Population Structure in Relation to Cost of Selection

Grant, Verne; Flake, Robert H.

doi:10.1073/pnas.71.5.1670

Cited by 10 publications

(10 citation statements)

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“…Self-compatibility is a mechanism that assures the production of seeds (e.g., Bertin, 1993;Grant and Flake, 1974;Grant and Grant, 1965;Levin, 1972), and it is a characteristic of early colonizing species of new or disturbed environments (Raimundez and Ramirez, 1998;Stebbins, 1970). Under such conditions, selfincompatible species seem to be at a disadvantage compared to facultative autogamous ones (that are capable of both self-fertilization and fertilization of other individuals; Raffl et al, 2007).…”

Section: Discussionmentioning

confidence: 99%

Reproductive biology of Launaea cervicornis: A keystone species of the Balearic coastal shrublands

Llorens

Gil

Boira

2009

Flora - Morphology, Distribution, Functional Ecology of Plants

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Section: Discussionmentioning

confidence: 99%

Reproductive biology of Launaea cervicornis: A keystone species of the Balearic coastal shrublands

Llorens

Gil

Boira

2009

Flora - Morphology, Distribution, Functional Ecology of Plants

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“…This paper is intended only as a new introduction to an important but confusing subject, and has deliberately been kept simple, with few references. Grant and Flake (15)(16)(17) treat the cost of selection more mathematically (stressing Wright's subdivided-population model, but differing from my conclusions in several ways) and give additional references.…”

Section: Two-class 1-episode Casesmentioning

confidence: 99%

“…Suppose that, in a given population, 1000 offspring are conceived; that 100 of them are homozygous for recessive alleles that kill them before or during birth, their loss going to the costs of eliminations of the lethal alleles; that of the remaining 900, 500 die nonselective deaths, by accidents including random predation; that of the remaining 400, 390 are selectively eliminated before maturity, their loss going to the costs of substitutions of alleles that affect immatures; and suppose finally that, of the 10 This case suggests two additional generalizations. [15] Substitutions made in series need not interfere with each other, and there is no obvious limit to the number of serial substitutions that may go on concurrently in an organism with a complex ontogeny. However, large populations can perhaps contain more serial substitutions and divide the costs more finely than small populations can.…”

Section: Two-class 1-episode Casesmentioning

confidence: 99%

The cost of evolution and the imprecision of adaptation.

Darlington¹

1977

Proc. Natl. Acad. Sci. U.S.A.

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Comparisons of six hypothetical cases suggest that Haldane overestimated the cost of natural selection by allele substitution. The cost is reduced if recessive alleles are advantageous, if substitutions are large and few, if selection is strong and substitutions are rapid, if substitutions are serial, and if substitutions in small demes are followed by deme-group substitutions. But costs are still so heavy that the adaptations of complex organisms in complex and changing environments are never completed. The rule probably is that most species most of the time are not fully adapted to their environments, but are just a little better than their competitors for the time being. During the "evolution" of a man-made machine, the maker of it can take it apart and eliminate inferior and substitute improved parts without throwing away whole machines. But in organic evolution, each slightest separate improvement made by natural selection in the great number of parts, processes, and behaviors in an evolving organism is made at the cost of eliminating-throwing away-all the whole individuals that lack the improvement. This is "the cost of natural selection," or of adaptive evolution. Calculation of this cost and of its consequences is one of the most important pieces of unfinished business in modern evolution theory.THEORY: THE COST OF SELECTION Haldane (1), in 1957, calculated that gene (allele) substitutions by selection cost so much that populations must (in effect) choose between evolving at low cost per generation but unadaptively slowly, or more rapidly but at a cost so high as to risk extinction. These alternatives constitute what is sometimes called "Haldane's dilemma." His conclusions have been much criticized, especially by means of complex mathematics; for partial reviews of the criticisms, see ref. 2, I shall re-examine the cost of selection in another way, by means of six hypothetical cases and simple arithmetic; the cases cannot prove generalizations but can suggest them or (sometimes) falsify them. And I shall then consider how costs limit actual, complex evolutionary processes and the precision of adaptations, including our own. Two-class, 1-episode cases Case A. Suppose that, in a population of four billion individuals, only one male and one female are homozygous for a recessive allele which allows them alone to survive an atomic holocaust which eliminates all the other individuals. (If all individuals survive, but only the two can reproduce, the others being sterilized by radiation, the effect is the same.) Then one complete allele substitution will have been made by selection (selective elimination) in one generation, at a cost of No(4 billion) -N1(2) = 3,999,999,998 individuals, and no additional selective substitutions can be made and paid for at the same time, although other, nonselective, random changes comparable to those expected of the "founder effect" may occur in the population's gene pool. 1647Case B. Now suppose that the two survivors escape other hazards and produce ten offspring of w...

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“…A number of other models have been analyzed in recent papers (see ref. 4 for references), but none of the deterministic models previously considered encompass the same generality as that presented here. In addition, we consider the cost-of-selection concept in terms of population structure and a general conservation principle.…”

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confidence: 98%

An Analysis of the Cost-of-Selection Concept

Flake¹,

Grant

1974

Proc. Natl. Acad. Sci. U.S.A.

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It is shown for a continuous haploid model that the common standard assumptions usedin calculating the cost of gene substitution, namely, large constant population size and small constant selective value, are unnecessary. Population size may fluctuate during the course of substitution without affecting the calculated total cost. The selective intensity does not need to be small and constant to give the standard result for substitution cost. Diploid models with multiple alleles are analyzed and contrasted with standard two-allele models in respect to calculation of substitution cost. The influence of population structure on the probability of occurrence of complete gene substitution is discussed on the basis of a numerical example. The robust nature of the cost-of-selection concept is examined in the light of a conservation principle.The original model of Haldane (1, 2) for the cost of selection and more recent standard models (3) assume constant large population size and constant small selective value. Using continuous deterministic models, both haploid and diploid, we have arrived at a more general formulation that does not require these assumptions. A number of other models have been analyzed in recent papers (see ref. 4 for references), but none of the deterministic models previously considered encompass the same generality as that presented here. In addition, we consider the cost-of-selection concept in terms of population structure and a general conservation principle. HAPLOID MODELThe cost of selection in the haploid or asexual case is first discussed for a discrete generation model, and then for a continuous model with random births and deaths. The calculation of cost for the discrete model follows the analysis of Crow and Kimura (3) closely, except that the presentation here begins explicitly with the difference equations describing the dynamic behavior of the number of individuals of each type in the population. The derivation for the continuous model is analogous to the discrete model argument. However, in the continuous case few restrictive assumptions or approximations are required. In particular, the latter approach for computing cost is valid for quite general population models, including those containing density-dependent fitness. In addition, the common assumptions of weak selection and stable population size during the process of the substitution are not required.Discrete Generation Model. We shall adopt the following customary notation for the fitnesses, frequencies, and numerical strength of the two competing types:The number of individuals of each type in successive generations is described by a pair of difference equations:

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Population Structure in Relation to Cost of Selection

Cited by 10 publications

References 12 publications

Reproductive biology of Launaea cervicornis: A keystone species of the Balearic coastal shrublands

Reproductive biology of Launaea cervicornis: A keystone species of the Balearic coastal shrublands

The cost of evolution and the imprecision of adaptation.

An Analysis of the Cost-of-Selection Concept

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