Thursday, October 23, 2008

Notes on Sewall Wright: The Shifting Balance Theory - Part 1   posted by DavidB @ 10/23/2008 03:52:00 AM

Finally, Sewall Wright's Shifting Balance theory of evolution. This will positively, definitely, categorically be my last note on Sewall Wright. Unless I think of something else.

For convenience I will split the note into two parts, one dealing with the theory in its original form, and the second dealing with subsequent developments.

Two catch-phrases indissolubly linked with Sewall Wright are the adaptive landscape, and the shifting balance. In preparing my note on Wright's concept of the adaptive landscape I was surprised to discover that Wright himself seldom if ever used this expression. I could not find a single example. I was therefore half-expecting that I would not find any reference to the shifting balance either - and I would have been half-right. Wright did use that term, but not, as far as I can find, until surprisingly late in his long career....

All page references are to Evolution: Selected Papers unless otherwise stated. See the References for details.

The first mention of 'the shifting balance'

Wright refers extensively to the 'shifting balance theory' in Volume 3 of his treatise Evolution and the Genetics of Populations, published in 1977, but I have not found this term in the first two volumes (1968 and 1969), or in anything else published by Wright before 1970. Nor was it used by authors such as Dobzhansky, Mayr, and Simpson, when describing Wright's ideas. The earliest use of the term I have found is in Wright's article of 1970 on 'Random drift and the shifting balance theory of evolution'. Admittedly, I have not read all of his 200-odd papers published before that year, but unless anyone can unearth an earlier use I suggest that the term was in fact coined in this article of 1970, some 50 years into Wright's career. The terminology of a theory is less important than its substance, but the absence of the term 'shifting balance' before 1970 (if I am right about this) does have two implications: first, we should not expect other authors (such as Fisher and Haldane) to have commented on the 'shifting balance theory' as such, and second, in the absence of a single label, it may not have been perceived as a single unified theory at all.

Earlier terminology

The apparent absence of the phrase 'shifting balance' before 1970 does not mean that Wright had never previously used the terms 'balance' or 'shifting', sometimes in close proximity. Wright was fond of the term 'balance', and related terms such as 'equilibrium' or 'poise', and used them for a variety of purposes, sometimes with a precise mathematical meaning, and sometimes more loosely. Here are some examples, chronologically arranged:

1931: 'The conditions favorable to progressive evolution as a process of cumulative change are neither extreme mutation, extreme selection, extreme hybridization nor any other extreme, but rather a certain balance between conditions which make for genetic homogeneity and genetic heterogeneity' (96)

1931: 'Evolution as a process of cumulative change depends on a proper balance of the conditions which... make for genetic homogeneity and genetic heterogeneity of the species' (158)

1941: 'The most general conclusion that can be drawn from the attempt to develop a mathematical theory of the simultaneous effects of all statistical processes that affect the genetic composition of populations is that in general the most favorable conditions for evolutionary advance are found when these are balanced against each other in certain ways, rather than when any one completely dominates the situation' (488)

1951: 'The general qualitative conclusion would still seem to hold that this [the evolution of culture] or any other evolutionary process depends on a continuously shifting but never obliterated state of balance between factors of persistence and change, and that the most favourable condition for this occurs when there is a finely subdivided structure in which isolation and cross-communication are kept in proper balance' (596)

1959: 'It is concluded that the most favorable conditions are those of balance: a balance among the directed processes that insures the maintenance of a high degree of heterozygosis in minor factors and a balance between the directed processes as a group and various sorts of random ones that insures extensive random drift around the equilibrium positions of the gene frequencies. All these conditions are met in the highest degree where there is a certain balance between isolation and crossbreeding within each of a large number of local populations of the species' (Tax, 470-1)

1960: 'In developing the balance theory of evolution, I was trying to arrive at a judgement of the most favorable conditions for evolution under the Mendelian mechanism' (619)

It will be noted that in the last of these passages Wright refers to the 'balance theory of evolution', and in another the 'balance between factors of persistence and change' is said to be 'continuously shifting'. Wright therefore comes very close to using the phrase 'shifting balance theory', but the fact that even in these passages he does not actually use it strengthens the suspicion that he had not yet coined the term as such.

What balance? And what shifts?

