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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

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I. COMPUTATIONAL EMERGENCE

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I. The concepts of emergence 1. Unpredictability -Irreducibility 2. Also (intuitively) : Order 3. Downward causation 4 ? Novelty - > later

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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 »

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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)

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Problem: Combinatorial emergence makes the concept of emergence trivial For ex. Wimsatt 2007: everything is an emergent property except the mass

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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 »)

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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)

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b. Causation in simulations - A cellular automaton displays counterfactual dependencies between properties at each step. a 1 a 2 ….. a 1+P a 2+P ……………… a k ….. A 1 n, j A 2 n, j ……… A k n, j ….. a 1 n+1 a 2 n+1 …………… a k n+1.. Property P n at Step n (Add (on i) Disj (on j) A i n, j ) Property P n+1 at Step n+1 (all the b i n+1 ) If P n had not been the case, P n+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:

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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:

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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

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EMERGENCE : KINDS OF PREDICTABILITY

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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.

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Unpredictability in computationnaly emergent CA XnXn C j- p n……….. C j n…… C j+P n…… ….. X n+1 C j n+1…. X n+m C j n+m…. XnXn C j- p n……….. C j n…… C j+P n… …….. X n+1 C j n+1…. X n+m C j n+m….= f ( C j n+m……) f non computable

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B. m-Predictability Earlier sets of states are good predictors (Shalizi et al. 2003) of later sets

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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 : Reynolds flocking boids, etc

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(Reynolds flocking boids, 1987)

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

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II. ANSWERING THE INACCURACY OBJECTION AND ANALYSING CAUSAL RELEVANCE

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II. The « inadequacy objection » Target phenomenon Model A Alternative model Computationally emergent (specific causal process etc.) No emergence

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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

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Testcase. Neutral theory in Ecology

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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.)

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Barro Colorado rain forest

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Often seems like lognormal distribution (Fishers statistical approximation) Why ? -> explain and predict patterns of relative species abundance The explanandum is biodiversity and biogeography (not adaptation)

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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?.

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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)

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

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OUtcomes

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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)

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The ancestor – Mc Arthur & Wilson (1967) Species equivalence Immigration, extinction are the only parameters No speciation, no metacommunity level

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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

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Hubbells 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.

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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, its 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

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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.

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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:

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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)

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Disturbance model in a community

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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

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Weakly Emergent Outcomes: neutral theory vs. lognormal predictions

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

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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 ) b. Robustness of the model

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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)

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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)

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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)

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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

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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

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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

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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 dont 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)

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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

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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.)

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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 models 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

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Corollary Reading off causal factors Analytic models: relevant factors are variables in the equations Simulations : relevant causal factors are parameters identified in robust models

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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.

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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?)

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