Transcript Modelling complex communities

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)
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)
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)
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
Number of species
• 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?
rare
common
Individuals per species
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
T1
Diversity characterised by
shape of trait-space
over time
T2
T3
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
Frequency distribution
Species: suite of trait distributions
Individual: in a species assigned
trait values from corresponding
distribution randomly
- ‘genuine’ ibm
trait range
Fitting a distribution
frequency
Estimated population
distribution
trait range
Some results
Number of
species
rare
common
Abundance
• Predict the same form for individuals as is observed for
species
• Relative abundance is governed by individual
behaviour
Evolution of the abundance curve
abundance
1000
t=50,000
t=10,000 t=20,000
t=1,000
100
t=30,000
t - time cycle in the
model simulation
t=100
10
t=0
1
0
20
40
60
ranked plant types
• System moves from log-normal indicative of short-term
dynamics to power-law associated with long-term
Evolution of ranks of plant types in time
140
number of plants
120
100
80
60
40
20
0
35000
40000
45000
50000
time cycle
• 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
Simplified set:
– Time to reproduction
3. Requested/essential uptake ratio
4. Structural store ratio
– Fecundity vs. time to
5. Surplus store release rate
6. General store release rate
reproduction relation
7. Development dependent reproduction
– Random death
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
What is it that promotes diversity?
• Compromise
fecundity
– individuals aren’t good at everything
– traits are traded-off
• Form of trade-offs
– dictates shape of abundance
distribution
– governs the stability of
ecosystems
time to reproduction
• 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
pattern 1, clustered
0.6
0.8
1.0
1.0
1.0
0.8
0.2
0.4
0.8
y
0.6
0.6
0.0
0.2
– clustered
– random
0.2
0.4
0.6
0.8
1.0
0.0
0.2
0.4
0.6
0.8
x
pattern 3, random
pattern 4, random
1.0
0.8
y
0.4
0.2
0.0
0.0
0.2
0.4
0.6
x
0.2
0.4
0.6
x
0.8
1.0
0.8
1.0
0.0
0.4
y
0.6
0.6
0.2
0.8
1.0
1.0
0.4
y
x
0.2
• method should
group these
accordingly
pattern 2, clustered
all four patterns
y
0.4
• consider two sets
of artificial
patterns:
0.0
0.2
0.4
0.6
x
0.8
1.0
toy example
smoothed pair correlation functions
values
0
-5
• smooth functions
using b-splines
5
10
• calculate pair
correlation function
0.0
0.1
0.2
0.3
distance
0.4
0.5
toy example
3.0
process2
process1
2
0
-2
1.5
0.1
0.2
0.3
process4
0.0
process3
1.0
• group according to
similarity to PCs
using hierarchical
clustering
4
principal components (PCs)
2.0
– linear comb.
dendrogram
2.5
• find 2
“representative”
functions,
i.e. PCs
0.4
0.5
A more typical data set …
Australian plants
0
50
100
y
150
200
varied by colour
0
50
100
150
x
200
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
Gene flow
T1
T2
T3
Field experiment and genetics
Source
30m x 30m
• All plants in sink and
control genotyped
Control
Sink
3m x
30m
– Rates of gene flow
– Tracking of individuals
• All plants in sink and
control phenotyped
Prevailing wind
Phenotype profiling: SCRI
Genotype profiling: CEH Dorset
– Time to germination
– Time to flowering
– Fecundity
• Known crosses studied
in (physiological) detail
Gene flow
P( [a] | [x], [y])
T1
[y]
[x]
[a]
[a]
T2
T3
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