Modelling complex communities – measuring what matters? Jim Bown, Janine Illian and John Crawford University of Abertay Dundee [email protected].

Modelling complex communities –

measuring what matters?

Jim Bown, Janine Illian and John Crawford

University of Abertay Dundee

[email protected]

The soil microbial system

• More diversity in the palm of your hand than in the mammalian kingdom

• Most important and abused ecosystem in the world

• Essential features– Species concept not useful– Feedback and feedforward coupling to dynamic

environment is central– Functionality– Can’t measure much (anything)

The soil microbial system

• More diversity in the palm of your hand than in the mammalian kingdom

• Most important and abused ecosystem in the world

• Essential features– Species concept not useful– Feedback and feedforward coupling to dynamic

environment is central– Functionality– Can’t measure much (anything)Most ecological theory

Most ecological theory

ignores individual ignores individual

variation within species

variation within species

groupsgroups

Any Any

ecosystemecosystem

The soil microbial system

• More diversity in the palm of your hand than in the mammalian kingdom

• Most important and abused ecosystem in the world

• Essential features– Species concept not useful– Feedback and feedforward coupling to dynamic

environment is central– Functionality– Can’t measure much (anything)

The fact that individuals

The fact that individuals

bothboth affect and are affect and are

affected by their local

affected by their local

environment is often environment is often

ignoredignored

Any Any

ecosystemecosystem

The soil microbial system

• More diversity in the palm of your hand than in the mammalian kingdom

• Most important and abused ecosystem in the world

• Essential features– Species concept not useful– Feedback and feedforward coupling to dynamic

environment is central– Functionality– Can’t measure much (anything)

Diversity measures Diversity measures

do not link dynamics do not link dynamics

to functionto function

Any Any

ecosystemecosystem

The soil microbial system

• More diversity in the palm of your hand than in the mammalian kingdom

• Most important and abused ecosystem in the world

• Essential features– Species concept not useful– Feedback and feedforward coupling to dynamic

environment is central– Functionality– Can’t measure much (anything)

What are the key What are the key

measurables and what is

measurables and what is

the consequence of the consequence of

missing knowledge?missing knowledge?

Any Any

ecosystemecosystem

Plant community modelling

• Our thinking on where to start …– Individual plants characterised by physiological

traits … what they do• Model parameters identified through experimentation

– Individuals should exist in real space with at least one limiting resource at differing levels

• Spatial mixing is crucial

– The model should relate the behaviour of the individuals to each other and the environment

• Feed-back and feed-forward

The most important pattern in ecology (?)

• The abundance curve is a community diagnostic

• Log-normal form– Shape of curve remarkably

conserved across communities

– Most diversity in rare species– Most individuals belong to a

few species groups

• Can we identify a link between individuals’ properties and community structure?

Individuals per species

Number of species

rare common

Our ecosystem model

• Define individuals in terms of functional traits describing:– how environment affects growth and reproduction – how the individual affects its environment

• Parameters that describe these traits form a multi-dimensional trait space

Biodiversity as a distribution in trait space

T3

T2

T1 Diversity characterised byshape of trait-spaceover time

Model structure

• Spatially explicit– individuals interact with neighbours over resource base– resource substrate may be spatially heterogeneous

• Process-based– generic physiological processes parameterised by traits

• Competition for resource and space in time– resource through uptake strategies– space through survival/ reproductive strategies

• Limitations: clonal reproduction, no seed bank– Later …

Sample parameterisation

Here, Scottish grassland species -

Rumex Acetosa

… could be anything

Currently working with OSR

Process of estimating trait distributions from data

Frequency distribution

trait range

freq

uenc

y

Estimated population distribution

trait range

freq

uenc

y

Fitting a distribution

Species: suite of trait distributionsIndividual: in a species assignedtrait values from correspondingdistribution randomly

- ‘genuine’ ibm

Some results

• Predict the same form for individuals as is observed for species

• Relative abundance is governed by individual behaviour

Abundance

Number of species

rare common

Evolution of the abundance curve

ranked plant types

0 20 40 60

ab

un

da

nce

1

10

100

1000

t=0

t=100

t=1,000

t=10,000 t=20,000t=30,000

t=50,000

t - time cycle in the model simulation

• System moves from log-normal indicative of short-term dynamics to power-

law associated with long-term

time cycle

35000 40000 45000 50000

nu

mb

er

of

pla

nts

0

20

40

60

80

100

120

140

Evolution of ranks of plant types in time

• Ranking of plant types is not constant in time

Simplified model via sensitivity analysis

Full set of traits:1. Essential uptake

2. Spatial distribution of uptake

3. Requested/essential uptake ratio

4. Structural store ratio

5. Surplus store release rate

6. General store release rate

7. Development dependent reproduction

relation

8. Time dependent reproduction relation

9. Dispersal pattern

10. Fecundity/store relation

11. Survival threshold and period

12. Probability of death due to external factors

The fecundity vs. time to reproduction relationship from model:

Fecundity= slope*(time to reproduction) + C

Simplified set:

– Time to reproduction

– Fecundity vs. time to

reproduction relation

– Random death

• Compromise– individuals aren’t good at everything– traits are traded-off

fecundity

time to reproduction

What is it that promotes diversity?