Many other uses of the terms 'balance' and 'shift' by Wright could be cited. I have quoted only those which come closest to his explicit term 'the shifting balance'. But even these examples, on a careful reading, leave it unclear what is the 'balance' that is seen by Wright as essential to effective evolution. Many different things are said to be 'balanced'. What exactly is a 'balance between factors of persistence and change', and is it the same as 'balance between conditions which make for genetic homogeneity and genetic heterogeneity'? Migration, for example, is a factor usually making for genetic homogeneity, but it is also often a factor making for 'change'. So which side of the balance does it fall on?

It might be hoped that in Wright's 1970 article, or in Volume 3 of Evolution and the Genetics of Populations, where the 'shifting balance theory' is discussed at length, we would find a clear statement of the meaning of the term itself. What is the relevant balance, how does it shift, and how does Wright's theory of evolution depend on the shifting of the balance? It may be that the answers are there, but if so, I have not found them. While Wright discusses various component parts of his theory, the overarching term 'the shifting balance' is not itself defined or explained. Moreover, whatever interpretation we give to the term 'balance', it does not seem that the 'shifting' of the balance itself plays any essential part in Wright's conception of the evolutionary process. The balance between the various factors of evolution, including selection, mutation, migration, environment, genetic drift, and population structure - to list the obvious ones - might stay constant, yet the process of evolution as described by Wright could still work, if the balance of factors is right. It is not the shifting of the balance, but the existence of the right kind of balance, which according to Wright is favourable to evolutionary progress. I conclude that the 'shifting balance theory' is a convenient and memorable label, but one without a precise literal meaning in isolation.

When was the theory first published?

Even if the label 'shifting balance theory' was not adopted until 1970, the doctrines covered by that label may have been propounded earlier. Wright himself, in 1970, claimed to have first published the theory as long ago as 1929. It can be confirmed that some of the key elements of the theory were contained in Wright's great 1931 paper 'Evolution in Mendelian populations', and summarised in shorter related papers beginning in 1929. Notably, these contain several key propositions which Wright maintained consistently to the end of his life:

a) The most favourable circumstances for evolution are in large populations subdivided into many small partially isolated populations;

b) Large freely interbreeding populations are not favourable to continuing evolution;

c) Genetic drift is an important part of the evolutionary process; and

d) The differential success of subpopulations, which Wright describes as 'intergroup selection', is an important contributor to cumulative evolutionary change.

If we regard these four propositions as constituting the shifting balance theory, then it was indeed first published in 1929.

Changes to the theory

This does not mean that there were no important changes to the theory after 1929. I believe there were changes both of substance and of emphasis, which I would summarise as follows:

1. In 1932 Wright adopted the metaphor of a multidimensional field of gene combinations and fitness values, which was later described (though not by Wright) as the 'adaptive landscape'. In my view this was more than just an illustrative device. The concept of selective peaks as alternative states of stable equilibrium was a valuable addition of substance to the theory, not corresponding to anything clearly stated in the original version.

2. Whereas in 1929-31 Wright had denied that temporary changes in environmental conditions would have major evolutionary effects, in 1932 he changed his position and accepted that environmental fluctuations could 'shuffle' populations from one evolutionary position of equilibrium to another, usually higher, one.

3. As a consequence of change (2), Wright reduced his emphasis on the importance of genetic drift, which he had originally claimed as essential to long-term evolutionary progress. After 1932 genetic drift was in principle only one of several mechanisms for change. But Wright did not make it sufficiently clear that his position had changed, and did not follow through the implications of the change for his views on the importance of population structure.

4. Throughout his career Wright maintained that the evolutionary process was partly adaptive and partly non-adaptive or 'random', but the emphasis he put on these elements shifted from the non-adaptive aspect to a greater emphasis on adaptation.

5. In his later writings on the subject Wright identified three 'phases' in the shifting balance process, but these are much less clear in the earlier versions of the theory.

Some but not all of these changes have already been identified in William Provine's admirable biography of Wright. The remainder of this note will mainly be concerned with documenting the various changes.

