Computational Emergence, Robustness and Realism: Considering Ecology and Its Neutral Models Philippe...

Computational Emergence, Robustness and Realism: Considering Ecology and Its

Neutral Models Philippe Huneman,

Institut d'Histoire et de Philosophie des Sciences et des Techniques,

Paris

I. COMPUTATIONAL EMERGENCE

I. The concepts of emergence

1. Unpredictability

- Irreducibility

2. Also (intuitively) : Order

3. Downward causation

4 ? Novelty - > later

I. The concepts of emergence

a. Combinatorial emergence (emergent vs aggregative properties, eg Wimsatt Phil Sci 1997)

« A is emergent iff A is a property of X (composed of x1……xN) but of none of xi »

I. The concepts of emergence

a. Combinatorial emergence (emergent vs aggregative properties, eg Wimsatt Phil Sci 1997)

« A is emergent iff A is a property of X (composed of x1……xN) but of none of xi »

b. Computational emergence (Bedau 1997, Hovda, Humphreys, Huneman (Minds and machines 2008)

• Problem:Combinatorial emergence makes the concept of

emergence trivialFor ex. Wimsatt 2007: everything is an emergent

property except the mass

• Computational emergence : A is emergent iff in a process going from Initial state to A there is no way to reach A to except by simulating all the steps.

(Bedau, Phil. Persp., 1997, « Weak emergence »)

a.Objectivity of computational emergence: criteria do not depend on our epistemic interests

and abilities

Arguments for the objectivity (Buss, Papadimitriou et al., 1995; Huneman Phil ci 2008)

= The prediction problem may be objectively longer than the simulation

Huneman P. « Emergence made ontological ? Emergent of properties vs. Emergent processes. » Phil. Sci. (2008)

b. Causation in simulations - A cellular automaton displays counterfactual dependencies between properties at each step.

a1 a 2 ….. a1+P a2+P ……………… ak …..

A1 n, j A2

n, j……… Ak n, j …..

a1

n+1 a2n+1 …………… ak

n+1..

Property P n at Step n (Add (on i) Disj (on j) Ai n, j )

Property Pn+1 at Step n+1 (all the bin+1 )

“If P n had not been the case, Pn+1 would not have been the case.”

Causation as counterfactual dependence between steps in CAs

Huneman P. (2008) Emergence and adaptation. Minds and machines, 18:

Robust emergence (as a subclass of emergent processes)– emergent causal laws

In some cases, during the emergent process we find a specific characterization of the causal behaviour of the system as a whole – a kind of global rule : “causal criterion of robustness”

Huneman P. (2008) Emergence and adaptation. Minds and machines, 18:

Robust emergence:Counterfactual relation between Ym and Ym+p

(1<p<N) (Y being in a CA a series of states) : « novel » global rule »

Example of Glider guns in GOL (« If G had not been there at t1 then G would not have been here at t8… »); Langton-Sayama Loop

EMERGENCE : KINDS OF PREDICTABILITY

0

1

2

3

4

5

6

7

8

9

10

This system allows predictions if the final values it reaches, starting from all different initial values in [i-d; i+d], are in a range f(d) which is not too much larger than the range (d) of initial values. If not, it means that the margin of error (represented here by d) of our measurements of those initial values will not ensure that the final result yielded by calculating the final state is in a same or analogous margin of error, so there will be no possible prediction.

Unpredictability in computationnaly emergent CA

Xn Cj-

pn………..

Cjn…… Cj+P

n……….

.

Xn+1 Cjn+1….

Xn+m Cjn+m….

Xn Cj-

pn………..

C’jn…… Cj+P

n…

……..

Xn+1 C’jn+1….

Xn+mC’j

n+m….= f

(Cjn+m……)

f non

computable

B. m-Predictability

Earlier sets of states are good predictors (Shalizi et al. 2003) of later sets

• Earlier sets of states are good predictors (Shalizi et al. 2003) of later sets

C-M predictability

Two classes of computer simulations

- Embody the equations of a system (Navier-Stokes discretized etc.)

- Pick up some empirical rough regularities and build a simulation : Reynold’s flocking boids, etc

(Reynolds flocking boids, 1987)

M-predictability: Possibility of macropredictions on the basis of many m-regularities appearing in each robustly emergent process

II. ANSWERING THE INACCURACY OBJECTION AND ANALYSING CAUSAL RELEVANCE

II. The « inadequacy objection »

Target phenomenon

Model AAlternative model Computationally emergent

(specific causal process etc.)

