Proc. Natl. Acad. Sci. USA Vol. 74, No. 4, pp. 1647-1651, April 1977 Evolution The cost of evolution and the imprecision of adaptation (Haldane's dilemma/multi-level feedback/human evolution/maximization) P. J. DARLINGTON, JR. Museum of Comparative Zoology, Harvard University, Cambridge, Massachusetts 02138 Contributed by P. J. Darlington, Jr., January 21, 1977 ABSTRACT Comparisons of six hypothetical cases suggest Case B. Now suppose that the two survivors escape other that Haldane overestimated the cost ofnatural selection by al- hazards and produce ten offspring of which two (6 9) are lele substitution. The cost is reduced if recessive alleles are ad- homozygous for another recessive allele which allows them to vantageous, if substitutions are large and few, if selection is strong and substitutions are rapid, if substitutions are serial, and survive (say) a protein shortage which results in the deaths (or if substitutions in small demes are followed by deme-group failure to reproduce) of the other eight individuals. Then an- substitutions. But costs are still so heavy that the adaptations other complete allele substitution will have been made in one of complex organisms in complex and changing environments generation at a cost of are never completed. The rule probably is that most species most of the time are not fully adapted to their environments, but are No(10) - N1(2) = 8 just a little better than their competitors for the time being. individuals, and again no additional selective substitutions can During the "evolution" of a man-made machine, the maker be made and paid for at the same time. of it can take it apart and eliminate inferior and substitute These cases suggest the following generalizations which, with improved parts without throwing away whole machines. But modifications, carry over to more complex cases. in organic evolution, each slightest separate improvement made [1 ] In simple, 2-class, 1-episode cases the cost of an allele by natural selection in the great number of parts, processes, and substitution is No - N1 individuals, No being the number of behaviors in an evolving organism is made at the cost of elim- individuals in the initial population, and N1 the number that inating-throwing away-all the whole individuals that lack survive selective elimination and produce the next generation. the improvement. This is "the cost of natural selection," or of These cases contradict Haldane's generalization (ref. 1, p. 520) adaptive evolution. Calculation of this cost and of its conse- that the cost of one allele substitution "always" exceeds the quences is one of the most important pieces of unfinished number of individuals in one generation of a population. business in modern evolution theory. [2] The cost of substitution is the same whether paid in se- lective deaths (individuals that die prematurely) or in reduced reproduction (individuals not born). THEORY: THE COST OF SELECTION [3] The relation of cost to ability to pay is independent of Haldane (1), in 1957, calculated that gene (allele) substitutions population size. The cost of a substitution, in numbers of indi- by selection cost so much that populations must (in effect) viduals eliminated, is enormously greater in very large than in choose between evolving at low cost per generation but unad- very small populations, but the larger populations can pay the aptively slowly, or more rapidly but at a cost so high as to risk enormously greater costs. I have never seen this simple but extinction. These alternatives constitute what is sometimes important generalization clearly stated. (But population size called "Haldane's dilemma." His conclusions have been much has other effects on rates and costs of substitutions; see ¶ 10, 13, criticized, especially by means of complex mathematics; for 15, 16, 19, and 21.) partial reviews of the criticisms, see ref. 2, pp. 72-74 and ref. [4] The cost of a substitution (No- N1) is independent of the 3, pp. 98-102. Here, I shall re-examine the cost of selection in magnitude of genetic or phenotypic difference, if the difference another way, by means of six hypothetical cases and simple results in complete substitution in one episode. The cost is the arithmetic; the cases cannot prove generalizations but can same for substitution of one allele, a set of linked alleles, a whole suggest them or (sometimes) falsify them. And I shall then chromosome, a whole genotype, or a whole deme gene pool in consider how costs limit actual, complex evolutionary processes deme-group selection. and the precision of adaptations, including our own. [5] The theoretical cost of a segment of evolution is therefore in proportion to the number of separate substitutions. An evo- Two-class, 1-episode cases lutionary advance made by 10 separate small substitutions costs Case A. Suppose that, in