The original version of the theory (1929-31)

The key propositions of the original version of the theory were conveniently summarised by Wright himself in a short paper of 1929, which I will quote in full:

The frequency of a given gene in the population is affected by mutation, selection, migration and chance variation. The pressure exerted by these factors (excluding chance) and the position of equilibrium between opposing pressures are easily found. Gene frequency fluctuates about this equilibrium in a distribution curve, determined by size of population and the various pressures. The mean and variability of characters, correlation between relatives and the evolution of the population, depend on these distributions. In too small a population, there is nearly complete random fixation, little variation, little effect of selection and thus a static condition, modified occasionally by chance fixation of a new mutation, leading to degeneration and extinction. In too large a freely interbreeding population, there is great variability, but such a close approach of all gene frequencies to equilibrium that there is no evolution under static conditions. Changed conditions cause a usually slight and reversible shift of the gene frequencies to new equilibrium points. With intermediate size of population, there is continual random shifting of gene frequencies and consequent alteration of all selection coefficients, leading to relatively rapid, indefinitely continuing, irreversible and large fortuitous but not degenerative changes even under static conditions. The absolute rate, however, is slow, being limited by mutation pressure. Finally, in a large but subdivided population, there is continually shifting differentiation among the local races, even under uniform static conditions, which through intergroup selection brings about indefinitely continuing, irreversible, adaptive and much more rapid evolution of the species as a whole. (78)

These propositions are all stated more fully and supported by arguments in the 1931 papers 'Statistical theory of evolution' and 'Evolution in Mendelian populations'. (Although 'Statistical theory of evolution' was published first, it seems that 'Evolution in Mendelian populations' was completed first and 'Statistical theory of evolution' written as a summary of it.) Some of them are also covered in Wright's 1930 review of Fisher's Genetical Theory of Natural Selection. Most of them are restated and defended throughout Wright's career. The arguments given by Wright to support the key propositions (quoted in italics from the 1929 article) can be summarised as follows:

In too small a population, there is nearly complete random fixation, little variation, little effect of selection and thus a static condition, modified occasionally by chance fixation of a new mutation, leading to degeneration and extinction.

For this purpose 'too small' a population is one in which 1/4N (where N is the effective population size) is much larger than selection and mutation rates. (148) In this case genetic drift will be the main factor in evolution. Most genes will soon be fixed, there will be little variation within each population, and random unadaptive changes will lead to extinction. (93, 142, 148)

In too large a freely interbreeding population, there is great variability, but such a close approach of all gene frequencies to equilibrium that there is no evolution under static conditions.

For this purpose 'too large' a population is one in which both selection and mutation rates are much larger than 1/4N. (148) In this case, genetic drift will have little effect, and gene frequencies will be determined by the balance of selection and mutation. If selection on a gene is much stronger than mutation pressure, there will be almost complete fixation at each locus and therefore no evolution under fixed conditions. (148-50) If selection is not much stronger than mutation pressure, there will be more genetic diversity, but all gene frequencies will be close to equilibrium and evolution will be very slow unless conditions change. (150) Note that these arguments tacitly assume that there are no new favourable mutations, or existing ones still under selection.

Changed conditions cause a usually slight and reversible shift of the gene frequencies to new equilibrium points.

In 'Statistical theory of evolution' Wright says that 'Changes in conditions should be followed by systematic changes in gene frequencies until all have reached the new positions of equilibrium. Return to the old conditions should be followed by return to the old equilibria' (92). No specific reason is given for this conclusion. In 'Evolution in Mendelian populations' the explanation is slightly fuller. Following a strengthening of selection, gene frequencies will change, but 'The rapid advance has been at the expense of the store of variability of the species and ultimately puts the latter in a condition in which any further change must be exceedingly slow. Moreover, the advance is of an essentially reversible type. There has been a parallel movement of all the equilibria affected and on cessation of the drastic selection, mutation pressure should (with extreme slowness) carry all equilibria back to their original positions. Practically, complete reversibility is not to be expected, and especially under changes in selection which are more complicated than can be described as alternately severe and relaxed. Nevertheless, the situation is distinctly unfavorable for a continuing evolutionary process' (150). Note that Wright does not claim the changes are always reversible, only that this is 'essentially' or 'usually' the case. Bur he gives no clear reasons for this position, and only a year later (1932) he abandons it. As this is one of the major developments in the theory I consider it more fully in Part 2 of this note.

With intermediate size of population, there is continual random shifting of gene frequencies and consequent alteration of all selection coefficients, leading to relatively rapid, indefinitely continuing, irreversible and large fortuitous but not degenerative changes even under static conditions. The absolute rate, however, is slow, being limited by mutation pressure.

