Evolutionary Transitions and Top-Down CausationSara Imari Walker1,2,3, Luis Cisneros4 and Paul C.W. Davies2,4

1NASA Astrobiology Institute, USA2 BEYOND: Center for Fundamental Concepts in Science, Arizona State University, Tempe AZ USA

3 Blue Marble Space Institute of Science, Seattle WA USA4 Center for the Convergence of Physical Science and Cancer Biology, Arizona State University, Tempe AZ USA

sara.i.walker@asu.edu

Abstract

Top-down causation has been suggested to occur at all scalesof biological organization as a mechanism for explaining thehierarchy of structure and causation in living systems (Camp-bell, 1974; Auletta et al., 2008; Davies, 2006b, 2012; Ellis,2012). Here we propose that a transition from bottom-up totop-down causation – mediated by a reversal in the flow ofinformation from lower to higher levels of organization, tothat from higher to lower levels of organization – is a driv-ing force for most major evolutionary transitions. We suggestthat many major evolutionary transitions might therefore bemarked by a transition in causal structure. We use logisticgrowth as a toy model for demonstrating how such a transi-tion can drive the emergence of collective behavior in replica-tive systems. We then outline how this scenario may haveplayed out in those major evolutionary transitions in whichnew, higher levels of organization emerged, and propose pos-sible methods via which our hypothesis might be tested.

IntroductionThe major evolutionary transitions in the history of life onEarth include the transition from non-coded to coded in-formation (the origin of the genetic code), the transitionfrom prokaryotes to eukaryotes, the transition from pro-tists to multicellular organisms, and the transition from pri-mate groups to linguistic communities (Szathmary and May-nard Smith, 1997; Jablonka and Lamb, 2006). A hallmarkof many of these transitions is that entities which had beencapable of independent replication prior to the transitioncan subsequently only replicate as part of a larger repro-ductive whole (Szathmary and Maynard Smith, 1995). Aclassic example is the origin of membrane bound organelleswithin modern eukaryotes, such as the mitochondria, whichare believed to have emerged through endosymbiosis withprokaryotes that later lost their autonomy (Sagan, 1967).Each such transition is typically viewed as marking a drasticjump in complexity: cells are much more complex than anyof their individual constituents (i.e. genes or proteins), eu-karyotes are more complex than prokaryotes, multicellularmore complex than unicellular organisms, and human so-cieties more complex than individuals. However, althoughsuch a hierarchy is conceptually easy to state, in practice it

is difficult to determine what, if any, universal principles un-derlie such large jumps in biological complexity.

Szathmary and Maynard Smith have suggested that allmajor evolutionary transitions involve changes in the wayinformation is stored and transmitted (Szathmary and May-nard Smith, 1995). An example is the origin of epigeneticregulation, whereby heritable states of gene activation leadto a potentially exponential increase in the amount of infor-mation that may be transmitted from generation to genera-tion (since a set of N genes, existing in two states - on or off- via epigenetic rearrangements, can have 2N distinct states).Such a vast jump in the potential information content of sin-gle cells is believed to have led to a dramatic selective advan-tage in unicellular populations capable of epigenetic regula-tion and inheritance (Jablonka and Lamb, 1995; Lachmannand Jablonka, 1996). The reasoning is straightforward: epi-genetic factors permit a single cell line with a given geno-type to express many different phenotypes on which natu-ral selection might act, thereby providing a competitive ad-vantage through diversification. Importantly, this innova-tion was crucial to the later emergence of multicellularity bypermitting differentiation of many cell types from a singlegenomic inventory. However, although epigenetic regula-tion was likely a necessary precondition for the emergenceof multicellular organization (at least in extant lineages), itdoes not necessitate that such a transition from unicellular-ity to multicellularity will occur or explain how it occurs.Plenty of protists are capable of phenotypic differentiationbut have never made the transition to true multicellularity,although they may exhibit highly collective and coordinatedbehaviors (see e.g. Nedelcu and Michod (2004) for a discus-sion of unicellular, multicellular, and a gamut of intermedi-ate forms within the Volvocalean green algal group). Moregenerally, while it is true that changes in how informationis stored and transmitted enable the possibility of new levelsof organization to evolve, such innovations are not neces-sarily a sufficient causative agent to drive the emergence ofgenuinely new, higher-level, entities.

