BioSystems, 15 (1~p82) 83--85 83 Elsevier/North-Holland Scientific Publishers Ltd.

NATURAL SELECTION AND THE EVOLUTION OF NEUTRALISM

MICHAEL CONRAD

Depts. of Computer Science and Biological Sciences, Wayne State University. Detroit, Michigan 48202, U.S.A.

(Received June 15th, 1981)

The efficiency of evolutionary search increases as the density of acceptable proteins in a protein space in- creases. Populations caught in regions whose density is too low to support evolution can be pulled into high density regions by hitchhiking selection. As they move into such regions, the action of natural selection becomes more effective, yet these populations will satisfy conditions which lead to predictions made by neutral, so-called non-Darwinian models.

According to the evo lu t ionary boots t rap principle (Conrad, 1977, 1979a) the amena- bility of biological systems to evolution is itself a trait whi.ch is subject to variation and natural selection. A number of different arguments have led to this conclusion, including arguments based on rate of evolu- tion (Conrad, 1972, 1978), arguments based on the relation between gene structure and gene action (Conrad, 1979b), as well as simu- lation studies (Conrad and Rizki, 1980). These discussions have been formulated in the framework of an adaptive surface which I have called molecular since the genes are described in t~rms of sequences of bases rather than in terms of gross frequencies of different alleles. The purpose of this note is to reformulate the rate argument in terms of the protein space concept first introduced by Maynard Smith (1970). This is a space of amino acid sequences with the property that neighboring sequences can be converted into one another by single amino acid changes. For all practic~J purposes a protein space is a projection of a molecular adaptive surface, but the slighl~Ly different point of view suggests an especially simple formulation of the argument as well as some important features of the bootstrapping process.

The important feature of a protein space

pointed ou t by Maynard Smith is that diver- gent protein evolution is impossible in histori- cal time unless fN > 1, where N is the number of proteins which can be derived from a functionally useful protein and f is the frac- t ion of these with an acceptable selective value, f can be interpreted as the density of acceptable proteins in the space. If fN = 1 evolution can occur, but divergent evolution cannot. If fN < 1, the possibility of evolution would be limited by the improbabili ty of double or multiple mutations (see Conrad, 1972, 1978 for calculations). But according to the bootstrap principle f is no t a fixed property. It is itself a phenotypic property which is variable and subject to a form of natural selection which can convert genes which do no t satisfy fN ~- 1 into genes which do. The argument, given below, expli- cates in a particularly clear way the deep connection which the bootstrapping prin- ciple establishes between the neutral aspect of evolution and the effectiveness of natural selection (cf. Conrad 1977, 1978}.

First consider how f is influenced by amino acid sequence. Slight alterations in the struc- ture of a protein are much more likely to pre- serve or improve its function than major ones. Thus any mechanisms which increase the fraction of mutat ions that only slightly alter

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folded shape will increase f. One mechanism is the incorporation of amino acids into the sequence for which there are structurally similar replacements (for example replace- ments with similar hydrophobicities, see Volkenstein, 1979). A second mechanism is the incorporation of extra amino acids which serve to increase the stability of the folding process to an extent which exceeds that required for the protein to perform its physiological function reliably. Even proteins which perform the same physiological func- tion could have different values of f.

Mechanisms which increase f generally require some expenditure of energy, hence are a slight liability in terms of fitness. Never- theless f-enhancing mutations should accumu- late by hitchhiking along with the fitness- increasing mutations whose probability of occurrence they increase. This hitchhiking is analogous to hitchhiking of genes for recombination (Strobeck et al., 1976) and high mutat ion rate (Cox and Gibson, 1974). But its quantitative importance is greater due to the threshold condition, fN > 1.

If fN < 1 evolution time scales as 1lAp n, where p is the mutat ion probability, n is the number of required mutations, and A is the population size. When fN _> 1 the mutations need not be simultaneous, so the time scales in the worst case as n/A'p. A' may be taken as the smallest size reached by any population in the chain on any time scale small in com- parison to 1lAp n. For p = 10 -8 and n as small~ as 2, fN _> 1 gives a speedup of (A'/2A)IO 8 over fN < 1 (see Conrad, 1978 for a more detailed calculation).

