@article{3658, abstract = {Females of the grasshopper Podisima pedestris were collected from the middle of a hybrid zone between two chromosomal races in the Alpes Maritimes. They had already mated in the field, and could therefore lay fertilised eggs in the laboratory. The embryos were karyotyped, and found to contain an excess of chromosomal homozygotes. No evidence of assortative mating was found from copulating pairs taken in the field. The excess appears to have been caused by a combination of multiple insemination and assortative fertilisation. The genetics of the assortment, and the implications for the evolution of reproductive isolation are discussed.}, author = {Hewitt, Godfrey and Nichols, R. and Barton, Nicholas H}, issn = {1365-2540}, journal = {Heredity}, number = {3}, pages = {457 -- 466}, publisher = {Nature Publishing Group}, title = {{Homogamy in a hybrid zone in the alpine grasshopper Podisma pedestris}}, doi = {10.1038/hdy.1987.156}, volume = {59}, year = {1987}, } @article{3659, abstract = {We develop models of the rates of evolution at sex-linked and autosomal loci and of the rates of fixation of chromosomal rearrangements involving sex chromosomes and autosomes. We show that the substitution of selectively favorable mutations often proceeds more rapidly for X- or Y-linked loci than for the autosomes, provided that mutations are recessive or partially recessive on the average. Selection acting on a quantitative character is expected to result in similar long-term rates of gene substitution for X-linked and autosomal loci, unless there is strong directional dominance. Short-term responses to such selection often preferentially fix alleles at autosomal loci. The fixation of slightly deleterious alleles by random drift and the stochastic turnover of alleles at loci controlling quantitative characters under stabilizing selection usually proceed somewhat more slowly at sex-linked loci. In contrast, the fixation of underdominant chromosomal rearrangements by random genetic drift is faster with sex linkage. Sex-specific selection may also differentially favor the fixation of sex-linked rearrangements. These results are discussed in relation to genetic and cytological data on species differences. We show that the frequently disproportionate effects of the sex chromosomes on interspecific inviability or sterility are consistent with the hypothesis that the gene differences concerned involve recessive or partially recessive alleles fixed by selection. Haldane's rule is readily interpreted in this light. There is little evidence for strong effects of the sex chromosomes on quantitative characters in interspecific crosses, in accordance with our theoretical results. Thus, the evolution of reproductive isolation may not be the byproduct of selective change in additively inherited, polygenic traits. Rather, it may be due mainly to the fixation of favorable mutations whose effects on fitness reflect locus-specific effects on the phenotype. These mutations behave as major genes in the sense of contributing the bulk of the genetic variance in the characters that they control during the course of the mutations' substitution. The data on the genetics of short-term responses to selection in Drosophila are hard to interpret, but, in accordance with theory, these responses do not usually seem to involve the X chromosome disproportionately. In some groups, there is evidence for a disproportionate role of the sex chromosomes in chromosomal changes, but others show no clear pattern. Factors that may distort the expectations of the simple models of chromosomal evolution are discussed.}, author = {Charlesworth, Brian and Coyne, Jerry and Barton, Nicholas H}, issn = {1537-5323}, journal = {American Naturalist}, number = {1}, pages = {113 -- 146}, publisher = {University of Chicago Press}, title = {{The relative rates of evolution of sex chromosomes and autosomes}}, doi = {10.1086/284701}, volume = {130}, year = {1987}, } @article{3660, abstract = {The maintenance of polygenic variability by a balance between mutation and stabilizing selection has been analysed using two approximations: the ‘Gaussian’ and the ‘house of cards’. These lead to qualitatively different relationships between the equilibrium genetic variance and the parameters describing selection and mutation. Here we generalize these approximations to describe the dynamics of genetic means and variances under arbitrary patterns of selection and mutation. We incorporate genetic drift into the same mathematical framework. The effects of frequency-independent selection and genetic drift can be determined from the gradient of log mean fitness and a covariance matrix that depends on genotype frequencies. These equations describe an ‘adaptive landscape’, with a natural metric of genetic distance set by the covariance matrix. From this representation we can change coordinates to derive equations describing the dynamics of an additive polygenic character in terms of the moments (means, variances, …) of allelic effects at individual loci. Only under certain simplifying conditions, such as those derived from the Gaussian and house-of-cards approximations, do these general recursions lead to tractable equations for the first few phenotypic moments. The alternative approximations differ in the constraints they impose on the distributions of allelic effects at individual loci. The Gaussian-based prediction that evolution of the phenotypic mean does not change the genetic variance is shown to be a consequence of the assumption that the allelic distributions are never skewed. We present both analytical and numerical results delimiting the parameter values consistent with our approximations.