  body e x p a n s i o n  [(.-5 l o g j ( - l ) T  t h e sum o f t h e  and c a l c u l a t e d ,  was m a t h e m a t i c a l l y  In equation  2  rate  and choos-  the data.  procedure  manner:  expansion  + T (T  (4b)  + T ) - T  let:  -T  I") -  conducted  184  T b =  so  that  T  - T  H  L  ( 4 b ) may be w r i t t e n as G = -K»a -  Again  i n equation  d =  [(.-5 T  H  (4b) i f T = T  l o g 1 (-1) T + T  H  -  T e =  T  H  - T  K  + T  2  log L  therefore equation  T  • T • b + C o  o  (T  log L  o  - T„ H  O  L  (4c)  then:  q  L T  and  - T  H T - T,  log  R  + T ) - T  T  T = T  (4b) w i t h  L  H  T  | ) -  "H - T,  c o u l d be w r i t t e n a s : o  Gmax  UK  • d - K • T • e + C o  (4d)  where Gmax i s t h e maximum g r o w t h v a l u e w h i c h must b y d e f i n i tion  occur  at T = T „ o From t h i s  fitting Briefly, equal T  procedure  p o i n t on t h e a c t u a l mechanics o f t h e  are identical  G i n equation  to T « L  i s s e t equal  (4c) i s s e t equal  G i n equation to T .  to those  t o zero  (4d) i s s e t e q u a l  Equations  s i m u l t a n e o u s l y , ' K and C a r e f o u n d tion and  employed  ( 4 b ) , and G i s c a l c u l a t e d .  i n Program I and T i s s e t  t o Gmax and  ( 4 c ) and ( 4 d ) a r e s o l v e d and s u b s t i t u t e d  f o r every  into  equa-  t e m p e r a t u r e between T  PAGE //  MCQUEEN  1  JOB T  MCQUEEN  LOG D R I V E 0000 V2  185  M06  CART S P E C 0001 ACTUAL  8K  CART A V A I L 0001 CONFIG  1  PHY D R I V E 0000  8K  * E Q U A T ( P R N T Z »PRNTY1 // FOR •ONE WORD I N T E G E R S • L I S T SOURCE PROGRAM SUBROUTINE DLAG(T»T0»TL»TH»K>C>DL) REAL K I F ( T - 9 . 0 ) 20,20,21 20 DL = 9 9 9 9 . 0 0 GO TO 24 21 IF(T-27.) 22.22,23 23 DL = 9 9 9 9 . 0 0 GO TO 24 22 DL = K * U - i 5 ) * A L O G ( ( - 1 . 0 ) * T * * 2 i O + ( T * ( T H + T L ) ) - ( T H * T L ) ) ) 1 K * ( ( (TH + T L ) / 2 . 0 ) * ( (1o 0 ) / ( T H - T L ) ) * 1 A L O G ( A B S ( ( T - T H ) / ( T - T L ) )) ) + 1 K*T0*((1.0)/(TH-TL))* 1 ALOG(ABS((T-TH)/(T-TL)))+C 24 RETURN END F E A T U R E S SUPPORTED ONE WORD I N T E G E R S " CORE REQUIREMENTS FOR DLAG COMMON 0 VARIABLES END  OF  34  PROGRAM  2 20  COMPILATION  // DUP •STORE CART  ID 0 0 0 1  WS  UA  DLAG  DB ADDR  5361  DB CNT  0012  // FOR •ONE WORD I N T E G E R S • L I S T SOURCE PROGRAM SUBROUTINE PLAG (T,TO»TL,TH•K,C»PL) REAL K I F ( T - 1 8 . ) 30,30,31 30 PL = 9 9 9 9 . 0 0 GO TO 34 31 I F I T - 3 7 . ) 32,32,33 33 PL = 9999.00 GO TO 34 32 P L = K*{ ( - . 5 ) * A L 0 G { ( - 1 . 0 ) * T * * 2 * 0 + ( T * ( T H + T L ) ) - ( T H * T L ) ) ) 1 K*( ( ( T H + T L ) / 2 . 0 ) • ( ( 1 . 0 ) / ( T H - T L ) )* 1 ALOG(ABS( ( T - T H ) / ( T - T L ) ) ) ) + 1 K*T0*((1.0)/(TH-TL))*  PAGE  2 1  34  MCQUEEN  186  A L O G ( A B S ( (T-TH) / ( T - T L ) ) )+C RETURN END  F E A T U R E S SUPPORTED ONE WORD I N T E G E R S CORE REQUIREMENTS FOR P L A G COMMON 0 VARIABLES  34  PROGRAM  220  END OF C O M P I L A T I O N //  DUP  •STORE CARJ  ID  WS 0001  UA  PLAG  DB ADDR  5373  DB CNT  0012  / / FOR •ONE WORD I N T E G E R S • L I S T SOURCE PROGRAM S U B R O U T I N E PFGRO( T» TO»TL»TH•K>C»PG) REAL K IFCT-18.J40.40.41 40 PG = 0 . 0 GO TO 44 41 IF(T-37.)42.42.43 43 PG = 0 . 0 GO TO 44 42 PG =-<*{ { - . 5 ) * A L O G { ( - 1 . 0 ) * T * * 2 . 0 + ( T * ( T H + T L ) ) - ( T H * T L ) ) ) + 1 K*( U T H + T L ) / 2 . 0 ) * ( ( 1 . 0 ) / ( T H - T L ) ) * 1 A L O G ( A B S ( ( T - T H ) / ( T - T L ) )) ) 1 -K*TO*( ( 1 . 0 ) / ( T H - T L ) )• 1 ALOG(ABS((T-TH)/(T-TL)))+C RETURN 44 END F E A T U R E S SUPPORTED ONE WORD I N T E G E R S CORE REQUIREMENTS FOR PFGRO COMMON 0 VARIABLES  36  PROGRAM  END OF C O M P I L A T I O N //  DUP  •STORE CART ID  0001  WS  UA PFGRO DB ADDR 5385  DB CNT  0012  / / FOR •ONE WORD I N T E G E R S • L I S T SOURCE PROGRAM SUBROUTINE D G R O W ( T . T O . T L • T H . K . C . D G ) REAL K IF(T-9.0) 1.1,2 1 DG = 0 . 0  2 26  PAGE  3 MCQUEEN GO TO 5 IF(T-26.5)3.3.4 DG = 0 . 0 GO TO 5 DG = ( A L O G ( T H - T ) > * K * ( T H - T O ) - K * T H + K * T + C RETURN END  2 4 3 5  !87  F E A T U R E S SUPPORTED ONE WORD I N T E G E R S CORE REQUIREMENTS FOR DGROW COMMON 0 VARIABLES END OF //  8  PROGRAM  98  COMPILATION  DUP  •STORE CART  ID  WS 0001  UA  DGROW  DB ADDR  5397  DB CNT  0008  / / FOR * O N E WORD I N T E G E R S • L I S T SOURCE PROGRAM S U B R O U T I N E PGROW (T»TO » T L • T H • K » C » P G ) REAL K IFIT-18.) 10.10.11 10 PG = 0 . 0 GO TO 14 11 IFCT-37.) 12.12.13 13 PG = 0 . 0 GO TO 14 12 PG = ( A L O G ( T H - T ) ) * K * ( T H - T O ) - K * T H + K * T + C 14 RETURN END F E A T U R E S SUPPORTED ONE WORD I N T E G E R S CORE REQUIREMENTS FOR PGROW COMMON 0 VARIABLES END OF //  8  PROGRAM  98  COMPILATION  DUP  •STORE CART  ID  WS 0001  UA  PGROW  DB ADDR  539F  DB CNT  0008  / / FOR • IOCS ( C A R D . 1 1 3 2 P R I N T E R * T Y P E W R I T E R ) • L I S T SOURCE PROGRAM •ONE WORD I N T E G E R S C THE FOLLOWING COMMENT CARDS I D E N T I F Y C T = TEMP. C TL = T E M P . LOW C TO = T E M P . OPTIMUM  THE SYMBOLS  USED  PAGE C  C C C C C C C C C C C C C C C C C C  99 101 C C  C  C  4  MCQUEEN  TH = TEMP  HIGH  K = CONSTANT C = CONSTANT LDA = LAG FOR DD AMOEBAE GDA = GROWTH INDEX FOR DD AMOEBAE LDF = LAG FOR DD F R U I T I N G B O D I E S GDF = GROWTH INDEX FOR DD F R U I T I N G B O D I E S L P A = LAG FOR PP AMOEBAE L P F = LAG FOR PP F R U I T I N G B O D I E S GPA = GROWTH FOR PP AMOEBAE GPF = GROWTH FOR PP F R U I T I N G B O D I E S THE DATA THAT IS INPUT SO THAT THE S U B R O U T I N E S CAN F U N C T I O N IS CODED IN FOUR P A R T S . . a . . . . . T H E F I R S T L E T T E R IS L FOR LAG OR G FOR GROWTH • « . . . THE SECOND ONE OR TWO L E T T E R S ARE TO»TH» T L . K . C A L L OF WHICH HAVE B E E N I D E N T I F I E D BEFORE a * a «•T HE SECOND TO THE LAST L E T T E R IS P OR D STANDING FOR PP OR D D . . . . T H E LAST L E T T E R IS A OR F S T A N D I N G FOR AMOEBAE OR F R U I T I N G B O D Y . . . . . A N E X A M P L E . . L T H P A . . S T A N D S FOR LAG TEMPERATURE HIGH P P A M O E B A E . o T H I S IS THE T E M P . HIGH FOR THE PP AMOEBAE LAG S U B R O U T I N E REAL L T O D A . L T L D A . L T H D A . L K D A . L C D A . L D A . 1 LTODF.LTLDF.LTHDF.LKDF.LCDF.LDF. 1 LTOPA.LTLPA.LTHPA.LKPA.LCPA.LPA. 1 L T O P F . L T L P F . L T H P F . L K P F . L C P F . LPF CONTINUE READ(2.101)T FORMAT1F10.5) A L L OF THE FOLLOWING INFORMATION IS READ INTO THE S U B R O U T I N E S D . D I S C O I D E U M AMOEBAE LTODA = 2 3 . 0 LTLDA a 9 . LTHDA = 2 7 . 5 LKDA = 1 . 6 0 1 3 7 LCDA = 4 . 7 4 4 0 3 C A L L DLAG !T»LTODA»LTLDA»LTHDA»LKDA»LCDA»LDA) GTODA = 2 1 . 