November 19, 2017

Complexity and stability in the real world

Does an ecosystem become more stable as it becomes more complex? Many do not think so. The problem, however, is that ‘stability’ and ‘complexity’ have never been defined. Published in The Ecologist Quarterly, Winter 1978.

Until recently ecologists have tended to assume along with Elton that as a system becomes more complex so does it become more stable. Fashions change, however, and this thesis now seems to be increasingly contested.

It is contested by the Institute of Ecology in its otherwise admirable book Man in the Living Environment. It is contested by Trenbath and also by Mellanby who goes so far as to intimate that only the most ecologically naive would fail to do so.

What, one might ask, has given rise to this new and paradoxical view? The answer appears to be R. M. May’s Stability and Complexity in Model Ecosystems, a book I have just finished reading.

May’s views seem to be influenced by Lotka and Volterra’s mathematical model of the relationship between complexity and stability. But this model has very obvious flaws. To begin with it regards a system’s complexity purely quantitatively i.e. in terms of the number of its components and of the interrelationships between them – and regardless of the nature of these components and interrelationships. Seen in this way an ecological invasion can be seen as increasing a system’s complexity and the fact that this tends to reduce stability can be seen as confirming May’s thesis that complexity reduces stability. Thus he points out that

“the stability of complex continental ecosystems was no armour against the Japanese beetle, the European gypsy moth or the Oriental chestnut blight Edothia parasitica in North America. It is trivial but not irrelevant to observe that stability was hardly enhanced by the extra links added to the trophic web in these instances.”

For May the reason why stability was reduced on these occasions appears to be that

“the greater the size and connectances of a web, the larger the number of characteristic modes of oscillation it possesses; since in general each mode is as likely to be unstable as to be stable (unless the increased complexity is of a highly special kind), the addition of more and more modes simply increases the chance for the total web to be unstable.”

He considers that “this is at the heart of the several general mathematical arguments reviewed above.”

The trouble is that the sort of complexity that Lotka, Volterra and May are describing does not exist in the real world.

The first lesson of ecology is that an ecosystem, like any other natural system for that matter, is not made up of random parts but of a specific set of differentiated parts which in turn are not interrelated in a random way but in very specific ways. A natural system is the product of evolution and it may have taken thousands of millions of years for a specific system to develop the specific subsystems that it requires and the specific set of interrelationships which enables it to fulfill its functions within the larger system of which it is a part.

A system displays order which is measured in terms of the influence of the whole over the parts or, what is the same thing, in terms of its degree of integration. The system’s complexity is the extent, as opposed to the degree, of this order. It cannot be increased by introducing into it something that has been designed to fulfill a very different role as a component of a very different system. All that this can increase is noise or entropy.

The question we must ask is whether we are concerned with behaviour in a mathematical model or in the real world? It is true that a ‘model’ is but another word for a hypothesis, though the latter need not necessarily constitute an explicit or formal model.

The building of a formal model is a useful exercise largely because it forces us to face all the implications of an hypothesis, or all the possible consequences of a given project i.e. it brings us face to face with a whole lot of factors we might not have taken into account, including basic assumptions we may not even be aware of having made.

However there is the danger that a model-builder may become so engrossed in his model that he may forget the reason for which it was built.

This appears to be the case with Lotka, Volterra and May. Though their model may display great internal consistency, it gives us very misleading information about the real world, a possibility, by the way, that May entertains quite openly. Thus he admits that the model only applies to systems with an even number of species, a ‘disquieting’ thought, he agrees, but not one that leads him to question its intrinsic value. Why not, one might ask? The answer is that, for his purposes

“whether or not the LotkaVolterra equations are applicable to real-world situations is beside the point being made here, which is that simple mathematical models are in general less stable than the corresponding simple mathematical models with few species”.

In other words he is not concerned with complexity and stability in the real world but only in his mathematical model.
In the real world, May admits (though only as an afterthought) things may be different:

“Natural ecosystems, whether structurally complex or simple, are the product of a long history of co-evolution of their constituent plants and animals. It is at least plausible that such intricate evolutionary processes have, in effect, brought about those relatively tiny and mathematically atypical regions of parameter space which endow the system with long-term stability.”

However, as May states himself, such an ecosystem is ‘mathematically atypical’ and hence, he intimates of little relevance to a mathematical model.

