Transcript Nonequilibrium dynamics in ecological communities Jef Huisman1, Elisa Benincà1 & Stephen Ellner2 1University of Amsterdam 2Cornell University.

Nonequilibrium dynamics in
ecological communities
Jef Huisman1, Elisa Benincà1 & Stephen Ellner2
1University of Amsterdam
2Cornell University
Why are there so many species?
Hutchinson. The Paradox of the Plankton. Am Nat 1961
Classic approach:
niche theory
Darwin’s voyage with The Beagle (1831-1836)
Patel, Nature 2006
Nee and Colgrave, Nature 2006
Opportunities for niche differentiation ?
Hypothesis:
White light contains many colors
 Niche differentiation in the light spectrum ?
Isaac Newton
Opticks 1704
[Stomp et al. Nature 2004]
Laboratory experiment
+
=
?
[Stomp et al. Nature 2004]
Competitive exclusion in colored light
Green species
wins
Red species
wins
Time (days)
[Stomp et al. Nature 2004]
Coexistence in white light
white light
+
=
[Stomp et al. Nature 2004]
Our life is
so
predictable…
I knew you
would say
that!
Thus, each species has its own niche?
What is chaos ?
Chaos is aperiodic dynamics
in a system driven by deterministic rules
with ‘sensitive dependence on the initial conditions’
Butterfly effect
[Lorenz, J. Atmospheric Sciences 1963]
Many models predict chaos
Two prey & one predator
(Gilpin 1979)
Three-trophic food chain
(Hastings & Powell 1991)
Multi-species competition
(Huisman & Weissing 1999)
Chaos &
biodiversity
[Huisman & Weissing Nature 1999, Am Nat 2001]
Experimental evidence?
Reinhard Heerkloss
constant conditions
2,319 days
counted 2x per week!
That’s 100 to 1000 plankton generations!
RESULTS
Plankton abundance
phytoplankton
Elisa Benincà
zooplankton
Never at
equilibrium!
Time (days)
[Benincà et al. Nature 2008]
A little bit of chaos theory
d
d  d0 e
t
λ = Lyapunov exponent
Time
Lyapunov exponent measures the rate
of exponential divergence
Divergence or convergence ?
Lyapunov exponents:
λ<0
Trajectories converge
 system is not chaotic
λ>0
Trajectories diverge
 chaos
Time
Divergence of trajectories !
positive
Lyapunov exponents
for all species
divergence
of trajectories
CHAOS !
[Benincà et al. Nature 2008]
Limits on predictability
R2
(R2)
Predictability
1.0
high predictability
in short term
0.8
0.6
0.4
low predictability
in long term
0.2
0.0
0
10
20
30
40
Prediction
timeTime
(days)
Prediction
50
[Benincà et al. Nature 2008]
Why chaos?
What are the underlying mechanisms?
Predator-prey interactions can generate oscillations
[Elton & Nicholson J Animal Ecology 1942]
Research question
What if there are multiple predator &
multiple prey species ?
Competition between
oscillating systems?
Coupling of two predator-prey systems
Coupled
through competition:
Anti-phase oscillations
of P1-P2 and Z1-Z2
Coupled
through predation:
In-phase oscillations
of P1-P2 and Z1-Z2
[Vandermeer American Naturalist 2004]
Our experimental food web
Dominated by
two predator & two prey species
[Benincà et al. Ecology Letters 2009]
Anti-phase fluctuations!
picocyanobacteria
nanoflagellates
rotifers
copepods
[Benincà et al. Ecology Letters 2009]
Parameter estimates
α = 1.5;  = 0.1
Strong coupling
through competition

Weak coupling
through predation
These values produce chaos!
small
pico’s
larger
nanoflags
 anti-phase fluctuations
in chaotic fashion
[Benincà et al. Ecology Letters 2009]
Hence,
Laboratory evidence:
Chaos in plankton communities
driven by species interactions
Predictability:
Time horizon of 15-30 days
Field data…
Monitoring data from the North Sea:
Katja Philippart
What happens in
seasonal environments?
Ups and downs
by external forces
or internal interactions?
[Dakos et al, Proc Roy Soc London B 2009]
Multispecies Plankton Model
10 phytoplankton species:
Vasilis Dakos
6 zooplankton species:
Regular season:
[Dakos et al, Proc Roy Soc London B 2009]
Model results – total biomass
Seasonal variation
entrains
total biomass
&
ecosystem functioning
phytoplankton
zooplankton
[Dakos et al, Proc Roy Soc London B 2009]
Model results – species composition
However,
species composition
varies
from year to year!
[Dakos et al, Proc Roy Soc London B 2009]
Model results
Stroboscopic sampling at 1st of January:
Poincaré map
has fractal nature

Not ‘quasi-periodicity’
but chaos
at species level!
[Dakos et al, Proc Roy Soc London B 2009]
Hence,
Seasonal variation
may entrain total biomass,
but can also amplify species fluctuations
Any field evidence
for seasonally-induced chaos?
Rocky intertidal community
Bill Ballantine
barnacles, mussels and
algae on rocky shores
Goat Island Bay, New Zealand
[Benincà et al, submitted]
A cyclic succession
[Benincà et al, submitted]
20 years of data…
Again,
the species
never settle
at equilibrium!
[Benincà et al, submitted]
Constant environment
Seasonal environment
model result:
Seasonalityinduced
chaos
with the
same signature
as the data!
Conclusions
Ecological Communities
Non-equilibrium dynamics pervade
So, how should we make predictions?
For multi-species
communities ?
For
tomorrow
we predict...
For
tomorrow
we predict...
1. Time scales
2. Time horizons
3. Monitoring!
Many thanks to:
Maayke Stomp, Klaus Jöhnk, University of Amsterdam
Thomas Haverkamp, Lucas Stal, Netherlands Institute of Ecology
Vasilis Dakos, Marten Scheffer, Wageningen University
Reinhard Heerkloss, University of Rostock
Bill Ballantine, Leigh Marine Laboratory
Cross-wavelet analysis:
Model predictions
show same signature
as the data!