Therefore to make progress in understanding the majortransitions, a key, and oft understated, distinction must be

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made between the evolutionary innovations leading up toa major transition that enable higher-levels of organizationto emerge, and the mechanism(s) underlying the physicaltransition itself. In general, the majority of unifying workon major evolutionary transitions has focused on the for-mer perspective by outlining the key steps that enabled aparticular transition to occur, such as the innovations in in-formation storage and transmission outlined by Szathmaryand Maynard Smith (Szathmary and Maynard Smith, 1997).While these innovations are certainly crucial to our under-standing of the historical sequence of evolutionary eventssurrounding each major transition – such as the example ofthe appearance of phenotypic differentiation via epigeneticregulation prior to the emergence of multicellularity citedabove – they tell us little about the underlying mechanismsgoverning the emergence of genuinely new higher-levels oforganization. If there are in fact any universal principlescommon to all such major jumps in biological complexity,we should expect there to be a common mechanism drivingeach such transition that is not dependent on a precise seriesof historical (evolutionary) events. In this paper, we focuson those major evolutionary transitions leading to the emer-gence of new, higher level entities, which are composed ofunits that previously reproduced autonomously. We proposethat these major transitions, corresponding to major jumps inbiological complexity, are associated with information gain-ing causal efficacy over higher levels of organization.

To outline our hypothesis, we first present an introduc-tion to top-down causation in biological systems, and outlinehow a transition to top-down causation via informational ef-ficacy over new, higher levels of organization might enablethe emergence of higher-level entities. We then present a toymodel, investigating the onset of non-trivial collective be-havior in a globally coupled logistic map lattice, to demon-strate how a reversal in the dominant direction of informa-tion flow, from bottom-up to top-down, is correlated withthe emergence of collective behavior in replicative systems.A key feature of our analysis is to determine the directionof causal information transfer. We then outline how a tran-sition in causal structure may have driven both the origin oflife and the origin of multicellularity, as two representativeexamples of major evolutionary transitions in which new,higher levels of organization emerged. We conclude withsome suggestions about possible methods via which our hy-pothesis might be tested.

Informational Efficacy and Top-DownCausation

Biological information is a notoriously difficult concept todefine (Kuppers, 1990). This difficultly stems in part fromthe fact that in living systems the dynamics are coupled tothe information content of biological states such that the dy-namics of the system change with the states and vice versa(Goldenfeld and Woese, 2011; Davies, 2012). This is in

Higher Level

Lower Level (a) (b)

Figure 1: Bottom-up and top-down modes of causation. (a)The standard (reductionist) view suggests everything in theuniverse is directed by bottom-up action only, such that cau-sation flows strictly from lower to higher levels. (b) Bi-ological organization suggests an alternative causal struc-ture whereby bottom-up modes of causation emanating fromlower-levels provide a space of possibilities, and higher-levels of organization modify the causal relations below viatop-down causation. Figure adapted from (Auletta et al.,2008).

marked contrast to the traditional approach to dynamics,where the physical states evolve with time but the dynamicallaws remain fixed, or change over much longer time scales.The coupling of states to dynamics is perhaps most evidentfor the case of the genome, in which the expressed set ofinstructions – i.e. the relative level of gene expression – de-pends on the state of the system - i.e. the composition ofthe proteome, environmental factors, etc. - that regulate theswitching on and off of individual genes. The result is thatthe update rules change with time in a manner which is botha function of the current state and the history of the organ-ism (Goldenfeld and Woese, 2011). This feature of “dynam-ical laws changing with states” (Davies, 2012), as far as weknow, seems to be unique to biological organization and is adirect result of the peculiar nature of biological information(although speculative examples from cosmology have alsobeen discussed, see e.g. (Davies, 2006a)).

Biological information is distinctive in its contextual orsemantic nature, in other words it means something (May-nard Smith, 2000). For example, a gene is just a randomsequence of nucleotides when taken in isolation, and is in-distinguishable from junk, or noncoding, DNA. It is mean-ingful, or biologically functional, only within the context ofthe cell, where a suite of molecular hardware collaboratein decoding and executing the encoded instruction (e.g. tomake a protein). As such, biological information is an ab-stract global systemic entity, carrying meaning only withinthe context of an entire living system. It is of course im-printed in biochemical structures, but one cannot point toany specific structure in isolation and say “aha! I see biologi-cal information here!”: even the information in genes is onlyefficacious and manifested in a relational sense (i.e. it mustbe decoded by the appropriate cellular machinery). Perhapseven more profound, this abstraction appears to have causalefficacy (Auletta et al., 2008; Ellis, 2012; Davies, 2012) - it

is the information that determines the state and hence the dy-namics. As such, it is the efficacy of information that leadsto the convolution of dynamical laws and states that makesbiology so unique.

