1. Travels in (C-S-R) space: adventures with cellular automata
Titles
Travels in (C-S-R) space:
adventures with cellular automata
Presentation ready
with acknowledgements to
Ric Colasanti (Corvallis)
Andrew Askew (Sheffield)

2. CA in a community of virtual plants
Community image
CA in a community of virtual plants
Seven different types of virtual plant are growing in this ‘community’.
The contrasting tones show patches of resource depletion in the above- and below-ground environments.
Contrasting tones represent patches of resource depletion

3. This is a single propagule of a virtual plant
CSR type, frame 1
This is a single propagule of a virtual plant
It is about to grow in a resource-rich above- and below-ground environment
This is a single plant propagule which is about to grow in a resource-rich environment.
(During a Slide Show the next nineteen slides display automatically in an animated sequence.)

4. ditto f. 2

5. ditto f. 3

6. ditto f. 4

7. ditto f. 5

8. ditto f. 6

9. ditto f. 7

10. ditto f. 8

11. ditto f. 9

12. ditto f. 10

13. ditto f. 11

14. ditto f. 12

15. ditto f. 13

16. ditto f. 14

17. ditto f. 15

18. ditto f. 16

19. ditto f. 17

20. ditto f. 18

21. ditto f. 19

22. The plant has produced abundant growth above- and below-ground
ditto f. 20
The plant has produced abundant growth above- and below-ground
The plant has produced abundant growth both above- and below-ground.
Distinct zones of resource depletion have emerged.
and zones of resource depletion have appeared

23. Each plant is built-up like this
Binary tree diagram
Above-ground binary tree ( = shoot system)
Each plant is built-up like this
A branching module
Above-ground array
Above-ground binary tree base module
Below-ground array
Below-ground binary tree base module
This is only a diagram, not a painting !
This is the structure of the self-assembling plant.
It is a schematic diagram only, it is not meant to look like a real plant.
The end-modules capture resources (light and CO2 from above-ground, water and nutrients from below-ground).
The branching, or parent, modules can pass resources to any other modules to which they are connected.
An end module
Below-ground binary tree ( = root system)

24. The end-modules capture resources:
Explanation
The end-modules capture resources:
Light and carbon dioxide from above-ground
Water and nutrients from below-ground
The branching modules (parent or offspring) can pass resources to any adjoining modules
In this way whole plants can grow

25. Explanation
The virtual plants interact with their environment (and with their neighbours) just like real ones do
They possess most of the properties of real individuals and populations
For example …

26. S-shaped growth curves Partitioning between root and shoot
Explanation
Size
Time
S-shaped growth curves
Partitioning between root and shoot
Allometric coefficient
Individual size
Self-thinning line
Foraging towards resources
Below-ground resource
Population density
Functional equilibria
Self-thinning in crowded populations

27. All of these plants have the same specification (modular rulebase)
Explanation
All of these plants have the same specification (modular rulebase)
And this specification can easily be changed if we want the plants to behave differently…
For example, we can recreate J P Grime’s system of C-S-R plant functional types
But what is that exactly?

28. ‘ The external factors which limit the amount of living and dead plant material present in any habitat may be classified into two categories ’
Opening sentence from J P Grime’s 1979 book Plant Strategies and Vegetation Processes

29. Category 1: Stress
Phenomena which restrict plant production
e.g. shortages of light, water, mineral nutrients, or non-optimal temperature

30. Category 2: Disturbance
Phenomena which destroy plant production
e.g. herbivory, pathogenicity, trampling, mowing, ploughing, wind damage, frosting, droughting, soil erosion, burning

31. Habitats may experience stress and disturbance to any degree and in any combination

32. Low or moderate combinations of stress and disturbance can support vegetation …
… but extreme combinations of stress and disturbance cannot

33. There are other ways of describing stress and disturbance
Habitat productivity (= resource level)
Stress
Disturbance
Habitat duration

34. In the domain where vegetation is possible …
Stress-tolerator where S is high but D is low S
Stress
Ruderal where S is low but D is high
Competitor where both S and D are low C R
Disturbance
… plant life has evolved different strategies for dealing with the different combinations

35. … and these are the ‘habitats’ where no plant life occurs at all
So this is ‘C-S-R space’ … C R

36. To navigate in C-S-R space we bend the universe a little …

37. S C R

38. S C R

39. S C R

40. S C R

41. S C R

42. S C R

43. C S R

44. C S R

45. C S R

46. C R S

47. C R S

48. C R S

49. … and recognize an intermediate type
CSR R S

50. … with further intermediates hereC CR CS
CSR R SR S

51. … and yet more intermediates hereC CR CS
CSR R SR S

52. So, how does all this relate to real vegetation?
The high dimensionality of real plant life is reduced to plant functional types
“ There are many more actors on the stage than roles that can be played ”