5 GTLDA a 9 . GTHDA = 2 7 . 5 GKDA = 0.80084 GCDA = 0.79554 C A L L DGROW (T»GTODA»GTLDA.GTHDA»GKDA,GCDA.GDA) D . D I S C O I D E U M F R U I T I N G BODY LTODF = 2 4 . LTLDF = 9. LTHDF = 2 7 . 5 LKDF = 2.47681 LCDF = 7.62542 C A L L DLAG ( T » L T O D F » L T L D F » L T H D F • L K D F » L C D F . L D F ) GTODF = 2 1 . GTLDF = 9 . GTHDF = 2 7 . 5 GKDF = 0.86318 GCDF = -0.65368 C A L L DGROW(T » G T O D F » G T L D F . G T H D F , G K D F . G C D F . G D F ) P . P A L L I D U M AMOEBAE LTOPA = 3 1 . LTLPA = 1 8 .  PAGE  C  300 309 308 310 301 C C C C  40 0 120 121 C 140 141 C 130 131  5  MCQUEEN  189 LTHPA = 3 7 . LKPA = 0.81132 LCPA = 2.59356 C A L L P L A G (T . L T O P A » L T L P A , L T H P A * L K P A » L C P A » L P A ) GTOPA = 3 1 . GTLPA = 1 8 . GTHPA = 4 1 . GKPA = 1 . 6 2 7 0 9 GCPA = - 1 3 . 5 9 4 2 3 C A L L PGROW (T»GTOPA»GTLPA,GTHPA»GKPA»GCPA»GPA) P . P A L L I D U M F R U I T I N G BODY LTOPF = 3 0 . LTLPF = 1 8 . LTHPF = 3 7 . LKPF = 1.28527 LCPF = 3.76145 CALL PLAG (T.LTOPF.LTLPF.LTHPF.LKPF.LCPF.LPF) GTOPF = 3 1 . GTLPF = 1 8 . GTHPF = 3 7 . 5 GKPF = 0 . 7 8 1 7 2 GCPF = 0 . 9 7 5 5 2 CALL PFGROIT .GTOPF»GTLPF,GTHPF»GKPF»GCPF»GPF) W R I T E ( 3 . 3 0 0 )T FORMAT( • TEMPERATURE = ' F 1 0 . 5 ) W R I T E ( 3 . 3 0 9) FORMAT( LDA GDA LDF GDF L PA 1GPA LPF GPF ') WRITE(3 .30 8 ) LDA,GDA.LDF.GDF»LPA.GPA»LPF.GPF FORMAT(8F10 .2 ) WRITE ( 3 . 3 1 0 ) FORMAT(1H0) WRITE!3.301) FORMAT( TIME DDA DDF PPA PPF • ) IN THE FOLLOWING AREA C A L C U L A T I O N S ARE M A D E . . . . . AREAS ARE C A L C U L A T E D FOR DD A M O E B A E . PP A M O E B A E . DD F R U I T I N G BODIES. AND PP F R U I T I N G BODIES. DO 1 0 0 0 I = 1 . 5 0 . 1  1  D.DISCOIDEUM  AMOEBAE  DATIM = I*.1 -LDA IF(DATIM ) 120.120.121 DATIM = 0,0 ADA = ( GDA*DATIM ADA = A D A * 6 . 4 5 1 6 P . P A L L I D U M AMOEBAE PATIM = I*.l - LPA I F(PATIM ) 140. 140.141 PATIM = 0,0 APA = ( GPA*PATIM APA = A P A * 6 . 4 5 1 6 D . D I S C O I D E U M F R U I T I N G BODY DFTIM = I*.l - LDF IFlDFTIM ) 130.130.131 DFTIM = 0,0 ADF = ( GDF*DFTIM ADF = A D F * 6 . 4 5 1 6  +2.0)**2.  + 2.01**2.  )**2.  PAGE C 150 151  302 1000 303 98  6  MCQUEEN  P . P A L L I D U M F R U I T I N G BODY PFTIM = - LPF IF(PFTIM ) 1 5 0 , 150 . 151 PFTIM = 0.0 APF = ( GPF*PFTIM APF = A P F * 6 . 4 - 5 1 6 TI ME= I * . l WRITE(3,30 2)TIME,ADA.ADF.APA.APF FORMAT(F5.2.4F10.2) CONTINUE W R I T E ( 3 , 3 0 3) FORMAT(1H11 IF(T-38.) 99,99,98 CALL EXIT END  190  )**2«  191  PROGRAM V I - EXPLOITATION OF SINGLE  P r o g r a m V I was u s e d by  amoebae a n d f r u i t i n g  time. but  did notinteract The  routines,  to calculate  bodies  B o t h D. d i s c o i d e u m  SPECIES  a t any t e m p e r a t u r e  occupied  and a t a n y  a n d P. p a l l i d u m were r u n t o g e t h e r  i n any way.  program i s broken i n t o  (2) d a t a  t h e area  input,  f o u r p o r t i o n s : (1) sub-  (3)c a l c u l a t i o n s  and (4) o u t p u t .  SUBROUTINES: There the D.  spore  arefive  germination  discoideum.  subroutines:  l a g and t h e f r u i t i n g  Equation  (2b)  27.0°C t h e l a g i s s e t equal the P.  spore  germination  pallidum.  £•  Equation  (2b)  i s used.  Equation  37.5°C t h e e x p a n s i o n  (4b)  ( 2 ) PLAG:  to infinity.  ( 3 ) PFGRO:  Below  rate i s set equal  Equation  f o r D. (3b)  0.0.  ( 5 ) PGROW: c a l c u l a t e s  for  P. p a l l i d u m amoebae.  and  above  37.5°C  theexpansion  ( 4 ) DGROW: discoideum  i sused. i s set  therate o f colony  Equation  (4b)  for  18.0°C and above  t o 0.0.  9.0°C and above 27.0°C t h e r a t e o f e x p a n s i o n to  lag for  body c o l o n y e x p a n s i o n  i sused.  bodies.  body  calculates  Below 1 8 . 0 ° C and a b o v e  t h er a t e o f colony expansion  amoebae a n d f r u i t i n g  lag for  B e l o w 9.0°C a n d above  to i n f i n i t y .  therate o f f r u i t i n g  pallidum.  calculates  i sused.  calculates  body  l a g and t h e f r u i t i n g  37.5°C t h e l a g i s s e t e q u a l calculates  ( 1 ) DLAG:  i sused.  rate i s set equal  Below equal  expansion Below  18.0°C  t o 0.0.  192  DATA  INPUT: Data i s i n p u t f o r e i g h t  amoebae  l a g , (2) D. d i s c o i d e u m  (3) Do d i s c o i d e u m ing  (8)  body  parameters. temperature explained  These  body e x p a n s i o n .  optimum, K, and C.  fruit-  l a g , (6) P. p a l l i d u m expansion,  Five  f o r the c a l c u l a t i o n  a r e : temperature  discoideum  (4) D. d i s c o i d e u m  l a g , (7) P. p a l l i d u m amoebae  a r e needed  ( 1 ) D.  body l a g ,  (5) P. p a l l i d u m amoebae  P. p a l l i d u m f r u i t i n g  information  fruiting  amoebae e x p a n s i o n ,  body e x p a n s i o n ,  fruiting  quantities:  pieces of  of these  eight  low, t e m p e r a t u r e  high,  The c o d i n g o f t h e s e d a t a i s  i n the program.  CALCULATIONS: The  a r e a o c c u p i e d by t h e f r u i t i n g  amoebae o f b o t h used  species i s calculated  i n a l l cases.  here.  bodies  and t h e  Equation  The c o n s t a n t C i n e q u a t i o n  (If)i s  (If) i sset  2 equal  t o 13 mm  f o r D. d i s c o i d e u m  because C equals For  D. d i s c o i d e u m  constant by  the i n i t i t a l  a r e a o c c u p i e d by t h e s p o r e s .  and P. p a l l i d u m f r u i t i n g 2  C. i s s e t e q u a l  the f r u i t i n g  and P. p a l l i d u m amoebae  bodies  t o 0.0 mm until  bodies the  b e c a u s e no a r e a i s o c c u p x e d  they begin t o form.  OUTPUT: Six ature,  quantities  (2) t i m e ,  amoebae a r e a ,  are output.  measured i n days,  T h e s e a r e (1) t e m p e r -  (3) DDA  = D.  discoideum  ( 4 ) PPA = P. p a l l i d u m amoebae a r e a ,  ( 5 ) DDF =  Do  discoideum  fruiting  body  f r u i t i n g body a r e a , area.  (6) P P F = P. pallidum  // JOB T  MCQUEEN  1  M 21 ABOVE RECORD NOT A SUPERVISOR CONTROL RECORD // FOR •IOCS (CARD»1132 PR INTER»TYPEWRITERJ • L I S T SOURCE PROGRAM •ONE WORD INTEGERS REAL LTODA»LTLDA»LTHDA,LKDA,LCDA»LDA» 1 LTODF.LTLDF.LTHDF.LKDF.LCDF.LDF. 1 LTOPA.LTLPA . LTHPA»LKPA.LCPA»LPA» 1 LTOPF.LTLPF»LTHPF.LKPF.LCPF» LPF c THE FOLLOWING COMMENT CARDS IDENTIFY THE SYMBOLS USED c T = TEMP. c TL = TEMP. LOW c TO = TEMP. OPTIMUM c TH = TEMP HIGH c K = CONSTANT c C = CONSTANT LDA = LAG FOR DD AMOEBAE c c GDA = GROWTH INDEX FOR DD AMOEBAE c LDF = LAG FOR DD FRUITING BODIES c GDF = GROWTH INDEX FOR DD FRUITING BODIES LPA = LAG FOR PP AMOEBAE c c LPF = LAG FOR PP FRUITING BODIES GPA = GROWTH FOR PP AMOEBAE c r GPF = GROWTH FOR PP FRUITING BODIES THE DATA THAT IS INPUT SO THAT THE SUBROUTINES CAN FUNCTION c c c c c c c c  99 101 C C  c  THE SECOND ONE OR TWO LETTERS ARE TO.TH. OR G FOR GROWTH TL»K»C ALL OF WHICH HAVE BEEN IDENTIFIED BEFORE THE SECOND THE LAST LETTER IS P OR D STANDING FOR PP OR DD.... THE LAST LETTER IS A OR F STANDING FOR AMOEBAE OR FRUITING BODY...