Niche Differentiation and Coexistence in a Multi-Resource Ecosystem with Competition

1. Niche Differentiation and Coexistence in a Multi-Resource Ecosystem with Competition Walter de Back1, Laszló Gulyás1,2, George Kampis1,3 1Collegium Budapest, Institute for Advanced Study, Hungary 2AITIA Int. Inc., Budapest, Hungary 3Department of Biology, East Tennessee State University, Johnson City, USA

2. The Institute

3. The Project • Funded by EC (#033883) • Modeling methodology development • ABM tools, RePast/Java, parallelization (ESS 07) • Parameter sweeps applications (EGEE 07) • Observers for Complex Systems (IEEE ALife 07) • Models developments • FATINT system (ALife IX, X, Alife Jnl) • Ecosystems models (ECCS 07)

4. Introduction: A-ecosystems • ABM („the moment of truth”) • Encapsulated objects • Fully embedded • ABM = IBM + ontology • Resource competition • K resources, N species • Control(lability) of resource limited populations • Niche differentiation • Niche as a dynamic phenomenon • Adaptive radiation, speciation, competition avoidance • Ecol-evol

5. Naive questions • Collapse into 1 species? • A universal consumer, or „anything” in genetic space • Does specific consumption have conditions/advantages? • Produce a mess? • e.g. long-lived transient, w/o recognizable patterns/rules • Structure • How do niches (available for species) and resources relate? • Extinction/stability? • vs. „free” system or a generic resource („energy”) • Does (specific) consumption stabilize systems? • (Does predation stabilize?)

6. (Pseudo-)Naive questions • Collapse into 1 species? • A universal consumer, or „anything” in genetic space • Does specific consumption have conditions/advantages • Produce a mess? • e.g. long-lived transient, w/o recognizable patterns/rules • Structure • How do niches (available for species) and resources relate? • Extinction/stability? • vs. „free” system or a generic resource („energy”) • Does (specific) consumption stabilize systems? • (Does predation stabilize?)

7. The Closer Problem • Generalists – Specialists • Do specialists arise? Under what conditions? • Are they stable? By themselves and against invasion? • Do generalists and specialists coexist? • Effect of stoichiometry • Energy as single currency structured energy • Stoichiometric constraints (need 2 of X, 3 of Y..)

8. The Model (I) • Minimal agent-based model • Non-spatial • Resources and Consumers • Representation: gene values in (0,1) • Basal level of foodweb • Steady influx of abiotic (non-replicating) resources • Asexual consumers

9. The Model (II) • Combines two trade-offs for the individual • Abilities trade-off: generalist-specialist • Needs trade-off: energy is a combination of resources • Genotype • If K resource types, consumers have K genes • Here: K = 3 (also performed experiments w/ k=10, 100 (!)) • Genes control ability and needs for each resource type

10. AbilitiesGeneralist – specialist tradeoff • Ability of agent ai for agiven resource type • Probability piof consumption upon encounter • Generalist – specialist trade-off • Consumer divides its consumption activity(ie. time) • Values of K genes normalized to 1: • Strength of trade-off s • Strong if s > 1 ; weak if s < 1 • „face value” if s = 1

11. NeedsStoichiometric trade-off • Need for a given resource type for agent ai • Energetic value eiof the resource type • Stoichiometric constraint • Need for a combinationof resources • Simplification: need is theinverse of ability • Energy is function of need and stored resources

12. Genes Gi ; trade-offs A and N

13. Pre-experiments • I. no trade-offs. Fast specialization on all resources • II. s = d = 0. Genes have no effect; drift

14. Results • Single-currency vs. Stoichiometry • Initial conditions • Initialized with generalists • Initialized with a specialist invader • Varying trade-off strengths

15. Results IImpact of stoichiometry on niche differentiation • Energy as single currency • Resource types contribute equally to energy • With stoichiometric constraint (next slide)

16. Results IImpact of stoichiometry on niche differentiation

17. Results IISpecialist invader

18. s = 1, d = 0; (single currency energy) Initialized with generalists. Rapid branching towards the extremes.

19. s=1, d=1 (spec/gen and stoichiometry) Initialized with generalists. Immediate branching/specialization into 3 species.

20. s=1, d=1 (spec/gen and stoichiometry) II Initialized with generalists, again. Branching into 2 species, and then….

21. s=1, d=1 (spec/gen and stoichiometry) III Initialized with specialists. Branching into 2 stable species

22. s=1, d=1 (spec/gen and stoichiometry) IV Initialized with specialists, again. Eventual branching into 3 specialist species

23. Summary table I. Normalized genes

24. Summary table II. Non-normalized genes

25. Summary: Niches and Resources • Essentially, resources are niches • N = K, ni = ki or N < K (often unstable) • Stable differentiation and coexistence • Competitive exclusion (Gause principle) • Increasing s is an attractive force to corners • Increasing d is a repelling force from corners • Dynamics matters (vs. analytic solution) • Best specializaton at mild params (s = 1, d < 1)

26. Summary: Niches and Resources • Essentially, resources are niches • N = K, ni = ki or N < K (often unstable) • Stable differentiation and coexistence • Competitive exclusion (Gause principle) • Increasing s is an attractive force • Increasing d is a repelling force • Dynamics matters (vs. analytic solution) • Best specializaton at mild params (s = 1, d < 1)

27. Where to go from here?

28. Predator/prey systems..

29. Predator/prey systems II

30. Predator/prey systems w/ N > K (!)

31. Conclusions… • (Resource limited populations are more stable) • Niche differentiation under specific conditions • Imperfect specialists dominate • Coexistence typically limited to Gause N ≤ K • Predation as a further control can exploit N > K • (noting that A and N are part of a GPM) • GPM-s are the key to ecosystem composition/stability

32. George Kampis Group leader Thank you! Walter de Back PhD student László Gulyás Researcher