}, author = {Barton, Nicholas H and Turelli, Michael}, issn = {1469-5073}, journal = {Genetical Research}, number = {2}, pages = {157 -- 174}, publisher = {Cambridge University Press}, title = {{Adaptive landscapes, genetic distance, and the evolution of quantitative characters}}, doi = {10.1017/S0016672300026951}, volume = {49}, year = {1987}, } @article{3661, abstract = {We derive a formula giving thefrequency with which random drift shifts a population betweenalternativeequilibria. This formula is valid when such shifts are rare (Ns >> 1), and applies over a wide range of mutation rates. When the number of mutations entering the population is low (4Nμ << 1), the rate of stochastic shifts reduces to the product ofthe mutation rate and the probability of fixation of a single mutation. However, when many mutations enter the population in each generation (4Nμ >> 1), the rate is higher than would be expected if mutations were established independently, and converges to that given by a gaussian approximation. We apply recent results on bistable systems to extend this formula to the general multidimensional case. This gives an explicit expression for thefrequencyof stochastic shifts, which depends only on theequilibrium probability distribution near the saddle point separating thealternative stable states. The plausibility of theories of speciation through random drift are discussed in the light of these results.}, author = {Barton, Nicholas H and Rouhani, Shahin}, issn = {1095-8541}, journal = {Journal of Theoretical Biology}, number = {4}, pages = {397 -- 418}, publisher = {Elsevier}, title = {{The frequency of shifts between alternative equilibria}}, doi = {10.1016/S0022-5193(87)80210-2}, volume = {125}, year = {1987}, } @book{3900, abstract = {Computational geometry as an area of research in its own right emerged in the early seventies of this century. Right from the beginning, it was obvious that strong connections of various kinds exist to questions studied in the considerably older field of combinatorial geometry. For example, the combinatorial structure of a geometric problem usually decides which algorithmic method solves the problem most efficiently. Furthermore, the analysis of an algorithm often requires a great deal of combinatorial knowledge. As it turns out, however, the connection between the two research areas commonly referred to as computa­ tional geometry and combinatorial geometry is not as lop-sided as it appears. Indeed, the interest in computational issues in geometry gives a new and con­ structive direction to the combinatorial study of geometry. It is the intention of this book to demonstrate that computational and com­ binatorial investigations in geometry are doomed to profit from each other. To reach this goal, I designed this book to consist of three parts, acorn binatorial part, a computational part, and one that presents applications of the results of the first two parts. The choice of the topics covered in this book was guided by my attempt to describe the most fundamental algorithms in computational geometry that have an interesting combinatorial structure. In this early stage geometric transforms played an important role as they reveal connections between seemingly unrelated problems and thus help to structure the field.}, author = {Edelsbrunner, Herbert}, isbn = {978-3-540-13722-1}, issn = {1431-2654}, pages = {XV, 423}, publisher = {Springer}, title = {{Algorithms in Combinatorial Geometry}}, doi = {10.1007/978-3-642-61568-9}, volume = {10}, year = {1987}, } @article{4094, abstract = {The visibility graph of a finite set of line segments in the plane connects two endpoints u and v if and only if the straight line connection between u and v does not cross any line segment of the set. This article proves that 5n - 4 is a lower bound on the number of edges in the visibility graph of n nonintersecting line segments in the plane. This bound is tight.