Let us now forget about mathematical models and try to determine the relationship between complexity and stability in the real world.

The first problem that faces us is that these terms are still used in a number of different ways, and must be defined more precisely. Let us start with the term ‘stability’. ‘Stability’ is regarded as the ability of a system to return to a ground position after a disturbance. But as Waddington points out, a natural system does not behave like a thermostat. It cannot return to a ground position after a disturbance because its experience is irreversible. What it does, in fact, is to return to a new position, though, if the system is stable, this new position will be as close as possible to the previous one. In other words the behavioural pattern of a stable system will be marked by very small discontinuities or oscillations.

It is easy to show that as behaviour evolves so does a system become more stable in this sense of the term. Thus, as a pioneer ecosystem develops into a climax ecosystem, its ability to resist predictable climatic changes is increased. The incidence of population explosions among the diverse forms of life that compose it is reduced to a minimum, that of floods and droughts is also diminished as is the system’s vulnerability to them. (Thus for instance there is no soil erosion in a tropical rain forest, though during the rainy season it may be subjected to 10 inches of rain in less than an hour.)

In fact one can regard the achievement of stability as the goal of behaviour within the biosphere and indeed that of the biosphere itself. The evolutionary process is generally regarded as ‘adaptive’, a term that has not been defined with any great precision, but which cannot mean anything else but that it is tending towards stability, that it is a ‘learning’ process taken in its widest sense; one that must gradually enable the biosphere to reduce to a minimum discontinuities, and hence oscillations, in its relationship with its environment.

But stability can mean something else. An arctic ecosystem, which is less complex and subjected to greater oscillations than a tropical one, can nevertheless be regarded as stable in the sense that oscillations are relatively constant (i.e. they are not getting any bigger).

In the first sense of the term, a system can be said to be more or less stable, or (in the case of a damped system) becoming more stable, in the second sense of the term, however, it is either stable or unstable.

Let us for the time being refer to these two uses of the term stability as stability (1) and stability (2).

Behaviour within the biosphere tends towards increasing stability (1), in other words a system adapts to or learns to live with its environment, which can be shown to involve the building up of complexity. Indeed, empirically, the main feature of the evolutionary process is the transformation of the primeval dust into more and more complex forms and at the same time more stable forms.

One way in which they are associated is obvious. Development in the biosphere proceeds by differentiation, which means that functions that were once fulfilled in a rudimentary manner by an unspecialised system become fulfilled in an ever more perfected manner, by increasingly differentiated and hence more specialised systems or subsystems. It is interesting to note that the basic behavioural functions are the same in a complex system such as man as in a simple one such as an amoeba. Both have to find their food, digest it and excrete the waste products. Both are capable of respiration, reproduction, and locomotion, but whereas an amoeba fulfils all these functions with but a single cell, man has developed the most elaborate and highly specialised mechanisms for fulfilling them in a very much more perfected manner with correspondingly increased stability (1).

The same is true of ecosystems. As in the case of an organism, both a simple and a complex ecosystem fulfill the same basic functions. Both use the energy from the sun to obtain carbon from the air and minerals from the soil (or the sea water) which they build up into different green plants whose populations are controlled quantitatively and qualitatively by predators. Both when they die are broken down by various decomposers into their constituent parts, so that they can provide the raw materials required for new generations. As an ecosystem becomes more complex, however, so are these functions fulfilled in an ever more differentiated and more highly perfected way by ever more specialised types of primary synthesizers, predators and decomposers.

Thus, the more differentiated they are the more capable they are, among other things, at checking internal instabilities. In a simple ecosystem, for instance, different species are relatively undifferentiated eaters. A mountain goat must be able to eat practically anything if it is to survive in its inhospitable habitat. Impalas and Elands in the African Bush however have a much more specific diet, so much so that a slight increase in the population of either species is sufficient to cause a shortage of the specialised foodstuffs required for further population growth, without affecting the food supply of other animals. An increase in the number of predator species must also further differentiate and hence further refine the quantitative and qualitative controls they apply on prey populations. In these, and a host of other ways, a system, as it becomes more complex, becomes correspondingly more stable.

