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Fitness and Synergy

by Chris Lucas

"Nature's stern discipline enjoins mutual help at least as often as warfare.
The fittest may also be the gentlest."

Theodosius Dobzhansky, Mankind Evolving, 1962

"The art of persistence is to be dead. Only inorganic things persist for great lengths of time. A rock survives for eight hundred million years; whereas the limit for a tree is about a thousand years... The problem set by the doctrine of evolution is to explain how complex organisms with such deficient survival power ever evolved. They certainly did not appear because they were better at that game than the rocks around them. It may be possible to explain "the origin of species" by the doctrine of the struggle for existence among such organisms. But certainly this struggle throws no light whatever upon the emergence of such a general type of complex organism, with faint survival power."

Alfred North Whitehead, The Function of Reason , 1929

Introduction

The concept of fitness occurs extensively in both the complexity and biology fields, but it is rarely spelled out just what is meant by this and what different forms fitness can take. Fitness usually occurs relative to something else and it is this relativity which is important in understanding the concept within complexity thought. This is not quite the same as when we say a person is 'fit' (an isolated evaluation), which assumes an absolute measure or value (as in Darwin's sense), but refers instead to a contextual evaluation, a comparative measure (a differential mode common to neo-Darwinian evolution).

Synergy in contrast relates to combinational effects, the systemic change in fitness that occurs when parts come together, when they interact. This brings into play a number of possible interactions and coevolutionary processes, and whilst somewhat neglected in complexity experiments (which are often dominated by 'conflict' scenarios) is expected to become of increasing importance as we attempt to evolve systems adequate in complexity to mimic living systems. It is synergy that relates more to absolute fitnesses, looking to maximise the available value of the combinations (but across the whole system rather than at an individual level).

What is Fitness ?

Ultimately this term has no single meaning, and in biology is often used rather tautologically - what exists must be fit (adaptive) by definition. This sense assumes that fitness relates only to survival and/or reproduction and makes no valid claim to optimisation (in fact most organisms are known to be anything but optimum - for example human eye design is poor compared to that of an octopus). A relative or differential fitness of this type is contextual, it has meaning only by comparison with the other options or variants available at that particular time and location.

In complexity thought we are often concerned more with what is the best that can be achieved (optimization), and in searching state space for all possible solutions, rather than just those that currently exist (as in biology). Additionally, values other than survival/reproduction can be important (e.g. economic, energetic, artistic, scientific) and thus we can extend the fitness idea to multiple values, giving a overall 'quality of life' performance measure for any complex task. In many treatments however the traditional concept of reproduction is retained and the reproduction rate or survival is made proportional, in some way, to the fitness function employed, in determining the evolutionary dynamics of the system.

Static Fitness

To investigate fitness more deeply, let us first consider a landscape, comprising hills and valleys. Over our lifetime it can be said to be static, it doesn't change. If we decide (arbitrarily) to make height our measure of fitness then we can see that if we move about the landscape then we can attempt to maximise this fitness, to climb the highest hill. This idea is central to Genetic Algorithms, which mutate and crossover genes to move the organism around a state space landscape, trying to find the highest (i.e. most fit) point. We can regard such a two dimensional landscape as the x and y co-ordinates of two continuously variable genes, but typically many genes are involved and thus we need a multidimensional landscape - a difficult to visualise hypercube.

Note that the measure (height) was arbitrary, thus we can choose any measure to maximise, and this depends critically upon the problem we wish to solve. Typically all we need to be able to do is to calculate a fitness for every combination of variables, we can then use GAs as a search technique to locate the optimum solution to our problem (or perhaps more typically one solution from many). It is important to note that a poor choice of fitness measure will generate an invalid initial landscape and thus invalid solutions to the problem (e.g. height may be quite appropriate for an mountaineer but poor for someone trying to get out of a freezing wind !).

Dynamic Fitness

Now let us consider instead seawater, here the wave peaks are not static they change position with time. Using the same height criterion we can see that our fitness will vary in time, even if we do nothing, our 'landscape' changes regardless of our behaviour. This scenario applies to cyclic weather effects in nature, as well as to longer term environmental changes. An animal or plant will experience different fitnesses depending upon the climate being experienced (and location, i.e. tropical forest, temperate grasslands, arctic waste), so fitness is always environmentally relative and is a function both of the changing landscape and the organism variables. Usually we keep one of these constant (as their timescales are usually different), maximising individual fitness for a given landscape or seeing how, say, a cooling landscape affects a particular individual optimum.

