UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Laboratory studies of competition in two species of cellular slime molds : Dictyostelium discoideum and.. 1970

You don't seem to have a PDF reader installed, try download the pdf

Item Metadata

Download

Media
UBC_1970_A1 M32_4.pdf [ 11.46MB ]
UBC_1970_A1 M32_4.pdf
Metadata
JSON: 1.0102011.json
JSON-LD: 1.0102011+ld.json
RDF/XML (Pretty): 1.0102011.xml
RDF/JSON: 1.0102011+rdf.json
Turtle: 1.0102011+rdf-turtle.txt
N-Triples: 1.0102011+rdf-ntriples.txt
Citation
1.0102011.ris

Full Text

LABORATORY STUDIES OF COMPETITION IN TWO SPECIES OF CELLULAR SLIME MOLDS; DICTYOSTELIUM DISCOIDEUM AND POLYSPHONDYLIUM PALLIDUM - by DONALD JAMES MCQUEEN B . S c , U n i v e r s i t y of B r i t i s h Columbia, 1966 M . S c , U n i v e r s i t y o f B r i t i s h Columbia, 1968 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n the Department o f ZOOLOGY We accept t h i s t h e s i s as conforming t o the r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA May, 1970 In presenting t h i s thesis in p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree at the University of B r i t i s h Columbia, I agree that the Library shall make i t f r e e l y available for reference and study. I further agree tha permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of t h i s thesis f o r f i n a n c i a l gain shall not be allowed without my written permission. Department of ZOOLOGY The University of B r i t i s h Columbia Vancouver 8, Canada Date May 25, 1970 i ABSTRACT The mechanics- o f a s h o r t term i n t e r s p e c i f i c c o m p e t i t i v e s i t u a t i o n and some o f t h e consequences o f l o n g t e r m i n t e r s p e c i f i c c o m p e t i t i o n were s t u d i e d i n t h e l a b o r a t o r y u s i n g two s p e c i e s o f c e l l u l a r s l i m e mold; D i c t y o s t e l i u i n d i s c o i d e u m and Po.1 ysphondy 1 ium p a l l i d u m . The m e c h a n i c s o f c o m p e t i t i o n were s t u d i e d u s i n g a components method i n w h i c h t h e p r o c e s s was d i v i d e d i n t o component p a r t s . These v/ere a s s e s s e d , e x p e r i m e n t a l l y , m o d e l l e d m a t h e m a t i c a l l y , and l i n k e d • t o g e t h e r t o f o rm a computer model, t h e p r e d i c t i o n s o f w h i c h were t e s t e d i n t h e l a b o r a t o r y . F i v e m a jor components c o n t r i b u t e d t o t h e c o m p e t i t i v e s i t u a t i o n . 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 , t h e e f f e c t o f p h y s i c a l f a c t o r s o r e x t e r n a l f o r c e s , t h e a v a i l a b i l i t y o f r e s o u r c e s , and t h e number o f p o t e n t i a l c o m p e t i t o r s engaged i n e x p l o i t a t i o n and i n t e r f e r e n c e . The e x p l o i t a t i o n component depended upon a l l o f t h e sub-components w h i c h c o n t r i b u t e d t o t h e l i f e c y c l e o f t h e c e l l u l a r s l i m e mold s p e c i e s . These were: t h e t i m e r e q u i r e d f o r s p o r e g e r m i n a t i o n , t h e r a t e and f o r m o f amoeba c o l o n y e x p a n s i o n , t h e t ime r e q u i r e d f o r f r u i t - i n g body p r o d u c t i o n , and t h e ir a t e and form o f f r u i t i n g body c o l o n y e x p a n s i o n . Both s p e c i e s i n t e r f e r e d w i t h t h e o t h e r ' s a b i l i t y t o form f r u i t i n g b o d i e s . I n mixed c u l t u r e s , D. d i s c o i d e u m amoebae d i v i d e d and consumed f o o d between 9 ° and 27°C but D. d i s c o i d e u m f r u i t i n g d i d n o t o c c u r above i i about 24 Co In mixed c u l t u r e s , P. p a l l i d u m amoebae d i v i d e d and consumed food between 1 8 ° and 3 7 ° C but 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 not form below about 2 4 ° C . In both cases i n t e r f e r e n c e was mediated by temperature and c o m p e t i t o r numbers> Temperature, the r e p r e s e n t a t i v e e x t e r n a l f o r c e , a l t e r e d the parameter v a l u e s o f a l l the sub-components c o n t r i b u t i n g to e x p l o i t a t i o n and i n t e r f e r e n c e . When a l l o f the components were a s s e s s e d they were i n c o r p o r a t e d i n t o a computer model which was used to p r e d i c t the area o c c u p i e d by the f r u i t i n g b o d ies o f both s p e c i e s . The s i m u l a t i o n was t e s t e d 324 times and was a c c u r a t e i n 90.1% o f the c a s e s . The long term e x p e r i m e n t a l s t u d i e s 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 a f t e r a p e r i o d 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 overcame the e f f e c t s o f D. discoideum i n h i b i t i o n and f r u i t e d i n the presence o f D. disco i d e u m . When grown alone P. p a l l i d u m f r u i t e d from 1 8 ° t o 3 7 ° C and D. discoideum f r u i t e d from 9 ° to 2 7 ° C . I n mixed c u l t u r e s , 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 from about 2 4 ° t o 3 7 ° C and D . discoideum from about 9 ° to 2 4 ° C . In mixed c u l t u r e s , 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 f r u i t e d from about 2 0 ° to 3 7 ° C and D. discoideum from about 9 ° to 2 4 ° C . A p p a r e n t l y P. p a l l i d u m converged towards D. discoideum, and at the same time D. discoideum i n c r e a s e d i t s r a t e o f r e s o u r c e use, and d i v e r g e d away from P. p a l l i d u m . The da t a i i i suggested that interference was re l a t e d to the production of chemicals during the aggregation stage. I t i s possible that acrasin, the chemical which a t t r a c t s amoebae to aggregation centers i s involved. Experimental evidence also suggested that the change experienced by P. pallidum might have resulted from para-sexuality. This e n t a i l s the production of d i p l o i d spores, the recombination of a l l e l e s , and chromosome lo s s , a l l of which tend to protect recessive and less f i t character- i s t i c s . PREFACE The work p r e s e n t e d i n t h i s t h e s i s i s d i r e c t e d towards the study o f c o m p e t i t i o n between two s p e c i e s o f c e l l u l a r s l i m e mold grown under l a b o r a t o r y c o n d i t i o n s . I t was a n t i c i p a t e d t h a t the mechanics of c o m p e t i t i o n c o u l d be s t u d i e d over s h o r t time p e r i o d s and t h a t some o f the r e s u l t s of c o m p e t i t i o n c o u l d be s t u d i e d d u r i n g long p e r i o d s o f c o m p e t i t i v e exposure. I t was a l s o hoped t h a t some o f the l a b o r a t o r y f i n d i n g s from t h i s study c o u l d be r e l a t e d to e x i s t i n g c o m p e t i t i v e t h e o r y t o o b t a i n an overview of competi- t i o n t h a t might be a p p l i c a b l e to f i e l d s t u d i e s . The f i r s t 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 mechanics d e s c r i b e s the way i n which the two s p e c i e s e x p l o i t t h e i r environment, b e g i n n i n g with the g e r m i n a t i o n o f spores and ending w i t h the p r o d u c t i o n o f f r u i t i n g b o d ies which c o n t a i n s p o r e s . As the e x p e r i m e n t a l evidence i s p r e s e n t e d , diagrams have been used to f o l l o w the b u i l d - u p o f i n f o r m a t i o n and to d e s c r i b e the way i n which the v a r i o u s p i e c e s o f evidence l i n k t o g e t h e r . A s i m i l a r procedure i s f o l l o w e d d u r i n g the d e v e l o p - ment o f the second s e c t i o n d e a l i n g with the way i n which the two s p e c i e s i n t e r f e r e w i t h one another. S i n c e i t was p o s s i b l e to express the a c t i o n o f the v a r i o u s components m a t h e m a t i c a l l y , a computer model was c o n s t r u c t e d to s i m u l a t e the way i n which the two s p e c i e s e x p l o i t e d t h e i r environment and i n t e r f e r e d w i t h one another. The r e s u l t s o f t h i s s i m u l a t i o n are p r e s e n t e d at the end o f the f i r s t s e c t i o n on c o m p e t i t i v e mechanics. V In the second r e s u l t s s e c t i o n which d e a l s with c o n t i n u e d c o m p e t i t i o n , hypotheses r e l a t i n g c o m p e t i t i v e p r e s s u r e , e c o l o g i c a l convergence, and e c o l o g i c a l d i v e r g e n c e are t e s t e d and some of the d a t a o b t a i n e d are used i n the s i m u l a t i o n model. The d i s c u s s i o n i s p r e s e n t e d i n two s e c t i o n s . The f i r s t c o n s i d e r s f i n d i n g s r e l e v a n t t o g e n e r a l c e l l u l a r s l i m e mold b i o l o g y . The second d e a l s w i t h the e c o l o g i c a l a s p e c t s of the st u d y . There are f o u r appendices. In the f i r s t , n i ne computer programs and t h e i r e x p l a n a t o r y w r i t e - u p s are p r e s e n t e d . The second c o n t a i n s s e v e r a l f i g u r e s which are i n d i r e c t l y r e f e r r e d to i n the r e s u l t s s e c t i o n s . The t h i r d i s concerned w i t h the g e n e r a l i t y and goodness o f f i t , of the e q u a t i o n which d e s c r i b e s the way i n which amoebae and f r u i t i n g body c o l o n i e s expand. The f o u r t h appendix c o n t a i n s an e x p l a n a t i o n of the t e s t s used to s t a t i s t i c a l l y determine the d e s c r i p t i v e a b i l i t y o f the v a r i o u s r a t e and l a g equ a t i o n s developed i n the r e s u l t s s e c t i o n . v i TABLE OF CONTENTS PAGE Abstract i Preface i v Table of Contents v i L i s t of Tables i x L i s t of Figures x i Acknowledgement x v i Introduction 1 The Animals 6 Materials and Methods 14 Laboratory Methods 14 Experimental Error 19 Mathematics 21 Results Section I: Mechanics of Competition 2 3 Spore Germination 2 3 Amoeba Colony Expansion 31 The Form of Colony Expansion 31 The Rate of Colony Expansion 36 F r u i t i n g Body Lag 46 F r u i t i n g Body Formation 50 The Form of F r u i t i n g Body Colony Expansion 50 The Rate of F r u i t i n g Body Colony Expansion 54 Testing the E x p l o i t a t i o n Models 60 Summary 65 The Exploitation-Competition Simulation 66 v i i PAGE Interference 73 I n h i b i t i o n of P. pallidum 73 Confidence Limits on P. pallidum Interference 33 I n h i b i t i o n of D. discoideum 8 3 The Completed Model 86 Tests of the Model 89 Area Occupied by F r u i t i n g Bodies 89 Continued Competition 92 Summary 92 Results Section I I : Consequences of Competition 95 Mixture of Stock Spores 97 Continued Mixtures 97 Culture Gradient I 99 Culture Gradient II 101 Culture Gradient I I I 102 Culture Gradient IV 103 Changes Between 18° and 24«,5°C 110 Which Competitors Changed 110 Mechanics of the Change 112 The Type of Change 115 Cloning Experiments 117 Changes Between 24° and 26.5°C 118 S i m i l a r i t y of Resource Use 119 Germination Lags 121 Colony Expansion Rates 121 Stock Spore Germination Rates 12 7 v i i i PAGE Stock Colony Expansion Rates 12 7 Summary 137 D i s c u s s i o n 139 S e c t i o n I : C e l l u l a r Slime Mold B i o l o g y 139 I n h i b i t i o n 139 G e n e t i c s 143 S e c t i o n I I : E c o l o g i c a l Relevance 147 Convergence and C o e x i s t e n c e 147 Components o f Comp e t i t i o n 149 L i t e r a t u r e C i t e d 157 Appendix I - Computer Programs 164 Program I - Curve F i t t i n g ( E q u a t i o n 2b) 165 Program I I - Form o f Colony Expansion ( E q u a t i o n l c ) 170 Program I I I - C a l c u l a t i o n o f Mean Slope 172 Program IV - Curve F i t t i n g ( E q u a t i o n 3c) 179 Program V - Curve F i t t i n g ( E q u a t i o n 4b) 181 Program VI - E x p l o i t a t i o n of S i n g l e S p e c i e s 185 Program VII - E x p l o i t a t i o n of Mixed S p e c i e s 194 Program V I I I - I n h i b i t i o n o f P. p a l l i d u m 198 Program IX - Completed Model 202 Appendix I I - F i g u r e s 216 Appendix I I I - Goodness o f F i t of E q u a t i o n ( l c ) 228 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 o f Eq u a t i o n s 2 33 (2b), ( 3 c ) , and (4b) i x LIST OF TABLES TABLE PAGE I A comparison o f D. discoideum 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 29 v a r i o u s spore c o n c e n t r a t i o n s . I I A comparison of P. p a l l i d u m l a g times 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 30 spore c o n c e n t r a t i o n s , I I I A comparison of D. discoideum V12 growth indexes from c u l t u r e s i n o c u l a t e d w i t h 44 v a r i o u s spore c o n c e n t r a t i o n s . IV A comparison of P. p a l l i d u m growth indexes 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 45 spore c o n c e n t r a t i o n s . V Changes i n the maximum area 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 , with changes 5 3 i n temperature. VI A comparison o f D. discoideum VC4 amoeba' c o l o n y a r e a observed and e s t i m a t e d from 61 Program V I . VII A comparison of P. p a l l i d u m amoeba.: c o l o n y area observed and e s t i m a t e d from Program VI. 62 V I I I A comparison of D. discoideum VC4 f r u i t i n g body area observed and e s t i m a t e d from 6 3 Program V I . IX A comparison of P. p a l l i d u m f r u i t i n g body area observed and e s t i m a t e d from Program V I I . 64 X A comparison o f P. p a l l i d u m spore germina- -^22 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 comparison of D. discoideum 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 12 3 c o m p e t i t i o n . X I I A comparison o f P. p a l l i d u m spore germina- t i o n l a g s beforehand a f t e r media 128 c o n d i t i o n i n g . X I I I A comparison o f D. discoideum VC4 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 media 129 c o n d i t i o n i n g . TABLE x PAGE XIV 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 ) . LIST 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 f r u i t i n g body grown at 24^C. 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 body grown at 36°C. I l l u s t r a t i o n o f D. discoideum f r u i t i n g body. I l l u s t r a t i o n o f c o - f r u i t i n g D. discoideum and P. p a l l i d u m . Diagram o f temperature g r a d i e n t apparatus i n p l a n and s i d e view. D. discoideum VC4 g e r m i n a t i o n l a g p l o t t e d a g a i n s t temperature. P. p a l l i d u m spore g e r m i n a t i o n l a g p l o t t e d a g a i n s t temperature. G e n e r a l c u r v e r e l a t i n g spore g e r m i n a t i o n l a g and temperature. S i m u l a t e d areas covered by amoeba c o l o n i e s at v a r i o u s i n t e r v a l s o f time and wi t h v a r i o u s v a l u e s o f g i n e q u a t i o n ( l c ) . The square r o o t o f ar e a p l o t t e d a g a i n s t t i me. A c t u a l and p r e d i c t e d l i n e s are p l o t t e d . 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 D. discoideum and P. p a l l i d u m . D. discoideum V12 c o l o n y expansion r a t e p l o t t e d a g a i n s t temperature. P. p a l l i d u m c o l o n y expansion r a t e p l o t t e d a g a i n s t temperature. D. dis c o i d e u m VC4 c o l o n y expansion r a t e p l o t t e d a g a i n s t temperature. General curve r e l a t i n g c o l o n y expansion and temperature. x i i FIGURE PAGE 16 D. discoideum VC4 f r u i t i n g body l a g p l o t t e d a g a i n s t temperature. 48 17 P. p a l l i d u m f r u i t i n g body l a g p l o t t e d a g a i n s t temperature. 49 18 The square 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 p l o t t e d a g a i n s t time f o r D. discoideum 51 and P. p a l l i d u m . 19 D. discoideum VC4 f r u i t i n g body growth index p l o t t e d a g a i n s t temperature. 56 20 £• p a l l i d u m f r u i t i n g body expansion r a t e s p l o t t e d a g a i n s t temperature. E q u a t i o n (2c) 5 7 was used to f i t the l i n e . 21 P. p a l l i d u m f r u i t i n g body expansion r a t e s p l o t t e d a g a i n s t temperature. E q u a t i o n (4b) 59 was used to f i t the l i n e . 22 Components diagram o f the completed e x p l o i t a t i o n model. 67 2 3 The area o c c u p i e d by the f r u i t i n g b o d i e s and amoebae of D. discoideum and P. p a l l i d u m 70 at one day i n t e r v a l s are p l o t t e d a g a i n s t time. The d a t a was generated from Program V I I . 24 The presence or absence o f D. discoideum and P. p a l l i d u m f r u i t i n g b o d i e s are i n d i c a t e d 7 1 w i t h r e s p e c t to temperature. Twenty spore c o n c e n t r a t i o n s were used. 2 5 The presence or absence o f D. discoideum and P. p a l l i d u m f r u i t i n g b o d i e s are i n d i c a t e d 72 w i t h r e s p e c t to temperature. F i v e spore c o n c e n t r a t i o n s were used. 2 6 Presence o r absence 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 75 s i z e and temperature. 2 7 The presence o r absence 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 to 81 D. discoideum spore c o n c e n t r a t i o n and temperature. The presence or absence of D. discoideum 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 D. discoideum spore c o n c e n t r a t i o n and temperature. Components diagram o u t l i n i n g the make-up of Program IX. E x t e r n a l f o r c e , i n t e r f e r e n c e and e x p l o i t a t i o n sub-components are shown. The area o c c u p i e d by P. p a l l i d u m and D. discoideum f r u i t i n g b o d i e s i s p l o t t e d a g a i n s t temperature. S i x spore c o n c e n t r a - t i o n s were used. The areas p r e d i c t e d from Program 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 . Areas o c c u p i e d by D. discoideum and P. p a l l i d u m stock f r u i t i n g b o d i e s are p l o t t e d w i t h r e s p e c t t o temperature. G r a d i e n t I - 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 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 w i t h r e s p e c t to temperature. £° p a l l i d u m agar b l o c k experiment: The areas o c c u p i e d by f r u i t i n g bodies are p l o t t e d with r e s p e c t t o temperature. The presence or absence of P. p a l l i d u m amoebae on agar b l o c k s i s noted. D. discoideum ( g r a d i e n t I) c o l o n y expansion index i s p l o t t e d a g a i n s t 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 expansion index i s p l o t t e d a g a i n s t temperature. D. discoideum ( g r a d i e n t I I ) c o l o n y expansion index i s p l o t t e d a g a i n s t temperature. p a l l i d u m ( g r a d i e n t I I ) c o l o n y expansion index i s p l o t t e d - . a g a i n s t temperature. The expansion 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 expansion r a t e s of D. discoideum VC4 b e f o r e 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. x i v F I G U R E 4 0 4 1 4 2 4 3 4 4 45 4 6 4 7 4 8 4 9 PAGE T h e e x p a n s i o n r a t e s o f D . d i s c o i d e u m V C 4 a f t e r m e d i a c o n d i t i o n i n g a r e p l o t t e d a g a i n s t t e m p e r a t u r e . 1 3 3 T h e a m o u n t o f a r e a o c c u p i e d b y t h e t w o c o m p e t i t o r s b e f o r e a n d a f t e r c o m p e t i t i o n 1 3 6 i s p l o t t e d a g a i n s t t e m p e r a t u r e . T h e d a t a w a s o u t p u t f r o m P r o g r a m V T I . T h e a r e a o c c u p i e d b y P . p a l l i d u m a n d R' d i s c o i d e u m V 1 2 i s p l o t t e d a g a i n s t t e m p e r - 2 1 7 a t u r e . F i v e s p o r e c o n c e n t r a t i o n s w e r e u s e d . T h e a r e a o c c u p i e d b y P . p a l l i d u m a n d D . d i s c o i d e u m V 1 2 i s p l o t t e d a g a i n s t 2 1 8 t e m p e r a t u r e . F i v e s p o r e c o n c e n t r a t i o n s w e r e u s e d . T h e a r e a o c c u p i e d b y P . p a l l i d u m a n d Q° d i s c o i d e u m V 1 2 i s p l o t t e d a g a i n s t 2 1 9 t e m p e r a t u r e . F i v e s p o r e c o n c e n t r a t i o n s w e r e u s e d . T h e a r e a o c c u p i e d b y P . p a l l i d u m a n d D . d i s c o i d e u m V 1 2 i s p l o t t e d a g a i n s t 2 2 0 t e m p e r a t u r e . F i v e s p o r e c o n c e n t r a t i o n s w e r e u s e d . G r a d i e n t I I - T h e 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 f r o m t w e l v e s e r i a l c u l t u r e 2 2 1 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 . G r a d i e n t I I I - T h e 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 f r o m t e n s e r i a l c u l t u r e 2 2 2 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 . G r a d i e n t I V - T h e 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 f r o m f i v e s e r i a l c u l t u r e 2 2 3 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 . T h e a r e a s o c c u p i e d b y P . p a l l i d u m a n d R' d i s c o i d e u m f r u i t i n g b o d i e s a r e p l o t t e d 2 2 4 w i t h r e s p e c t t o t e m p e r a t u r e . V a r i o u s c o m b i n a t i o n s o f s p o r e s w h i c h h a d a n d h a d n o t e x p e r i e n c e d c o n t i n u e d c o m p e t i t i o n w e r e u s e d . X V FIGURE PAGE 50 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 are p l o t t e d w i t h r e s p e c t t o temperature. Some spores used to i n o c u l a t e g r a d i e n t s 225 ex p e r i e n c e d i n t r a s p e c i f i c c o m p e t i t i o n , o t h e r s d i d n o t . 51 C l o n i n g experiment: 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 are p l o t t e d w i t h r e s p e c t 226 to temperature. The P. p a l l i d u m spores used i n each g r a d i e n t came from s e p a r a t e c l o n e s . 52 D. discoideum agar b l o c k experiment: The areas o c c u p i e d by f r u i t i n g b o d i es are p l o t t e d w i t h r e s p e c t to temperature. The 227 presence o r absence o f D. discoideum amoebae on the agar b l o c k s i s noted. 53 The square 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 a g a i n s t time. A l l . d a t a i s transformed 2 31 to f i t the l i n e PH = 3t where A i s a r e a and t i s ti m e . 54 The square 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' discoideum ( s o l i d dots) and P. p a l l i d u m 2 32 (open c i r c l e s ) . A l l data i s transformed t o conform t o the l i n e d e s c r i b e d by e q u a t i o n ( 7 ) . x v i ACKNOWLEDGEMENT I would e s p e c i a l l y l i k e to thank my major p r o f e s s o r , Dr. P.A. L a r k i n , who was a source o f c o n s t r u c t i v e c r i t i c i s m , enthusiasm, and support, throughout t h i s study. I am a l s o i n d e b t e d t o ; Dr. D.W. F r a n c i s f o r c u l t u r e s and t e c h n i c a l i n f o r m a t i o n , Dr. K.B. Raper f o r c e l l u l a r s l i m e mold and b a c t e r i a c u l t u r e s , and Dr. C.S. M o i l i n g f o r manuscript comments and h e l p with the f o r m u l a t i o n o f some of the mathematical components, and Mr. F. Maurer f o r ph o t o g r a p h i c s e r v i c e s . Dr. J.T. Bonner, Dr. C.L. McLay, Dr. J.D. M c P h a i l , and Dr. N.J. Wilimovsky made many su g g e s t i o n s which I have i n c o r p o r a t e d i n t o the man u s c r i p t . F i n a l l y , I would l i k e to thank my w i f e , Winnie, who typed the manuscript s e v e r a l times o v e r . 1 INTRODUCTION The p r o c e s s o f animal c o m p e t i t i o n has f a s c i n a t e d a g r e a t many e c o l o g i s t s over the y e a r s ; and t h e i r i n t e r e s t has y i e l d e d a l a r g e number of d e s c r i p t i v e , e x p e r i m e n t a l , and t h e o r e t i c a l s t u d i e s . I t has a l s o r e s u l t e d i n a c e r t a i n amount of c o n f u s i o n over the exact meaning o f the term c o m p e t i t i o n . M i l n e (1961) and B i r c h (1957) have devoted e n t i r e papers t o the s u b j e c t , and have noted t h a t d e f i n i t i o n s ranged from broad t o s t r i c t c overage. F o r example, Odum (1959) i n c l u d e s any p r o c e s s i n v o l v i n g the common use of space, f o o d and l i g h t ; o r waste m a t e r i a l a c t i o n , o r mutual p r e d a t i o n , o r s u s c e p t - i b i l i t y t o c a r n i v o r e s and d i s e a s e . Clements-, and S h e l f o r d (1939) p r o v i d e a s t r i c t d e f i n i t i o n . In t h e i r words: "... the p r o c e s s may be d e f i n e d i n c l u s i v e l y as a more o r l e s s a c t i v e demand i n excess o f the immediate s u p p l y o f m a t e r i a l o r c o n d i t i o n on the p a r t o f two o r more organisms". The term has a l s o been s u b - d i v i d e d . N i c h o l s o n (1954) used the terms " c o n t e s t " c o m p e t i t i o n (the c o m p e t i t o r s c o n t e s t f o r t h e i r r e q u i s i t e s "... and a l l o f the gov e r n i n g r e q u i s i t e c o l l e c t i v e l y s e cured by animals i s used e f f e c t i v e l y i n m a i n t a i n i n g the p o p u l a t i o n . " ) and "scramble" c o m p e t i t i o n ("... some, and at times a l l , o f the r e q u i s i t e secured by the competing animals takes no p a r t i n s u s t a i n i n g the p o p u l a - t i o n b e i n g d i s s i p a t e d by i n d i v i d u a l s which o b t a i n i n s u f f i c i e n t f o r s u r v i v a l . " ) . A l l e e e t a l (1949) have i d e n t i f i e d "co- o p e r a t i v e c o m p e t i t i o n " ( b e n e f i c i a l e f f e c t ) and " d i s - o p e r a t i v e 2 c o m p e t i t i o n " (harmful e f f e c t ) . The one i d e a t h a t runs throughout a l l the d e f i n i t i o n s and s u b d i v i s i o n s i s t h a t animals compete when they use a r e s o u r c e t h a t i s i n s h o r t s u p p l y . A l s o , both N i c h o l s o n (1954) and Park (1954) d i s c u s s the importance o f p h y s i c a l f a c t o r s , such as temperature. F i n a l l y , Park (1954) p o i n t s out t h a t e x p l o i t a t i o n (the common use o f a r e s o u r c e i n s h o r t supply) and i n t e r f e r e n c e (the d i r e c t i n t e r a c t i o n s between c o m p e t i t o r s ) can p l a y a c t i v e r o l e s i n the d e t e r m i n a t i o n o f c o m p e t i t i v e outcomes. As a s t a r t i n g p o i n t f o r t h i s study the r o l e o f e x p l o i t a t i o n f o r r e s o u r c e s i n s h o r t s u p p l y , the e f f e c t s o f p h y s i c a l f a c t o r s , and the o c c u r r e n c e o f i n t e r f e r e n c e , w i l l a l l be c o n s i d e r e d . To t h i s end, the components method w i l l be used. The b i o l o g i c a l r e l e v a n c e o f the method has been demonstrated by H o l l i n g (1963, 1964, 1965) d u r i n g the c o n s t r u c t i o n o f a p r e d a t i o n model, and has been d i s c u s s e d i n a s e r i e s o f papers e d i t e d by Watt (1966). S i x b a s i c s t e p s are i n v o l v e d . A pr o c e s s i s broken i n t o what appear to be e x p e r i m e n t a l l y t r a c t a b l e components. The e f f e c t o f a component i s demonstrated e x p e r i m e n t a l l y and modelled m a t h e m a t i c a l l y . The sub-model i s then used to make p r e d i c t i o n s which are t e s t e d i n d e p e n d e n t l y . F a i l u r e o f the sub-model i n i t i a t e s a r e a s s e s s - ment o f the component and s t a r t s the c y c l e back a t the f i r s t s t e p . Sub-models are l i n k e d t o g e t h e r as they are f o r m u l a t e d and the r e s u l t i n g model i s p e r i o d i c a l l y t e s t e d a g a i n s t 3 independent d a t a . The use o f the components method i s p o s s i b l e o n l y because p a s t work on the mechanisms which mediate c o m p e t i t i v e i n t e r a c t i o n s has advanced s i g n i f i c a n t l y through use o f e x p e r i m e n t a l t e c h n i q u e s i n both the l a b o r a t o r y (Park 1954, 1965) and the f i e l d ( U l l y e t t 1950, C o n n e l l 1961a, b ) . S t u d i e s of the consequences of c o n t i n u e d c o m p e t i t i o n have p r o g r e s s e d at a d i f f e r e n t l e v e l . F o r the most p a r t they have been of a t h e o r e t i c a l n ature and have c e n t e r e d around the L o t k a - V o l t e r r a model o f i n t e r s p e c i e s c o m p e t i t i o n (Gause 1934, K o s t i t z i n 1939, S l o b o d k i n 1961, L a r k i n 1963). Through the y e a r s t h i s model has been c l a r i f i e d and s l i g h t l y a l t e r e d but the f o u r o r i g i n a l p r e d i c t i o n s r e g a r d i n g the outcome o f c o m p e t i t i v e s i t u a t i o n s have remained i n t a c t . The p r e d i c t i o n s o f e x c l u s i o n ( c o m p e t i t o r p o p u l a t i o n "a" e x c l u d e s "b", o r the r e v e r s e ) have been demonstrated i n the l a b o r a t o r y (Gause 19 34) and i n the f i e l d ( E l t o n e t a l 1946, B r i a n 1952). The p r e d i c t i o n s of s t a b l e e q u i l i b r i u m (both c o m p e t i t o r p o p u l a t i o n s s t a b i l i z e i r r e s p e c t i v e o f the i n i t i a l numbers) and u n s t a b l e e q u i l i b r i u m ( s t a b i l i t y depends upon i n i t i a l numbers, under some i n i t i a l number c o n d i t i o n s both p o p u l a t i o n s s t a b i l i z e and p e r s i s t ; under o t h e r s , one p o p u l a t i o n e x c l u d e s the o t h e r ) remain u n t e s t e d and un- demonstrated i n nature because the parameters r e q u i r e d by t h e model are d i f f i c u l t to a s s e s s . R e c o g n i z i n g t h i s f a c t , MacArthur and L e v i n s (1964, 1967) have r e s t r i c t e d i n i t i a l 4 c o n d i t i o n s and t h e o r e t i c a l l y d e r i v e d r e l a t i o n s h i p s between c o m p e t i t i o n and c o e x i s t e n c e . They demonstrated t h a t when t h r e e p o p u l a t i o n s compete so t h a t 1 and 3 i n t e r a c t with 2 i n the same way ( C< ) and with each o t h e r i n the same way ( (3 ) , p o p u l a t i o n 2 can do one of t h r e e t h i n g s . When (X i s l a r g e 2 can be exc l u d e d o r can converge wi t h 1 or 3. When 0( i s s m a l l 2 can d i v e r g e from 1 and 3 towards a phenotype i n t e r - mediate between the two. In t h i s s i t u a t i o n c o m p e t i t i o n i s a s e l e c t i v e f o r c e , convergence o r di v e r g e n c e are d i r e c t i o n s o f movement with r e s p e c t to s e l e c t i o n , and c o e x i s t e n c e i s the end r e s u l t . There i s a l s o 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 e v i d e n c e (Keast 1968, F i c k e n e t al 1968) and at l e a s t one l a b o r a t o r y study (Seaton and An t o n o v i c s 1967) l i n k i n g c o m p e t i t i o n , d i v e r g e n c e , and c o e x i s t e n c e . And t h e r e are l a b o r a t o r y s t u d i e s ( M i l l e r 1964a, b, 1967) i n which D r o s o p h i l a melanoqaster and D. simulans have been used to demonstrate a r e l a t i o n s h i p between convergence and c o e x i s t e n c e . In g e n e r a l , however, the l i n k between c o m p e t i t i o n , convergence o r d i v e r g e n c e , and c o e x i s t e n c e i s tenuous and i n need of f u r t h e r e x p e r i m e n t a l work. S i n c e t h i s study was conducted i n the l a b o r a t o r y under r e s t r i c t e d c o n d i t i o n s i t should be p o s s i b l e to t e s t the h y p o t h e s i s t h a t c o m p e t i t i o n can r e s u l t i n c o e x i s t e n c e . By n o t i n g the changes e x p e r i e n c e d by the competing p o p u l a t i o n s i t might a l s o be p o s s i b l e to ass e s s the magnitude and the d i r e c t i o n o f s e l e c t i v e f o r c e s 5 involved, and to determine some of the conditions under which convergence or divergence might occur. THE ANIMALS The A c r a s i a l e s o r " c e l l u l a r s l i m e molds" were f i r s i d e n t i f i e d i n 1880 by Van Tieghem. T h e i r l i f e c y c l e b e g i n s i n the spore stage which germinates to produce v e g e t a t i v e amoebae which d i v i d e by m i t o s i s , consume b a c t e r i a and aggregate to produce f r u i t i n g b o d i e s . The s i z e , shape, and c o l o u r of P. p a l l i d u m Salvado and D. discoideum VC4 and V12 spores are d i f f e r e n t . , ( D. discoideum VC4 spores are about 18 /j l o n g and 8 ja wide. They are k i d n e y shaped and have a d i s t i n c t i v e g r e e n - g o l d hue P. p a l l i d u m Salvador spores are about h a l f t h i s s i z e , e l l i p s o i d , and p a l e y e l l o w . 7 The s i z e d i f f e r e n c e suggests t h a t the D. discoideum VC4 s t r a i n i s t y p i c a l l y " d i p l o i d " and has 14 chromosomes w h i l e the P. p a l l i d u m S a l v a d o r s t r a i n i s " h a p l o i d " . Upon g e r m i n a t i o n the spores produce amoebae, which i n most c a s e s , are v e r y s i m i l a r . Both' s p e c i e s produce amoebae, which are s m a l l "with a number o f f i l o s e pseudopods" (Bonner 1967). The amoebae are cap a b l e o f consuming at l e a s t 9 3 d i f f e r e n t s t r a i n s o f b a c t e r i a (Singh 1946) although some b a c t e r i a appear t o i n h i b i t r a t h e r than support growth. Raper (19 37) found t h a t Gram-negative, non-slimy b a c t e r i a l i k e E s c h e r i c h i a c o l i were the most s u i t a b l e s t r a i n f o r l a b o r a t o r y c u l t u r e o f c e l l u l a r s l i m e molds. The amoebae d i v i d e by m i t o s i s and when f o o d becomes s c a r c e a substance which has been c a l l e d a c r a s i n (and which remains l a r g e l y u n i d e n t i f i e d ) i s produced by founder c e l l s . T h i s substance a t t r a c t s o t h e r amoebae which move towards the a g g r e g a t i o n c e n t e r p r o d u c i n g a c r a s i n themselves. In D. discoideum the ch e m i c a l g r a d i e n t a l o n g which the c e l l s move, i s shortened by the p r o d u c t i o n of p h o s p h o d i e s t e r a s e which breaks the a c r a s i n down. The exact mechanics o f t h i s procedure v a r y from s p e c i e s to s p e c i e s . In the case o f D„ discoideum, a g g r e g a t i o n o c c u r s i n p u l s e s and the a g g r e g a t i n g amoebae form l o o s e l y i n t e g r a t e d streams f l o w i n g towards the a g g r e g a t i o n c e n t e r ( S h a f t e r 1956). As a g g r e g a t i o n advances the streams become more dense and the amoebae adhere s t r o n g l y to one another. The a g g r e g a t i n g streams produce a mass o f amoebae o r 8 pseudoplasmodium which m i g r a t e s . During t h i s p r o c e s s the amoebae b e g i n t o d i f f e r e n t i a t e to form p r e - s p o r e and p r e - s t o c k c e l l s . Not so much i s known about a g g r e g a t i o n i n P. p a l l i d u m , but i t has been observed d u r i n g the cou r s e o f t h i s study t h a t pseudoplasmodia migrate i n response t o l i g h t as they do i n D. disco i d e u m . K o n i j n e t a l (1969) a l s o r e p o r t s t h a t £• p a l l i d u m does not produce a c h e m i c a l t o break down a c r a s i n . F o l l o w i n g the a g g r e g a t i o n stage the c e l l s b e g i n t o d i f f e r e n t i a t e t o form st o c k and spore c e l l s . In D. discoideum about 20% o f the c e l l s are i n v o l v e d i n stock f o r m a t i o n . The stock c e l l s b u i l d up the stock with the spore c e l l s f o l l o w i n g b e h i n d . When st o c k f o r m a t i o n i s complete the spores are a t the top o f the s t o c k , i n the case o f D. discoideum, o r d i s t r i b u t e d a t i n t e r v a l s along the s t o c k , i n the case o f P. p a l l i d u m . The two s p e c i e s used i n the p r e s e n t study are e a s i l y d i s t i n g u i s h e d at the f r u i t i n g body s t a g e . P. p a l l i d u m f r u i t i n g b o d i e s are d i s t i n c t when formed at about 24°C ( F i g . 1) but become d i s o r g a n i z e d at h i g h e r temperatures ( F i g . 2 ) . D. discoideum f r u i t i n g b o d i e s remain much the same over i t s e n t i r e growth range ( F i g . 3 ) . When mixed, the c o - f r u i t i n g s t r a i n s produce w e l l o r g a n i z e d and d i s t i n c t f r u i t i n g b o d i e s ( F i g . 4 ) . C e l l u l a r s l i m e mold s p e c i e s r e a c t to s e v e r a l e n v i r o n m e n t a l c h a r a c t e r i s t i c s . T h e i r pH t o l e r a n c e ranges from about 4.0 t o 7.8 (Cavender 1963) and h u m i d i t y (Whittingham and Raper 1957) and l i g h t (Bonner 1950) are 9 i m p o r t a n t i n some c a s e s . The two s t r a i n s used had w e l l d e f i n e d temperature t o l e r a n c e s with D. discoideu m growing from 9.0° to 26.5° and P. p a l l i d u m from 18.0° t o 37.5° c e n t i g r a d e . P. p a l l i d u m i s a l s o g r e a t l y i n f l u e n c e d by r i c h - ness of the medium and amount o f fo o d a v a i l a b l e . F o r t h i s r e a s o n a simple medium was used and food c o n c e n t r a t i o n was c l o s e l y c o n t r o l l e d . F i n a l l y , the g e n e t i c s of the A c r a s i a l e s are s t i l l v e r y much a mystery. I t i s g e n e r a l l y assumed t h a t 14 chromosome amoebae are d i p l o i d and t h a t 7 chromosome amoebae i are h a p l o i d . Sussman e t a l (1962) r e p o r t t h a t some s t r a i n s are d i p l o i d and t h a t o t h e r s are h a p l o i d and t h a t o t h e r s c o n t a i n both h a p l o i d s and d i p l o i d s . Loomis ( p e r s . comm.) adds t h a t amoebae c o a l e s c e about one i n a thousand times d u r i n g a g g r e g a t i o n to form d i p l o i d s which l o s e chromosomes on subsequent m i t o t i c d i v i s i o n s so t h a t a p o p u l a t i o n c o u l d have members wit h from 7 to 14 chromosomes. I t i s g e n e r a l l y agreed t h a t m e i o s i s does not o c c u r . Sussman (1956) met w i t h no success when t r y i n g to demonstrate the o c c u r r e n c e o f r e c o m b i n a t i o n and Sussman e t a l (1961) r e p o r t e d one recombina- t i o n which has not been repeated.- Figure 1 £• pallidum f r u i t i n g body grown at 24° centigrade. , 0 .25mm r F i g u r e 2 pallidum f r u i t i n g body grown at 36 centigrade. 0.25mm F i g u r e 3 D. d iscoideum f r u i t i n g b o d i e s grown at 2 0 c e n t i g r a d e .  