However, this is as far as we can relate complexity to stability without taking into account another key variable – one that has been taken into account neither by May, nor by Lotka and Volterra – I refer to ‘order’ which I shall take to be synonymous with ‘degree of integration’ or with ‘negative-entropy’.

Order, as already mentioned, is normally defined as the influence of the whole over the parts. The greater this influence, the more a given number of parts become specialised in dealing with their specific environment. For oscillations within a system i.e. between its subsystems, to be reduced to a minimum, the system must not only be complex but also integrated. It is the combination of these two qualities that permits the maximum division of labour or specialisation among the maximum number of subsystems. However there is a cost to pay for this, the greater the specialization, the smaller the range of possible responses which a subsystem is capable of mediating, and hence the smaller the number of environmental situations to which it can respond adaptively. This means that the more highly integrated a system, the less capable it is of tolerating serious internal change.

Thus a tropical rain forest is a highly integrated and complex system judged by the standard of other ecosystems (though clearly it displays nothing like the degree of integration of a biological organism). For this reason it does not withstand improbable internal disturbances. Cut down its trees, for instance, and it is destroyed and it does not really recover, whereas a simpler and less integrated system such as a savannah can recover from similar treatment much more readily. That is why Geertz wrongly regards a tropical rain forest as being less stable than a rice paddy field.

But a human organism, being still more highly integrated, is correspondingly more vulnerable to a disturbance. Deprive it of its basic parts, the liver, kidneys, etc. that assure essential metabolic functions, and it too will be destroyed, and will also fail to recover. Systems, regardless of their degree of integration can only function adaptively within certain specific parameters. The human species is considered to be highly adaptable, but if the basic parameters required to sustain human life ceased to be respected, i.e. if the temperature of the earth were suddenly doubled, or the world’s topsoil were blown away, the human species would also be destroyed.

Systems are designed by their evolution and ontogeny to adapt to a specific set of conditions and whether these conditions are highly specialised or are not, the strategy they use for increasing stability (1) and surviving is based on the assumption that these conditions will continue to be maintained. The fact that the biosphere has thrived and developed ever greater complexity over the last three billion years – that is until modern man set about reversing the process – is a sign that this assumption has on the whole been justified.

There is a reason for this. The natural systems that make up the biosphere are organised hierarchically. A system plus its environment constitutes a larger system and this larger system, by, maintaining its own stability (2) assures the orderliness of the environment to which its sub-systems are submitted and hence the stability (1) of their relationship with their particular environment.

Thus an embryo requires a very highly ordered environment from which it can put up with but slight divergences. However it cannot on this account be regarded as unstable (2) as the requisite orderliness of its environment is assured by the behaviour of the larger system of which it is part i.e. its mother. Similarly a child can only function in an environment displaying a certain measure of order, that of the family.

This does not mean that it is unstable because this orderly environment is maintained by the various members of the family unit. The family itself is designed to function in an environment that also displays a certain measure of order though it be lower than that required by the individual members of the family. This is provided by the community which in normal conditions displays suitable cohesion.

The community also requires an environment which displays a certain degree of order though not as great as that required by the individual families that compose it. This is provided by the ecosystem of which it is part while the still lower degree of order required by an ecosystem is provided by the geological and climatic conditions in which it functions.

Thus the embryo is stable so long as it is part of a hierarchical organisation of systems which is itself stable. One might say of such a system that it is ‘stable within the biosphere’.

An integrated system cannot deal with a large number of different environmental changes but in terms of the model of its relationship with its environment that it has built up over the course of its experience – such changes are extremely improbable.

An unintegrated system may have a greater capacity for dealing with change but in this case, the probability of the occurrence of such changes is correspondingly higher. In both cases, the capacity to deal with change is commensurate with the probability * of the occurrence of such change. (I am clearly not using the term probability in the way in which it is used by communication engineers or by those involved in thermodynamics. For them the most simple organisation of information, that displaying the lowest negative entropy and thereby capable of handling the smallest number of different signals is the most probable regardless of the way the evolutionary process has affected the orderliness of the system’s environment from which the signals it must handle are derived – this notion of probability is of no value in a behavioural context.)

This is clearly not the case of man in an industrial society. The latter’s relationship within the biosphere could not be more unstable since an industrial society can only survive by methodically destroying its environment, a process which must spell its own rapid demise.

