ELSEVIER Physica D 75 (1994) 275-291 Multilevel evolution: replicators and the evolution of diversity P. Hogeweg Bioinformatica, University of Utrecht, Padualaan 8, 3584 CH, Utrecht, The Netherlands Abstract In this paper we report on an initial attempt at studying evolution as a multilevel process, in which interactions of different space/time scales mutually determine the evolutionary potential. Side effects of processes on one scale may form a substrate for evolution at another scale. We study the generation and maintenance of diversity in a multilevel replicator system and focus on the role of local information processing and pattern formation. We show how the conflicting requirements of the generation and maintenance of diversity are met in different ways in completely mixed (stirred) and poorly mixed (diffusive) systems. In the former diversity is maintained primarily by non-invadability, and operates at the lowest level; in the latter case diversity is maintained by locally contained invasions which are subsequently eliminated by higher level processes. 1. Introduction coevolution. Coevolutionary processes are most often modelled as (one level) dynamical systems, Four lines of reasoning converged on the rather than optimization systems, and the attrac- research reported in this paper. tors are characterized. Although the important insights in evolution (1) Evolution as a multilevel process. so far have been obtained by virtue of squeezing the multiple levels into one level, we think the Evolution is most often studied as a one level time has come to start exploring evolution as a process involving informatic entities which can multiple-level process in which patterns gener- mutate in various ways and are selected by the ated at one level may determine the evolutionary environment through differential replication or dynamics and the evolutionary potential at other decay (“survival of the fittest”). In this frame- levels. Indeed we think that such a multiple-level work evolution is studied most often as an approach is a prerequisite for studying the cru- optimization process. Indeed, Genetic Algo- cial questions of evolution, i.e. how novel struc- rithms exploit this paradigm successfully as a tures and functions can arise. In the above method for optimization. Realising that most of mentioned one level models either the coding the relevant environment of biotic systems may structure and the target are fixed (optimization consist of other biotic systems, i.e. systems which models), or the variables and interactions are may change their characteristics at a similar fixed (dynamical systems). By modelling evolu- time-scale, this paradigm is extended to include tion as a multiple-level process the ‘side effects’ 0167-2789/94/$07.00 @ 1994 Elsevier Science B.V. All rights reserved SSDI 0167-2789(93)00082-2 276 P. Hogeweg I Physica D 75 (1994) 27.5-291 of one level can modify the targets, the coding [17,18] which studies the coevolution and coding structure and/or the interaction structure at structure of entities which evolve the coding of other levels [lO,ll]. the replicative process itself, and the (spatial) Extension of one-level models to multiple game dynamics studied by Lindgren [14,25] levels can be done starting from the optimization which studies the coevolution of interaction viewpoint, starting from the coevolutionary ‘strategies’ in relation to the spatial structures viewpoint, or from both. generated by these strategies under different parameter regimes. In this paper we combine 1.1. Evolution of the coding structure in coevolution and coding the other way around, optimization models i.e. we study a system in which the coding structure of the higher level entities is modelled By recognising that the ‘targets’ of evolution in terms of a coevolutionary process of (self (i.e. continued existence) are such that they can replicating) molecules. The higher level entities be realised as effectively in many different ways, optimize a very general optimization criterion, we can study which ‘solutions’ are preferred by i.e. the diversity of the underlying coevolution- the dynamics of the evolutionary process. In ary system. We show that generation and mainte- other words we can study how the choice be- nance of diversity in the system is achieved in tween ‘neutral peaks’ in the fitness landscape is very different ways dependent on pattern forma- not a ‘neutral choice’, and how such non-neutral tion or the absence thereof in the lower level neutral choices affect the coding structure and coevolutionary system. thence the future evolutionary dynamics. In this vein we have studied the generation of multiple (2) The cell as the environment for an evolv- or single coding under respectively high and low ing genome mutation rates [ll] and generation of patterns in RNA sequences by evolutionary dynamics lead- Possibly even more important than interacting ing to relatively smooth or rugged parts of the with other biotic systems, a biotic system has to RNA secondary structure landscape [ 121. deal with itself in its most direct environment. More specifically, the