*oAN EXAMPLE..LTHPA..STANDS FOR LAG TEMPERATURE HIGH PP AMOEBAE.. THIS IS THE TEMP. HIGH FOR THE PP AMOEBAE LAG SUBROUTINE CONTINUE READ(2 »101 )T FORMAT(F10.5) ALL OF THE FOLLOWING INFORMATION IS READ INTO THE SUBROUTINES D.DISCOIDEUM AMOEBAE LTODA = 23.0 LTLDA = 9. LTHDA = 27.5 LKDA = 1.60137 LCDA s 4,74403 CALL DLAG (T »LTODA.LTLDA»LTHDA»LKDA.LCDA*LDA) GTODA = 21.5 GTLDA = 9. GTHDA = 27.5 GKDA = 0.80084 GCDA ». 0.79554 CALL DGROW (T .GTODA.GTLDA.GTHDA.GKDA.GCDA,GDA) D.DISCOIDEUM FRUITING BODY LTODF = 2 4 . LTLDF = 9. LTHDF = 27.5 LKDF = 2.47681  PAGE  C  C  300 309 30 8 310 301 C C C  C  2  MCQUEEN  LCDF = 7*62542 C A L L DLAG ( T » L T O D F , L T L D F » L T H D F » L K D F » L C D F > L D F ) GTODF = 2 1 . GTLDF = 9 . GTHDF = 2 7 . 5 GKDF = 0.86318 GCDF = -0.65368 C A L L DGROW<T .GTODF»GTLDF.GTHDF.GKDF,GCDF•GDF) P . P A L L I D U M AMOEBAE LTOPA = 3 1 . LTLPA = 1 8 . LTHPA = 3 7 . LKPA = 0.81132 LCPA = 2.59356 CALL PLAG (T.LTOPA.LTLPA.LTHPA.LKPA.LCPA.LPA) GTOPA = 3 1 . GTLPA = 1 8 . GTHPA = 4 1 . GKPA = 1 . 6 2 7 0 9 GCPA = - 1 3 . 5 9 4 2 3 C A L L PGROW (T.GTOPA.GTLPA.GTHPA.GKPA.GCPA.GPA) P . P A L L I D U M F R U I T I N G BODY LTOPF = 3 0 . LTLPF = 1 8 . LTHPF = 3 7 . LKPF = 1.28527 LCPF = 3.76145 CALL PLAG (T.LTOPF,LTLPF,LTHPF,LKPF>LCPF•LPF) GTOPF = 3 1 . GTLPF = 1 8 . GTHPF = 3 7 . 5 GKPF = 0 . 7 8 1 7 2 GCPF = 0 . 9 7 5 5 2 CALL PFGRO(T ,GTOPF,GTLPF,GTHPF,GKPF,GCPF,GPF) WRITE(3,300)T FORMAT( ' TEMPERATURE = ' F 1 0 . 5 ) WRITE(3,309) FORMAT( LDA GDA LDF GDF LPA 1GPA LPF GPF •) WRITE(3 ,30 8 ) L D A , G D A . L D F , G D F , L P A , G P A , L P F , G P F FORMAT(8F10.2) WRITE ( 3 , 3 1 0 ) FORMAT(1H0) WRITE(3,301 ) FORMAT( TIME DDA DDF PPA PPF SUMA 1 SUMF ') IN THE FOLLOWING AREA C A L C U L A T I O N S ARE M A D E . . . . . AREAS ARE C A L C U L A T E D FOR DD A M O E B A E , PP A M O E B A E , DD F R U I T I N G B O D I E S , AND PP F R U I T I N G B O D I E S . SUMA = 0 . 0 SUMF = 0 . 0 APF = 0 . 0 ADF = 0 . 0 DO 1 0 0 0 I = 1 , 5 0 IF(SUMF-1935.) 400,400,401 D.DISCOIDEUM AMOEBAE 1  1  195  PAGE 400 120 121 C 140 141 401 500 C 503 150 151 C 504 510 130 131 501 302 1000 303 98  3  MCQUEEN  DATIM = I*.l -LDA IF(DATIM ) 120,120*121 DATIM =0.0 ADA = ( GDA*DATIM +2.0)**2. ADA = A D A * 6 . 4 5 1 6 P . P A L L I D U M AMOEBAE PATIM = I*.l - LPA IF(PATIM ) 140,140,141 PATIM = 0.0 APA = ( GPA*PAT-IM + 2-0)**2. APA = A P A * 6 . 4 5 1 6 SUMA = ADA+APA IF(SUMF-19 3 5 . ) 5 0 0 , 5 0 0,501 CONTINUE P . P A L L I D U M F R U I T I N G BODY IF(APF-40.) 503,503,504 CONTINUE PFTIM ' = LPF IF(PFTIM ) 150,150,151 PFTIM = 0.0 APF = ( GPF*PFTIM )**2. APF = A P F * 6 . 4 5 1 6 D . D I S C O I D E U M F R U I T I N G BODY CONTINUE I F (ADF - ADA) 5 1 0 , 5 1 0 , 5 0 1 CONTINUE DFTIM = - LDF IFtDFTIM ) 130,130,131 DFTIM =0.0 ADF = ( GDF*DFTIM 1**2. ADF = A D F * 6 . 4 5 1 6 SUMF = ADF + APF TIME" I**l WRITE(3,302)TIME,ADA,ADF,APA,APF,SUMA,SUMF FORMAT(F5.1,6F10.2) CONTINUE WRITE(3,303) FORMATtlHl) IFCT-38. ) 99,99,98 CALL EXIT END  1  9  6  197  PROGRAM V I I - EXPLOITATION OF MIXED S P E C I E S Program V I I s i m u l a t e s b e t w e e n D. d i s c o i d e u m conditions  and any t e m p e r a t u r e .  same as P r o g r a m V I w i t h  and  the data  been m o d i f i e d The mm  2  occupied  input.  to the subroutines  The c a l c u l a t i o n s  t o account  for  environment  and d a t a  output  used have  exploitation.  (60 mm p e t r i 2  dish)  of bacterial  b y t h e two s p e c i e s g r o w i n g monitored  laboratory  The program i s g e n e r a l l y  respect  o f s p a c e o r 1935 mm  constantly  interaction  a n d P. p a l l i d u m grown u n d e r  the  1935  the exploitation  contained  lawn.  The a r e a  simultaneously i s  b y t h e SUM f u n c t i o n .  When SUM  equals  2 1935 P.  mm  amoebae e x p a n s i o n  pallidum f r u i t i n g  occupied bodies  bodies  b y P. p a l l i d u m  are allowed  stops.  i s limited  amoebae.  t o cover  The area o c c u p i e d by to l/7th  D. d i s c o i d e u m  the remaining  area.  o f the area fruiting  PAGE //  1  MCQUEEN  JOB  LOG D R I V E 0000 V2 M06 //  MCQUEEN  CART S P E C 0001 ACTUAL  8K  CART A V A I L 0001 CONFIG  PHY D R I V E 0000  8!<  FOR  • L I S T SOURCE PROGRAM • IOCS ( C A R D , T Y P E W R I T E R , 1 1 3 2 PR I N T E R , K E Y B O A R D ) REAL N E E D ! 3 3 ) R E A L KNEED D I M E N S I O N P R O B U 0 0 ) , CUM( 100 ) , TQ ( 100 ) • R E A D ( 2 , 3 0 5 1 ) ( N E E D ( I ) ,1 = 1 , 3 3 1 30 51 FORMAT(F5.1) 4053 WRITE(1,4000) 4000 FORMAT( ' ONWARDS I S ONE • ) R E A D ( 6 , 4 0 0 i ) ON 4001 FORMAT( F 1 0 . 5 ) IF(ON)4002,4002,4003 4003 WRITE(1,4020) 4020 FORMAT( » TEMP = ' ) READ(6,4021) T 4021 F O R M A T ( F 5 . 1) WRITE(1,4004) 4004 FORMAT( • SPORE NUMBER IS • ) R E A D ( 6 , 4 0 0 5 ) SNUM 4005 FORMAT(F10•5) AREA = 1 0 0 . X = SNUM/AREA . WRITE{3,4022) T 4022 FORMAT( TEMPERATURE IS 'F5.D WRITE(3,4006) X 4006 FORMAT( ' MEAN SPORE NUMBER IS ' F 1 0 . 5 ) W R I T E ( 3 , 4 0 0 7 ) SNUM 4007 FORMAT( TOTAL NUMBER PER P L A T E IS ' F 1 0 . 5 ) W R I T E ( 3 , 4 0 0 8 ) AREA 4008 FORMAT! •• NUMBER OF AREA U N I T S IS ' F 1 0 . 5 ) PZERO = E X P ! ( - X ) ) DO 4 0 1 8 K = 1 , 1 0 0 IF (K-1) 4010,4010,4011 4010 TQ ( 1 ) = X GO TO 4 0 1 2 4011 TQ(K) = ( X / K ) * T Q ( K - 1 ) 4012 CONTINUE PROB(K) = E X P ( - X ) * T Q ( K ) IF(K-l) 4013,4013,4014 4013 C U M ( l ) = PZERO + P R O B ( l ) GO TO 4 0 1 5 4014 CUM(K) = CUM(K-1) + PROB(K) 4015 CONTINUE SQNUM = C U M ( K ) • AREA S Q L E F = AREA - SQNUM IF(1.0-SQLEF) 4016,4016,4017 4016 CONTINUE 4018 CONTINUE 1  1  198  PAGE 4017 4030 3052 3053 3055 3054 3081 3056 4050 4052 4051 4054 4019 4002  2  MCQUEEN  AVAIL = K WRITE(3,4030) AVAIL FORMAT( ' NUMBER OF PP SPORES A V A I L A B L E I F U - 2 1 .7) 3052 , 3 0 5 2 *3053 KNEED = 1 0 0 0 . GO TO 3 0 8 1 IF(T-25.) 3054,3054,3055 KNEED = 1. GO TO 3 0 8 1 Z=(T-21.7)*10. I = Z KNEED = N E E D ( I ) CONTINUE WRITE(3,3056) KNEED FORMAT( ' KNEED = ' F 7 . 1 ) IF(KNEED - AVAIL) 4 0 5 0 , 4 0 5 1 , 4 0 5 1 CONTINUE WRITE(3,4052) FORMAT! ' P P WILL GROW ' ) GO TO 4 0 5 3 CONTINUE W R I T E ( 3 , 4 0 5 4) FORMAT( PP WILL NOOOOOOOOOOT GROW ' ) WRITE ( 3 , 4 0 1 9 ) FORMAT*1H1) GO TO 4 0 5 3 CALL EXIT END 1  199  = '  F5.1)  200  PROGRAM V I I I  - I N H I B I T I O N OF  Program V I I I £•  pallidum  of  two  fruiting  size  and  clump  necessary  size,  AVAILABLE  CLUMP  two  an  agar  discoideum  at  The  size, any  any  which c a l c u l a t e s  given  spore the  calculations  of  During  available  the  clump  experimental  concentration; clump  size  P.  pallidum  discoideum  spores,  were a b l e  size  are  work i t spores  s u r f a c e c o n t a i n i n g a known number o f D.  the  temperature.  