a population of four billion indi- 10 times as much as the same advance made by one large sub- viduals, only one male and one female are homozygous for a stitution. (And the cost-advantage of the larger substitution is recessive allele which allows them alone to survive an atomic increased if the larger phenotypic difference results in stronger holocaust which eliminates all the other individuals. (If all in- selection and more rapid substitution; see ¶ 14.) dividuals survive, but only the two can reproduce, the others [6] A consequence of ¶ 5 is that multi-level (feedback) se- being sterilized by radiation, the effect is the same.) Then one lection should favor genetic systems in which genes (alleles) are complete allele substitution will have been made by selection linked or combined into sets which are selected as wholes. (selective elimination) in one generation, at a cost of "Regulator genes" (4), which regulate the actions of sets of other - = genes, may have this effect, although I am not sure about this. No(4 billion) N1(2) 3,999,999,998 However, the initial formation of a linked set of favorable alleles individuals, and no additional selective substitutions can be presumably requires that each allele be substituted separately, made and paid for at the same time, although other, nonse- at the same cost (in elimination of whole individuals) as other lective, random changes comparable to those expected of the allele substitutions. Only after a linked or regulated set of genes "founder effect" may occur in the population's gene pool. has been formed at this cost can it reduce the cost of further 1647 Downloaded by guest on September 30, 2021 1648 Evolution: Darlington Proc. Natl. Acad. Sci. USA 74 (1977) substitutions. So, I doubt if linkages and gene-regulators reduce Table 1. Costs of substitution in Case C the costs of evolution of new genetic-structural-functional- behavioral systems, although they may reduce the costs of No. of secondary diversifications. Generation As as Cost [7] "Truncation selection" is sometimes suggested as an al- ternative or supplement to linkage. It supposes an array of ge- no (N- 2) 2 notypes (individuals) distributed along a "scale of fitness," with N-2 N all those above a dividing line surviving, and all those below 2 --1 2 2 selectively eliminated (e.g., ref. 3, p. 100, Fig. 17, with further references). But fitness (W) expresses statistical chances of n, (N - 4) 4 survival, not certainties. The truncation hypothesis first pos- N-4 N 4 --2 tulates a series of individuals graded in fitness, and then gives 2 2 the same individuals new fitnesses, of either 1 (sure to survive in this case, although W = 1 is not by definition a guarantee of n. (N- 8) 8 survival; in fact no genotype can be sure to survive) or 0 (no N-8 N 8 --4 chance of surviving). This change of fitnesses in mid-hypothesis 2 2 is not logically permissible. I do not see how "truncation" can (N- 16) 16 reduce the costs of allele substitution in real cases. n3 N - 1 6 N [8] In simple, 2-class, 1-episode cases, the minimum cost of 16 -- 8 one substitution is also the maximum cost that a population can 2 2 pay in one generation, if N1 is the minimum viable size of the population. The equation is then Cost to this point, about 2N - 15 the numbers ofAs and as before and after se- Maximum payable cost = No - N1 minimum For each generation lection are given under "No. of," and the cost of the selective episode If this maximum is paid for one substitution in one generation, is given on the right. no additional costs of other selective substitutions can be paid in the same generation, although other, random genetic changes increasing the quality rather than the quantity of substitu- may occur. The total cost paid in one generation may be, and tions.) probably usually is, divided into fractions paid against several [11] Another consequence of ¶ 8 is that, if a population pays or many separate concurrent substitutions, but since the max- the maximum cost of one allele (or other) substitution (No- imum cost paid per generation cannot exceed No- N1 minimum NI minimum) in each generation, a maximum of x substitutions (if it does, the population becomes extinct), payments made to can be made in x generations. This maximum is probably re- one fractional substitution reduce the payments that can be duced in many ways in real cases, but there presumably is a made to others. A corollary is that, in these cases, the number direct relation: the more generations, the more substitutions that of individuals substituted in one generation cannot exceed NI; can be made. This would seem to give an advantage in rate of a population after selection cannot contain more new-allele evolution to small plants and animals with many generations bearers than the number of individuals in the population.