TY - JOUR
AB - This paper investigates the combinatorial and computational aspects of certain extremal geometric problems in two and three dimensions. Specifically, we examine the problem of intersecting a convex subdivision with a line in order to maximize the number of intersections. A similar problem is to maximize the number of intersected facets in a cross-section of a three-dimensional convex polytope. Related problems concern maximum chains in certain families of posets defined over the regions of a convex subdivision. In most cases we are able to prove sharp bounds on the asymptotic behavior of the corresponding extremal functions. We also describe polynomial algorithms for all the problems discussed.
AU - Chazelle, Bernard
AU - Herbert Edelsbrunner
AU - Guibas, Leonidas J
ID - 4093
IS - 1
JF - Discrete & Computational Geometry
TI - The complexity of cutting complexes
VL - 4
ER -
TY - JOUR
AB - Three methods for estimating the average level of gene flow in natural population are discussed and compared. The three methods are FST, rare alleles, and maximum likelihood. All three methods yield estimates of the combination of parameters (the number of migrants [Nm] in a demic model or the neighborhood size [4πDσ2] in a continuum model) that determines the relative importance of gene flow and genetic drift. We review the theory underlying these methods and derive new analytic results for the expectation of FST in stepping-stone and continuum models when small sets of samples are taken. We also compare the effectiveness of the different methods using a variety of simulated data. We found that the FST and rare-alleles methods yield comparable estimates under a wide variety of conditions when the population being sampled is demographically stable. They are roughly equally sensitive to selection and to variation in population structure, and they approach their equilibrium values at approximately the same rate. We found that two different maximum-likelihood methods tend to yield biased estimates when relatively small numbers of locations are sampled but more accurate estimates when larger numbers are sampled. Our conclusion is that, although FST and rare-alleles methods are expected to be equally effective in analyzing ideal data, practical problems in estimating the frequencies of rare alleles in electrophoretic studies suggest that FST is likely to be more useful under realistic conditions.
AU - Slatkin, Montgomery
AU - Nicholas Barton
ID - 4309
IS - 7
JF - Evolution; International Journal of Organic Evolution
TI - A comparison of three methods for estimating average levels of gene flow
VL - 43
ER -
TY - JOUR
AU - Nicholas Barton
AU - Turelli, Michael
ID - 4312
JF - Annual Review of Genetics
TI - Evolutionary quantitative genetics: how little do we know ?
VL - 23
ER -
TY - CHAP
AU - Nicholas Barton
ED - Otte, Daniel
ED - Endler, John A
ID - 4313
T2 - Speciation and its consequences
TI - Founder effect speciation
ER -
TY - JOUR
AB - Polygenic variation can be maintained by a balance between mutation and stabilizing selection. When the alleles responsible for variation are rare, many classes of equilibria may be stable. The rate at which drift causes shifts between equilibria is investigated by integrating the gene frequency distribution W2N II (pq)4N mu-1. This integral can be found exactly, by numerical integration, or can be approximated by assuming that the full distribution of allele frequencies is approximately Gaussian. These methods are checked against simulations. Over a wide range of population sizes, drift will keep the population near an equilibrium which minimizes the genetic variance and the deviation from the selective optimum. Shifts between equilibria in this class occur at an appreciable rate if the product of population size and selection on each locus is small (Ns alpha 2 less than 10). The Gaussian approximation is accurate even when the underlying distribution is strongly skewed. Reproductive isolation evolves as populations shift to new combinations of alleles: however, this process is slow, approaching the neutral rate (approximately mu) in small populations.
AU - Nicholas Barton
ID - 4314
IS - 1
JF - Genetical Research
TI - The divergence of a polygenic system under stabilising selection, mutation and drift
VL - 54
ER -
TY - CONF
AB - A real-time temporal logic for the specification of reactive systems is introduced. The novel feature of the logic, TPTL, is the adoption of temporal operators as quantifiers over time variables; every modality binds a variable to the time(s) it refers to. TPTL is demonstrated to be both a natural specification language and a suitable formalism for verification and synthesis. A tableau-based decision procedure and model-checking algorithm for TPTL are presented. Several generalizations of TPTL are shown to be highly undecidable.