This convolution results in multidirectional causality withcausal influences running both up and down the hierarchyof structure of biological systems (e.g. both from genometo proteome, and from proteome to genome via the switch-ing on and off of genes). A full explanatory framework forbiological processes should therefore include both bottom-up causation (Fig. 1a) – such as when a gene is read-out tomake a protein that affects cellular behavior – and top-downcausation (Fig. 1b) – as occurs when changes in the environ-ment initiate an organismal response that permeates all theway down to the level of individual genes (Davies, 2012).A striking of the latter is provided by the phenomenon of“mechanotransduction”, where physical forces, such as thesheer stress on a cell or the Youngs modulus of an adjacentsurface to which the cell attaches, actually affect gene ex-pression (Alberts et al., 2002). Bottom-up causation is thestatus-quo in modern physics, whereas top-down causationis less familiar and difficult to quantify. Generally, top-downcausation is characterized by a ’higher’ level influencing a’lower’ level by setting a context (for example, by chang-ing some physical constraints) by which the lower level ac-tions take place (Auletta et al., 2008; Davies, 2006b; Ellis,2006, 2012). An interesting example of top-down causa-tion is provided by natural selection in evolution (Campbell,1974; Okasha, 2012), where the history as well as the fate ofan organism is determined by the wider environmental con-text. This is particularly evident for cases of convergent evo-lution (Davies, 2006b), of which the wing is a classic exam-ple. Birds, pterodactyls, and bats each developed wings, de-spite the fact that their last common ancestor did not possesswings. The commonality of form is attributable to physical(environmental) constraints imposed on wing design, whichmanifests a particular phenotypic trait in the organism (i.e. awing). However, the effect is also a local physical one: thebiochemical interactions – dictated in part by both geneticand epigenetic programming – that govern the morpholog-ical development of something as complex as a bird wingare inherently local. As such, natural selection provides awell-known example of how higher level processes (e.g. en-vironmental selection) constrain and influence what happensat lower levels (e.g. biochemistry).1

1Although it is normal for biologists to discuss causal narra-tives in informational terms (e.g. cells signal each other, and re-cruit molecules to express instructions . . . ) a determined reduc-tionist would argue that, in principle, this narrative would parallelan, albeit vastly more complicated, account in terms of molecu-lar interactions alone, in which only material objects enjoy truecausal efficacy. In this paper we remain agnostic on the questionof such promissory reduction because our principal claims remainvalid even if the informational-causal narrative is accepted as amere facon de parler.

(a)

(b)

Figure 2: Schematic illustrating a shift in causal structuremediated by the transition from a collective of lower levelentities to a new higher level entity. (a) Prior to the transi-tion, higher levels of organization are dictated by bottom-upcausation directed by lower level entities (which themselvesmay be hierarchal in nature). (b) A new (higher level) en-tity emerges that may be identified as an “individual” whena transition to top-down causation with efficacy over a new,higher-level of organization (in this case the medium greylevel) occurs. Dotted lines are used to indicate an individualentity (i.e. an organism as in the case for the transition fromunicellular to multicellular organisms)

The foregoing discussion indicates that top-down causa-tion – mediated by informational efficacy – plays an impor-tant role in dictating the dynamics of living systems, wherecausal influences can run both up and down structural hier-archies. In many of the major evolutionary transitions, newhigher-level entities emerge from the collective and coordi-nated behavior of lower-level entities, eventually transition-ing to a state of organization where the lower–level entitiesno longer have reproductive autonomy. Examples of tran-sitions where lower-level units have lost their autonomy in-clude the the origin of life (i.e. the hypothetical RNA world),the origin of multicellularity, and the origin of eusociality(Szathmary and Maynard Smith, 1997). During such transi-tions, the dynamics of lower level entities come under the di-rection of the emergent high-level entity. This, coupled withthe multidirectional causal influences in biological organi-zation, suggests that evolutionary transitions that incorpo-rate new, higher levels of organization into a biological sys-tem should be characterized by a transition from bottom-upto top-down causation, mediated by a reversal in the dom-inant direction of information flow. Therefore, we suggestthat major shifts in biological complexity – from lower levelentities to the emergence of new, higher level entities – areassociated with a physical transition (perhaps akin to a ther-

modynamic phase transition), and this physical transition isin turn associated with a fundamental change in causal struc-ture (schematically illustrated in Fig. 2). To illustrate thisclaim, we turn to a toy model investigating the emergence ofnon–trivial collective behavior in a globally coupled chaoticmap lattice (Cisneros et al., 2002; Ho and Shin, 2003).

