@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}, } @article{4098, abstract = {To points p and q of a finite set S in d-dimensional Euclidean space Ed are extreme if {p, q} = S ∩ h, for some open halfspace h. Let e2(d)(n) be the maximum number of extreme pairs realized by any n points in Ed. We give geometric proofs of , if n⩾4, and e2(3)(n) = 3n−6, if n⩾6. These results settle the question since all other cases are trivial.}, author = {Edelsbrunner, Herbert and Stöckl, Gerd}, issn = {1096-0899}, journal = {Journal of Combinatorial Theory Series A}, number = {2}, pages = {344 -- 349}, publisher = {Elsevier}, title = {{The number of extreme pairs of finite point-sets in Euclidean spaces}}, doi = {10.1016/0097-3165(86)90075-0}, volume = {43}, year = {1986}, } @article{4099, abstract = {Let S denote a set of n points in the Euclidean plane. A halfplanar range query specifies a halfplane h and requires the determination of the number of points in S which are contained in h. A new data structure is described which stores S in O(n) space and allows us to answer a halfplanar range query in O(nlog2(1+√5)−1) time in the worst case, thus improving the best result known before. The structure can be built in O(n log n) time.}, author = {Edelsbrunner, Herbert and Welzl, Emo}, issn = {1872-6119}, journal = {Information Processing Letters}, number = {5}, pages = {289 -- 293}, publisher = {Elsevier}, title = {{Halfplanar range search in linear space and O(n0.695) query time}}, doi = {10.1016/0020-0190(86)90088-8}, volume = {23}, year = {1986}, } @article{4103, abstract = {Let A be an arrangement of n lines in the plane. Suppose F1,…, Fk are faces in the dissection induced by A and that Fi is a t(Fi)-gon. We give asymptotic bounds on the maximal sum ∑i=1kt(Fi) which can be realized by k different faces in an arrangement of n lines. The results improve known bounds for k of higher order than n(1/2).}, author = {Edelsbrunner, Herbert and Welzl, Emo}, issn = {1096-0899}, journal = {Journal of Combinatorial Theory Series A}, number = {2}, pages = {159 -- 166}, publisher = {Elsevier}, title = {{On the maximal number of edges of many faces in an arrangement}}, doi = {10.1016/0097-3165(86)90078-6}, volume = {41}, year = {1986}, } @article{4104, abstract = {Point location, often known in graphics as “hit detection,” is one of the fundamental problems of computational geometry. In a point location query we want to identify which of a given collection of geometric objects contains a particular point. Let $\mathcal{S}$ denote a subdivision of the Euclidean plane into monotone regions by a straight-line graph of $m$ edges. In this paper we exhibit a substantial refinement of the technique of Lee and Preparata [SIAM J. Comput., 6 (1977), pp. 594–606] for locating a point in $\mathcal{S}$ based on separating chains. The new data structure, called a layered dag, can be built in $O(m)$ time, uses $O(m)$ storage, and makes possible point location in $O(\log m)$ time. Unlike previous structures that attain these optimal bounds, the layered dag can be implemented in a simple and practical way, and is extensible to subdivisions with edges more general than straight-line segments. © 1986 Society for Industrial and Applied Mathematics}, author = {Edelsbrunner, Herbert and Guibas, Leonidas and Stolfi, Jorge}, issn = {1095-7111}, journal = {SIAM Journal on Computing}, number = {2}, pages = {317 -- 340}, publisher = {SIAM}, title = {{Optimal point location in a monotone subdivision}}, doi = {10.1137/0215023}, volume = {15}, year = {1986}, } @article{4105, abstract = {A finite set of lines partitions the Euclidean plane into a cell complex. Similarly, a finite set of $(d - 1)$-dimensional hyperplanes partitions $d$-dimensional Euclidean space. An algorithm is presented that constructs a representation for the cell complex defined by $n$ hyperplanes in optimal $O(n^d )$ time in $d$ dimensions. It relies on a combinatorial result that is of interest in its own right. The algorithm is shown to lead to new methods for computing $\lambda $-matrices, constructing all higher-order Voronoi diagrams, halfspatial range estimation, degeneracy testing, and finding minimum measure simplices. In all five applications, the new algorithms are asymptotically faster than previous results, and in several cases are the only known methods that generalize to arbitrary dimensions. The algorithm also implies an upper bound of $2^{cn^d } $, $c$ a positive constant, for the number of combinatorially distinct arrangements of $n$ hyperplanes in $E^d $. © 1986 Society for Industrial