1. Modelling complex communities – measuring what matters? Jim Bown, Janine Illian and John Crawford University of Abertay Dundee j.bown@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 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 Any ecosystem

4. 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) The fact that individuals both affect and are affected by their local environment is often ignored Any ecosystem

5. 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) Diversity measures do not link dynamics to function Any ecosystem

6. 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) What are the key measurables and what is the consequence of missing knowledge? Any ecosystem

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? Individuals per species Number of species rarecommon

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 T3T3 T2T2 T1T1 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 Fitting a distribution Species: suite of trait distributions Individual: in a species assigned trait values from corresponding distribution randomly - genuine ibm

14. Some results Predict the same form for individuals as is observed for species Relative abundance is governed by individual behaviour Abundance Number of species rarecommon

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 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

18. Compromise –individuals arent 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

19. 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

20. 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 …

26. 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 T3T3 T2T2 T1T1

29. 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 Sink 3m x 30m Source 30m x 30m Control Prevailing wind Phenotype profiling: SCRI Genotype profiling: CEH Dorset

30. Gene flow T3 T2 T1 P( [a] | [x], [y]) [x] [y] [a]

31. Up-scaling and model abstraction Requirement –Scale up from 10 4 to 10 6- 10 9 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