53. And what does that mean, exactly?
Functional types provide a continuous view of vegetation when relative abundances, and even identities, of constituent species are in flux
Tools that allocate C-S-R type to species, and C-S-R position to whole communities, can link separate vegetation into one conceptual framework
Then effects of environment or management on biodiversity, vulnerability and stability can be evaluated on a common basis

54. We can recreate C-S-R plant functional types within the self-assembling model …
… if we change the rulebases controlling morphology, physiology and reproductive behaviour …

55. We use one morphological trait, one physiological and one reproductive to distinguish between the seven types.
However, these are really super-traits, e.g. longevity in the absence of resource uptake is entrained with relative growth rate, specific leaf area, palatability and decomposability.
With three levels possible within each of three traits, 27 different types could be constructed.
However, we model only seven types; the other twenty would include ‘Darwinian demons’ that do not respect evolutionary tradeoffs.

56. Explanation
With three levels possible in each of three traits, 27 simple functional types could be constructed
However, we model only 7 types; the other 20 would include Darwinian Demons that do not respect evolutionary tradeoffs

57. Let’s see some competition between different types of plant
Explanation
Let’s see some competition between different types of plant
Initially we will use only two types …

58. Small size, rapid growth and fast reproduction
R-CSR-R, frame 1
Small size, rapid growth and fast reproduction
Medium size, moderately fast in growth and reproduction
The two young red plants are small-sized, rapidly growing and fast reproducing.
The single young white plant is more moderate in all three of these traits.
(The next nineteen slides animate.)

59. ditto f. 2

60. ditto f. 3

61. ditto f. 4

62. ditto f. 5

63. ditto f. 6

64. ditto f. 7

65. ditto f. 8

66. (Red enters its 2nd generation)
ditto f. 9
(Red enters its 2nd generation)

67. ditto f. 10

68. ditto f. 11

69. ditto f. 12

70. ditto f. 13

71. ditto f. 14

72. ditto f. 15

73. ditto f. 16

74. ditto f. 17

75. ditto f. 18

76. ditto f. 19

77. ditto f. 20
White has won !
The longer-lived white plant has outcompeted the red ones, despite the latters’ frequent attempts at re-establishment.
However, if there had been periodic disturbances there would have been the reverse outcome.

78. Now let’s see if white always wins
Explanation
Now let’s see if white always wins
This time, the opposition is rather different …

79. Medium size, moderately fast in growth and reproduction
CSR-C-CSR, frame 1
Medium size, moderately fast in growth and reproduction
Large size, very fast growing, slow reproduction
The two young white plants are again moderate in all three traits.
The single young blue plant has a rulebase which gives it large modules, rapid growth and slow-reproduction.
(The next 22 slides animate.)

80. ditto f.2

81. ditto f.3

82. ditto f.4

83. ditto f.5

84. ditto f.6

85. ditto f.7

86. ditto f.8

87. ditto f.9

88. ditto f.10

89. ditto f.11

90. ditto f.12

91. ditto f.13

92. ditto f.14

93. ditto f.15

94. ditto f.16

95. ditto f.17

96. ditto f.18

97. ditto f.19

98. ditto f.20

99. ditto f.21

100. ditto f.22

101. ditto f.23
The huge blue plant has outcompeted the white ones both above- and below-ground.
However, if there had been fewer resources there would have been the reverse outcome.

102. And the simulation has run out of space …
Explanation
The huge blue type has out-competed both of the white plants, both above- and below-ground
And the simulation has run out of space …

103. ditto f.23 again
The huge blue plant has outcompeted the white ones both above- and below-ground.
However, if there had been fewer resources there would have been the reverse outcome.

104. So competition can be demonstrated realistically …
Explanation
So competition can be demonstrated realistically …
… but most real communities involve more than two types of plant

105. Explanation
We need seven functional types to cover the entire range of variation shown by herbaceous plant life
To a first approximation, these seven types can simulate complex community processes very realistically

106. Explanation
For example, an equal mixture of all seven types can be grown together …
… in an environment which has high levels of resource, both above- and below-ground

107. 7 types, high nutrient, f.1
These young plants are of seven different types, all about to grow in a rich environment.
(The next nineteen slides animate.)

108. ditto f.2

109. ditto f.3

110. ditto f.4

111. ditto f.5

112. ditto f.6

113. ditto f.7

114. ditto f.8

115. ditto f.9

116. ditto f.10

117. ditto f.11

118. ditto f.12

119. ditto f.13

120. ditto f.14

121. ditto f.15

122. ditto f.16

123. ditto f.17

124. ditto f.18

125. ditto f.19

126. ditto f.20
The eventual winners are those types with medium- or large-sized modules.

127. And the simulation has almost run out of space again …
Explanation
The blue type has eliminated almost everything except white and green types
And the simulation has almost run out of space again …

128. ditto f.20 again
The eventual winners are those types with medium- or large-sized modules.