}, author = {Edelsbrunner, Herbert and Shen, Xiaojun}, issn = {1872-6119}, journal = {Information Processing Letters}, number = {2}, pages = {61 -- 64}, publisher = {Elsevier}, title = {{A tight lower bound on the size of visibility graphs}}, doi = {10.1016/0020-0190(87)90038-X}, volume = {26}, year = {1987}, } @article{4095, abstract = {he kth-order Voronoi diagram of a finite set of sites in the Euclidean plane E2 subdivides E2 into maximal regions such that all points within a given region have the same k nearest sites. Two versions of an algorithm are developed for constructing the kth-order Voronoi diagram of a set of n sites in O(n2 log n + k(n - k) log2 n) time, O(k(n - k)) storage, and in O(n2 + k(n - k) log2 n) time, O(n2) storage, respectively.}, author = {Chazelle, Bernard and Edelsbrunner, Herbert}, issn = {1557-9956}, journal = {IEEE Transactions on Computers}, number = {11}, pages = {1349 -- 1354}, publisher = {IEEE}, title = {{An improved algorithm for constructing kth-order Voronoi diagrams}}, doi = {10.1109/TC.1987.5009474}, volume = {36}, year = {1987}, } @article{4100, abstract = {This paper investigates the existence of linear space data structures for range searching. We examine thehomothetic range search problem, where a setS ofn points in the plane is to be preprocessed so that for any triangleT with sides parallel to three fixed directions the points ofS that lie inT can be computed efficiently. We also look atdomination searching in three dimensions. In this problem,S is a set ofn points inE 3 and the question is to retrieve all points ofS that are dominated by some query point. We describe linear space data structures for both problems. The query time is optimal in the first case and nearly optimal in the second. }, author = {Chazelle, Bernard and Edelsbrunner, Herbert}, issn = {1432-0444}, journal = {Discrete & Computational Geometry}, number = {1}, pages = {113 -- 126}, publisher = {Springer}, title = {{Linear space data structures for two types of range search}}, doi = {10.1007/BF02187875}, volume = {2}, year = {1987}, } @article{4101, abstract = {In a number of recent papers, techniques from computational geometry (the field of algorithm design that deals with objects in multi-dimensional space) have been applied to some problems in the area of computer graphics. In this way, efficient solutions were obtained for the windowing problem that asks for those line segments in a planar set that lie in given window (range) and the moving problem that asks for the first line segment that comes into the window when moving the window in some direction. In this paper we show that also the zooming problem, which asks for the first line segment that comes into the window when we enlarge it, can be solved efficiently. This is done by repeatedly performing range queries with ranges of varying sizes. The obtained structure is dynamic and yields a query time of O(log2n) and an insertion and deletion time of O(log2n), where n is the number of line segments in the set. The amount of storage required is O(n log n). It is also shown that the technique of repeated range search can be used to solve several other problems efficiently.}, author = {Edelsbrunner, Herbert and Overmars, Mark}, issn = {1872-6119}, journal = {Information Processing Letters}, number = {6}, pages = {413 -- 417}, publisher = {Elsevier}, title = {{Zooming by repeated range detection}}, doi = {10.1016/0020-0190(87)90120-7}, volume = {24}, year = {1987}, } @article{4102, abstract = {Determining or counting geometric objects that intersect another geometric query object is at the core of algorithmic problems in a number of applied areas of computer science. This article presents a family of space-efficient data structures that realize sublinear query time for points, line segments, lines and polygons in the plane, and points, line segments, planes, and polyhedra in three dimensions.}, author = {Dobkin, David and Edelsbrunner, Herbert}, issn = {1090-2678}, journal = {Journal of Algorithms}, number = {3}, pages = {348 -- 361}, publisher = {Academic Press}, title = {{Space searching for intersecting objects}}, doi = {10.1016/0196-6774(87)90015-0}, volume = {8}, year = {1987}, } @article{4319, abstract = {The grasshopper Podisma pedestris contains two chromosomal races, which differ by a Robertsonian fusion between the sex chromosome and an autosome, and which meet in a narrow hybrid zone in the Alpes Maritimes. DNA content variation across this hybrid zone was investigated by optical densitometry of Feulgen stained spermatids. Spermatids from males with the unfused sex chromosome stain more strongly than those from males with the fused chromosome. The difference between the karyotypes is greater in the centre of the hybrid zone, suggesting that it is not a pleiotropic effect of the fusion itself, but is due instead to differences at closely linked loci.