Logistic Growth as a Toy ModelTo explore the emergence of non–trivial collective behav-ior and its connection to transitions in causal structure,we focus on a lattice of chaotic logistic maps. The lo-gistic growth model was chosen for its connection to thereplicative growth of biological populations (Murray, 1989),thereby enabling us to make an analogy with the transitionfrom independent replicators to collective reproducers, citedas a hallmark of many major evolutionary transitions as out-lined above (Szathmary and Maynard Smith, 1995). Ouraim with this simplified model is to provide a clear exampleof how a reversal in information flow – from bottom-up totop-down – can describe a transition from a group of inde-pendent low-level entities to the emergence of a new higher-level (collective) entity.

Our model system is defined as

xi,n+1 = (1− ε)fi(xi,n) + ε mn ; (i = 1, 2, . . . N) (1)

where the function fi(xi,n) specifies the local dynamics ofelement i,N is the total number of elements, n is the currenttime-step (generation), and ε is the global coupling strengthto the instantaneous dynamics of the mean-field, mn, de-fined below in eq. 4. In analogy with biological populations,the element index i may be associated with a specific phe-notype within a given population, and ε marks the strengthof the global informational control over the local dynamicsof each such element. The local dynamics of each element iis defined by the discrete logistic growth law

fi(xi,n) = rixi,n

(1− xi,n

K

)(2)

where ri is the reproductive fitness of population i, and Kis the carrying capacity – set to K = 100 for all i, for theresults presented here. The instantaneous state of the entiresystem at time step n is specified as an average over all localstates by the instantaneous mean-field Mn,

Mn =1

N

N∑j=1

xj,n (3)

and the instantaneous dynamics of the mean-field,

mn =1

N

N∑j=1

fj(xj,n) (4)

is a global systemic entity (i.e. it cannot be identified withany specific local attribute), which has direct impact on the

dynamics of local elements i in our model system. The in-fluence of this abstract global entity is dictated by the globalcoupling strength ε.

The system was initialized with xi,0 = 1 for all elementsi, representing an initial population size of one individual foreach population. Values for the fitness parameters ri wererandomly drawn from the range of values [3.9, 4.0], whereselection of replicative fitness was restricted to this range toensure that all elements individualistically display chaoticdynamics even when coupled to the global dynamics (re-quired to determine cause and effect for this model system,see e.g. Cisneros et al. (2002)). Following the dynamics ofa set of N = 1000 coupled logistic maps, a time series ofboth the instantaneous states of the local elements, xi,n, andof the mean-field, Mn, was generated from which causaldirectionality and the associated flow of information weredetermined. In what follows, we introduce a definition ofa measure of causal information transfer based on analysesof multivariable time series and then present results for thecausal structure of our coupled logistic growth model usingthis measure.

Quantifying Causal Information Transfer

Standard measures of information, such as Shannon entropy(Shannon and Weaver, 1949), which provides the averagenumber of bits needed to encode independent events of adiscrete process, and mutual information, used to measurethe joint probability of two process, rely on static probabil-ities. However, in order to infer causal information transfer(i.e. from higher to lower levels versus from lower to higherlevels of organization, or here from the mean-field to localelements versus from local elements to the mean-field), ameasure that can capture dynamical structure by means oftransition probabilities rather than static probabilities is re-quired. The dynamical character of the interactions can bestudied by introducing a time lag in order to compute therelevant transition probabilities.

Consider, for example, a Markov process of order k.The conditional probability p(xn+1|xn, . . . , xn−k+1) =p(xn+1|xn, . . . , xn−k+1, xn−k) describes a transition prob-ability whereby each state xn+1 of the process is dependent(conditional) on the last k-states but is independent of thestate xn−k and all previous states. This conditional relation-ship can be extended to any k-dimensional dynamical sys-tem as prescribed by Takens embedding theorem (Takens,1980). To simplify notation, we define an embedded stateas x(k)n = (xn, . . . , xn−k+1), which describes a state in thek-dimensional phase space, such that the series of vectors{x(k)n } contains all of the information necessary to charac-terize the trajectory of the dynamical variable x. Using thisdefinition, the dynamical information shared between twoprocesses, x and y, can be determined by the Transfer En-

tropy (Schreiber, 2007):

T(k)Y→X =

∑n

p(xn+1, x(k)n , y(k)n ) log

[p(xn+1|x(k)n , y

(k)n )

p(xn+1|x(k)n )

](5)

This measure incorporates causal relationships by relatingdelayed (embedded) states, x(k)n and y(k)n , to the state xn+1,and quantifies the incorrectness of assuming independencebetween the two processes x and y. In short, the transferentropy tells us the deviation from the expected entropy oftwo completely independent processes.

