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 InstructorTues. 21 Sept. History and philosophy of stochasticity in ecology VellendThurs. 23 Sept. Null models SrivastavaTues. 28 Sept. Implementing null models in R KraftThurs. 30 Sept. Student-led discussion - Null modelsTues. 5 Oct. Stochasticity in evolutionary biology John Beatty*Thurs. 7 Oct. Student-led discussion - History, Philosophy, EvolutionTues. 12 Oct. Theoretical models: Drift and selection VellendThurs. 14 Oct. Student-led discussionTues. 19 Oct. Theoretical models: Incorporating dispersal VellendThur. 21 Oct. Student-led discussionTues. 26 Oct. Statistical models: Partitioning variance in community composition SrivastavaThurs. 28 Oct. Student-led discussionTues. 2 Nov. Empirical issues: Priority effects SrivastavaThurs. 4 Nov. Student-led discussionTues. 9 Nov. Empirical issues: Testing for dispersal limitation SrivastavaThurs. 11 Nov. Student-led discussionTues. 16 Nov. Empirical issues: Experimental manipulating of something “stochastic”

or “neutral”Vellend

Thurs. 18 Nov. Student-led discussionTues. 23 Nov. Project presentations / workThurs. 25 Nov. Project presentations / workTues. 30 Dec. Project presentations / workThurs. 2 Dec. Project presentations / work

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 ECOLOGYThe 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 =

A place

One individual organism (each colour a different species)

speciation

Let’s start with the number of species, S, in a particular place

How can S change over time?

St+1 - St =

A place

One individual organism (each colour a different species)

speciation

Some otherplace

+ immigration

Let’s start with the number of species, S, in a particular place

How can S change over time?

St+1 - St =

A place

One individual organism (each colour a different species)

speciation + immigration - extinction

stochastic(drift)xIndividuals 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 =

A place

One individual organism (each colour a different species)

speciation + immigration - extinction

deterministic(selection)

stochastic(drift)

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 =

A place

One individual organism (each colour a different species)

speciation + immigration - extinction

deterministic(selection)

stochastic(drift)

IMPORTANTOther 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.

X

X

X X

X

Tim

e

X

X X

Possible outcomes of ecological drift between two species in a community of size, J = 4

How do you tell the difference between this and selection?

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

A Different Structure for Community Ecology

Regional community

Dispersal

SpeciationDrift

Selection

Dispersal

LocalCommunity

SpeciationDrift

Selection

Dispersal

Global community

Dispersal

SpeciationDrift

Selection

Note: Extinction results from drift & selection

Everything you need to know… …about ecological communities

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.

From the Oxford English Dictionary (The definitive record of the English language)

(2) What is stochasticity?

A process or variable is stochastic if we can specify its value or magnitude only as a probability distribution rather than a single number.

But what does that mean?

Early application of probability theory: human life tables and projections of population growth/structure (i.e., ecology of Homo sapiens)

(3) Philosophical perspectivesThe crux of the matter:

+

-1 0 1 2Log (patch area)

1

2

3

4

5

6

7Lo

g (p

opu l

atio

n si

z e)

y = ax + bWhat is

that?

“…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 = Ignorance

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

“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

Forest type Primary Secondary

+ smaller than before)y = ax + b + d

-1 0 1 2Log (patch area)

1

2

3

4

5

6

7

Log

(pop

u lat

ion

size

)

21

Forest Type

Scientific progress?Is the theoretical value of zero?

If so, is achieving = 0 a practical goal?

Is the theoretical value of 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 zero?Is achieving = 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 )

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

Back to “what is stochasticity?”…

1. Doak et al. (2009, In: The Princeton Guide to Ecology)

Kingsland (1995, Modeling Nature); Real & Brown (1991, Foundations of 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

The big current debate: niche vs. neutralMaybe 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?

Kinetic theory of ideal gases(Statistical mechanics)

Randomness at one level

Order/predictability at another

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?

“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)

“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)

“there is no evidence for stochasticity in nature at observable scales. Stochasticity is an attribute of models.” (Clark 2009, TREE)

Is there an alternative to the (seemingly obvious) “continuum” consensus?

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 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