Why, we might ask, are the larger systems able to deal with less orderly environments than the subsystems that compose them? The answer is partly that they are less integrated. Thus the family is a less integrated system than the individuals that compose it. The community is less integrated than the family and the ecosystem less so than the community. By being less integrated the relationship between the subsystems displays less stability (1).

On the other hand they are capable of acting on their own and the range of possible responses which they are capable of mediating must correspondingly increase. If we take a man and his environment as constituting a system, then this system’s lack of integration makes him – one of the subsystems – capable of a wide range of different responses thereby assuring the normal functioning of his bodily metabolism in the face of all sorts of environmental changes.

Let us look at the question slightly differently. Since in a loosely integrated ecosystem, changes are always occurring, its component systems cannot be unchanging. The best they can do is try to maintain their basic structure in the face of change. This is possible because they are organised hierarchically and are capable of adapting the particularities of their structure in such a way as to eliminate the necessity for changing the generalities.

In other words it is the relatively small oscillations that characterise the behaviour pattern of a stable (1) and (2) system functioning in a disorderly environment, that prevent the occurrence of much larger oscillations. If these were allowed to occur, they would disrupt the functioning of the highly-integrated and highly vulnerable component sub-systems that assure its basic metabolism; a disruption that it could not survive.

This brings us back to the question of complexity. The more complex a system the more stable it is. The reason, as we have seen, is that complexity (in the real world) means differentiation and differentiation permits a system to fulfil whatever functions, it has to fulfil in a more refined way thereby enabling it to better achieve its goal, that of increased stability (1). The technique for achieving stability (1) however varies in accordance with whether the environment is an orderly one (which in turn depends, as we have seen, on the ability of the larger system of which it is part and which provides it with its environment, to maintain its own stability (2) with its own environment.)

If it is orderly, then it can set about maximising stability (1) with relative impunity i.e. without running the risk of being rendered unstable (2) and eventually annihilated by an improbable change.

If it is disorderly, then it must set about increasing its capacity for dealing with an increasing number of probable changes. In both cases, this means building up complexity, but complexity of a different sort.

Let us refer to the first sort as complexity (1) and the second sort as complexity (2). The former is associated with a high degree, the latter with a lower degree of integration.

Whereas complexity (1) is built up in order to achieve the highest possible adaptation to a specific environment for the purpose of maximising stability (1), complexity (2) is designed to enable a system to adapt, though perhaps less perfectly i.e. with a lower degree of stability (1), to an ever greater number of different environments, or more precisely to an increasing number of environmental changes. Both, however, are designed to maintain stability (2).

It is generally recognised that this is made possible by increased genetic complexity or diversity. A gene pool however is only one of the organisations of information that assure this function, within the biosphere. The nucleus of a cell is another; so too is the brain. I have coined the term “cybernism” to apply to all such functionally similar organisations of information. A cybernism can display greater or lesser complexity. Again we are not talking of random complexity since information is not accumulated at random but organised for a specific purpose, that of providing a model of the associated system’s relationship with its environment, on the basis of which responses are mediated and monitored. That part of the brain which is most highly integrated is responsible for assuring an organism’s correspondingly integrated metabolic functions. It can be regarded as displaying greater or lesser cybernismic complexity (1).

During the last stages of the evolutionary process that led to the appearance of man, behaviour became increasingly encorticalised i.e. rendered dependent on the expanding neo-cortex. This has clearly led to an increase in its cybernismic complexity (2) and hence in the number of environmental challenges to which he could adapt and thereby correspondingly increased his ability to maintain his basic biological and social structure in the face of change.

Whereas a serious and improbable change could lead to the elimination of a large proportion of the members of a particular population that displayed low cerebral complexity (2), leaving but those genetically equipped to adapt to the new conditions, such a change would be likely to have a far less drastic effect in one displaying a high level of cerebral complexity (2). In this sense cerebral complexity (2) will have partly at least reduced the genetic complexity (2) and hence the systemic complexity (2) required to deal with given challenges. Since adaptation in the new conditions will give rise to very much smaller discontinuities or oscillations, the development of cerebral complexity (2) will assure correspondingly greater stability (1).

