Transcript Computational Emergence, Robustness and

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 trivial
For 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 …..
a1n+1 a2n+1 …………… akn+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
10
9
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.
8
7
6
5
4
3
2
1
0
Unpredictability in computationnaly
emergent CA
Xn
Cjp
Xn+1
Xn+m
Cjn……
n………..
Cj+Pn……
Xn
p
…..
Cj
n+1….
Cjn+m….
Cj-
C’jn……
Cj+Pn…
n………..
……..
Xn+1
C’jn+1….
Xn+m
C’jn+m….=
f
j
(C n+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 A
Alternative model
No emergence
Computationally emergent
(specific causal process etc.)
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 rules
Dictated 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 project
Dispersal assembly, ecological
drift, and random speciation are reasonable approximations
to 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 species
Deterministic effects
(competition, muitualism etc. - >
modes of selection)
Niche tehory is better
In community ecology
Many species
Stochastic effects
Ecological drift
Neutral theory is better
The « stochastic/deterministic »
gradient
Few individuals
Small population
drfit may overcome selection
PG includes drift essentially
In population genetics
Many individuals
Large populations
Selection is the most efficient
PG 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 Macropredictions (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?)