and Applied Mathematics}, author = {Edelsbrunner, Herbert and O'Rourke, Joseph and Seidel, Raimund}, issn = {1095-7111}, journal = {SIAM Journal on Computing}, number = {2}, pages = {341 -- 363}, publisher = {SIAM}, title = {{Constructing arrangements of lines and hyperplanes with applications}}, doi = {10.1137/0215024}, volume = {15}, year = {1986}, } @article{4106, abstract = {Let B be a set of nb black points and W a set of nw, white points in the Euclidean plane. A line h is said to bisect B (or W) if, at most, half of the points of B (or W) lie on any one side of h. A line that bisects both B and W is called a ham-sandwich cut of B and W. We give an algorithm that computes a ham-sandwich cut of B and W in 0((nh+nw) log (min {nb, nw}+ 1)) time. The algorithm is considerably simpler than the previous most efficient one which takes 0((nb + nw) log (nb + nw)) time.}, author = {Edelsbrunner, Herbert and Waupotitsch, Roman}, issn = {1095-855X}, journal = {Journal of Symbolic Computation}, number = {2}, pages = {171 -- 178}, publisher = {Elsevier}, title = {{Computing a ham-sandwich cut in two dimensions}}, doi = {10.1016/S0747-7171(86)80020-7}, volume = {2}, year = {1986}, } @article{4107, abstract = {A set of m planes dissects E3 into cells, facets, edges and vertices. Letting deg(c) be the number of facets that bound a cellc, we give exact and asymptotic bounds on the maximum of ∈cinCdeg(c), if C is a family of cells of the arrangement with fixed cardinality.}, author = {Edelsbrunner, Herbert and Haussler, David}, issn = {1872-681X}, journal = {Discrete Mathematics}, number = {C}, pages = {139 -- 146}, publisher = {Elsevier}, title = {{The complexity of cells in 3-dimensional arrangements}}, doi = {10.1016/0012-365X(86)90008-7}, volume = {60}, year = {1986}, } @article{4108, abstract = {We propose a uniform and general framework for defining and dealing with Voronoi diagrams. In this framework a Voronoi diagram is a partition of a domainD induced by a finite number of real valued functions onD. Valuable insight can be gained when one considers how these real valued functions partitionD ×R. With this view it turns out that the standard Euclidean Voronoi diagram of point sets inR d along with its order-k generalizations are intimately related to certain arrangements of hyperplanes. This fact can be used to obtain new Voronoi diagram algorithms. We also discuss how the formalism of arrangements can be used to solve certain intersection and union problems.}, author = {Edelsbrunner, Herbert and Seidel, Raimund}, issn = {1432-0444}, journal = {Discrete & Computational Geometry}, number = {1}, pages = {25 -- 44}, publisher = {Springer}, title = {{Voronoi diagrams and arrangements}}, doi = {10.1007/BF02187681}, volume = {1}, year = {1986}, } @article{4109, abstract = {Rectangle location search in d dimensions is finding the d-dimensional axis-parallel box of a non-overlapping collection C that contains a query point. A new data structure is proposed that requires optimal space and 0(logd|C|) time for a search. The significance of this data structure in practical applications is substantiated by empirical examinations of its behaviour.}, author = {Edelsbrunner, Herbert and Haring, Günter and Hilbert, D}, issn = {1460-2067}, journal = {Computer Journal}, number = {1}, pages = {76 -- 82}, publisher = {Oxford University Press}, title = {{Rectangular point location in d-dimensions with applications}}, doi = {10.1093/comjnl/29.1.76}, volume = {29}, year = {1986}, } @article{4110, abstract = {For H a set of lines in the Euclidean plane, $A(H)$ denotes the induced dissection, called the arrangement of H. We define the notion of a belt in $A(H)$, which is bounded by a subset of the edges in $A(H)$, and describe two algorithms for constructing belts. All this is motivated by applications to a host of seemingly unrelated problems including a type of range search and finding the minimum area triangle with the vertices taken from some finite set of points.