Transcript Slide 1

Stochasticity in Community Ecology
BIOL 548B 102
Why are we here?
Stochasticity (randomness, chance) is a concept that is central to
theoretical and empirical ecology, and at the crux of some of the
most lively debates.
BUT…
What is stochasticity? Which ecological processes are stochastic
and which are deterministic? How do you detect/quantify
stochastic effects? Is “deterministic vs. stochastic” the same
thing as “niche vs. neutral”? Do different authors answer these
questions in the same way?
The answer to the latter question is “no”, but for the others the
answers are not so clear.
SO…
Let’s run a course on the topic, and write a paper laying out the
issues clearly, synthesizing different perspectives, and pointing
the way to future progress.
Schedule
Date
Topic
Instructor
Tues. 21 Sept.
History and philosophy of stochasticity in ecology
Vellend
Thurs. 23 Sept.
Null models
Srivastava
Tues. 28 Sept.
Implementing null models in R
Kraft
Thurs. 30 Sept.
Student-led discussion - Null models
Tues. 5 Oct.
Stochasticity in evolutionary biology
Thurs. 7 Oct.
Student-led discussion - History, Philosophy, Evolution
Tues. 12 Oct.
Theoretical models: Drift and selection
Thurs. 14 Oct.
Student-led discussion
Tues. 19 Oct.
Theoretical models: Incorporating dispersal
Thur. 21 Oct.
Student-led discussion
Tues. 26 Oct.
Statistical models: Partitioning variance in community composition
Thurs. 28 Oct.
Student-led discussion
Tues. 2 Nov.
Empirical issues: Priority effects
Thurs. 4 Nov.
Student-led discussion
Tues. 9 Nov.
Empirical issues: Testing for dispersal limitation
Thurs. 11 Nov.
Student-led discussion
Tues. 16 Nov.
Thurs. 18 Nov.
Empirical issues: Experimental manipulating of something “stochastic” Vellend
or “neutral”discussion
Student-led
Tues. 23 Nov.
Project presentations / work
Thurs. 25 Nov.
Project presentations / work
Tues. 30 Dec.
Project presentations / work
Thurs. 2 Dec.
Project presentations / work
John Beatty*
Vellend
Vellend
Srivastava
Srivastava
Srivastava
Grading breakdown
Participation in discussions: 25%
Leadership in discussions: 25%
Final project: 50%
Projects:
We have a vision of a single contribution, the impact of which
will be maximized if we join efforts, “skim the cream” from
each of our individual contributions, and integrate them into a
synthetic perspective
That would mean we compartmentalize the “big” topic into
pieces that each of you (or pairs of you) work on in detail
BUT…
We don’t want to insist that your efforts are subsumed by the
larger project, so we can see how things go and discuss as
we go along…
FOR NOW…
Let’s get our feet wet and re-visit projects in a week or two
Today:
1) What is community ecology?
2) What is stochasticity?
3) Philosophical perspectives on
stochasticity in ecology.
4) Historical perspectives on
stochasticity in ecology (how we got
to where we are)
(1) COMMUNITY ECOLOGY
The study of patterns in the diversity,
abundance, and composition of
species in communities, and the
processes underlying these patterns
Let’s start with the number of species, S, in a particular place
How can S change over time?
St+1 - St = speciation
A place
One individual
organism (each
colour a different
species)
Let’s start with the number of species, S, in a particular place
How can S change over time?
St+1 - St = speciation + immigration
A place
One individual
organism (each
colour a different
species)
Some other
place
Let’s start with the number of species, S, in a particular place
How can S change over time?
St+1 - St = speciation + immigration - extinction
A place
One individual
organism (each
colour a different
species)
x
stochastic
(drift)
Individuals of rare
species might die
before reproducing
“by accident”
(Theory of Island
Biogeography)
Let’s start with the number of species, S, in a particular place
How can S change over time?
St+1 - St = speciation + immigration - extinction
A place
One individual
organism (each
colour a different
species)
stochastic deterministic
(drift)
(selection)
Some species have
a fitness advantage
over other species
(lots of specific
reasons)
Let’s start with the number of species, S, in a particular place
How can S change over time?
St+1 - St = speciation + immigration - extinction
A place
stochastic deterministic
(drift)
(selection)
IMPORTANT
One individual
organism (each
colour a different
species)
Other forms of
selection can counter
tendency towards
local extinction (we’ll
get to this)
Only 4 kinds of process can change the distribution, diversity,
and abundances of species in a community
• Speciation
• Dispersal
• Drift
• Selection
But isn’t (natural) selection a concept that applies
only to evolutionary change within species?