No emergence

Answer : robustness analysis (Levins 1966; Wimsatt, 1989; Weisberg 2006)

Change :- The values of the variables- the set of parameters

-> However, it might be that some parameters do not change the patterns of behavior: robustness of the model

In this case, for a robust model satisfying the computational emrgence criterion, the reality itself can be said to display emergent processes or emergent properties, since this emergence has been made manifest in a robust model of its causal structure

Testcase. Neutral theory in Ecology

Hubbell. The Unified neutral theory of biodiversity and biogeography (2001)

Modeling abundance and (same trophic level) species distribution in communities and metacommunities

(many species of trees, mostly resident species, etc.)

Barro Colorado rain forest

• Often seems like lognormal distribution (Fisher’s statistical approximation)

• Why ?-> explain and predict patterns of relative

species abundance

The explanandum is biodiversity and biogeography (not adaptation)

Situating the problem – a reminder

• Population genetics: one species, a population, explaining the changes in allele frequencies; explanantia = natural selection, genetic drift, migration

• Ecology: many species, patterns of succession, abundance, distribution (hence, timescale higher than in PG)

Explanantia : niche-effects (= naturel selection) - > competitive exclusion principle; XXX?.

• Question here : how to articulate the evolutionary process within each species of each population, and the general macropattern of all species ?

-> A question of synthesis between macroecology and evolution

• Hubbell ’s aim: a new notion of drift, which parallels drift in PG and molecular evolution (Kimura, neutral theory : evolution at the level of nucleotides is often pure drift)

The fact

Neutral ecology models “raised the bar in discussions of emergent patterns in this field” (Holyoak & Loreau, ecology, 2006)

OUtcomes

It was surprising to find that spatial neutral models give rise to frequency distributions of precision that are very similar to those estimated from biological surveys, as a consequence of the spatial patterns produced by local dispersal alone (Bell et al Ecology 2006 )

Models fit the data concerning distributions and abundance (Barro Colorado, Panama; Peru, Ecuador; Cameroon's forests)

The ancestor – Mc Arthur & Wilson (1967)

• Species equivalence• Immigration, extinction

are the only parameters• No speciation, no

metacommunity level

2 kinds of models Dispersal-assembly(eg McA-W sland biogeography

model)

“It asserts that communities are open, nonequilibrium assemblages of species largely thrown together by chance, history, and random dispersal. Species come and go, their presence or absence is dictated by random dispersal and stochastic local extinction”

Niche-effects models• Assembly rulesDictated by niche differences• Yielded by natural selection

acting on the individuals of the population

« This view holds that communities are groups of interacting species whose presence or absence and even their relative abundance can be deduced from “assembly rules” that are based on the ecological niches or functional roles of each species”

Hubbell’s projectDispersal assembly, ecologicaldrift, and random speciation are reasonable approximationsto the large-scale behavior of biodiversity in a biogeographic context. In

essence,(Neutraslit authors) took a statistical-mechanical approach to understanding macro-ecological patterns of biodiversity. I believe that this approach will prove more successful in the long run than attempts to scale up from the reductionistic approach that has preoccupied community ecology for so much of the twentieth century.

The model

• (wrt Island model) Changing the equivalence assumption: not about species, but about individuals in the species

-> « In the theory of island biogeography, neutrality is defined at the species level. However, in the present theory, neutrality is defined at the individual level.”

Namely each individuals in each species have the same death and birth rates; ie, it’s as if there were no natural selection

• Extinction rates are not the same for alll species but result from the model; the model allows for speciation; metacommunity versions

• Relation between individuals and area -> “the dynamics of ecological communities are a zero-sum game. If, as the relationship implies, the density of individuals ρ is a constant, then any increase in one species must be accompanied by a matching decrease in the collective number of all other species in the community. The sum of all changes in abundance is always zero.”