F i g u r e 4 D. discoideum and P. p a l l i d u m c o - f r u i t i n g at about 23.0° c e n t i g r a d e . i C 0 . 25 mm 14 MATERIALS AND METHODS L a b o r a t o r y Methods The b a c t e r i a ( E s c h e r i c h i a c o l i 281) used as a food source were o b t a i n e d from Dr. K.B. Raper, Department o f B a c t e r i o l o g y , The U n i v e r s i t y o f W i s c o n s i n . They were main- t a i n e d by a s e r i e s o f bi - w e e k l y s e r i a l t r a n s f e r s . The medium used was pre p a r e d from 1000 cc o f water, 15 g of D i f c o - B a c t o Agar, 5 g o f y e a s t e x t r a c t , 5 g o f t r i p t o s e , and 1 g o f d e x t r o s e . The c o n s t i t u e n t s were d i s s o l v e d i n 100 cc of c o l d water and the s o l u t i o n made up to 1000 c c wit h b o i l i n g d i s t i l l e d water. The medium was a u t o c l a v e d f o r 20 minutes at 15 pounds per square i n c h and 25 7°F, and poured i n t o s t e r i l e p e t r i d i s h e s . V/hen the agar had s e t , b a c t e r i a were s t r e a k e d on the s u r f a c e and allowed to grow f o r two days at room temperature, then removed from the s u r f a c e w i t h a s p a t u l a . A mixture o f 0.6 ml o f b a c t e r i a and 4.4 ml o f s t e r i l e d i s t i l l e d water was p l a c e d i n a 5 cc s y r i n g e and was then ready f o r use i n the c e l l u l a r s l i m e mold c u l t u r e d i s h e s . The c e l l u l a r s l i m e mold medium was pre p a r e d by h e a t i n g 5 g o f hay i n 1000 cc o f d i s t i l l e d water f o r 15 minutes. The hay was then removed, 20 g of D i f c o - B a c t o Agar, and 1 g o f de x t r o s e were added, the s o l u t i o n was a u t o c l a v e d f o r 20 minutes at 15 pounds per square i n c h and 2 57°F, and was poured i n t o s t e r i l e growth chambers (the type o f chamber depending upon the experiment b e i n g c o n d u c t e d ) . The chambers were then p l a c e d i n a r e f r i g e r a t o r at about 4°C f o r seven days. 15 The chambers were then removed from the r e f r i g e r a t o r and allowed to achieve room temperature. The b a c t e r i a l food was then added. 2 F o r every 2000 mm o f s u r f a c e a r e a on the c u l t u r e d i s h , 0.2 ml o f s t a n d a r d b a c t e r i a l - w a t e r s o l u t i o n was added. The a l e q u o t o f b a c t e r i a l s o l u t i o n was p l a c e d i n the c e n t e r o f the growth s u r f a c e and was spread over the s u r f a c e by r e v o l v - i n g the chamber at a 45° a n g l e . The chambers were then allowed to s i t f o r two hours d u r i n g which time the m o i s t u r e i n the b a c t e r i a l - w a t e r s o l u t i o n was absorbed by the agar. T h i s procedure produced a dry agar s u r f a c e covered w i t h a homogeneous "lawn" o f b a c t e r i a . During the course o f the study s e v e r a l d i f f e r e n t e x p e r i m e n t a l set-ups were used. The t h r e e major v a r i a t i o n s are mentioned here and any minor changes are d e s c r i b e d w i t h the r e s u l t s . Method 1 was used t o grow s i n g l e s p e c i e s and mixed s p e c i e s from p o i n t source i n o c u l a t i o n s . The c u l t u r e chambers 2 were 60 mm p l a s t i c p e t r i d i s h e s w i t h a p p r o x i m a t e l y 2000 mm s u r f a c e a r e a . The d i s h e s were h a l f f i l l e d with c e l l u l a r s l i m e mold agar, a l l o w e d to s i t f o r one week, and covered with 0.2 ml o f s t a n d a r d f o o d s o l u t i o n . C e l l u l a r s l i m e mold spores from e i t h e r s p e c i e s were p i c k e d from the f r u i t i n g b o d i e s o f s t o c k c u l t u r e s , suspended i n water, a g i t a t e d to break up clumps, and counted u s i n g a haemocytometer. At l e a s t f o u r and u s u a l l y s i x or e i g h t counts were made. The mean spore number 16 per ml o f spore s o l u t i o n was c a l c u l a t e d , and the s o l u t i o n was d i l u t e d t o the 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 . A known number of spores suspended i n .001 ml o f water was then p l a c e d i n the c e n t e r o f the p e t r i d i s h . The d i s h was p l a c e d i n an i n c u b a t o r and the spores were allowed to germinate and produce amoebae v/hich produced a c o l o n y . The area covered by the c o l o n y a t v a r i o u s p e r i o d s o f time was observed under a b i n o c u l a r d i s s e c t i n g microscope. Method 2 was used to grow s i n g l e s p e c i e s and mixed s p e c i e s from many p o i n t s of i n o c u l a t i o n . The c u l t u r e chambers were 60 mm p e t r i d i s h e s which were h a l f f i l l e d with c e l l u l a r s l i m e mold medium and p l a c e d i n a r e f r i g e r a t o r f o r one week. The spores were counted as i n Method 1, and a p p r o p r i a t e mixtures of the two s p e c i e s were made up. The spore m i x t u r e s were then mixed with the b a c t e r i a - w a t e r s o l u t i o n which was added to the s u r f a c e o f the p l a t e i n the u s u a l manner. In t h i s way spores were d i s p e r s e d over the s u r f a c e o f the growth p l a t e . The p l a t e s were i n c u b a t e d and the appearance o f f r u i t i n g b o d i e s was noted. Method 3 was used to grow mixed s p e c i e s c u l t u r e s over a c o n t i n u o u s temperature range. The c u l t u r e chambers were long s t a i n l e s s s t e e l troughs with g l a s s l i d s and c o n t a i n - 2 i n g about 11,000 mm s u r f a c e a r e a . They were f i l l e d w ith agar and p l a c e d i n the r e f r i g e r a t o r . Spore m i x t u r e s were added w i t h the 1.2 ml a l e q u o t of b a c t e r i a l f o o d . The chambers were then p l a c e d on a temperature g r a d i e n t and allowed to i n c u b a t e 17 f o r 7 o r 14 days. At the end o f the I n c u b a t i o n p e r i o d the ar e a covered by " f r u i t i n g - b o d i e s "was noted. Most o f the i n c u b a t i o n was conducted i n a temperature g r a d i e n t d e v i c e which was c o n s t r u c t e d f o r t h i s study. A 200 pound aluminum b l o c k heated at one end and c o o l e d at the o t h e r , was i n s u l a t e d w i t h p o l y - u r e t h a n e . C u l t u r e d i s h e s were p l a c e d i n s m a l l h o l e s i n the i n s u l a t i o n next to the b l o c k ( F i g . 5 ) . Two temperature g r a d i e n t s were used. The main g r a d i e n t was heated by a HAAKE model FS c o n s t a n t temperature c i r c u l a t o r c a p a b l e o f c o n t r o l l i n g temperature to w i t h i n i .004° c e n t i g r a d e ; the c o l d end was m a i n t a i n e d by a PARMETIC compressor, c o o l i n g water i n a 100 1 v a t and c o n t r o l l e d w i t h a HONEYWELL thermostat model T6 75 A1011, c a p a b l e o f 0.1° c e n t i g r a d e a c c u r a c y . The secondary g r a d i e n t had the same c o l d water c o n t r o l but the hot end was ma i n t a i n e d u s i n g a HAAKE model ED UNITHERM which was a c c u r a t e t o w i t h i n 0.01°C. For both arrangements, the g r a d i e n t c o u l d be shortened o r lengthened by changing water temperature at e i t h e r end. Temperature was monitored and r e c o r d e d c o n t i n u o u s l y at seven p o s i t i o n s along the l e n g t h o f the g r a d i e n t s u s i n g a YSI TELETHERMOMETER and YSI MODEL 80 RECORDER. Throughout the study one s t r a i n o f P. p a l l i d u m was used. I t was m a i n t a i n e d at 34°C from A p r i l 1968 t o May 1969, and at 29°C from May 1969 to A p r i l 19 70. C u l t u r e s were m a i n t a i n e d w i t h a s e r i e s o f weekly o r bi-we e k l y s e r i a l t r a n s - f e r s and c a r e was taken t o mix the spores from each r e p l i c a t e Fiqure 5 Plan (top) and side (bottom) view of the temperature gradient constructed f o r t h i s study. The l e t t e r "a" represents p e t r i dish chambers, "b" represents the cu l t u r e gradient chamber, "c" represents the cold water l i n e , "d" represents the hot water l i n e , "e" represents the aluminum block i n side view, and " f " the urathane i n s u l a t i o n . A l l measurements are i n inches.  19 b e f o r e e s t a b l i s h i n g new stock c u l t u r e s . Separate s t o c k s were ma i n t a i n e d a t o t h e r temperatures f o r v a r i e d l e n g t h s o f time as checks f o r experiments i n p r o g r e s s . Three s e p a r a t e s t r a i n s of D. discoideum were used. R' discoideum V12 was m a i n t a i n e d from F e b r u a r y 1968 t o F e b r u a r y 1969 when i t was d e s t r o y e d by an i n c u b a t o r f a i l u r e . D. discoideum VC4 was used as a replacement and k e p t from March 1968 t o A p r i l 1970 at 20°C. D. discoideum DF was used f o r a s h o r t p e r i o d from March 1968 t o June 1968. The VC4 stock was l y o p h i l i z e d t o a v o i d f u r t h e r stock l o s s . Throughout the study s t o c k s have been i d e n t i f i e d and d a t a from one s t o c k has not been used t o s i m u l a t e o u t p u t s from another. E x p e r i m e n t a l E r r o r The e x p e r i m e n t a l methods o u t l i n e d on the p r o c e e d i n g pages i n v o l v e d s e v e r a l s o u r ces of e r r o r which were c o n s t a n t throughout the study. The temperature equipment was a c c u r a t e to w i t h i n 0.5°C f o r the f i r s t y e a r and a f t e r improvement, a c c u r a c y was i n c r e a s e d to at l e a s t - 0.3°C. Whenever a temperature i s mentioned i n the r e s u l t s s e c t i o n a 0.3°C v a r i a t i o n i s i m p l i e d u n l e s s o t h e r w i s e s t a t e d . The medium used f o r c e l l u l a r s l i m e mold growth was kept homogeneous by u s i n g the same hay f o r a p e r i o d o f two y e a r s from the b e g i n n i n g to end o f the study. The hay was 20 kept i n a s e a l e d p l a s t i c bag at a l l times and although t h e r e was a breakdown 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 changes o c c u r r e d . The b a c t e r i a were grown at room temperature through- out the study. During the two year experiment p e r i o d the s t r a i n may have undergone some media c o n d i t i o n i n g or m u t a t i o n a l changes. In an attempt to guard a g a i n s t t h i s , Dr. D, F r a n c i s (who was a l s o u s i n g the E. c o l i 281 stock) made d i l u t e spreads, and p i c k e d up 281 plaques on two o c c a s i o n s ( d u r i n g the summer o f 1968 and the s p r i n g o f 1969). C e l l u l a r ' s l i m e mold growth on the E. c o l i 281 food source was a l s o checked d u r i n g the study p e r i o d . The b a c t e r i a l "lawn" on the s u r f a c e o f the c u l t u r e d i s h e s was assumed t o be homogeneous i n t h i c k n e s s . However, v i s u a l checks with a b i n o c u l a r d i s s e c t i n g microscope suggested t h e r e p r o b a b l y were some areas where the lawn was t h i c k e r , even though c a r e was taken t o spread the b a c t e r i a i n a. standard way. When spores were mixed and spread with the b a c t e r i a they too were s u b j e c t to p o s s i b l e non-homogeneous s p r e a d i n g . Since t h e r e was no way to check exact spore d i s t r i b u t i o n i t was assumed t h a t they were d i s t r i b u t e d on the agar s u r f a c e randomly. Spore counts p r i o r to i n o c u l a t i o n were made u s i n g a haemocytometer. C o n f i d e n c e l i m i t s (95%) were c a l c u l a t e d f o r every mean count when the work f i r s t began, but i t was soon d i s c o v e r e d t h a t i n most cases s i x counts y i e l d e d optimum r e s u l t s c o n s i d e r i n g the work i n v o l v e d i n c o u n t i n g and the accuracy a t t a i n e d . The cases i n which c o n f i d e n c e l i m i t s were c a l c u l a t e d suggested t h a t the mean count may d e v i a t e from the 21 a c t u a l count by as much as 20%. But s i n c e a c c u r a c y i n c r e a s e s i n p r o p o r t i o n to the r e c i p r o c a l o f the number o f counts t h i s was deemed a c c e p t a b l e . Mathematics A mathematical d e s c r i p t i o n o f each sub-component c o u l d have been a c h i e v e d by a c t u a l l y d e s c r i b i n g the mechanics of the p r o c e s s i n mathematical terms, o r by f i t t i n g a p o l y - nomial e q u a t i o n t o the observed r e l a t i o n s h i p . In a l l cases an attempt was made to implement the former approach. T h i s attempt met w i t h success d u r i n g the d e s c r i p t i o n o f the form o f amoebae and f r u i t i n g body expansion ( e q u a t i o n l c ) and d u r i n g the d e s c r i p t i o n o f the r e l a t i o n s h i p between c o m p e t i t o r numbers, temperature, and P. p a l l i d u m i n h i b i t i o n (Program V I I I ) . However, the l a g e q u a t i o n s (2b) and the expansion r a t e e q u a t i o n s (3c, 4b) were not s t r i c t l y m e c h a n i s t i c . The mechanisms i n v o l v e d i n these p r o c e s s e s were undoubtedly complex and 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 , d i s p e r s a l mechanics, and f e e d i n g mechanics. Rather than t r e a t each o f these p r o c e s s e s i n d e p e n d e n t l y , t h e i r t o t a l e f f e c t was c o n s i d e r e d w i t h r e s p e c t to temperature. T h i s meant t h a t the l a g and r a t e e q u a t i o n s were not m e c h a n i s t i c , nor were they d e t e r m i n i s t i c . A l l o f the parameters i n the e q u a t i o n s were both meaningful and measurable i n b i o l o g i c a l terms. In a l l c a s e s , once the e x p e r i m e n t a l d a t a had been g a t h e r e d , a p p r o p r i a t e e q u a t i o n s were f o r m u l a t e d . The b e s t 22 set of parameter values was then chosen by an i t e r a t i v e f i t t i n g procedure and by the c a l c u l a t i o n of the sum of squares of the deviations between the observed and ca l c u l a t e d r e l a t i o n - ships. The d e s c r i p t i v e power of the r e l a t i o n s h i p chosen by t h i s procedure was then tested by c a l c u l a t i n g the c o r r e l a t i o n c o e f f i c i e n t . 23 RESULTS SECTION I MECHANICS OF COMPETITION Before any a c t u a l c o m p e t i t i v e experiments were conducted i t was important t o d e s c r i b e both the way i n which, and the r a t e s a t which, the two s p e c i e s consumed the r e s o u r c e s of food and space i n s e p a r a t e c u l t u r e s . I t was known from the l i t e r a t u r e , and c o n f i r m e d by o b s e r v a t i o n , t h a t the c e l l u l a r s l i m e mold l i f e c y c l e went from spore, to v e g e t a t i v e amoebae, to a g g r e g a t i o n , t o f r u i t i n g body, to spore. I t was a l s o known t h a t o n l y the v e g e t a t i v e amoebae a c t u a l l y used up food and space, but t h e i r a c t i o n depended upon a l l the o t h e r steps i n the l i f e c y c l e . T h e r e f o r e , to d e s c r i b e adequately the r a t e of use of f o o d and space, a l l the stages i n the l i f e c y c l e had t o be i n v e s t i g a t e d . Spore Germination When spores were p l a c e d on an agar s u r f a c e i n the p r e s e n c e o f b a c t e r i a l food they r e q u i r e d a c e r t a i n p e r i o d o f time to germinate and produce amoebae. T h i s time p e r i o d might be c a l l e d the spore g e r m i n a t i o n l a g . I t was f u r t h e r observed t h a t as the temperature changed the spore g e r m i n a t i o n l a g a l s o changed. To q u a n t i f y these o b s e r v a t i o n s , d a t a were c o l l e c t e d f o r both s p e c i e s by p l a c i n g a known number o f spores i n the c e n t e r o f an agar f i l l e d p e t r i d i s h and o b s e r v i n g the time r e q u i r e d f o r spore g e r m i n a t i o n . The d a t a f o r D. discoideum ( F i g . 6) and P. p a l l i d u m ( F i g . 7) suggested t h a t the g e r m i n a t i o n F i g u r e 6 The 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 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 t e m p e r a t u r e 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 from e q u a t i o n ( 2 b ) . T„ = 27.5, T_ = 9.0, T = 23.0, K = 1.60137, C = 4 . 7 4 4 0 3 . L ' o ' ' F i g u r e 7 The 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 t e m p e r a t u r e i n degrees 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 (2b)„ T = 37.0, T = 18.0, T = 31.0, K = 0.81132, C = 2.59356. CO >-< Q LU < 2 2 or LU -j O ' ' i ' i J 1 I I I I I I 1 1 1 1 1 L_ 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 TEMPERATURE °C CO >- < . Q UJ O S 1 z cr LU O o 1 1 V \ \ \ 1 - \ o o \ \ o o ° v ° o o \ \ \ o X <$> o ° X . ^ o o ° o oo'o~~~$-08-~ • • • • 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 decreased as temperature i n c r e a s e d , reached a minimum at some optimum temperature and then i n c r e a s e d with f u r t h e r i n c r e a s e s i n temperature. These o b s e r v a t i o n s form the b a s i s o f t h r e e assump- t i o n s which must be met by any e q u a t i o n which d e s c r i b e s the r e l a t i o n s h i p between l a g and temperature. The assumptions are: (1) the spores do not germinate below some temperature T T , (2) spores do not germinate above some temperature T^, (3) the g e r m i n a t i o n time i s o p t i m i z e d at some optimum temperature T . ^ o The assumptions demand t h a t the curves have a s l o p e of minus i n f i n i t y a t T L and T H and have a s l o p e o f zero at T q ( F i g . 8 ) . The absence of any o t h e r r e s t r i c t i o n s on the curve i m p l i e s t h a t T o may o c c u r anywhere between T^ and T H and t h a t the curve may move t o any p o s i t i o n on the time a x i s . A f a m i l y o f curves which i n c o r p o r a t e s the t h r e e assumptions i s r e p r e s e n t e d by the f o l l o w i n g e q u a t i o n : ^ - K dT " K T - T ° ' (2a) ( - l ) T ^ + T'-T H + T • T L - T H « T L where dL/dT i s the r a t e of change of g e r m i n a t i o n time with r e s p e c t t o temperature, T i s temperature, T Q i s temperature optimum, i s temperature low (below which no g e r m i n a t i o n o c c u r s ) , T^ i s temperature h i g h (above which no g e r m i n a t i o n o c c u r s ) , and K i s a c o n s t a n t . T h i s e q u a t i o n may be i n t e g r a t e d F i g u r e 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 c u r v e s which have i n f i n i t e s l o p e s at T (A) and T (B), and a s l o p e o f zero a t T ( C ) . TIME OF GERMINATION o •-»> r\> GO ^ - :—i — r 1 r~ m m XI > H C J3 m o O 27 b y m a k i n g u s e o f t h e f o l l o w i n g i d e n t i t i e s ( D w i g h t 1947) dx X X - £ x - q xdx X 1 l o g | x | - |. 2a 2a dx X where X = ax + bx + c and where p and q a r e r o o t s o f t h e q u a d r a t i c . The i n t e g r a t i o n y i e l d s t h e f o l l o w i n g g e n e r a l e q u a t i o n : L = K [ ( - . 5 l o g | ( - 1 ) T 2 + T ( T H + T L ) - T R • T L | ) - T + T H L - 1 l o g T - T H [ 2 T - T H L T - T L K • T T - T H L l o g T - T H T - T. + C (2b) where L i s t h e s p o r e g e r m i n a t i o n l a g and C i s a c o n s t a n t o f i n t e g r a t i o n . A l l t h e o t h e r t e r m s were d e f i n e d f o r ( 2 a ) . T h i s e q u a t i o n , and a l l t h o s e t h a t f o l l o w , i s n o t j u s t a c u r v e o f " b e s t f i t " . I t i s b a s e d upon r e a l i s t i c b i o l o g i c a l f a c t s and a s s u m p t i o n s and c o n t a i n s o n l y m e a s u r a b l e v a r i a b l e s . T h e r e a r e no unknown v a r i a b l e s , o r v a r i a b l e s w h i c h t a k e up unknown s o u r c e s o f e r r o r . The e q u a t i o n does c o n t a i n two c o n s t a n t s K and C. But t h e s e d e p e n d d i r e c t l y u p o n Lmin and T , and r e m a i n c o n s t a n t o n c e f i t t o a s e t o f d a t a . 2 8 To t e s t t h e d e s c r i p t i v e a b i l i t y o f e q u a t i o n ( 2 b ) t h e d a t a ( F i g . 6 , F i g . 7 ) w e r e f i t u s i n g P r o g r a m I . A c o m p l e t e l i s t i n g o f t h e p r o g r a m and a d e s c r i p t i o n o f t h e c u r v e f i t t i n g p r o c e d u r e i s p r e s e n t e d i n A p p e n d i x I . The l i n e f i t t e d t o t h e D. d i s c o i d e u m V C 4 d a t a e x p l a i n s 7 5 % o f t h e v a r i a t i o n a n d t h e c o r r e l a t i o n c o e f f i c i e n t ( T a b l e X I V - A p p e n d i x I V ) i s " s i g n i f i c a n t " a t 0( = 0 . 0 2 5 . T h e l i n e f i t t e d t o t h e P . p a l l i d u m d a t a a c c o u n t s f o r 8 8 % o f t h e v a r i a t i o n a n d i s a l s o " s i g n i f i c a n t " a t o( = 0 . 0 2 5 ( T a b l e X I V - A p p e n d i x I V ) . T h i s l e a d s t o t h e a c c e p t a n c e o f t h e c u r v e a s an a d e q u a t e d e s c r i p t i o n o f t h e r e l a t i o n s h i p b e t w e e n s p o r e l a g and t e m p e r a t u r e . I t i s p o s s i b l e t o b e g i n b u i l d i n g t h e f i r s t s t a g e s o f a d e s c r i p t i v e c o m p o n e n t s m o d e l . The i n f o r m a t i o n c o n s i d e r e d i n t h i s s e c t i o n d e a l s w i t h c o m p o n e n t s 1 t o 4 i n F i g u r e 2 2 ( p a g e 6 7 ) . The s p o r e s (SPORE) e x p e r i e n c e a g e r m i n a t i o n l a g (GERM LAG) w h i c h i s t e m p e r a t u r e (TEMP) m e d i a t e d a n d t h e f i r s t g r o u p o f amoebae (AMOEBAE PRESENT) a r e f o r m e d . The e f f e c t o f i n i t i a l s p o r e c o n c e n t r a t i o n o n l a g t i m e s was a l s o c o n s i d e r e d . P a i r e d and r e p l i c a t e d c u l t u r e s w e r e g r o w n a t s e v e r a l t e m p e r a t u r e s , and t h e i n i t i a l c o n c e n t r a - t i o n was v a r i e d . L a g t i m e was r e g r e s s e d ( u s i n g t h e s t a n d a r d I B M 1 1 3 0 r e g r e s s i o n p a c k a g e ) a g a i n s t a r e a s o t h a t t h e c o n s t a n t C i n t h e e q u a t i o n Y = C + B X a p p r o x i m a t e d t h e l a g t i m e due t o g e r m i n a t i o n . The r e s u l t s f o r b o t h D. d i s c o i d e u m V 1 2 ( T a b l e I ) and P. p a l l i d u m ( T a b l e I I ) s u g g e s t t h a t i n i t i a l 29 TABLE I Do discoideum V12. 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 w i t h v a r i e d spore c o n c e n t r a t i o n s . A c t u a l l a g s 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 5% CON LIMIT ACTUAL LAG 18.2 20000 5000 1.27 0.89 + + 0.28 20.07 1.55 19.5 32000 80000 1.43 1.12 + + 0.34 0.44 1.15 20.7 32000 80000 0.65 0.52 + + 0.46 0.70 1.00 21.9 32000 80000 0.82 0.65 + + 2.29 0.22 0.95 21.9 20000 5000 . 0.94 0.94 + + 0.18 0.33 0.95 23.4 20000 5000 0.91 0.67 + + 0.74 0.58 1.10 30 TABLE I I P„ p a l l i d u m . A comparison of 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 w i t h v a r i e d spore c o n c e n t r a t i o n s . A c t u a l l a g s are compared t o the 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. REGRESSED 5% CON. ACTUAL SPORES PER ml LAG LIMITS 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 c o n c e n t r a t i o n does not a l t e r l a g time. I t might be a l s o noted t h a t the l a g s generated i n t h i s way agree with those t h a t were a c t u a l l y measured and approximated with e q u a t i o n (2b). These d a t a agree with the f i n d i n g s o f R u s s e l l and Bonner (1960) and Cohen and C e c c a r i n i (1967) who observed t h a t 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. discoideum caused some spore i n h i b i t i o n . In t h e i r work g e r m i n a t i o n success dropped from about 99% at low c o n c e n t r a t i o n s to about 70% at 2 spore c o n c e n t r a t i o n s o f 2000 spores per mm . In the p r e s e n t work c o n c e n t r a t i o n s v a r i e d from about 0.1 to 3.0 spores per 2 mm , and t h e r e f o r e l i t t l e i n h i b i t i o n was expected. Amoeba Colony Expansion A f t e r the spores germinate the amoebae b e g i n to d i v i d e , d i s p e r s e , and use f o o d . In the c u l t u r e d i s h e s these p r o c e s s e s were observed t o g e t h e r as the amoebae f r o n t moved over the b a c t e r i a l lawn removing the f o o d . Rather than d i v i d e t h i s r a t h e r complex p r o c e s s i n t o i t s component p a r t s , both the r a t e and the form of c o l o n y expansion were a s s e s s e d and modelled as one component. The Form o f Colony Expansion When spores were p l a c e d at one p o i n t i n a 20 x 60 mm agar f i l l e d p e t r i d i s h i n the presence o f b a c t e r i a , the c o l o n y expanded i n a r e l a t i v e l y u n i f o r m c i r c l e away from the 32 point of i n o c u l a t i o n . The amoebae divided and moved into new areas so that the area covered by the en t i r e colony grew slowly at f i r s t and then increased u n t i l the rate of a c q u i s i - t i o n became almost constant ( i f the area became i n f i n i t e l y large the rate of a c q u i s i t i o n would become constant, because 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 l i n e f r o n t ) , Horn (1969) has observed that movement along a front i s constant. As the amoebae moved over the surface of the agar they consumed a l l the food, thereby securing that area from invasion by other c e l l u l a r slime mold species. These observations suggested that i t was only the amoebae on the perimeter of the colony which expanded the colony. In mathematical terms, the rate of increase i n the area covered by a colony i s proportional to the circumference of the colony. This i s : |£ = g • 2 - T T . 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 . S i n c e TT • r h. e q u a l s A r e a ( d e n o t e d by A ) , t h e n r = (A/TT ) „ I n c o r p o r a t i n g t h i s s u b s t i t u t i o n i n t o ( l a ) : ^ = f g • 2 • "r r ] - (A/vr)^ (lb) rearranging and i n t e g r a t i n g : Figure 9 Areas covered by c e l l u l a r slime mold cultures growing from point sources as ca l c u l a t e d by Program I I and equation (Id). Both the time and area units are a r b i t r a r y . 3 0 0 Q L U DC UJ g o < 2 0 0 < < 100 • f (g) = IOO / f (g) = 0 - 5 0 9 • y • ' f (g) = 0-30 JL. L J _ J L 2 4 6 8 10 12 14 16 18 T I M E 34 The r e l a t i o n between A and t a t v a r i o u s v a l u e s o f g was examined u s i n g Program I I (Appendix I ) , and the output ( F i g . 9) was compared t o the a c t u a l growth of c e l l u l a r s l i m e mold c u l t u r e s . The a c t u a l c u l t u r e s expanded t h e i r areas s l o w l y at f i r s t , and then moved q u i c k l y , with the r a t e of area a c q u i s i t i o n t e n d i n g towards a c o n s t a n t . T h i s g e n e r a l p r o c e s s i s w e l l d e s c r i b e d by the f a m i l y of c u r v e s generated by e q u a t i o n ( l c ) and drawn i n F i g u r e 9. A q u a n t i t a t i v e comparison i s a l s o p o s s i b l e . I f the square r o o t o f the area c a l c u l a t e d from e q u a t i o n ( l c ) i s p l o t t e d a g a i n s t time, a s t r a i g h t l i n e s hould r e s u l t . To t e s t t h i s h y p o t h e s i s , s e v e r a l D. discoideum V12 c u l t u r e s were e s t a b l i s h e d w i t h a p o i n t source i n o c u l a t i o n at a temperature o f 18.9 - 0.2°C. T h i s simple experiment y i e l d e d two v e r y important p i e c e s o f i n f o r m a t i o n . When p l o t t e d a g a i n s t time, the square r o o t o f a r e a d i d f a l l along a s t r a i g h t l i n e ( F i g . 10-A). Subsequent work has r e a f f i r m e d t h i s o b s e r v a t i o n many ti m e s . The s t r a i g h t l i n e through the data p o i n t s ( F i g . 10-A) passed through the x - a x i s at 1.0 days, but the s t r a i g h t l i n e o f the same s l o p e p r e d i c t e d by e q u a t i o n ( l c ) passed through 0.0 days ( F i g . 10-B) s u g g e s t i n g t h a t the spore g e r m i n a t i o n l a g d e s c r i b e d i n the p r e v i o u s s e c t i o n must be accounted f o r . The l a g can be i n c o r p o r a t e d by l e t t i n g the l a g e q u a t i o n (2b) e q u a l a f u n c t i o n of temperature L ( T ) . T h i s can then be s u b s t i t u t e d i n t o ( l c ) to y i e l d : F i g u r e 10 F i g . l O - A : The square r o o t s o f the areas covered by- f o u r c u l t u r e s of D. discoideum V12 are 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. F i g . l O - B : The square r o o t s of the areas generated by e q u a t i o n ( l c ) with g = 3.61 are p l o t t e d t o form l i n e one. L i n e two i s the 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 t = [ l . 7 7 2 8 g ( t - L(T) ) + c] 2 (Id) The Rate o f Amoeba Colony Expansion Both D. discoideum and P. p a l l i d u m show v a r i a t i o n s i n the r a t e o f c o l o n y expansion w i t h v a r i a t i o n s i n temperature. In view o f t h i s , the c o n s t a n t g i n e q u a t i o n (Id) must be m o d i f i e d t o a f u n c t i o n o f temperature g ( T ) . To q u a n t i f y t h i s r e l a t i o n s h i p , c u l t u r e s were grown at temperatures r a n g i n g from 9° to 37.5°C. Two o b s e r v a t i o n s were made: (1) There was a 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 area and time. R e p r e s e n t a t i v e c u l t u r e s are p l o t t e d i n F i g u r e 11. (2) Both s p e c i e s used a l l the food and space a v a i l a b l e . These o b s e r v a t i o n s were made i n 100% of the 400 - 500 c u l t u r e s run, but i t might be argued t h a t because a s m a l l number o f d a t a p o i n t s were a v a i l a b l e from each c u l t u r e 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 observed might be due to a l a c k o f da t a ( i t i s not d i f f i c u l t to f i t a s t r a i g h t l i n e to o n l y 4 or 5 d a t a p o i n t s ) . To prove t h a t t h i s h y p o t h e s i s was i n c o r r e c t data from many temperatures were transformed and p l o t t e d t o g e t h e r . A s t r a i g h t l i n e r e l a t i o n s h i p r e s u l t e d ( F i g . 53 - Appendix I I I ) demonstrating t h a t the i n d i v i d u a l o b s e r v a t i o n s and e q u a t i o n ( l c ) are v a l a d . S i n c e many c u l t u r e s were run at each temperature, Program I I I (Appendix I) was used t o c a l c u l a t e the sl o p e s o f i n d i v i d u a l c u l t u r e s , t o group the d a t a to form mean s l o p e s at v a r i o u s temperature i n t e r v a l s , and to p l o t the i n d i v i d u a l F i q u r e 11 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) grown at 24.5° and f o r P. p a l l i d u m (bottom) grown at 30.5OC. 1 2 3 4 5 T I M E - D A Y S j i 1 1 2 3 4 5 TIME - DAYS 38 s l o p e s and mean s l o p e s . The s l o p e d a t a o b t a i n e d from the above procedure was then p l o t t e d a g a i n s t temperature. The da t a from D. discoideum V12 ( F i g . 12), P. p a l l i d u m ( F i g . 13), and D. discoideum VC4 ( F i g . 14) suggested t h a t the r a t e o f c o l o n y expansion i n c r e a s e d w i t h i n c r e a s e d temperature, reached a maximum at some optimum temperature, and decreased with f u r t h e r temperature i n c r e a s e s . The c o n f i d e n c e l i m i t s (95%) around the i n d i v i d u a l P. p a l l i d u m d a t a p o i n t s were r a t h e r l a r g e due to u n r e c o g n i z e d b a c t e r i a l f o o d c o n t a m i n a t i o n . However, d e s p i t e the f a c t t h a t the source o f e r r o r was d i s c o v e r e d , i t was i m p o s s i b l e to do the experiments a g a i n because the stock had e x p e r i e n c e d media c o n d i t i o n i n g . On the b a s i s o f the f o r e g o i n g d a t a an e q u a t i o n was fo r m u l a t e d t o d e s c r i b e the r e l a t i o n s h i p between c o l o n y ex- pan s i o n r a t e and temperature. The e q u a t i o n had to meet t h r e e c o n d i t i o n s : (1) t h a t the r a t e o f expansion be zero a t some low temperature T^, (2) t h a t the r a t e o f expansion be zero a t some h i g h temperature T^, (3) t h a t the r a t e o f c o l o n y expansion be o p t i m i z e d at some optimum temperature T Q between T^ and T L . An example o f a curve t h a t meets these c o n d i t i o n s i s p r e s e n t e d i n F i g u r e 15. At T the expansion r a t e i s z e r o . From t h i s p o i n t the s l o p e ( F i g . 15) g r a d u a l l y d e c r e a s e s , r e a c h i n g zero at T = T q . As T i n c r e a s e s beyond T Q t h e s l o p e decreases r a p i d l y becoming n e g a t i v e l y i n f i n i t e at T.- T H . F i q u r e 12 The r e l a t i o n s h i p between growth i n d e c and temperature f o r D. discoideum V12. The p o i n t s are 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 the means. The growth index has 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 the l i n e of b e s t f i t from e q u a t i o n (3c) with T = 26.5°, T, = 13.0O, T Q = 22.5°, Gmax = 4.5, K = 0.97009, and C = 2.99964. F i q u r e 13 The r e l a t i o n s h i p between growth index and temperature f o r P. p a l l i d u m . The p o i n t s are 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 the means. The growth index has 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 the 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 H = 37.0, T L = 18.0, T q = 30.0, Gmax = 8.3, K = 1.71712 and C = -4.77034. 10 • 9 - 8 - 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 T E M P E R A T U R E 10 9 8 x 7 LU | 6 i 5 £ « • oc O 3 2 1 1 V°- — t- - - - i l 1 ! '1 „ 1 N 0 1 N £ i bJL, J I 1 i I I 1 L _i L i i a 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 T E M P E R A T U R E F i g u r e 14 The r e l a t i o n s h i p between growth index and temperature f o r D. dis c o i d e u m VC4. The p o i n t s are mean da t a p o i n t s i 5% c o n f i d e n c e l i m i t s on the means. The growth index has 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 the l i n e o f b e s t f i t from e q u a t i o n (3c) wi t h T H = 2 7.5°, 7 T L = 9.0°, T Q = 21.5°, Gmax = 4.6, K = 0.80084, and G = 0.79554. m m > H C J3 m G R O W T H INDEX ro co J> cn o> -̂ i T 00 r CO T 41 One e q u a t i o n which r e p r e s e n t s t h i s type o f response and which f u l f i l s the t h r e e requirements s t a t e d above i s the f o l l o w i n g : dG dT = K T - T o T - T (3a) where dG/dT i s the r a t e of change of area a c q u i s i t i o n with r e s p e c t to temperature, and K i s a c o n s t a n t . T h i s e q u a t i o n must be i n t e g r a t e d by p a r t s : dG = K«T dT T - T H K T dT T - T H (3b) Dwight (1947) g i v e s the f o l l o w i n g i d e n t i t i e s o f i n t e g r a t i o n : f * . 1 l o g I X i ^ = i j [ x - a l o g I X I ] where X = a + bx„ I n t e g r a t i n g (2b) i t i s found that : = [ l o g IT - T I ] [K • (T - T ) ] - K • T + K • T + C (3c) where G i s the r a t e o f area a c q u i s i t i o n and C i s a c o n s t a n t . But t h i s e q u a t i o n and i t s assumptions are o n l y h y p o t h e t i c a l . I t must be proven t h a t i t d e s c r i b e s the F i q u r e 15 One o f a f a m i l y o f c u r v e s designed t o d e s c r i b e the r e l a t i o n s h i p between the r a t e o f c o l o n y expansion and temperature. At TL and T H the r a t e i s zero and T 0 the r a t e i s optimum. G R O W T H R A T E 43 r e l a t i o n s h i p between area, a c q u i s i t i o n and temperature. To t e s t the d e s c r i p t i v e a b i l i t y o f e q u a t i o n (3c) Program IV (Appendix I) was used t o f i t one c u r v e from the f a m i l y d e s c r i b e d by (3c) t o each s e t o f d a t a . The l i n e f i t t e d to the D. discoideum V12 d a t a ( F i g . 12) e x p l a i n s 94% o f the v a r i a t i o n . The l i n e f i t t e d to the P. p a l l i d u m data ( F i g . 13) e x p l a i n s 56% o f the v a r i a t i o n . The l i n e f i t t e d t o the D. discoideum VC4 d a t a ( F i g . 14) e x p l a i n s 95% o f the v a r i a t i o n . A l l t h r e e are " s i g n i f i c a n t " at c* = 0.025 (T a b l e XIV - Appendix I V ) . The d e s c r i p t i v e power o f e q u a t i o n (3c) was accepted i n a l l c a s e s . With the 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 ( l d ) and (3c) i t was p o s s i b l e to add st e p s 5, 6 and 7 t o the components model o u t l i n e d i n F i g u r e 22 (page 6 7 ) . A f t e r the f i r s t amoebae emerge from the spores (AMOEBAE PRESENT) they b e g i n t o expand the c o l o n y i n the form d e s c r i b e d by e q u a t i o n ( l d ) and at the r a t e d e s c r i b e d by (3c) (COLONY EXP.). T h i s p r o c e s s i s temperature dependent. At any p o i n t i n time the c o l o n y s i z e (COLONY SIZE) i s known and the amount o f food and space (FOOD-SPACE) used can be c a l c u l a t e d . I t i s a l s o p o s s i b l e t o modify e q u a t i o n ( l d ) to account f o r the temperature dependence of the c o l o n y expansion r a t e . When g(T) (a summarized form o f e q u a t i o n (3c)).'is s e t i n p l a c e o f g i n e q u a t i o n ( l d ) the f o l l o w i n g e q u a t i o n r e s u l t s : A t = [1.7728 g(T) ( t - L ( T ) ) + c] 2 ( l e ) TABLE I I I D. discoideum V12 - a comparison o f growth indexes 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 MEAN GROWTH 5% CON NUM/ML INDEX 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 IV H° p a l l i d u m - a compar ison o f growth indexes from c u l t u r e s i n o c u l a t e d w i th 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 MEAN GROWTH 5% CON NUM/ML INDEX LIMIT 20.1 100 50 000 000 3.50 2.74 + + 2.26 0.33 20.7 20 5 000 000 4.16 2.96 + + 2.10 1.83 21.9 20 5 000 000 5.33 4.72 + + 5.60 0.95 25.5 100 50 000 000 7.10 5.60 + + 2.61 0.98 28.7 100 50 000 000 8.66 7.67 + + 3.16 0.74 46 where g(T) i s c o l o n y expansion r a t e mediated by temperature. The h y p o t h e s i s t h a t i n i t i a l spore c o n c e n t r a t i o n a l t e r s the expansion r a t e must a l s o be t e s t e d . T h i s t e s t was conducted by i n o c u l a t i n g p l a t e s 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 , o b s e r v i n g and r e c o r d i n g the areas covered by the c o l o n y , and u s i n g Program I I I to c a l c u l a t e the mean growth index - 5% c o n f i d e n c e l i m i t s . No growth i n h i b i t i o n was d e t e c t e d at the c o n c e n t r a t i o n s used, f o r D. discoideum V12 (T a b l e I I I ) and P. p a l l i d u m ( T a b l e I V ) . F r u i t i n g Body Lag To t h i s p o i n t the development o f a c e l l u l a r s l i m e mold c o l o n y has been c o n s i d e r e d from the spore s t a g e , through the spore g e r m i n a t i o n l a g t o the amoebae stage, through the development o f a c o l o n y , to the c o l o n y s t a g e . But, as the amoebae reproduce and d i s p e r s e u s i n g up food and space, the amoebae i n the c e n t e r of the c o l o n y f i n d themselves i n an a r e a without f o o d . A c r a s i n i s then produced and a g g r e g a t i o n and f r u i t i n g body p r o d u c t i o n b e g i n s . These p r o c e s s e s r e q u i r e a p e r i o d o f time t h a t might be r e f e r r e d to as the f r u i t i n g body l a g . T h i s p e r i o d o f time i n c l u d e s the spore g e r m i n a t i o n l a g and the time r e q u i r e d f o r a g g r e g a t i o n a f t e r the amoebae appear- To q u a n t i f y the r e l a t i o n s h i p between the f r u i t i n g body l a g and temperature, d a t a was c o l l e c t e d by i n o c u l a t i n g agar f i l l e d and b a c t e r i a covered p e t r i d i s h e s with a known 47 number o f spo r e s , i n c u b a t i n g at v a r i o u s temperatures, and n o t i n g the time between i n o c u l a t i o n and the f o r m a t i o n of the f i r s t f r u i t i n g body. F o r both D. discoideum VC4 ( F i g . 