For this purpose an intermediate size of population is one where, for many genes, the selection pressure is not much stronger than the mutation rate, and neither selection pressure not mutation rate are much higher than 1/4N (150-1). (Since mutation rates were known by Wright not to be much higher than 1 in 100,000, this implies an effective population size of the order of 25,000.) In these circumstances genetic drift will be strong enough to cause considerable fluctuation in gene frequencies, but not to lead to rapid fixation of genes and loss of genetic diversity. Wright describes the result as 'a kaleidoscopic shifting of the average characters of the population through predominant types which practically are never repeated' (95, see also 151). But Wright emphasises that it would be a very slow process, as 'hundreds of thousands of generations are required for important evolutionary changes' (95). He mentions the effect of mutation rates as limiting the speed of change (78, 95, 151), presumably because with mutation rates not very different from the rate of genetic drift, mutation pressure tends to maintain genetic uniformity. But surely the main reason for slowness is that genetic drift itself is very slow in a population of many thousands.

Finally, in a large but subdivided population, there is continually shifting differentiation among the local races, even under uniform static conditions, which through intergroup selection brings about indefinitely continuing, irreversible, adaptive and much more rapid evolution of the species as a whole.

This is the most important proposition of the shifting balance theory in its original form. Wright never abandoned his view that a large subdivided population is most favourable to evolution. The subdivisions must be small enough, and isolated enough from each other, that the subpopulations can diverge in gene frequencies (151-2). Curiously, there is an important difference between Wright's accounts in his two 1931 presentations of the theory. In 'Statistical theory of evolution' Wright mentions only 'random drift' as causing the divergence between subpopulations, with the result that there is a 'geologically rapid drifting apart of the various sub-groups, even under uniform conditions. This is a non-adaptive radiation, but, on the average, not such as to lead to appreciable deterioration' (95). In 'Evolution in Mendelian populations', on the other hand, Wright mentions both genetic drift and local variation in selection pressures, so that the result is 'a partly nonadaptive, partly adaptive radiation among the subgroups' (151). There is of course no reason why both processes should not occur at once, perhaps in different subgroups or at different loci in the same subgroups at the same time. But the difference does have implications for the final phase of the process, which is 'intergroup selection'. On this, Wright says that 'Those [subgroups] in which the most successful types are reached presumably flourish and tend to overflow their boundaries while others decline, leading to changes in the mean gene frequencies of the population as a whole' (152). But if adaptive variation among subgroups is due only to local circumstances of selection (as seems to be suggested in 'Evolution in Mendelian populations'), those types which have highest fitness in their own locality cannot be expected to succeed elsewhere. If on the other hand the variation among subgroups is purely due to random drift (as seems to be suggested in 'Statistical theory of evolution'), it is not obvious that they will differ significantly in fitness for genetic reasons. 'Statistical theory of evolution' does however contain a very important development or clarification of the theory: 'Exceptionally favorable combinations of genes may come to predominate in some of the subgroups. These may be expected to expand their range while others dwindle. This process of intergroup selection may be very rapid as compared with mass selection of individuals, among whom favorable combinations are broken up by the reduction-fertilization mechanism in the next generation after formation' (95). The reference to 'favorable combinations' here is the first sign of the emphasis on epistatic fitness interactions which becomes increasingly important in the later development of the theory. But in the original statement, in 1931, it comes out of the blue and unsupported by any detailed analysis.

Likewise, the concept of 'intergroup selection' is not explored in any depth, and the claim that it would be more rapid than 'mass selection of individuals' is little more than a bare assertion. The suggested advantage that 'favorable combinations' are not immediately broken up by sexual reproduction seems to require not only a high degree of genetic unity within the subgroups, but the maintenance of that unity during the process of 'intergroup selection', despite the probable intermingling of different groups. The credibility of this process has been one of the main areas for recent controversy and research on the shifting balance theory. It should incidentally be stressed (see also Provine, p.288) that 'intergroup selection' as envisaged by Wright has little to do with 'group selection' as envisaged by most of its recent advocates. Wright does not suggest that successful groups have evolved adaptations for group living, or that their members behave 'altruistically' towards each other (though his theory does not exclude this either, and he later made some comments in this direction). His claim is rather that the subdivided population structure allows some groups, by chance, to form combinations of genes that are advantageous to individual fitness. The higher mean fitness of the groups is the resultant of these individual fitness advantages.