t h a t a s m a l l number o f  distributed  of  p r o g r a m i s composed  which c a l c u l a t e s  at  inhibition  SIZE  assumptions.  observed  clump  available  for fruiting  on  D.  body f o r m a t i o n .  necessary  The  PALLIDUM  simulates  sections; available  maximum c l u m p  P.  based  was  placed  on  randomly to c o n t r o l  the  2 use  of food,  surrounding influence 60  mm  f o r at least their  dish.  dish  c o u l d be  also  assumed  a petri  spores  at  II  total  i t was  This  area  sphere  of  surface area of  assumed  spheres  19 mm  of  were s p r e a d  that a  petri  influence. on  the  a  It  surface  (methods s e c t i o n ) t h a t  was of  they  random. distribution  i n each  program c o n t i n u e s  influence  the  100  t h a t when s p o r e s  d i s h u s i n g Method  number o f  of  Therefore,  A poisson  The  l/100th  divided into  were d i s t r i b u t e d  days, i n the  point of inoculation.  i s about  petri  three  of  the  was 100  to c a l c u l a t e  used  to c a l c u l a t e  spheres the  c o n t a i n i n g v a r i o u s numbers o f  the  of influence.  number o f spores  spheres  until  of  a l l of  201  the  spheres  o f i n f l u e n c e have been used  maximum number o f s p o r e s This  quantity i s called  NEEDED CLUMP  data i n p u t from fruiting  In this  of influence  t h e maximum clump  way t h e  i s found.  size.  SIZE  The n e c e s s a r y  for  p e r sphere  up=  clump  size  i s calculated  F i g u r e 26, o n w h i c h t h e clump  i s plotted  against  by r e a d i n g  size  necessary  temperature.  COMPARISON When t h e t e m p e r a t u r e s p o r e s have been r e a d necessary  clump  a r e compared £•  size  into  t h e c o m p u t e r t h e a v a i l a b l e and  c a n be c a l c u l a t e d .  and i f a v a i l a b l e  pallidum f r u i t i n g  and t h e number o f P. p a l l i d u m  i s larger  takes place.  T h e two q u a n t i t i e s than  necessary  then  PAGE //  1  MCQUEEN  202  JOB T  LOG D R I V E 0000 V2 M06  MCQUEEN CART S P E C 0001 ACTUAL  8K  CART A V A I L 0001 CONFIG  1  PHY D R I V E 0000  8K  •EQUAT(PRNTZ.PRNTY) / / FOR •ONE WORD I N T E G E R S • L I S T SOURCE PROGRAM SUBROUTINE DLAG(T»T0»TL»TH»K.C.DL) REAL K IF(T-9.0) 20.20.21 20 DL = 9 9 9 9 . 0 0 GO TO 24 21 IF(T-27.) 22.22,23 23 DL = 9 9 9 9 . 0 0 GO TO 24 22 DL = K * ( ( - . 5 ) * A L O G ( ( - 1 . 0 ) * T * * 2 . 0 + ( T * ( T H + T L ) ) - ( T H * T L ) ) ) 1 K*U (TH+TL)/2.0)*((1.0)/(TH-TL))• 1 ALOG(ABS((T-TH)/(T-TL)))) + 1 K*TO*((1.0)/(TH-TL))• 1 ALOG(ABS((T-TH)/(T-TL)))+C 24 RETURN END F E A T U R E S SUPPORTED ONE WORD I N T E G E R S CORE REQUIREMENTS FOR DLAG COMMON 0 VARIABLES END OF C O M P I L A T I O N  34  PROGRAM  2 20  203  / / DUP •STORE CART  WS  ID 0 0 0 1  UA  DLAG  DB ADDR  5361  DB CNT  0012  / / FOR •ONE WORD I N T E G E R S • L I S T SOURCE PROGRAM SUBROUTINE PLAG (T»TO»TL»TH•K«C«PL) REAL K IF(T-18.) 30.30.31 30 PL = 9 9 9 9 . 0 0 GO TO 34 31 I F ( T - 3 7 . ) 32 .32 . 3 3 33 PL = 9 9 9 9 . 0 0 GO TO 34 32 PL = K * ( l - . 5 ) * A L O G ( ( - 1 . 0 ) * T * * 2 . 0 + ( T * ( T H + T L ) ) - t T H * T L ) ) ) - . 1 K*t ( (TH + T L ) / 2 . 0 ) • ( ( 1 . 0 ) / ( T H - T L ) ) • 1 ALOG(ABS((T-TH)/(T-TL)))) + 1 K*TO*((l.O)Z(TH-TL))* 34  1  ALOG(ABS((T-TH)/(T-TL)))+C RETURN END  204  F E A T U R E S SUPPORTED ONE WORD I N T E G E R S CORE REQUIREMENTS FOR P L A G COMMON 0 VARIABLES  34  PROGRAM  2 20  END OF C O M P I L A T I O N //  DUP  •STORE  CART  WS  ID 0 0 0 1  UA  PLAG  DB ADDR  5373  DB CNT  0012  / / FOR •ONE WORD I N T E G E R S • L I S T SOURCE PROGRAM SUBROUTINE PFGRO(T»TO»TL»TH>K,C.PG) REAL K IF(T-18«)40,40,41 40 PG = 0 . 0 GO TO 44 41 I F I T - 3 7 . )42 , 4 2 , 4 3 43 . PG = 0 . 0 GO TO 44 42 PG = - K * ( ( - . 5 ) * A L O G { ( - 1 . 0 ) * T * * 2 .0 + ( T * ( TH+TL ) ) - ( TH*TL> )) + 1 <•(((TH+TL)/2.0)*<<1.0)/(TH-TL))* 1 AL0G(A3S((T-TH)/(T-TL)))) 1 - K * T O * ( ( 1 . 0 ) / ( T H - T L ) )• 1 ALOG(ABS((T-TH)/(T-TL)))+C 44 RETURN END  205  FEATURES SUPPORTED ONE WORD I N T E G E R S CORE REQUIREMENTS FOR PFGRO COMMON 0 VARIABLES  36  PROGRAM  END OF C O M P I L A T I O N //  DUP  •STORE  CART  ID  WS  0001  UA  PFGRO  DB ADDR  5385  DB CNT  0012  / / FOR •ONE WORD I N T E G E R S • L I S T SOURCE PROGRAM S U B R O U T I N E DGROW ( T » TO » TL » TH »i< » C • DG ) REAL K IFIT-9.0) 1,1,2 1 DG = 0 . 0 GO TO 5 2 IF(T-26.0)3,3,4 4 DG = 0 . 0 GO TO 5 3 DG = ( A L O G ( T H - T ) ) * K * < T H - T O } - K * T H + K * T + C 5 RETURN END  2 26  206  F E A T U R E S SUPPORTED ONE WORD I N T E G E R S CORE REQUIREMENTS FOR DGROW COMMON 0 VARIABLES  8  PROGRAM  END OF C O M P I L A T I O N //  DUP  •STORE  CART  ID  WS  0001  UA  DGROW  . DB ADDR  5397  DB CNT  0008  / / FOR •ONE WORD I N T E G E R S • L I S T SOURCE PROGRAM S U B R O U T I N E PGROW (T»TO»TL»TH»K»C»PG> REAL K IF(T-18.) 10,10,11 10 PG = 0 . 0 GO TO 14 11 IF(T-37.) 12,12,13 13 PG = 0 . 0 GO TO 14 12 PG = ( A L O G ( T H - T ) ) * K * { T H - T O ) - K * T H + K * T + C 14 RETURN END  98  207  FEATURES SUPPORTED ONE WORD INTEGERS CORE REQUIREMENTS FOR PGROW COMMON 0 VARIABLES  8  PROGRAM  98  END OF COMPILATION // DUP •STORE  CART  WS  ID 0001  UA  PGROW  DB ADDR  539F  DB CNT  0008  // FOR •ONE WORD INTEGERS • L I S T SOURCE PROGRAM SUBROUTINE DDFRU(DDCON,T,QUIT»DFRU,TQUIT) DIMENSION DFRUI 1) IF(DDCON - 2000e ) 1,2,2 1 R = (DDCON - 100. )/100. I =R TQUIT = DFRU(I) GO TO 6 2 TQUIT = 23.9 6 I F ( T - TQUIT) 3,3,4 3 QUIT = 1. GO TO 5 4 QUIT = - 1 . 5 CONTINUE RETURN END FEATURES SUPPORTED ONE WORD INTEGERS CORE REQUIREMENTS FOR DDFRU COMMON 0 VARIABLES  4  PROGRAM  80  CART  ID  0001  DB ADDR  53A7  DB CNT  0007  / / FOR • IOCS ( C A R D » T Y P E W R I T E R » 1 1 3 2 PR I NTER»KEYBOARD) • L I S T SOURCE PROGRAM •ONE WORD I N T E G E R S R E A L LTODA»LTLDA•LTHDA,LKDA » L C D A , L D A , 1 LTODF,LTLDF,LTHDF,LKDF,LCDF,LDF« 1 LTOPA,LTLPA»LTHPA,LKPA»LCPA»LPA» 1 L T O P F , L T L P F , L T H P F , L K P F , L C P F , LPF REAL N E E D ( 3 3 ) R E A L KNEED DIMENSION TIME150) , A D A ( 5 0 ) »ADF(50) , A P A ( 5 0 ) > A P F ( 5 Q ) , S U M A ( 5 0 ) » 1 SUMF(50),PROB(50),CUM(50),TQ(50),DFRU(18! R E A D ( 2 , 3 0 5 1 ) ( N E E D ( I ) ,1 = 1 , 3 3 ) 3051 FORMAT(F5.1 ) R E A D ( 2 , 8 0 4 0 ) ( D F R U ( I ) ,1 = 1 , 1 8 ) 8040  99  4000 4001 4003 4020 4021 4004 400 5 4874 48 84  4022 4006 4007 400 8  4010 4011 4012 4013 4014  FORMAT(F10.5)  CONTINUE WRITE(1,4000) FORMAT( ' ONWARDS IS ONE ) R E A D ( 6 , 4 0 0 1 ) ON F O R M A T ( F10.5) IF(ON) 9 8 , 9 8 , 4 0 0 3 WRITE(1,4020) FORMAT( ' TEMP = • ) READ(6,4021) T FORMAT(F5. 