Let the probability that the replacing individual is of species i be given by the current relative abundance of species i. Let the current abundance of species i be Ni. Then, the transition probabilities that species i will decrease by one individual remain unchanged in abundance, or increase by one individual during

one time step are given by:

• Ecological drift : “Species in this simple neutral model are identical and equal competitors on a per capita basis. They have identical per capita chances of dying and of reproducing. Each species has an average stochastic rate of increase, r, of zero. The dynamics of the model community is therefore a random walk. For this reason, I call this process ecological drift in analogy with genetic drift » (Hubbell 2001)

• “An important question to answer is: How long does it take an arbitrary species to go extinct or to achieve complete dominance under zero-sum ecological drift? Species drift to the absorbing abundance states of 0 or J . The time to “fixation” or absorption will depend on the size of the community J , the disturbance rate, D, and the initial abundance of the focal species, Ni. I first focus on the analytically more tractable case of D = 1.” (Hubbell) -> parallels population genetics (fixation probability by pure drift of a rare allele)

Disturbance model in a community

• If N(t) is a row vector of probabilities that

• species i is at abundances 0 through J at time t, then the row

• vector of probabilities at time t + 1 can be found simply as

• N(t + 1) = N(t) · M

Weakly Emergent Outcomes:neutral theory vs. lognormal predictions

• Falsified predictions = coral reef. Hypothesis : environmental stochasticity outreaches demographic stochasticity (ie ecological drift)

The problem

a. Falsity of the equivalence assumption& Accuracy of the predicted patterns- > Why ?

« justifying why a model whose principal assumption looks so evidently false still deserves consideration.” (Chave 2006 250)

b. Robustness of the model

• Why are ecological niches and fitness differences legitimately equalised in a neutral model ?

-> In general: there are always a very large number of parameters for a given system, but parameters are connected such that the effects of some of their values are compensated for by others, so that in the end they are inefficient regarding the outcome. (connection with statistical mechanics ? Strevens 2003)

• Here : Natural selection plays a role in each species population, but at the level of the (meta)communities you can explain away from natural selection.

• « neutral theories are useful, not because the real world is neutral (it is not) but because the functional differences we observe among species or among individuals are not essential to predict some of the patterns observed at larger scales. » (Chave 250)

Conditions for such averaging away

• « Theories of coexistence by niche differentiation are mostly concerned with purely deterministic processes, and a small number of species that interact through fixed rules, as prescribed in the Lotka-Volterra equations. By contrast, the neutral theory is primarily concerned with species-rich communities (tropical forests, coral reefs) with many rare species, where the role of stochasticity at the individual scale becomes unavoidable. » (Chave 241)

The « stochastic/deterministic » gradient

Few speciesDeterministic effects(competition, muitualism etc. - > modes of selection)Niche tehory is better

In community ecology

Many species

Stochastic effectsEcological drift Neutral theory is better

The « stochastic/deterministic » gradient

Few individualsSmall population drfit may overcome selectionPG includes drift essentially

In population genetics

Many individualsLarge populations

Selection is the most efficientPG models rely on seletcion

But : Difference in explanatory scope

1. Explaining the patterns of abundance: neutral theory is often correct

Differs from

2. Explaining which species are more represented than others : appeal to niche differences, ie functional differences between species and selection

Comparing niche and neutral models in abundance patterns predictions

• Niche-effects models often have the same pattern outcomes

• So what is causally relevant is the parameters of ecological drift, because the niche effects don’t change anything

(sort of parcimonious argument : if you can explain without

the function differences, those are not expanatory/causally relevant because without them the

phenomenon is already explained)

Comparing niche and neutral models

• If we incorporate “niche effects” in those models which successfully represent actual distributions, the fact is that the outcomes will not change much (Chave Ecology 2004, 246).

• So the neutral model of species abundance distribution in the tropical rainforest is robust in the sense that adding niche parameters does not change the outcome

Consequences from robustness analysis

• The neutral dynamics, for which the only parameters are the general parameters of the populations (namely the size, immigration and speciation rates, etc.), is causally responsible for the emergent patterns of distribution

• The model picks out really emergent patterns, and the causal factors relevant in Macro-predictions (ie dispersal limitation, population size, etc.)

Relevant causal factors.

• Claim : the parameters not causally responsible for the emergent features are the ones that are not making a difference to the robust model’s behavior.

• Whereas those parameters involve many effects in the behaviors of the individual “agents,” they must not be held as causes of the qualitative patterns of outcome behaviors considered here

Corollary

Reading off causal factors

• Analytic models: relevant factors are variables in the equations

• Simulations : relevant causal factors are parameters identified in robust models

Conclusions

• Neutral models : a novel object for the philosopher of science

Caveat. Neutrality at the molecular level is not resulting from a false assumptions; one can argue than some genome sequences are neutral; whether neutrality at the ecological level is a result of lower level causal relatiosn abstracted away.

Conclusions

• Neutral models successful at both ends of biological scale: molecular evolution / metacommunity ecology

-> Why ?• Difference null hypothesis / neutral model (at

which conditions is the NH a Neutral model?)