It is this aspect of fitness that is often treated in evolutionary biology, when we claim that the organism evolves to fit its landscape. Bear in mind that several behaviours (e.g. hibernation, migration, woolly jumpers) can compensate for environmental changes of this sort, so fitness can be said to relate to how well the organism can compensate for adverse conditions or exploit good ones. This tracking of a moving landscape relates to Neural Networks, where the system tries to recognise and adapt to changing inputs. This also shows that rather than evolving body features over multiple generations, lifetime learning is also a way of improving fitness - a dynamic correlation between short term landscape variation and behaviour.

Coevolutionary Fitness

In most of nature however there is not just one organism on the landscape, there are many, and they affect each other (e.g. predator and prey). In this case the fitness values for any behaviour depends not only on our own action but upon those of our neighbours - we affect each other's decisions. For example if the prey moves North then that becomes the 'fit' direction (increasing landscape height) for the predator (assuming it is hungry) - the fitness peak is where the prey is. Note here that the opposite is true for the prey - its fitness peak is where the predator is not ! This is not always the case as we see later in the synergy discussion.

The dynamic nature of such interactions means that the fitness landscape of every organism distorts somewhat following the actions of all those other organisms with which it interacts. This is coevolution in action, sometimes called the 'Red Queen' effect or an 'arms race' on the (invalid) assumption that coevolution means competition - two adaptations oppose each other and cancel, we "run on the spot". This form of interaction however is common in Artificial Life studies (as well as in ecologies) and means that we cannot impose an external global fitness measure on the system, fitnesses must arise in a dynamic internal way as the system evolves (taking into account all interactional effects).

Epistasis and Multioptimisation

So far we have assumed that fitnesses for organisms were single values, i.e. that the effects of the genes could be summed to give a specific phenotype value such that all genetic combinations would be different. That is rarely the case. Genes affect each other, the effect of one depends upon the values of others, giving a nonlinear phenotype function. This effect, called epistasis, means that we often need to compromise between genetic values (in a similar way that we often need to trade, say, speed and cost in transport - we can't optimise both at the same time). This means, crucially, that the maximum practical fitness may be much less than a derived theoretical one which assumes each gene can be independently optimised (reductionist style).

Several techniques have been developed to calculate fitnesses for such combinations of incompatible values (e.g. multioptimisation, schemas). When this is done we often find that many combinations give the same compromise fitness, thus there may be no single 'global optimum' solution available if we take everything into account. The difficulty of dealing with these more realistic multidimensional cases is what makes fitness such a difficult concept in practice, especially where multiple individual values combine with multiple organisms in a complex environmental ecology (e.g. Kauffman's NKCS model).

Landscape Structure

When we study how the structure of the fitness landscape varies with epistasis K (once again assuming a static landscape for simplicity here) we find three styles:

a) No Epistasis - all variables independent (K=0)
These static landscapes have a single hill, with a global maximum that can be reached by single mutations at a time. The fittest organisms cluster around the peak as a single optimised population, but drift will prevent the genotype becoming completely homogeneous.

b) Maximum Epistasis - all variables affect each other (K=N)
These are maximally disorganised landscapes (chaotic) with multiple low peaks. Evolution quickly finds a local optimum (one peak at random) but cannot easily escape that niche. Multiple separate populations can coexist, distributed across the landscape.

c) Optimum Epistasis - on average only a few dependencies (K=2 or so)
These are correlated landscapes where peaks cluster together, giving linked populations (rather like islands connected by bridges) of good compromise fitnesses.

If we again introduce the dynamics of coevolution we find that the organisms mutually evolve in a way that maximises their combined fitnesses (or at least achieves a stable balance, called an Evolutionary Stable Strategy or ESS). This position, called the 'edge of chaos', corresponds to optimised epistasis since mutations have tried different combinations (higher and lower connectivity) and the fittest has prevailed.

Survival and Values

Once we allow for values other than reproduction then fitness becomes a multi-dimensional spatial and temporal measure, instead of just a multi-generational temporal one. Higher organisms at least, unlike bacteria, generally do not choose to reproduce as fast as possible, i.e. many creatures spend very little of their time doing anything 'useful' in this sense... The set of choices available to organisms expands once they become more complex and aware. We need to consider then just what animals (and humans) are valuing, what is being 'selected' in context (and this context is not the same for all organisms, even of the same type, it is heterogeneous in both time and space). If not mainly reproductive ability then what ? Little attention has been given to this aspect of life processes, but taking humans as an example many other interests are evident. How are these affected by fitness concepts and how do they relate to the traditional view of competitive exclusion (the idea that the fastest reproducing 'winner' strain will take all) ? Here we need to go somewhat beyond the 'Nature, red in tooth and claw' image so close to the neo-Darwinist heartland.