It will also enable a system to obtain the best of both worlds so to speak. A man is a highly integrated system and at the same time he can deal with a relatively disorderly environment. This is the consequence of replacing unintegrated systemic complexity (2) with unintegrated cybernismic or more precisely cerebral complexity (2).

Cybernisms are sometimes regarded as containing redundant information. Lashley pointed out (his equipotency principle) that a man can still function normally after being deprived of 40 percent of his neo-cortex. So presumably can a population, if its gene pool has been reduced in a similar manner. This shows that the degree of integration in a population of neurons (i.e. a brain) as in a gene pool is very low indeed. However if this occurs, the number of environmental changes to which the system is capable of adapting (unless its environment suddenly becomes correspondingly more orderly) is also correspondingly reduced and hence so must be its stability (1) and (2).

A point that seems to be generally forgotten is that cybernismic complexity is of no value unless it can be translated into the appropriate physical responses. It is not built up for its own sake but as an essential part of a system’s control mechanism i.e. as a means of adapting to its environment. Thus the frequency of the different genes in a gene pool must be related to the probability of the occurrence of the environmental conditions to which the responses they mediate are adaptive. In other words the information is there because it is required for the purpose of triggering off responses that may one day be adaptive. This means that the system must be capable of providing these responses i.e. of implementing the instructions it receives from the cybernism.

Clearly, a population will not, at a given moment, display all the physical characteristics that its gene pool might allow it to display but – since it only has the ability to develop such characteristics because of the probability of the occurrence of the environmental situations to which they are adaptive – in the long-term it must do so. Thus, though in the case of a population, cybernismic complexity (2) is not reflected in systemic complexity (2) at any given moment, it must be over a sufficient time-scale.

The situation is similar with cerebral complexity (2). A man does not do all the things that his brain allows him to do at any given moment, indeed not even in his life time. It is only if one takes the species as a whole over a long period that the relationship between cerebral complexity and behavioural complexity becomes empirically apparent. If man however is capable of such a wide variety of responses it is not just because of the information in his brain but also because of his physical structure. If man had been designed to live in a highly ordered environment like a tapeworm for instance he would not only have developed a very different brain but also a very different body and a very different social structure.

Much of the complexity displayed by man and the societies he is organised into, must thereby be required for the purpose of implementing instructions that would never have been issued if they had not built up genetic and cerebral complexity (2) i.e. if it were not for the need to maintain stability (2) in a disorderly environment. Much of it should thereby be classified as complexity (2).

From these considerations it must follow that both systemic complexity (1) and systemic complexity (2) must contribute towards increasing stability.

Conclusion: New terms are required

The terms stability (1), stability (2), complexity (1) and complexity (2) are clearly unsatisfactory. New terms are required. I suggest that the term ‘stability’ be reserved for stability (2) which means that a system would now be either ‘stable’ or ‘unstable’ and that one could no longer talk of a system becoming more or less stable. I suggest that stability (1) be referred to as ‘homeostasis’ or ‘homeorhesos’ to use Waddington’s term. ‘Homeostasis’ would thereby refer to a system’s ability to return as close as possible to a ground position after a disturbance. The term ‘complexity’ would also be reserved for complexity (1). Complexity (2) in line with current usage would be referred to as ‘diversity’.

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I myself many years ago devised a whole new terminology for dealing with behaviour. I adopted the term ‘anergy’ as used by the physiologist Child to refer to adaptive behaviour. Non-adaptive behaviour tending towards instability would then he ‘catergy’ (again to use Child’s term). The unit of behaviour would be the ‘anergism’ a term that would be used to replace the much abused ‘system’. Phylogeny would be referred to as ‘phyloanergy’ and the unit of phyloanergy would be the ‘phyloanergism’. Ontogeny would then be ‘ontoanergy’ and the unit or anergism involved would be the ontoanergism. Day-to-day behaviour (i.e. that mediated by the brain) for which there is today no specific term, would be ‘neuro-anergy’. An organism would thereby be referred to as a ‘neuroanergism’. These types of behaviour would be mediated respectively by the phylocybernism (the gene-pool), the ontocybernism (the information contained in the fertilised egg) and the neurocybernism (the brain). Complexity would be referred to as ‘epianergy’ and diversity ‘stereanergy’ (from stereo meaning ‘concrete’ as in ‘steroscopic’ and ‘stereophonic’).

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