AU - Alur, Rajeev
AU - Thomas Henzinger
ID - 4596
TI - A really temporal logic
ER -
TY - JOUR
AB - Asymmetrical displacement currents and Na currents of single myelinated nerve fibers of Xenopus laevis were studied in the temperature range from 5 to 24 degrees C. The time constant of the on-response at E = 4 mV, tau on, was strongly temperature dependent, whereas the amount of displaced charge at E = 39 mV, Qon, was only slightly temperature dependent. The mean Q10 for tau on-1 was 2.54, the mean Q10 for Qon was 1.07. The time constant of charge immobilization, tau i, at E = 4 mV varied significantly (alpha = 0.001) with temperature. The mean Q10 for tau i-1 was 2.71 +/- 0.38. The time constants of immobilization of gating charge and of fast inactivation of Na permeability were similar in the temperature range from 6 to 22 degrees C. The Qoff/Qon ratio for E = 4 mV pulses of 0.5 msec duration decreased with increasing temperature. The temperature dependence of the time constant of the off-response could not be described by a single Q10 value, since the Q10 depended on the duration of the test pulse. Increasing temperature shifted Qon (E) curves to more negative potentials by 0.51 mV K-1, but shifted PNa (E) curves and h infinity (E) curves to more positive potentials by 0.43 and 0.57 mV K-1, respectively. h infinity (E = -70 mV) increased monotonously with increasing temperature. The present data indicate that considerable entropy changes may occur when the Na channel molecule passes from closed through open to inactivated states.
AU - Peter Jonas
ID - 3465
IS - 3
JF - Journal of Membrane Biology
TI - Temperature dependence of gating current in myelinated nerve fibers
VL - 112
ER -
TY - JOUR
AB - Amphibian myelinated nerve fibers were treated with collagenase and protease. Axons with retraction of the myelin sheath were patch-clamped in the nodal and paranodal region. One type of Na channel was found. It has a single-channel conductance of 11 pS (15 degrees C) and is blocked by tetrodotoxin. Averaged events show the typical activation and inactivation kinetics of macroscopic Na current. Three potential-dependent K channels were identified (I, F, and S channel). The I channel, being the most frequent type, has a single-channel conductance of 23 pS (inward current, 105 mM K on both sides of the membrane), activates between -60 and -30 mV, deactivates with intermediate kinetics, and is sensitive to dendrotoxin. The F channel has a conductance of 30 pS, activates between -40 and 60 mV, and deactivates with fast kinetics. The former inactivates within tens of seconds; the latter inactivates within seconds. The third type, the S channel, has a conductance of 7 pS and deactivates slowly. All three channels can be blocked by external tetraethylammonium chloride. We suggest that these distinct K channel types form the basis for the different components of macroscopic K current described previously.
AU - Peter Jonas
AU - Bräu, Michael E
AU - Hermsteiner, Markus
AU - Vogel, Werner
ID - 3466
IS - 18
JF - PNAS
TI - Single-channel recording in myelinated nerve fibers reveals one type of Na channel but different K channels
VL - 86
ER -
TY - CONF
AU - Herbert Edelsbrunner
ID - 3549
TI - Spatial triangulations with dihedral angle conditions
ER -
TY - JOUR
AB - Frequency-dependent selection against rare forms can maintain clines. For weak selection, s, in simple linear models of frequency-dependence, single locus clines are stabilized with a maximum slope of between {complex}s/{complex}8 {sigma} and {complex}s/{complex}12 {delta}, where {sigma} is the dispersal distance. These clines are similar to those maintained by heterozygote disadvantage. Using computer simulations, the weak-selection analytical results are extended to higher selection pressures with up to three unlinked genes. Graphs are used to display the effect of selection, migration, dominance, and number of loci on cline widths, speeds of cline movements, two-way gametic correlations (``linkage disequilibria''), and heterozygote deficits. The effects of changing the order of reproduction, migration, and selection, are also briefly explored. Epistasis can also maintain tension zones. We show that epistatic selection is similar in its effects to frequency-dependent selection, except that the disequilibria produced in the zone will be higher for a given level of selection. If selection consists of a mixture of frequency-dependence and epistasis, as is likely in nature, the error made in estimating selection is usually less than twofold. From the graphs, selection and migration can be estimated using knowledge of the dominance and number of genes, of gene frequences and of gametic correlations from a hybrid zone.
AU - Mallet, James L
AU - Nicholas Barton
ID - 3652
IS - 4
JF - Genetics
TI - Inference from clines stabilized by frequency-dependent selection
VL - 122
ER -