The transition probabilities can be systematically mea-sured from the time series by coarse graining the phasespace. Calculation of the conditional probabilities

pr(xn+1|x(k)n , y(k)n ) =pr(xn+1, x

(k)n , y

(k)n )

pr(x(k)n , y

(k)n )

(6)

pr(xn+1|x(k)n ) =pr(xn+1, x

(k)n )

pr(x(k)n )

. (7)

then yields all of the necessary quantities required to calcu-late the transfer entropy T (k)

Y→X as defined in equation (5).Larger values for the information transfer are expected tobe measured when the defined embedded space is a betterrepresentation of the real phase space of the dynamical pro-cess that generates the set of states {xn}. Therefore, se-lection of the dimension of embedding k is done such thatTY→X = Max{T (k)

Y→X}.

Information Flow Between Global and Local ScalesThe coupled system described by eqs. (1), (2), and (4)displays several different phases with interesting dynamicalproperties (Fig. 3). A detailed description of the dynamicalfeatures of these phases is outlined in the study by Balm-forth et al. (Balmforth et al., 1999). Here we focus our dis-cussion on the observed collective behavior in the contextof the measured causal information transfer characterized ineq. (5). We compare the flow of information from local toglobal scales and from global to local scales – TX→M andTM→X respectively – to demonstrate how causal informa-tion transfer from the global to the local dynamics corre-sponds to the emergence of collective organization.

The time series for 1, 000 logistic maps were recorded forten thousand generations (time-steps), including the time se-ries of the mean field, M , and that of an arbitrarily chosenlocal element, x, selected at random to be representative oftypical local dynamical behavior. The dynamics of the sys-tem varies widely as a function of the coupling parameterε, indicative of variations in the degree to which the localand mean-field dynamics influence the dynamics of individ-ual local elements. For ε = 0, the system is completelyuncoupled (each local element acts independently), and thedynamics are that of 1, 000 isolated subpopulations. The

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Figure 3: Return map for varying values of the global cou-pling strength ε. Shown are return maps for ε = 0 (magenta),ε = 0.075 (red), ε = 0.1 (blue), ε = 0.2 (orange), ε = 0.225(aqua), ε = 0.25 (dark green), ε = 0.3 (stars), and ε = 0.4(black). Also shown is the return map for a single logisticmap (bright green). The inset shows an expanded view.

opposite extreme, ε = 1, corresponds to complete coupling,where all the logistic maps evolve identically to each otherwith fully synchronized dynamics (i.e. they may be identi-fied as part the same higher-level “organisms”).

As the coupling strength is increased from no coupling atε = 0, a rich diversity of self-organized collective phenom-ena are observed to emerge. A sampling of this variety aredetailed by the return-map of the mean field M , shown inFig. 3. For ε = 0 (the uncoupled limit), the return-map ofthe mean-field is a cloud of dispersed points around a fixedvalue (Fig. 3, magenta), as is characteristic of dynamics withrandom oscillations about a fixed value. For ε = 0.075 (Fig.3, red) a clear quasi-periodic three state oscillatory dynamicis observed, as evidenced by the three clouds in the returnmap (with some dispersion), indicating that the system hasachieved a moderate degree of collectivity. Although thecoupling strength is relatively low, the system self–organizesin such a way that the mean field has a simpler dynamic thanthe typical chaotic behavior of the individuals. The systemorganizes by forming clusters, within which the individualshave very similar behavior. Here it is likely that top-downinformation transfer is highest within clusters, resulting inintermediate size scales (between local and global) drivingthe emergence of collective behavior: this dynamic is notaccurately captured by our global measure M . As such,the transfer entropy, shown in Fig. 4 for top-down (TM→X ,

0 0.2 0.4 0.6 0.8 1Global Coupling Strength

0

0.5

1

1.5

2[B

its]

Top-DownBottom-Up

Figure 4: Top-down, TM→X (solid), and bottom-up TX→M

(dashed), causal information transfer for varying global cou-pling strength ε of a system of coupled logistic maps.

solid) and bottom-up (TX→M , dashed), do not quite reflectthe onset of this collective dynamic, although TX→M andTM→X are nearly equal, indicating that the dynamics of theglobal mean-field is driving, at least partially, the collectivebehavior in a top-down manner.

Increasing the coupling strength to ε = 0.1, the systemfalls back into the dynamics of a seemingly disorganizedsystem, and no particularly interesting global behavior isobserved. This is shown in the return map as a randomlydispersed cloud around a fixed value (Fig. 3, blue). How-ever, further increasing the coupling strength to ε = 0.2,yields the onset of a new collective phase (Fig. 3, orange).Here, collective behavior manifests as four phase periodicoscillation with large dispersion. A small dominance of thetop-down transfer entropy TM→X is observed. Here, the on-set of collective behavior corresponds to a transition to top-down information flow being the dominate mechanism of in-formation transfer. This provides the first presented exampleof a clear case where top-down causation drives the emer-gence of collective behavior. It is interesting that this occursat a fairly low value of the coupling strength, at ε = 0.2.