NO!
“This preservation of favourable individual
differences and variations, and the
destruction of those which are injurious, I
have called Natural Selection.”
Charles Darwin (1859)
(Note: there is no stipulation that individuals be of the same species)
Selection happens among and within species
Kudzu has an advantage over
other plants on disturbed soils
in the southeastern U.S.
Dark-coloured moths have an
advantage over lighter-coloured
moths on dark tree trunks
Ecological drift  demographic stochasticity
In a community of stable (i.e., constant) size,
each organism leaves on average one
offspring.
Even if all organisms are identical, they will not
all leave exactly one offspring – e.g., they
might leave 0, 1 or 2 offspring.
The abundances of species in such a
community will “drift” over time.
Possible outcomes of ecological drift between two species
in a community of size, J = 4
Time
X
X
X
X
X
X X
How do you tell the
difference between
this and selection?
X
A Different Structure for Community Ecology
Processes
Primary patterns
• Drift
• Speciation
• Migration
• Selection
(across space & time)
• Species diversity
• Species composition
Constant
- Freq. dependent
+ Freq. dependent
(identity and traits)
• Species abundances
Emergent patterns
• Productivity
• Stability
• Food web connectance
• Whatever you can think of
…about ecological communities
Everything you need to know…
Global community
Speciation
Drift
Selection
Dispersal
Regional community
Dispersal
Speciation
Drift
Selection
Dispersal
Dispersal
Local
Community
Speciation
Drift
Selection
Note: Extinction results from drift & selection
(2) What is stochasticity?
From the Oxford English Dictionary (The definitive record of the English language)
stochasticity: the property of being stochastic.
stochastic: Randomly determined; that follows some random probability
distribution or pattern, so that its behaviour may be analysed statistically but
not predicted precisely; stochastic process = random process
random adj.
a. Having no definite aim or purpose; not sent or guided in a particular
direction; made, done, occurring, etc., without method or conscious choice;
haphazard.
b. Statistics. Governed by or involving equal chances for each of the actual or
hypothetical members of a population; (also) produced or obtained by a such a
process, and therefore unpredictable in detail.
A process or variable is stochastic if
we can specify its value or magnitude
only as a probability distribution
rather than a single number.
Early application of probability theory:
human life tables and projections of
population growth/structure (i.e.,
ecology of Homo sapiens)
But what does that mean?
(3) Philosophical perspectives
The crux of the matter:
y = ax + b + e
What is
that?
7
Log (population size)
6
5
4
3
2
1
-1
0
1
Log (patch area)
2
Stochasticity = Ignorance
“…probabilities measure human ignorance, not genuine chance”1
“…probabilities had to be states of mind rather than states of the world”1
“…stochastic elements stand in for unknown processes”2
Stochasticity is real
“For decades physicists, mathematicians, engineers, and fluid dynamicists
have used the intrinsic stochastic nature of the world to their benefit.”3
“Real animals, plants, and micro-organisms are continually buffeted by the
effects of random processes”4
It doesn’t matter one way or the other, in practice
“As a practical matter, the dividing line between “deterministic” and
“stochastic” is open to interpretation…often drawn as a matter of
convenience.”3
“Acceptance of this point of view (indeterminism) requires little change in
the actual practice of science, especially as determinism has never been
more than an ideal admittedly unrealizable in full because of the invariable
errors of observation and in many cases, practically irreducable
probabilities like those in the fall of dice” (Sewall Wright quoted in 1)
1. Gigerenzer et al. 1990, Empire of Chance; 2. J. Clark 2007 TREE; 3. Denny & Gaines 2000, Chance in biology; Coulson & Godfray 2007 in: Theoretical Ecology
Scientific progress?
Is the theoretical value of e zero?
If so, is achieving e = 0 a practical goal?
y = ax + b + d + e
(smaller than before)
7
Log (population size)
6
5
4
3
Forest type
Primary
Forest
Type
1 Secondary
2
1
-1
0
1
Log (patch area)
2
2
Is the theoretical value of e zero?
Heisenberg’s Uncertainty Principle
You can’t determine precisely both the momentum and
position of a particle.
It’s not that we don’t have the tools to do so, but that
the nature of the system makes it theoretically impossible.
Is the theoretical value of e zero?
Is achieving e = 0 a practical goal?