1 ) WRITE(1,4004) FORMAT( SPORE NUMBER IS ' ) R E A D ( 6 , 4 0 0 5 ) SNUM FORMAT(F10.5) WRI T E ( 1 , 4 8 7 4 ) FORMAT( • DD SPORE C O N C E N T R A T I O N R E A D ( 6 , 4 8 8 4 ) DDCON 1  1  )  1  FORMAT(F10.5)  AREA = 1 0 0 . X = SNUM/AREA WRITE(3,4022 ) T FORMAT( • TEMPERATURE IS » F 5 . 1 ) W R I T E ( 3 , 4 0 0 6) X FORMAT f ' MEAN P . P A L L I D U M SPORE NUMBER IS • F 1 0 . 5 ) W R I T E ( 3 , 4 0 0 7 ) SNUM FORMAT( ' P . P A L L SPORE NUMBER PER P L A T E IS ' F 1 0 . 5 ) W R I T E ( 3 , 4 0 0 8 ) AREA FORMAT( NUMBER OF AREA U N I T S IS F10.5 ) PZERO = E X P ( ( - X ) ) DO 4 0 1 8 K = 1 , 1 0 0 IF (K-1) 4010,4010,4011 TQ ( 1 ) = X GO TO 4 0 1 2 TQ(K) = ( X / K ) * T Q ( K - 1 ) CONTINUE PROB(K) = E X P ( - X ) * T Q ( K ) IF(K-l) 4013,4013,4014 C U M ( l ) = PZERO + P R O B ( l ) GO TO 4 0 1 5 CUM(K) = C U M ( K - l ) + PROB(K) 1  1  208  PAGE 4015  4016 4018 4017 4030 3052 3053 3055 3054 3081 305 6 40 5 0 40 5 2 4051 4054 4053  C C C C C C C C C C C C . C C C C C C C  2  MCQUEEN  CONTINUE SQNUM = C U M ( K ) * AREA S Q L E F = AREA - SQNUM IF(1.0-SQLEF) 4016,4016,4017 CONTINUE CONTINUE AVAIL = K WRITE(3,4030) AVAIL FORMAT( ' NUMBER OF PP SPORES A V A I L A B L E IF(T-21.7J 3052»3052»3053 KNEED = 1 0 0 0 . GO TO 3 0 8 1 IF(T-25«) 3054,3054*3055 KNEED = 1 . GO TO 3 0 8 1 Z=(T-21.7)*10. I = Z KNEED = N E E D ( I ) CONTINUE WRITE(3,3056) KNEED FORMAT( ' KNEED = ' F 7 . 1 ) IF(KNEED - AVAIL) 4 0 5 0 , 4 0 5 0 , 4 0 5 1 CONTINUE WRITE(3,4052) FORMAT( PP WILL F R U I T ' ) GO = 1 . 0 GO TO 4 0 5 3 CONTINUE WRITE(3,4054) FORMAT( ' PP WILL NOT F R U I T • ) GO = - 1 . 0 GO TO 4 0 5 3 CONTINUE  209  =  1  F5.1)  1  THE FOLLOWING COMMENT CARDS I D E N T I F Y THE SYMBOLS USED T = TEMP. TL = T E M P . LOW TO = T E M P . OPTIMUM TH = TEMP H I G H K = CONSTANT C = CONSTANT LDA = LAG FOR DD AMOEBAE GDA = GROWTH INDEX FOR DD AMOEBAE L D F = L A G FOR DD F R U I T I N G B O D I E S GDF = GROWTH INDEX FOR DD F R U I T I N G B O D I E S LPA = LAG FOR PP AMOEBAE L P F = LAG FOR PP F R U I T I N G B O D I E S GPA = GROWTH FOR PP AMOEBAE GPF = GROWTH FOR PP F R U I T I N G B O D I E S THE DATA THAT IS INPUT SO THAT THE S U B R O U T I N E S CAN F U N C T I O N IS CODED IN FOUR P A R T S THE F I R S T L E T T E R IS L FOR LAG OR G FOR GROWTH THE SECOND ONE OR TWO L E T T E R S ARE TO,TH» T L , K , C A L L OF WHICH HAVE BEEN I D E N T I F I E D B E F O R E . . . . . T H E SECOND TO  PAGE C C C C C C  C  C  C  3  MCQUEEN  210  THE L A S T L E T T E R IS P OR D S T A N D I N G FOR PP OR D D . . . . THE LAST L E T T E R IS A OR F S T A N D I N G FOR AMOEBAE OR F R U I T I N G BOD Y . . . . . . AN E X A M P L E . . L T H P A . . S T A N D S FOR LAG T E M P E R A T U R E H I G H PP A M O E B A E . . T H I S IS THE T E M P . HIGH FOR THE PP AMOEBAE LAG S U B R O U T I N E A L L OF THE FOLLOWING INFORMATION IS READ INTO THE S U B R O U T I N E S D . D I S C O I D E U M AMOEBAE LTODA = 2 3 . 0 LTLDA = 9 . LTHDA = 2 7 . 5 LKDA = 1 . 5 0 1 3 7 LCDA = 4 . 7 4 4 0 3 C A L L DLAG (T»LTODA»LTLDA»LTHDA»LKDA•LCDA.LDA) GTODA = 2 1 . 5 GTLDA = 9 . GTHDA = 2 7 . 5 GKDA = 0.80084 GCDA = 0.79554 C A L L DGROW (T»GTODA»GTLDA»GTHDA•GKDA»GCDA•GDA) D . D I S C O I D E U M F R U I T I N G BODY LTODF = 2 4 . LTLDF = 9 . LTHDF = 2 7 . 5 LKDF = 2.47681 LCDF = 7.62542 C A L L DLAG ( T » L T O D F • L T L D F • L T H D F i L K D F » L C D F * L D F ) GTODF = 2 1 . GTLDF = 9 . GTHDF = 2 7 . 5 GKDF = 0.86318 GCDF = -0.65368 C A L L DGROW(T »GTODF»GTLDF»GTHDF,GKDF.GCDF »GDF) P . P A L L I D U M AMOEBAE LTOPA = 3 1 . LTLPA = 1 8 . LTHPA = 3 7 . LKPA = 0.81132 LCPA = 2.59356 CALL PLAG (T»LTOPA»LTLPA»LTHPA»LKPA»LCPA»LPA) GTOPA = 3 1 . GTLPA = 1 8 . GTHPA = 4 1 . GKPA = 1 . 6 2 7 0 9 GCPA = - 1 3 . 5 9 4 2 3 C A L L PGROW ( T»GTOPA»GTLPA»GTHPA»GKPA»GCPA»GPA) P . P A L L I D U M F R U I T I N G BODY LTOPF = 3 0 . LTLPF = 1 8 . LTHPF = 3 7 . LKPF = 1.28527 LCPF = 3.76145 CALL PLAG ( T » L T O P F » L T L P F » L T H P F » L K P F , L C P F » L P F ) GTOPF = 3 1 . GTLPF = 1 8 . GTHPF = 3 7 . 5 GKPF = 0 . 7 8 1 7 2 GCPF = 0 . 9 7 5 5 2  PAGE  . 4 CALL  491 492 484 488 485 489 46 8  309  211  MCQUEEN P F G R O ( T » G T O P F » G T L P F » G T H P F . G K P F »GCPF »GPF)  C A L L D D F R U ( D D C O N i T » Q U I T . D F R U , T Q U I T) WRITE ( 3 » 4 9 1 ) T Q U I T FORMAT( MAX TEMP FOR DD F R U I T I N G IS ' F 1 0 . 5 ) W R I T E ( 3 # 4 9 2) DDCON FORMAT( ' D . D I S C O I D E U M SPORE C O N C E N T R A T I O N IS F10.5) IF (QUIT) 4 8 4 , 4 8 4 . 4 8 5 WRITE(3»488) FORMAT ( DD WILL NOT F R U I T • ) GO TO 4 6 8 WRITE(3.489) QUIT FORMAT( ' DD WILL F R U I T B E C A U S E QUIT IS ' F 1 0 . 5 ) CONTINUE 1  1  1  W R I T E ( 3 * 3 0 9) FORMAT( • LDA GDA LDF GDF 1GPA LPF GP F ) WRITE(3 *30 8 ) LDA»GDA»LDF,GDF•LPA.GPA* LPF»GPF F O R M A T ( 8 F 1 0 • 2) WRITE ( 3 * 3 1 0 ) FORMAT(1H0) WRITE(3*301) FORMAT( ' T I M E DDA DDF PPA PPF 1 SUMF •)  LPA  1  308 310 301  C C C  IN THE FOLLOWING AREA C A L C U L A T I O N S ARE C A L C U L A T E D FOR DD AMOEBAE* PP A M O E B A E . AND PP F R U I T I N G B O D I E S .  SUMA(1) = 0 . 0 SUMF(1) = 0 . 0 APF(1 ) = 0.0 ADF(1) = 0 . 0  79 78 C 400 12 0  DO 1 0 0 0 I = 1 . 5 0 IF(I-l) 78.78.79 IF(SUMA(I-1) - 1935.) 400.400,401 CONTINUE D . D I S C O I D E U M AMOEBAE DATIM = I*.l -LDA IF(DATIM ) 120.120*121 DATIM = 0.0  SUMA  M A D E . . . . . AREAS ARE DD F R U I T I N G B O D I E S .  PAGE 121 C 140 141 401 936 1000  5  MCQUEEN  ADA(I) = ( GDA*DATIM ADA'f I ) = ADA ( I ) #6 • 45 1 6 P . P A L L I D U M AMOEBAE PATIM = I*.l - LPA IF(PATIM ) 140,140,141 PATIM =0.0 APA(I) = ( GPA*PATIM APA(I) = APA(I)*5»4516 GO TO 9 3 6 ADA(I) = ADA(I-l) APA(I) = APA(I-l) SUMA(I) = ADA(I) + APA(I) CONTINUE  +2.0)**2«  + 2«0)**2.  501 760 1098  DO 1 0 9 8 J = l , 5 0 P . P A L L I D U M F R U I T I N G . BODY IF(GO) 1 5 0 , 1 5 0 , 8 6 CONTINUE IF ( J - l ) 81,81,82 IF(APF(J~1)-APA<50)/7.5) 503,503*504 CONTINUE CONTINUE P FT IM = Jtf.l - LPF IFtPFTIM ) 150.150,151 PFTIM = 0.0 APF(J) = ( GPF*PFTIM )**2* APF(J) = APFIJ)*6.4516 GO TO 7 2 7 D . D I S C O I D E U M F R U I T I N G BODY CONTINUE APF(J) = APF(J-l) IF(QUIT)130,130,695 IF(J-l) 83,83,84 IF(ADF(J-l)-ADA(50)) 510,510,501 CONTINUE CONTINUE DFTIM = J*.l - LDF IF(DFTIM ) 130,130,131 DFTIM = 0.0 ADF(J) = ( GDF*DFTIM ) **2 • A D F ( J ) = A D F ( J ) * 6 . 