• Form of trade-offs– dictates shape of abundance

distribution– governs the stability of

ecosystems

• Trade-offs link individual to community

E. Pachepsky et al., 2001. Nature, 410, 923-926

Key points

• Model results consistent with general experimental observations

• Model operates in terms of individuals and communities– link not blurred by pseudo-processes or spatial averaging

• e.g. population growth, birth rate

– transparency not without cost• difficult to interpret• sensitivity analysis allows collapse to driving traits

– in R. acetosa time to reproduction and fecundity

• Those driving traits are where to focus subsequent measurements (iterative cycle)– They matter the most

But …

• What about more general, complex case …– Wider range in physiological form … more types,

memory in the system, larger numbers

• Raises key challenges– We are trying to build a toolkit to address those

challenges– … to work out via modelling what it is we should

concentrate on experimentally … to better inform our understanding … to improve our models … etc.

Challenges in complexity

• Spatial analysis of functional types– Spatial point process extension

• Parameter space– AI search to link scales

• Individual and community

• Memory in the system– Gene flow (in Oil Seed Rape)– Seed banking (not covered here)

• Up-scaling and model abstraction

Spatial analysis: toy example

• consider two sets of artificial patterns:– clustered– random

• method should group these accordingly

0.2 0.4 0.6 0.8 1.0

x

0.2

0.4

0.6

0.8

1.0

y

pattern 1, clustered

0.0 0.2 0.4 0.6 0.8 1.0

x

0.0

0.2

0.4

0.6

0.8

1.0

y

pattern 2, clustered

0.2 0.4 0.6 0.8 1.0

x

0.2

0.4

0.6

0.8

1.0

y

pattern 3, random

0.0 0.2 0.4 0.6 0.8 1.0

x

0.0

0.2

0.4

0.6

0.8

1.0

y

pattern 4, random

0.0 0.2 0.4 0.6 0.8 1.0

x

0.0

0.2

0.4

0.6

0.8

1.0

y

all four patterns

toy example

• calculate pair correlation function

• smooth functions using b-splines

0.0 0.1 0.2 0.3 0.4 0.5

distance

-50

510

valu

es

smoothed pair correlation functions

0.0 0.1 0.2 0.3 0.4 0.5

-20

24

principal components (PCs)

toy example

• find 2 “representative” functions, i.e. PCs– linear comb.

1.0

1.5

2.0

2.5

3.0

proc

ess1

proc

ess2

proc

ess3

proc

ess4

dendrogram

• group according to similarity to PCs using hierarchical clustering

A more typical data set …

0 50 100 150 200

x

050

100

150

200

y

Australian plantsvaried by colour

Searching trait (parameter) space

• Bi-modal search algorithm developed– identify combinations of individuals that maintain diversity

(community-scale)• compacted descriptions of spatial mixing

– Patterns across individuals trait trade-offs• Also (in)sensitivities to parameter values

• Trait-space is:– 12 dimensional – 1 dimension per trait

• Don’t know which traits matter most a priori

– Large – wide range of values per trait– Complex – interrelations amongst traits

• Two modes of search– Genetic algorithm for rough mapping– Hill climbing for hot spots

Tentative results

• Search able to identify communities that maintain biodiversity – work in progress– Fine-grained search is needed for this

0

500

1000

1500

2000

2500

3000

0 10 20 30 40 50 60 70 80 90 100

Generations

Best

Average

Worst

Steepest Ascent [1]1822 - 2022

Steepest Ascent [2]2045 - 2456

Gene flow

T3

T2

T1

Field experiment and genetics

• All plants in sink and control genotyped– Rates of gene flow– Tracking of individuals

• All plants in sink and control phenotyped– Time to germination– Time to flowering– Fecundity

• Known crosses studied in (physiological) detail

Sink3m x30m

Source30m x 30m Control

Prevailing wind

Phenotype profiling: SCRIGenotype profiling: CEH Dorset

Gene flow

T3

T2

T1

P( [a] | [x], [y])

[x][y]

[a][a]

Up-scaling and model abstraction

• Requirement– Scale up from 104 to 106-109 individuals without losing

essential detail

• Opportunities– I-B-M characterises local dynamics– Statistical representation of spatial mixing over time– AI search to link individuals to emergent, community

scale behaviour– Patterns in those links (should) reveal trait trade-offs

• Sensitivities & insensitivities in parameter sets

– Reformulate model as an abstraction wrt trade-offs

• Any ideas?

Acknowledgements

• Prof. Geoff Squire– Scottish Crop Research Institute

• Contributing work:– Alistair Eberst, Ruth Falconer, Michael Heron,

Claire Johnstone, SIMBIOS, UAD– Joanna Bond, Rebecca Mogg, Samantha Hughes,

CEH Dorset

• BBSRC, NERC, EPSRC and DEFRA funding