For a given process, what matters is whether it acts
at random with respect to a particular outcome of
interest. Some examples of “true” randomness:
• Kinetic theory of gases: motion of particle
effectively random with respect to other particles.
• Mutation: Effects are random with respect to
traits/fitness.
• Recombination: Ditto.
• Drift: Differences in fitness between individuals is
random with respect to allelic/species identity.
McShea & Brandon (2010, Biology’s First Law: The Tendency of Diversity and Complexity to Increase in Evolutionary Systems)
Back to “what is stochasticity?”…
Types of stochasticity in the ecological literature:
Demographic: “Unpredictability through time in a population’s
demography (how many individuals die, how many reproduce, etc.)
caused by randomness of individual fates.”1
Colonization: Unpredictability in the rate of arrival, and species
identity, of colonists/immigrants.
Environmental: “Unpredictable changes through time in average
demographic rates…caused by vacillations in weather, food…”1
Genetic: “Unpredictable changes in gene frequencies as a result of
processes such as random genetic drift”1
1. Doak et al. (2009, In: The Princeton Guide to Ecology)
Historical Debates in Ecology Concerning
“The Balance of Nature”
(typically with undercurrents of deterministic vs. stochastic process)
• Superorganismal vs. individualistic communities
• Density-dependent vs. density-independent population
regulation
• Equilibrium vs. non-equilibrium communities
• Competition as the dominant structuring force in
communities (or not)
• Local vs. regional factors determining local community
structure
Kingsland (1995, Modeling Nature); Real & Brown (1991, Foundations of Ecology)
The big current debate: niche vs. neutral
Maybe the many obvious differences among
species (i.e., tropical trees) don’t really matter
with respect to which individual organisms
live/die/reproduce in a community (i.e., a tropical
forest). [Niches/selection don’t matter]
A theory that makes this assumption actually
predicts the shape of species-area curves and
relative abundance distributions really well
2001
How can a model
based on randomness
predict anything?
Randomness at one level
Order/predictability at another
Kinetic theory of ideal gases
(Statistical mechanics)
Randomness at one level
Order/predictability at another
Neutral theory (drift + dispersal + speciation, no selection)
The big current debate: niche vs. neutral
Consensus: Continuum – neutral & niche,
stochastic & deterministic
“the prevailing notion is that stochastic forces exist on
one end of a continuum while deterministic forces occupy
the other. Finding any truth that lies between is the
challenge. It’s not niche or neutral…it’s determining the
relative importance of the two.”
Gewin (2006, PLoS Biology)
Results considered evidence of stochastic processes:
Spatial proximity is a good predictor of differences in
community composition.
Order of species arrival has persistent effect on community
composition.
Population dynamics equally sensitive to density of
conspecifics and heterospecifics.
Results attributed to stochastic processes by default:
Neutral theory provides a satisfactory fit to the pattern
No significant difference from distribution of null-model
outcomes.
Are we re-inventing the
wheel…again?
Is there an alternative to the (seemingly
obvious) “continuum” consensus?
“Contrary to the emerging consensus, while models do indeed
represent a continuum, there is no evidence for such a continuum in
the underlying causes. Moreover, the continuum in models is one of
knowledge, not cause.” (Clark et al. Ecology Letters 2007)
“there is no evidence for stochasticity in nature at observable
scales. Stochasticity is an attribute of models.” (Clark 2009, TREE)
“the neutral view of biodiversity maintenance is without explicit
process (rather than acknowledge species differences, it relies on
models having stochastic elements that make species differences
implicit)” (Clark 2009, TREE)
Some key questions for a review/synthesis:
• Is dispersal a stochastic process?
• Is disturbance a stochastic process?
• What is the empirical evidence for drift? (e.g., sensitivity to
density of conspecifics and heterospecifics)
• What exactly is Jim Clark trying to say? (Is there any utility
in the perspective that there is no “real” stochasticity? How
big will e be once we approach the limits of knowledge?)
• Why do some patterns fit neutral predictions really well?
(keep in mind that neutral theory is not only about drift but
dispersal as well)
The Litmus Test of Stochastic Effects in Biology:
Replaying Life’s Tape
“I call this experiment “replaying life’s tape.” You
press the rewind button…go back to any time and
place in the past…Then let the tape run again and
see if the repetition looks at all like the original”
“any replay of the tape would lead evolution down a
pathway radically different from the road actually
taken”
Stephen J. Gould, Wonderful Life