The attractor observed for ε = 0.2 breaks apart into twodispersed clouds for ε = 0.225 (Fig. 3, aqua) and then con-centrates into smaller clouds for ε = 0.25 (Fig. 3, darkgreen), where the system enters a collective two-phase peri-odic oscillation. These observed collective phases also cor-respond to the top-down transfer entropy being the domi-nant causal driving force, as shown in Fig. 4. Increasing εto ε = 0.3 leads to complete synchronization of the system(Fig. 3, stars), yielding a transfer entropy measure of zero.In general, we expect both TM→X and TX→M to be zerofor states of complete synchronization since no informationcan be gained from a coding by considering a second time

series that is dynamically identical to the first one. In otherwords, when full synchronization is achieved, two series be-come dynamically identical and it no longer makes senseto discuss transfer entropy between them. In this particularcase, full synchronization indicates the local dynamics arecoincident with the mean-field, i.e. a transition to a fullycollective emergent entity has occurred. It is interesting thatthese dynamics are first observed for such a low value of ε,and that increasing ε still further yields states which are notfully synchronized. Additionally, in this regime where syn-chronization emerges dynamically, any collective dynamicsin which transfer entropy can be measured (i.e. not syn-chronized) are dominated by top-down transfer entropy (e.g.see ε = 0.25 and 0.35 in Figure 4), suggesting that the dy-namical synchronization occurs due to top-down dynamicaldriving. For ε = 0.4, the return map approaches the form ofthe chaotic attractor for a logistic map (Fig 3, black), indi-cating that the dynamics are collectively logistic. The meanfield is dynamically chaotic, as are the individual maps in thelattice; however, here the individual maps are not synchro-nized with each other, yielding non-trivial organization. Theemergence of this highly collective state is again reflectedby a dominance of the top-down transfer entropy relative tothe bottom-up transfer entropy. This trend is continued forincreasing ε until ε = 0.7, at which point the mean-fieldand local dynamics are fully synchronized and it no longermakes sense to discuss information transfer, as noted above.

In general, the trends observed indicate that each time acollective state emerges, causal information transfer is dom-inated by information flow from global to local scales. Par-ticularly interesting is that top-down causation dominates forcollective states in regimes with 0.2 < ε < 0.7, where thecontribution from the global dynamics is not necessarily thedominant contribution in eq. (1) (i.e. for 0.2 < ε < 0.5).In this regime, although the weight of the contribution fromthe global scale may be less than the contribution from thelocal scale in dictating the local dynamics, collective statesself-organize which are driven by top-down causal informa-tion transfer from the mean-field. Although we have fo-cused on a coupling to the global mean-field for the workpresented here, other studies of coupled chaotic map latticeshave shown that strictly local coupling leads to similar dy-namical behavior (Cisneros et al., 2002; Ho and Shin, 2003)- i.e. even in cases where the mean-field never appears in thedynamical equations, the global dynamics can still drive theemergence of collective behavior via top-down causation.

Major Transitions in Causal StructureThe results presented for this toy model system indicate thata transition from a population of independent replicators,to a collective representing a higher-level of organization,can be mediated by a physical transition from bottom-upto top-down information flow, where non-trivial collectivebehavior is associated with the degree to which local ele-

ments receive information from the global network. The dy-namical system investigated was designed to parallel tran-sitory dynamics believed to be a hallmark feature of manymajor evolutionary transitions – i.e. those characterized bythe emergence of higher–level reproducers from lower levelunits (Szathmary and Maynard Smith, 1995). For the modelsystem presented above, new high-level entities would beexpected to emerge as ε → 1 (although non–trivial collec-tive behavior is observed to emerge in intermediate regimes,as discussed above). Examples of major evolutionary tran-sitions where similar dynamics are expected to have playedout include the origin of life, the origin of eukaryotes, theorigin of multicellularity, and the origin of eusociality. Herewe focus on discussing the origin of life and the originof multicellularity as two representative examples of majorevolutionary transitions that may potentially be driven bytransitions in causal structure as dictated by informationalgaining efficacy over higher-levels of organization.