}, author = {Westerman, Michael and Barton, Nicholas H and Hewitt, Godfrey}, issn = {1365-2540}, journal = {Heredity}, pages = {221 -- 228}, publisher = {Nature Publishing Group}, title = {{Differences in DNA content between two chromosomal races of the grasshopper Podisma pedestris}}, doi = {10.1038/hdy.1987.36}, volume = {58}, year = {1987}, } @article{4320, abstract = {Bosonic field theories may be formulated in terms of stochastic differential equations. The characteristic long term behaviour of these systems is a decay into the global minimum of their Hamiltonian. If local minima exist, the rate of this decay is determined by instanton effects. We calculate the decay rate and perform computer simulations on a 1 + 1 dimensional model to test the instanton approximation. We find the instanton approximations to be in very good agreement with the simulation results.}, author = {Rouhani, Shahin and Barton, Nicholas H}, issn = {1873-2119}, journal = {Physica A: Statistical Mechanics and its Applications}, number = {1-2}, pages = {220 -- 226}, publisher = {Elsevier}, title = {{Instantons in stochastic quantization}}, doi = {10.1016/0378-4371(87)90064-1}, volume = {143}, year = {1987}, } @article{4322, abstract = {A method is developed for calculating the probability of establishment of an allele which is favoured in some places, but not others, in a large subdivided population. This method is quite general, and could be used to calculate the chance that any system which is linear near an absorbing boundary will move away from that boundary. The results are applied to a population distributed along one dimension. Only mutants which arise within a distance σ/ √2s of the region in which they are favoured stand an appreciable chance of establishment. The net chance of establishment of mutations distributed randomly across the habitat will be decreased by gene flow if selection against them is sufficiently strong. However, if the mutations are only weakly deleterious outside some limited region, gene flow may increase the net chance of establishment.}, author = {Barton, Nicholas H}, issn = {1469-5073}, journal = {Genetical Research}, number = {1}, pages = {35 -- 40}, publisher = {Cambridge University Press}, title = {{The probability of establishment of an advantageous mutation in a subdivided population}}, doi = {10.1017/S0016672300023314}, volume = {50}, year = {1987}, } @article{3464, abstract = {The effects of the major neurotoxic fraction isolated from scorpion venom of Tityus serrulatus, TiTx gamma, on peripheral nerve membrane of Xenopus laevis were studied under current- and voltage-clamp conditions. 700 nmol/l TiTx gamma depolarized the membrane and induced spontaneous activity (150 s-1, maximum value), which ceased within a few minutes. It reduced the amplitude of the action potentials from 109 mV to 52 mV and increased their duration from 1.25 ms to 4.5 ms. 440 nmol/l TiTx gamma induced inward Na current flow at resting potential. The descending branch of the Na current-voltage curve was flattened and shifted approximately 10 mV to more negative potentials. Maximum Na permeability was reduced to about 20%. Both development of and recovery from inactivation of Na permeability were slowed. The steepness of the steady-state inactivation curve was decreased, but the mid-potential changed only insignificantly. No prepulse was necessary to elicit either a shift of activation or an inward current at resting potential. Expressing the toxin effect either in terms of the decrease of Na peak current or of the slowing of inactivation, half-maximum effects were found with 0.3 +/- 0.1 and 3.7 +/- 0.7 mumol/l TiTx gamma, respectively.}, author = {Jonas, Peter M and Vogel, Werner and Arantes, Eliane and Giglio, Jose}, issn = {1432-2013}, journal = {Pflugers Archiv : European Journal of Physiology}, number = {1}, pages = {92 -- 99}, publisher = {Springer}, title = {{Toxin γ of the scorpion Tityus serrulatus modifies both activation and inactivation of sodium permeability of nerve membrane}}, doi = {10.1007/BF00580727}, volume = {407}, year = {1986}, } @article{3579, author = {Edelsbrunner, Herbert and Jaromczyk, Jerzy}, issn = {0384-9864}, journal = {Congressus Numerantium}, pages = {193 -- 200}, publisher = {Utilitas Mathemtica Publ. Inc.}, title = {{How often can you see yourself in a convex configuration of mirrors?}}, volume = {53}, year = {1986}, } @article{3580, abstract = {An edge-skeleton in an arrangementA(H) of a finite set of planes inE 3 is a connected collection of edges inA(H). We give a method that constructs a skeleton inO(√n logn) time per edge. This method implies new and more efficient algorithms for a number of structures in computational geometry including order-k power diagrams inE 2 and space cutting trees inE 3. We also give a novel method for handling special cases which has the potential to substantially decrease the amount of effort needed to implement geometric algorithms.