Synergy

The idea that organisms do not compete destructively to reproduce (if predators ate all the available prey they would then starve and go extinct !) but must ultimately achieve a balance beneficial to all (i.e. somehow 'husband' their resources) brings us to synergy. This says that parts combined have different effects than the parts alone (i.e. the whole is not equal to the sum of the parts) and extends epistasis to the whole system. We already know that one organism can have a negative effect on another (e.g. the predator on prey) but it is often forgotten in our competitive society that this is a minor aspect of nature, cooperative effects are far more common, and are fitter in absolute terms.

These include the emergence effects common to complexity thinking (molecules making cells, cells making organisms, organisms making societies) but also much more. A group of people can achieve what a single one cannot (e.g. building a Cathedral), division of labour increases efficiency and thus group fitness. Symbiosis between fungi and plants is essential for survival in 90% of species, eukaryotic cells are forms of symbiosis, humans also cannot survive without bacterial symbionts. At all levels of nature advantages arise from associations between organisms and this should be true also in our artificial systems.

Evolution Strategies

Given that interactions can be both positive and negative in fitness terms, what forms of fitness effects can we expect to see ? These can be divided into many forms but classify into 4 types:

Forms of Interaction

The first two forms enhance absolute 'system' fitness overall (positive-sum), the last two decrease it in the long term (negative-sum).

Forms of Synergy [from Corning]

  1. Linear Effects - size advantages due to grouping together, e.g. army power
  2. Threshold Phenomena - overcoming a barrier, e.g. lifting a large rock
  3. Phase Transitions - e.g. oxygenation of the primordial atmosphere
  4. Emergent Phenomena - e.g. alloys with different properties to the constituents
  5. Functional Complementaries - complementary parts, e.g. Velcro
  6. Augmentation & Facilitation - e.g. catalysts
  7. Environmental Conditioning - e.g. huddling together to save warmth
  8. Risk & Cost Sharing - e.g. flocking, collective foraging
  9. Information Sharing - gaining knowledge without trial and error
  10. Society - division of labour, mutual help
  11. Functional Convergencies - fortuitous by-products of selfish actions, e.g. market prices

Given this collection of mutually beneficial ways to improve our fitness, we must say that the emphasis on 'competition' seen throughout both complex system and biological evolutionary studies is strange. Given that we wish to build complex systems (or in biology explain those that exist), it seems clear that mechanisms that build up complexity (positive-sum synergies) are to be preferred to those that destroy (negative-sum dysergies).

Competitive Losses

Having stressed the fitness benefits of synergistic ideas, we need to indicate why competition is negative-sum, especially as such behaviours are so evident in our societies. What does competition achieve ? In biology survival relates to differential fitness, not to absolute fitness, thus competition can improve relative survival (biologically, a quantitative change in genotype frequency) - presuming a choice must be made between you and me, and that is a critical point. In most scenarios several other options are available, opportunities for 'value add', for increasing the fitness of both parties (ecologically, a qualitative change in phenotype properties). These relate to untried options in state space, and allow for growth and innovation. Failure to consider these wider aspects of fitness (the coevolutionary interplay between coding/replicator and expression/interactor spaces, along with environmentally mediated developmental processes) - due to a blinkered and dogmatic idea of what is 'fit', can lead to many unforeseen and hidden losses, e.g. in business areas:

Competition is often said to drive innovations (necessity being the mother of invention), but it seems clear that such innovations must be limited to the level of the competitive entity, growth beyond that level (i.e. emergence) can only logically come from the non-destructive interaction of units. Competition between population members by itself isn't adequate to lead towards a synthesis of new constructs since no incentive exists towards cooperative interactions. Yet, in all realms, cooperative behaviour has not gone extinct. Furthermore in most areas, of the biological realm as well as in social ones, it is the crucial property which has led to evolutionary increases in complexity.

Modular Fitness

The emphasis on conflict (either/or) within fitness studies obscures the fact that nature operates extensively at a modular level, by the use of cooperative components that together (both) create some added functionality. In other words, the population of different phenotypes do not compete with each other but evolve to give a better collective fitness by mutualism effects than would be possible for any of them as individuals. Studies on the fitness effects of such synergies (compositional evolution) are rare (this mutually beneficial cooperation is not the same as the altruism sometimes considered in population genetics) and may perhaps best be seen in work in Game Theory, where in scenarios like the 'Iterated Prisoners Dilemma' ongoing cooperation can be shown to be fitter than selfish behaviours [Axelrod], but even here studies are limited to a single level of simplified behaviours.

It is hard however to relate this one-dimensional fitness to the synergistic benefits of multi-organism interactions, using multiple values or functions. In part this reflects the peremptory avoidance of group selection in genetics, and the corresponding neglect of higher level effects elsewhere in biology. All levels however are equally important to a complexity view and an overall fitness evaluation must consider them. Some progress in recognising the importance of modularity as a way of improving absolute fitness and generating complexity is now evident, but much work needs to be done before such an approach is put on a solid footing. This also needs to take into account how such synergistic effects completely change the fitness criteria for survival itself, thus differential fitness in human society is very different than it was before the advent of cooperative society - neither competition by exploitation nor by interference need play any part in our future evolution.