16) and P. p a l l i d u m ( F i g . 17) the l a g decreased with i n c r e a s e d temperature reached a minimum at some optimum temperature and i n c r e a s e d with f u r t h e r temperature i n c r e a s e s . I t appeared t h a t the assumptions p e r t a i n i n g t o the model c o n s t r u c t e d f o r the g e r m i n a t i o n l a g might a l s o be a p p l i c a b l e t o the f r u i t i n g body l a g . These assumptions demand t h a t the curve r e l a t i n g f r u i t i n g body l a g and temperature have an i n f i n i t e l y n e g a t i v e s l o p e at T L (temperature low) and an i n f i n i t e s l o p e at T^ (temperature h i g h ) and t h a t the s l o p e be zero at T Q (temperature optimum) ( F i g . 8 ) . E q u a t i o n (2b) d e s c r i b e s t h i s r e l a t i o n s h i p . To t e s t the d e s c r i p t i v e power o f e q u a t i o n (2b) Program I (Appendix I) was used t o f i t a l i n e to the d a t a . The l i n e r e l a t i n g f r u i t i n g body l a g and temperature f o r D. discoideum VC4 e x p l a i n e d 96% o f the t o t a l v a r i a b i l i t y ( F i g . 16). The l i n e f o r P. p a l l i d u m e x p l a i n e d 97% of the v a r i a t i o n . In both cases the f i t was " s i g n i f i c a n t " at OC = 0.025 (Table XIV - Appendix I V ) . E q u a t i o n (2b) a p p a r e n t l y can be used t o d e s c r i b e the r e l a t i o n s h i p between f r u i t i n g body l a g and temperature. T h i s new i n f o r m a t i o n can be used to expand the components model through the a d d i t i o n o f st e p s 8 and 9 ( F i g . 22, page 67)„ A f t e r the f i r s t amoebae are p r e s e n t F i g u r e 16 The time n e c e s s a r y f o r D. discoideum f r u i t i n g body 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 dots are d a t a p o i n t s , the 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 (2b). T H = 27.5, T L = 9.0, T = 24.0, K = 2.47681, C = 7.62542. 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 TEMPERATURE F i g u r e 17 The time f o r P. p a l l i d u m f r u i t i n g body 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 open c i r c l e s are data p o i n t s , the 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^ = 37. T L = 18.0, T Q = 30.0, K = 1.28527, C = 3.76145. 4 > < a < \ \ 2 r 1 r o - - o_ o _ _ O — "O o <5" ~~ o - — o — o o — o — o J I l_ L Jl I ' » 19 20 21 22 23 24 25 26 27 2 8 29 30 31 32 33 34 35 3 6 T E M P E R A T U R E 50 t h e r e i s a temperature dependent l a g p e r i o d (F.B. LAG) b e f o r e the f i r s t f r u i t i n g b o d i e s are produced (F.B. PRESENT). F r u i t i n g Body Formation Once the f i r s t f r u i t i n g b o d i e s have formed the number i n c r e a s e s as more amoebae aggregate. Both the way i n which t h i s p r o c e s s o c c u r s (the form), and the r a t e at which i t o c c u r s (the r a t e ) , must be d e s c r i b e d . The Form o f F r u i t i n g Body Colony Expansion F r u i t i n g body c o l o n i e s expand s l o w l y at f i r s t and then i n c r e a s e t h e i r expansion r a t e s as the a r e a o c c u p i e d i n c r e a s e s . I t appeared p o s s i b l e t h a t expansion r a t e might be d i r e c t l y r e l a t e d t o p e r i m e t e r s i z e j u s t as i t was f o r the amoeba c o l o n y expansion. In t h i s case the form o f c o l o n y expansion should be d e s c r i b e d by e q u a t i o n ( l d ) . To t e s t t h i s h y p o t h e s i s c u l t u r e s were grown at a number o f temperatures and the f r u i t i n g body c o l o n y a r e a was noted at v a r i o u s i n t e r v a l s of time. The square r o o t o f a r e a was then p l o t t e d a g a i n s t time and 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 f o r both D. discoideum VC4 ( F i g . 18) and P. p a l l i d u m ( F i g . 18). These experiments were r e p e a t e d s e v e r a l hundred times and i n e v e r y case 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 were found. But, because o n l y a few d a t a p o i n t s were used f o r each s t r a i g h t l i n e r e l a t i o n s h i p i t might be h y p o t h e s i z e d t h a t the s t r a i g h t l i n e s r e s u l t e d from a l a c k of d a t a . To t e s t F i g u r e 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 root of area (measured i n cm^) and time i s demonstrated f o r D« discoideum VC4 (top) and P. pallidum (bottom). The temperatures at which these cultures were grown are noted on the graph.  t h i s h y p o t h e s i s , d a t a from D. discoideum VC4 and P. p a l l i d u m f r u i t i n g body expansions were transformed and p l o t t e d t o - g e t h e r ( F i g . 54 - Appendix I I I ) . A s t r a i g h t l i n e r e l a t i o n - s h i p r e s u l t e d , demonstrating t h a t the square r o o t o f area p l o t t e d a g a i n s t time does y i e l d a s t r a i g h t l i n e , and t h a t e q u a t i o n ( l c ) can be used to d e s c r i b e t h i s r e l a t i o n s h i p . Two o t h e r o b s e r v a t i o n s r e s u l t e d from these e x p e r i - ments. (1) D. discoideum f r u i t i n g b o d i e s covered a l l o f the a r e a o c c u p i e d by the amoeba c o l o n y ( F i g . 18), and (2) the P. p a l l i d u m f r u i t i n g body c o l o n i e s stopped expanding long b e f o r e they o c c u p i e d the area used by the amoeba c o l o n i e s ( F i g . 18). In the case o f P. p a l l i d u m S a l v a d o r the amoebae a p p a r e n t l y used up a l l o f the f o o d on the p l a t e and then r e t r a c e d t h e i r r o u t e back to the c e n t e r of the p l a t e where one l a r g e d i s o r g a n i z e d f r u i t i n g body c o l o n y formed. The response i s p e c u l i a r t o t h i s s t r a i n of P. p a l l i d u m and has been observed by both Dr. Raper ( p e r s . comm.) and m y s e l f . The maximum are a 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 may be expressed as a percentage of the maximum a r e a o c c u p i e d by the amoeba c o l o n i e s . When 40 experiments were run i t was found t h a t P. p a l l i d u m f r u i t i n g b o d i e s o c c u p i e d 14.08 - 0.85 p e r c e n t o f the maximum area o c c u p i e d by the amoeba c o l o n y (the d a t a are g i v e n as the mean - the 95% c o n f i d e n c e l i m i t around the mean). A l s o , t h e r e was no s i g n i f i c a n t change i n t h e maximum are a a t t a i n e d by P. p a l l i d u m over the f u l l range o f temperature a t which t h i s s p e c i e s grew (T a b l e V ) . A l l o f TABLE V The change i n maximum area with temperature f o r P. p a l l i d u m . TEMPERATURE NUM. REP. MEAN AREA 95% CON LIMIT 20.5 3 41.0 - 17.2 21.5 5 38.3 t H 0 2 22.5 4 39.3 i 5.7 23.5 4 40.5 i 16.1 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 - 7.0 31.5 5 45.5 t 7.1 32.5 4 44.2 i 16.2 33.5 6 54.1 - 5.3 35.5 5 44.5 - 11.3 54 the 95% c o n f i d e n c e l i m i t s , e x c e p t i n g the i n t e r v a l around the mean c a l c u l a t e d f o r 33.5°, o v e r l a p p e d , s u g g e s t i n g t h a t a r e a d i d not change with temperature (Table V ) . In summary, D. discoideum f r u i t i n g body c o l o n i e s c o v e r a l l o f the a r e a covered by the amoeba c o l o n y w h i l e P. p a l l i d u m f r u i t i n g body c o l o n i e s are l i m i t e d to about 14.08% of the a r e a c o v e r e d by the amoeba c o l o n y . E q u a t i o n ( l c ) can be used to d e s c r i b e the form o f c o l o n y expansion f o r b o t h . The Rate o f F r u i t i n g Body Colony Expansion Both D. discoideum and P. p a l l i d u m show v a r i a t i o n s i n the r a t e o f f r u i t i n g body c o l o n y expansion w i t h v a r i a t i o n s i n temperature. T h e r e f o r e , the c o n s t a n t g i n the "form" e q u a t i o n ( l c ) must be m o d i f i e d to become a f u n c t i o n o f temperature g ( T ) . To q u a n t i f y t h i s r e l a t i o n s h i p data were c o l l e c t e d by n o t i n g 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 at v a r i o u s i n t e r v a l s of time. Program I I I (Appendix I) was used to group the d a t a with r e s p e c t to temperature, and to c a l c u l a t e mean s l o p e s - 95% c o n f i d e n c e i n t e r v a l s . The mean sl o p e s and c o n f i d e n c e i n t e r v a l s were p l o t t e d a g a i n s t temperature. F o r b o t h D. discoideum VC4 ( F i g . 19) and P. p a l l i d u m ( F i g . 20) the f r u i t i n g body expansion r a t e i n c r e a s e d w i t h i n c r e a s e d temperature, reached a maximum at some optimum temperature 55 and decreased w i t h f u r t h e r temperature i n c r e a s e . A p p a r e n t l y e q u a t i o n (3c), which was used to d e s c r i b e the r e l a t i o n s h i p between amoeba c o l o n y expansion and temperature, might a l s o be a p p l i c a b l e t o t h i s s i t u a t i o n . To t e s t t h i s h y p o t h e s i s c u r v e s were f i t from e q u a t i o n (3c) u s i n g Program IV (Appendix I ) . F o r D. discoideum VC4 the f i t t e d c u r v e accounted f o r 69% of the t o t a l v a r i a t i o n and the f i t was " s i g n i f i c a n t " at CX = 0 . 0 2 5 . F o r P. p a l l i d u m ( F i g . 2 0 ) the f i t was not " s i g n i f i c a n t " at (A = 0 . 0 2 5 (Table XIV - Appendix I V ) . E q u a t i o n (3c) demands t h a t the expansion r a t e i n c r e a s e s g r a d u a l l y with i n c r e a s e d temperature, r e a c h e s a maximum at temperature-optimum, and d e c r e a s e s r a p i d l y to n e g a t i v e i n f i n i t y at some h i g h temperature. However, the P. p a l l i d u m d a t a suggests t h a t the r a t e of c o l o n y expansion i n c r e a s e s r a p i d l y a t T^, remains approximately c o n s t a n t between T L and T^, and decreases r a p i d l y to zero at T^. In view of these f i n d i n g s , a new e q u a t i o n was developed which meets the s p e c i a l c r i t e r i a imposed by P. p a l l i d u m f r u i t i n g body f o r m a t i o n . Such an e q u a t i o n i s : dG dT = K T o " (-l)T + T •. T + T H (4a) T — T • T - L H L where dG/dT i s the r a t e of change of c o l o n y expansion with r e s p e c t t o temperature, T i s temperature, T i s temperature F i q u r e 19 D. discoideum VC4; f r u i t i n g body expansion r a t e s with r e s p e c t to temperature. The p o i n t s are 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 the means. The growth index has 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 the l i n e o f b e s t f i t from e q u a t i o n (2c) wi t h T H = 27.5, T L = 9.0, T Q = 21.0, Gmax = 4.4, K = 0.86318, and C = -0.65368. G R O W T H INDEX ro GO 4^ 01 0) . ->l — 1 g — — r * 0 0 CO m ro co L 5) " 0 _ L m -NI r .33 H 0 0 c m CD ro o ro ro ro ro co ro J> ro ro CD ro \ t—®—\ \ \ t • ©—i i i 11—©—i I- ' 57 m T J rn ID > —1 c ZO m CD IO O IO ro ro CO ro J> ro cn ro 0) ro ro 00 ro CD CO O CO CO ro CO Co CO c o c n c o CD GROWTH INDEX ro co J> cn CD ->J 00 CD \ v \ \ K H J — 0 — 3 58 optimum, T L i s temperature low, T H i s temperature h i g h , and K i s a c o n s t a n t . U s i n g two i d e n t i t i e s o f i n t e g r a t i o n (Dwight 1947) t h i s e q u a t i o n can 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 L ) - T H " T^ I ) - (4b) T - T H * 1 l o g T - T H L T - T where G i s the expansion c o e f f i c i e n t and C i s a c o n s t a n t o f i n t e g r a t i o n . T h i s e q u a t i o n was f i t to the d a t a ( F i g . 21) u s i n g Program V (Appendix I ) . The l i n e accounted f o r 75% o f the t o t a l v a r i a t i o n and the f i t was " s i g n i f i c a n t " at 0\ = 0.025 (T a b l e XIV - Appendix I V ) . T h e r e f o r e , e q u a t i o n (4b) was accept e d as an adequate d e s c r i p t i o n o f the r e l a t i o n s h i p between P. p a l l i d u m f r u i t i n g body expansion r a t e and temper- a t u r e . The i n f o r m a t i o n c o n s i d e r e d i n t h i s s e c t i o n can be i n c o r p o r a t e d i n t o the components diagram ( F i g . 22, page 67) as s t e p s 10, 11, 12 and 13. A f t e r the f i r s t f r u i t i n g b o d i e s are formed (F.B. PRESENT) the c o l o n y expands (F.B. EXP) with F i g u r e 21 P. p a l l i d u m f r u i t i n g body expansion r a t e s with r e s p e c t to temperature. The p o i n t s are 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 the means. The growth index has no u n i t s , temperature i s measured i n degrees c e n t i - grade. The d o t t e d l i n e i s the l i n e o f b e s t f i t from e q u a t i o n (4b) w i t h Tu = 37.5, T L 18.0, T = 31.0, K = 0.78172, and C = 0.97552. 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 GROWTH INDEX ro co 4^ cn o) -NI OO CO T " 1 1 T 1 1 1 1 " &-0—8 60 the r a t e o f expansion mediated by temperature. At any p o i n t i n time 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 i s known (F.B, AREA) and i t i s p o s s i b l e to c o n v e r t a r e a to spore 2 numbers (S. PER AREA). Fo r D. discoideum VC4, 6.4 mm = 47000 - 18000 spores and f o r P. p a l l i d u m , 6.4 mm2 = 300000 - 62000 spores (mean - 95% c o n f i d e n c e l i m i t ) . The spores can then produce new amoebae i n a food renewed s i t u a t i o n . The t h i r t e e n t h component (LIMIT), l i m i t s the area c o v e r e d by f r u i t i n g b o d i e s . D. discoideum f r u i t i n g b o d i e s can cover 100% o f the a r e a o c c u p i e d by the amoebae, P. p a l l i d u m f r u i t i n g b o d i e s can occupy 14.08% of the a r e a o c c u p i e d by amoebae. T e s t i n g the E x p l o i t a t i o n Models Both s p e c i e s have been d e s c r i b e d by models which sh o u l d p r e d i c t the amount o f f o o d and space taken up by the amoebae and f r u i t i n g body c o l o n i e s at any p o i n t i n time. Before these models can be used i t must be proven t h a t they a c t u a l l y mimic the expansion o f a c e l l u l a r s l i m e mold c o l o n y . The p r e d i c t i v e power o f the two models was t e s t e d by s i m u l a t i n g the growth of both s p e c i e s (Program VI - Appendix I) and comparing the output to independent e x p e r i m e n t a l d a t a . Data were c o l l e c t e d a t e l e v e n temperatures f o r D. discoideum VC4 amoebae and i n every case t h e r e was no s i g n i f i c a n t d i f f e r e n c e ( a t the 95% l e v e l ) between the observed and the p r e d i c t e d ( Table V I ) . Data were c o l l e c t e d at e l e v e n TABLE VI D. discoideum VC4 amoebae. The output 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 area d a t a . A s t a r 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 (95% l e v e l ) between the d a t a and the o u t p u t . TEMP. TIME REP. NO. 95% CON AROUND PREDICTED MEAN AREA AREA 14.5 5.0 6 138.4 - 168.2 120 15.5 4.0 6 95.9 - 135.3 97 16.5 4.0 6 84.5 - 184.4 126 17.5 4.0 6 153.5 - 217.4 158 18.5 4.0 6 181.4 - 2 39.2 190 19.5 4.0 7 203.2 - 263.6 218 20.5 3.3 6 115.3 - 196.6 151 21.5 3.3 6 131.0 - 214.6 160 22.5 3.3 6 124.0 - 233.2 146 23.5 3.3 5 73.7 - 185.8 142 24.5 4.0 4 110.7 197.7 169 TABLE VII P_o p a l l i d u m amoebae. The output 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 d a t a . A s t a r 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 (95% l e v e l ) between the output and the d a t a . TEMP. TIME REP. NO. 95% CON AROUND PREDICTED MEAN AREA AREA 18.5 5.0 6 26 - 67 10.6 19.5 3.9 7 23 - 62 25.4 20.5 3.9 6 34 - 107 57.1 21.5 3.9 9 95 - 178 102.7 22.5 3.9 3 134.8 - 257.8 160.8 23.5 3.3 5 124.7 - 212.4 154 24.5 3.2 4 154.4 - 275.5 192 25.5 3.2 3 159.4 - 285.2 243 27.5 3.0 4 223.4 - 294.5 294 28.5 2.3 6 162.1 - 201.8 173 29.5 2.4 3 21.4 - 289.9 209 30.5 2.2 5 98.1 - 272.2 176 32.5 2.2 4 235.2 - 261.7 167* 33.5 2.2 7 136.7 230.6 146 TABLE V I I I D. disc o i d e u m VC4 f r u i t i n g body. The output from Program VI i s compared with i n d e p e n d e n t l y c o l l e c t e d area d a t a . A s t a r 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 (95% l e v e l ) between the output and the d a t a . TEMP. TIME REP. NO. 95% CON AROUND PREDICTED MEAN AREA AREA 14.5 4.8 6 17.3 - 22.3 20.5 15.5 4.8 6 25.6 - 43.9 37.7 16.5 4.8 6 28.2 - 60.4 60 17.5 5.0 6 78.6 - 123.0 99 18.5 5.0 6 106.4 - 185.2 130 19.5 4.1 7 77.8 - 107.8 79 20.5 4.1 6 48.4 - 113.5 93 21.5 4.1 6 130.7 - 160.2 101* 22.5 4.1 6 74.8 - 167.4 99 23.5 4.1 5 64.3 - 163.6 83 ' 24.5 4.0 4 0.0 72.6 49 TABLE IX P. p a l l i d u m f r u i t i n g body. The output 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 s t a r 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 (95% l e v e l ) between the output and the data*. TEMP. TIME REP. MO. 95% CON AROUND PREDICTED MEAN AREA, AREA 19.5 5.0 3 11.8 - 26.8 32* 20.5 3.7 5 13.9 - 20.4 19 21.5 3.8 5 19.9 - 30.8 30 22.5 3.9 4 33.5 - 44.9 41 24.5 3.2 3 24.8 - 57.1 32 25.5 3.2 3 13.6 - 70.3 36 27.5 3.2 3 37.7 - 46.5 41 28.5 3.2 5 37.4 - 52.1 43 29.5 3.2 3 13.0 - 57.6 44 30.5 3.2 7 37.7 - 51.6 44 32.5 3.3 6 36.7 — 53.8 45 65 temperatures f o r D. discoideum VC4 f r u i t i n g b o d i e s and i n ten o f the e l e v e n cases t h e r e was no s i g n i f i c a n t d i f f e r e n c e between the observed and the p r e d i c t e d (Table V I I ) . Data were c o l l e c t e d at f o u r t e e n temperatures f o r P_. p a l l i d u m amoebae, and i n twelve o f the f o u r t e e n c a s e s t h e r e was no d i f f e r e n c e between the observed and the p r e d i c t e d (Table V I I I ) . ' Data were c o l l e c t e d at e l e v e n temperatures f o r P. p a l l i d u m f r u i t - i n g b o d i e s and i n t e n o f e l e v e n cases t h e r e was no d i f f e r e n c e between the observed and the p r e d i c t e d ( T a b l e I X ) . These d a t a seem to support the c o n t e n t i o n t h a t the two e x p l o i t a t i o n models do d e s c r i b e both the form and the r a t e o f c o l o n y expansion f o r both s p e c i e s over the e n t i r e range o f temperature used. Summary: E x p l o i t a t i o n (1) The c e l l u l a r s l i m e mold l i f e c y c l e i s composed o f f i v e s t e p s : spores germinate t o produce amoebae which d i v i d e , d i s p e r s e , and consume fo o d , the amoebae aggregate, f r u i t i n g b o d i e s form, and the f r u i t i n g b o d i e s c o n t a i n spores o (2) S i n c e f o o d i s the r e s o u r c e i n s h o r t s u p p l y , o n l y t h i s s tep i n the l i f e c y c l e i s d i r e c t l y r e l e v a n t to the study of e x p l o i t a t i o n . ( 3 ) But the r a t e o f food use depends upon a l l the o t h e r steps i f any more than one g e n e r a t i o n i s c o n s i d e r e d , t h e r e f o r e a l l the s t e p s were modelled. 66 (4) The spore g e r m i n a t i o n l a g s , and the f r u i t i n g body p r o d u c t - i o n l a g s were both temperature dependent and were d e s c r i b e d by e q u a t i o n (2b). (5) The form o f amoeba c o l o n y expansion and f r u i t i n g body c o l o n y expansion was d e s c r i b e d by e q u a t i o n ( l c ) because the r a t e of expansion was d i r e c t l y p r o p o r t i o n a l to the p e r i m e t e r of the c o l o n y . (6) The r a t e of amoeba and f r u i t i n g body c o l o n y expansion was temperature dependent. Amoebae c o l o n y expansion r a t e s f o r both s p e c i e s , and D. discoideum f r u i t i n g body expansion r a t e s were d e s c r i b e d by e q u a t i o n ( 3 c ) . P. p a l l i d u m f r u i t i n g body expansion r a t e s were d e s c r i b e d by e q u a t i o n (4b). (7) The components were l i n k e d t o g e t h e r ( F i g . 22) to form e x p l o i t a t i o n models which were t e s t e d a g a i n s t independent d a t a . The model proved to be a c c u r a t e i n at l e a s t 90% of the c a s e s . 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 I f the two s p e c i e s , when grown t o g e t h e r , o n l y e x p l o i t t h e i r environment ( i n t h i s c a s e : compete f o r food and space) i t should be p o s s i b l e t o p r e d i c t e x a c t l y what the two s p e c i e s w i l l do when put t o g e t h e r , on the b a s i s of the i n d e p e n d e n t l y d e r i v e d e x p l o i t a t i o n models. I f the two e x p l o i t a t i o n models f a i l to p r e d i c t the outsome of a r e a l F i g u r e 22 D i a g r a m a t i c 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 model s i m u l a t e d i n Program 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 . EXTERNAL FORCE P 2 SPORE S. PER AREA FOOD SPACE FOOD SPACE F . B , EXP- 68 c o m p e t i t i v e s i t u a t i o n then i t must be assumed t h a t the c o m p e t i t o r s are d i r e c t l y i n t e r f e r i n g with one another. A c o m p e t i t i v e s i t u a t i o n f o r c e l l u l a r s l i m e mold s p e c i e s i n the l a b o r a t o r y was s i m u l a t e d by j o i n i n g the two independent e x p l o i t a t i o n models t o g e t h e r i n Program V I I (Appendix I ) . F i g u r e 22 i l l u s t r a t e s the system used. A l l but f o u r components were i d e n t i f i e d i n p r e v i o u s s e c t i o n s . The "SUM" component sums the f o o d and space used by both s p e c i e s . I t o u t p u t s the "TOTAL FOOD-SPACE" used by both s p e c i e s . T h i s q u a n t i t y i n p u t s t o two "LIMIT" components which stop the "COLONY EXPANSION" components when a l l the f o o d and space has been used. The r e s u l t s o f 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 can be a s s e s s e d at two l e v e l s : (1) the presence o r ab- sence of P. p a l l i d u m and D. discoideum at any temperature, and (2) the amount o f fo o d and space used by amoebae and f r u i t i n g b o d i e s at any time and temperature. At l e v e l (1) the model p r e d i c t s t h a t from 9.0° to 18.0°C D. discoideum s h o u l d be the o n l y s p e c i e s a b l e to grow and consume food ( F i g . 23). From 18,1° to 26,5°C both s p e c i e s should, be c a p a b l e o f growing and u s i n g food discoideum becomes l e s s f i t as the temperature i n c r e a s e s towards 26,5°C and P, p a l l i d u m becomes f i t ) . Beyond 26.5°C and up to 37.5°C P. p a l l i d u m i s the o n l y s p e c i e s t h a t s h o u l d be a b l e to consume food and f r u i t ( F i g . 2 3 ) . At l e v e l (2) the v a r i o u s areas o c c u p i e d by f r u i t i n g b o d i e s and amoebae o f both s p e c i e s were output by the s i m u l a t i o n at i n t e r v a l s o f 2.4 hours ( F i g . 23). The p r e d i c t i o n s were t e s t e d by growing the two s p e c i e s t o g e t h e r . T e s t s were conducted at the presence or absence l e v e l ( l e v e l 1) by i n o c u l a t i n g b a c t e r i a covered p l a t e s with s i n g l e drops of water c o n t a i n i n g known numbers o f s p o r e s . Both s p e c i e s d i d not f r u i t between 18.0° and 26.5 as 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 p r e d i c t e d ( F i g . 24 F i g . 25). These d a t a a l s o i n d i c a t e d t h a t D. discoideum V12 never f r u i t s above 24.3°C and t h a t the p r o b a b i l i t y o f £• p a l l i d u m f r u i t i n g below 24.3°C depends upon the i n t i a l P. p a l l i d u m c o n c e n t r a t i o n . I t s h o u l d be noted t h a t the d a t a are such t h a t o n l y the presence or absence of f r u i t i n g b o d i e s i s d e t e c t e d . Amoebae may be p r e s e n t ori n o n - f r u i t i n g body p l a t e s but s i n c e the two s p e c i e s are i n d i s t i n g u i s h a b l e at the amoebae stage, i t i s i m p o s s i b l e to determine which amoebae occupy any g i v e n p l a t e . T h i s shortcoming was c ircumvented by experiments which w i l l be p r e s e n t e d l a t e r . Now i t i s enough to know t h a t the model p r e d i c t s t h a t both R' discoideum and P. p a l l i d u m should f r u i t between 18.0° and 2 6.5°C when i n f a c t D. discoideum V12 never f r u i t s above 24.3°C and P. p a l l i d u m f r u i t s below 24.0°C o n l y under c o n d i - t i o n s of h i g h spore c o n c e n t r a t i o n . In s h o r t , the e x p l o i t a t i o n - c o m p e t i t i o n model does not c o m p l e t e l y d e s c r i b e the c o m p e t i t i v e i n t e r a c t i o n , and the two s p e c i e s must d i r e c t l y i n t e r f e r e w i t h one another. F i g u r e 2 3 Output from the 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 over f i v e s u c c e s s i v e days are shown. Area covered ( p r o p o r t i o n a l to the amount of f o o d used) i s p l o t t e d on the y - a x i s . Temperature along t h e x - a x i s . Four q u a n t i t i e s are r e p r e s e n t e d : (1) Area c o v e r e d by D. discoideum amoebae ( s o l i d l i n e ) . (2) Area covered by D. discoideum f r u i t i n g b o d i e s ( d o t t e d l i n e ) . (3) A r e a covered by P. p a l l i d u m amoebae (dashed l i n e ) . (4) A r e a covered by 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 dashed l i n e ) . RE D  15 20 25 30 35 A R EA  C O V EI  Oi  O  DAY 4 / / / / \ 1 / \ 1 / V / \ / \ / \ •'* ' \ ^ .—«-•'' ^ \ 15 20 25 30 35 1290 DAY 5 / \ / / \ / \  1 -\ / \ / A 645 / ' '\ / \\ ' i . ... • A _.. s 1 1 — i 15 20 25 30 35 T E M P E R A T U R E F i g u r e 24 The presence or absence of D. discoideum 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 to (1) temperature - x - a x i s , (2) r e l a t i v e spore 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 spore concentration,, A b l a c k dot i n d i c a t e s t h a t S° discoideum V12 f r u i t e d at any temperature and r e l a t i v e c o n c e n t r a t i o n . An open 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 a b s o l u t e spore c o n c e n t r a t i o n s used: (a) 8800 spores p e r p l a t e , (b) 4400 spores per p l a t e , (c) 2200 spores per p l a t e , (d) 1100 spores per p l a t e . An example: I f a c u l t u r e were s e t up with a t o t a l spore 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. discoideum V12 and 4400 P. p a l l i d u m (5/57, and i f t h i s c u l t u r e were grown at 2 2.3° then o n l y D. discoideum V12 would f r u i t . CD m TJ m za > H cr m ro O ro ro ro ro OJ ro ro 01 ro ro ro oo ro CD O OJ C o n c e n t r a t i o n « * CD cn CH JL CD "T © s ° 9 0 • • oo »o 9 -,o£' s> o o o • o osO» OO? oo cops 09 o / Os oo/ O G o» O -tJo oo oo o o o o o CD ~ ro _» O 9 ro o so ro _ ro ro OJ ro ro ro -j ro CD ro co o i O OJ b~~ of P. p a ! I i d u m / C o n c e n t r a t i o n of D cn OJ T CM "© CD — — CO o oo oo e oo a o o 0 # e$ Oo Oo OSD3 OsOa O s O v ' O O ""6~"""o" O O to ro o ro ro ro ro OJ ro 8 ro ro ro oo ro co OJ oi 4- cn cw C0 TT -u. CD ©. • • O o p» • • •• •• •• • ' oo ••' o« oo •• ,'0©Oo •O OoQ* o o • O DO • C O O O O OO 65 So O o o o o o o o o o o o o d i s c o i d e u m OJ cn CD ro O ro ro ro ro OJ to ro ro co OJ O OJ CO OJ — © • • . o« Iff °o° °o° °§ % b o o o o C O o o o F i g u r e 25 The p r e s e n c e o r absence 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 f r u i t e d . An open c i r c l e d enotes 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 i v e p a r t s t o denote t h e v a r i o u s s p o r e c o n c e n t r a t i o n s u s e d : (a) 6500, (b) 8000, (c) 5000, (d) 4400, (e) 2000 s p o r e s p e r p l a t e . If. - 19 20 21 22 19 20 21 22 19 20 21 22 © O 0 O o 8 J — 8 1 8 I l » 19 20 21 22 23 24 25 26 27 28 29 30 31 19 20 21 J _ L J -A. 25 26 27 28 29 30 31 TEMPERATURE ° C \ \ 73 I n t e r f e r e n c e The d i s c r e p a n c y between the s i m u l a t e d c o m p e t i t i v e outcome ( F i g . 23) and the a c t u a l outcome ( F i g . 24, F i g . 25) suggests t h a t e x p l o i t a t i o n alone cannot e x p l a i n the mechanics o f c o m p e t i t i o n f o r f o o d between D. discoideum and P. p a l l i d u m . I n t e r f e r e n c e must be p l a y i n g some p a r t i n the p r o c e s s . At t h i s p o i n t f o u r c h a r a c t e r i s t i c s of the i n t e r f e r e n c e p r o c e s s are known: (1) both s p e c i e s d i d not f r u i t between 18° and 2 6° as 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 p r e d i c t e d , (2) the p r o b a b i l i t y o f P. p a l l i d u m f r u i t i n g a t any temperature depended upon the i n i t i a l c o n c e n t r a t i o n o f P. p a l l i d u m s p o r e s . As the spore number i n c r e a s e d f r u i t i n g o c c u r r e d at lower and lower temperatures ( F i g . 24), (3) D. discoideum V12 a p p a r e n t l y p r e v e n t e d P. p a l l i d u m from f r u i t i n g over most o f the range e x t e n d i n g from 18° t o 24°C, (4) P. p a l l i d u m prevented D. discoideum V12 from f r u i t i n g i n the temperature range extend i n g from 24.3° t o 26.0°C ( F i g . 24, 2 5 ) . From these o b s e r v a t i o n s i t can be h y p o t h e s i z e d t h a t two d i s t i n c t types of i n t e r f e r e n c e o c c u r : (1) D. discoideum V12 i n t e r f e r e s with P. p a l l i d u m below 24°C and, (2) P. p a l l i d u m i n t e r f e r e s with D. discoideum V12 above 24.3°C. These two p r o c e s s e s were t r e a t e d s e p a r a t e l y . I n h i b i t i o n o f P. p a l l i d u m At the o u t s e t i t can be s t a t e d t h a t P. p a l l i d u m i s i n h i b i t e d a t t h e f r u i t i n g b o d y f o r m a t i o n s t a g e . T h e e v i d e n c e f o r t h i s s t a t e m e n t w i l l b e m o r e l o g i c a l l y p r e s e n t e d l a t e r ( F i g . 3 3 ) , b u t P. p a l l i d u m s p o r e s d o g e r m i n a t e i n t h e p r e s e n c o f D . d i s c o i d e u m a n d t h e v e g e t a t i v e a m o e b a e d o c o n s u m e f o o d a n d d i v i d e b u t a r e u n a b l e t o a g g r e g a t e t o p r o d u c e f r u i t i n g b o d i e s . P r e s u m a b l y D . d i s c o i d e u m i n t e r f e r e s w i t h t h i s p r o c e s s , p o s s i b l y w i t h t h e p r o d u c t i o n o f a c h e m i c a l i n h i b i t o r S i n c e P . p a l l i d u m i s a b l e t o f r u i 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 u n d e r c o n d i t i o n s o f h i g h P . p a l l i d u m c o n c e n t r a t i o n i t c a n b e h y p o t h e s i z e d t h a t s m a l l c l u m p s o f P . p a l l i d u m s p o r e s m i g h t b e a b l e t o o v e r c o m e D . d i s c o i d e u m 0 a n d p r o d u c e f r u i t i n g b o d i e s . T h e h i g h e r t h e P . 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 t h e g r e a t e r t h e l i k e l i h o o d o f s p o r e c l u m p f o r m a t i o n . I f t h i s h y p o t h e s i s i s t o b e t e s t e d , t h e t e r m " s p o r e c l u m p " m u s t f i r s t b e d e f i n e d . I t w a s o b s e r v e d t h a t w h e n 2 s p o r e s w e r e s u s p e n d e d i n . 0 0 1 m l o f w a t e r a n d p l a c e d o n a c u l t u r e d i s h c o n t a i n i n g b a c t e r i a a n d D . d i s c o i d e u m s p o r e s ( c o n c e n t r a t e d f r o m 1 0 0 0 t o 5 0 0 0 s p o r e s p e r p l a t e ) , t h e y w e r e a b l e t o i n f l u e n c e t h e u s e o f f o o d i n a n a r e a o f a b o u t 1 6 t o 2 2 2 mm . I n t h i s a r e a D . d i s c o i d e u m w a s u n a b l e t o u s e t h e f o o d f o r a p e r i o d o f a t l e a s t t h r e e d a y s . E v e n t u a l l y , t h e t i m e d e p e n d i n g u p o n t h e t e m p e r a t u r e , D . d i s c o i d e u m o v e r c a m e P . p a l l i d u m a n d u s e d t h e f o o d p r e v e n t i n g P . p a l l i d u m f r o m f r u i t i n g . F i g u r e 26 The r e l a t i o n s h i p between P. pallidum clump s i z e and temperature. Single black dots denote the occurrence of D. discoideum VC4 f r u i t i n g bodies only. Open c i r c l e s denote the occurrence of both P. pallidum and D. discoideum VC4 f r u i t i n g bodies. The l i n e i s f i l l e d by eye and the shaded area denotes other positions that the l i n e could have taken. In a l l cases the plates were inoculated with a random spread of 1000 D. discoideum VC4 spores. Appropriate numbers of P. pallidum spores were inoculated i n .001 ml of water. LU 21 22 23 24 25 TEMPERATURE 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 " c o u l d 2 be t h e s p o r e s o c c u p y i n g each 19 mm a r e a u n i t on t h e s u r f a c e o f a p e t r i d i s h . Each clump a r e a c o n s t i t u t e s about l / 1 0 0 t h o f t h e s u r f a c e a r e a o f a 60 mm p e t r i d i s h . T h e r e f o r e , i f i t were p o s s i b l e t o d i v i d e a p e t r i d i s h i n t o 100 s e c t i o n s t h e s p o r e s i n each c o u l d r e p r e s e n t one "clump". T h i s p r o c e d u r e was f o l l o w e d i n t h e f i r s t s e c t i o n o f Program V I I I ( A ppendix I ) where a p l a t e was d i v i d e d i n t o 100 e q u a l s e c t i o n s , t h e s p o r e s were s p r e a d a t random, and t h e clump c o n t a i n i n g t h e g r e a t e s t number o f s p o r e s was i d e n t i f i e d . From t h e o u t p u t o f Program V I I I i t was found t h a t as t h e number o f P. p a l l i d u m s p o r e s used t o i n o c u l a t e a p l a t e i n c r e a s e d t h e s i z e o f t h e maximum clump i n c r e a s e d . Because t h e h y p o t h e s i s s t a t e d t h a t o n l y one clump o f a p a r t i c u l a r s i z e would be r e q u i r e d t o overcome the i n h i b i t o r y e f f e c t o f D. d i s c o i d e u m o n l y t h e l a r g e s t clump was o f i n t e r e s t . To r e c a p i t u l a t e : (1) F o r l a c k o f any i n f o r m a t i o n t o t h e c o n t r a r y 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 on t h e s u r f a c e 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 random. (2) A random d i s t r i b u t i o n f u n c t i o n mimics t h i s o c c u r r e n c e . (3) The p l a t e i s d i v i d e d i n t o 100 e q u a l a r e a u n i t s o r s p h e r e s o f i n f l u e n c e . (4) The maximum clump s i z e f o r any s p o r e c o n c e n t r a t i o n i s c a l c u l a t e d . (5) T h i s clump s i z e w i l l 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 s p o r e c o n c e n t r a t i o n . T h i s i n f o r m a t i o n i s summarized i n a components 7 7 diagram ( F i g . 29, page 8 7 ) by steps 1, 2, 3, and 4. Where the number of P. p a l l i d u m spores (SPORE PP), the s i z e of the a r e a c o n t r o l l e d by a spore clump (SPHERE INF), and the t o t a l a r e a of the p l a t e (TOTAL AREA); a l l a c t as i n p u t s to a p o i s s o n d i s t r i b u t i o n (POISSON) which d i v i d e s the p l a t e i n t o a p p r o p r i a t e a r e a u n i t s , d i s t r i b u t e s the spores at random, and chooses the a r e a u n i t c o n t a i n i n g the most spores (AVAILABLE CLUMP S I Z E ) . Having found the " a v a i l a b l e clump s i z e " f o r any spore c o n c e n t r a t i o n o f P. p a l l i d u m the clump s i z e n e c e s s a r y f o r f r u i t i n g i n the presence o f D. discoideum grown at any temperature must be d e r i v e d . To f i n d the "necessary clump s i z e " b a c t e r i a covered p e t r i d i s h e s c o n t a i n i n g 1000 D. discoideum spores were e s t a b l i s h e d . V a r i o u s numbers o f P. p a l l i d u m spores were suspended i n d i s t i l l e d water and i n o c u l a t e d onto the p l a t e s i n .001 ml s u s p e n s i o n s . The p l a t e s were i n c u b a t e d a t v a r i o u s temperatures and the presence o r absence o f P. p a l l i d u m and J2° discoideum f r u i t i n g b o d i e s were noted a f t e r seven days growth. I t was found t h a t as the c o n c e n t r a t i o n of P. p a l l i d u m spores i n c r e a s e d f r u i t i n g o c c u r r e d at lower and lower temper- a t u r e s ( F i g . 26). Due t o the nature of t h i s e x p e r i m e n t a l t e c h n i q u e i t was d i f f i c u l t t o judge the p r e c i s e temperature at which P. p a l l i d u m was unable to f r u i t . T h e r e f o r e , the ' boundary l i n e i n F i g u r e 26 was f i t t e d by eye and the shaded a r e a i n d i c a t e s o t h e r p o s s i b l e p o s i t i o n s t h a t the l i n e c o u l d 78 have assumed. In F i g u r e 26 the area on t h e r i g h t s i d e of the l i n e i s the area i n which P. p a l l i d u m can f r u i t . The a r e a on the l e f t i s the a r e a i n which P. p a l l i d u m cannot f r u i t . The boundary l i n e i s composed of t h r e e s t r a i g h t l i n e s which were d e s c r i b e d as an a r r a y and i n c o r p o r a t e d i n t o t h e second s e c t i o n of Program V I I I (Appendix I)„ In terms o f the components diagram ( F i g . 