Wright also gives mixed messages about the adaptiveness of the process. While repeatedly claiming that in the long run the process is adaptive, Wright accepted the common view of many biologists at the time that the differences between subspecies and even between species of the same genera are usually non-adaptive (154, see also Provine p.288-99), a view which would seem to require the adaptive process of 'intergroup selection' to occur mainly between different genera or even higher taxa! But in this case 'intergroup selection' between small subgroups of the same species would be irrelevant to the process. Yet in 'Evolution in Mendelian populations' Wright also suggests that intergroup selection within the species may be responsible for 'peculiar adaptations' and 'extreme perfection' (154-5), a claim which is not, I think, repeated anywhere else. Overall, the emphasis in these early writings is more on the nonadaptive than the adaptive aspects of the process.

Taking stock

Before exploring the subsequent development of the theory (in Part 2), I will try to take stock of the position reached by 1931.

Already in his summary note of 1929 Wright had stated some of the key propositions of the shifting balance theory. In the two articles of 1931 he began the task of justifying these propositions. The arguments he put forward were ingenious, stimulating, and not implausible, but far from conclusive. There were moreover a number of tensions, if not actual inconsistencies, within Wright's accounts. One of these concerned the extent to which the process was adaptive, as has been explored fully by Provine. Another is the respective roles of genetic drift and local selection, on which I have pointed out an apparent difference between the two articles of 1931. Another is the problem of migration between groups. As suggested in my earlier note on migration, Wright did not attempt to quantify the effects of migration until after he had committed himself to the importance of random drift within semi-isolated subgroups. Only then, in 1929, did he discover 'that isolation in districts must be much more nearly complete than I realized at first' for the process to work. 'Evolution in Mendelian populations' makes an attempt to remedy the deficiency (128), but further work was clearly needed.

Several important aspects of the theory in its mature form are also lacking from the original version. Notably, there is nothing clearly corresponding to Wright's later emphasis on alternative local optima - 'selective peaks' - available to populations or subpopulations. These local optima depend heavily on epistatic fitness interactions, which are hardly mentioned in the original version. In the mature theory, subpopulations 'explore' the field of possibilities under the influence of random factors (genetic drift, but also environmental fluctuations) until they wander into the zone of attraction of a new selective peak. The stage of 'exploration' is Phase 1 of the process, while the climbing of the population up a peak is Phase 2, and intergroup selection is Phase 3. In the original version of the theory there is no clear distinction between Phase 1 and Phase 2, because there is nothing to suggest that the process of 'exploration' ever stops, short of the exhaustion of genetic variation by random fixation of genes. The phrase 'continually shifting differentiation' seems inconsistent with any sharp distinction between two phases. The first signs of a new approach are to be found in 'Statistical theory of evolution', with its reference to some groups finding 'exceptionally favorable combinations of genes', implying epistatic peaks of fitness. Quite possibly this had been in Wright's mind all along, but I do not think it can be identified in anything written before 'Statistical theory', including the much more widely read 'Evolution in Mendelian populations'.

Another important omission is any serious discussion of the probability of favourable new mutations. Wright's negative assessment of the prospects for evolution in large freely interbreeding populations depends on the tacit assumption that new mutations can be neglected. Wright later developed arguments to support this position.

Overall, a careful reader of Wright's publications up to 1931, without knowledge of subsequent developments, might reasonably conclude that Wright had put forward a remarkably original, ingenious, and comprehensive theory of evolution, consistent with most of what was then believed about the observed pattern of evolution, and free of any obvious fatal defects. This is itself was a very major achievement. But the same reader might also think that the theory was sketchy and speculative, and in need of further elaboration, not to mention empirical tests. Wright himself was no doubt aware of this, and continued to develop the theory for another 50 years, as I will discuss in Part 2.

William B. Provine, Sewall Wright and Evolutionary Biology, 1986.
Sewall Wright: 'Physiological genetics, ecology of populations, and natural selection', in Evolution After Darwin, vol. 1, ed. Sol Tax, 1960 (Tax). (Article first published in 1959.)
Sewall Wright: Evolution: Selected Papers (ESP), ed. William B.Provine, 1986.
Sewall Wright: 'Random drift and the shifting balance theory of evolution', in Mathematical Topics in Population Genetics, ed. Kojima, 1970.

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