}, author = {Edelsbrunner, Herbert and Welzl, Emo}, issn = {1095-7111}, journal = {SIAM Journal on Computing}, number = {1}, pages = {271 -- 284}, publisher = {SIAM}, title = {{Constructing belts in two-dimensional arrangements with applications}}, doi = {10.1137/0215019}, volume = {15}, year = {1986}, } @article{4321, abstract = {The fire-bellied toads Bombina bombina and B. variegata differ extensively in biochemistry, morphology, and behavior. We use a survey of five diagnostic enzyme loci across the hybrid zone near Cracow in Southern Poland to estimate the dispersal rate, selection pressures, and numbers of loci which maintain this zone. The enzyme clines coincide closely with each other and with morphological and mitochondrial DNA clines. Although the zone lies on a broad transition between environments suitable for bombina and variegata, the close concordance of diverse characters, together with increased aberrations and mortality in hybrids, suggest that the zone is maintained largely by selection against hybrids. There are strong “linkage disequilibria” between each pair of (unlinked) enzyme loci (R̄ = 0.129 [2-unit support limits: 0.119–0.139]). These are probably caused by gene flow into the zone, and they give an estimate of dispersal (σ = 890 [790–940] m gen−½). The clines are sharply stepped, with most of the change occurring within 6.15 (5.45–6.45) km, but with long tails of introgression on either side. This implies that the effective selection pressure on each enzyme marker (due largely to disequilibrium with other loci) is s* = 0.17 (0.159–0.181) at the center but that the selection acting directly on the enzyme loci is weak or zero (se < 0.0038). The stepped pattern implies a barrier to gene flow of 220 (48–415) km. This would substantially delay neutral introgression but would have little effect on advantageous alleles; the two taxa need not evolve independently. Strong selection is needed to maintain such a barrier: hybrid populations must have their mean fitness reduced by a factor of 0.65 (0.60–0.77). This selection must be spread over a large number of loci to account for the concordant patterns and the observed cline widths (N = 300 [80–2,000]).}, author = {Szymura, Jacek and Barton, Nicholas H}, issn = {1558-5646}, journal = {Evolution; International Journal of Organic Evolution}, pages = {1141 -- 1159}, publisher = {Society for the Study of Evolution}, title = {{Genetic analysis of a hybrid zone between the fire-bellied toads Bombina bombina and B. variegata, near Cracow in Southern Poland}}, doi = {10.1111/j.1558-5646.1986.tb05740.x}, volume = {40}, year = {1986}, } @article{4323, abstract = {It is noted that the sibling competition model for the evolution of sex and recombination, as it has been developed so far, involves truncation selection. After briefly reviewing aspects of the development and behaviour of such models an analytical treatment is presented which involves additive selection. Additive selection, as compared with truncation selection, decreases the advantage of sex to such an extent that it is unlikely that sibling competition could overcome its intrinsic two-fold cost, although it could still be important in promoting family variability produced by other mechanisms, such as polyandry.}, author = {Barton, Nicholas H and Post, R.J.}, issn = {1095-8541}, journal = {Journal of Theoretical Biology}, number = {4}, pages = {381 -- 387}, publisher = {Elsevier}, title = {{Sibling competition and the advantage of mixed families}}, doi = {10.1016/S0022-5193(86)80033-9}, volume = {120}, year = {1986}, } @article{4324, abstract = {The maintenance of polygenic variation through a balance between mutation and stabilizing selection can be approximated in two ways. In the ‘Gaussian’ approximation, a normal distribution of allelic effects is assumed at each locus. In the ‘House of Cards’ approximation, the effect of new mutations is assumed to be large compared with the spread of the existing distribution. These approximations were developed to describe models where alleles may have a continuous range of effects. However, previous analyses of models with only two alleles have predicted an equilibrium variance equal to that given by the ‘House of Cards’ approximation. These analyses of biallelic models have assumed that, at equilibrium, the population mean is at the optimum. Here, it is shown that many stable equilibria may coexist, each giving a slight deviation from the optimum. Though the variance is given by the ‘House of Cards’ approximation when the mean is at the optimum, it increases towards a value of the same order as that given by the ‘Gaussian’ approximation when the mean deviates from the optimum. Thus, the equilibrium variance cannot be predicted by any simple model, but depends on the previous history of the population.}, author = {Barton, Nicholas H}, issn = {1469-5073}, journal = {Genetical Research}, number = {3}, pages = {209 -- 216}, publisher = {Cambridge University Press}, title = {{The maintenance of polygenic variation through a balance between mutation and stabilising selection}}, doi = {10.1017/S0016672300023156}, volume = {47}, year = {1986}, }