29, page 87) t h i s i n f o r m a t i o n i s summarized by components 5, 6, and 7. The a r r a y d e s c r i b i n g the r e l a t i o n s h i p between clump s i z e and temperature (PP DATA INPUT), and temperature (TEMP), a c t as i n p u t s to a f u n c t i o n which s e l e c t s the n e c e s s a r y clump s i z e which a l l o w s f r u i t i n g (NECESSARY CLUMP SIZ E ) . In the f o r e g o i n g s e c t i o n i t has been assumed t h a t P. p a l l i d u m f r u i t i n g a b i l i t y i s independent o f D. discoideum background c o n c e n t r a t i o n . T h i s assumption i s p r o b a b l y not a b s o l u t e l y c o r r e c t , however, the v a r i a t i o n i s so s m a l l t h a t i t cannot be d e t e c t e d u s i n g the methods employed i n t h i s s t u d y . The e v i d e n c e f o r t h i s statement comes from two sources o f d a t a . Data, source 1: P l a t e s were e s t a b l i s h e d with random d i s t r i b u t i o n s o f v a r i o u s numbers of D. discoideum V12 and P. p a l l i d u m s p o r e s . I f e x p e r i m e n t a l s e t s i n o c u l a t e d w i t h e q u a l numbers o f P. p a l l i d u m spores are compared i t c o u l d be h y p o t h e s i z e d t h a t i f D. discoideum background i s important 7 9 then P. p a l l i d u m should be abl e to f r u i t at lower temper- a t u r e s on the p l a t e s with low D. discoideum background c o n c e n t r a t i o n s . Comparisons are made i n the : f o l l o w i n g t a b l e : EXPERIMENTAL EXPERIMENTAL SET NO, . 1 SET NO. 2 PP Dd. LOWEST PP Dd. LOWEST CON CON PP. F.B. CON CON PP. F.B. F i g u r e 42-a F i g u r e 43-c 90 10 24.3° 66 600 24.3° * F i g u r e 42-a F i g u r e 44-d 600 66 21.8° 798 1862 25.0° F i g u r e 43-d F i g u r e 44-e 200 466 24.3° 266 2394 24.3° * F i g u r e 44-b F i g u r e 45-e 1862 798 24.3° 1600 14400 23.0° * One s t a r i n the extreme r i g h t hand column i n d i c a t e s t h a t the comparison r e f u t e d the h y p o t h e s i s t h a t D. discoideum c o n c e n t r t i o n a l t e r s P. p a l l i d u m ' s a b i l i t y t o f r u i t . The h y p o t h e s i s was r e f u t e d t h r e e out o f f o u r times, s u g g e s t i n g t h a t P. p a l l i d u m f r u i t i n g i s independent of D. discoideum c o n c e n t r t i o n . 8 0 Data Source 2: A more d i r e c t t e s t o f the h y p o t h e s i s t h a t D o discoideum background a l t e r e d P. p a l l i d u m f r u i t i n g was conducted by e s t a b l i s h i n g p l a t e s c o n t a i n i n g 1000 P. p a l l i d u m spores and s i x d i f f e r e n t D. discoideum VC4 c o n c e n t r a t i o n s . P. p a l l i d u m might have been a b l e t o f r u i t at a s l i g h t l y lower temperature ( P i g . 27) as D. discoideum back- ground d e c r e a s e d . But t h i s t r e n d was v e r y weak i t i t e x i s t e d a t a l l . In both cases the d a t a f a i l e d t o show any r e a l t r e n d i n P. p a l l i d u m f r u i t i n g a b i l i t y with r e s p e c t t o changes i n D. discoideum c o n c e n t r a t i o n . When c o n s i d e r e d w i t h the f a c t t h a t the boundary l i n e ( F i g . 26) may be i m p r e c i s e and the temperature measurements may be i n a c c u r a t e by as much as 0 . 3 ° C , i t i s apparent t h a t the t r e n d , i f i t e x i s t s , i s s m a l l e r than the e x p e r i m e n t a l e r r o r . T h e r e f o r e , the e x p e r i m e n t a l method p r e c l u d e s i n c l u s i o n of any i n t e r a c t i o n between P. p a l l i d u m f r u i t i n g a b i l i t y and D. discoideum c o n c e n t r a t i o n . R e t u r n i n g to the main body o f the i n t e r f e r e n c e s e c t i o n i t has been shown t h a t both "necessary clump s i z e " and " a v a i l a b l e clump s i z e " are c a l c u l a b l e q u a n t i t i e s . T h e r e f o r e , under any c o n d i t i o n s o f temperature and P. p a l l i d u m spore c o n c e n t r a t i o n i t s h o u l d be p o s s i b l e t o l i n k these two q u a n t i t i e s t o g e t h e r and make a d e c i s i o n about whether o r not P. p a l l i d u m w i l l f r u i t . T h i s procedure was c a r r i e d out u s i n g the f i n i s h e d v e r s i o n o f Program V I I I (Appendix I ) . F i g u r e 2 7 P. p a l l i d u m c o n c e n t r a t e d at 1000 spores per p l a t e was grown wit h D, discoideum c o n c e n t r a t e d at 200, 1000, 2000, 3000, 4000, and 5000 spores per p l a t e . Temperature i n degrees c e n t i g r a d e i s measured along the x - a x i s and D, discoideum spore c o n c e n t r a - t i o n i s measured along the y - a x i s . An open c i r c l e denotes the presence 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 dot r e p r e s e n t s a d i s h i n which 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 not appear. The 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 components were a l s o added t o the components diagram ( F i g . 29, page '87) as s t e p s 8 and 9. The COMPARISON f u n c t i o n compares the a v a i l a b l e and n e c e s s a r y clump s i z e s . I f the a v a i l a b l e clump s i z e exceeds the n e c e s s a r y clump s i z e then f r u i t i n g o c c u r s . I f not, then P. p a l l i d u m does not f r u i t . The p r e d i c t i v e a b i l i t y o f t h i s model was t e s t e d u s i n g the data i n F i g u r e s 42, 43, 44 (Appendix I I ) and F i g u r e 2 7. In the f i g u r e s a s t a r appears at p o i n t s where the model f a i l s t o p r e d i c t the outcome. The f o l l o w i n g t a b l e l i s t s t he r e s u l t s o f comparing expected with o bserved. FIGURE NUMBER NUMBER % NUMBER CULTURES RUN FAILURES FAILURE F i g . 42 45 3 6.6% F i g . 43 39 1 2.5% F i g . 44 45 3 6.6% F i g . 27 115 6 5.2% TOTAL 244 13 5.3% Out o f the 244 c u l t u r e s run the model f a i l e d to p r e d i c t the c o r r e c t outcome 5.3% o f the time. These r e s u l t s are a c c e p t a b l e . 83 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 S i n c e the a v a i l a b l e clump s i z e i s c a l c u l a t e d u s i n g a p o i s s o n d i s t r i b u t i o n i t i s p o s s i b l e t o a t t a c h 95% c o n f i d e n c e l i m i t s t o each e s t i m a t e . For clump s i z e s l a r g e r than 10 a standar d t a b l e o f p o i s s o n c o n f i d e n c e i n t e r v a l s was used ( R i c k e r 1936) but f o r e s t i m a t e s l e s s than 10 a c o r r e c t e d t a b l e (Stevens 1942) was used. The procedure i s e x e m p l i f i e d by the d a t a i n F i g u r e 2 7. In t h i s example 1000 P. p a l l i d u m spores were used and the a v a i l a b l e clump s i z e was c a l c u l a t e d t o be 18 s p o r e s . E i g h t e e n spores per clump a l l o w s £• p a l l i d u m growth at 22.7°C ( F i g . 2 6 ). The 95% c o n f i d e n c e l i m i t around the mean e s t i m a t e o f 18 i s 10.7 to 28.4 and the c o r r e s p o n d i n g temperatures are 2 3° and 22„6°C. T h e r e f o r e , when 1000 spores are used t o e s t a b l i s h a c u l t u r e d i s h the maximum a v a i l a b l e clump s i z e might v a r y from 10.7 to 28.4 spores,and the temperature at which P. p a l l i d u m might b e g i n p r o d u c i n g f r u i t i n g b o d i e s v a r i e s from 22.6° t o 23.0° ( F i g . 27). I n h i b i t i o n o f D. Discoideum Experiments i n which D. discoideum was grown alone i n d i c a t e d t h a t D. discoideum V12 was capa b l e o f growing up t o about 26°C and t h a t D. discoideum VC4 was capable o f growing up to about 26.5°C. But when D. discoideum V12 was mixed wi t h P. p a l l i d u m i t s growth was always t e r m i n a t e d at about 24.3°C ( F i g s . 24, 25, and 41, 42, 43, 44 - Appendix I I ) . 84 A p p a r e n t l y , t h e r e was no i n t e r a c t i o n between P_. p a l l i d u m spore c o n c e n t r a t i o n and D. discoideum f r u i t i n g a b i l i t y . Changes i n D. discoideum spore c o n c e n t r a t i o n a l t e r e d discoideum f r u i t i n g a b i l i t y i n the presence o f P. p a l l i d u m . As the spore c o n c e n t r a t i o n i n c r e a s e d from 200 spores per p l a t e t o 2000 spores per p l a t e the temperature a t which f r u i t i n g o c c u r r e d i n c r e a s e d ( F i g . 28). T h i s r e l a t i o n s h i p can be expressed by the f o l l o w i n g e q u a t i o n : T p = 23.9° - C/1800 ; C ^ 2000 (5) Above 2000 spores per p l a t e ( F i g . 28) D. discoideum VC4 was, on the average, unable to f r u i t above 23.9°C. T h i s r e l a t i o n s h i p can be expressed as: Tp = 23.9° ; C )> 2000 (6) where Tp i s the maximum temperature at which D. discoideum can f r u i t and C i s spore c o n c e n t r a t i o n . The f o r e g o i n g i n f o r m a t i o n was i n c o r p o r a t e d i n t o Program IX (Appendix I) as a s u b r o u t i n e , and was added to the d i a g r a m a t i c r e p r e s e n t a t i o n ( F i g . 29, page 87) as components 10, 11, and 12. The r e l a t i o n s h i p s d e s c r i b e d by the above e q u a t i o n s (DATA INPUT), the temperature (TEMP), and the D. discoideum spore c o n c e n t r a t i o n (SPORE DD) a l l feed i n t o a s e l e c t i o n f u n c t i o n (DD SELECTION) which r e g u l a t e s the 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 . F i g u r e 28 The f r u i t i n g a b i l i t y o f D. discoideum grown i n the presence o f 1000 P. p a l l i d u m spores i s p l o t t e d with r e s p e c t t o temperature and D. discoideum spore c o n c e n t r a t i o n . A b l a c k dot r e p r e s e n t s the presence of D. discoideum 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 open 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 with no D. discoideum f r u i t i n g b o d i e s . The l i m i t i n g l i n e i s f i t by eye and 0.3°C temperature i n t e r v a l s have been e s t a b l i s h e d on e i t h e r s i d e o f the l i n e . CO o cc LU O -z. o o LU LX O Q- CO © Q 0 e © O aaapRstansgBBioEC OO O O 0 8 0 © o @ o o le || 1 I at I I I _ )9oo8ĉ.8 8888 0080 8 8 0 © © © © o » e o o I '8 08 / o / w O O O O O o -2. 22 23 " T " 24 25 — 1 — 26 TEMPERATURE 86 The l i n e s drawn i n F i g u r e 28 and d e s c r i b e d by e q u a t i o n s (5) and (6) do not have 95% c o n f i d e n c e l i m i t s . However, the p o s i t i o n i n g o f the l i n e i s i m p r e c i s e because t h e r e undoubtedly i s some d a t a e r r o r and t h e r e i s a l s o e r r o r i n the measurement o f temperature. I t was i m p o s s i b l e to measure the e r r o r i n the data but the temperature e r r o r was- measured and c o u l d have been as much as - 0.3°C. Fo r t h i s r e a s o n an i n t e r v a l r a t h e r than a l i n e must be used to d e s c r i b e t h e temperature above which D. discoideum i s unable t o f r u i t i n the presence of P. p a l l i d u m ( F i g . 28). The Completed Model The model d e s c r i b i n g c o m p e t i t i o n between D. discoideum and P. p a l l i d u m must i n c l u d e an e x p l o i t a t i o n s e c t i o n , a P. p a l l i d u m i n t e r f e r e n c e s e c t i o n , a D. discoideum i n t e r f e r e n c e s e c t i o n , and an e x t e r n a l f o r c e s e c t i o n . These f o u r components have been l i n k e d t o g e t h e r i n Program IX (Appendix I - Program I X ) . A components r e p r e s e n t a t i o n of t h e model appears i n F i g u r e 29. From the model, s e v e r a l q u a n t i t i e s can be p r e d i c t e d . These a r e : (1) the g e r m i n a t i o n r a t e s , (2) the r a t e o f f o o d use, ( 3 ) the r a t e of f r u i t i n g body f o r m a t i o n , ( 4 ) the number o f spores produced, (5) the presence o r absence of f r u i t i n g b o d i e s , (6) the number of a v a i l a b l e clumps o f the n e c e s s a r y s i z e formed by P. p a l l i d u m . F i q u r e 29 Flow diagram d e s c r i b i n g the way i n which the 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. discoideum and P. p a l l i d u m are l i n k e d t o g e t h e r . The terms are e x p l a i n e d i n the t e x t . Program IX i n c l u d e s a l l o f the i n f o r m - a t i o n summarized h e r e . i E X T E R N A L FORCE TEMP I N T E R F E R E N C E TOTAL AREA P P DATA I N P U T P O I S S O N A V A I L A B L E CLUMP S I Z E COMPAR- I S O N j 8 Y E S NO N E C E S S A R Y CLUMP S I Z E 10 DATA I N P U T 8 8 Estimates of the e r r o r attached t o each of these outcomes can a l s o be made. In a previous s e c t i o n i t was demonstrated t h a t 95% confidence l i m i t s c o uld be e s t a b l i s h e d around the temperature at which P. p a l l i d u m f r u i t e d . The e r r o r i n the estimate of the temperature at which D„ discoideum should f r u i t has a l s o been c o n s i d e r e d . F i n a l l y , i t i s a l s o p o s s i b l e t o estimate the e r r o r attached to the model's p r e d i c t i o n s of food use and area covered by f r u i t i n g b odies. These q u a n t i t i e s depend upon many sources of e r r o r such as: (1) e r r o r i n temperature measurement, (2) e r r o r i n germina- t i o n times, (3) e r r o r i n colony expansion, (4) e r r o r i n f r u i t i n g body l a g time, (5) e r r o r i n f r u i t i n g body expansion r a t e s , and (6) e r r o r i n spore counts. With the exception of the spore count e r r o r , i t has been i m p o s s i b l e to do any more than assume t h a t the e r r o r s attached to each of these components i s random. , Since a l l of these components together produce a p r e d i c t i o n of the amount of area occupied by f r u i t i n g bodies at any time i t can be assumed from the theorem f o r the a d d i t i o n of Poisson d i s t r i b u t i o n s ( B r o w n l e e 1965) t h a t the e r r o r attached to t h i s and s i m i l a r p r e d i c t i o n s i s a l s o randomly d i s t r i b u t e d . Therefore 95% confidence l i m i t s from a Poisson d i s t r i b u t i o n may be placed around simulated p r e d i c t i o n s of spore number, area occupied by f r u i t i n g b o d i e s , and food use. 89 T e s t s o f the Model A r e a Occupied by F r u i t i n g Bodies S e v e r a l p r e d i c t i o n s are made by the model, but the one t h a t c a l l s upon the most components i s the p r e d i c t i o n of the r e l a t i v e areas covered by D. discoideum 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 f t e r a l l of the f o o d and space has been used. F o r t h i s reason most of the emphasis i n t e s t i n g the model has been i n t h i s a r e a . C u l t u r e s were e s t a b l i s h e d u s i n g known spore numbers o f both s p e c i e s . Method I I (methods s e c t i o n ) was employed. Temperature and growth p r o g r e s s were monitored, and when a l l the f o o d and area were used, the areas o c c u p i e d by the f r u i t i n g b o d i e s o f the two s p e c i e s were noted. Experiments were conducted at a range o f temperatures and spore c o n c e n t r a t i o n s . With each change i n P. p a l l i d u m c o n c e n t r a t i o n the minimum f r u i t i n g temper- a t u r e changed, and w i t h each change i n D. discoideum spore c o n c e n t r a t i o n the maximum f r u i t i n g temperature changed. The d a t a from these experiments are p r e s e n t e d i n a s e r i e s of f i g u r e s ( F i g . 30-A-F), one f i g u r e f o r each p a i r o f P. p a l l i d u m and D. discoideum spore c o n c e n t r a t i o n v a l u e s . The r e s u l t s of t h e s e t e s t s are summarized as f o l l o w s : F i g u r e 30 The a c t u a l and 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. 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 f t e r a l l t h e a v a i l a b l e f o o d and s p a c e h a s b e e n u s e d . A r e a o c c u p i e d i s m e a s u r e d 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 l i n e 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 model ( F i g . 20) ( P r o g r a m 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 a r o u n d t h e p r e d i c t i o n s a r e i n d i c a t e d w i t h s h a d e d a r e a s . The f i g u r e on t h e f i r s t p age 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 v i e w e d i n p r o p e r p e r s p e c t i v e . The r e m a i n i n g s i x p a g e s o f f i g u r e s a r e b l o w - u p s of'..the s e c t i o n s w h i c h d a t a p o i n t s a p p e a r . The e x p e r i m e n t s were c o n d u c t e d a t s e v e r a l d i f f e r e n t s p o r e c o n c e n t r a t i o n s and one f i g u r e h a s b e e n a l l o t t e d t o e a c h c o n c e n t r a t i o n . FIGURE NUMBER SPORE CONCENTRATION D. DISCOIDEUM P. PALLIDUM 30-A 3000 1500 30-B 4000 1000 30-C 2000 1000 30-D 3000 3000 30-E 4000 , 4000 30-F 5000 5000 TEMPERATURE TEMPERATURE TEMPERATURE 2 1 2 2 2 3 2 4 TEMPERATURE 21 2 2 2 3 2 4 T E M P E R A T U R E TEMPERATURE 0 FIGURE REPLICATE NUMBER NUMBER OF FAILURES % FAILURE 30-A 30-B 30-C 30-D 30-E 30-F 62 36 38 50 66 72 TOTAL 324 5 9 2 1 7 8 8.0% 25.0% 5.2% 2.0% 10.6% 11.1% 32 9.9% C l o s e i n s p e c t i o n o f the f i g u r e i n d i c a t e s t h a t many o f the f a i l u r e s are o f the type where P. p a l l i d u m i s too low and D. discoideum i s too h i g h . These f i n d i n g s can p o s s i b l y be e x p l a i n e d by the f a c t t h a t at temperatures c l o s e t o the minimum f r u i t i n g temperature, o n l y one o r two a v a i l a b l e clumps are l a r g e r than the ne c e s s a r y clump s i z e . T h e r e f o r e , a l l the amoebae from every s e c t i o n o f the p l a t e must converge on one or two f r u i t i n g c e n t e r s . I t i s d i f f i c u l t to b e l i e v e t h a t the c o n c e n t r a t i o n g r a d i e n t from one c e n t e r would be g r e a t enough t o a t t r a c t a l l amoebae, and t h e r e f o r e , some amoebae might be unable t o f i n d a f r u i t i n g c e n t e r and add to 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 . T h i s s i t u a t i o n r e s u l t s i n an o v e r - e s t i m a t e o f P. p a l l i d u m f r u i t i n g body a r e a . U n f o r t u n a t e l y , t h e r e i s no l e g i t i m a t e way to i n c o r p o r a t e t h i s h y p o t h e s i s i n t o the model u n t i l more i s known about the a t t r a c t i v e area o f a c r a s i n i n mixed c u l t u r e s . 92 C ontinued C o m p e t i t i o n S i n c e the average P. p a l l i d u m f r u i t i n g body c o n t a i n s from 100 to 10000 spores the model p r e d i c t s t h a t once such a f r u i t i n g body forms anywhere above 22.5°C i t should be abl e to p e r p e t u a t e i t s e l f i n a s i t u a t i o n where fo o d i s c o n s t a n t l y b e i n g r e p l a c e d . To t e s t t h i s h y p o t h e s i s two c u l t u r e d i s h e s c o n t a i n i n g 4000 D. discoideum and 4000 P. p a l l i d u m spores were grown at 2 3.5°C. When the food was gone and f r u i t i n g b o d i e s had formed the completed d i s h e s were p l a c e d f a c e t o f a c e w i t h new b a c t e r i a covered d i s h e s . The second d i s h e s were allowed to grow and a f a c e t o f a c e t r a n s f e r was made to a t h i r d d i s h . The r e s u l t s o f t h i s s h o r t experiment are as f o l l o w s : TIME PERIOD AREA P. PALL. AREA D. DISC. 1 8, 12 292, 288 2 10, 11 290, 289 3 10, 13 290, 287 P. p a l l i d u m f r u i t e d the f i r s t time as expected and c o n t i n u e d to f r u i t throughout the e n t i r e time sequence. A l s o P. p a l l i d u m d i d not g a i n o r l o s e any are a d u r i n g the sequence. Summary - I n t e r f e r e n c e (1) The p r e d i c t i o n s made by the e x p l o i t a t i o n model d i d not agree w i t h the r e s u l t s o f experiments i n which the two 93 s p e c i e s were grown t o g e t h e r . I n t e r f e r e n c e was o c c u r r i n g . (2) P. p a l l i d u m i n t e r f e r e d w i t h D. discoideum f r u i t i n g above about 24°C. (3) D. discoideum i n t e r f e r e d w i t h P. p a l l i d u m f r u i t i n g below about 24°C. (4) The f r u i t i n g a b i l i t y o f P. p a l l i d u m depended upon maximum clump s i z e . The term "clump" was d e f i n e d as the number of spores occupying l/100th o f the s u r f a c e area of a. 60 mm p e t r i d i s h . (5) The clump s i z e n e c e s s a r y f o r f r u i t i n g was temperature dependent and was assessed e x p e r i m e n t a l l y . (6) The maximum clump s i z e a v a i l a b l e f o r any P. p a l l i d u m spore c o n c e n t r a t i o n was car-lculated u s i n g a P o i s s o n d i s t r i b u t i o n . (7) When " a v a i l a b l e clump s i z e " exceeded 'necessary clump s i z e " f r u i t i n g o c c u r r e d . The model f o r t h i s p r o c e s s i s d e s c r i b e d i n Program V I I I (Appendix I ) . (8) D. discoideum f r u i t i n g a b i l i t y changed wi t h r e s p e c t t o temperature and spore c o n c e n t r a t i o n ( F i g . 28). (9) The two i n t e r f e r e n c e models were l i n k e d t o the e x p l o i t a - t i o n model ( F i g . 29) (Program IX - Appendix I) and the completed model was t e s t e d . 94 (10) A t o t a l of 324 predicted cultu r e areas were used to t e s t the model which proved accurate i n 90ol% of the test cases. 9 5 RESULTS SECTION I I CONSEQUENCES OF COMPETITION The model c o n s t r u c t e d i n the p r e c e d i n g s e c t i o n d e a l s o n l y with c e l l u l a r s l i m e mold c o m p e t i t i o n over s h o r t time i n t e r v a l s . No attempt was made to p r e d i c t the r e s u l t s of c o m p e t i t i o n c o n t i n u i n g f o r long p e r i o d s o f time, because such p r e d i c t i o n s c o u l d o n l y be made i f the organisms 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 . The r e s u l t s o f o t h e r s t u d i e s (Keast 1968, F i c k e n e t a l , 1968, M i l l e r 1967) suggest t h a t t h i s i s u n l i k e l y , p a r t i c u l a r l y w i t h simple organisms l i k e the c e l l u l a r s l i m e molds. In view o f t h i s i n f o r m a t i o n , a s e r i e s o f long term c o m p e t i t i v e s i t u a t i o n s were c o n t r i v e d i n the l a b o r a t o r y . I t was hoped t h a t the r e s u l t s o f these experiments would d e s c r i b e any changes t h a t D. discoideum and P. p a l l i d u m might e x p e r i e n c e , and t h a t the r e s u l t s might a l s o add to our knowledge of the s e l e c t i v e f o r c e s i n v o l v e d i n the maintenance o f 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 model demonstrated t h a t the two s p e c i e s excluded one another between 18° and 2 6°C, making i t i m p o s s i b l e to compete f o r long time p e r i o d s . To remedy t h i s s i t u a t i o n r e f u g e s were p r o v i d e d by growing the two s p e c i e s i n long c u l t u r e d i s h e s which were p l a c e d on a temper- a t u r e g r a d i e n t e x t e n d i n g from about 15°C to 30°C. When grown al o n e , D. discoideum was a b l e t o consume food and f r u i t 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° 25° 30° When grown alone, P . p a l l i d u m c o u l d consume food and f r u i t between about 18° and 37°C 0 P. P a l l i d u m 15° 20° 25° 30° T h e r e f o r e the l a b o r a t o r y d e s i g n p r o v i d e d r e f u g e s f o r both s p e c i e s . I f d i v e r g e n c e , convergence o r c o n t i n u e d e x c l u s i o n were t o o c c u r , an a r e a o f c o n f l i c t s hould be p r o v i d e d . The above diagrams i n d i c a t e t h a t i f the two s p e c i e s were grown t o g e t h e r they both c o u l d compete f o r the food and space between 18° and 26°C. F i n a l l y , an attempt was made t o produce an e n v i r o n - ment t h a t was homogeneous i n every r e s p e c t save temperature. The environment was two-dimensional, the agar s u r f a c e was as f l a t as p o s s i b l e , and o n l y one b a c t e r i a l s p e c i e s was used as a food s o u r c e . Under the s e 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 t h a t the animals might both converge t o use the r e s o u r c e a t the 97 same r a t e , and thereby ensure c o e x i s t e n c e ; o r t h a t one s p e c i e s might i n c r e a s e i t s r a t e o f r e s o u r c e use making i t i m p o s s i b l e f o r the o t h e r to compete, th e r e b y e n s u r i n g c o m p e t i t i v e e x c l u s i o n . M i x t u r e of Stock Spores A f i f t y - f i f t y m ixture o f spores coming d i r e c t l y from the stock c u l t u r e s was used t o e s t a b l i s h c u l t u r e g r a d i e n t s p e r i o d i c a l l y throughout the two ye a r p e r i o d over which t h i s study was conducted. In every case the two s p e c i e s d i d not f r u i t t o g e t h e r . D. discoideum V12 f r u i t e d up t o about 24.5°C ( F i g . 31-A, B, C ) . D. discoideum DF f r u i t e d up to about 26.5°C ( F i g . 31-D,. E ) . In both cases P. p a l l i d u m f r u i t e d o v e r the remaining p o r t i o n o f the c u l t u r e g r a d i e n t . T h i s i n f o r m a t i o n i s summarized i n the f o l l o w i n g diagram: 1 1 1 1 1 1 1 D. discoideum P. p a l l i d u m 1 1 1 1 1 1 1 15 20 25 30 Continued M i x t u r e s I t was h y p o t h e s i z e d t h a t i f the two c o m p e t i t o r s were t o c o n t i n u e t o compete i n the homogeneous c u l t u r e g r a d i e n t s they might converge and c o e x i s t . S i n c e i t was i m p o s s i b l e t o promote c o n t i n u e d c o m p e t i t i o n by simply l e a v i n g the two s p e c i e s i n the same F i g u r e 31 C u l t u r e g r a d i e n t drawings demonstrating 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 o f both s p e c i e s . The spores used came from stock c u l t u r e s . The v e r t i c a l l y shaded areas were co v e r e d with D . discoideum f r u i t i n g b o d i e s , the h o r i z o n t a l l y shaded areas with P. p a l l i d u m f r u i t i n g b o d i e s . The unshaded areas had no f r u i t i n g b o d i e s . F o r g r a d i e n t s A, B, and C D. discoideum V12 was used. F o r g r a d i e n t s D and E D. discoideum DF was used.  99 c u l t u r e g r a d i e n t , because the media soon became f o u l e d with waste p r o d u c t s and the food was soon used up; c o m p e t i t i o n was c o n t i n u e d by a s e r i a l t r a n s f e r t e c h n i q u e . The f i r s t g r a d i e n t was l e f t f o r about two weeks, u n t i l the f o o d was gone and f r u i t i n g was f i n i s h e d , then then the spore p r o d u c t i o n from t h i s g r a d i e n t was h a r v e s t e d a t random and used to e s t a b l i s h a new c u l t u r e g r a d i e n t . The spores from the second g r a d i e n t were used to e s t a b l i s h a t h i r d , and so on. The changes e x p e r i e n c e d by the two c o m p e t i t o r s were observed i n f o u r r e p l i c a t e c u l t u r e experiments. S i n c e minor d i f f e r e n c e s were encountered i n each o f the s e r i e s they must be c o n s i d e r e d s e p a r a t e l y . C u l t u r e G r a d i e n t I C u l t u r e g r a d i e n t I was e s t a b l i s h e d d u r i n g J u l y 1968 and completed d u r i n g March 1969. The spore progeny o f each g r a d i e n t was used to e s t a b l i s h the next i n the s e r i e s , but i n t h i s one case, the spores used t o make the s e r i a l t r a n s f e r were not chosen at random. They came from the area of the t r o u g h t h a t was c l o s e s t to the area o c c u p i e d by the o t h e r s p e c i e s . T h i s p r a c t i c e was not f o l l o w e d i n the o t h e r g r a d i e n t experiments. The d a t a i n d i c a t e d t h a t D. discoideum V12 o c c u p i e d the a r e a from about 15° to 24.5 - 25.5°C and c o n t i n u e d t o occupy t h i s a r e a throughout the s e r i e s . P. p a l l i d u m , on the o t h e r hand, o c c u p i e d the area e x t e n d i n g from 24 - 25°C to F i g u r e 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 the 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 shaded areas 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 , the v e r t i c a l l y shaded ar e a by D. discoideum f r u i t i n g b o d i e s . The areas shaded with 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 both s p e c i e s . The unshaded areas were unoccupied. Temperature i s marked a t i n t e r v a l s under each diagram.  101 30°C d u r i n g the f i r s t few c u l t u r e s but wit h 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 extended i t s range down to about 20°C ( F i g . 32). To summarize: b e f o r e c o m p e t i t i o n the two s p e c i e s were unable t o c o - f r u i 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 began to f r u i t between 20° and 24°C, along with D. discoideum V12. I t should be noted t h a t P. p a l l i d u m was always c a p a b l e o f f r u i t i n g i n t h i s area when grown alone, i t was o n l y the i n t e r f e r e n c e by D. discoideum t h a t prevented i t from d o i n g so. T h i s i n t e r f e r e n c e f a c t o r was a p p a r e n t l y overcome by some change r e s u l t i n g from c o n t i n u e d c o m p e t i t i o n . C u l t u r e G r a d i e n t I I C u l t u r e g r a d i e n t I I was begun d u r i n g September 1968 and f i n i s h e d d u r i n g May 1969. I t s e s t a b l i s h m e n t and co n t i n u a n c e was e x a c t l y the same as t h a t o f c u l t u r e g r a d i e n t I except t h a t the spores used t o make the s e r i a l t r a n s f e r s came from the e n t i r e f f r u i t i n g a r e a and were chosen at random. As i n c u l t u r e g r a d i e n t I the two s p e c i e s began by f r u i t i n g i n s e p a r a t e areas but 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 began t o c o - f r u i t with D. discoideum. C o - f r u i t i n g i n c u l t u r e g r a d i e n t I I was not as e x t e n s i v e nor as r e g u l a r 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 - Appendix I I ) . No r e a l e x p l a n a t i o n can be g i v e n f o r t h i s , except t h a t the spore, s e l e c t i o n i n c u l t u r e g r a d i e n t I I was not as p r e c i s e as t h a t 102 employed i n I, and t h e r e f o r e , s e l e c t i o n may not have o c c u r r e d as q u i c k l y o r as s u r e l y . However, c o - f r u i t i n g d i d o c c u r . As i n c u l t u r e g r a d i e n t I the r e s u l t s of I I suggest t h a t D. discoideum was unable to f r u i t between 25° and 26°C through the e n t i r e s e r i e s . On the o t h e r hand P. p a l l i d u m overcame the i n h i b i t o r t h a t p r e v e n t e d i t from f r u i t i n g . F i n a l l y , g r a d i e n t I I - E ( F i g . 46 - Appendix I I ) and g r a d i e n t I-G ( F i g . 32) both d e p i c t D. discoideum f r u i t i n g up t o 26°C. Both g r a d i e n t s were run at the same time (October 1968) and e x p e r i e n c e d an equipment f a i l u r e which caused a s h i f t i n the g r a d i e n t temperature d u r i n g the f i r s t two days o f i n c u b a t i o n . T h i s s h o r t term s h i f t was enough to a l t e r the f i n a l c o m p e t i t i v e outcome, s u g g e s t i n g t h a t the temperatures d u r i n g the f i r s t s t a g e s of i n c u b a t i o n determine th e outcome o f the e n t i r e c o m p e t i t i v e s i t u a t i o n . C u l t u r e G r a d i e n t I I I C u l t u r e g r a d i e n t I I I was e s t a b l i s h e d d u r i n g May 1969 and was completed d u r i n g September 1969. The g e n e r a l r e s u l t s o f t h i s experiment are e x a c t l y as they were f o r the p r e c e d i n g g r a d i e n t s ( F i g . 47 - Appendix I I ) . There were two d i f f e r e n c e s however: (1) The c u l t u r e d i s h e s were o n l y h a l f as wide as those used i n o t h e r experiments, but the spore number r e l a t i v e t o a rea was i d e n t i c a l . (2) The D. discoideum s t r a i n was D. discoideum DF which has a h i g h e r temperature t o l e r a n c e than 103 e i t h e r VC4 o r V12. T h i s h i g h e r t o l e r a n c e allowed D. discoideum DF t o grow up to about 2 6°C as i t d i d i n the p r e l i m i n a r y c u l t u r e s ( F i g . 30-D, E ) . D e s p i t e the f a c t t h a t the D. discoideum s t r a i n was d i f f e r e n t , the r e s u l t s were the same. Before 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 was unable t o c o - f r u i t w i t h £° discoideum, and 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 c o - f r u i t i n g o c c u r r e d . D. discoideum d i d not a l t e r i t s f r u i t i n g a b i l i t y . C u l t u r e G r a d i e n t IV A r a t h e r 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 used t o generate the spores t h a t were e v e n t u a l l y used t o e s t a b l i s h g r a d i e n t IV. The d a t a from the t h r e e p r e v i o u s g r a d i e n t s has 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 over a long temperature g r a d i e n t c o u l d r e s u l t i n c o - f r u i t i n g . But whether the same r e s u l t s c o u l d be a c h i e v e d at any one temperature w i t h i n the range e x t e n d i n g from 18° to 26°C was unknown. To answer t h i s q u e s t i o n D. discoideum V12 c u l t u r e s were grown a t 18°C and 24°C, and P. p a l l i d u m c u l t u r e s were grown a t 24°C and 36°C. The spores t h a t came from these f o u r stock c u l t u r e s were mixed i n a l l combinations and the mixtures were grown at 24°C. The p e r c e n t o f c u l t u r e s y i e l d i n g f r u i t i n g b o d i e s from both s p e c i e s was then c a l c u l a t e d . The s t o c k s were main t a i n e d by s e r i a l t r a n s f e r s , and mixtures and comparisons were made a second time. T h i s procedure was c o n t i n u e d f o r nine time p e r i o d s . The f o l l o w i n g diagram may h e l p t o e x p a l i n the method: 104 TIME TEMPERATURE REMARKS 18v 24 v 36^ n~ Dd stock Dd stock- -PP stock rrPp stock s t o c k s were s e t up (1) mix- /H<2) mix« :Dd stock ]=5fe»Dd stock" _=»PP s t o c k - 'Dd stock •Dd stock •PP stock (1) mix' (2) mix- ( 3 ) mix> _ZPp stock •Pp stock - a l l s t o c k s c o n t i n u e d - (1) mix i s Dd stock 24 and PP stock 24° - (2) mix i s Dd stock 18° and PP stock 36° a l l s t o c k s c o n t i n u e d (1) mix i s Dd stock 24°, and PP stock 24° (2) mix i s Dd stock 18° and PP stock 36° ( 3 ) mix i s from number ( 1 ) mix 105 From the p r e v i o u s work i t was apparent t h a t none o f the mixtures would produce f r u i t i n g b o d i e s o f both s p e c i e s i f homogeneous mixtures o f spores were used as the inoculum. To circumvent t h i s problem the mix c u l t u r e s were e s t a b l i s h e d by- making two s m a l l h o l e s i n the agar, 5 mm i n diameter and 1 t o 2 mm a p a r t , P. p a l l i d u m spores were p l a c e d i n one h o l e and D. discoideum spores i n the o t h e r . The mixtures were i n c u b a t e d at 24°C f o r 4 t o 7 days, and the presence o r absence o f c o - f r u i t i n g was noted. The f o l l o w i n g s e r i e s o f t a b l e s summarizes the f i n d i n g s . I t should be noted t h a t : mix (1) = Dd stock 24° + PP stock 24° mix (2) = Dd stock 18° + PP stock 18° mix (3) = output o f mix (3) from time t-1 TIME 2 - TEMPERATURE 24.0° - 0.5° MIX NUMBER REPLICATE % CO-FRUIT TIME 3 - TEMPERATURE 2 3.6° - 0.6° 100% MIX NUMBER REPLICATE % CO-FRUIT 1 2 3 4 4 4 25% 75% 100% 106 TIME 4 - TEMPERATURE 2 3.0 - 0.0° MIX NUMBER REPLICATE % CO-FRUIT 1 4 100% 2 4 100% 3 4 100% TIME 5 - TEMPERATURE 22.5° - 0.5° MIX NUMBER REPLICATE % CO-FRUIT 1 4 100% 2 3 100% 3 3 100% By t h i s time i t had become c l e a r t h a t v e r y l i t t l e d i f f e r e n c e c o u l d be found between the t h r e e types o f mix c u l t u r e s when they were e s t a b l i s h e d u s i n g s m a l l and s e p a r a t e agar h o l e s . I t had been observed, however, t h a t i n some i n s t a n c e s the f r u i t i n g b o d i e s o f the two s p e c i e s were a c t u a l l y i n t e r - d i s p e r s e d with one another. I t was r e a l l y the degree o f i n t e r m i n g l i n g t h a t was o f i n t e r e s t , and t h e r e f o r e , a mixing index was e s t a b l i s h e d . A c u l t u r e was awarded one p o i n t on the mixing index f o r every p a i r o f P. p a l l i d u m and D. discoideum f r u i t i n g b o d i e s t h a t were s e p a r a t e d by not more than f i v e mm. T h e r e f o r e , i f a D. discoideum f r u i t i n g body grew i n the middle 107 o f a " f o r e s t " 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 t would have a mixing index o f f o u r . One p o i n t f o r each o f the f o u r s i d e s a d j a c e n t t o P. p a l l i d u m . From t h i s p o i n t on the mixing t a b l e s r e g i s t e r the percen t a g e o f the c u l t u r e which had a mixing index o f one o r more. The mean index - one sta n d a r d d e v i a t i o n i s a l s o g i v e n . TIME 6 - TEMPERATURE 2 3.2° - 0.2° MIX NUMBER REPLICATE % WITH INDEX INDEX 3 8 6% 1.6 - 3.0 2 none - - 1 none TIME 7 - TEMPERATURE 24.5° - 0.5° MIX NUMBER REPLICATE % WITH INDEX INDEX 1 none — _ 2 none - - 3 11 2 3% 2.0 - 4.4 TIME 8 - TEMPERATURE 22.7° i 1.2° MIX NUMBER REPLICATE % WITH INDEX INDEX 1 8 40% 1.8 - 1.8 2 8 0.0% o.o i 0.0 3 24 40% 5.1 i 9.1 108 TIME 9 - TEMPERATURE 2 3.5° - 0,5° MIX NUMBER REPLICATE % WITH INDEX INDEX 1 8 12% 0.9 - 1.8 2 8 0% 0 . 0 - 0.0 3 18 22% 2.0 i 4.1 Mi x t u r e - t y p e 3 c o n s i s t e n t l y had the g r e a t e s t mixing index and u s u a l l y the h i g h e s t percentage o f mix i n g , but t h e r e was s t i l l no way to support o r r e f u t e the h y p o t h e s i s t h a t c o n t i n u e d mixing i n c r e a s e d the chance o f c o - f r u i t i n g . The e x p e r i m e n t a l method used was si m p l y not s e n s i t i v e enough. To r e c t i f y t h i s s i t u a t i o n the mix c u l t u r e s were e s t a b l i s h e d by suspending the two types o f spores t o g e t h e r i n water and i n o c u l a t i n g the c u l t u r e s w i t h the s u s p e n s i o n . TIME: 10 - TEMPERATURE MIX NUMBER 21.0° i 1.0° REPLICATE % MIXING 3 16 43.6% TIME 11 - TEMPERATURE MIX NUMBER 22.0° i 1.0° REPLICATE % MIXING 3 6 100% 1 0 9 TIME 12 MIX NUMBER REPLICATE % WITH INDEX INDEX TEMPERATURE 2 1 . 