genome interacts with its 1.2. Evolution of new levels of selection in own products (i.e. the cell), rather than with the coevolutionary models environment, and the interaction of the cell with the environment just ensures continued existence By embedding coevolutionary systems in of the system. Any new ingredient of the system space, the interaction between the selfreplicating in the first place should be sufficiently compat- units may form spatial structures. The dynamics ible with what is already there. Moreover genes of these spatial structures may determine the are a passive form of information storage; only evolutionary fate of the selfreplicating units transcribed genes play any role in the system. which generate them and therewith the low level Thus the cellular environment should not only be definition of the (co)evolutionary system [l-4]. undisrupted by a new gene, it should also acti- In other words the ‘emergent properties’ of a vate it. Gene regulation has been modelled with (one-level) coevolutionary system may generate Boolean networks by Kauffman [13] and the a new level of selection. amenability of such networks to optimization, and coevolution has been studied by him in 1.3. Combining coevolution and coding models in which these processes are quenched into a powerful and extremely simple representa- Interesting combinations of these two ap- tion. proaches include the Tierra system of Ray In this paper we intend to focus on the internal P. Hogeweg I Physica D 75 (1994) 275-291 277 aspects of evolution by including explicit in- Embedding the coevolution in a spatial con- tracellular dynamics in an evolutionary system text does alleviate some of the difficulties occur- which takes a ‘solipsistic’ view of a cell. What- ring with the well-mixed systems: temporal fhc- ever a cell ‘is’ or ‘does’ is fine as long as it can tuations are stabilized, noncyclic interaction continue doing it. However the external environ- structures are stable, and the system can be ment is represented in the form of an optimi- resistant to parasites through the generation of zation criterion: the more ‘information’ the cell higher levels of selection. Nevertheless infor- carries the more it might be able to “do”. Thus mation accumulation appears to be limited also we maximize diversity of the system. in these systems, and in some cases we have shown that evolutionary processes tend to lead (3) Generation and maintenance of diversity the system to an area of parameter space where, in selfreplicating systems e.g., they are not resistant to parasites [l- 5,8,16]. Maintenance of diversity in non-self- Selfreplicating systems which interact through replicating systems is less of an issue. Fontana [7] competition for a common resource tend to therefore initially constrains his system excluding exclude each other. In an ecological context this selfreplication of his primary building blocks. In phenomenon is called “competitive exclusion”, fact ecological systems as well as evolutionary in evolutionary context “survival of the fittest”. systems and also other selfreplicating systems Although the former term has definitely a more such as the immune system, are not purely negative connotation than the latter, the mainte- selfreplicating systems: influx from the ‘external’ nance of diversity is a crucial question in models environment (other areas, seed banks, bone of evolution as well. This is in particular the case marrow/thymus), or by mutations occurs. In- because the amount of information which can be deed such an influx tends to stabilize the system, stored in one replicator is limited by the exist- as is shown by Stadler et al. [21,22] in replicator ence of a so called ‘error threshold’ (or ‘in- systems including mutations. formation threshold’): only by reducing the mu- In this paper we study the generation and tation rate can more information be included in maintenance of diversity as mediated by higher one replicator. However, the reduction of the level selection and influx. The higher level pro- mutation rate is presumably only possible by cesses maximising diversity select interaction more sophisticated replication mechanisms (e.g. topologies and can control the influx of the proofreading), which require more information ‘environment’ (in our system the ‘genome’). to be stored in the genome. Therefore an im- portant open question in (prebiotic) evolution is (4) De-coupling of dynamics and information how the information threshold can be crossed storage and how information accumulation can occur. Eigen and Schuster’s classical proposal to cross Complex information processing can occur in the information threshold by coevolution of dynamical systems when there are entities catalysing each other’s selfreplication, is (1) stable configurations which provide for in- hampered by the difficulty of maintaining high formation storage; diversity in selfreplicative systems. In well-mixed (2) moving configurations (for information systems only relatively small cyclic interaction transfer) structures can persist, and these structures are (3) nonlinearity (decision making) (e.g.