129. Now let’s grow the equal mixture of all seven types again …
Explanation
Now let’s grow the equal mixture of all seven types again …
… but this time the environment has low levels of mineral nutrient resource
(as indicated by the many grey cells)

130. 7 types, low nutrient, f.1
These are the same seven types, but this time about to grow in a poor environment.
(The next 21 slides animate.)

131. ditto f.2

132. ditto f.3

133. ditto f.4

134. ditto f.5

135. ditto f.6

136. ditto f.7

137. ditto f.8

138. ditto f.9

139. ditto f.10

140. ditto f.11

141. ditto f.12

142. (a gap has appeared here)
ditto f.13
(a gap has appeared here)

143. ditto f.14

144. (red tries to colonize)
ditto f.15
(red tries to colonize)

145. ditto f.16

146. ditto f.17

147. ditto f.18

148. ditto f.19

149. ditto f.20
(but is unsuccessful)

150. ditto f.21

151. ditto f.22
The eventual winners are those types with small- or medium-sized modules.
Total biomass is much reduced, too.

152. White, green and yellow finally predominate …
Explanation
White, green and yellow finally predominate …
… blue is nowhere to be seen …
… and total biomass is much reduced

153. ditto f.22 again
The eventual winners are those types with small- or medium-sized modules.
Total biomass is much reduced, too.

154. Explanation
Environmental gradients can be simulated by increasing resource levels in steps
Whittaker-type niches then appear for contrasting plant types within these gradients

155. Whittaker-type gradient
(types)
Environmental gradients can be simulated by increasing resource levels in steps.
Whittaker-type niches appear for contrasting plant types within these gradients.

156. Let’s grow the equal mixture of all seven types again …
Explanation
Let’s grow the equal mixture of all seven types again …
… but this time under an environmental gradient of increasing mineral nutrient resource

157. Greatest biodiversity is at intermediate stress
Stress-driven hump
Greatest biodiversity is at intermediate stress
The resource gradient controls how many types survive from an initial planting of all seven types.
This result reproduces Grime’s ‘stress-driven humpbacked model’ (1973).

158. Explanation
Remember that environmental disturbance was defined as ‘removal of biomass after it has been created’
Trampling is therefore a disturbance
It can be simulated by removing shoot material from certain sizes of patch at certain intervals of time and in a certain number of places

159. So we grow the equal mixture of all seven types again …
Explanation
So we grow the equal mixture of all seven types again …
… under an environmental gradient of increasing ‘trampling’ disturbance

160. Disturbance-driven hump
Greatest biodiversity is at intermediate disturbance …
… but the final number of types is low
Disturbances can be applied which simulate trampling, e.g. they can remove above-ground biomass in patches.
A disturbance gradient controls how many types survive from an initial planting of all seven types.
This result reproduces Grime’s ‘disturbance -driven humpbacked model’ (1973) …
…. and also Connell’s ‘intermediate disturbance hypothesis’ (1979).

161. Explanation
Environmental stress and disturbance can, of course, be applied together …
… and this can be done in all forms and combinations

162. So, again we grow the equal mixture of all seven types …
Explanation
So, again we grow the equal mixture of all seven types …
… but in all factorial combinations of seven levels of stress and seven levels of disturbance

163. Productivity-driven hump
Greatest biodiversity is at intermediate productivity
When we apply both stress and disturbance in factorial combinations, total biomass varies enormously.
The biomass gradient controls how many types survive from an initial planting of all seven types.
This result reproduces Grime’s ‘biomass-driven humpbacked model’ (1979), one of the highest-level properties that plant communities possess.

164. Explanation
The biomass-driven ‘humpbacked’ relationship is one of the highest-level properties that real plant communities possess
Yet it emerges from the model solely because of the resource-capturing activity of modules in the self-assembling plants

165. Productivity-driven hump
When we apply both stress and disturbance in factorial combinations, total biomass varies enormously.
The biomass gradient controls how many types survive from an initial planting of all seven types.
This result reproduces Grime’s ‘biomass-driven humpbacked model’ (1979), one of the highest-level properties that plant communities possess.

166. These are all real experiments with virtual plants
… and the plant, population and community processes all emerge from the one modular rulebase
We can now ‘plant’ whole communities of any kind and subject them to different environments or management regimes
Then we can look at topics such as biodiversity, vulnerability, resistance, resilience, stability, habitat / community heterogeneity, etc, etc.

167. And as the modular rulebase is simply a string of numbers
which controls how big, how much, how long, how often …
(seems familiar?)
… we can modify this virtual genome wherever we like
either accurately
or inaccurately
and then follow the downstream consequences of GM

168.  In real experiments with virtual plants …
One overnight run on one PC
Approx. 100 person-years of growth experiments 
(not including the transgenic work!)
Any takers?

169. (Dissolve to black)