5 ° ' i 0.7° 3 1 100% 25 TEMPERATURE 2 3 , 6 ° - 0.7° 3 6 8 3 % 2 3 - 1 6 . 8 TEMPERATURE 2 4 . 4 ° - 0 . 6 ° 8 3 % 9.8 — 6.3 The mix c u l t u r e s 3 t h a t came from p r e v i o u s mix c u l t u r e s appeared to be a b l e t o c o - f r u i t i n almost every i n s t a n c e , p a r t i c u l a r l y a f t e r the s e l e c t i o n d u r i n g time p e r i o d 10. To prove t h i s p o i n t the spores from time p e r i o d 12 were, used t o e s t a b l i s h c u l t u r e g r a d i e n t IV. In g r a d i e n t IV c o - f r u i t i n g o c c u r r e d immediately and c o n t i n u e d throughout the experiment ( F i g . 48 - Appendix I I ) . To summarize; t h i s experiment demonstrated t h a t t h e a b i l i t y o f P. p a l l i d u m t o overcome D. discoideum i n h i b i t i o n does not depend upon growth over the wide range o f temperatures p r o v i d e d i n the g r a d i e n t but can o c c u r at one temperature i n the o v e r l a p range o f 18° to 25°C. 110 I t might be h y p o t h e s i z e d t h a t c o m p e t i t i o n had n o t h i n g t o do w i t h the change i n f r u i t i n g a b i l i t y undergone ky £• p a l l i d u m . One o r both s p e c i e s might have a c c l i m a t e d t o temperatures i n the middle range (20°C t o 2 4 ° C ) , and t h i s a c c l i m a t i o n might have been enough to cause c o - f r u i t i n g . T h i s h y p o t h e s i s was t e s t e d i n the f o l l o w i n g manner. The c u l t u r e s t h a t were used t o e s t a b l i s h g r a d i e n t s I and I I were grown at 18°C (D. discoideum) and 34°C (P. p a l l i d u m ) f o r about f o u r months b e f o r e the g r a d i e n t s were e s t a b l i s h e d . In both c a s e s no c o - f r u i t i n g o c c u r r e d i n the f i r s t c u l t u r e g r a d i e n t . The c u l t u r e s t h a t were used to e s t a b l i s h the p r e l i m i n a r y g r a d i e n t s ( F i g . 31A, B, C) were grown at room temperature (22.0° - 2.0°) f o r a minimum o f f o u r months b e f o r e b e i n g used t o e s t a b l i s h t h e s e g r a d i e n t s . Again no o v e r l a p o c c u r r e d . T h e r e f o r e , temperature alone was not enough to cause c o - f r u i t i n g . A t t h i s p o i n t i n the study the d a t a s t r o n g l y suggests t h a t c o m p e t i t i o n alone i s both n e c e s s a r y and s u f f i c i e n t t o cause c o - f r u i t i n g . But t h r e e q u e s t i o n s remain unanswered: (1) which s p e c i e s changed? (2) what are the mechanics o f the change? (3) what k i n d o f change o c c u r r e d ? Changes Between 18° And 24° Which Competitor Changed? With the d a t a a v a i l a b l e i t was known o n l y t h a t c o m p e t i t i o n caused something to happen which r e s u l t e d i n I l l c o - f r u i t i n g . These r e s u l t s c o u l d have been o b t a i n e d i n one o f t h r e e ways: (1) D. discoideum c o u l d have stopped i n h i b i t - i n g P. p a l l i d u m , (2) P. p a l l i d u m c o u l d have overcome the i n h i b i t i o n from D. discoideum, o r (3) both c o m p e t i t o r s c o u l d have changed. To f i n d which o f these hypotheses was the most r e a s o n a b l e the f o l l o w i n g experiment was d e s i g n e d : D. discoideum ( s t o c k ) was grown wi t h P. p a l l i d u m (changed) g r a d i e n t A D. discoideum (changed) was grown with P. p a l l i d u m ( s t o c k ) g r a d i e n t B where " s t o c k " denotes stock c u l t u r e s t h a t had not e x p e r i e n c e d c o m p e t i t i o n and "changed" denotes c u l t u r e s which came from c o - f r u i t i n g g r a d i e n t s . I f g r a d i e n t A r e s u l t e d i n c o - f r u i t i n g , then P. p a l l i d u m must have changed. I f g r a d i e n t B r e s u l t e d i n c o - f r u i t i n g then D. discoideum must have changed. I f both g r a d i e n t s A and B r e s u l t e d i n c o - f r u i t i n g then both must have changed. The experiment o u t l i n e d above was r e p l i c a t e d f o u r times and i n every case o n l y g r a d i e n t A r e s u l t e d i n c o - f r u i t - i n g ( F i g . 49 - Appendix I I ) . I t i s s a f e to assume t h a t o n l y 112 p a l l i d u m changed. In a l l p r o b a b i l i t y t h i s s p e c i e s was, i n some way, a b l e to overcome D„ discoideum i n h i b i t o r y a b i l i t y . Mechanics o f the Change Having found t h a t P. p a l l i d u m r e a c t e d t o c o m p e t i t i v e p r e s s u r e by overcoming i t s i n a b i l i t y t o grow i n the presence o f D. discoideum i t would be d e s i r a b l e t o know something about the n a t u r e o f the i n h i b i t o r y e f f e c t . A l l o f the work up to t h i s p o i n t i n d i c a t e d o n l y t h a t P. p a l l i d u m f r u i t i n g b o d i es were not found i n the presence o f D. discoideum b e f o r e c o m p e t i t i o n and t h a t they were found a f t e r an extended p e r i o d o f 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 have been stopped a t any one of t h r e e stages and the above d e s c r i p t i o n would s t i l l be a p p l i c a b l e . The t h r e e stages a r e : (1) P. p a l l i d u m sp o r e s might have been unable to germinate, (2) the spores might have germinated to produce amoebae but the amoebae may have been unable to reproduce, or (3) both the spores and amoebae may have a c t e d n o r m a l l y but the amoebae may have been unable to aggregate to produce f r u i t i n g b o d i e s . The f o l l o w i n g experiment was d e s i g n e d to f i n d which o f the t h r e e hypotheses was c o r r e c t . A c u l t u r e g r a d i e n t was s e t up i n the u s u a l way w i t h a b a c t e r i a lawn and a random d i s p e r s a l of spores o f both s p e c i e s . Small b l o c k s o f agar, a l s o c o v e r e d w i t h a b a c t e r i a lawn, were p l a c e d at i n t e r v a l s down the l e n g t h o f the g r a d i e n t . I n p l a n view the g r a d i e n t appears: 113 agar block- o o o o o o 15 20 25 30 and i n s i d e view: -agar b l o c k 15 20 25 30 The agar b l o c k g r a d i e n t was then i n c u b a t e d on the temperature g r a d i e n t . I f P. p a l l i d u m spores were g e r m i n a t i n g i n the presence o f D. discoideum and i f the amoebae were moving around and d i v i d i n g 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 amoebae on top o f the agar b l o c k s . T h e r e f o r e , a f t e r i n c u b a t i o n a smear was taken from the top o f each agar b l o c k and i n c u b a t e d a t 36.0°C. P. p a l l i d u m was found down the l e n g t h o f the g r a d i e n t ( F i g . 33-A, B, C) ( s t a r s denote b l o c k s on which R° p a l l i d u m was f o u n d ) . These d a t a s t r o n g l y suggest t h a t P.» discoideum was a b l e to i n h i b i t P. p a l l i d u m a t the f r u i t i n g body f o r m a t i o n s t a g e . As a check a g a i n s t the h y p o t h e s i s t h a t the amoebae found on top o f the agar b l o c k s m i g r a t e d down from the a r e a above 25°C, the c u l t u r e g r a d i e n t s were run i n p a i r s , one u n d i v i d e d , and one w i t h aluminum f o i l d i v i d e r s between each agar b l o c k . The d i v i d e r s were s e a l e d i n p l a c e w i t h s i l i c o n e F i g u r e 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 to f r u i t below about 24°C. H o r i z o n t - a l l y shaded areas 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 . V e r t i c a l l y shaded areas 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 shaded areas by both s p e c i e s . Unshaded areas 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 the agar b l o c k s i n p l a n view. The d i v i d e r s between b l o c k s are shown i n A DIV, B DIV AND C DIV. The s t a r s over the b l o c k s denote b l o c k s on which P. p a l l i d u m was found. 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 g r e a s e . In the d i v i d e d g r a d i e n t s P. p a l l i d u m was s t i l l found on top o f the agar b l o c k s ( F i g . 33-A DIV, B DIV, C DIV). To summarize: D. discoideum was, i n some way, a b l e t o s t o p P. p a l l i d u m v e g e t a t i v e amoebae from a g g r e g a t i n g and f r u i t i n g , but the two s p e c i e s o f amoebae compete f o r f o o d at a l l n o n - l e t h a l temperatures. The type on i n h i b i t o r used by D. discoideum remains unknown. The Type o f Change S i n c e the s p e c i e s t h a t changed, and the p o i n t a t which the change o c c u r r e d were i d e n t i f i e d , the k i n d o f change t h a t took p l a c e was c o n s i d e r e d . P. p a l l i d u m c o u l d have changed g e n e t i c a l l y , or a d a p t i v e l y , o r i n some o t h e r un- h y p o t h e s i z e d manner. In an attempt to narrow the f i e l d two experiments were conducted. In the f i r s t e x p e r i m e n t a l s e t P. p a l l i d u m (changed) (from g r a d i e n t I) was mixed 50:50 w i t h £• p a l l i d u m ( s t o c k ) and the c u l t u r e d i s h was grown at 27°C. At the same time D. discoideum V12 from g r a d i e n t I was mixed 50:50 w i t h D. discoideum V12 ( s t o c k ) ( i t was unnecessary to make the D. discoideum mixture but when t h i s experiment was done i t was not known t h a t o n l y P. p a l l i d u m had changed). At the same time P. p a l l i d u m (changed) was grown by i t s e l f . The f o l l o w i n g diagram e x p l a i n s the d e s i g n . 116 PP (change) Dd (change) PP (change) Dd ( s t o c k ) PP ( s t o c k ) O O o o o o 0 • c o - f r u i t - * **o "-no- Q O O c o - f r u i t O O - c o - f r u i t O O O _ ^ c o - f r u i t O During time p e r i o d 1 the f i r s t p l a t e o f each l i n e was allowed to grow u n t i l a l l f r u i t i n g stopped (a p e r i o d o f one week). The spore progeny were then used t o s e t up p l a t e s f o r time p e r i o d 2, and so on. At the end o f time p e r i o d 3 a c u l t u r e g r a d i e n t was e s t a b l i s h e d with the output o f l i n e 1 (PP change) and l i n e 2 (Dd change + Dd s t o c k ) . C o - f r u i t i n g o c c u r r e d . The l i n e s were c o n t i n u e d and c o - f r u i t i n g c o n t i n u e d to o c c u r ( F i g . 50-A, B, C - Appendix I I ) . When l i n e 2 was mixed w i t h l i n e 3 (PP change + PP s t o c k ) no c o - f r u i t i n g o c c u r r e d i n time p e r i o d 3 ( F i g . 50-D - Appendix I I ) . Two k i n d s o f i n f o r m a t i o n are y i e l d e d by t h i s s e t o f e xperiments. F i r s t , the c u l t u r e s c o n t a i n i n g o n l y P. p a l l i d u m (changed) were ab l e t o m a i n t a i n t h e i r c o - f r u i t i n g a b i l i t y even i n the absence o f i n t e r s p e c i f i c c o m p e t i t i v e p r e s s u r e . Second, the c u l t u r e s c o n t a i n i n g both (changed) and ( s t o c k ) s t r a i n s l o s t t h e i r a b i l i t y to produce c o - f r u i t i n g s pores, 117 s u g g e s t i n g t h a t the (changed) stock was at an i n t r a s p e c i f i c c o m p e t i t i v e d i s a d v a n t a g e . These d a t a suggest, but do not prove, t h a t P. p a l l i d u m d i d not e x p e r i e n c e an a d a p t i v e change. I f the change were a d a p t i v e one might expect t h a t the c u l t u r e s c o n t a i n i n g o n l y £• p a l l i d u m (changed) would l o s e some, o r a l l , o f t h e i r c o - f r u i t i n g a b i l i t y i n the absence o f i n t e r s p e c i f i c s e l e c t i v e p r e s s u r e . The s t a b i l i t y o f the change suggests, but does not prove, t h a t the change may have been g e n e t i c . C l o n i n g Experiments I f s e l e c t i o n r e a l l y was o c c u r r i n g t h e r e are s e v e r a l p o s s i b l e pathways which might be f o l l o w e d . F o r example: (1) A c o - f r u i t i n g mutant might have o c c u r r e d and been f a v o u r e d d u r i n g c o m p e t i t i o n , o r (2) the p o p u l a t i o n ' s gene p o o l might have c o n t a i n e d one or more c o - f r u i t i n g genotypes which were f a v o u r e d d u r i n g c o m p e t i t i o n . One o f the most 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 t h i s type o f problem i s to c l o n e out i n d i v i d u a l spores and t e s t t h e i r a b i l i t y to c o - f r u i t . In the case o f c e l l u l a r s l i m e molds the c l o n i n g procedure p r e s e n t s no problems, but the t e s t i n g procedure i n v o l v e s the e s t a b l i s h m e n t o f a s e p a r a t e mixed c u l t u r e g r a d i e n t f o r each c l o n e . D e s p i t e t h i s d i f f i c u l t y i t was d e c i d e d t h a t a maximum o f ten t e s t s would be conducted u s i n g t e n s e p a r a t e P. p a l l i d u m c l o n e s and a s t a n d a r d stock 118 Do discoideum c u l t u r e . The f i f t h t e s t resulted' i n c o - f r u i t i n g by P. pallidum and D. discoideum ( F i g . 51 - Appendix II) suggesting that the stock population of P. pallidum contained spores with co- f r u i t i n g a b i l i t y . This experiment does not allow any s t a t i s t i c a l s i g n i f i c a n c e to be attached to the evidence. Apparently, however., the a b i l i t y to c o - f r u i t was contained within the stock gene pool. Changes Between 24.0° And 26.5°C When grown alone D. discoideum was capable of using food and space, and f r u i t i n g between 24° and 2 6.5°C. But, when grown with P. pallidum, f r u i t i n g bodies were not o o observed above 24 to 25 C. After continued periods of competition D. discoideum V12 was unable to improve i t s f r u i t i n g a b i l i t y over t h i s short temperature range. The lack of improvement i n f r u i t i n g a b i l i t y i s unexplained, but i t was observed that beyond 24.5°C the expansion rate of D. discoideum V12 dropped r a p i d l y to become zero at 2 6.4°C ( F i g , 12). This put D. discoideum at a very severe competitive disadvantage i n t h i s area, so that the changes that would have to occur would undoubtedly involve changes i n growth ra t e , as well as changes i n f r u i t i n g a b i l i t y . Despite the f a c t that no change was observed i t was s t i l l important to ascertain the point at which 1 R° discoideum was i n h i b i t e d . J u s t as i n the case of P. p a l l i d u m the i n h i b i t i o n c o u l d have o c c u r r e d a t the spore s t a g e , the v e g e t a t i v e amoebae st a g e , o r the a g g r e g a t i o n stage To d i s t i n g u i s h between these p o s s i b i l i t i e s , t e s t s l i k e those used f o r P. p a l l i d u m were employed. A c u l t u r e g r a d i e n t was i n o c u l a t e d w i t h e q u a l numbers o f both D. discoideum and P. p a l l i d u m s p o r e s . B a c t e r i a c o v e r e d agar b l o c k s were s e t on top o f the agar s u r f a c e and the g r a d i e n t was i n c u b a t e d . A f t e r i n c u b a t i o n smears were taken from the tops o f the agar b l o c k s and i n c u b a t e d at 20°C. D. discoideum was found on a l l o f the agar b l o c k s ( F i g . 52-A, B, C - Appendix I I ) s u g g e s t i n g t h a t the spores germinated and the amoebae d i v i d e d and consumed f o o d , but t h a t a g g r e g a t i o n d i d not o c c u r . To t e s t t h e h y p o t h e s i s t h a t amoebae were moving from the g r a d i e n t a r e a below 24°C, a d i v i d e d c u l t u r e g r a d i e n t was used ( F i g . 52-C-DIV - Appendix I I ) and D. discoideum amoebae were s t i l l found growing above 25°C. While the i n h i b i t i o n o f D. discoideum f r u i t i n g i s p r o b a b l y r e l a t i v e l y unimportant due t o the s m a l l temperature span over which i t o c c u r s , the mechanism:, i n v o l v e d appears to be the same as the mechanism i n v o l v e d i n P. p a l l i d u m i n h i b i t i o n . S i m i l a r i t y o f Resource Use The f o r e g o i n g d a t a have i n d i c a t e d t h a t c o m p e t i t i v e p r e s s u r e s e l e c t e d - f o r P. p a l l i d u m i n d i v i d u a l s t h a t were a b l e 120 t o c o - f r u i t w i t h D. discoideum between 20° and 24.5°C. T h i s o c c u r r e n c e makes c o n t i n u e d c o e x i s t e n c e p o s s i b l e . When the s p e c i e s were unable to c o - f r u i t i t was i m p o s s i b l e f o r £° p a l l i d u m t o produce more than one g e n e r a t i o n s i n c e the l a c k of spores p r e c l u d e d the p r o d u c t i o n o f f u r t h e r g e n e r a t i o n s . But w i t h the a c q u i s i t i o n o f c o - f r u i t i n g a b i l i t y the chances t h a t P. p a l l i d u m c o u l d s u c c e s s f u l l y c o e x i s t between 18° and 24°C was i n c r e a s e d . L o g i c a l l y , however, c o n t i n u e d c o e x i s t e n c e c o u l d o n l y come about i n s i t u a t i o n s where the c o m p e t i t o r s were d i v e r g e n t with r e s p e c t t o r e s o u r c e use o r where irhey used the r e s o u r c e at e x a c t l y the same r a t e . T h e r e f o r e , 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 i t might be expected t h a t one o f t h r e e types o f s e l e c t i o n w i t h r e s p e c t t o r e s o u r c e use might o c c u r . These are:; (1) the c o m p e t i t o r s might d i v e r g e and use a l t e r n a t e r e s o u r c e s , (2) they might converge u s i n g the r e s o u r c e at e x a c t l y the same r a t e , or (3) one c o m p e t i t o r might i n c r e a s e i t s r a t e of r e s o u r c e use to exclude the o t h e r . In an attempt to f i n d which o f these paths were f o l l o w e d i n the c e l l u l a r s l i m e mold s i t u a t i o n , the components d e t e r m i n i n g r a t e s o f resource-.use were a s s e s s e d a f t e r a p e r i o d of c o n t i n u e d c o m p e t i t i o n . The components i n v o l v e d are the g e r m i n a t i o n l a g s and the c o l o n y expansion r a t e s . 121 Germination Lags F o r P. p a l l i d u m S a l v a d o r , g e r m i n a t i o n l a g d a t a was c o l l e c t e d a f t e r a p e r i o d o f c o n t i n u e d c o m p e t i t i o n , from c u l t u r e g r a d i e n t s I and I I , by r e g r e s s i n g c u l t u r e expansion d a t a and n o t i n g the p o i n t s at which the r e g r e s s i o n l i n e s i n t e r c e p t e d the x - a x i s ( F i g . 10). These d a t a were compared wit h measurements o f spore g e r m i n a t i o n l a g c o l l e c t e d b e f o r e c o m p e t i t i o n began ( F i g . 7 ) . There was no s i g n i f i c a n t d i f f e r - ence b e f o r e and a f t e r c o m p e t i t i o n ( T a b l e X ) . F o r D. discoideum V12 g e r m i n a t i o n l a g d a t a was c o l l e c t e d both b e f o r e and 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 by the r e g r e s s i o n method. A g a i n d a t a from c u l t u r e g r a d i e n t s I and I I were c o n s i d e r e d t o g e t h e r . No change b e f o r e and 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 was d e t e c t e d i n D. discoideum at the 95% l e v e l o f c o n f i d e n c e (Table X I ) . Colony Expansion Rates The second and most important component cap a b l e o f d i r e c t l y a l t e r i n g r a t e s of r e s o u r c e use are the c o l o n y expansion r a t e s . F o r P. p a l l i d u m the r a t e s o f c o l o n y expansion were measured s e p a r a t e l y f o r c u l t u r e g r a d i e n t I and I I a f t e r a p e r i o d o f c o n t i n u e d c o m p e t i t i o n (measurements were made on the progeny o f g r a d i e n t s J , K, L i n both c a s e s ) . Two p o i n t s s h o u l d be noted: (1) the p o s t - c o m p e t i t i v e d a t a from g r a d i e n t I ( F i g . 35) and g r a d i e n t I I ( F i g . 37) are v e r y 122 TABLE X P. p a l l i d u m S a l v a d o r (from g r a d i e n t s I and I I ) spore germina- 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 (change) c o n t i n u e d c o m p e t i t i o n . R e p l i c a t i o n i s shown from.the changed c u l t u r e s and 95% c o n f i d e n c e i n t e r v a l s around the change mean are g i v e n . Stock l a g s come from F i g u r e 7. TEMPERATURE REPLICATE GERM LAG 95% CON GERM LAG CHANGE CHANGE 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. disco i d e u m V12 (from g r a d i e n t s one and two) spore germ- 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 (change) c o n t i n u e d c o m p e t i t i o n . R e p l i c a t i o n i s l i s t e d f o r the 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 around the change mean are g i v e n . TEMP REP GERM LAG 95% CON REP GERM LAG 95% CON CHANGE CHANGE STOCK STOCK 18.5 7 0.75 0.37-1.14 4 0.72 0.20-1.24 19.5 7 0.57 0.32-0.82 5 0.70 0.18-1.21 20.5 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 s i m i l a r . T h i s was expected because the two g r a d i e n t s are r e p l i c a t e s , (2) the p o s t - c o m p e t i t i v e d a t a i s not s i g n i f i c a n t l y d i f f e r e n t from the p r e - c o m p e t i t i v e d a t a ( F i g . 13). For D. discoideum the r a t e s o f c o l o n y expansion were 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 I and I I , and measurements were a l s o made on g r a d i e n t s J , K, L. Here too t h e r e are two p o i n t s which should be n o t i c e d : (1) the p o s t - c o m p e t i t i v e data f o r g r a d i e n t s I ( F i g . 34) and I I ( F i g . 36) are not d i f f e r e n t , and (2) the p o s t - c o m p e t i t i v e d a t a and the p r e - c o m p e t i t i v e d a t a ( F i g . 12) are ve r y d i f f e r e n t . Both c u l t u r e g r a d i e n t s y i e l d e d organisms which were a b l e t o expand the c o l o n y at a much g r e a t e r r a t e a f t e r c o m p e t i t i o n than they were b e f o r e . The h y p o t h e s i s t h a t r a t e s o f r e s o u r c e use changed i n response t o c o m p e t i t i o n cannot be t e s t e d on the b a s i s o f these d a t a a l o n e . A se a r c h must be made f o r changes i n g e r m i n a t i o n r a t e s and r a t e s of c o l o n y expansion o f s t o c k c u l t u r e s which never e x p e r i e n c e d c o m p e t i t i o n but which were grown f o r the same l e n g t h o f time t h a t the c o m p e t i t i o n ex- periments were r u n . I t i s e n t i r e l y p o s s i b l e t h a t changes i n r a t e s o f food use e x p e r i e n c e d i n the c o m p e t i t i v e c u l t u r e s were the r e s u l t o f media c o n d i t i o n i n g o r some o t h e r cause not r e l a t e d t o c o m p e t i t i o n a t a l l . F i q u r e 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 expansion r a t e s with r e s p e c t to temperature. Growth index has 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 the l i n e o f b e s t f i t from the family- 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 are means - 95% c o n f i d e n c e l i m i t s on the means. T^ = 2 7.5, T L s 13.0, ' Gmax = 6.2. T q = 23.25, K = 1.16758, C = 4.79121, F i q u r e 35 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 expansion r a t e s with r e s p e c t - t o temperature. Growth index has 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 the l i n e of b e s t f i t from the f a m i l y d e s c r i b e d by e q u a t i o n (2c) The p o i n t s are means - 95% c o n f i d e n c e l i m i t s on the means. T^ = 37.5, T L = 18.0, T 0 = 30.0, K = 1.73781, C = -4.82781, Gmax = 8.4. 10 9 8 x 7 LU | 6 i 5 h- cr e> 3 2 h 1 JL. l_ i - 1 _i i i • • • _i 1 a i i_ 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 T E M P E R A T U R E 10 V 9 8 7 x LU i 6 I 5 r- 5 4 cr O 3 2 1 , 1 " .5- • i ' L . I I 1 1 U _J 1_ -I 1 I I SI 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 T E M P E R A T U R E F i q u r e 36 Do discoideum c u l t u r e g r a d i e n t I I expansion r a t e s w i t h r e s p e c t t o temperature. Growth index has 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 the 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 by e q u a t i o n ( 2 c ) . The p o i n t s are means £ 95% c o n f i d e n c e l i m i t s on the means. T H = 27.5, T L = 13.0, T Q = 23.0, K = 1.22500, C = 3.02126, Gmax = 5.8. F i q u r e 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 expansion r a t e s w i t h r e s p e c t t o temperature. Growth index has 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 the 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 by e q u a t i o n ( 2 c ) . The p o i n t s are means - 95% c o n f i d e n c e l i m i t s on the means. Ty = 37.5, T L = 18.0, T 0 = 30.4, K = 1.53059, C = -2.4335, Gmax = 8.0. 10 9 8 x 7 LU | 6 x 5 | 4 cc o 3 2 1 ir f 5 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 32 33 34 35 36 TEMPERATURE 12 7 Stock Spore Germination Rates Fo r P. p a l l i d u m the spore g e r m i n a t i o n r a t e s were measured d u r i n g October and November o f 1968. The c u l t u r e s were then m a i n t a i n e d by a s e r i e s of b i - w e e k l y s e r i a l t r a n s f e r s and the spore g e r m i n a t i o n times were again c a l c u l a t e d u s i n g the r e g r e s s i o n method. The data i n d i c a t e s t h a t no s i g n i f i c a n t change i n spore g e r m i n a t i o n time was e x p e r i e n c e d (Table X I I ) . £° discoideum p r e s e n t e d problems. Due to an,equip- ment f a i l u r e i n the s p r i n g o f 1969 the V12 stock t h a t was used t o e s t a b l i s h g r a d i e n t s I and I I was l o s t . T h i s meant t h a t i t was i m p o s s i b l e t o t e s t f o r changes t h a t might have o c c u r r e d i n the stock c u l t u r e i n the absence of c o m p e t i t i v e p r e s s u r e . As a p a r t i a l remedy t o t h i s problem D. discoideum VC4 stock was e s t a b l i s h e d i n August 1969 and run through 12 b i - w e e k l y t r a n s f e r s which ended i n Fe b r u a r y 1970. D e s p i t e the f a c t t h a t the s t r a i n was d i f f e r e n t the changes t h a t o c c u r r e d d u r i n g t h i s p e r i o d o f time p r o b a b l y do p a r a l l e l the changes e x p e r i e n c e d by the V12 s t o c k . The data from these experiments (Table X I I I ) i n d i c a t e s t h a t no change i n spore g e r m i n a t i o n time was e x p e r i e n c e d by the stock c u l t u r e s . Sltock Colony Expansion Rates F o r P. p a l l i d u m the c o l o n y expansion r a t e s were measured i n October o f 1968 ( F i g . 13) and a g a i n d u r i n g June 1969 ( F i g . 38). A v i s u a l comparison o f the two f i g u r e s 128 TABLE X I I P. p a l l i d u m S a l v a d o r : comparison o f stock 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 an extended p e r i o d o f i n t r a s p e c i f i c growth. R e p l i c a t i o n i s l i s t e d f o r c u l t u r e s t e s t e d a f t e r a p e r i o d o f growth and 95% c o n f i d e n c e l i m i t s around the " a f t e r " means are g i v e n . TEMPERATURE REPLICATE GERM LAG 95% CON MEAN AFTER AFTER 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 1 2 9 T A B L E X I I I D. d i s c o i d e u m V C 4 : 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 a f t e r e x t e n d e d p e r i o d s o f 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 l i s t e d f o r c u l t u r e s t e s t e d a f t e r g r o w t h a n d 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 " a f t e r " m e a n s a r e g i v e n . T E M P E R A T U R E R E P L I C A T E G E R M L A G 9 5 % C O N M E A N A F T E R A F T E R B E F O R E 1 5 . 9 3 1 . 6 0 0 . 8 6 - 2 . 3 3 1 . 4 3 1 7 . 9 9 1 . 4 0 1 . 1 8 - 1 . 6 1 1 . 1 8 1 8 . 8 5 0 . 9 8 0 . 6 2 - 1 . 3 3 1 . 1 0 1 9 . 4 4 1 . 0 0 0 . 7 7 - 1 . 2 2 1 . 0 4 2 0 . 1 4 1 . 2 0 0 . 6 7 - 1 . 7 2 . 1 . 0 2 2 1 . 0 4 1 . 1 0 0 . 9 7 - 1 . 2 2 1 . 0 0 2 2 . 5 8 0 . 9 8 0 . 9 0 - 1 . 0 7 0 . 9 8 2 3 . 5 3 0 . 9 0 0 . 4 0 - 1 . 3 9 0 . 9 6 2 4 . 1 3 1 . 2 0 0 . 9 5 - 1 . 4 4 0 . 9 8 2 5 . 0 3 1 . 2 0 0 . 9 5 - 1 . 4 4 1 . 0 3 F i q u r e 38 £• p a l l i d u m amoebae expansion r a t e s w i t h r e s p e c t to temperature. The spores used had 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 index 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 . The p o i n t s are mean d a t a p o i n t s - 95% c o n f i d e n c e l i m i t s on the means. The d o t t e d l i n e i s the l i n e of b e s t f i t from e q u a t i o n (2c) with T H = 41.0, T T = 18.0, T Q = 31.0, Gmax = 7.6, K = 1.62709, C = -13.59423. G R O W T H INDEX ro co ^ 01 O) -si oo CD O T 1 r T r CD ro o ro ro ro ro co ro m w ro ro m > H c JD ro m oo ro , CD co o co \ KH \ \ N N KH \ K H N S K H \ K H \ \ \ \ KH \ CO ro co CO CO / h-OH / I / h-O-l CO 0 1 CO 0 ) 131 suggests t h a t the r a t e s o f c o l o n y expansion may have decreased s l i g h t l y but the 95% c o n f i d e n c e i n t e r v a l s around the da t a p o i n t s used to e s t a b l i s h these c u r v e s o v e r l a p , making i t i m p o s s i b l e t o f i n d any s i g n i f i c a n t s t a t i s t i c a l d i f f e r e n c e i n r a t e s o f c o l o n y expansion b e f o r e and a f t e r a long p e r i o d o f growth i n stock c u l t u r e s . S i n c e the D. discoideum V12 stock was l o s t , the VC4 stock was used as an i n d i c a t o r o f changes t h a t might have o c c u r r e d i n the absence of c o m p e t i t i v e p r e s s u r e . Colony expansion r a t e s were measured d u r i n g August 1968 ( F i g . 39) and a g a i n d u r i n g F e b r u a r y 1970 ( F i g . 40) a f t e r a s e r i e s o f 12 bi-weekly t r a n s f e r s . The r a t e s o f c o l o n y expansion changed s i g n i f i c a n t l y (95% l e v e l ) over the s i x month p e r i o d . The r a t e o f c o l o n y expansion " a f t e r " ( F i g . 40) was g r e a t e r than " b e f o r e " ( F i g . 39). E v i d e n t l y media c o n d i t i o n i n g o r some o t h e r unknown f a c t o r allowed D. discoideum t o i n c r e a s e i t s r a t e o f r e s o u r c e use. The changes t h a t d i d o c c u r due to c o m p e t i t i v e p r e s s u r e alone are summarized i n the f o l l o w i n g t a b l e . P. PALLIDUM BEFORE AFTER C o - f r u i t i n g 19° t o 24.5° Spore g e r m i n a t i o n Colony expansion No Same Same Yes Same Same F i q u r e 39 2° discoideum VC4 expansion r a t e s with r e s p e c t to temperature. The spores used had not 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 index has 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 the 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 by e q u a t i o n ( 2 c ) . The p o i n t s are means - 95% c o n f i d e n c e l i m i t s on the means. T H = 27.5, T L = 9.0, T Q = 22.25, K = 0.63277, C = 2.01331, Gmax =4.2. GROWTH INDEX r o c o J> c n O ) CO CD \ \ m T J m J3 > c J3 m co ai O) CO CD ro o ro ro ro ro CO ro -p* ro cn ro 0) ro T — ~ T — i — — i r T \ \ \ V 4 V \r-©H \ \ \ I O I \ \ \ \ \ \ r f H I F i g u r e 40 D. discoideum VC4 expansion r a t e s w i t h r e s p e c t to temperature. The spores used had 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 index has no u n i t s , temper- 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 the l i n e o f b e s t f i t from the family- 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 are means - 95% c o n f i d e n c e l i m i t s on the means. T H = 27.0, T L = 9.0, T Q = 22.0, K = 0.90973, C = 3.22786, Gmax = 6.0. GROWTH INDEX _ L ro co -P* cn CD - N J 00 CD O m m no > —i ez ID m ro L CO __L -p* Ol CD oo K CD ro o ro ro ro ro co ro J> ro ov ro CD ro \ \ T 1 r i r r © i I"1 © j I j l , i . n i n Q n | / 134 DISCOIDEUM BEFORE AFTER C o - f r u i t i n g 24.5° t o 26.5° No No Spore g e r m i n a t i o n Same Same Colony expansion Lower P o s s i b l y * Higher S i n c e the V12 stock c o u l d not be 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 sure t h a t the c o l o n y expansion r a t e d i d not change i n response to c o m p e t i t i v e p r e s s u r e . The VC4 da t a does suggest t h a t the change t h a t was observed was not caused by c o m p e t i t i o n . f r u i t i n g a b i l i t y o f P. p a l l i d u m and p o s s i b l y a l t e r e d the r a t e o f food use i n D. discoideum. A l l the o t h e r parameters t e s t e d remained u n a l t e r e d . But these two changes alone are enough to g r e a t l y i n f l u e n c e the outcome o f c o m p e t i t i o n between the two s p e c i e s . parameter v a l u e s d e r i v e d b e f o r e c o m p e t i t i o n and a f t e r compe- t i t i o n . The output i n d i c a t e s t h a t i n time p e r i o d one the r a t e s o f r e s o u r c e use were more s i m i l a r b e f o r e c o n t i n u e d c o m p e t i t i o n ( F i g . 41-A) than a f t e r ( F i g . 41-B). But, i f the spore progeny o f time p e r i o d one were used to e s t a b l i s h a new c o m p e t i t i v e s i t u a t i o n i n time p e r i o d two, o n l y D. discoideum would be a v a i l a b l e t o use the r e s o u r c e b e f o r e c o m p e t i t i o n ( F i g . 41-C), w h i l e both s p e c i e s would use food a f t e r c o m p e t i t i o n , In summary, c o m p e t i t i v e p r e s s u r e changed the co- T h i s can be demonstrated u s i n g Program VII wit h 135 because the c o - f r u i t i n g P. p a l l i d u m c o u l d produce spores ( F i g . 41-D). L o g i c a l l y i t would seem t h a t P. p a l l i d u m would e v e n t u a l l y be e x c l u d e d because of i t s i n a b i l i t y t o use f o o d as q u i c k l y as D. d i s c o i d e u m | b u t the i n t e r f e r e n c e experiments suggested t h a t once P. p a l l i d u m becomes e s t a b l i s h e d i t c o u l d i n h i b i t D. discoideum i n areas of h i g h spore c o n c e n t r a t i o n and p e r s i s t even i n the f a c e of c o n s i d e r a b l e e x p l o i t a t i o n p r e s s u r e . These f i n d i n g s suggest t h a t the o r i g i n a l h y p o t h e s i s o f e x c l u s i o n on.the b a s i s o f unequal r e s o u r c e use or c o - e x i s t e n c e due t o convergence and/or d i v e r g e n c e , are too s i m p l e . In the case of the c e l l u l a r s l i m e mold s p e c i e s used i n t h i s work, P. p a l l i d u m converged towards D„ discoideum when i t became a b l e to c o - f r u i t , and D. discoideum d i v e r g e d from P. p a l l i d u m i n response to e i t h e r c o m p e t i t i v e o r media c o n d i t i o n i n g p r e s s u r e . Both o f these changes worked a g a i n s t one another. In time p e r i o d one i t appeared t h a t the r a t e s o f r e s o u r c e use had d i v e r g e d d u r i n g the p e r i o d o f extended c o m p e t i t i o n and t h a t P. p a l l i d u m would soon be e x c l u d e d . However, i n time p e r i o d two the r a t e s o f r e s o u r c e use a f t e r c o m p e t i t i o n were more convergent than they were b e f o r e , because P. p a l l i d u m was a b l e to produce progeny which c o u l d use the r e s o u r c e . F i g u r e 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 b y c o m p e t i t o r s b e f o r e a n d a f t e r c o m p e t i t i o n . P e r c e n t 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 f o u n d o n t h e y - a x i s , t e m p e r a t u r e o n t h e x - a x i s . The s h a d e d a r e a r e p r e s e n t s t h e amount o f r e s o u r c e u s e d b y D. d i s c o i d e u m , 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 b y P. p a l l i d u m . The p r o g e n y o f t i m e p e r i o d o n e w e r e u s e d t o e s t a b l i s h t h e c o m p e t i t i v e s i t u a t i o n o f t i m e p e r i o d t w o . n I I y I llllllllH 19 21 137 Summary - Continued C o m p e t i t i o n (1) Stock spores grown i n c u l t u r e g r a d i e n t s which extended from about 15° t o 30°C produced D, discoideum f r u i t i n g b o d i e s up t o about 24°C and P. p a l l i d u m f r u i t i n g b o d i e s beyondo (2) A f t e r p e r i o d s 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 changed i t s f r u i t i n g a b i l i t y but D. discoideum e x p e r i e n c e d no change, D„ discoideum f r u i t e d up to about 24°C and P. p a l l i d u m f r u i t e d down to about 20°C, (3) P. p a l l i d u m overcame D, discoideum f r u i t i n g body i n h i b i - t i o n between about 20° and 24°C 0 (4) D, discoideum d i d not overcome P. p a l l i d u m i n h i b i t i o n between about 24° and 2 6°C. (5) C o m p e t i t i o n alone was both a n e c e s s a r y and s u f f i c i e n t f o r c e t o cause P. p a l l i d u m to change, (6) P. p a l l i d u m amoebae always reproduced and competed f o r f o o d from about 20° t o 24°C, but b e f o r e the c o m p e t i t i o n i n d u c e d change,P. p a l l i d u m f r u i t i n g body p r o d u c t i o n was stopped i n t h i s a r e a , (7) A p p a r e n t l y the P. p a l l i d u m gene p o o l c o n t a i n e d genotypes t h a t c o u l d c o - f r u i t and these were s e l e c t e d f o r by c o m p e t i t i o n . 138 (8) P, p a l l i d u m spore g e r m i n a t i o n l a g s and amoebae c o l o n y expansion r a t e s d i d not change i n response t o c o n t i n u e d c o m p e t i t i o n . (9) D. discoideum V12 spore g e r m i n a t i o n l a g s d i d not change, but the c o l o n y expansion r a t e s i n c r e a s e d 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 . ( C o m p e t i t i o n alone may not have been r e s p o n s i b l e f o r the change). (10) The s i m u l a t i o n model suggested t h a t P. p a l l i d u m c o u l d c o - e x i s t w i t h D. discoideum between 20° and 24°C more r e a d i l y 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 than b e f o r e . 