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ABSTRACT: Most theoretical models in population genetics fail to deal in a realistic manner with the process of mutation. They are consequently not informative about the central evolutionary problem of the origin, progression, and limit of adaptation. Here we present an explicit distribution of phenotypes expected in an ensemble of populations under a mutationselectiondrift model that allows mutations with a distribution of adaptive values to occur randomly in time. The model of mutation is a geometrical model in which the effect of a new mutation is determined by a random angle in n dimensional space and in which the adaptive value (fitness) of an organism decreases as the square of the deviation of its phenotype from an optimum. Each new mutation is subjected to random genetic drift and fixed or lost according to its selective value and the effective population number. Time is measured in number of fixation events, so that, at any point in time, each population is regarded as genetically homogeneous. In this mutationselectiondrift model, among an ensemble of populations, the equilibrium average phenotype coincides with the optimum because the distribution of positive and negative deviations from the optimum is symmetrical. However, at equilibrium the mean of the absolute value of the deviation from the optimum equals square root of n/8Ns), where n is the dimensionality of the trait space, N is the effective population size, and s is the selection coefficient against a mutation whose phenotype deviates by one unit from the optimum. Furthermore, at equilibrium, the average fitness across the ensemble of populations equals 1  (n + 1)/8N. When n is sufficiently large, there is a strong mutation pressure toward the fixation of slightly deleterious mutations. This feature relates our model to the nearly neutral theory of molecular evolution. Genetica 02/1998; 102103(16):52533. DOI:10.1023/A:1017071901530 · 1.75 Impact Factor

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ABSTRACT: One implication of Kacser's analysis of complex metabolic systems is that mutations with small effects exist as a consequence of the typically small flux control coefficient relating enzyme activity to the rate of a metabolic process. Although a slightly detrimental mutation is somewhat less likely to become fixed by chance than a slightly favorable mutation, mutations that are slightly detrimental might be expected to be more numerous than favorable mutations owing to the previous incorporation of favorable mutations by a long history of natural selection. The result is that, as Ohta has pointed out, a significant fraction of mutations that are fixed in evolution are slightly detrimental. In the long run, the fixation of detrimental mutations in a gene increases the opportunity for the occurrence of a compensatory favorable mutation, either in the same gene or in an interacting gene. On a suitably long timescale, therefore, every gene incorporates favorable mutations that compensate for detrimental mutations previously fixed. This form of evolution is driven primarily by natural selection, but it results in no change or permanent improvement in enzymatic function. Journal of Theoretical Biology 11/1996; 182(3):3039. DOI:10.1006/jtbi.1996.0168 · 2.30 Impact Factor

C.H. Taubes
Journal of the American Mathematical Society 07/1996; 9(3):845918. · 3.06 Impact Factor

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ABSTRACT: The lowtemperature relaxation dynamics of supercooled liquids are a longstanding theoretical problem of considerable interest. The vast amount of experimental data on such liquids indicates that viscosity and diffusion in supercooled liquids are nonArrhenius over a wide range of temperatures. The nonArrhenius temperature dependence of the relaxation time of the slow modes in glassforming liquids is investigated in connection with the topology of the potential energy landscape in configuration space. An analogy is made between the derived dynamical equations and Cooper's formulation of the pair equation in superconductivity. Science 11/1994; 266(5184):4257. DOI:10.1126/science.266.5184.425 · 31.48 Impact Factor

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ABSTRACT: Orientationbased representations (OBR's) have many advantages. Three orientationbased differential geometric representations in computer vision literature are critically examined. The three representations are the extended Gaussian image (EGI), the supportfunctionbased representation (SFBR), and the generalized Gaussian image (GGI). The scope of unique representation, invariant properties from matching considerations, computation and storage requirements, and relations between the three representations are analyzed. A constructive proof of the uniqueness of the SFBR for smooth surfaces is given. It is shown that an OBR using any combination of locally defined descriptors is insufficient to uniquely characterize a surface. It must contain either global descriptors or ordering information to uniquely characterize a surface. The GGI as it was originally introduced requires the recording of one principle vector. It is shown in this paper that this is unnecessary. This reduces the storage requirement of a GGI, therefore making it a more attractive representation. The key ideas of the GGI are to represent the multiple folds of a Gaussian image separately; the use of linked data structures to preserve ordering at all levels and between the folds; and the indexing of the data structures by the unit normal. It extends the EGI approach to a much wider range of applications IEEE Transactions on Pattern Analysis and Machine Intelligence 04/1994; 16(3):249258. DOI:10.1109/34.276124 · 5.69 Impact Factor

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ABSTRACT: Orientationbased representations (OBR) have many advantages. Three orientationbased differential geometric representations in computer vision literature are critically examined. The three representations are the extended Gaussian image (EGI),3 the support function based representation (SFBR),5 and the generalized Gaussian image (GGI).4 The scope of unique representation, invariant properties from matching considerations, computation and storage requirements, and relations between the three representations are analyzed. It is shown that an OBR using any combination of local descriptors is insufficient to uniquely characterize a surface. It must contain either global descriptors or connectivity information. The GGI as it was introduced4 requires the mapping of one principal vector onto the unit sphere. It is shown in this paper that this is unnecessary. This reduces the storage requirement of a GGI by half, therefore, making it a more attractive representation. It is also concluded that if the intention is to reconstruct surfaces from their representations, a SFBR should be used. If the intention is recognition, a truly orientationbased representation such as the GGI should be used.© (1991) COPYRIGHT SPIEThe International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.