1. Stochasticity in Community Ecology
BIOL 548B 102

2. 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.

3. Schedule

4. Grading breakdown
Participation in discussions: 25%
Leadership in discussions: 25%
Final project: 50%

5. 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

6. Today:
What is community ecology?
What is stochasticity?
Philosophical perspectives on stochasticity in ecology.
Historical perspectives on stochasticity in ecology (how we got to where we are)

7. (1) COMMUNITY ECOLOGY
The study of patterns in the diversity, abundance, and composition of species in communities, and the processes underlying these patterns

8. 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)

9. St+1 - St = speciation + immigration
Let’s start with the number of species, S, in a particular place
How can S change over time?
St+1 - St =
speciation
+ immigration
Some other
place
A place
One individual organism (each colour a different species)

10. x St+1 - St = speciation + immigration - extinction
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
stochastic
(drift) x
A place
Individuals of rare species might die before reproducing “by accident” (Theory of Island Biogeography)
One individual organism (each colour a different species)

11. St+1 - St = speciation + immigration - extinction
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
stochastic
(drift)
deterministic
(selection)
A place
Some species have a fitness advantage over other species (lots of specific reasons)
One individual organism (each colour a different species)

12. St+1 - St = speciation + immigration - extinction IMPORTANT
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
stochastic
(drift)
deterministic
(selection)
A place
IMPORTANT
Other forms of selection can counter tendency towards local extinction (we’ll get to this)
One individual organism (each colour a different species)

13. Speciation Dispersal Drift Selection
Only 4 kinds of process can change the distribution, diversity, and abundances of species in a community
Speciation
Dispersal
Drift
Selection

14. 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)

15. Selection happens among and within species
Dark-coloured moths have an advantage over lighter-coloured moths on dark tree trunks
Kudzu has an advantage over other plants on disturbed soils in the southeastern U.S.

16. 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.

17. Possible outcomes of ecological drift between two species in a community of size, J = 4X X X X X
Time X X
How do you tell the difference between this and selection?

18. A Different Structure for Community Ecology
Processes
Drift
Speciation
Migration
Selection
Constant
- Freq. dependent
+ Freq. dependent
Primary patterns
(across space & time)
Species diversity
Species composition
(identity and traits)
Species abundances
Emergent patterns
Productivity
Stability
Food web connectance
Whatever you can think of

19. Note: Extinction results from drift & selection
Everything you need to know…
…about ecological communities
Global community
Speciation
Drift
Selection
Regional community
Dispersal
Dispersal
Speciation
Drift
Selection
Dispersal
Dispersal
Local
Community
Speciation
Drift
Selection
Note: Extinction results from drift & selection

20. (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.

21. 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?

22. (3) Philosophical perspectives
The crux of the matter:
y = ax + b
+ e
What is that?

23. 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
“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
Stochasticity is real
“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)
It doesn’t matter one way or the other, in practice
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

24. + e(smaller than before)
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)
Forest type
Primary
Secondary

25. Heisenberg’s Uncertainty Principle
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.

26. Is the theoretical value of e zero?
Is achieving e = 0 a practical goal?

27. Mutation: Effects are random with respect to traits/fitness.
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)

28. 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)

29. 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)

30. 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

31. How can a model based on randomness predict anything?

32. Randomness at one level Order/predictability at another
Kinetic theory of ideal gases
(Statistical mechanics)

33. Randomness at one level Order/predictability at another
Neutral theory (drift + dispersal + speciation, no selection)

34. 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)

35. 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.

36. Are we re-inventing the wheel…again?

37. 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)

38. 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)

39. 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