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 were 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 some o f t h e h y p o t h e s e s r e l a t i n g c o m p e t i t i o n , c o v e r g e n c e o r d i v e r g e n c e , and c o e x i s t e n c e ; and t o d e v i s e a p r e l i m i n a r y g e n e r a l method f o r a p p r o a c h i n g c o m p e t i t i v e p roblems i n t h e l a b o r a t o r y and i n t h e f i e l d . The r e s u l t s have i n d i c a t e d t h a t i t was o v e r l y o p t i m i s t i c t o hope f o r an immediate s o l u t i o n i n any o f t h e s e a r e a s , b u t i t has been p o s s i b l e t o add a l i t t l e i n f o r m a t i o n t o e a c h . The work a l s o t o u c h e d on some a s p e c t s o f c e l l u l a r s l i m e mold 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 c o n d u c t e d i n o t h e r l a b o r a t o r i e s . 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 one o f t h e d i s c u s s i o n , w h i l e t h e more e c o l o g i c a l l y o r i e n t e d work i s d i s c u s s e d i n t h e second s e c t i o n . S e c t i o n I : C e l l u l a r S l i m e Mold B i o l o g y I n h i b i t i o n D u r i n g t h e s t u d y i t was o b s e r v e d t h a t c e l l u l a r s l i m e mold c o m p e t i t i o n was composed o f b o t h an e x p l o i t a t i o n and an i n t e r f e r e n c e component. S i n c e t h e e n v i r o n m e n t was s i m p l e 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 components 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 o f f o o d and space a c c u r a t e l y enough t o s i m u l a t e t h e amount o f f o o d and space u s e d a t any t i m e . B u t , when t h e two c o m p e t i t o r s 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 a b i l i t y to produce f r u i t i n g b o d i e s . The i n t e r f e r e n c e 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 t o assess because the a c t u a l i n h i b i t o r y substance c o u l d not be i d e n t i f i e d . The r e s u l t s suggested t h a t two s e p a r a t e i n h i b i t o r y a c t i o n s took p l a c e . D. discoideum i n h i b i t e d P. p a l l i d u m f r u i t i n g body f o r m a t i o n below some temperature, which was determined by P. p a l l i d u m spore c o n c e n t r a t i o n , and P. p a l l i d u m i n h i b i t e d D. discoideum above some temperature, which was dependent upon D. discoideum spore c o n c e n t r a t i o n . S i m i l a r o b s e r v a t i o n s have been made by Raper and Thorn (1941) who found t h a t P. v i o l a c e u m i n h i b i t e d D. discoideum f r u i t i n g , and Cohen and C e c c a r i n i (1967) r e p o r t e d t h a t D. purpureum prevented P. v i o l a c e u m from a g g r e g a t i n g . The nature of the i n h i b i t o r remains unknown. Any one o f at l e a s t t h r e e c l a s s e s o f c h e m i c a l s produced d u r i n g f r u i t i n g body f o r m a t i o n might be r e s p o n s i b l e . Bonner and Dodd (1962) and Bonner and Hoffman (1963) s t u d i e d ammonia and carbon d i o x i d e p r o d u c t i o n and found t h a t i n some s p e c i e s , f r u i t i n g body s p a c i n g was l i n k e d to the p r o d u c t i o n o f these gases. Bonner and Hoffman (1963) a l s o found t h a t when D. mucoroides was c o n f r o n t e d with D. purpureum o r D. discoideum i n p e t r i d i s h e s which had agar on the top and bottom s u r f a c e s , t o t a l i n h i b i t i o n resulted:'.in f o u r of the seven c u l t u r e s r u n . In view o f these f i n d i n g s i t i s p o s s i b l e t h a t these c h e m i c a l s are r e s p o n s i b l e f o r the i n t e r s p e c i f i c i n h i b i t i o n observed i n t h i s study. 141 A second c l a s s of i n h i b i t o r y c h e m i c a l was f i r s t o bserved by Russrell and Bonner (1960) and has subsequently been s t u d i e d by Snyder and C e c c a r i n i (1966), C e c c a r i n i and Cohen (1967) and Cohen and C e c c a r i n i (1967). They observed t h a t a c h e m i c a l i n t r a s p e c i f i c a l l y i n h i b i t e d spore g e r m i n a t i o n . That i s , Polysphondylium s p e c i e s were not i n h i b i t e d a t the spore stage by D i c t y o s t e l i u m s p e c i e s . They a l s o observed t h a t P. violaceum was unable to f r u i t i n the presence o f D. purpureum. T h i s f r u i t i n g i n h i b i t i o n appears t o be v e r y much l i k e the phenomena observed i n the p r e s e n t study, but a g a i n t h e r e was no d i r e c t l i n k between the i n t r a s p e c i f i c i n h i b i t o r y c h e m i c a l which C e c c a r i n i and Cohen (1967) i s o l a t e d and i n t e r s p e c i f i c f r u i t i n g body i n h i b i t i o n . At the p r e s e n t time, c e l l u l a r s l i m e mold b i o l o g i s t s (Bonner p e r s . comm.) tend to b e l i e v e t h a t the c h e m i c a l of C e c c a r i n i and Cohen i s o n l y e f f e c t i v e i n the f r u i t - i n g body, where i t p r e v e n t s spore g e r m i n a t i o n w i t h i n the f r u i t - i n g body head. A . t h i r d g e n e r a l c l a s s of c h e m i c a l p r o d u c t s produced by c e l l u l a r s l i m e mold s p e c i e s might be r e s p o n s i b l e . Raper and Thorn (1941) observed t h a t D i c t y o s t e l i u m s p e c i e s mixed d u r i n g a g g r e g a t i o n but s e p a r a t e d by the time f r u i t i n g b o d i e s formed. D i c t y o s t e l i u m and Polysphondylium s p e c i e s , however, d i d not approach one another, even i n mixed c u l t u r e s . Bonner (1947) showed t h a t the a g g r e g a t i o n s were forming along g r a d i e n t s o f a c h e m i c a l which he c a l l e d a c r a s i n . K o n i j n e t a l (1968) have shown t h a t c y c l i c AMP a t t r a c t s D. discoideum and 142 P. p a l l i d u m . K o n i j n (1969) has shown t h a t both o f the above s p e c i e s produce c y c l i c AMP and t h a t D. discoideum a l s o produces p h o s p h o d i e s t e r a s e which c o n v e r t s c y c l i c AMP t o 5'AMP (Chang 1968). C y c l i c AMP a c t s as an a t t r a c t a n t l i k e a c r a s i n , w h i l e 5'AMP i s i n e r t with r e s p e c t t o a t t r a c t i v e a b i l i t y . More r e c e n t work (Bonner p e r s . comm.) suggests t h a t o t h e r c h e m i c a l s a l s o a c t l i k e a c r a s i n and t h a t c y c l i c AMP i s produced by many organisms such as E. c o l i the b a c t e r i a l f o o d used i n most c e l l u l a r s l i m e mold work. From a l l o f t h i s work s e v e r a l p o i n t s r e g a r d i n g the p r o d u c t i o n and e f f e c t s o f a c r a s i n can be made: (1) c y c l i c AMP a c t s l i k e a c r a s i n , (2) c y c l i c AMP i s produced by D. discoideum and P. p a l l i d u m , (3) c y c l i c AMP i s produced by many o t h e r organisms, (4) D. discoideum produces a s m a l l p r o t e i n which breaks down c y c l i c AMP and (5) o t h e r c h e m i c a l s a l s o have the a t t r i b u t e s o f a c r a s i n . Some f a c t s are a l s o unknown and these might h o l d the key t o i n t e r s p e c i f i c i n h i b i t i o n o f f r u i t i n g b o d i e s . I t i s p o s s i b l e , f o r example, t h a t the p h o s p h o d i e s t e r a s e produced by D. discoideum might break down the a c r a s i n produced by P. p a l l i d u m . I t i s a l s o p o s s i b l e t h a t the a c r a s i n produced by D. discoideum might i n t e r f e r e w i t h the p r o d u c t i o n o r the r e c e p t i o n o f the a c r a s i n produced by P. p a l l i d u m . S i n c e the i n t e r s p e c i f i c i n h i b i t i o n observed here, and i n the o t h e r s t u d i e s , o c c u r s at the a g g r e g a t i o n stage, the most l i k e l y h y p o t h e s i s i s t h a t the substances produced d u r i n g 143 aggregation act as i n t e r s p e c i f i c aggregation i n h i b i t o r s , A c r a s i n and chemicals which break i t down are most abundant at t h i s p e r i o d i n the l i f e c y c l e of c e l l u l a r s l i m e molds, and t h e r e f o r e , must be the most l i k e l y c a n d i d a t e s . However, u n t i l 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 , and u n t i l i t s response to phosphodiesterase 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 to make any d e f i n i t e statements. Genetics The r e s u l t s of t h i s study a l s o suggested t h a t D. discoideum was able to i n h i b i t P. p a l l i d u m f r u i t i n g before 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 c o m p e t i t i o n P. p a l l i d u m overcame the i n h i b i t i o n and began to f r u i t i n the presence of D. discoideum. Apparently the change was g e n e t i c r a t h e r than a c c l i m a t i v e and the gene pool of stock P. p a l l i d u m Salvador contained spores with c o - f r u i t i n g a b i l i t i e s . These c o n c l u s i o n s are d i f f i c u l t to accept when considered along with two other pieces of i n f o r m a t i o n . (1) G l i v e (1963), Sussman and Sussman (1963), Huffman and O l i v e (1964) and Huffman (1967) a l l concluded t h a t there i s no meiosis i n c e l l u l a r slime molds. (2) The data from t h i s study i n d i c a t e s t h a t when stock P. p a l l i d u m and c o - f r u i t i n g P. p a l l i d u m are mixed and grown f o r approximately 120 genera- t i o n s at 2 7°C c o - f r u i t i n g P. p a l l i d u m can no longer be detected. The data makes i t appear t h a t the c o - f r u i t i n g s t r a i n 144 i s l e s s f i t than the s t o c k s t r a i n , and t h a t d u r i n g i n t r a - s p e c i f i c c o m p e t i t i o n the c o - f r u i t i n g s t r a i n c o m p l e t e l y or almost c o m p l e t e l y d i s a p p e a r s . Yet a c o - f r u i t i n g spore was found i n a s t o c k c u l t u r e . Without m e i o s i s i t i s d i f f i c u l t t o see how the c o - f r u i t i n g s t r a i n s are p r o t e c t e d . The b e s t answer to t h i s dilemma comes from some r e c e n t g e n e t i c a l work on c e l l u l a r s l i m e molds. Sussman and Sussman (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 and u n s t a b l e d i p l o i d s t r a i n s e x i s t . Wilson and Ross (1957), Huffman and O l i v e (1964), Huffman (1967), and S i n h a and Ashworth (1969) have observed c e l l f u s i o n s as the v e g e t a t i v e amoebae aggregate t o form f r u i t i n g b o d i e s . Loomis and Ashworth (1968), and S i n h a and Ashworth (1969) s t a t e t h a t these f u s i o n s r e s u l t i n the f o r m a t i o n o f one d i p l o i d c e l l from two h a p l o i d c e l l s . Loomis ( p e r s . comm. 1970) r e p o r t s t h a t f u s i o n o c c u r s about once i n a thousand t i m e s . These o b s e r v a t i o n s p l u s the r e s u l t s o f g e n e t i c marker experiments had l e d t o the c o n c l u s i o n t h a t p a r a - s e x u a l i t y (Pontecorvo 1958) takes p l a c e . The g e n e r a l mechanism can be summarized by a m o d i f i e d v e r s i o n o f a diagram p r e s e n t e d by S i n h a and Ashworth (1969). 145 h a p l o i d s t r a i n xy n = 7 h a p l o i d s t r a i n XY n = 7 h e t e r o z y g o t i c spore n = 14 a n e u p l o i d spore c e l l f u s i o n • h e t e r o c aryon (xy) + (XY) n u c l e a r f u s i o n h e t e r o z y g o t i c myxamoebae n = 14 XY h a p l o i d i z a t i o n a n e u p l o i d myxamoebae n = 7+1, 2, 3, 4, 5 or 6 h a p l o i d spores n = 7 (|-), (^), (2EZ), o r 'XY X h a p l o i d i z a t i o n h a p l o i d myxamoebae (x y ) , (XY), (xY), o r (Xy) where x/X and y/Y are two u n l i n k e d genes. 146 The diagram demonstrates t h a t r e c e s s i v e c h a r a c t e r - i s t i c s can be hidden by dominants and t h a t l e s s f i t a l l e l e s can be p r o t e c t e d . S i n c e spores c o n s i d e r a b l y l a r g e r ( d i p l o i d ) than the average ( h a p l o i d ) have been observed i n the P. p a l l i d u m s t o c k c u l t u r e used f o r the work p r e s e n t e d i n t h i s paper, i t appears t h a t p a r a - s e x u a l i t y might be i n v o l v e d . I t seems p o s s i b l e t h a t the a b i l i t y o f P. p a l l i d u m Salvador to c o - f r u i t i n the presence of D. discoideum i s determined by a number of a l l e l e s , some o f which may be r e c e s s i v e and l e s s f i t i n the i n t r a s p e c i f i c c u l t u r e s but more f i t i n the i n t e r - s p e c i f i c c u l t u r e s . Because of p a r a - s e x u a l i t y the n e c e s s a r y a l l e l e s c o u l d be p r o t e c t e d i n the stock c u l t u r e s and be s e l e c t e d f o r d u r i n g c o m p e t i t i o n . In g e n e r a l , the p e r i o d i c f u s i o n o f c e l l s , recombina- t i o n , and chromosome l o s s , r e s u l t s i n an extremely v a r i a b l e p o p u l a t i o n d e s p i t e the f a c t t h a t m e i o s i s does not o c c u r . T h i s v a r i a b i l i t y makes i t p o s s i b l e t o f i n d i n d i v i d u a l c o - f r u i t i n g spores i n the stock c u l t u r e , and at the same time, to mask t h i s a t t r i b u t e a t the p o p u l a t i o n l e v e l , p r o v i d e d t h a t a s i g n i f i c a n t number of c o - f r u i t i n g c e l l s are n e c e s s a r y f o r f r u i t i n g t o take p l a c e i n mixed c u l t u r e s . The s u p p o s i t i o n t h a t p a r a - s e x u a l i t y and i t s a t t e n - dent g e n e t i c v a r i a b i l i t y o c c u r s i n P. p a l l i d u m l e a d s t o the p r e d i c t i o n t h a t i n s i t u a t i o n s where c o m p e t i t i o n i s c o n t i n u o u s , P. p a l l i d u m and D. discoideum s h o u l d c o - f r u i t almost a l l the time. These two s p e c i e s have been found t o g e t h e r i n t h e i r 147 n a t u r a l h a b i t a t by Cavender (1963), Cavender and Raper (1965), and Horn (1969). And Horn demonstrated t h a t the two s p e c i e s c o u l d f r u i t t o g e t h e r i n the l a b o r a t o r y . The P. p a l l i d u m s t r a i n used here came from S a l v a d o r and the i n f o r m a t i o n a v a i l a b l e i n d i c a t e s t h a t i t never e x p e r i e n c e d c o m p e t i t i o n from D. disco i d e u m . In the l a b o r a t o r y D . discoideum i n h i b i t e d £° p a l l i d u m f r u i t i n g . S e c t i o n I I : E c o l o g i c a l Relevance Convergence and C o e x i s t e n c e The e f f e c t s o f c o n t i n u e d c o m p e t i t i o n have been the c e n t e r o f some c o n t r o v e r s y f o r a c o n s i d e r a b l e p e r i o d o f time. G r i n n e l l (quoted i n Udvardy 1959 and Ross 1958), and l a t e r Gause (1934), advanced the t h e o r y o f c o m p e t i t i v e e x c l u s i o n which b a s i c a l l y s t a t e s t h a t animals c o e x i s t o n l y when t h e i r r e s o u r c e use i s d i v e r g e n t . T h i s axiom has prompted a c o n s i d e r a b l e number o f s t u d i e s which have l i n k e d c o n t i n u e d c o m p e t i t i o n to m o r p h o l o g i c a l and e c o l o g i c a l d i v e r g e n c e (Johannes and L a r k i n 1961, F i c k e n e t a l 1967, Keast 1967), which i n t u r n r e s u l t e d i n c o e x i s t e n c e . On the o t h e r hand, r e c e n t work suggests t h a t c o n t i n u e d c o m p e t i t i o n might a l s o r e s u l t i n convergence i n the form o f mimicry Moynihan (1968), o r m o r p h o l o g i c a l 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 t e r r i t o r i a l i t y Cody (1969). M i l l e r (1964) has a l s o shown 148 t h a t e c o l o g i c a l convergence i n f r u i t f l i e s can r e s u l t i n c o - e x i s t e n c e and Park and L l o y d (1955) l i s t i n s t a n c e s o f f l o u r b e e t l e c o m p e t i t i o n l a s t i n g f o r s e v e r a l years i n s m a l l homogeneous l a b o r a t o r y environments. In a l l p r o b a b i l i t y the axiom of c o m p e t i t i v e ex- c l u s i o n and the h y p o t h e s i s o f convergent c o e x i s t e n c e are both c o r r e c t i n many s i t u a t i o n s . But the work p r e s e n t e d here suggests t h a t both may be too simple t o have any r e a l p r e d i c t i v e v a l u e . F o l l o w i n g the h y p o t h e s i s o f convergent c o e x i s t e n c e , the c e l l u l a r s l i m e mold experiments were de s i g n e d so t h a t the environment was homogeneous o f f e r i n g no a l t e r n a t e source of f o o d , and the two s p e c i e s each had a r e f u g e to guard a g a i n s t immediate e x t i n c t i o n . I t was assumed t h a t under thes e c o n d i t i o n s o n l y convergence c o u l d o c c u r and t h a t t h i s would r e s u l t i n c o e x i s t e n c e . Two changes d i d o c c u r ; P. p a l l i d u m gained c o - f r u i t i n g a b i l i t y and D„ discoideum used foo d f a s t e r . The tv/o s p e c i e s d i d end up c o - f r u i t i n g and c o - e x i s t i n g but f o r the wrong r e a s o n s . They d i d n ' t converge and t h e r e f o r e c o e x i s t , nor d i d they c o m p l e t e l y d i v e r g e with r e s p e c t to r e s o u r c e use. They used the same r e s o u r c e at d i f f e r e n t r a t e s and c o e x i s t e d o n l y because P. p a l l i d u m was always a b l e to produce at l e a s t one f r u i t i n g body i n an a r e a where i t was at a r e a l disadvantage from an e x p l o i t a t i v e p o i n t o f view. C o e x i s t e n c e o c c u r r e d because the advantage 149 g a i n e d from i n t e r f e r e n c e was g r e a t e r than the disadvantage from e x p l o i t a t i o n , . Because G r i n n e l l ' s axiom (Udvardy's term) and i t s o p p o s i t e ( M i l l e r 1964) are o n l y concerned with r a t e s o f r e s o u r c e use, t h i s r e s u l t c o u l d not be p r e d i c t e d by e i t h e r . Park (1954) has s t a t e d t h a t "no p r e d i c t i o n about the outcome of s u s t a i n e d c o m p e t i t i o n i s i n h e r e n t i n the d e f i n i t i o n - t h i s b e i n g a matter f o r e m p i r i c a l i n v e s t i g a t i o n o r a b s t r a c t d e d u c t i o n . " To t h i s I would add t h a t e m p i r i c a l knowledge, r a t h e r than a b s t r a c t d e d u c t i o n , i s n e c e s s a r y , b e f o r e any c o n c l u s i o n s can be reached with r e s p e c t to the consequences o f c o n t i n u e d c o m p e t i t i o n . Components of C o m p e t i t i o n A second o b j e c t i v e o f t h i s study was to a n a l y z e the mechanics o f c o m p e t i t i o n and to i d e n t i f y the b a s i c components and feedbacks which might be a p p l i c a b l e to most c o m p e t i t i v e s i t u a t i o n s . The c e l l u l a r s l i m e mold study has suggested t h a t t h e r e are f i v e b a s i c components i n v o l v e d . The p r i m a r y c o n s i d e r a t i o n i s e x p l o i t a t i o n (Park 1954). S i n c e i t i s g e n e r a l l y accepted t h a t organisms must compete f o r something o t h e r than l i f e i t s e l f , c o m p e t i t i o n cannot occur u n t i l some r e s o u r c e i s e x p l o i t a t e d . The c e l l u l a r s l i m e mold s p e c i e s demonstrated t h i s p o i n t by competing f o r both food and space. T h e i r i n t e r a c t i o n was mediated through the r e s o u r c e , because r e s o u r c e used by one c o m p e t i t o r c o u l d not 150 be used by the o t h e r . S y m b o l i c a l l y the p r o c e s s can be r e p r e s e n t e d as: where and C2 are c o m p e t i t o r s 1 and 2 and where R i s the l i m i t e d r e s o u r c e . by o t h e r components, but t h e r e have been l i t e r a t u r e r e p o r t s o f s i t u a t i o n s i n which e x p l o i t a t i o n was the o n l y c o m p e t i t i v e component i n v o l v e d . F o r example, U l l y e t t (1950) observed t h a t when Chrysomyia c h l o r o p y q a and L u c i l i a s e r i c a t a were p l a c e d on 140 grams o f meat they i n t e r a c t e d o n l y because the f o o d eaten by one c o u l d not be eaten by the o t h e r . i n t h i s study i s i n t e r f e r e n c e . I t was found t h a t the two s p e c i e s i n t e r f e r e d with one another's f r u i t i n g a b i l i t y at c e r t a i n temperatures, and i t was h y p o t h e s i z e d t h a t the c h e m i c a l s produced d u r i n g a g g r e g a t i o n and f r u i t i n g were r e s p o n s i b l e . S i n c e i n t e r f e r e n c e a l t e r s the c o m p e t i t i v e o u t - come, changing the e x p l o i t a t i o n r a t e s , i t may be s y m b o l i c a l l y expressed as: where the two c o m p e t i t o r s d i r e c t l y a l t e r e x p l o i t a t i o n r a t e s . The c e l l u l a r s l i m e mold s i t u a t i o n was c o m p l i c a t e d The o t h e r important c o m p e t i t i v e component observed 151 The c e l l u l a r s l i m e mold work suggested t h a t animals c o u l d i n t e r f e r e by p r o d u c i n g t o x i c chemicals,, S i m i l a r o b s e r v a t i o n s have been made by Grummer and Beyer (1960) who r e p o r t t h a t f l a x i s i n h i b i t e d by c h e m i c a l s washed out o f the l e a v e s o f Camelina. And t o x i c i n t e r f e r e n c e has been invoked to e x p l a i n the s p a c i n g i n L a r r e a . Grummer (1961) p r o v i d e s numerous o t h e r examples o f c h e m i c a l l y i n d u c e d i n h i b i t i o n . Two o t h e r c l a s s e s o f i n t e r f e r e n c e appear i n the l i t e r a t u r e but were not observed i n the c e l l u l a r s l i m e mold study. O r i a n s and Horn (1969), Lack (1954), and numerous o t h e r authors have r e p o r t e d t h a t b e h a v i o r a l i n t e r f e r e n c e , p a r t i c u l a r l y with r e s p e c t t o t e r r i t o r i a l i t y , a l t e r s e x p l o i t a t i o n f o r both food and space. 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 i n t e r f e r e n c e a l s o a l t e r s e x p l o i t a t i o n r a t e s . Park (1965) r e p o r t e d t h a t T r i b o l i u m castaneum ate both i t s own pupae and the pupae o f T. confusum at 20°C and 70% RH. c o n t r o l o f the c o m p e t i t o r s , were very important i n the c e l l u l a r s l i m e mold s i t u a t i o n . In t h i s case temperature was the e x t e r n a l f o r c e , and i t was found t h a t below about 22°C D. discoideum c o u l d always exclude P. p a l l i d u m w h i l e above about 24°C the r e v e r s e was t r u e . Between 22° and 24°C i n t e r f e r e n c e became imp o r t a n t but temperature c o n t r o l l e d t h a t a l s o . E x t e r n a l f o r c e can be s y m b o l i c a l l y r e p r e s e n t e d as: External forces, defined as any forces outside the 152 where E r e p r e s e n t s an e x t e r n a l f o r c e . E x t e r n a l f o r c e s are u s u a l l y a b i o t i c and can be e x e m p l i f i e d by temperature, pH, h u m i d i t y , hours of s u n l i g h t , e t c . The l i t e r a t u r e suggests t h a t they may a l s o be b i o t i c . P aine (1966) noted t h a t s t a r - f i s h remove s e v e r a l f o r e s h o r e s p e c i e s which o r d i n a r i l y compete f o r n u t r i e n t s and space, and C o n n e l l (1967) has observed t h a t t h r e e s p e c i e s o f T h a i s c u r t a i l o r prevent Balanus g l a n d u l a and B. c a r i o s u s c o m p e t i t i o n f o r space at F r i d a y Harbor. A f o u r t h c o n s i d e r a t i o n and one t h a t d i d not p l a y an i m p o r t a n t r o l e i n t h i s study i s r e s o u r c e a v a i l a b i l i t y . In the l a b o r a t o r y s i t u a t i o n c o n s t a n t amounts o f food were used at a l l times, but Horn ( p e r s . comm.) r e p o r t s t h a t the r a t e o f c o l o n y expansion i s p r o p o r t i o n a l to f o o d c o n c e n t r a t i o n , t hereby a l t e r i n g the r a t e of e x p l o i t a t i o n . In f i e l d s i t u a t i o n s t h i s component can be v e r y i m p o r t a n t . F i l t e r f e e d i n g zoo- p l a n k t o n a l t e r t h e i r r a t e s o f e x p l o i t a t i o n w i t h changes i n f o o d a v a i l a b i l i t y ( M u l l i n 1963), and G r i f f i t h s and H o l l i n g (1969) r e p o r t t h a t the degree of c o n t a g i o n o f h o s t s a l t e r p a r a s i t e a t t a c k r a t e s . F i n a l l y , c o m p e t i t o r a v a i l a b i l i t y g r e a t l y a l t e r e d the e f f e c t o f the i n t e r f e r e n c e component i n t h i s study. F i e l d e v i d e n c e a l s o suggests t h a t c o m p e t i t o r a v a i l a b i l i t y over a l o n g time span i s . . i m p o r t a n t . O r i a n s and Horn (1969) found t h a t "three s p e c i e s of b l a c k b i r d s compete f o r food and space i n the P o t h o l e s o f c e n t r a l Washington. But they o n l y 153 compete at c e r t a i n times of the day and d u r i n g one p e r i o d o f the y e a r . In t h i s s i t u a t i o n i t i s p o s s i b l e t h a t e x c l u s i o n does not o c c u r because the p e r i o d o f c o m p e t i t i o n i s too s h o r t , and r e g u l a t i n g m o r t a l i t y o c c u r s at o t h e r p l a c e s and d u r i n g d i f f e r e n t p e r i o d s o f time. e x t e r n a l f o r c e s and a v a i l a b i l i t i e s c o u l d be c o n t r o l l e d i t was p o s s i b l e to assess i n some d e t a i l the f a c t o r s i n v o l v e d i n a c o m p e t i t i v e s i t u a t i o n . I t was a l s o p o s s i b l e t o determine the ways i n which the components i n t e r a c t . Because a l a b o r a t o r y s i t u a t i o n was used i n which EXTERNAL FORCE (TEMPERATURE) 1 i x RESOURCE (FOOD) AVAILABILITY COMPETITOR (MOLD) AVAILABILITY INTERFERENCE (TOXIC) E x p l o i t a t i o n was the c e n t e r o f c o m p e t i t i o n and a l t e r e d i n t e r f e r e n c e by a l t e r i n g the number o f c o m p e t i t o r s a v a i l a b l e . I t , i n t u r n , was a l t e r e d by the amount o f b a c t e r i a l 154 f o o d a v a i l a b l e and the number of c o m p e t i t o r s a v a i l a b l e . I n t e r f e r e n c e a l t e r e d e x p l o i t a t i o n by i n h i b i t i n g f e e d i n g i n areas o f h i g h d e n s i t y f o r s h o r t p e r i o d s of time and by a l t e r - i n g the number o f c o m p e t i t o r s a v a i l a b l e i n time p e r i o d two. Temperature a f f e c t e d e x p l o i t a t i o n and i n t e r f e r e n c e but was not a l t e r e d by c o m p e t i t i o n . In the l a b o r a t o r y the' temperature d i d not d i r e c t l y change f o o d a v a i l a b i l i t y o r c o m p e t i t o r a v a i l a b i l i t y but i n f i e l d s i t u a t i o n s these l i n k s (shown by the d o t t e d l i n e s ) would almost c e r t a i n l y be made. The r e a l v a l u e o f the g e n e r a l system which has emerged from t h i s study can o n l y be a s s e s s e d by f u t u r e f i e l d s t u d i e s . But i f i t has any g e n e r a l i t y , the component p a r t s of f i e l d s t u d i e s r e p o r t e d i n the l i t e r a t u r e s h o u l d f i t the above o u t l i n e . One of the b e s t s t u d i e s i n the l i t e r a t u r e was conducted by U l l y e t t (1950), and concerned c o m p e t i t i o n between f o u r s p e c i e s of blow f l i e s ; L u c i l i a s e r i c a t a , Chrysomyia c h l o r o p y q a , C. a l b i c e p s , and C. m a r g i n a l i s . Both f i e l d and l a b o r a t o r y d a t a w e r e . i n c l u d e d . U l l y e t t found t h a t a l l f o u r s p e c i e s e x p l o i t e d c a r r i o n i n both the l a b o r a t o r y and the f i e l d . He d i d not measure r a t e s of f o o d use, but when he c o n s i d e r e d i n t e r s p e c i f i c c o m p e t i t i v e s i t u a t i o n s , a l l l a r v a l numbers were c o n v e r t e d to L u c i l i a u n i t s . In most i n t e r - s p e c i f i c s i t u a t i o n s o n l y e x p l o i t a t i o n was important but when C„ a l b i c e p s was i n v o l v e d he found t h a t t h i s s p e c i e s i n t e r f e r e d w i t h the o t h e r s by e a t i n g l a r v a e . The e x t e n t o f p r e d a t o r y 155 i n t e r f e r e n c e depended upon r e s o u r c e q u a l i t y and l a r v a l numbers. One b i o t i c and two a b i o t i c e x t e r n a l f o r c e s were a l s o i m p o r t a n t . Temperature and h u m i d i t y a l t e r e d the r a t e s of o v i p o s i t i o n and a d u l t d i s p e r s a l , and a p a r a s i t e Mormoniella v i t r i p e n n i s Walk i n c r e a s e d C. a l b i c e p s pupal m o r t a l i t y . Food a v a i l a b i l i t y i n the f i e l d was v e r y i m p o r t a n t w i t h r e s p e c t to q u a n t i t y , q u a l i t y and d i s p e r s i o n . U n f o r t u n a t e l y t h i s component was v e r y d i f f i c u l t to assess and f o r t h i s reason l i t t l e i n f o r m a t i o n was i n c l u d e d . F i n a l l y , c o m p e t i t o r a v a i l a b i l i t y r e s t r i c t e d f i e l d c o m p e t i t i o n . Because two o f the c o m p e t i t o r s breed i n the summer and two i n the w i n t e r a p o t e n t i a l l y complex f o u r c o m p e t i t o r s i t u a t i o n was reduced t o two s e p a r a t e two c o m p e t i t o r s i t u a t i o n s . In g e n e r a l , a l l o f the components of c o m p e t i t i o n found i n the c e l l u l a r s l i m e mold s i t u a t i o n were a l s o found i n U l l y e t t * s study and a l l - o f U l l y e t t ' s data c o u l d be i n c l u d e d i n the system. I t would have been b e t t e r i f the system c o u l d have been f i t t o c e l l u l a r s l i m e mold f i e l d s t u d i e s . U n f o r t u n a t e l y , however, the o n l y f i e l d work known to t h i s author was concerned o n l y with the d i s t r i b u t i o n o f s p e c i e s i n v a r i o u s h a b i t a t s (Cavender 1963). However, Horn (1969) has p o i n t e d out t h a t food q u a l i t y was v e r y important t o the f o u r s p e c i e s he s t u d i e d , and he h y p o t h e s i z e d t h a t ; s i n c e most s p e c i e s had a s e r i e s o f foods on which they c o u l d o u t - compete the o t h e r s , c o m p e t i t i o n c o u l d be r e s o l v e d and c o - e x i s t e n c e c o u l d be a t t a i n e d on the b a s i s o f f o o d q u a l i t y a l o n e . The p r e s e n t study suggests t h a t w h i l e food q u a l i t y 156 i s v e r y i m p o r t a n t , response t o environmental f a c t o r s , and i n some cases i n t e r f e r e n c e , a l s o determine the outcome of c o m p e t i t i o n on any p a t c h of b a c t e r i a . Beyond t h i s , l i t t l e can be s a i d due to the l a c k o f i n f o r m a t i o n about the n a t u r a l e c o l o g y o f c e l l u l a r s l i m e mold s p e c i e s . I t i s hoped t h a t the g e n e r a l model developed from 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 the major components and feedbacks which are i n v o l v e d i n c o m p e t i t i v e systems. The k i n d s o f i n f o r m a t i o n i n c l u d e d w i t h i n each component sh o u l d a l s o be g e n e r a l i n n a t u r e . During the course o f t h i s work each component was s t u d i e d i n some d e t a i l and the r e s u l t i n g model s i m u l a t e d c o m p e t i t i o n between two s p e c i e s of c e l l u l a r s l i m e mold w i t h a r e a s o n a b l e amount of a c c u r a c y . I t i s u n l i k e l y , however, t h a t the minute mechanics i n v o l v e d i n t h i s s i t u a t i o n would be u s e f u l i n o t h e r i n s t a n c e s o f c o m p e t i t i o n . The ways i n which i n f o r m a t i o n i s a s s e s s e d and i n c o r p o r a t e d i n t o each component must depend upon the system under study. S t u d i e s o f the s h o r t term mechanics and the long term r e s u l t s o f c o n t i n u e d c o m p e t i t i o n suggests t h a t to date t h e r e are no g e n e r a l laws which w i l l a l l o w e c o l o g i s t s to make p r e d i c t i o n s about c o m p e t i t i o n . However, t h e r e do seem t o be a f i n i t e number of s t r a t e g i e s a v a i l a b l e and a f i n i t e number of s e l e c t i v e f o r c e s a c t i n g on c o m p e t i t o r s . F o r the moment, i t appears t h a t c o m p e t i t i v e problems can o n l y be s o l v e d by o n - s i t e study of both o f these f a c t o r s . 157 LITERATURE CITED A l l e e , W.C., A.E. Emerson, T. Park, 0. Park, and K„P. Schmidt, 1949. P r i n c i p l e s of Animal E c o l o g y . P h i l a d e l p h i a : W.B. Saunders Co. B i r c h , L.C.,1957. The meanings of c o m p e t i t i o n . Amer. N a t u r a l i s t . 91: 5-18. Bonner, J.T., 1947. Evidence f o r the f o r m a t i o n of c e l l aggregates by chemotaxis i n the development o f the s l i m e mo'ld P i c t y o s t e l i u m d iscoideum. J . E x p t l . Z o o l . 106: 1-26. Bonner, J.T., 1950. O b s e r v a t i o n s on p o l a r i t y i n the s l i m e mold P i c t y o s t e l i u m d iscoideum. B i o l . B u l l . 99: 143-151. Bonner, J.T. and M.R. Dodd, 1962. Evidence f o r gas induced o r i e n t a t i o n i n the c e l l u l a r s l i m e molds. Develop. B i o l . 5: 344-361. Bonner, J.T. and M.E. Hoffman, 1963. Evidence f o r a substance r e s p o n s i b l e f o r the s p a c i n g p a t t e r n of a g g r e g a t i o n and f r u i t i n g i n the c e l l u l a r s l i m e molds. J . Embryol. E x p t l . Morphol. 11: 571-589. Bonner, J.T., 1967. The C e l l u l a r Slime Molds, P r i n c e t o n U n i v e r s i t y P r e s s . B r i a n , M.V., 1952. The s t r u c t u r e of a n a t u r a l dense ant p o p u l a t i o n . J . Anim. E c o l . 21: 12-24. Brownlee, K.A., 1965. S t a t i s t i c a l Theory and Methodology In S c i e n c e and E n g i n e e r i n g . John Wiley and Sons, In c . , New York. Cavender, J . C , 1963. The Occurrence and d i s t r i b u t i o n o f A c r a s i e a e i n f o r e s t s o i l s . Ph.D. T h e s i s , The U n i v e r s i t y of W i s c o n s i n . Cavender, J.C. and K.B. Raper, 1965. The A c r a s i e a e i n n a t u r e . I I . F o r e s t s o i l as a p r i m a r y h a b i t a t . Amer. J o u r . Bot. 52: 297-302. 158 C e c c a r i n i , C. and A. Cohen, 1967. G e r m i n a t i o n i n h i b i t o r from t h e c e l l u l a r s l i m e mold D i c t y o s t e l i u m d i s c o i d e u m . N a t u r e , 214: 1354-1346. Chang, Y.Y., 1968. C y c l i c 3*, 5'-Adenosine monophosphate p h o s p h o d i e s t e r a s e p r o d u c e d by t h e s l i m e mold D i c t y o s t e l i u m d i s c o i d e u m . S c i e n c e , 160: 5 7. C l e m e n t s , F.E. and V.E. S h e l f o r d , 1939. B i o e c o l o q y . New Y o r k : J ohn W. W i l e y and Sons. Cody, M.L., 1969. A p o s s i b l e r e l a t i o n t o i n t e r s p e c i f i c c o m p e t i t i o n and a g g r e s s i o n . The Condor, 71: 222-2 39. Cohen, A. and C. C e c c a r i n i , 1967. I n h i b i t i o n o f s p o r e germ- i n a t i o n i n c e l l u l a r s l i m e moulds. A n n a l s o f B o t a n y , N.S. 31-123: 479-487. C o n n e l l , J.H., 1961. The i n f l u e n c e o f i n t e r s p e c i f i c c o m p e t i - t i o n and o t h e r f a c t o r s on t h e d i s t r i b u t i o n o f t h e b a r n a c l e Chthamalus s t e l l a t u s . E c o l o g y 42: 710-723. C o n n e l l , J.H., 1961. E f f e c t s o f c o m p e t i t i o n by T h a i s l a p i l l u s , and o t h e r f a c t o r s on n a t u r a l p o p u l a t i o n s o f t h e b a r n a c l e B a l a n u s b a l a n o i d e s . E c o l . Mon. 31: 61-104. Dwight, H.B., 1947. T a b l e s o f I n t e g r a l s and Other M a t h e m a t i c a l D a t a . The M a c M i l l a n Company, N.Y. E l t o n , C.S. and R.S. M i l l e r , 1954. The e c o l o g i c a l s u r v e y o f a n i m a l c ommunities w i t h a p r a c t i c a l system o f c l a s s i f y i n g h a b i t a t s by s t r u c t u r a l c h a r a c t e r s . J . E c o l . 42: 460-496. F i c k e n , R.W., M.S. F i c k e n , and D.H. Morse, 1968. C o m p e t i t i o n and c h a r a c t e r d i s p l a c e m e n t i n two s y m p a t r i c p i n e - d w e l l i n g w a r b l e r s ( D e n d r o i c a , P a r u l i d a e ) . E v o l u t i o n 22: 307-314. Gause, G.F., 1934. The S t r u g g l e f o r E x i s t e n c e . B a l t i m o r e : W i l l i a m s and W i l k i n s . 159 G r i f f i t h s , K.J. and C.S. H o l l i n g , 1969. A c o m p e t i t i v e submodel f o r p a r a s i t e s and p r e d a t o r s . Canadian E n t o m o l o g i s t , 101: 785-818. Grummer, G. and H. Beyer, 1960. In B i o l o g y o f Weeds, p. 153. Ed. J . L . Harper. Oxford: B l a c k w e l l . Grummer, G., 1961. The r o l e o f t o x i c substances i n the i n t e r - r e l a t i o n s h i p s between h i g h e r p l a n t s . In Mechanisms In B i o l o g i c a l C o m p e t i t i o n . E d i t e d by F.L. M i l t h r o p e , The U n i v e r s i t y P r e s s , Cambridge, U.K. H o l l i n g , C.S., 1963. An e x p e r i m e n t a l component a n a l y s i s o f p o p u l a t i o n p r o c e s s e s . Mem. E n t . Soc. Can. 32: 22-32. H o l l i n g , C.S., 1964. An a n a l y s i s o f complex p r o c e s s e s . Canad. Ent . 96: 335-347. H o l l i n g , C.S., 1965. The f u n c t i o n a l response o f p r e d a t o r s to prey d e n s i t y and i t s r o l e i n m i n i c r y and p o p u l a - t i o n r e g u l a t i o n . Mem. E n t . Soc. Can. 45: 3-60. Horn, E., 1969. Some asp e c t s o f c o m p e t i t i o n among the c e l l u l a r s l i m e molds. Ph.D. t h e s i s . P r i n c e t o n U n i v e r s i t y , Department o f Zoology. Huffman, D.M. and L.S. O l i v e , 1964. Engulfment and anastomosis i n the c e l l u l a r s l i m e molds ( A c r a s i a l e s ) . Am. J . Bot. 51: 465-471. Huffman, D.M., 1967. The r o l e o f engulfment i n the D i c t y o s t e l a c e a e . J . P r o t o z o o l . 14: 762-764. Johannes, R.E. and P.A. L a r k i n , 1961. C o m p e t i t i o n f o r food between Redside S h i n e r s ( R i c h a r d s o n i u s b a l t e a t u s ) and Rainbow T r o u t (Salmo g a i r d n e r i l i n two B r i t i s h Columbia l a k e s . J . F i s h . Res. Bd. Canada, 18: 203- 219. K e a s t , A., 1968. C o m p e t i t i v e i n t e r a c t i o n and the e v o l u t i o n o f e c o l o g i c a l n i c h e s as i l l u s t r a t e d by the A u s t r a l i a n Honeyeater genus M e l i t h r e p t u s ( M e l i p h a q i d a e ) . E v o l u t i o n 22: 762-784. K o n i j n , T.M., D.S. B a r k l e y , Y.Y. Chang, and J.T. Bonner., 1968. C y c l i c AMP: A n a t u r a l l y o c c u r r i n g a c r a s i n i n the c e l l u l a r s l i m e molds. Amer. N a t u r a l i s t , 102: 225. 