Functional Integration

When different organisms or individuals come together as a group, i.e. they cooperate, then it becomes possible for them to specialise. The efficiency of this mode has been clear ever since Adam Smith's 'pin' example in "The Wealth of Nations", and of course it forms the basis of all modern 'division-of-labour' business practices. It is often not recognised however that not only does the same process apply to the organization of societies, but that once again nature did it first. Ecosystems are largely maintained by such synergic (niche oriented) processes, but there is a problem. How can the resultant 'integrated whole' remain stable to invasion by selfishness, in other words how can it exclude cheaters (parasites) who gain the benefits whilst avoiding the costs ? A further aspect seems necessary here and that is localisation.

In modular organisations there is sufficient local knowledge to detect the cheaters, and thus to impose costs upon them sufficient to limit their spread. In other words interactions are not random, but selected, historical behaviour constrains future interactions, based upon a form of trust. Socially cooperating organisms ostracise exploitative behaviour, they can detect the untrustworthy (an evolved instinctive trait). In a large global society there are however many places to hide, and this historical knowledge can be lost, cheaters can then thrive - a problem we see throughout the modern human world. In synergic terms, homogeneity (one 'best' phenotype does it all) is fitness reducing, heterogeneous modularity (a set of niched and localised cooperating phenotypes) is potentially superior - if this invasion problem can be overcome, an area still very much under researched (even in game theory).

Multi-Level Selection

The key to such containment may lie in multi-level selection. This is the idea that group effects force a 'downward causation' selection on the lower level individuals, e.g. human (higher level) social laws incarcerate criminals (individual cheaters). It is beginning to be realised that these effects are ubiquitous, in natural as well as in cultural evolution (e.g. in multicellular modifiers). This form of 'group selection' does not actually need competition between groups (as usually thought) but is self-contained, an 'internal selection' or self-organization operates instead, the social or modular group itself acts as an adaptive environment for the individuals contained within it. Thus the behaviours of other individuals within the group can constrain deviants by coevolutionary processes. This implies that fitnesses vary with the composition of the group, which acts as another level of selective relevance upon the evolution of varying structures (e.g. frequency-dependent selection). A group-dependent competitive evolution of this sort is sometimes called a 'structured-deme model'. These concepts can be easily generalised to incorporate multiple species, i.e. ecological multilevel evolution.

Rather than thinking of groups as isolated and competing however we must recognise the possibilities of dynamic migration both into and out of each group, in this way the different behaviours and values that have evolved in the separate groups can mix, i.e. a cultural exchange is made possible. By limiting in some way such dispersal between groups however we act to freeze their dynamics (a static move, allowing equilibrium to develop, e.g. a totalitarian closed society), whilst by opening them up to free movement we act to disrupt their local dynamics (a chaotic move, constantly perturbing with 'new blood', e.g. a society fully open and keen to embrace the latest fads). The balance between these effects, i.e. a society or ecology that can maintain its traditions (is sustainable) yet also adapt (evolves), is epitomised by the term 'edge of chaos'. This relates to a balance between the rate of variation (mutation or influx) and the rate of selection (control or expulsion) - both need to be in the middle range to be effective in combination (synergic) within changing environments. The perturbation dynamics of various levels of migration between heterogeneous groups has again been under-investigated to date.

Conclusion

We have looked at two linked concepts here, firstly that of fitness, the idea that different behaviours can have different relative consequences, in conjunction with the equally important idea that fitness isn't an isolated characteristic of one organism but is intimately linked to environmental context. The second concept, synergy, stresses that absolute fitness can be enhanced more by cooperative actions than by competitive ones. This relates to global fitness measurements, the determination of overall system fitness rather than that of a single component and emphasises the coevolutionary niched nature of all interaction regimes.

Complex Systems require, by definition, complexity and this needs to be built up from smaller systems (in one way or another). It is philosophically strange that so many researchers seem to imagine that this will occur by destructive interactions, and totally neglect the inclusion of cooperative effects in their models. It is to be hoped that future systems will be designed more on the basis of mutual benefit or synergy (a compositional, rather than sexual or accretive form of evolution). If, as expected, this proves more effective in building up emergent layers of complexity (agents merging into larger symbionts and cultural groups) then we may be on the way to obtaining a far better understanding of natural complex systems and their fitness advantages than is currently the case.

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Page Version 4.83 April 2006 (paper V1.2 July 2004, original March 2000)