4 516 GO TO 7 6 0 ADF(J) = ADF(J-l) SUMF(J) = ADF(J) + APF(J) CONTINUE  1032  DO 1 0 3 2 K = 1 , 5 0 TIME(K) = K * . l CONTINUE  C 86 82 81 503 150 151 C 504 727 695 84 83 510 130 131  212  PAGE  3 02 303 98  6  MCQUEEN  213  WRITE(3,302) (TIME(L) » ADA(L)» ADF(L) »APA(L),APF(L) iSUMA(L) »SUMF(L) » 1 L = 1,50) FORMAT(F5.1»6F10.2) WRITE(3»303) FORMAT(1H1) I F ( T - 3 8 . ) 99,99,98 CALL EXIT END  214  PROGRAM  I X - COMPLETED MODEL  Program for in  IX c o m p r i s e s  D. d i s c o i d e u m  the finished  a n d P. p a l l i d u m  Salvador  t h e l a b o r a t o r y a t temperatures  The  program  ranging  s i m u l a t i o n model growing  9°C to 37„5°Co  from  i s composed o f s i x s u b r o u t i n e s  together  and a m a i n l i n e  program.  SUBROUTINES: The Appendix  this  spores  ability  subroutine per plate  dimensional will  five  I - Program V I .  P. p a l l i d u m ' c to  first  to- i n h i b i t  a t any g i v e n or negative  R'  discoideum  can f r u i t ,  The i n p u t s discoideum  ( T ) , and t h e o n e  above which  D.  discoideum  concentration. (QUIT).  negative  The o u t p u t  Positive i f  i f not.  PROGRAM The  output,  mainline colony  program  i s composed  and f r u i t i n g  fruiting  has been  expansion  body p r o d u c t i o n .  e x p l a i n e d i n Appendix  has been e x p l a i n e d  o f four  body e x p a n s i o n ,  w h i c h d e s c r i b e s D. d i s c o i d e u m ^  P. p a l l i d u m ference  describes  number o f D.  spore  number  explained i n  subroutine  (DDCON), t h e t e m p e r a t u r e  a positive  section  have been  D. d i s c o i d e u m .  are: the total  is  input,  The s i x t h  array o f temperatures  not f r u i t  MAINLINE  subroutines  - ability  sections: and a  to inhibit  P. p a l l i d u m  inter-  I - Program V I I I , and  i n Appendix  I - Program V I .  215  T h e i n p u t i s composed spores per p l a t e , plate,  t h e number o f D. d i s c o i d e u m  data input,  and amount o f a r e a c o v e r e d b y  and amoebae o f b o t h The o u t p u t  thirteen  body  ( 8 ) D. d i s c o i d e u m time,  size, ature.  (7) P. p a l l i d u m f r u i t i n g  fruiting  body  ( 1 1 ) n e c e s s a r y clump  and ( 1 3 ) D. d i s c o i d e u m From  this  fruiting  sections: spore l a g ,  l a g , (4) D. d i s c o i d e u m  l a g , (5) P. p a l l i d u m amoeba c o l o n y a r e a ,  amoeba c o l o n y a r e a ,  (10)  into  l a g , ( 2 ) D. d i s c o i d e u m  (3) P. p a l l i d u m f r u i t i n g  the i n t e r -  s p e c i e s a t any t i m e t .  i s divided  (1) P. p a l l i d u m s p o r e  body  spores per  t h e g r o w t h p a r a m e t e r s f o r t h e two s p e c i e s ,  ference bodies  o f t h e number o f P. p a l l i d u m  ( 6 ) D. body  (9)  temperature,  size,  (12) a v a i l a b l e body b o u n d a r y  i n f o r m a t i o n 95% c o n f i d e n c e l i m i t s  s p o r e numbers c a n be  calculated.  discoideum  area,  area,  fruiting  fruiting  clump temperand  216  APPENDIX  II  Figure  42  P. p a l l i d u m and D. d i s c o i d e u m V12 were i n o c u l a t e d together at f i v e r e l a t i v e c o n c e n t r a t i o n s . Plates were grown a t s e v e r a l t e m p e r a t u r e s , a n d when f r u i t i n g body e x p a n s i o n t e r m i n a t e d , the t o t a l a r e a o c c u p i e d b y f r u i t i n g b o d i e s o f b o t h s p e c i e s was noted. Temperature i s p l o t t e d along the x - a x i s ( i n degrees c e n t i g r a d e ) and a r e a c o v e r e d i s p l o t t e d a l o n g t h e y-axis. B l a c k d o t s r e p r e s e n t D. d i s c o i d e u m , o p e n c i r c l e s P. p a l l i d u m . A l i n e j o i n i n g a black dot and an o p e n c i r c l e i n d i c a t e s t h a t b o t h s p e c i e s fruited together. The f i v e e x p e r i m e n t a l s e t s a r e l i s t e d (a) t o (e) from t h e top t o the b o t t o m . The spore c o n c e n t r a t i o n s used are: EXPERIMENTAL SET 42-a 42-b 42-c 42-d 42-e  CON PP.  CON Dd.  90 70 50 30 10  10 30 50 70 90  j=  130-  ©  6.5 i  i  i  i  \  l  *  •  •  0  I  pl  1  I  n  pl  1  I  »  I  L  fl  -J  29  30  13.0 6-5 J  J  »  6  '  L-2.  I  Q  13-Oh  o  6.5h  © 130h 6.5 h J  19  ,  j  L  20  21  23  LJ2  24  I _ J  25  26  i  i  27 28  TEMPERATURE  0  L  31  Fiqure  43  £ • p a l l i d u m and D. d i s c o i d e u m V 1 2 were i n o c u l a t e d together at f i v e r e l a t i v e c o n c e n t r a t i o n s . Plates were grown a t s e v e r a l t e m p e r a t u r e s , and when f r u i t i n g body e x p a n s i o n t e r m i n a t e d , the t o t a l a r e a o c c u p i e d b y f r u i t i n g b o d i e s o f b o t h s p e c i e s was noted. Temperature i s p l o t t e d along the x - a x i s ( i n d e g r e e s c e n t i g r a d e ) and a r e a c o v e r e d i s p l o t t e d along the y - a x i s . B l a c k d o t s r e p r e s e n t D„ discoideum, o p e n c i r c l e s P. p a l l i d u m . A l i n e joining a black d o t and an o p e n c i r c l e i n d i c a t e s t h a t b o t h s p e c i e s f r u i t e d together. The f i v e e x p e r i m e n t a l s e t s a r e l i s t e d ( a ) t o (e) f r o m t h e t o p t o t h e b o t t o m . The spore c o n c e n t r a t i o n s used a r e :  EXPERIMENTAL SET  CON PP.  CON Dd.  43-a 4 3-b 43-c 43-d 43-e  600 466 333 200 66  66 200 333 466 600  Figure  44  P. p a l l i d u m and D. d i s c o i d e u m V12 were i n o c u l a t e d t o g e t h e r at f i v e r e l a t i v e c o n c e n t r a t i o n s . Plates were grown a t s e v e r a l t e m p e r a t u r e s , and when f r u i t i n g body e x p a n s i o n t e r m i n a t e d , t h e t o t a l a r e a o c c u p i e d b y f r u i t i n g b o d i e s o f b o t h s p e c i e s was noted. Temperature i s p l o t t e d along the x - a x i s ( i n d e g r e e s c e n t i g r a d e ) and a r e a c o v e r e d i s p l o t t e d along the y - a x i s . B l a c k d o t s r e p r e s e n t D. discoideum, o p e n c i r c l e s P. p a l l i d u m . A line joining a black d o t and an o p e n c i r c l e i n d i c a t e s t h a t b o t h s p e c i e s fruited together. The f i v e e x p e r i m e n t a l s e t s a r e l i s t e d (a) t o (e) from the top t o the bottom. The spore c o n c e n t r a t i o n s used are:  EXPERIMENTAL SET 44-a 44-b 44-c 44-d 44-e  CON PP. 2394 1862 1330 798 266  CON Dd. 266 798 1330 1862 2 394  13.0 6.5h «  »  '  '  i  i  '  '  LS  I  »o  j  L  13.0 6.5 '  1  »  1  I  >  I  i  I  o  »  13.0 6.5  0 JL.  19  2 0 21  22  23  24  25 26  27 