with acknowledgements to

Travels in (C-S-R) space:

adventures with cellular automata

Ric Colasanti (Corvallis)Andrew Askew (Sheffield)

Presentation ready

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 base module

Below-ground binary tree base module

Above-ground array

Below-ground array

Above-ground binary tree ( = shoot system)

Below-ground binary tree ( = root system)

A branching module

An end module

Each plant is built-up like this

This is only a diagram, not a painting !

Water and nutrients from below-ground

The branching modules (parent or offspring) can pass resources to any adjoining modules

The end-modules capture resources:

Light and carbon dioxide from above-ground

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 …

S-shaped growth curves Partitioning between root and shoot

Functional equilibria

Foraging towards resources

Self-thinning in crowded populations

0

500

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0 20 40 60 80 100 120 140Time (iterations)

Bio

mas

s (m

odul

es p

er p

lant

)

Light 1 Nutrient 6 Light 2 Nutrient 6

Light 1 Nutrient 8 Light 2 Nutrient 8

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0 5 10 15 20Units of nutrient per cell

1 Light unit

2 Light units

Root/shoot allometric coefficient

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1 10 100

Planting density

Bio

mass (

mo

du

les)

per

pla

nt

Slope -2/1

Size

Time

Allometric coefficient

Below-ground resource

Individual sizeSelf-thinning line

Population density

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

Disturbance

Habitat duration

Habitat productivity (= resource level)

In the domain where vegetation is possible …

Stress

Disturbance

… plant life has evolved different strategies for dealing with the different combinations

Competitor where both S and D are low

Stress-tolerator where S is high but D is low

Ruderal where S is low but D is high

C

S

R

C

S

RSo this is ‘C-S-R space’ …

… and these are the ‘habitats’ where no plant life occurs at all

C

S

R

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

C

S

R

C

S

R

C

S

R

C

S

R

C

S

R

C

S

R

C S

R

C

S

R

C

S

R

C

SR

C

R S

C

R S

C

R S

CSR

… and recognize an intermediate type

C

R S

CSRCR CS

SR

… with further intermediates here

C

R S

CSRCR CS

SR

… and yet more intermediates here

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

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0 5 10 15 20 25 30

Resource (= 1/stress)

% B

iom

ass

in m

ixtu

re

C

S

SC

(types)

Let’s grow the equal mixture of all seven types again …

… but this time under an environmental gradient of increasing mineral nutrient resource

0

1

2

3

4

5

0 5 10 15 20 25 30 35

Resources (= 1/stress)

Num

ber o

f pla

nt ty

pes

surv

ivin

g (m

ax 7

)

Greatest biodiversity is at intermediate stress

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

0

1

2

0 0.2 0.4 0.6 0.8 1

Probability of disturbance

Num

ber

of p

lant

type

s su

rviv

ing

(max

7)

Greatest biodiversity is at intermediate disturbance …

… but the final number of types is

low

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

R 2 = 0.534

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0 2000 4000 6000 8000 10000 12000

Total biomass (productivity)

Num

ber o

f pla

nt ty

pes

surv

ivin

g (m

ax 7

)

Greatest biodiversity is at intermediate 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

R 2 = 0.534

0

1

2

3

4

5

0 2000 4000 6000 8000 10000 12000

Total biomass (productivity)

Num

ber o

f pla

nt ty

pes

surv

ivin

g (m

ax 7

)

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 numbers2 3 1 4 2 3 2 1 2 2 1 3 3 1 2 3

which controls how big, how much, how long, how often …

2 3 1 4 2 3 2 1 2 2 1 3 3 1 2 3

2 3 1 4 2 3 2 1 2 2 1 2 3 1 2 3

2 3 1 4 2 3 2 1 2 2 3 2 1 1 2 3

(seems familiar?)

… we can modify this virtual genome wherever we like

either accurately

or inaccurately

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/