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

1. Computational Emergence, Robustness and Realism: ConsideringEcology and ItsNeutralModels Philippe Huneman, Institut d'Histoire et de Philosophie des Sciences et des Techniques, Paris

2. I. computational emergence

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

4. I. The concepts of emergence a. Combinatorial emergence (emergent vs aggregative properties, eg Wimsatt Phil Sci1997) « A is emergent iff A is a property of X (composed of x1……xN) but of none of xi »

5. I. The concepts of emergence a. Combinatorial emergence (emergent vs aggregative properties, eg Wimsatt Phil Sci1997) « 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)

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

7. 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 »)

8. 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)

9. b. Causation in simulations - A cellular automaton displays counterfactualdependenciesbetween properties ateachstep. a1 a 2 ….. a1+P a2+P ………………ak ….. A1 n, j A2 n, j……… Akn, 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:

10. 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:

11. Robust emergence: Counterfactual relation between Ym and Ym+p (1<p<N) (Y being in a CA a series of states) : « novel » global rule »

12. 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

15. Emergence : kinds of predictability

16. 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.

17. Unpredictability in computationnaly emergent CA

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

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

20. 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

21. (Reynolds flockingboids, 1987)

22. M-predictability: Possibility of macropredictions on the basis of many m-regularitiesappearing in eachrobustly emergent process

23. Ii. answering the inaccuracy objection and analysing causal relevance

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

25. 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

26. Testcase. Neutraltheory in Ecology

27. 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.)

28. Barro Colorado rainforest

30. Oftenseemslikelognormal distribution (Fisher’sstatistical approximation) • Why ? -> explain and predict patterns of relative speciesabundance The explanandum is biodiversity and biogeography (not adaptation)

31. Situating the problem – a reminder • Population genetics: one species, a population, explaining the changes in allelefrequencies; explanantia = natural selection, genetic drift, migration • Ecology: manyspecies, patterns of succession, abundance, distribution (hence, timescalehigherthan in PG) Explanantia : niche-effects (= naturel selection) - > competitive exclusion principle; XXX?.

32. Question here : how to articulate the evolutionary processwithineachspecies of each population, and the generalmacropattern of all species ? -> A question of synthesisbetweenmacroecology and evolution • Hubbell ’s aim: a new notion of drift, whichparallelsdrift in PG and molecularevolution(Kimura, neutraltheory : evolutionat the level of nucleotides is often pure drift)

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

34. OUtcomes

35. 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)

36. The ancestor – Mc Arthur & Wilson (1967) • Speciesequivalence • Immigration, extinction are the onlyparameters • No speciation, no metacommunity level

37. 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-effectsmodels • Assemblyrules Dictated by niche differences • Yielded by natural selection acting on the individuals of the population « This viewholdsthatcommunities 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”

38. Hubbell’sproject 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.

39. The model • (wrt Island model) Changing the equivalenceassumption: not about species, but about individuals in the species -> « In the theoryof island biogeography, neutrality is defined at the species level. However, in the present theory, neutrality is defined at the individual level.” Namelyeachindividuals in eachspecies have the samedeath and birth rates; ie, it’s as if therewere no natural selection • Extinction rates are not the same for alllspecies but result from the model; the model allows for speciation; metacommunity versions

40. 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.”

41. 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:

42. 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 analogywithgenetic 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)

43. Disturbance model in a community

44. 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

45. Weakly Emergent Outcomes:neutraltheory vs. lognormalpredictions

46. Falsifiedpredictions = coralreef. Hypothesis : environmental stochasticity outreachesdemographic stochasticity (ie ecological drift)

47. The problem a. Falsity of the equivalenceassumption & 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

48. 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)

49. 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. • «  neutraltheories 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 observedatlargerscales. » (Chave 250)

50. 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 becomesunavoidable. » (Chave 241)