160 K o n i j n , T.M., Y.Y. Chang, and J.T. Bonner, 1969. S y n t h e s i s o f C y c l i c AMP i n D i c t y o s t e l i u m discoideum and PolysphondyHum p a l l i d u m . Nature 224: 1211-1212. K o s t i t z i n , V.A., 19 39. Mathematical B i o l o g y . T o r o n t o : George G. Harrap and Company L t d . Lack, D., 1954. The L i f e o f the Robin, Penguin Books, B a l t i m o r e . L a r k i n , P.A., 1963. I n t e r s p e c i f i c c o m p e t i t i o n and e x p l o i t a t i o n . J . F i s h . Res. Bd. Canada. 20: 647-678. Loomis, W.F. and J.M. Ashworth, 1968. Plaque s i z e mutants of the c e l l u l a r s l i m e mould D i c t y o s t e l i u m discoideum. J . Gen. M i c r o b i o l . 53: 181-186. "" Loomis, W.F., 1969. Temperature s e n s i t i v e mutants o f D i c t y o s t e l i u m discoideum. J o l . o f B a c t e r i o l o g y . 99: 65-69. Loomis, W.F., 1970. Dept. of B i o l o g y , U n i v e r s i t y of C a l i f o r n i a , La J o l l a . 92037. MacArthur, R. and R. L e v i n s , 1964. C o m p e t i t i o n , h a b i t a t s e l e c t i o n and c h a r a c t e r displacement i n a patchy environment. P r o c . Nat. Acad. S c i . 51: 1207-1210. MacArthur, R. and R. L e v i n s , 1967. The l i m i t i n g s i m i l a r i t y , convergence, and d i v e r g e n c e of c o e x i s t i n g s p e c i e s . Amer. Nat. 101: 377-385. M i l l e r , R.S., 1964. I n t e r s p e c i e s c o m p e t i t i o n i n l a b o r a t o r y p o p u l a t i o n s of D r o s o p h i l a melanogaster and D r o s o p h i l a s i m u l a n s . Amer. Nat. 98: 221-2 38. M i l l e r , R.S., 1964. L a r v a l c o m p e t i t i o n i n D r o s o p h i l a melanogaster and D. simulans. Ecology 45: 132-148. M i l l e r , R.S., 1967. P a t t e r n and p r o c e s s i n c o m p e t i t i o n . Advances i n E c o l o g i c a l Research IV. J.B. Cragg, Ed. M i l n e , A., 1961. D e f i n i t i o n of c o m p e t i t i o n among animals. Mechanisms i n B i o l o g i c a l C o m p e t i t i o n . Cambridge: at the U n i v e r s i t y P r e s s . 161 Moynihan, M., 1968. S o c i a l m i n i c r y ; c h a r a c t e r convergence ve r s u s c h a r a c t e r d i s p l a c e m e n t . E v o l u t i o n 22: 315-331. M u l l i n , M.M., 1963. Some f a c t o r s a f f e c t i n g the f e e d i n g o f marine copepods o f the genus Calanus. L i m n o l . Oceanogr. 8: 239-250. N i c h o l s o n , A . J . , 1954. An o u t l i n e o f the dynamics o f animal p o p u l a t i o n s . A u s t . J . Z o o l . 2: 9-65. Odum, E.P., 1959. Fundamentals of E c o l o g y . P h i l a d e l p h i a : W.B. Saunders Company. O l i v e , L.S., 1963. The q u e s t i o n o f s e x u a l i t y i n c e l l u l a r s l i m e molds. B u l l . T o r r e y Botan. Club 90: 144-147. O r i a n s , G.H. and H.S. Horn, 1969. Overlap i n food o f f o u r s p e c i e s o f b l a c k b i r d s i n the p o t h o l e s of c e n t r a l Washington. Ecology, 50: 930-938. Pa i n e , R.T., 1966. Food Web Complexity and s p e c i e s d i v e r s i t y . Am. N a t u r a l i s t . 100: 65-75. Park, T., 1954. E x p e r i m e n t a l s t u d i e s o f i n t e r s p e c i e s c o m p e t i t i o n . I I . Temperature, hum i d i t y , and c o m p e t i t i o n i n two s p e c i e s o f T r i b o l i u m . P h y s i o l . Z o o l . 27: 177-238. Park, T. and M. L l o y d , 1955. N a t u r a l s e l e c t i o n and the out- come of c o m p e t i t i o n . Amer. Nat. 89: 2 35-240. Park, T., D.B. Mertz, W. G r o d z i n s k i , and T. Prus, 1965. C a n n i b a l i s t i c p r e d a t i o n i n p o p u l a t i o n s o f f l o u r b e e t l e s . P h y s i o l . Z o o l . 38:'289-321. Pontecorvo, G., 1958. Trends i n Ge n e t i c A n a l y s i s . Columbia U n i v e r s i t y P r e s s , N.Y. Raper, K.B., 1937. Growth and development of D i c t y o s t e l i u m discoideum w i t h d i f f e r e n t b a c t e r i a l a s s o c i a t e s . J . Agr. Res. 55: 289-316. Raper, K.B. and C. Thorn, 1941. I n t e r s p e c i f i c mixtures i n the D i c t y o s t e l i a c e a e , Am. J . Botany 28: 69-78. 162 R i c k e r , W.E., 1937. The concept of c o n f i d e n c e o r f i d u c i a l l i m i t s a p p l i e d to the p o i s s o n f r e q u e n c y d i s t r i b u t i o n . J o l . Amer. S t a t i s t i c a l A ssoc. 32: 349-356. Ross, H.H., 1958. F u r t h e r comments on n i c h e s and n a t u r a l c o e x i s t e n c e . E v o l u t i o n 12: 112-113. R u s s e l l , G.K. and J.T. Bonner, 1960. A note on spore g e r m i n a t i o n i n the c e l l u l a r s l i m e mold D i c t y o s t e l i u m mucoroides. B u l l . T o r r e y Botan. Club 87: 187-191. S c h a f f e r , B.M., 1956. A c r a s i n , the ch e m o t a c t i c agent i n c e l l u l a r s l i m e moulds. J . E x p t l . B i o l . 33: 645-657. Seaton, A.P.C. and J . A n t o n o r i c s , 1967. P o p u l a t i o n i n t e r - r e l a t i o n s h i p s . 1. E v o l u t i o n i n mix t u r e s of D r o s o p h i l a mutants. H e r e d i t y 22: 19-32. Sing h , B.N., 1946. S o i l A c r a s i a e and t h e i r b a c t e r i a l food s u p p l y . Nature 157: 133-134. S i n h a , U. and J.M. Ashworth, 1969. Evidence f o r the e x i s t e n c e of elements o f a p a r a - s e x u a l c y c l e i n the c e l l u l a r s l i m e mould, D i c t y o s t e l i u m discoideum. P r o c . Roy. Soc. B„ 173: 531-540. S l o b o d k i n , L.B., 1961. Growth and R e g u l a t i o n o f Animal P o p u l a t i o n s . T o r o n t o . H o l t . R i n e h a r t and Winston. Snyder, H.M. and C. C e c c a r i n i , 1966. I n t e r s p e c i f i c spore i n h i b i t i o n i n c e l l u l a r s l i m e molds. Nature, Long. 208: 1152. Stevens, W.L., 1942. Accuracy o f mutation r a t e s . J o l . of G e n e t i c s 43: 301-307. Sussman, M., 1956. The b i o l o g y o f the c e l l u l a r s l i m e molds. Ann. Rev. M i c r o b i o l . 10: 21-50. Sussman, M. and R.R. Sussman, 1961. A g g r e g a t i v e performance. E x p t l . C e l l . Res. S u p p l . 8: 91-106. C i t e d i n Bonner, J.T. 1967. The C e l l u l a r Slime Molds. P r i n c e t o n U n i v e r s i t y P r e s s . Sussman, M. and R.R. Sussman, 1962. P l o i d a l i n h e r i t a n c e i n D i c t y o s t e l i u m discoideum I : S t a b l e h a p l o i d , s t a b l e d i p l o i d and metas t a b l e s t r a i n s . J . Gen. M i c r o b i o l . 28: 417-429. 163 Sussman, R.R. and M„ Sussman, 1963. P l o i d a l i n h e r i t a n c e i n the s l i m e mould D i c t y o s t e l i u m discoideum: h a p l o i d - i z a t i o n and g e n e t i c s e g r e g a t i o n of d i p l o i d s t r a i n s . . J . Gen. M i c r o b i o l . 30: 349-355. Tieghem, P. van, 1880. Sur quelques myxomycetes a plasmode agrege. B u l l . Soc. Botan. France 27: 317-322. C i t e d i n Bonner, J.T. 1967. The C e l l u l a r Slime Molds, P r i n c e t o n U n i v e r s i t y P r e s s . Udvardy, M.F.D., 1959. Notes on the e c o l o g i c a l concepts of h a b i t a t , b i o t o p e and n i c h e . E c o l o g y 40: 725-728. U l l y e t t , G.C, 1950. C o m p e t i t i o n f o r food and a l l i e d phenomena i n s h e e p - b l o w f l y p o p u l a t i o n s . P h i l . T r a n s . Roy. Soc. London. B. 234: 77-174. Watt, K.E., 1966. Systems A n a l y s i s In E c o l o g y . E d i t e d by K.E.F. Watt, New York, Academic P r e s s . Whittingham, W.F. and K.B. Raper, 1957. Environmental f a c t o r s i n f l u e n c i n g the growth and f r u c t i f i c a t i o n o f D i c t y o s t e l i u m polycephalum. Am. J . Botany 44: 619-627. W i l s o n , C M . and I.K. Ross, 1957. F u r t h e r c y t o l o g i c a l s t u d i e s i n the A c r a s i a l e s . Am. J . Botany 44: 345-350. Witkamp, M., 1969. C y c l e s of temperature and carbon d i o x i d e e v o l u t i o n from l i t t e r and s o i l . E c o l o g y 50: 922-924. APPENDIX I COMPUTER PROGRAMS PAGE 1 165 // JOB LOG DRIVE 0 0 0 0 CART SPEC 0001 CART A V A I L 0001 PHY DRIVE 0000 V2 MO 6 ACTUAL 8K CONFIG 8!< // FOR •L I ST SOURCE PROGRAM •ONE WORD INTEGERS • IOCS <CARD»1132 PRINTER) 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 = J J = KK = LL = READ(2»1000) ( T ( I ) * Q ( I ) » 1 = 1 .11 ) 10 00 FORMAT(2F10 # 5) READ(2»2000) (TO( J ) .J = 1 , J J ) . 2 0 0 0 F 0 R M A T I F 1 0 . 5 ) READ(2»3000) ( LMIN(K )»K=1»KK) 3 0 0 0 F O R M A T ( F 1 0 . 5 ) READC2»4000) ( TT ( L ) > AC T ( L ) » L=1» LL ) 4 0 0 0 FORMATC2F10 .5 ) DO 1 I = 1 » I I A = ( - • 5 * A L 0 G ( { - 1 . 0 ) * T { I ) * * 2 « 0 + T ( I ) # ( T H + T L ) - T H * T L ) ) - 1 ( ( (TH+TL ) / 2 . 0 ) » ( 1 . 0 / ( T H - T L ) ) * 1 ( A L O G ( A B S ( 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 + T 0 ( J ) # ( T H + T L ) - T H * T L ) ) - 1 ( ( ( T H + T L ) / 2 . 0 ) * < ( l e O ) / ( T H - T L ) ) * 1 ( A L O G ( A B S ( T 0 ( J ) - T H ) / ( T O ! J ) - T L ) ) ) ) E = ( ! 1 . 0 ) / ( T H - T L ) ) * { A L 0 G ( A B S ( T 0 ( J ) - T H ) / ( T 0 U ) - T L ) ) ) DO 3 K=1,KK KON = ( Q ( I ) - L M I N ( K ) ) / ( A + B * T O ( J ) - D - E * T O ( J ) ) CON = ( L M I N ( K ) - ( ( Q ( I ) - L M I N ( K ) ) * ( D + E * T O ( J ) ) ) / 1 ( A + B * T 0 ( J ) - D - E * T 0 ( J ) ) ) W R I T E ( 3 » 2 0 0 ) T ! I ) » Q ( I ) PAGE 2 166 2 0 0 FORMAT*' 1 TEMP OF POINT USED IS • F 1 0 . 5 ». AND POINT IS 1 F 1 0 « 5 ! W R I T E ( 3 * 3 0 0 ) TO I J ) 3 0 0 FORMAT( • TEMP OPTIMUM IS 1 F 1 0 . 5 ) WR ITE (3»400 ) LMIN(K ) 4 0 0 FORMAT( 1 LAG MIN IS • F 1 0 . 5 ) WRITE O f 500 ) KON 500 FORMAT( ' K I S 1 F 1 0 . 5 ) WR ITE (3»600 ) CON 6 0 0 FORMAT( ' C I S ' F 1 0 . 5 ) WRITE (3>700) 700 FORMAT( ' TEMP LAG PRE LAG ACT 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 + . ( T T ( L ) * ( T H + TL) ) - 1 ( T H * T L ) ) ) - 1 K O N * ( ( ( T H + T D / 2 . 0 ) * < ( 1 . 0 ) / ( T H - T L ) ) • 1 A L O G ( A B S ( ( T T ( L ) - T H ) / ( T T ( L ) - T L ) ) ) ) + 1 K O N * T O ( J ) * { ( 1 . 0 ) / ( T H - T L ) > * 1 ALOGtABS t ( T T ( L ) - T H ) / ( T T ( L ) - T L ) ) ) + C O N SQ(L ) = ( L A G ( L ) - A C T ( L ) ) * * 2 « 0 SUMSQ = SUMSQ + SQ (L ) WRITE (3»10 0 )TT ( L ) »LAG(L )»ACT(L )»SUMSQ 100 FORMA T ( 4 F 1 0 . 5 ) 4 CONTINUE 3 CONTINUE 2 CONTINUE 1 CONTINUE CALL EX IT END 167 PROGRAM I - CURVE FITTING ( E q u a t i o n 2b) Program I i s designed t o f i t curves d e s c r i b e d by e q u a t i o n (2b) to spore g e r m i n a t i o n l a g d a t a . T h i s problem i s c o m p l i c a t e d by the f a c t t h a t i n e q u a t i o n (2b) t h e r e are two unknowns; Lag minimum, and T , which i n t u r n determine K and C. In view o f t h i s , e q u a t i o n (2b) has been f i t t e d to the l a g d a t a by t r y i n g many p o s s i b l e Lag minimum and T Q v a l u e s , comparing the c a l c u l a t e d Lag v a l u e s with those observed, c a l c u l a t i n g the sum o f the squared d e v i a t i o n between observed and c a l c u l a t e d , and c h o o s i n g the c u r v e t h a t b e s t f i t s the data. In mathematical terms the f o l l o w i n g steps were t a k e n . E q u a t i o n 2b i s broken up so t h a t : a = [ ( - . 5 l o g | ( - l ) T 2 + T ( T H + T T ) - T^T T | ) -"H L T + T H L T - T H L - l o g T H T - T, b = "H l o g T - T. H T - T, then e q u a t i o n 2b can be w r i t t e n as: L = K>a + K>T • b + C o (2c) I f T s T then e q u a t i o n 2b can be broken up a g a i n t o y i e l d : 168 d = [ ( . - 5 l o g | (-1) T^ + T Q ( T H + T L ) - TH- T L 0 - T + T H L T - T H L l o g T - T H T — T, e = T - T H L l o g Q H o L and e q u a t i o n ( 2 b ) w i t h T = T c o u l d be w r i t t e n as L . = K • d + K • T • e + C mm o ( 2 d ) where L . i s the minimum l a g v a l u e , which, by d e f i n i t i o n , min 7 7 must o c c u r a t T = T . o To s o l v e ( 2 c ) and ( 2 d ) s i m u l t a n e o u s l y some d a t a v a l u e f o r L and i t s c o r r e s p o n d i n g T v a l u e i s s u b s t i t u t e d i n t o ( 2 c ) , and L . and T are e s t i m a t e d and s u b s t i t u t e d i n t o ( 2 d ) . ' mm o Having made these s u b s t i t u t i o n s i t i s p o s s i b l e to s o l v e f o r K and C. These K and C and T v a l u e s may then be s u b s t i t u t e d o J back i n t o ( 2 b ) , which can then be s o l v e d . There i s no way o f knowing which 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 i n t o ( 2 d ) and t h e r e i s no way o f knowing the b e s t v a l u e s o f L . and T . J J mm o F o r t h i s reason Program T has been designed so t h a t a l l o f the a v a i l a b l e d a t a p o i n t s may be t r i e d i n combination with a l l o f the r e a s o n a b l e L ,_ and T v a l u e s . min o In g e n e r a l about 2 0 0 combinations of T , L . , and 3 o' mm' d a t a v a l u e s , are examined b e f o r e a curve i s chosen by the l e a s t o f squares method. The c u r v e chosen must have a sum o f 169 squared deviations which i s i n a "sink" ( i e . the sum of squared deviations f o r every other combination of L m i n > T 0> and data i s l a r g e r ) . PAGE 1 MCQUEEN 170 // JOB MCQUEEN LOG DRIVE CART SPEC CART AVAIL PHY DRIVE 0000 0001 0001 0000 V2 M06 ACTUAL 8K CONFIG 8K // FOR •LIST SOURCE PROGRAM • IOCS ( TYPEWRITER»1132 PR INTER * KEYBOARD) DIMENSION A(25) Z=1.0 16 WRITE(3,5)Z 5 FORMAT(3H1Z=»F10.5) WRITE(3tl2) 12 FORMAT(20X»20H J A) DO 1 J = 1»25 IF(J-1)2»2*3 3 A!J) = ( M Z*3e 54490 * J ) + l ) / 2 ) * * 2 GO TO 4 2 A(1) = loO 4 CONTINUE WRITE(3»13) J»A(J) 13 FORMAT (20X»I3»7X»F10.5) 1 CONTINUE READ(6»14)Z 14 FORMAT(F6•0) IF (Z)15»15»16 15 CALL EXIT END . 171 PROGRAM I I - FORM OF COLONY EXPANSION (E q u a t i o n l c ) Program I I i s designed t o c a l c u l a t e the area o c c u p i e d by a c o l o n y at any time t . In the program n o t a t i o n A ( J ) i s a r e a , J i s time, Z i s g i n e q u a t i o n ( I d ) , and C has been s e t to 1.0 a r e a u n i t s . The output i n d i c a t e s t h a t as Z (or g) i n c r e a s e s ; the s l o p e o f the l i n e , which may be i n t e r p r e t e d as the growth r a t e o f the c o l o n y , a l s o i n c r e a s e s . Values of Z are i n p u t , u s i n g the keyboard and A(J) and J are output v i a the p r i n t e r . PAGE 1 // JOB 172 LOG DRIVE CART SPEC CART AVAIL PHY DRIVE 0000 0001 0001 0000 V2 MO6 ACTUAL 8K CONFIG 8K // FOR •LIST SOURCE PROGRAM •ONE WORD INTEGERS *I0CS (CARD» 1132 PRINTER. PLOTTER) DIMENSION A(14)» X ( 5 0 ) , Y ( 5 0 ) . ANS(16)» STORE(8»65). IUSED(65)» 1 TABLE(30) . TTEST(50 ) READ(2.900)(TTEST(JJ)»JJ=1»50) 900 F O R M A T ( 8 F 1 0 .5) READ(2.901)(TABLE(NN)>NN=1.30) 901 FORMAT ( 8 F 1 0 . 5 ) DO 501 I = 1.75 501 IUSEDfl) = 0 L = 0 C CARD COUNTER TO GET DATA FOR EACH REGRESSION K = 0 3 READ(2.100)TEMP » T I M,A 10 0 FORMAT (15F5*0.F4»0) IF(TEMP)2»1>2 2 IF(K)16.6.16 6 SAVE = TEMP L = L+1 N = 0 K=l GO TO 3 1 DO 4 1=1.14 IF ( A ( I ) J 3 . 3 . 5 5 N = N+1. X(N) =TIM Y ! N) = SORT(A ( I ) ) C • DATA IS WRITTEN OUT HERE WRITE (3.200) X(N!.Y!N) 200 FORMA T(2 F10•5) 4 CONTINUE GO TO 3' 16 WRITE (3.101) SAVE 101 FORMAT (//' L= '» F6.2) C ' REGRESSION CARRIED OUT AND ANSWERS ARE WRITTEN CALL LREG(X.Y.N.AMS) CALL LREGO(ANS) WRITE (3.400) PAGE 173 40 0 FORMAT (1H0) WRITE (3.401) ANS(4) 401 FORMAT ( 1 SUM OF XY = F10.5) WRITE (3»402) ANSt5) 402 FORMAT ( ' SUM OF X SQUARED = ' » F10.5) WRITE (3 .403) ANSI 9) 403 FORMAT ( • SUM OF Y SQUARED = • . FlOoS) SUMDS = ANS(9) - (ANS(4)**2)/ANS(5> WRITE (3.404) SUMDS 404 FORMAT ( 1 SUM OF DEVIATION SQUARED OF XY = 1 > F10.5) WRITE(3»832) WRITE(3.S32 ) WRITE(3.832) 332 FORMAT(1H0) C ALL THE BASIC PLOTTING INFORMATION IS COLLECTED HERE STORE(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 C THE DATA IS SORTED ACCORDING TO TEMPERATURE 11 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 SED(LD) 601.602.601 602 IF (STORE(8»LL) - TABLE(NN)) 603.601.601 603 IUSED(LL)=1 T = STORE!8.LL) WRITE (3.525) STORE(8»LL) 525 FORMAT (' STORE(8.LL) IS TEMP = •» F10.5) WRITE (3.888! 88 8 FORMAT ( » N YBAR XBAR SUMXY SUMXSQ 1 SUMYSQ SUMDXY ' ) WRITE (3 .526) ( STORE ( KK.» LL ) . KK = 1.7) 5 26 FORMAT (7F10.5) SLOP = (ST0RE(4.LL))/(STORE(5.LL)) WRITE (3.560) SLOP 560 FORMAT (• SLOP OF SINGLE LINE = 1.F10.5) WRITE(3»832) PAGE 3 1 7 4 61 62 88 89 90 75 76 77 78 628 601 22 527 889 528 999 529 LC = LC +1 IF(LC - 1) CALL SCALF CALL CALL CALL YE = IF ( XE = GO XE YE 61,61,62 (7.0/7.0,10.0/20.0» 0.0,0*0) FGRID(0,0.0.0.0,1.0,7) FGRlDllf0.0.0.0,1.0,20) FCHAR!0.0,0.0,0.07,0.07,1.570796) = ST0RE(2,LL) + SLOP*(7.0 - ST0RE(3»LL)J ( YE - 20. ) 88,88,89 7.0 TO 90 = (20. ~ STORE(2,LL) + SLOP*(STORE(3,LL)))/SLOP = 20. CONTINUE XS = (-STORE(2»LL)/SLOP) IF (XS) 75,76,76 YS = STORE(2»LL) - ( SLOP* GO TO 77 YS = 0. GO TO 78 XS = 0. CONTINUE CALL FPLOT CALL FPLOT WRITE(7,628) FORMAT (12) CALL FPLOT ( 0,0.0,0,0) SUMN = STORE(l,LL) + SUMM + STORE(3,LL) STORE(3 iLL) J ) (-2 »XS,YS (-1,XE,YE) LC STORE(2,LL) +. STORE(3»LL) + STOREU»LL) + STORE(5,LL) + STORE(6,LL) + STORE(7,LL) + YMEAN XMEAN SUMXY SUMXS SUMYS SSUMD CONTINUE IF (LC) 600,600,22 WRITE(3,527) T FORMAT ( 1 T WRITE (3,889) FORMAT( • SUMN 1SUMYS SSUMD ' ) WRITE(3,528) SUMN, FORMAT(7F10.5) SLOPE = (SUMXY) / YMEAN XMEAN SUMXY SUMXS SUMYS SSUMD IS TEMP = » F10.5) YMEAN XMEAN SUMXY SUMXS YMEAN, XMEAN» SUMXY, SUMXS, SUMYS, (SUMXS) - (LC) - / (D FREE) (SUMXS) SB DFREE = (SUMN) SSYX - (SSUMD) SS8 = (SSYX) / SB = SQRT(SSB) J J = DFREE DEVIA = TTEST(JJ)* XPLOT = XMEAN/LC YPLOT = YMEAN / LC WRITE (3,999) FORMAT ( 1 SLOPE 1 XPLOT YPLOT 1 WRITE (3,529) SLOPE, FORMAT(8F9.5) 1. ) DFREE SSYX S S B S B DEVIA DFREE, SSYX, SSB, SB, DEVIA,XPLOT, YPLOT PAGE 4 WR ITE (3»832 ) WRITE(3 » 83 2) W R I T E ( 3 . 832 ) WR ITE (3»832 ) YEM = YPLOT + S L O P E * ! 7 . 0 - XPLOT) IF (YEM - 2 0 . ! 30 , 30 .31 3 0 XEM = 7 . 0 GO TO 32 31 XEM = ( 2 0 . 0 - YPLOT + S LOPE*XPLOT ) / SLOPE YEM = 2 0 . 3 2 CONTINUE XSM = XPLOT - (YPLOT/SLOPE ) IF ( X S M ) 3 3 . 3 4 , 3 4 3 3 YSM = YMEAN - ( SLOPE*XMEAN) GO TO 35 34 YSM = 0 . 0 GO TO 36 3 5 XSM = 0 . 0 36 CONTINUE CALL FPLOT ( - 2 , X S M , Y S M ! CALL FPLOT ! - l . X E M . Y E M ) W R I T E ( 7 . 6 2 9 ) 6 29 FORMAT( ' MEAN L INE » ) CALL FCHAR ( 1 . 0 . 1 9 . 0 . 0 . 1 4 . 0 . 1 4 . 0 . 0 ) WRITE ( 7 . 2 2 3 ) T 223 FORMAT( 1 TEMP = • F 1 0 . 5 ) CALL FCHAR ( 1 . 0 . 1 8 . 0 , 0 . 1 4 , 0 . 1 4 , 0 . 0 ) W R I T E ( 7 . 2 2 4 ) SLOPE 2 2 4 FORMAT( ' SLOPE = ' F 1 0 . 5 ) CALL FCHAR ( 1 . 0 , 1 7 . 0 , 0 . 1 4 , 0 . 1 4 . 0 . 0 ) W R I T E ( 7 , 2 2 5 ) DEVIA 225 FORMAT ( • DEVIA = 1 F 1 0 . 5 ) CALL FCHAR ( 1 . 0 , 1 6 . 0 , 0 . 1 4 , 0 . 1 4 , 0 . 0 ) W R I T E ( 7 , 2 2 6 ) S U M N 226 FORMAT( 1 SUMN = ' F 1 0 . 5 ) CALL FPLOT ( 0 , 1 0 . 0 , 0 . 0 ) 6 0 0 CONTINUE CALL EX IT END FEATURES SUPPORTED ONE WORD INTEGERS IOCS CORE REQUIREMENTS FOR COMMON 0 VAR IABLES 1610 PROGRAM 1452 END OF COMPILAT ION / / XEQ 1 7 6 P R O G R A M I I I - C A L C U L A T I O N O F M E A N S L O P E P r o g r a m I I I c a l c u l a t e s t h e m e a n s l o p e s o f t h e l i n e s w h i c h r e s u l t f r o m p l o t t i n g a r e a o c c u p i e d b y a c o l o n y a g a i n s t t i m e ( F i g . 1 1 ) . e a c h c u l t u r e a r e c o n s i d e r e d s e p a r a t e l y . T h e c u l t u r e t e m p e r - a t u r e i s r e a d a n d t h e n t h e t i m e - a r e a d a t a f o r t h a t c u l t u r e a r e r e a d . A . r e g r e s s i o n l i n e ( t i m e a n d s q u a r e r o o t o f a r e a ) i s t h e n c a l c u l a t e d u s i n g t h e s t a n d a r d I B M 1 1 3 0 L R E G a n d L R E G O s u b r o u t i n e s . A f t e r a l l t h e c u l t u r e s h a v e b e e n p r o c e s s e d a n d a r e g r e s s i o n l i n e o b t a i n e d f o r e a c h , t h e r e g r e s s i o n l i n e s a r e g r o u p 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 ( i e . a l l t h e l i n e s r e s u l t i n g f r o m c u l t u r e s g r o w n a t 2 0 . 5 ° a r e g r o u p e d , a l l t h o s e g r o w n a t 2 1 . 5 ° a r e g r o u p e d e t c . ) . D u r i n g t h i s g r o u p i n g p r o c e s s e i g h t p i e c e s o f i n f o r m a t i o n a r e p r i n t e d o u t f r o m e a c h r e g r e s s i o n . T h e s e a r e : I n t h e f i r s t s e c t i o n o f t h e p r o g r a m t h e d a t a f r o m ( 1 ) n n u m b e r o f d a t a p o i n t s ( 2 ) y m e a n t i m e ( 3 ) x m e a n s q u a r e r o o t o f a r e a (4) Ixy ( 5 ) ^x 2 (6) 2y 2 ( 7 ) Id 2. x y [(SX) ( £ Y ) 1 /n (X X) 2/n ( % Y ) 2 / n 2 2 C E x y ) / x (8) T t e m p e r a t u r e A f t e r a l l o f t h e r e g r e s s i o n s f o r a n y p a r t i c u l a r 177 t e m p e r a t u r e 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 l i n e i s c a l c u l a t e d . T h i s i s a c c o m p l i s h e d i n t h e f o l l o w i n g m a n n e r : F o u r q u a n t i t i e s a r e summed: 2 2 c- 2 ^ 2 C"cr _ 7 < -̂ c <csr 2 c - 2 ^-2 _ 2 k k 2 % X Y = ( ^ x y ^ + C § : x y ) 2 . . . C S x y ) k w h e r e k i s t h e t o t a l number o f r e g r e s s i o n l i n e s f o r t h e t e m p e r a t u r e b e i n g c o n s i d e r e d . W i t h t h i s i n f o r m a t i o n a mean s l o p e c a n b e c a l c u l a t e d . b _ IdEiiY— S S x 2 w h e r e b i s t h e mean s l o p e . A 5 % c o n f i d e n c e l i m i t c a n a l s o be e s t a b l i s h e d a r o u n d b . S 2 = %Zd2 /Zn - k - 1 yx yx S 2 = S 2 /%%x2 b yx s o t h a t : b " S b "  t ( S n-k-1) , CX = .05 w h e r e n i s t h e t o t a l number o f r e g r e s s i o n p o i n t s and k i s t h e t o t a l number o f r e g r e s s i o n l i n e s i n c o r p o r a t e d t o p r o d u c e t h e 178 mean regression l i n e . This mean regression l i n e i s placed i n space by c a l c u l a t i n g the mean x and y values so that mean x mean y When a l l of the regression l i n e s have been grouped and t h e i r mean regression l i n e s c a l c u l a t e d the p l o t t e r routine i s c a l l e d and each set of l i n e s along with t h e i r mean l i n e i s p l o t t e d . The p l o t t e r also writes the mean slope and the 5 % confidence l i m i t around the mean slope f o r every temperature. This slope and 5 % confidence i n t e r v a l can then be used as the growth index. k = !>, V k i = l k = x . /k i = l PAGE 1 MCQUEEN 179 / / J O B MCQUEEN LOG DRIVE OOOO CART SPEC 0001 CART A V A I L PHY DRIVE 0001 0000 V2 MO 6 ACTUAL 8K CONFIG 8I< // FOR •ONE WORD INTEGERS •L I ST 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 = J J = I I = READ ( 2 .51 ) (GD< I) >T( I) . 1 = 1 . I I ) 51 FORMAT ( 2 F 1 0 . 5 ) R E A D ( 2 . 2 0 0 ) ( T O ( J ) . J = 1 . J J ) 200 FORMAT ( F 1 0 . 5 ) R E A D ( 2 . 2 0 1 ) ( Q ( L ) . L = 1 . L L ) 201 F O R M A T ( F 1 0 . 5 ) DO 203 J = l . J J A = (ALOG(TH-TL ) )• (TH-TO( J ) ) - (TH) + ( TL ) B = (ALOG(TH-TO( J ) ) ) • (TH-TO( J ) J - (TH) + ( T O I J I ) DO 204 L = 1 » LL K = Q ( L ) / ( B - A ) C= - A # { Q ( L ) / ( B - A ) ) DO 205 1 = 1 » I I G d ) = ( A L O G ( T H - T ( I ) ) ) * K * ( T H - T O < J ) ) - K * T H + K * T ( I ) + C 20 5 CONTINUE S S Q ( l ) = (GD(1 ) - G ( 1 ) ) * * 2 . DO 206 I =2 .11 SSQ ( 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 ) 2 0 9 FORMAT ( IX » 5HQ( I ) = » F10•5 ) WRITE ( 3 . 1 0 0 J K 100 FORMAT(3H K=.F10„5 ) WRITE ( 3 . 1 0 D C 101 FORMAT(3H C = . F 1 0 . 5 ) WRITE ( 3 . 1 0 2 ) 102 FORMAT(3 6H T GD G SSQ) WRITE (3 . 1 0 3 ) ( T ( I ) . G D ( I ) . G ( I ) . S S Q ( I ) ,1 = 1 .11 ) 103 F O R M A T ( 4 F 1 0 . 5 ) 204 CONTINUE 203 CONTINUE 30 CALL EX IT END 180 PROGRAM IV - CURVE FITTING ( E q u a t i o n 3c) Program IV f i t s e q u a t i o n (3c) t o the growth index d a t a . T h i s problem i s c o m p l i c a t e d by the f a c t t h a t two unknowns must be found b e f o r e the e q u a t i o n can be f i t . These are the maximum growth o f the c o l o n y (Gmax) and the optimum temperature ( T Q ) at which Gmax o c c u r s . T q and Gmax determine K and C. One s o l u t i o n t o the e q u a t i o n can be found by s e t t i n g T = T^ and G = 0.0 i n e q u a t i o n (3c) so t h a t : 0.0 = l o g | TH - T | • K ( T H - T ) - K « T H + K * T ^ + C where T H and T L are known. I t i s a l s o known t h a t g = gmax when T = T so t h a t (2c) may a l s o be w r i t t e n : o Gmax = l o g | T u - T ( ' K ( T - T ) — K - T „ + K » T + C 3 1 H O H O H o There are now two eq u a t i o n s and two unknowns ( K , C) so a s o l u t i o n may be found. However, the b e s t v a l u e s f o r T and Gmax are unknown, ' o To overcome t h i s problem the curve was f i t t e d i t e r a t i v e l y to the d a t a . A l l the r e a s o n a b l e Gmax and T v a l u e s were t r i e d , o 7 e q u a t i o n (3c) was s o l v e d f o r each p a i r , v a l u e s o f G at every T were c a l c u l a t e d , and the sum o f the squared d e v i a t i o n s between the observed and c a l c u l a t e d v a l u e s o f G was c a l c u l a t e d , The p a i r o f T Q and Gmax va l u e s which y i e l d e d the curve o f b e s t f i t ( s m a l l e s t sum o f squared d e v i a t i o n s ) was used. PAGE 1 181 // JOB LOG DRIVE 0 0 0 0 CART SPEC 0001 CART AVA I L 0001 PHY DRIVE 0000 V2 MO6 ACTUAL 8K CONFIG 8K // FOR * L I S T SOURCE PROGRAM *ONE WORD INTEGERS *IOCS ( C A R D , 1 1 3 2 PRINTER) 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 = J J = I I = R E A D ( 2 , 1 0 0 0 ) ( T ( I ) , Q ( I ) , 1 = 1 , 1 1 ) 1000 FORMA T ( 2 F10 » 5 ) R E A D ( 2 , 2 0 0 0 ) (TO( J ) ,J = 1 , J J ) 2 0 0 0 F O R M A T ( F 1 0 . 5 ) R E A D ( 2 , 3 0 0 0 ) (GMAX(K) ,K=1»KK) 3000 F O R M A T ( F 1 0 . 5 ) R E A D ( 2 , 4 0 0 0 ) ( T T ( L ) , A C T ( L ) , L = 1 , L L ) 4 0 0 0 F O R M A T ( 2 F 1 0 . 5 J DO 1 I = 1 , 1 T J. A = ( - . 5 * A L O G ( ( - 1 . 0 ) * T ( I ) * *2«0 + T ( I ) * { T H + T L ) - Th ' *T l _ ) ) - 1 ( ( ( T H + T L ) / 2 . 0 ) * ( 1 . 0 / ( T H - T L ) ) * 1 (ALOG(ABS < T! I) - T H ) / ( T ! I )-TL) ) ) ) B = ( ( ( 1 . 0 ) / ( T H - T L ) ) » A L O G ( A B S ( T ( I ) - T H ) / ( T ( I ) - T L ) ) ) 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 ( ( ( T H + T L ) / 2 . 0 ) * ( ( 1 . 0 ) / ( T H - T L ) ) * 1 ( A L O G ( A B S ( T O ( J ) - T H ) / ( T O ( J ) - T D ) ) ) 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,KK KON = ( Q ( I ) - G M A X ( K ) ) / ( - A - B * T O ( J ) + D + E * T O ( 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 ) ) ) W R I T E ( 3 , 2 0 0 ) T ( I ) , Q ( I ) 2 0 0 FORMAT( • TEMP OF POINT USED IS * F 1 0 . 5 • AND POINT IS 1 F 1 0 . 5 ) W R I T E ( 3 , 3 0 0 ) TO( J ) 300 FORMAT( • TEMP OPTIMUM IS ' F 1 0 . 5 ) W R I T E ( 3 , 4 0 0 ) GMAX(K) 4 0 0 FORMAT( 1 GRO MAX IS ' F 1 0 . 5 1 W R I T E ( 3 , 5 0 0 ) KON 5 0 0 FORMAT! 1 K IS 1 F 1 0 . 5 ) W R I T E ( 3 , 6 0 0 ) CON 60 0 FORMAT( 1 C IS ' F 1 0 . 5 ) WRITE ( 3 , 7 0 0 ) 70 0 FORMAT( 1 TEMP GRO PRE GRO ACT SUMSQ 1 ) SUMSQ = 0 . 0 DO 4 L = 1 , L L PAGE 2 182 GRO(L ) =-KON*( ( - . 5 ) * A L O G ( ( - 1 . 0 ) * T T ( L ) * * 2 . 0 + ( T T ( L ) * ( T H + TL )) - 1 ( T H * T L ) ) ) + 1 K O N * ( ( ( T H + T L ) / 2 . 0 ) * { ( 1 . 0 ) / ( T H - T L ! ) • 1 A L O G ( A B S ( ! T T ( L ) - T H ) / ( T T ( L ) - T L ) ) ) ) - 1 K O N * T O ( J ) » ( ( 1 . 0 ) / ( T H - T L ) } * 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 + SQ (L ) W R I T E ( 3 » 1 0 0 ) T T ( L ) » G R O ( L ) » A C T ( L ) » S U M S Q 100 FORMAT(4F10•5 ) 4 CONTINUE 3 CONTINUE 2 CONTINUE 1 CONTINUE CALL EX IT " END 183 PROGRAM V - CURVE FITTING ( E q u a t i o n 4b) Program V was used t o f i t c u r v e s o f the type d e s c r i b e d by e q u a t i o n (4b) to f r u i t i n g body expansion d a t a from P. p a l l i d u m . In e q u a t i o n (4b) where: G = -K ["(-.5) l o g | (-1) T 2 + T ( T H + T L ) - T^» T^ | ) - T + T H L T - T H L j l o g T - T H T - T K T - T H L lo g T T. H T - T, + C The f i t t i n g procedure i s c o m p l i c a t e d by the f a c t t h a t t h e r e are two unknowns; growth maximum and T Q which i n t u r n determine K and C. There i s a l s o o n l y one e q u a t i o n . These f a c t o r s have made i t n e c e s s a r y to use an i t e r a t i v e f i t t i n g method u s i n g a l l the r e a s o n a b l e combinations o f growth max and T , comparing the c a l c u l a t e d expansion r a t e v a l u e s with those observed, c a l c u l a t i n g the sum of the squared d e v i a t i o n s between observed and c a l c u l a t e d , and choos- i n g the curve t h a t b e s t f i t s the d a t a . T h i s f i t t i n g procedure was m a t h e m a t i c a l l y conducted i n the f o l l o w i n g manner: In e q u a t i o n (4b) l e t : a = [(.-5 l o g j ( - l ) T 2 + T (T + T ) - T - T I") - 184 b = T - T H L l o g T - T T - T, H so t h a t (4b) may be w r i t t e n as G = -K»a - K • T • b + C o (4c) Again i n e q u a t i o n (4b) i f T = T q then: d = [ ( . - 5 l o g 1 (-1) T 2 + T o ( T R + T L ) - T H T | ) - T + T H L T - T H L l o g "H T - T, e = T - T H L l o g T - T„ o H O L and t h e r e f o r e e q u a t i o n (4b) with T = T c o u l d be w r i t t e n as: o Gmax UK • d - K • T • e + C o (4d) where Gmax i s the maximum growth v a l u e which must by d e f i n i - t i o n o c c u r a t T = T „ o From t h i s p o i n t on the a c t u a l mechanics o f the f i t t i n g procedure are i d e n t i c a l to those employed i n Program I B r i e f l y , G i n e q u a t i o n (4c) i s s e t equal t o zero and T i s s e t e q u a l t o T L « G i n e q u a t i o n (4d) i s s e t equal t o Gmax and T i s s e t eq u a l t o T . Equations (4c) and (4d) are s o l v e d s i m u l t a n e o u s l y , ' K and C are found and s u b s t i t u t e d i n t o equa- t i o n (4b), and G i s c a l c u l a t e d f o r every temperature between T and . PAGE 1 MCQUEEN 185 // JOB T MCQUEEN 1 LOG DRIVE CART SPEC CART AVAIL PHY DRIVE 0000 0001 0001 0000 V2 M06 ACTUAL 8K CONFIG 8K *EQUAT(PRNTZ »PRNTY1 // FOR •ONE WORD INTEGERS • 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 = 9999.00 GO TO 24 21 I F ( T - 2 7 . ) 22.22,23 23 DL = 9999.00 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 ALOG(ABS( ( T - T H ) / ( T - T L ) )) ) + 1 K * T 0 * ( ( 1 . 0 ) / ( T H - T L ) ) * 1 A L O G ( A B S ( ( T - T H ) / ( T - T L ) ) ) + C 24 RETURN END FEATURES SUPPORTED ONE WORD INTEGERS " CORE REQUIREMENTS FOR DLAG COMMON 0 VARIABLES 34 PROGRAM 2 20 END OF COMPILATION // DUP •STORE WS UA DLAG CART ID 0001 DB ADDR 5361 DB CNT 0012 // FOR •ONE WORD INTEGERS • 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 = 9999.00 GO TO 34 31 I F I T - 3 7 . ) 32,32,33 33 PL = 9999.00 GO TO 34 32 PL = K*{ (-.5)*AL0G{ (-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 * T 0 * ( ( 1 . 0 ) / ( T H - T L ) ) * PAGE 2 MCQUEEN 186 1 ALOG(ABS ( (T-TH) / ( T - T L ) ) )+C 34 RETURN END FEATURES SUPPORTED ONE WORD INTEGERS CORE REQUIREMENTS FOR PLAG COMMON 0 VAR IABLES 34 PROGRAM 220 END OF COMPILATION // DUP •STORE WS UA PLAG CARJ ID 0001 DB ADDR 5373 DB CNT 0012 // FOR •ONE WORD INTEGERS • L I S T SOURCE PROGRAM SUBROUTINE PFGRO( T» TO»TL»TH•K>C»PG) REAL K I F C T - 1 8 . J 4 0 . 4 0 . 4 1 40 PG = 0 . 0 GO TO 44 41 I F ( T - 3 7 . ) 4 2 . 4 2 . 4 3 43 PG = 0 . 0 GO TO 44 42 PG =-<*{ { - .5 ) *ALOG{ ( - 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 ALOG(ABS ( ( T - T H ) / ( T - T L ) )) ) 1 -K*TO*( ( 1 . 0 ) / ( T H - T L ) )• 1 A L O G ( A B S ( ( T - T H ) / ( T - T L ) ) ) + C 44 RETURN END FEATURES SUPPORTED ONE WORD INTEGERS CORE REQUIREMENTS FOR PFGRO COMMON 0 VAR IABLES END OF COMPILAT ION 36 PROGRAM 2 26 // DUP •STORE WS UA PFGRO CART ID 0001 DB ADDR 5385 DB CNT 0012 // FOR •ONE WORD INTEGERS • 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 I F ( T - 9 . 0 ) 1 . 1 , 2 1 DG = 0 . 0 PAGE 3 MCQUEEN ! 8 7 GO TO 5 2 I F ( T - 2 6 . 5 ) 3 . 3 . 4 4 DG = 0 . 0 GO TO 5 3 DG = (ALOG (TH-T )>*K* (TH-TO )-K*TH+K*T+C 5 RETURN END FEATURES SUPPORTED ONE WORD INTEGERS CORE REQUIREMENTS FOR DGROW COMMON 0 VAR IABLES 8 PROGRAM 98 END OF COMPILAT ION // DUP •STORE WS UA DGROW CART ID 0001 DB ADDR 5397 DB CNT 0008 // FOR *ONE WORD INTEGERS •L I ST SOURCE PROGRAM SUBROUTINE PGROW (T»TO » TL•TH•K»C»PG) REAL K I F I T - 1 8 . ) 1 0 . 1 0 . 1 1 10 PG = 0 . 0 GO TO 14 11 I F C T - 3 7 . ) 1 2 . 1 2 . 1 3 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 FEATURES SUPPORTED ONE WORD INTEGERS CORE REQUIREMENTS FOR PGROW COMMON 0 VAR IABLES 8 PROGRAM 98 END OF COMPILAT ION // DUP •STORE WS UA PGROW CART ID 0001 DB ADDR 539F DB CNT 0008 // FOR • IOCS ( C A R D . 1 1 3 2 PRINTER *TYPEWRITER) • L I S T SOURCE PROGRAM •ONE WORD INTEGERS C THE FOLLOWING COMMENT CARDS IDENTIFY THE SYMBOLS USED C T = TEMP. C TL = TEMP. LOW C TO = TEMP. OPTIMUM PAGE 4 MCQUEEN C TH = TEMP HIGH C K = CONSTANT C C = CONSTANT C LDA = LAG FOR DD AMOEBAE C GDA = GROWTH INDEX FOR DD AMOEBAE C LDF = LAG FOR DD FRU IT ING BODIES C GDF = GROWTH INDEX FOR DD FRU IT ING BODIES C LPA = LAG FOR PP AMOEBAE C LPF = LAG FOR PP FRU IT ING BODIES C GPA = GROWTH FOR PP AMOEBAE C GPF = GROWTH FOR PP FRU IT ING BODIES C THE DATA THAT IS INPUT SO THAT THE SUBROUTINES CAN FUNCTION C IS CODED IN FOUR PARTS ..a.....THE F IRST LETTER IS L FOR LAG C OR G FOR GROWTH • « . . . THE SECOND ONE OR TWO LETTERS ARE TO»TH» C T L . K . C ALL OF WHICH HAVE BEEN I D E N T I F I E D BEFORE a * a «•T HE SECOND TO C THE LAST LETTER IS P OR D STANDING FOR PP OR D D . . . . T H E LAST C LETTER IS A OR F STANDING FOR AMOEBAE OR FRU IT ING BODY. . . . . A N C E X A M P L E . . L T H P A . . S T A N D S FOR LAG TEMPERATURE HIGH PP AMOEBAE.o C THIS IS THE TEMP. HIGH FOR THE PP AMOEBAE LAG SUBROUTINE 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 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 . 1 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 . 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 99 CONTINUE R E A D ( 2 . 1 0 1 ) T 101 F O R M A T 1 F 1 0 . 5 ) C ALL OF THE FOLLOWING INFORMATION IS READ INTO THE SUBROUTINES C D.DISCOIDEUM 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 CALL DLAG !T»LTODA»LTLDA»LTHDA»LKDA»LCDA»LDA) GTODA = 2 1 . 5 GTLDA a 9 . GTHDA = 2 7 . 5 GKDA = 0 . 8 0 0 8 4 GCDA = 0 . 7 9 5 5 4 CALL DGROW (T»GTODA»GTLDA.GTHDA»GKDA,GCDA.GDA) C D.DISCOIDEUM FRU IT ING BODY LTODF = 2 4 . LTLDF = 9 . LTHDF = 2 7 . 5 LKDF = 2 . 4 7 6 8 1 LCDF = 7 . 6 2 5 4 2 CALL DLAG (T»LTODF»LTLDF»LTHDF•LKDF»LCDF . LDF) GTODF = 2 1 . GTLDF = 9 . GTHDF = 2 7 . 5 GKDF = 0 . 8 6 3 1 8 GCDF = - 0 . 6 5 3 6 8 CALL DGROW(T »GTODF»GTLDF.GTHDF,GKDF.GCDF.GDF) C P . P A L L I D U M AMOEBAE LTOPA = 3 1 . LTLPA = 1 8 . PAGE 5 MCQUEEN 189 LTHPA = 3 7 . LKPA = 0 . 8 1 1 3 2 LCPA = 2 . 5 9 3 5 6 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 CALL PGROW (T»GTOPA»GTLPA,GTHPA»GKPA»GCPA»GPA) C P . P A L L I D U M FRUIT ING BODY LTOPF = 3 0 . LTLPF = 1 8 . LTHPF = 3 7 . LKPF = 1 . 2 8 5 2 7 LCPF = 3 . 7 6 1 4 5 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 CALL PFGROIT .GTOPF»GTLPF,GTHPF»GKPF»GCPF»GPF) W R I T E ( 3 . 3 0 0 )T 300 FORMAT( • TEMPERATURE = ' F 1 0 . 5 ) W R I T E ( 3 . 3 0 9) 309 FORMAT( 1 LDA GDA LDF GDF L PA 1GPA LPF GPF ' ) WRITE(3 . 3 0 8 ) LDA,GDA.LDF .GDF»LPA .GPA»LPF .GPF 308 FORMAT(8F10 .2 ) WRITE ( 3 . 3 1 0 ) 310 FORMAT(1H0) W R I T E ! 3 . 3 0 1 ) 301 FORMAT( 1 T IME DDA DDF PPA PPF • ) C IN THE FOLLOWING AREA CALCULAT IONS ARE M A D E . . . . . AREAS ARE C CALCULATED FOR DD AMOEBAE. PP AMOEBAE. DD FRU IT ING B O D I E S . C AND PP FRU IT ING BOD IES . DO 1000 I = 1 .50 . C D.DISCOIDEUM AMOEBAE 40 0 DATIM = I*.1 - L D A I F (DAT IM ) 1 2 0 . 1 2 0 . 1 2 1 120 DATIM = 0 , 0 121 ADA = ( GDA*DATIM + 2 . 0 ) * * 2 . ADA = A D A * 6 . 4 5 1 6 C P . P A L L I D U M AMOEBAE PATIM = I * . l - LPA I F ( PAT IM ) 1 4 0 . 1 4 0 . 1 4 1 140 PATIM = 0 , 0 141 APA = ( GPA*PAT IM + 2 . 0 1 * * 2 . APA = A P A * 6 . 4 5 1 6 C D.DISCOIDEUM FRUIT ING BODY DFTIM = I* . l - LDF I F l D F T I M ) 1 3 0 . 1 3 0 . 1 3 1 130 DFTIM = 0 , 0 131 ADF = ( GDF*DFT IM ) * * 2 . ADF = A D F * 6 . 4 5 1 6 PAGE 6 MCQUEEN 190 C P . P A L L I D U M FRU IT ING BODY PFT IM = - LPF I F ( P F T I M ) 1 5 0 , 150 . 151 150 PFT IM = 0 . 0 151 APF = ( GPF *PFT IM )**2« APF = APF*6 .4-516 T I M E = I * . l W R I T E ( 3 , 3 0 2 ) T I M E , A D A . A D F . A P A . A P F 302 F O R M A T ( F 5 . 2 . 4 F 1 0 . 2 ) 1000 CONTINUE W R I T E ( 3 , 3 0 3) 303 FORMAT(1H11 I F ( T - 3 8 . ) 9 9 , 9 9 , 9 8 98 CALL EX IT END 191 PROGRAM VI - EXPLOITATION OF SINGLE SPECIES Program VI was used to c a l c u l a t e t he are a o c c u p i e d by amoebae and f r u i t i n g b o d i e s at any temperature and at any time . Both D. discoideum and P. p a l l i d u m were run t o g e t h e r but d i d not i n t e r a c t i n any way. The program i s broken i n t o f o u r p o r t i o n s : (1) sub- r o u t i n e s , (2) dat a i n p u t , (3) c a l c u l a t i o n s and (4) ou t p u t . SUBROUTINES: There are f i v e s u b r o u t i n e s : (1) DLAG: c a l c u l a t e s the spore g e r m i n a t i o n l a g and the f r u i t i n g body l a g f o r D. d i s c o i d e u m . E q u a t i o n (2b) i s used. Below 9.0°C and above 27.0°C the l a g i s s e t equal to i n f i n i t y . (2) PLAG: c a l c u l a t e s the spore g e r m i n a t i o n l a g and the f r u i t i n g body l a g f o r P. p a l l i d u m . E q u a t i o n (2b) i s used. Below 18.0°C and above 37.5°C the l a g i s s e t equal t o i n f i n i t y . (3) PFGRO: c a l c u l a t e s the r a t e o f f r u i t i n g body c o l o n y expansion f o r £• p a l l i d u m . E q u a t i o n (4b) i s used. Below 18.0°C and above 37.5°C the expansion r a t e i s s e t e q u a l t o 0.0. (4) DGROW: c a l c u l a t e s the r a t e of c o l o n y expansion f o r D. discoideum amoebae and f r u i t i n g b o d i e s . E q u a t i o n (3b) i s used. Below 9.0°C and above 27.0°C the r a t e o f expansion i s s e t e q u a l t o 0.0. (5) PGROW: c a l c u l a t e s the r a t e o f c o l o n y expansion f o r P. p a l l i d u m amoebae. E q u a t i o n (4b) i s used. Below 18.0°C and above 37.5°C the expansion r a t e i s se t equal t o 0.0. 