Modelling complex communities

1
Modelling complex communities measuring what
matters?

• Jim Bown, Janine Illian and John Crawford
• University of Abertay Dundee
• j.bown_at_tay.ac.uk

2
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
• Cant measure much (anything)

3
The soil microbial system
Any ecosystem

• 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
• Cant measure much (anything)

Most ecological theory ignores individual
variation within species groups
4
The soil microbial system
Any ecosystem

• 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
• Cant measure much (anything)

The fact that individuals both affect and are
affected by their local environment is often
ignored
5
The soil microbial system
Any ecosystem

• 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
• Cant measure much (anything)

Diversity measures do not link dynamics to
function
6
The soil microbial system
Any ecosystem

• 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
• Cant measure much (anything)

What are the key measurables and what is the
consequence of missing knowledge?
7
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

8
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?

Number of species
rare
common
Individuals per species
9
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

10
Biodiversity as a distribution in trait space
Diversity characterised by shape of
trait-space over time
11
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

12
Sample parameterisation

• Here, Scottish grassland species -
• Rumex Acetosa
• could be anything
• Currently working with OSR

13
Process of estimating trait distributions from
data
Species suite of trait distributions Individual
in a species assigned trait values from
corresponding distribution randomly - genuine
ibm
Fitting a distribution
14
Some results

• Predict the same form for individuals as is
  observed for species
• Relative abundance is governed by individual
  behaviour

15
Evolution of the abundance curve
t - time cycle in the model simulation

• System moves from log-normal indicative of
  short-term dynamics to power-law associated with
  long-term

16
Evolution of ranks of plant types in time

• Ranking of plant types is not constant in time

17
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

• Simplified set
• Time to reproduction
• Fecundity vs. time to reproduction relation
• Random death

The fecundity vs. time to reproduction
relationship from model Fecundity slope(time
to reproduction) C
18
What is it that promotes diversity?

• Compromise
• individuals arent good at everything
• traits are traded-off

• 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
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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

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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.

21
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

22
Spatial analysis toy example

• consider two sets of artificial patterns
• clustered
• random
• method should group these accordingly

23
toy example

• calculate pair correlation function
• smooth functions using b-splines

24
toy example

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

• group according to similarity to PCs using
  hierarchical clustering

25
A more typical data set
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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
• Dont 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

27
Tentative results

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

28
Gene flow
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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

Source 30m x 30m
Control
Sink 3m x 30m
Prevailing wind
Phenotype profiling SCRI Genotype profiling CEH
Dorset
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Gene flow
P( a x, y)
T1
y
x
a
a
T2
T3
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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?

32
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