Now suppose that the evolution of the protein reaches a bottleneck, that is, a point in the protein space for which fN ~ 1 is not satisfied. Further evolution could await a fitness-increasing event requiring time on the order of 1/Ap 2, or it could proceed by drifting through m f-enhancing mutations, each of which is slightly fitness-reducing, but which leads to a protein species which does satisfy fN --> 1. The time for reaching a pro- tein which is fitness-increasing in this way

scales as (v + m)/A'p, where v is the number of fitness-increasing mutations required to give a net increase in fitness. Even in the unlikely circumstance that v and m are both large, such a sequence of mutations still gives a speedup of the order (A'/2A)108 over the pathway which requires a double mutation. This means that at a bottleneck evolution will almost always proceed by the hitchhiking route and therefore entail the accumulation of f-enhancing mutations.

When fN -> 1, f-enhancing mutations still speed up the evolution process, though only by the constant factor fN. f-enhancing muta- tions which make it possible to circumvent a first bottleneck may be carried for some time, either because they hitchhike with this mild speedup or because they are only slightly fitness-reducing. If they are still pre- sent when a second bottleneck is reached, the whole process will iterate itself. In this way a considerable load of f-enhancing muta- tions may accumulate. The argument has actually been made under an unfavorable assumption. In the realistic case of a changing environment, a species without a load of f- enhancing mutat ions will be forced into bottlenecks which require double mutations.

The value of f required to satisfy fN >- 1 depends on the size of the protein and the number of f-enhancing amino acids required to support this value depends on the number of functional sites. As pointed out by Maynard Smith (1970), N can be taken as the number of possible point mutat ions allowed by the genetic code, implying that N ~ 10L, where L is the number of amino acids in the protein. The threshold condition for fitness-increasing evolution is then lOlL :> 1. If L increases due to the addition of f-enhancing amino acids, f will increase as well. If L increases due to an increase in the number of functional sites, the likelihood of bottlenecks increases, imply- ing that the number of f-enhancing amino acids required to maintain any given value of f must increase. There is a third important possibility. If all the variants of a protein are less well adapted, the species which sheds f-

enhancing mutat ions and falls below the threshold will have the advantage. The varia- bility of f and L can thus serve to lock in adaptation as well as to increase adaptability.

The hitchhiking of f-enhancing mutat ions adds a new element to the discussion (Kimura, 1968; King and Jukes, 1969) of neutral drift vs. selection in evolution. Hitchhiking around bott lenecks leads to proteins on which natural selection can act effectively. But the presence of the f-enhancing amino acids necessarily resu]ts in a higher degree of neutra- lism, implying that the striking phenomenon of neutral variation confirms rather than disconfirms the; importance of selection in evolution. In recent discussions of the neutral theory Kimura (1979) has argued that the degree of neutxal variation, hence the rate of evolution, should decrease as functional constraints are added to a protein. The pre- sent analysis leads to the same conclusion since the addition of constraints, such as extra functional sites, decreases f. But it adds the prediction that f increases with the number of f-enhancing amino acids. This number is ult imately determined by selection through the hitchhiking process.

Step by step incorporation of f-enhancing amino acids and iterated hitchhiking make it possible for the mechanism of variation and natural selection to move biological systems into regions of the protein space which fulfill the condition for fitness-increasing evolution. It is not necessary to assume that the possibi- lity of evolution, even in its earliest stages, depends on the; fortui tous circumstance that the threshold conditions lOlL ~_ 1 is always satisfied in advance. The argument thus implies an important internal consistency between Darwinian theory and its molecular basis. By simplifying the requirements which must be met by the first Darwinian systems, it narrows the gap between living and non- living nature.

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Acknowledgement

This work was supported by Contract N00014-80-C-0365 from the Division of Information Systems, Office of Naval Research It was prepared in part during a U.S. National Academy of Sciences exchange visit to the Institute of Problems of Information Trans- mission, USSR Academy of Sciences.

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