Travels in (C-S-R) space:
adventures with cellular automata
Presentation ready
with acknowledgements to
Ric Colasanti (Corvallis)
Andrew Askew (Sheffield)
CA in a community of virtual plants
Contrasting tones represent
patches of resource depletion
This is a single propagule of a
virtual plant
It is about to grow in a
resource-rich above- and
below-ground environment
The plant has produced abundant
growth above- and below-ground
and zones of resource depletion
have appeared
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 !
An end module
Below-ground binary tree ( = root system)
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
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 …
3000
Size
Biomass (modules per plant)
2500
2000
1500
1000
Light 1 Nutrient 6
Light 2 Nutrient 6
Time
500
Light 1 Nutrient 8
Light 2 Nutrient 8
0
0
20
40
60
80
Time (iterations)
100
120
140
Partitioning between root
and shoot
S-shaped growth curves
10000
1 .3
Allometric coefficient
Individual size
R o o t/s h o o t a llo m e tric c o e ffic ie n t
Self-thinning
line
1 .1
1 L ig h t u n it
2 L ig h t u n it s
1
0 .9
Foraging towards
resources
Biomass (modules) per plant
1000
1 .2
Slope -2/1
100
10
1
0
5
10
15
U n its o f n u trie
n t p e r c e ll
Below-ground
resource
Functional equilibria
20
1
10
Population density
100
Planting density
Self-thinning in crowded populations
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?
‘ 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
Category 1: Stress
Phenomena which restrict plant production
e.g. shortages of light, water, mineral
nutrients, or non-optimal temperature
Category 2: Disturbance
Phenomena which destroy plant production
e.g. herbivory, pathogenicity, trampling,
mowing, ploughing, wind damage, frosting,
droughting, soil erosion, burning
Habitats may experience stress and disturbance to any
degree and in any combination
Stress
Disturbance
Low or moderate combinations of stress and
disturbance can support vegetation …
Stress
Disturbance
… but extreme combinations of stress and
disturbance cannot
There are other ways of describing stress
and disturbance
Stress
Habitat productivity
(= resource level)
Disturbance
Habitat duration
In the domain where vegetation is possible …
S
Stress-tolerator where S is
high but D is low
Stress
Competitor
where both S
and D are low
C
R
Disturbance
Ruderal where S is
low but D is high
… plant life has evolved different strategies for
dealing with the different combinations
… and these are
the ‘habitats’
where no plant
life occurs at all
S
So this is ‘C-S-R
space’ …
C
R
To navigate in C-S-R space we bend the universe a little …
S
C
R
S
C
R
S
C
R
S
C
R
S
C
R
S
C
R
S
C
R
C
R
S
C
S
R
C
S
R
C
R
S
C
R
S
C
R
S
… and recognize an
intermediate type
C
CSR
R
S
… with further
intermediates here
CR
R
C
CSR
SR
CS
S
… and yet more
intermediates here
CR
R
C
CSR
SR
CS
S
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 ”
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
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 …
Combinations of plant attributes for seven C-S-R functional types
—————————————————————————————
Functional
Module
Module
Propensity to
type
size
longevity
flowering
—————————————————————————————
C
High
Low
Low
S
Low
High
Low
R
Low
Low
High
SC
Medium
Medium
Low
SR
Low
Medium
Medium
CR
Medium
Low
Medium
CSR
Medium
Medium
Medium
—————————————————————————————
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
Let’s see some competition between
different types of plant
Initially we will use only two types …
Small size,
rapid growth
and fast
reproduction
Medium size,
moderately fast
in growth and
reproduction
(Red enters its 2nd generation)
White has won !
Now let’s see if white always wins
This time, the opposition is rather different …
Medium size,
moderately fast
in growth and
reproduction
Large size,
very fast
growing, slow
reproduction
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 …
So competition can be demonstrated
realistically …
… but most real communities involve more
than two types of plant
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
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
The blue type has eliminated almost
everything except white and green types
And the simulation has almost run out of
space again …
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)
(a gap has appeared here)
(red tries to colonize)
(but is unsuccessful)
White, green and yellow finally predominate …
… blue is nowhere to be seen …
… and total biomass is much reduced
Environmental gradients can be simulated
by increasing resource levels in steps
Whittaker-type niches then appear for
contrasting plant types within these gradients
% Biomass in mixture
100
80
60
C
S
40
SC
(types)
20
0
0
5
10
15
20
25
Resource (= 1/stress)
30
Let’s grow the equal mixture of all seven
types again …
… but this time under an environmental
gradient of increasing mineral nutrient
resource
Number of plant types
surviving (max 7)
5
Greatest biodiversity is
at intermediate stress
4
3
2
1
0
0
5
10
15
20
25
Resources (= 1/stress)
30
35
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
So we grow the equal mixture of all seven
types again …
… under an environmental gradient of increasing
‘trampling’ disturbance
Number of plant types
surviving (max 7)
2
Greatest biodiversity is at
intermediate disturbance …
… but the final
number of types is low
1
0
0
0.2
0.4
0.6
0.8
Probability of disturbance
1
Environmental stress and disturbance can, of
course, be applied together …
… and this can be done in all forms and
combinations
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
Number of plant types
surviving (max 7)
Greatest biodiversity is at intermediate productivity
5
R 2 = 0.534
4
3
2
1
0
0
2000 4000
6000
8000 10000 12000
Total biomass (productivity)
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
Number of plant types
surviving (max 7)
5
R 2 = 0.534
4
3
2
1
0
0
2000 4000
6000
8000 10000 12000
Total biomass (productivity)
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.
And as the modular rulebase is simply a string of numbers
2314232122133123
which controls how big, how much, how long, how often …
(seems familiar?)
… we can modify this virtual
genome wherever we like 2 3 1 4 2 3 2 1 2 2 1 3 3 1 2 3
either accurately 2 3 1 4 2 3 2 1 2 2 1 2 3 1 2 3
or inaccurately
2314232122321123
and then follow the downstream consequences of GM
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?
http://www.ex.ac.uk/~rh203/