The Origin of Life. In the original classification schemeof Szathmary and Maynard Smith, three major transitionsare associated with the origin of life: from replicatingmolecules to populations of molecules in compartments,from unlinked replicators to chromosomes, and from RNAto RNA + DNA + protein (i.e. the origin of the geneticcode). However, given that we do not know the specific se-quence of events leading to the emergence of the first knownlife, a more pragmatic perspective is to assume that whenlife as we know it first emerged, it was surely character-ized by the same distinctive hierarchical and causal struc-ture as all known life. Adopting this viewpoint, Walker andDavies have recently suggested that a transition in causalstructure, from bottom-up to top-down, was the critical stepin the origin of life (Walker and Davies, 2012). In this con-text, the origin of life is associated with the emergence ofa collective contextual information processing system withtop-down causal efficacy over the matter it is instantiated in(Walker and Davies, 2012). The transition from non-livingto living matter may therefore be identified when informa-tion (stored in the state of the system) gains causally efficacy.A constructive measure of how close chemical systems areto the living state – a quantity notoriously absent in almostall discussions of the origin of life – may therefore be pro-vided by adopting a variant of the parameter ε and applyingit to the relevant chemical kinetics. This may provide newavenues of research into the origin of life by directing effortstoward understanding how chemical systems come under di-rection of the global context rather than focusing strictly onthe evolutionary processes that might enable a transition tothe living state but do not necessitate it.

The Origin of Multicellularity. Unlike the emergence oflife, where the frequency of origination events is entirely un-known, multicellularity is believed to have arisen dozens of

times in the history of life on Earth (Bonner, 1999). A possi-ble explanation for the numerous transitions to multicellular-ity is that many of the hallmarks of multicellular organismsare laid out by epigenetic factors and physical effects in uni-cellular aggregates that only later come under information(i.e. genetic) control. For example, Newman and collabora-tors have proposed that the variety of metazoan body planswere originally laid out by physical interactions, such thatthe phenotype of multi-cellular aggregates was determinedat first by physical environmental influences (Newman andMuller, 2000; Newman et al., 2006). They suggest that thesephysical varieties of form were only later to be taken over byinnovations in genetic programming. An explicit example ofa similar process whereby information control dictates theemergence of collective states is provided within the genusVolvox: the multicellular green alga, Volvox carteri has agene controlling cellular differentiation that is related to ananalogous gene dictating cellular phenotype in its unicel-lular relative, Chlamydomonas reinhardtii (Nedelcu, 2009),which may have played a crucial role in its transition to mul-ticellularity. This suggests that a key feature of the transi-tion to multicellular organization is biological informationgaining efficacy over new scales of organization by redirect-ing features already present in collectives of the lower-levelunits. As such, the physical transition should be markedby a transition in causal structure. An interesting consid-eration is therefore that multicellularity emerges frequently,requiring only the physical transition from bottom-up to top-down causation via information control once the underlyinglower-level units posses evolutionary innovations necessaryto prime them for the transition. An important question inthen: how hard is it for the physical transition to occur?From the viewpoint of the perspective provided here, fur-ther investigations into the causal structure of biological sys-tems are required to address this question. The relevant or-der parameter ε could be measure of the degree of signalingbetween individual cells (i.e. their response to intercellularsignaling), or a measure reproductive viability as presentedwith the simple logistic growth model detailed above. Ingeneral this approach requires innovations in understandingthe degree to which the whole dictates the parts in biologicalcollectives, as much as understanding the degree to whichthe parts dictate the whole.

Given that the we do not have a clear picture of the causalstructure of biological systems, it is at present unclear whatthe relative role of bottom-up and top-down causative effectsare in directing biological organization. Here we have pro-posed that increasing levels of biological complexity, cor-responding to increased depth in the hierarchical organiza-tion of living systems, correspond to information gainingcausal efficacy over increasingly higher levels of organiza-tion. Each major evolutionary transition leading to the emer-gence of genuinely new, higher-level entities from lower-level units, should therefore be characterized by a transition

in causal structure mediated by a reversal in the dominantdirection of information flow from bottom-up to top-down.We have demonstrated the dynamics of such a transition byappealing to a toy system of coupled logistic maps. The dy-namics observed verify that collective states emerge in as-sociation with a transition to top-down causal informationtransfer as the dominant direction of information flow. Thenature of the reversal in causal structure presented here sug-gests that biological systems cannot jump up the ladder ofhierarchical structure - information must first gain controlover a lower-level of organization before the emergence ofefficacy over higher–levels can take-hold. Rapid diversifi-cation may occur after each such transition due to the newcapacity for directing physical processes at the higher level.

AcknowledgementsSIW gratefully acknowledges support from the NASA As-trobiology Institute through the NASA Postdoctoral Fellow-ship Program. LC and PCWD were supported by NIH grantU54 CA143682.

ReferencesAlberts, B., Johnson, A., Lewis, J., Raff, M., Roberts, K., and Wal-

ter, P. (2002). Molecular Biology of the Cell, page 1357. Gar-land Science, New York, 4 edition.

