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Impact of Environmental Noise in communities of neutral species - Jordi Hidalgo

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QUANTITATIVE LAWS June 13 -June 24

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Impact of Environmental Noise in communities of neutral species - Jordi Hidalgo

  1. 1. Impact of Environmental Noise in communities of neutral species Jordi Hidalgo – University of Padova
  2. 2. Samir Suweis, Amos Maritan Tommaso Spanio, Miguel Á. Muñoz J. Hidalgo, S. Suweis and A. Maritan, Species coexistence in a neutral dynamics with environmental noise (submitted) T. Spanio, J. Hidalgo and M. A. Muñoz, Impact of environmental colored noise in population dynamics with extinction (in preparation)
  3. 3. Neutral Theory of Biodiversity Many of the observed patterns can be explained by the simple mechanisms of birth, death and migration, assuming EQUIVALENCE AMONG SPECIES (NEUTRALITY) (e.g. Species abundance distribution, Species Area Relationship, ...) (from Cell.com)
  4. 4. However... Role of temporal scales?? (we will avoid white noise approximation) PRECIPITATIONS TEMPERATURE NUTRIENTS IN SOIL ETC... 1) Most of the approaches based on neutral assumptions do not consider that ABIOTIC CONDITIONS may change 2) Different species can have different responses to such fluctuations Can we study the effect of environmental variability in neutral dynamics without compromising the NEUTRAL assumption?
  5. 5. Environmental variability has important consequences in the functioning and organization of ecological systems BET-HEDGING STRATEGIES (see Ricardo's next talk!) MECHANISMS FOR SPECIES COEXISTENCE (Chesson's storage effect) PATTERNS IN ECOLOGICAL SYSTEMS Neutral Theory leads to successful predictions for static patterns, BUT fails to estimate several dynamical measures (e.g. scaling of population fluctuations)
  6. 6. Some simple questions ● Coexistence of species or monodominance? ● Under which conditions a species get extinguished? ● How much time does it take to disappear? We propose a SUPER top-down approach, and start from simple models for single and multiple (NEUTRAL) species dynamics IMPACT OF ENVIRONMENTAL NOISE?? TEMPORAL SCALES?
  7. 7. Colored noise is not that bad...
  8. 8. Analytical tools to deal with COLORED Noise Tool #1: Unified Color Noise Approximation (UCNA) 2-variable Markovian problem 1-variable Markovian problem Adiabatic approximation (Exact when ) “Interpolation” for intermediate white noise
  9. 9. Analytical tools to deal with COLORED Noise Tool #2: Dichotomic Markov Noise (DMN) Many analytical tools with DMN: Stationary state distributions, mean first passage times, ...
  10. 10. Environmental noise in single species dynamics
  11. 11. The Contact Process DYNAMICS A = ACTIVE (INFECTED, COLONIZED RESOURCES, ...) I = INACTIVE (SUSCEPTIBLE, AVAILABLE RESOURCE, …) WE FOCUS ON THE MEAN-FIELD CASE (FULLY CONNECTED NETWORK) N Interacting “particles”
  12. 12. The Contact Process Deterministic “mean-field” equation Phase diagram BUT! Any FINITE system can eventually reach the absorbing state... How Mean Extinction Times (MET) scale with the system size N?
  13. 13. The Contact Process Phase diagram Scaling of Mean Extinction Times Dependence on the parameters? Survival threshold? How much time does activity take to disappear? How probable is it? IF RATES FLUCTUATE IN TIME... ● Just more parameters? ● Do we have to change the way in which we understand Absorbing Vs Active phase? ● Role of time-scales?
  14. 14. Contact Process with environmental Noise + UCNA white noise
  15. 15. Contact Process with environmental Noise SIMULATIONS “AVOIDING” THE ABSORBINGSTATE! (e.g. recovering after absorbing...) Physically real? What if the system can fall into the absorbing state? (FINITE SYSTEMS)
  16. 16. Environmental noise smears the usual phase diagram into a more variegated one in which the absorbing behavior slowly blends into the active one
  17. 17. Environmental noise in communities of NEUTRAL Species
  18. 18. Some recent works on the impact of Environmental Variability in neutral communities ● Model for multiple bacterial colonies growing under limited resources (logistic model) ● Species respond differently to the environmental conditions (neutral on average) Environmental variability FAVORS one of the species to monodominate ● Neutral Theory of Biodiversity (Voter model with speciation) ● Species respond differently to the environment (neutral on average) Environmental variability increases the TOTAL number of species for highly variable environments (CHESSON STORAGE EFFECT)
  19. 19. Voter model with 2 species
  20. 20. Voter model with 2 species COEXISTENCE?? The system can always reach MONODOMINANCE... NO PARAMETERS, NO PHASE DIAGRAM... Cox, J., 1989, Ann. Probab. 17 (4), 1333. What is the impact of environmental noise on species coexistence? NEUTRAL ASSUMPTION
  21. 21. Voter model with 2 species + Env. Noise Neutrality is kept on TEMPORAL AVERAGE EXPLICIT TIME-DEPENDENCY? PROBLEM: DETAILS MATTER!!! Environment affects mortality: Environment affects fitness:
  22. 22. Linear fitness case For constant environments (mean-field) EXTINCTION TIMES In agreement with: (Environment modulates GROWTH RATES linearly)
  23. 23. Relative fitness case For constant environments (mean-field) EXTINCTION TIMES In agreement with: (Environment modulates species fitness, but effective fitness is re- scaled by the total one)
  24. 24. CHESSON'S STORAGE EFFECT Different responses to environmental fluctuations depending on the species abundance: Small populations are slowly decimated during unfavorable conditions and rapidly grow during favorable periods (in relation to its abundance), (The opposite occurs for large populations) Effective drift that propitiates species to coexist
  25. 25. Take home message Further questions: ● Observables that we should measure in order to identify the “correct dependence” with environmental fluctuations? ● Interplay between demographic & environmental noise? ● Environmental variability ↔ Spatial patterns? (soon on Arxiv!) T. Spanio, J. Hidalgo and M. A. Muñoz, Impact of environmental colored noise in population dynamics with extinction J. Hidalgo, S. Suweis and A. Maritan, Species coexistence in a neutral dynamics with environmental noise (in Review) ● Environmental variability changes the way in which we understand phase transitions in the context of population dynamics. ● In neutral dynamics, environmental variability can favor/disfavor species coexistence depending on how the environment modulates species fitness. ● The interplay between the timescales of the dynamics and the environment plays a fundamental role (white noise approximation are not always valid) THANKS FOR YOUR ATTENTION!

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