192 DATA INPUT: Data i s i n p u t f o r e i g h t q u a n t i t i e s : (1) D. discoideum amoebae l a g , (2) D. discoideum f r u i t i n g body l a g , (3) Do discoideum amoebae expansion, (4) D. discoideum f r u i t - i n g body expansion, (5) P. p a l l i d u m amoebae l a g , (6) P. p a l l i d u m f r u i t i n g body l a g , (7) P. p a l l i d u m amoebae expansion, (8) P. p a l l i d u m f r u i t i n g body expansion. F i v e p i e c e s o f i n f o r m a t i o n are needed f o r the c a l c u l a t i o n o f these e i g h t parameters. These a r e : temperature low, temperature h i g h , temperature optimum, K, and C. The c o d i n g o f these d a t a i s e x p l a i n e d i n the program. CALCULATIONS: The area o c c u p i e d by the f r u i t i n g b o d i e s and the amoebae of both s p e c i e s i s c a l c u l a t e d h e r e . E q u a t i o n ( I f ) i s used i n a l l c a s e s . The c o n s t a n t C i n e q u a t i o n ( I f ) i s s e t 2 e q u a l t o 13 mm f o r D. discoideum and P. p a l l i d u m amoebae because C equals the i n i t i t a l a rea o c c u p i e d by the s p o r e s . F o r D. discoideum and P. p a l l i d u m f r u i t i n g b o d i e s the 2 c o n s t a n t C. i s s e t equal t o 0.0 mm because no area i s occupxed by the f r u i t i n g b o d i es u n t i l they b e g i n t o form. OUTPUT: S i x q u a n t i t i e s are o u t p u t . These are (1) temper- a t u r e , (2) time, measured i n days, (3) DDA = D. discoideum amoebae area, (4) PPA = P. p a l l i d u m amoebae ar e a , (5) DDF = Do discoideum f r u i t i n g body area, ( 6 ) P P F = P. pallidum f r u i t i n g body area. // JOB T MCQUEEN 1 M 21 ABOVE RECORD NOT A SUPERVISOR CONTROL RECORD // FOR •IOCS (CARD»1132 PR INTER»TYPEWRITERJ •LIST 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 c LDA = LAG FOR DD AMOEBAE c GDA = GROWTH INDEX FOR DD AMOEBAE c LDF = LAG FOR DD FRUITING BODIES c GDF = GROWTH INDEX FOR DD FRUITING BODIES c LPA = LAG FOR PP AMOEBAE c LPF = LAG FOR PP FRUITING BODIES c GPA = GROWTH FOR PP AMOEBAE r GPF = GROWTH FOR PP FRUITING BODIES c THE DATA THAT IS INPUT SO THAT THE SUBROUTINES CAN FUNCTION c c OR G FOR GROWTH THE SECOND ONE OR TWO LETTERS ARE TO.TH. c TL»K»C ALL OF WHICH HAVE BEEN IDENTIFIED BEFORE THE SECOND c THE LAST LETTER IS P OR D STANDING FOR PP OR DD.... THE LAST c LETTER IS A OR F STANDING FOR AMOEBAE OR FRUITING BODY...*oAN c EXAMPLE..LTHPA..STANDS FOR LAG TEMPERATURE HIGH PP AMOEBAE.. c THIS IS THE TEMP. HIGH FOR THE PP AMOEBAE LAG SUBROUTINE 9 9 CONTINUE READ(2 »101 )T 101 FORMAT(F10.5) C ALL OF THE FOLLOWING INFORMATION IS READ INTO THE SUBROUTINES C 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) c D.DISCOIDEUM FRUITING BODY LTODF = 24. LTLDF = 9. LTHDF = 27.5 LKDF = 2.47681 PAGE 2 MCQUEEN 195 LCDF = 7 * 6 2 5 4 2 CALL DLAG (T»LTODF,LTLDF»LTHDF»LKDF»LCDF>LDF) GTODF = 2 1 . GTLDF = 9 . GTHDF = 2 7 . 5 GKDF = 0 . 8 6 3 1 8 GCDF = - 0 . 6 5 3 6 8 CALL DGROW<T .GTODF»GTLDF.GTHDF.GKDF,GCDF•GDF) C P . P A L L I D U M AMOEBAE LTOPA = 3 1 . LTLPA = 1 8 . LTHPA = 3 7 . LKPA = 0 . 8 1 1 3 2 LCPA = 2 . 5 9 3 5 6 CALL PLAG ( 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 CALL PGROW ( T . G T O P A . G T L P A . G T H P A . G K P A . G C P A . G P A ) C P . P A L L I D U M FRU IT ING BODY LTOPF = 3 0 . LTLPF = 1 8 . LTHPF = 3 7 . LKPF = 1 . 2 8 5 2 7 LCPF = 3 . 7 6 1 4 5 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 CALL PFGRO(T , G T O P F , G T L P F , G T H P F , G K P F , G C P F , G P F ) W R I T E ( 3 , 3 0 0 ) T 300 FORMAT( ' TEMPERATURE = ' F 1 0 . 5 ) W R I T E ( 3 , 3 0 9 ) 309 FORMAT( 1 LDA GDA LDF GDF LPA 1GPA LPF GPF •) WRITE (3 , 3 0 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 30 8 F O R M A T ( 8 F 1 0 . 2 ) WRITE ( 3 , 3 1 0 ) 310 FORMAT(1H0) W R I T E ( 3 , 3 0 1 ) 301 FORMAT( 1 TIME DDA DDF PPA PPF SUMA 1 SUMF ' ) C IN THE FOLLOWING AREA CALCULATIONS ARE M A D E . . . . . AREAS ARE C CALCULATED FOR DD AMOEBAE, PP AMOEBAE, DD FRU IT ING B O D I E S , C AND PP FRU IT ING BOD IES . SUMA = 0 . 0 SUMF = 0 . 0 APF = 0 . 0 ADF = 0 . 0 DO 1000 I = 1 ,50 I F ( S U M F - 1 9 3 5 . ) 4 0 0 , 4 0 0 , 4 0 1 C D.DISCOIDEUM AMOEBAE PAGE 3 MCQUEEN 1 9 6 400 DATIM = I* . l -LDA I F (DAT IM ) 1 2 0 , 1 2 0 * 1 2 1 120 DATIM = 0 . 0 121 ADA = ( GDA*DATIM + 2 . 0 ) * * 2 . ADA = A D A * 6 . 4 5 1 6 C P . P A L L I D U M AMOEBAE PATIM = I* . l - LPA I F ( P A T I M ) 1 4 0 , 1 4 0 , 1 4 1 140 PATIM = 0 . 0 141 APA = ( GPA*PAT-IM + 2 - 0 ) * * 2 . APA = A P A * 6 . 4 5 1 6 401 SUMA = ADA+APA I F ( SUMF-19 3 5 . ) 5 0 0 , 5 0 0 , 5 0 1 500 CONTINUE C P . P A L L I D U M FRU IT ING BODY I F ( A P F - 4 0 . ) 5 0 3 , 5 0 3 , 5 0 4 503 CONTINUE PFT IM ' = LPF I F ( P F T I M ) 1 5 0 , 1 5 0 , 1 5 1 150 PFT IM = 0 . 0 151 APF = ( G P F * P F T I M ) * * 2 . APF = A P F * 6 . 4 5 1 6 C D.DISCOIDEUM FRU IT ING BODY 504 CONTINUE IF (ADF - ADA) 5 1 0 , 5 1 0 , 5 0 1 510 CONTINUE DFTIM = - LDF I F t D F T I M ) 1 3 0 , 1 3 0 , 1 3 1 130 DFTIM = 0 . 0 131 ADF = ( GDF*DFT IM 1 * * 2 . ADF = A D F * 6 . 4 5 1 6 501 SUMF = ADF + APF T I M E " I**l W R I T E ( 3 , 3 0 2 ) T I M E , A D A , A D F , A P A , A P F , S U M A , S U M F 302 F O R M A T ( F 5 . 1 , 6 F 1 0 . 2 ) 1000 CONTINUE W R I T E ( 3 , 3 0 3 ) 303 F O R M A T t l H l ) I F C T - 3 8 . ) 9 9 , 9 9 , 9 8 98 CALL EX IT END 197 PROGRAM VII - EXPLOITATION OF MIXED SPECIES Program V II s i m u l a t e s the e x p l o i t a t i o n i n t e r a c t i o n between D. discoideum and P. p a l l i d u m grown under l a b o r a t o r y c o n d i t i o n s and any temperature. The program i s g e n e r a l l y the same as Program VI wit h r e s p e c t to the s u b r o u t i n e s used and the d a t a i n p u t . The c a l c u l a t i o n s and data output have been m o d i f i e d t o account f o r e x p l o i t a t i o n . The environment (60 mm p e t r i d i s h ) c o n t a i n e d 2 2 1935 mm of space o r 1935 mm o f b a c t e r i a l lawn. The area o c c u p i e d by the two s p e c i e s growing s i m u l t a n e o u s l y i s c o n s t a n t l y monitored by the SUM f u n c t i o n . When SUM equa l s 2 1935 mm amoebae expansion s t o p s . The area 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 ies i s l i m i t e d to l / 7 t h o f the area o c c u p i e d by P. p a l l i d u m amoebae. D. discoideum f r u i t i n g b o d i e s are allowed t o co v e r the remaining a r e a . PAGE 1 MCQUEEN 198 // JOB MCQUEEN LOG DRIVE CART SPEC CART A V A I L PHY DRIVE V2 M06 ACTUAL 8K CONFIG 8!< // FOR •L I ST SOURCE PROGRAM • IOCS ( C A R D , T Y P E W R I T E R , 1 1 3 2 PR INTER,KEYBOARD) REAL N E E D ! 3 3 ) REAL KNEED DIMENSION P R O B U 0 0 ) , CUM( 100 ) , TQ ( 100 ) • READ(2 , 3 0 5 1 ) (NEED( I ) ,1 = 1,331 30 51 F O R M A T ( F 5 . 1 ) 4 0 5 3 W R I T E ( 1 , 4 0 0 0 ) 4 0 0 0 FORMAT( ' ONWARDS IS ONE • ) R E A D ( 6 , 4 0 0 i ) ON 4 0 0 1 FORMAT( F 1 0 . 5 ) I F ( O N ) 4 0 0 2 , 4 0 0 2 , 4 0 0 3 4 0 0 3 W R I T E ( 1 , 4 0 2 0 ) 4 0 2 0 FORMAT( » TEMP = ' ) R E A D ( 6 , 4 0 2 1 ) T 4 0 2 1 FORMAT ( F5 . 1) W R I T E ( 1 , 4 0 0 4 ) 4 0 0 4 FORMAT( • SPORE NUMBER IS • ) R E A D ( 6 , 4 0 0 5 ) SNUM 4 0 0 5 FORMAT(F10•5 ) AREA = 1 0 0 . X = SNUM/AREA . W R I T E { 3 , 4 0 2 2 ) T 4022 FORMAT( 1 TEMPERATURE IS ' F 5 . D W R I T E ( 3 , 4 0 0 6 ) X 4 0 0 6 FORMAT( ' MEAN SPORE NUMBER IS ' F 1 0 . 5 ) W R I T E ( 3 , 4 0 0 7 ) SNUM 4 0 0 7 FORMAT( 1 TOTAL NUMBER PER PLATE IS ' F 1 0 . 5 ) W R I T E ( 3 , 4 0 0 8 ) AREA 4 0 0 8 FORMAT! •• NUMBER OF AREA UNITS IS ' F 1 0 . 5 ) PZERO = E X P ! ( - X ) ) DO 4018 K = 1 ,100 IF (K-1) 4 0 1 0 , 4 0 1 0 , 4 0 1 1 4 0 1 0 TQ (1) = X GO TO 4012 4011 TQ(K) = ( X / K ) * T Q ( K - 1 ) 4 0 1 2 CONTINUE PROB(K) = E X P ( - X ) * T Q ( K ) I F ( K - l ) 4 0 1 3 , 4 0 1 3 , 4 0 1 4 4 0 1 3 C U M ( l ) = PZERO + P R O B ( l ) GO TO 4015 4 0 1 4 CUM(K) = CUM(K-1) + PROB(K ) 4 0 1 5 CONTINUE SQNUM = CUM(K) • AREA SQLEF = AREA - SQNUM I F ( 1 . 0 - S Q L E F ) 4 0 1 6 , 4 0 1 6 , 4 0 1 7 4 0 1 6 CONTINUE 4 0 1 8 CONTINUE 0 0 0 0 0001 0001 0000 PAGE 2 MCQUEEN 199 4 0 1 7 AVA I L = K W R I T E ( 3 , 4 0 3 0 ) AVA IL 4 0 3 0 FORMAT( ' NUMBER OF PP SPORES A V A I L A B L E = ' F 5 . 1 ) I F U - 2 1 . 7 ) 3052 , 3 0 5 2 *3053 3052 KNEED = 1 0 0 0 . GO TO 3081 3053 I F ( T - 2 5 . ) 3 0 5 4 , 3 0 5 4 , 3 0 5 5 3055 KNEED = 1. GO TO 3081 3 0 5 4 Z = ( T - 2 1 . 7 ) * 1 0 . I = Z KNEED = NEED ( I ) 3081 CONTINUE W R I T E ( 3 , 3 0 5 6 ) KNEED 3 0 5 6 FORMAT( ' KNEED = ' F 7 . 1 ) I F (KNEED - A V A I L ) 4 0 5 0 , 4 0 5 1 , 4 0 5 1 4 0 5 0 CONTINUE W R I T E ( 3 , 4 0 5 2 ) 4052 FORMAT! ' PP WILL GROW ' ) GO TO 4053 4051 CONTINUE W R I T E ( 3 , 4 0 5 4) 4 0 5 4 FORMAT( 1 PP WILL NOOOOOOOOOOT GROW ' ) WRITE ( 3 , 4 0 1 9 ) 4 0 1 9 FORMAT*1H1) GO TO 4053 4002 CALL EX IT END 2 0 0 PROGRAM V I I I - INHIBITION OF P. PALLIDUM Program V I I I s i m u l a t e s D. discoideum i n h i b i t i o n o f £• p a l l i d u m f r u i t i n g body f o r m a t i o n . The program i s composed o f two s e c t i o n s ; a v a i l a b l e clump s i z e , which c a l c u l a t e s the maximum clump s i z e a v a i l a b l e at any g i v e n spore c o n c e n t r a t i o n ; and n e c e s s a r y clump s i z e , which c a l c u l a t e s the clump s i z e n e c e s s a r y f o r f r u i t i n g at any temperature. AVAILABLE CLUMP S I Z E The c a l c u l a t i o n s of a v a i l a b l e clump s i z e are based on two assumptions. During the e x p e r i m e n t a l work i t was observed t h a t a s m a l l number of P. p a l l i d u m spores p l a c e d on an agar s u r f a c e c o n t a i n i n g a known number o f randomly d i s t r i b u t e d D. discoideum s p o r e s , were able to c o n t r o l the 2 use o f f o o d , f o r a t l e a s t t h r e e days, i n the 19 mm area s u r r o u n d i n g t h e i r p o i n t o f i n o c u l a t i o n . T h i s sphere of i n f l u e n c e i s about l/ 1 0 0 t h o f the t o t a l s u r f a c e area o f a 60 mm p e t r i d i s h . T h e r e f o r e , i t was assumed t h a t a p e t r i d i s h c o u l d be d i v i d e d i n t o 100 spheres o f i n f l u e n c e . I t was a l s o assumed t h a t when spores were spread on the s u r f a c e o f a p e t r i d i s h u s i n g Method I I (methods s e c t i o n ) t h a t they were d i s t r i b u t e d at random. A p o i s s o n d i s t r i b u t i o n was used to c a l c u l a t e the number o f spores i n each of the 100 spheres o f i n f l u e n c e . The program c o n t i n u e s to c a l c u l a t e the number o f spheres o f i n f l u e n c e c o n t a i n i n g v a r i o u s numbers o f spores u n t i l a l l o f 201 the spheres o f i n f l u e n c e have been used up= In t h i s way the maximum number o f spores per sphere o f i n f l u e n c e i s found. T h i s q u a n t i t y i s c a l l e d the maximum clump s i z e . NEEDED CLUMP SIZE The n e c e s s a r y clump s i z e i s c a l c u l a t e d by r e a d i n g data i n p u t from F i g u r e 26, on which the clump s i z e n e c e s s a r y f o r f r u i t i n g i s p l o t t e d a g a i n s t temperature. COMPARISON When the temperature and the number o f P. p a l l i d u m spores have been r e a d i n t o the computer the a v a i l a b l e and n e c e s s a r y clump s i z e can be c a l c u l a t e d . The two q u a n t i t i e s are compared and i f a v a i l a b l e i s l a r g e r than n e c e s s a r y then £• p a l l i d u m f r u i t i n g t a k e s p l a c e . PAGE 1 MCQUEEN 2 0 2 // JOB T MCQUEEN 1 LOG DRIVE 0000 CART SPEC 0001 CART A V A I L 0001 PHY DRIVE 0000 V2 M06 ACTUAL 8K CONFIG 8K •EQUAT (PRNTZ .PRNTY ) // FOR •ONE WORD INTEGERS •L I ST SOURCE PROGRAM SUBROUTINE DLAG(T»T0»TL»TH»K.C .DL ) REAL K I F ( T - 9 . 0 ) 2 0 . 2 0 . 2 1 20 DL = 9 9 9 9 . 0 0 GO TO 24 21 I F ( T - 2 7 . ) 2 2 . 2 2 , 2 3 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 ( 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 * T O * ( ( 1 . 0 ) / ( T H - T L ) ) • 1 A L O G ( A B S ( ( T - T H ) / ( T - T L ) ) ) + C 24 RETURN END FEATURES SUPPORTED ONE WORD INTEGERS CORE REQUIREMENTS FOR DLAG COMMON 0 VAR IABLES 34 PROGRAM 2 20 END OF COMPILAT ION // DUP 2 0 3 •STORE WS UA DLAG CART ID 0001 DB ADDR 5361 DB CNT 0012 // FOR •ONE WORD INTEGERS •L I ST SOURCE PROGRAM SUBROUTINE PLAG (T»TO»TL»TH•K«C«PL) REAL K I F ( T - 1 8 . ) 3 0 . 3 0 . 3 1 30 PL = 9 9 9 9 . 0 0 GO TO 34 31 I F ( T - 3 7 . ) 32 .32 . 33 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 A L O G ( A B S ( ( T - T H ) / ( T - T L ) ) ) ) + 1 K * T O * ( ( l . O ) Z ( T H - T L ) ) * 1 A L O G ( A B S ( ( T - T H ) / ( T - T L ) ) ) + C 34 RETURN END FEATURES SUPPORTED ONE WORD INTEGERS 2 0 4 CORE REQUIREMENTS FOR PLAG COMMON 0 VAR IABLES 34 PROGRAM 2 20 END OF COMPILAT ION // DUP •STORE WS UA PLAG CART ID 0001 DB ADDR 5373 DB CNT 0012 // FOR •ONE WORD INTEGERS • L I S T SOURCE PROGRAM SUBROUTINE PFGRO(T»TO»TL»TH>K ,C .PG) REAL K I F ( T - 1 8 « ) 4 0 , 4 0 , 4 1 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 ) *ALOG{ ( - 1 . 0 ) * T * * 2 .0 + ( T* ( TH+TL ))-( TH*TL> )) + 1 < • ( ( ( T H + T L ) / 2 . 0 ) * < < 1 . 0 ) / ( T H - T L ) ) * 1 A L 0 G ( A 3 S ( ( T - T H ) / ( T - T L ) ) ) ) 1 -K*TO* ( ( 1 . 0 ) / ( T H - T L ) )• 1 A L O G ( A B S ( ( T - T H ) / ( T - T L ) ) ) + C 44 RETURN END FEATURES SUPPORTED ONE WORD INTEGERS 2 0 5 CORE REQUIREMENTS FOR PFGRO COMMON 0 VAR IABLES 36 PROGRAM 2 26 END OF COMPILAT ION // DUP •STORE WS UA PFGRO CART ID 0001 DB ADDR 5385 DB CNT 0012 // FOR •ONE WORD INTEGERS •L I ST SOURCE PROGRAM SUBROUTINE DGROW ( T » TO » TL » TH »i< » C • DG ) REAL K I F I T - 9 . 0 ) 1 , 1 , 2 1 DG = 0 . 0 GO TO 5 2 I F ( T - 2 6 . 0 ) 3 , 3 , 4 4 DG = 0 . 0 GO TO 5 3 DG = (ALOG(TH-T ) ) *K*<TH-TO}-K*TH+K*T+C 5 RETURN END FEATURES SUPPORTED ONE WORD INTEGERS 2 0 6 CORE REQUIREMENTS FOR DGROW COMMON 0 VAR IABLES 8 PROGRAM 98 END OF COMPILATION // DUP •STORE WS UA DGROW CART ID 0001 . DB ADDR 5397 DB CNT 0008 // FOR •ONE WORD INTEGERS •L I ST SOURCE PROGRAM SUBROUTINE PGROW (T»TO»TL»TH»K»C»PG> REAL K I F ( T - 1 8 . ) 1 0 , 1 0 , 1 1 10 PG = 0 . 0 GO TO 14 11 I F ( T - 3 7 . ) 1 2 , 1 2 , 1 3 13 PG = 0 . 0 GO TO 14 12 PG = (ALOG (TH-T ) ) *K * {TH-TO )-K*TH+K*T+C 14 RETURN END FEATURES SUPPORTED ONE WORD INTEGERS 2 0 7 CORE REQUIREMENTS FOR PGROW COMMON 0 VARIABLES 8 PROGRAM 98 END OF COMPILATION // DUP •STORE WS UA PGROW CART ID 0001 DB ADDR 539F DB CNT 0008 // FOR •ONE WORD INTEGERS •LIST 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 IF(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 2 0 8 // FOR • IOCS (CARD»TYPEWRITER»1132 PR I NTER»KEYBOARD) •L I ST 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 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 NEED (33 ) REAL KNEED DIMENSION T IME150 ) , A D A ( 5 0 ) »ADF(50) , A P A ( 5 0 ) > A P F ( 5 Q ) , S U M A ( 5 0 ) » 1 S U M F ( 5 0 ) , P R O B ( 5 0 ) , C U M ( 5 0 ) , T Q ( 5 0 ) , D F R U ( 1 8 ! READ(2 , 3 0 5 1 ) (NEED( I ) ,1 = 1 ,33 ) 3051 F O R M A T ( F 5 . 1 ) R E A D ( 2 , 8 040 ) (DFRU( I ) ,1 = 1 ,18 ) 8 0 4 0 F O R M A T ( F 1 0 . 5 ) 99 CONTINUE W R I T E ( 1 , 4 0 0 0 ) 4 0 0 0 FORMAT( ' ONWARDS IS ONE 1 ) R E A D ( 6 , 4 0 0 1 ) ON 4 0 0 1 F O R M A T ( F 1 0 . 5 ) I F (ON) 9 8 , 9 8 , 4 0 0 3 4 0 0 3 W R I T E ( 1 , 4 0 2 0 ) 4 0 2 0 FORMAT( ' TEMP = • ) R E A D ( 6 , 4 0 2 1 ) T 4 0 2 1 F O R M A T ( F 5 . 1 ) W R I T E ( 1 , 4 0 0 4 ) 4 0 0 4 FORMAT( 1 SPORE NUMBER IS ' ) R E A D ( 6 , 4 0 0 5 ) SNUM 400 5 F O R M A T ( F 1 0 . 5 ) WRI TE (1 , 4 8 7 4 ) 4 8 7 4 FORMAT( • DD SPORE CONCENTRATION 1 ) R E A D ( 6 , 4 8 8 4 ) DDCON 48 84 F O R M A T ( F 1 0 . 5 ) AREA = 1 0 0 . X = SNUM/AREA W R I T E ( 3 , 4 0 2 2 ) T 4 0 2 2 FORMAT( • TEMPERATURE IS » F5 .1 ) W R I T E ( 3 , 4 0 0 6) X 4006 FORMAT f ' MEAN P . PALL IDUM SPORE NUMBER IS • F 1 0 . 5 ) W R I T E ( 3 , 4 0 0 7 ) SNUM 4 0 0 7 FORMAT( ' P . P A L L SPORE NUMBER PER PLATE IS ' F 1 0 . 5 ) W R I T E ( 3 , 4 0 0 8 ) AREA 400 8 FORMAT( 1 NUMBER OF AREA UNITS IS 1 F 1 0 . 5 ) PZERO = E X P ( ( - X ) ) DO 4018 K = 1 ,100 IF (K-1) 4 0 1 0 , 4 0 1 0 , 4 0 1 1 4 0 1 0 TQ (1) = X GO TO 4012 4 0 1 1 TQ(K) = ( X / K ) * T Q ( K - 1 ) 4 0 1 2 CONTINUE PROB(K) = E X P ( - X ) * T Q ( K ) I F ( K - l ) 4 0 1 3 , 4 0 1 3 , 4 0 1 4 4 0 1 3 C U M ( l ) = PZERO + P R O B ( l ) GO TO 4015 4 0 1 4 CUM(K) = C U M ( K - l ) + PROB(K) PAGE 2 MCQUEEN 2 0 9 4 0 1 5 CONTINUE SQNUM = CUM(K) * AREA SQLEF = AREA - SQNUM I F ( 1 . 0 - S Q L E F ) 4 0 1 6 , 4 0 1 6 , 4 0 1 7 4 0 1 6 CONTINUE 4018 CONTINUE 4 0 1 7 AVA I L = K W R I T E ( 3 , 4 0 3 0 ) AVA IL 4 0 3 0 FORMAT( ' NUMBER OF PP SPORES A V A I L A B L E = 1 F 5 . 1 ) I F ( T - 2 1 . 7 J 3052»3052»3053 3052 KNEED = 1 0 0 0 . GO TO 3081 3053 I F ( T - 2 5 « ) 3 0 5 4 , 3 0 5 4 * 3 0 5 5 3055 KNEED = 1. GO TO 3081 3054 Z = ( T - 2 1 . 7 ) * 1 0 . I = Z KNEED = NEED ( I ) 3081 CONTINUE W R I T E ( 3 , 3 0 5 6 ) KNEED 305 6 FORMAT( ' KNEED = ' F 7 . 1 ) I F (KNEED - A V A I L ) 4 0 5 0 , 4 0 5 0 , 4 0 5 1 40 5 0 CONTINUE W R I T E ( 3 , 4 0 5 2 ) 40 5 2 FORMAT( 1 PP WILL FRUIT ' ) GO = 1.0 GO TO 4053 4051 CONTINUE W R I T E ( 3 , 4 0 5 4 ) 4 0 5 4 FORMAT( ' PP WILL NOT FRUIT • ) GO = - 1 . 0 GO TO 4053 4 0 5 3 CONTINUE 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 C LDA = LAG FOR DD AMOEBAE C GDA = GROWTH INDEX FOR DD AMOEBAE C LDF = LAG FOR DD FRU IT ING BODIES C GDF = GROWTH INDEX FOR DD FRU IT ING BODIES C . LPA = LAG FOR PP AMOEBAE C LPF = LAG FOR PP FRU IT ING BODIES C GPA = GROWTH FOR PP AMOEBAE C GPF = GROWTH FOR PP FRU IT ING BODIES C THE DATA THAT IS INPUT SO THAT THE SUBROUTINES CAN FUNCTION C IS CODED IN FOUR PARTS THE F IRST LETTER IS L FOR LAG C OR G FOR GROWTH THE SECOND ONE OR TWO LETTERS ARE TO,TH» C T L , K , C ALL OF WHICH HAVE BEEN IDENT I F I ED B E F O R E . . . . . T H E SECOND TO PAGE 3 MCQUEEN 2 1 0 C THE LAST LETTER IS P OR D STANDING FOR PP OR D D . . . . THE LAST C LETTER IS A OR F STANDING FOR AMOEBAE OR FRU IT ING BOD Y . . . . . . AN C E X A M P L E . . L T H P A . . S T A N D S FOR LAG TEMPERATURE HIGH PP A M O E B A E . . C THIS IS THE TEMP. HIGH FOR THE PP AMOEBAE LAG SUBROUTINE C ALL OF THE FOLLOWING INFORMATION IS READ INTO THE SUBROUTINES C D.DISCOIDEUM 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 CALL DLAG (T»LTODA»LTLDA»LTHDA»LKDA•LCDA.LDA) GTODA = 2 1 . 5 GTLDA = 9 . GTHDA = 2 7 . 5 GKDA = 0 . 8 0 0 8 4 GCDA = 0 . 7 9 5 5 4 CALL DGROW (T»GTODA»GTLDA»GTHDA•GKDA»GCDA•GDA) C D.DISCOIDEUM FRU IT ING BODY LTODF = 2 4 . LTLDF = 9 . LTHDF = 2 7 . 5 LKDF = 2 . 4 7 6 8 1 LCDF = 7 . 6 2 5 4 2 CALL DLAG (T»LTODF•LTLDF•LTHDF iLKDF»LCDF*LDF) GTODF = 2 1 . GTLDF = 9 . GTHDF = 2 7 . 5 GKDF = 0 . 8 6 3 1 8 GCDF = - 0 . 6 5 3 6 8 CALL DGROW(T »GTODF»GTLDF»GTHDF,GKDF.GCDF »GDF) C P . PALL IDUM AMOEBAE LTOPA = 3 1 . LTLPA = 1 8 . LTHPA = 3 7 . LKPA = 0 . 8 1 1 3 2 LCPA = 2 . 5 9 3 5 6 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 CALL PGROW ( T»GTOPA»GTLPA»GTHPA»GKPA»GCPA»GPA) C P . PALL IDUM FRUIT ING BODY LTOPF = 3 0 . LTLPF = 1 8 . LTHPF = 3 7 . LKPF = 1 . 2 8 5 2 7 LCPF = 3 . 7 6 1 4 5 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 MCQUEEN PFGRO(T »GTOPF»GTLPF»GTHPF.GKPF »GCPF »GPF) 211 CALL DDFRU(DDCONiT»QUIT.DFRU,TQUI T) WRITE (3»491)TQUIT 491 FORMAT( 1 MAX TEMP FOR DD FRU IT ING IS ' F 1 0 . 5 ) WRITE (3#49 2) DDCON 492 FORMAT( ' D .DISCOIDEUM SPORE CONCENTRATION IS 1 F 1 0 . 5 ) IF (QUIT) 4 8 4 , 4 8 4 . 4 8 5 4 8 4 WR ITE (3»488 ) 488 FORMAT ( 1 DD WILL NOT FRUIT • ) GO TO 468 485 W R I T E ( 3 . 4 8 9 ) QUIT 489 FORMAT( ' DD WILL FRUIT BECAUSE QUIT IS ' F 1 0 . 5 ) 46 8 CONTINUE WRITE ( 3 * 3 0 9) 309 FORMAT( • LDA GDA LDF GDF LPA 1GPA LPF GP F 1 ) WRITE(3 *30 8 ) LDA»GDA»LDF,GDF•LPA.GPA* LPF»GPF 308 FORMAT(8F10 • 2) WRITE ( 3 * 3 1 0 ) 310 FORMAT(1H0) W R I T E ( 3 * 3 0 1 ) 301 FORMAT( ' T IME DDA DDF PPA PPF SUMA 1 SUMF •) C IN THE FOLLOWING AREA CALCULATIONS ARE M A D E . . . . . AREAS ARE C CALCULATED FOR DD AMOEBAE* PP AMOEBAE. DD FRU IT ING B O D I E S . C AND PP FRU IT ING BOD IES . SUMA(1) = 0 . 0 SUMF(1 ) = 0 . 0 A P F ( 1 ) = 0 . 0 ADF (1 ) = 0 . 0 DO 1000 I = 1 .50 I F ( I - l ) 7 8 . 7 8 . 7 9 79 I F ( S U M A ( I - 1 ) - 1 9 3 5 . ) 4 0 0 . 4 0 0 , 4 0 1 7 8 CONTINUE C D.DISCOIDEUM AMOEBAE 4 0 0 DATIM = I* . l -LDA I F (DAT IM ) 1 2 0 . 1 2 0 * 1 2 1 12 0 DATIM = 0 . 0 PAGE 5 MCQUEEN 212 121 A D A ( I ) = ( GDA*DATIM + 2 . 0 ) * * 2 « ADA'f I ) = ADA ( I ) #6 • 45 1 6 C P . P A L L I D U M AMOEBAE PATIM = I* . l - LPA I F ( P A T I M ) 1 4 0 , 1 4 0 , 1 4 1 140 PATIM = 0 . 0 141 A P A ( I ) = ( GPA*PAT IM + 2 « 0 ) * * 2 . A P A ( I ) = A P A ( I ) * 5 » 4 5 1 6 GO TO 936 401 A D A ( I ) = A D A ( I - l ) A P A ( I ) = A P A ( I - l ) 936 SUMA( I ) = A D A ( I ) + A P A ( I ) 1000 CONTINUE DO 1098 J = l , 5 0 C P . P A L L I D U M FRUIT ING. BODY I F (GO) 1 5 0 , 1 5 0 , 8 6 86 CONTINUE IF ( J - l ) 8 1 , 8 1 , 8 2 82 I F ( A P F ( J ~ 1 ) - A P A < 5 0 ) / 7 . 5 ) 5 0 3 , 5 0 3 * 5 0 4 81 CONTINUE 503 CONTINUE P FT IM = J t f . l - LPF I F t P F T I M ) 1 5 0 . 1 5 0 , 1 5 1 150 PFT IM = 0 . 0 151 A P F ( J ) = ( G P F * P F T I M )**2* A P F ( J ) = A P F I J ) * 6 . 4 5 1 6 GO TO 727 C D.DISCOIDEUM FRUIT ING BODY 504 CONTINUE A P F ( J ) = A P F ( J - l ) 727 I F ( Q U I T ) 1 3 0 , 1 3 0 , 6 9 5 695 I F ( J - l ) 8 3 , 8 3 , 8 4 84 I F ( A D F ( J - l ) - A D A ( 5 0 ) ) 5 1 0 , 5 1 0 , 5 0 1 83 CONTINUE 510 CONTINUE DFTIM = J * . l - LDF I F ( D F T I M ) 1 3 0 , 1 3 0 , 1 3 1 130 DFTIM = 0 . 0 131 A D F ( J ) = ( GDF*DFT IM ) * * 2 • A D F ( J ) = A D F ( J ) * 6 . 4 516 GO TO 760 501 A D F ( J ) = A D F ( J - l ) 760 SUMF ( J ) = A D F ( J ) + A P F ( J ) 1098 CONTINUE 1032 DO 1032 K = 1 ,50 T IME (K ) = K * . l CONTINUE PAGE 6 MCQUEEN 2 1 3 WRITE(3,302) (TIME(L) » ADA(L)» ADF(L) »APA(L),APF(L) iSUMA(L) »SUMF(L) » 1 L = 1,50) 3 02 FORMAT(F5.1»6F10.2) WRITE(3»303) 303 FORMAT(1H1) IF(T-38.) 99,99,98 98 CALL EXIT END 214 PROGRAM IX - COMPLETED MODEL Program IX comprises the f i n i s h e d s i m u l a t i o n model f o r D. discoideum and P. p a l l i d u m S a l v a d o r growing t o g e t h e r i n the l a b o r a t o r y at temperatures r a n g i n g from 9°C to 3 7 „ 5 ° C o The program i s composed o f s i x s u b r o u t i n e s and a m a i n l i n e program. SUBROUTINES: The f i r s t f i v e s u b r o u t i n e s have been e x p l a i n e d i n Appendix I - Program V I . The s i x t h s u b r o u t i n e d e s c r i b e s P. pa l l i d u m ' c a b i l i t y to- i n h i b i t D. disco i d e u m . The i n p u t s t o t h i s s u b r o u t i n e a r e : the t o t a l number of D. discoideum spores per p l a t e (DDCON), the temperature ( T ) , and the one di m e n s i o n a l a r r a y o f temperatures above which D. discoideum w i l l not f r u i t at any g i v e n spore c o n c e n t r a t i o n . The output i s a p o s i t i v e o r n e g a t i v e number (QUIT). P o s i t i v e i f R' discoideum can f r u i t , n e g a t i v e i f not. MAINLINE PROGRAM The m a i n l i n e program i s composed o f f o u r s e c t i o n s : i n p u t , output, c o l o n y and f r u i t i n g body expansion, and a s e c t i o n which d e s c r i b e s D. discoideum^ - a b i l i t y 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 body p r o d u c t i o n . P. p a l l i d u m i n t e r - f e r e n c e has been e x p l a i n e d i n Appendix I - Program V I I I , and expansion has been e x p l a i n e d i n Appendix I - Program VI. 215 The i n p u t i s composed o f the number o f P. p a l l i d u m spores per p l a t e , the number of D. discoideum spores per p l a t e , the growth parameters f o r the two s p e c i e s , the i n t e r - f e r e n c e d a t a i n p u t , and amount of ar e a c o v e r e d by f r u i t i n g b o d i e s and amoebae o f both s p e c i e s at any time t . The output i s d i v i d e d i n t o t h i r t e e n s e c t i o n s : (1) P. p a l l i d u m spore l a g , (2) D. discoideum spore l a g , (3) P. p a l l i d u m f r u i t i n g body l a g , (4) D. discoideum f r u i t i n g body l a g , (5) P. p a l l i d u m amoeba c o l o n y a r e a , (6) D. discoideum amoeba c o l o n y a r e a , (7) P. p a l l i d u m f r u i t i n g body area, (8) D. discoideum f r u i t i n g body a r e a , (9) temperature, (10) time, (11) n e c e s s a r y clump s i z e , (12) a v a i l a b l e clump s i z e , and (13) D. discoideum f r u i t i n g body boundary temper- a t u r e . From t h i s 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 and spore numbers can be c a l c u l a t e d . 216 A P P E N D I X I I F i g u r e 42 P. p a l l i d u m and D. discoideum 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 . P l a t e s were grown at s e v e r a l temperatures,and when f r u i t i n g body expansion 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 by f r u i t i n g b o d ies of both 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 covered i s p l o t t e d along the y - a x i s . B lack dots r e p r e s e n t D. discoideum, open 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 b l a c k dot and an open c i r c l e i n d i c a t e s t h a t both s p e c i e s f r u i t e d t o g e t h e r . The f i v e e x p e r i m e n t a l s e t s are l i s t e d (a) to (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 a r e : EXPERIMENTAL SET CON PP. CON Dd. 42-a 42-b 42-c 42-d 42-e 90 70 50 30 10 10 30 50 70 90 1 3 0 - 6.5 © i i i i * • • 1 n I p l 1 I 13.0 6-5 J J \ l » 6 ' 0 I p l L-2. I Q » I L j= 13-Oh o 6.5h 130h 6.5 h © J , L j L J 2 I _ J i i 0fl -J L 19 2 0 21 23 24 25 2 6 27 28 29 3 0 31 T E M P E R A T U R E F i q u r e 4 3 £• p a l l i d u m and D. discoideum V 1 2 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 . P l a t e s were grown at s e v e r a l temperatures, and when f r u i t - i n g body expansion 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 by f r u i t i n g b o d i e s o f both s p e c i e s was n o t e d . 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 area c o v e r e d i s p l o t t e d a long the y - a x i s . Black dots r e p r e s e n t D„ discoideum, open 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 b l a c k dot and an open c i r c l e i n d i c a t e s t h a t both s p e c i e s f r u i t e d t o g e t h e r . The f i v e e x p e r i m e n t a l s e t s are l i s t e d (a) to (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 CON PP. CON Dd. 4 3 - a 4 3-b 4 3 - c 4 3 - d 4 3 - e 6 0 0 4 6 6 3 3 3 2 0 0 6 6 6 6 2 0 0 3 3 3 4 6 6 6 0 0  F i g u r e 44 P. p a l l i d u m and D. discoideum 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 . P l a t e s were grown at s e v e r a l temperatures, and when f r u i t - i n g body expansion 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 by f r u i t i n g b o d i e s of both 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 covered i s p l o t t e d a long the y - a x i s . Black dots r e p r e s e n t D. discoideum, open 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 b l a c k dot and an open c i r c l e i n d i c a t e s t h a t both s p e c i e s f r u i t e d t o g e t h e r . The f i v e e x p e r i m e n t a l s e t s are l i s t e d (a) to (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 CON CON SET PP. Dd. 44-a 2394 266 44-b 1862 798 44-c 1330 1330 44-d 798 1862 44-e 266 2 394 13.0 6.5h « » ' ' i i ' ' LS I L 13.0 6.5 ' 1 » 1 I > I i »o j I o » 13.0 6.5 0 JL. 19 2 0 21 22 23 24 25 26 27 28 29 3 0 31 TEMPERATURE F i q u r e 45 P. p a l l i d u m and D. discoideum V12 were i n o c u l a t e d t o g e t h e r a t f iv e " ~ " r e l a t i v e c o n c e n t r a t i o n s . P l a t e s were grown a t s e v e r a l temperatures, and when f r u i t - i n g body expansion 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 by f r u i t i n g b o d ies of both s p e c i e s was not e d . 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 area covered i s p l o t t e d a l o n g the y - a x i s . Black dots r e p r e s e n t D. discoideum, open 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 b l a c k dot and an open c i r c l e i n d i c a t e s t h a t both s p e c i e s f r u i t e d t o g e t h e r . The f i v e e x p e r i m e n t a l s e t s are l i s t e d (a) to (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 CON PP. CON Dd. 45-a 45-b 45-c 45-d 45-e 14400 11200 8000 4800 1600 1600 4800 8000 11200 14400 • • 13-0 a 4 ' 6.5 - i i i i i lO i O 1 i i b • • • • • 13.0 6-5 i i i i « 1 1 Q-i .° 1 ° 1 13.0- 13.0- 6.5 [ » 1 i L <"> » <Q 8 I I 1> 13.0- 19 2 0 21 22 23 24 25 2 6 27 T E M P E R A T U R E 28 29 3 0 31 F i q u r e 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 the change 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 shaded areas 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 , the v e r t i c a l l y shaded areas by D. discoideum f r u i t i n g b o d i e s . The areas shaded 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 of both s p e c i e s . The unshaded areas were unoccupied. Temperature i s marked a t i n t e r v a l s under each diagram.  F i g u r e 4 7 C u l t u r e g r a d i e n t I I I . G r a d i e n t drawings showing the change 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 shaded areas 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 ; the v e r t i c a l l y shaded areas by D. discoideum f r u i t i n g b o d i e s . The areas shaded 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 both s p e c i e s . The unshaded areas were unoccupied. Temperature i s marked a t i n t e r v a l s under each diagram.  F i g u r e 48 C u l t u r e g r a d i e n t IV. G r a d i e n t 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. discoideum 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 shaded areas 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 ; the v e r t i c a l l y shaded area by D. discoideum f r u i t i n g b o d i e s . The areas shaded with 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 of both s p e c i e s . The unshaded areas were uno c c u p i e d . Temperature i s marked at i n t e r v a l s under each diagram.  F i g u r e 49 C u l t u r e g r a d i e n t drawings demonstrating 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 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 not change i n response t o 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 shaded areas 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 . The v e r t i c a l l y shaded areas by D . discoideum f r u i t i n g b o d i e s . The areas shaded w i t h both 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 by f r u i t i n g b o d ies o f both s p e c i e s . The unshaded areas were not o c c u p i e d by any f r u i t i n g b o d i e s . Temperature i s marked at i n t e r v a l s under each diagram. The s e t s were made up o f the f o l l o w i n g : SET # GRADIENT # P. PALLIDUM D. DISCOIDEUM 1 A g r a d . 1-K VC4 stock 1 B stock g r a d . 1-K 2 A grad. 1-L DF stock 2 B stock g r a d . 1-L 3 A g r a d . 2-K DF stock 3 B stock g r a d . 2-K 4 A g r a d . 2-K VC4 stock 4 B stock grad. 2-L  F i g u r e 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 (changed) 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 alone (A, B, C) but l o s t t h i s a b i l i t y when grown wit 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 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 . V e r t i c a l l y shaded areas D. d i s c o i d e u m . Areas shaded both ways c o n t a i n both s p e c i e s . 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 alo n g the x - a x i s . D F i g u r e 51 C u l t u r e g r a d i e n t drawings demonstrating t h a t some P. p a l l i d u m c l o n e s have 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 not (A, B, C, D). The c l o n e d spores came from a stock c u l t u r e . 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 . V e r t i c a l l y shaded areas D. discoideum 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 along the x - a x i s .  F i g u r e 52 C u l t u r e g r a d i e n t drawings demonstrating t h a t D. d i s c o i d e u m amoebae are produced and grow above 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 about 24 - 25°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 . V e r t i c a l l y shaded, areas D. discoideum V12 f r u i t i n g b o d i e s . Areas shaded both ways c o n t a i n both 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 along the 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 the 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. discoideum v e g e t a t i v e amoebae.  2 2 8 APPENDIX I I I 2 2 9 GOODNESS OF F I T OF EQUATION ( l c ) I f amoebae and f r u i t i n g body c o l o n i e s expand a t r a t e s w h i c h a r e p r o p o r t i o n a l t o t h e c o l o n y c i r c u m f e r e n c e t h e n e q u a t i o n ( l c ) s h o u l d d e s c r i b e t h e way i n w h i c h c o l o n i e s expand. The a p p l i c a b i l i t y o f e q u a t i o n ( l c ) was t e s t e d by g r o w i n g c u l t u r e s , n o t i n g t h e a r e a c o v e r e d a t v a r i o u s t i m e i n t e r v a l s and p l o t t i n g t h e s q u a r e r o o t o f a r e a a g a i n s t t i m e . Both amoeba and f r u i t i n g body 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 s q u a r e r o o t o f a r e a and t i m e . Example c u l t u r e s were r u n and p l o t t e d ( F i g . 11, 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 can o n l y be measured f o u r o r f i v e t i m e s d u r i n g i t s growth p e r i o d o n l y f o u r o r f i v e d a t a p o i n t s a r e a v a i l a b l e . I t might 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 f rom t h e f a c t t h a t o n l y a few d a t a p o i n t s were used t o f i t each r e g r e s s i o n l i n e . 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 , and t h a t 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 do e x i s t between t h e square r o o t o f a r e a and t i m e , t h e d a t a 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 t o g e t h e r . S i n c e each c u l t u r e t h a t was used was grown 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 from b o t h P. p a l l i d u m and D. d i s c o i d e u m were i n c l u d e d ; each d a t a p o i n t had t o be t r a n s f o r m e d w i t h r e s p e c t t o a r e a and t i m e . I t was a r b i t r a r i l y d e c i d e d t h a t t h e d a t a would be t r a n s f o r m e d t o f i t a s t r a i g h t l i n e p a s s i n g t h r o u g h z e r o and h a v i n g a s l o p e o f t h r e e . T h i s r e l a t i o n s h i p i s d e s c r i b e d by: A T^ = 3t (7) 230 where A T i s the transformed area and t i s time. The equation f o r a regression l i n e r e s u l t i n g from any one culture was: h2 = | + b»t ( 8 ) where a i s the y int e r c e p t and b i s the slope. To transform equation ( 8 ) to equation (7), a/b must be subtracted from the r i g h t hand side, and both sides must be divided by 3/b, producing: U •A = 3*t (9) b and s u b s t i t u t i n g equation (7) into (9): A T 2 = %'h2 (10) The transformed square root of area was p l o t t e d against the transformed time (t - a/b). Both D. discoideum and P. pallidum amoeba colony expansion data ( F i g . 53) and f r u i t i n g body colony expansion data ( 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 predicted by equation ( l c ) . These data represent f i n a l proof that ( l c ) does describe both amoeba and f r u i t i n g body colony expansion and that 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 of a small number of data p o i n t s . Fiqure 5 3 The square root of amoeba colony area i s p l o t t e d against time f o r both D. discoideum ( s o l i d dots) and P. pallidum (open c i r c l e s ) . A l l data i s transformed to conform to the l i n e described by - 3 t , where A i s area and t i s . time. 6 4 O 321 co oo " o • o So •2° of "o o o o o oo 0 2 3 TIME-DAYS F i g u r e 54 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 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 (open c i r c l e s ) . A l l d a t a i s t r a n s f o r m e d t o c o n f o r m t o t h e 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 6 4 < UJ DC < o o DC 6 32j CO o o O 0 0 e o o • o o oo O L i _j 1 L . 1 2 3 4 TIME-DAYS 2 3 3 APPENDIX IV 234 STATISTICAL SIGNIFICANCE OF EQUATIONS (2b), ( 3 c ) , AND (4b) Throughout r e s u l t s s e c t i o n I e q u a t i o n s (2b), ( 3 c ) , and (4b) were f i t t o the amoeba c o l o n y expansion d a t a , the f r u i t i n g body expansion d a t a , the spore g e r m i n a t i o n l a g d a t a , and the f r u i t i n g body l a g d a t a . The l e a s t o f squares method (Appendix I , Programs I , IV, V) was used t o ensure t h a t the b e s t l i n e from the f a m i l y of l i n e s d e s c r i b e d by (2b) o r (3c) o r (4b) was used f o r each s e t o f d a t a . But t h i s procedure d i d not a t t a c h any s t a t i s t i c a l s i g n i f i c a n c e to the d e s c r i p t i v e a b i l i t y o f the l i n e chosen. T h i s second s t e p was a c h i e v e d by c a l c u l a t i n g the t o t a l d e v i a t i o n around the mean y v a l u e , the d e v i a t i o n unaccounted f o r by the d e s c r i p t i v e l i n e , and f i n a l l y the d e v i a t i o n s accounted f o r by the l i n e . From t h i s the c o r r e l a t i o n c o e f f i c i e n t s were c a l c u l a t e d ( T a b l e X I V ) . In e v e r y case except one the observed d a t a and the f i t t e d l i n e were i n agreement at the 95% l e v e l o f c o n f i d e n c e . The one case ( F i g . 20) t h a t f a i l e d was r e p l a c e d by F i g u r e 21 i n which a s p e c i a l e q u a t i o n (4b) was used to d e s c r i b e the P. p a l l i d u m f r u i t i n g body expansion d a t a . 235 TABLE XIV The p r o p o r t i o n o f v a r i a b i l i t y accounted f o r by eq u a t i o n s (2b), ( 3 c ) , and (4b) and the s i g n i f i c a n c e o f the f i t i s l i s t e d f o r the f i g u r e s i n which 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 . FIGURE NUMBER PROPORTION VARIABILITY ACCOUNTED CORRELATION COEFFICIENT df SIGNIFICANT AT 95% LEVEL 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

Cite

Citation Scheme:

    

Usage Statistics

Country Views Downloads
China 16 0
Canada 3 0
United States 3 1
City Views Downloads
Hangzhou 8 0
Unknown 4 0
Dongguan 4 0
Beijing 4 0
Redmond 1 0
Ashburn 1 0

{[{ mDataHeader[type] }]} {[{ month[type] }]} {[{ tData[type] }]}

Share

Share to:

Comment

Related Items