}, author = {Edelsbrunner, Herbert}, issn = {1432-0541}, journal = {Algorithmica}, number = {1-4}, pages = {93 -- 109}, publisher = {Springer}, title = {{Edge-skeletons in arrangements with applications}}, doi = {10.1007/BF01840438}, volume = {1}, year = {1986}, } @article{3662, abstract = {The evolution of the probabilities of genetic identity within and between tandemly repeated loci of a multigene family is investigated analytically and numerically. Unbiased intrachromosomal gene conversion, equal crossing over, random genetic drift, and mutation to new alleles are incorporated. Generations are discrete and nonoverlapping; the diploid, monoecious population mates at random. Under the restriction that there is at most one crossover in the multigene family per individual per generation, the dependence on location of the probabilities of identity is treated exactly. In the “homogeneous” approximation to this “exact” model, end effects are disregarded; in the “exchangeable” approximation, to which all previous work was confined, all position dependence is neglected. Numerical results indicate that (i) the exchangeable and homogeneous models are both qualitatively correct, (ii) the exchangeable model is sometimes too inaccurate for quantitative conclusions, and (iii) the homogeneous model is always more accurate than the exchangeable one and is always sufficiently accurate for quantitative conclusions.}, author = {Nagylaki, Thomas and Barton, Nicholas H}, issn = {1096-0325}, journal = {Theoretical Population Biology}, number = {3}, pages = {407 -- 437}, publisher = {Academic Press}, title = {{Intrachromosomal gene conversion, linkage, and the evolution of multigene families}}, doi = {10.1016/0040-5809(86)90017-1}, volume = {29}, year = {1986}, } @article{3663, abstract = {The conditional average frequency of rare alleles has been shown in simulations to provide a simple and robust estimator of the number of individuals exchanged between local populations in an island model (Nm). This statistic is defined as the average frequency of an allele in those samples in which the allele is present. Here, we show that the conditional average frequency can be calculated from the distribution of allele frequencies. It is a measure of the spread of this distribution, and so is analogous to the standardised variance, FST. Analytic predictions for the island model of migration agree well with the corresponding simulation results. These predictions are based on the assumption that the rare alleles found in samples have reached a "quasi-equilibrium" distribution. As well as relating the conditional average frequency to the underlying allele frequency distribution, our results provide a more accurate method of estimating Nm from the conditional average frequency of private alleles in samples of different sizes.}, author = {Barton, Nicholas H and Slatkin, Montgomery}, issn = {1365-2540}, journal = {Heredity}, number = {3}, pages = {409 -- 416}, publisher = {Nature Publishing Group}, title = {{A quasi-equilibrium theory of the distribution of rare alleles in a subdivided population}}, doi = {10.1038/hdy.1986.63}, volume = {56}, year = {1986}, } @article{3664, abstract = {Suppose that selection acts at one or more loci to maintain genetic differences between hybridising populations. Then, the flow of alleles at a neutral marker locus which is linked to these selected loci will be impeded. We define and calculate measures of the barrier to gene flow between two distinct demes, and across a continuous habitat. In both cases, we find that in order for gene flow to be significantly reduced over much of the genome, hybrids must be substantially less fit, and the number of genes involved in building the barrier must be so large that the majority of other genes become closely linked to some locus which is under selection. This conclusion is not greatly affected by the pattern of epistasis, or the position of the marker locus along the chromosome.}, author = {Barton, Nicholas H and Bengtsson, Bengt}, issn = {1365-2540}, journal = {Heredity}, pages = {357 -- 376}, publisher = {Nature Publishing Group}, title = {{The barrier to genetic exchange between hybridising populations}}, volume = {57}, year = {1986}, } @article{3665, abstract = {The rate of gene flow across a hybrid zone may be reduced by the presence of a physical barrier, by a reduction of population density caused by reduced fitness of hybrids (the “hybrid sink” effect), and by linkage. If the reduction in hybrid fitness is not extreme, the strength of the barrier to gene flow caused by these effects is. Here, w is the width of the cline; ρ* is the carrying capacity; W̄* is the mean fitness of the population, excluding effects of density; R is the strength of density-dependent regulation; and r̄ is the harmonic mean recombination rate between the locus whose flow is being calculated, and loci under selection. +, 0 denote populations outside the hybrid zone, and at its centre, respectively. This relation is illustrated using data from hybrid ones in Bombina and Podisma, and its implications for interpretation of data from nature are discussed.}, author = {Barton, Nicholas H}, issn = {1365-2540}, journal = {Heredity}, pages = {415 -- 426}, publisher = {Nature Publishing Group}, title = {{The effects of linkage and density-dependent regulation on gene flow}}, volume = {57}, year = {1986}, }