2 8  TEMPERATURE  29 3 0  31  Fiqure  45  P. p a l l i d u m and D. d i s c o i d e u m V12 were i n o c u l a t e d together a t f ive"~"relative c o n c e n t r a t i o n s . Plates were grown a t s e v e r a l t e m p e r a t u r e s , and when f r u i t i n g body e x p a n s i o n t e r m i n a t e d , t h e t o t a l a r e a o c c u p i e d b y f r u i t i n g b o d i e s o f b o t h s p e c i e s was noted. Temperature i s p l o t t e d along the x - a x i s ( i n d e g r e e s c e n t i g r a d e ) and a r e a c o v e r e d i s p l o t t e d along the y - a x i s . B l a c k d o t s r e p r e s e n t D. d i s c o i d e u m , o p e n c i r c l e s P. p a l l i d u m . A l i n e joining a black d o t and an o p e n c i r c l e i n d i c a t e s t h a t b o t h s p e c i e s f r u i t e d together. The f i v e e x p e r i m e n t a l s e t s a r e l i s t e d (a) t o (e) from the top to the bottom. The spore c o n c e n t r a t i o n s used a r e :  EXPERIMENTAL SET 45-a 45-b 45-c 45-d 45-e  CON PP.  CON Dd.  14400 11200 8000 4800 1600  1600 4800 8000 11200 14400  •  a  13-0  •  4  ' 6.5 i  •  b  13.0  i  i  •  i  i  Q-i  .°  1 ° 1  <"> »  <Q  8  O  i  i  I  I  1>  29  30  31  1  •  •  •  lO  i  6-5 i  i  i  i  i  L  21  22  «  1  1  13.0-  13.06.5  [  »  1  13.0-  19  20  23  24  25  26  TEMPERATURE  27 2 8  Fiqure  46  C u l t u r e g r a d i e n t I I . G r a d i e n t drawings showing t h e c h a n g e i n f r u i t i n g a b i l i t y e x p e r i e n c e d by P. p a l l i d u m . The h o r i z o n t a l l y s h a d e d a r e a s were o c c u p i e d b y P. p a l l i d u m f r u i t i n g b o d i e s , t h e v e r t i c a l l y s h a d e d a r e a s b y D. d i s c o i d e u m f r u i t i n g b o d i e s . The a r e a s s h a d e d w i t h h o r i z o n t a l and v e r t i c a l l i n e s were o c c u p i e d b y f r u i t i n g b o d i e s o f b o t h s p e c i e s . The u n s h a d e d a r e a s were u n o c c u p i e d . Temperature i s marked a t i n t e r v a l s under each diagram.  Figure 4 7  Culture gradient I I I . G r a d i e n t drawings showing t h e c h a n g e i n f r u i t i n g a b i l i t y e x p e r i e n c e d by P. p a l l i d u m . The h o r i z o n t a l l y s h a d e d a r e a s were o c c u p i e d b y P. p a l l i d u m f r u i t i n g b o d i e s ; t h e v e r t i c a l l y s h a d e d a r e a s b y D. d i s c o i d e u m f r u i t i n g b o d i e s . The a r e a s s h a d e d w i t h h o r i z o n t a l and v e r t i c a l l i n e s were o c c u p i e d b y f r u i t i n g b o d i e s o f b o t h s p e c i e s . The u n s h a d e d a r e a s were u n o c c u p i e d . Temperature i s marked a t i n t e r v a l s u n d e r each diagram.  Figure  48  C u l t u r e g r a d i e n t IV. Gradient drawings p r o v i n g t h a t a f t e r c o n t i n u e d c o m p e t i t i o n P. p a l l i d u m and D. d i s c o i d e u m f r u i t e d t o g e t h e r . The h o r i z o n t a l l y s h a d e d a r e a s were o c c u p i e d b y P. p a l l i d u m f r u i t i n g b o d i e s ; t h e v e r t i c a l l y s h a d e d a r e a b y D. d i s c o i d e u m f r u i t i n g bodies. The a r e a s s h a d e d w i t h h o r i z o n t a l and v e r t i c a l l i n e s were o c c u p i e d b y f r u i t i n g bodies of both s p e c i e s . The u n s h a d e d a r e a s were unoccupied. T e m p e r a t u r e i s marked a t i n t e r v a l s under each diagram.  Figure  49  C u l t u r e g r a d i e n t drawings demonstrating t h a t after c o n t i n u e d c o m p e t i t i o n P, p a l l i d u m c o u l d c o - f r u i t w i t h Do d i s c o i d e u m . D. discoideum d i d n o t change i n response t o continued competition. The h o r i z o n t a l l y s h a d e d a r e a s were o c c u p i e d b y P. p a l l i d u m f r u i t i n g b o d i e s . The v e r t i c a l l y shaded areas by D. d i s c o i d e u m f r u i t i n g b o d i e s . The a r e a s s h a d e d w i t h b o t h v e r t i c a l and h o r i z o n t a l l i n e s were o c c u p i e d b y f r u i t i n g b o d i e s o f b o t h s p e c i e s . The u n s h a d e d a r e a s were n o t o c c u p i e d b y any f r u i t i n g bodies. T e m p e r a t u r e i s marked a t i n t e r v a l s under each diagram. The s e t s were made up o f t h e following:  SET #  GRADIENT #  P. PALLIDUM  D.  1 1  DISCOIDEUM  A B  grad. stock  1-K  VC4 s t o c k g r a d . 1-K  2 2  A B  grad. stock  1-L  DF s t o c k g r a d . 1-L  3 3  A B  grad. stock  2-K  DF s t o c k g r a d . 2-K  4 4  A B  grad. stock  2-K  VC4 s t o c k g r a d . 2-L  Figure  50  C u l t u r e g r a d i e n t drawings demonstrating t h a t P. p a l l i d u m ( c h a n g e d ) r e t a i n e d i t ' s c o - f r u i t i n g a b i l i t y when grown a l o n e (A, B, C) b u t l o s t t h i s a b i l i t y when grown w i t h P. p a l l i d u m ( s t o c k ) . H o r i z o n t a l l y s h a d e d a r e a s c o n t a i n P. p a l l i d u m f r u i t i n g bodies. V e r t i c a l l y shaded areas D. d i s c o i d e u m . A r e a s s h a d e d b o t h ways c o n t a i n both species. Areas unshaded c o n t a i n n e i t h e r . Temperature i n degrees c e n t i g r a d e i s measured along the x - a x i s .  D  Figure  51  C u l t u r e g r a d i e n t d r a w i n g s d e m o n s t r a t i n g t h a t some P. p a l l i d u m c l o n e s h a v e c o - f r u i t i n g a b i l i t y ( E ) and o t h e r s do n o t (A, B, C, D ) . T h e c l o n e d s p o r e s came f r o m a s t o c k c u l t u r e . H o r i z o n t a l l y shaded a r e a s c o n t a i n P. p a l l i d u m f r u i t i n g b o d i e s . V e r t i c a l l y s h a d e d a r e a s D. d i s c o i d e u m VC4. Areas unshaded c o n t a i n n e i t h e r T Temperature i n degrees c e n t i g r a d e i s measured a l o n g t h e x - a x i s .  Figure  52  C u l t u r e g r a d i e n t drawings demonstrating that D. d i s c o i d e u m amoebae a r e p r o d u c e d and grow a b o v e 24°C even though f r u i t i n g body p r o d u c t i o n stops a t a b o u t 24 - 2 5 ° C . H o r i z o n t a l l y shaded areas c o n t a i n P.- p a l l i d u m f r u i t i n g b o d i e s . Vertically shaded, a r e a s D. d i s c o i d e u m V12 f r u i t i n g bodies. A r e a s s h a d e d b o t h ways c o n t a i n b o t h s p e c i e s . Unshaded areas c o n t a i n n e i t h e r s p e c i e s . Temperature i n degrees c e n t i g r a d e i s measured along the x - a x i s . The c i r c l e s a l o n g t h e l e n g t h o f the g r a d i e n t s r e p r e s e n t areas i n which agar b l o c k s were p l a c e d . S t a r s above t h e c i r c l e s i n d i c a t e the agar b l o c k s t h a t c o n t a i n e d D. d i s c o i d e u m v e g e t a t i v e amoebae.  