Auletta, G., Ellis, G. F. R., and Jaeger, L. (2008). Top-down cau-sation by information control: from a philosophical prob-lem to a scientific research programme. J. R. Soc. Interface,5(27):1159–72.

Balmforth, N. J., Jacobson, A., and Provenzale, A. (1999). Syn-chronized family dynamics in globally coupled maps. Chaos,9:738–754.

Bonner, J. T. (1999). The origins of multicellularity. IntegrativeBiol., 1:27–36.

Campbell, D. (1974). Downward causation in hierarchically organ-ised biological systems. In Ayala, F. J. and Dobzhansky, T.,editors, Studies in the philosophy of biology: Reduction andrelated problems, pages 179–186. Macmillan, London, UK.

Cisneros, L., Jimenez, J., Cosenza, M. G., and Parravano, A.(2002). Information transfer and nontrivial collective be-havior in chaotic coupled map networks. Phys. Rev. E,65:045204.

Davies, P. C. W. (2006a). The Goldilocks Enigma. Penguin Books,New York.

Davies, P. C. W. (2006b). The physics of downward causation. InClayton, P. and Davies, P. C. W., editors, The re-emergenceof emergence, pages 35–52. Oxford University Press, Oxford,UK.

Davies, P. C. W. (2012). The epigenome and top-down causation.J. R. Soc. Interface, 2(1):42–48.

Ellis, G. F. R. (2006). On the nature of emergent reality. In Clay-ton, P. and Davies, P. C. W., editors, The re-emergence ofemergence, pages 79–107. Oxford University Press, Oxford,UK.

Ellis, G. F. R. (2012). Top-down causation and emergence: somecomments on mechanisms. J. R. Soc. Interface, 2(1):126–140.

Goldenfeld, N. and Woese, C. (2011). Life is Physics: Evolutionas a Collective Phenomenon Far From Equilibrium. AnnualReview of Condensed Matter Physics, 2(1):375–399.

Ho, M.-C. and Shin, F.-C. (2003). Information flow and nontriv-ial collective behavior in chaotic-coupled-map lattices. Phys.Rev. E, 67:056214.

Jablonka, E. and Lamb, M. J. (1995). Epigenetic Inheritance andEvolution. Oxford University Press, Oxford.

Jablonka, E. and Lamb, M. J. (2006). The evolution of informationin the major transitions. J. Theor. Biol., 239(2):236–46.

Kuppers, B. (1990). Information and the Origin of Life. MIT Press,Cambridge.

Lachmann, M. and Jablonka, E. (1996). The inheritance of pheno-types: an adaptation to fluctuating environments. Journal ofTheoretical Biology, 181(1):1–9.

Maynard Smith, J. (2000). The concept of information in biology.Philosophy of Science, 67(2):177–194.

Murray, J. D. (1989). Mathematical Biology. Springer-Verlag,Berlin.

Nedelcu, A. and Michod, R. E. (2004). Evolvability, modularity,and individuality during the transition to multicellularity involvocalean green algae. In Schlosser, G. and Wagner, G., ed-itors, Modularity in Development and Evolution, pages 466–489. University of Chicago Press, Chicago, IL.

Nedelcu, A. M. (2009). Environmentally induced responses co-opted for reproductive altruism. Biol. Lett., 5(6):805–808.

Newman, S. A., Forgacs, G., and Muller, G. B. (2006). Beforeprograms: the physical origination of multicellular forms. Int.J. Dev. Biol., 50(2-3):289–99.

Newman, S. a. and Muller, G. B. (2000). Epigenetic mechanismsof character origination. J Exp. Zool., 288(4):304–317.

Okasha, S. (2012). Emergence, hierarchy and top-down causationin evolutionary biology. J. R. Soc. Interface, 2(1):49–54.

Sagan, L. (1967). On the origin of mitosing cells. J. Theor. Biol.,14(3):225.

Schreiber, T. (2007). Measuring information transfer. Phys. Rev.Lett., 85:461.

Shannon, C. E. and Weaver, W. (1949). The Mathematical Theoryof Information. University of Illinois Press, Urbana IL.

Szathmary, E. and Maynard Smith, J. (1995). The major evolution-ary transitions. Nature, 374(6519):227–232.

Szathmary, E. and Maynard Smith, J. (1997). The major transitionsin evolution. Oxford University Press, Oxford.

Takens, F. (1980). Detecting strange attractors in turbulence. Dy-namical Systems and Turbulence, 898:366.

Walker, S. I. and Davies, P. C. W. (2012). The algorithmic originsof life. arXiv:0517.466.