228  APPENDIX  III  229 GOODNESS OF F I T OF EQUATION ( l c ) If  amoebae a n d f r u i t i n g b o d y c o l o n i e s e x p a n d a t  r a t e s which are p r o p o r t i o n a l t o the colony then equation expand.  ( l c ) should  describe  t h e way i n w h i c h  The a p p l i c a b i l i t y o f e q u a t i o n  growing c u l t u r e s , noting intervals  and p l o t t i n g  the area  circumference colonies  ( l c ) was t e s t e d b y  covered  at various  the square root o f area  time  against  time.  B o t h amoeba a n d f r u i t i n g b o d y c o l o n i e s y i e l d e d s t r a i g h t l i n e r e l a t i o n s h i p s between t h e square r o o t o f area  and  time.  E x a m p l e c u l t u r e s w e r e r u n a n d p l o t t e d ( F i g . 1 1 , 17) i n t h e t e x t , b u t s i n c e one c u l t u r e c a n o n l y be measured f o u r o r f i v e times during are  i t s growth p e r i o d only  available.  four or f i v e  data  points  I t m i g h t be p o s s i b l e t h a t t h e s t r a i g h t l i n e  r e l a t i o n s h i p s r e s u l t e d from the f a c t t h a t only p o i n t s were u s e d t o f i t each r e g r e s s i o n  a few  data  line.  To p r o v e t h a t t h i s was n o t t h e c a s e , a n d t h a t straight of  area  l i n e r e l a t i o n s h i p s do e x i s t b e t w e e n t h e s q u a r e and t i m e ,  together.  Since  the data  f r o m s e v e r a l c u l t u r e s was p l o t t e d  e a c h c u l t u r e t h a t was u s e d was g r o w n a t a  d i f f e r e n t t e m p e r a t u r e , and s i n c e d a t a and  f r o m b o t h P.  D. d i s c o i d e u m w e r e i n c l u d e d ; e a c h d a t a  transformed  with  respect  to area  I t was a r b i t r a r i l y transformed having  and  decided  of three.  This A ^ T  pallidum  p o i n t h a d t o be  time. that the data  to f i t a s t r a i g h t l i n e passing  a slope  root  w o u l d be  t h r o u g h z e r o and  r e l a t i o n s h i p i s described = 3t  by: (7)  230  where A  T  i s the transformed  a r e a and t i s t i m e .  The e q u a t i o n  f o r a r e g r e s s i o n l i n e r e s u l t i n g from any one c u l t u r e was:  h  = | + b»t  2  (8)  where a i s the y i n t e r c e p t and b i s the s l o p e . equation  ( 8 ) to equation  To t r a n s f o r m  (7), a/b must be s u b t r a c t e d from the  r i g h t hand s i d e , and both  s i d e s must be d i v i d e d by 3/b,  producing: b •A and  s u b s t i t u t i n g equation  a g a i n s t t h e transformed and  = 3*t  (9)  (7) i n t o ( 9 ) : A  The t r a n s f o r m e d  U  2 T  = %'h  (10)  2  square r o o t o f a r e a was p l o t t e d  time  ( t - a/b).  P. p a l l i d u m amoeba c o l o n y expansion  f r u i t i n g body c o l o n y expansion  data  Both D. data  discoideum  ( F i g . 53) and  ( F i g . 54) conformed to  the s t r a i g h t l i n e r e l a t i o n s h i p p r e d i c t e d by e q u a t i o n ( l c ) . These d a t a r e p r e s e n t f i n a l p r o o f t h a t ( l c ) does d e s c r i b e both  amoeba and f r u i t i n g body c o l o n y expansion  and t h a t the  s t r a i g h t l i n e r e l a t i o n s h i p s presented i n the text  ( F i g . 11, 17)  are not the r e s u l t o f a s m a l l number o f d a t a p o i n t s .  Fiqure 5 3  The square r o o t o f amoeba c o l o n y a r e a i s p l o t t e d a g a i n s t time f o r both D. discoideum ( s o l i d d o t s ) and P. p a l l i d u m (open c i r c l e s ) . A l l data i s transformed t o conform to the l i n e d e s c r i b e d by - 3 t , where A i s area and t i s . time.  64  oo  o  "  •  o So  O 321 co  •2°  "o  of o  oo o  oo  0 2  3  TIME-DAYS  Figure  54  The s q u a r e r o o t o f f r u i t i n g b o d y c o l o n y a r e a i s p l o t t e d a g a i n s t t i m e f o r b o t h D„ d i s c o i d e u m ( s o l i d d o t s ) and P. p a l l i d u m ( o p e n c i r c l e s ) . A l l data i s transformed to conform to the l i n e d e s c r i b e d by e q u a t i o n ( 7 ) .  9 0  64 <  UJ DC <  o oO  o o  DC  6 CO  00 e  32j  o  o •o  o  oo  OL  i  1  1  _j  2  3  TIME-DAYS  L.  4  233  APPENDIX  IV  234  S T A T I S T I C A L SIGNIFICANCE OF  Throughout and  (4b)  and  results  were f i t t o t h e  fruiting  body e x p a n s i o n  the f r u i t i n g  EQUATIONS  body  section  data, the  lag data.  I , P r o g r a m s I , I V , V)  best  from  or  (4b) was  did  not  ability  used  of the  deviation  unaccounted deviations correlation every case  f o r each  which P.  used  of  data,  set of data.  But  method  that  (2b)  this  the  lag data,  squares  to ensure  the  or  (3c)  procedure  to the  a c h i e v e d by  descriptive  f o r by  one  the  line.  the observed  failed  equation  pallidum fruiting  line,  used  body e x p a n s i o n  the  the  the  In  fitted  of confidence.  r e p l a c e d by  (4b) was  finally  (Table XIV).  d a t a and  level  was  and  The  F i g u r e 21  in  to d e s c r i b e the  data.  the  deviation  From t h i s  were c a l c u l a t e d  a t the 95%  that  calculating  t h e mean y v a l u e , t h e  coefficients  a special  least  d e s c r i b e d by  the d e s c r i p t i v e  accounted  ( F i g . 20)  was  lines  s t e p was  around  f o r by  (2b), (3c),  spore germination The  (4b)  chosen.  second  except  I equations  statistical significance  line  were i n a g r e e m e n t case  family of  a t t a c h any  This total  the  ( 3 c ) , AND  amoeba c o l o n y e x p a n s i o n  (Appendix line  (2b),  line one  235  TABLE X I V The p r o p o r t i o n o f v a r i a b i l i t y a c c o u n t e d f o r by e q u a t i o n s ( 2 b ) , ( 3 c ) , and ( 4 b ) and t h e s i g n i f i c a n c e o f t h e f i t i s l i s t e d f o r t h e f i g u r e s i n w h i c h l i n e s were f i t t o e x p e r i m e n t a l d a t a .  df SIGNIFICANT AT 9 5 % LEVEL  PROPORTION VARIABILITY ACCOUNTED  CORRELATION COEFFICIENT  6  0.75  0.86  3/15  Yes  7  0.88  0.93  3/27  Yes  12  0.94  0.96  3/10  Yes  13  0.56  0.75  3/22  Yes  14  0.71  0.84  3/13  Yes  16  0.96  0.98  3/11  Yes  17  0.97  0.98  3/14  Yes  19  0.69  0.81  3/11  Yes  20  0.00  0.00  3/14  No  21  0.75  0.86  3/14  Yes  34  0.76  0.87  3/7  Yes  35  0.84  0.91  3/11  Yes  36  0.94  0.97  3/8  Yes  37  0.87  0.93  3/9  Yes  38  0.67  0.81  3/13  Yes  39  0.91  0.95  3/9  Yes  40  0.93  0.96  3/8  Yes  FIGURE NUMBER  

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