Tradeoffs between hydraulic efficiency and mechanical strength in the stems of four co-occurring species of chaparral shrubs

Possible tradeoffs between efficiency of water transport and mechanical strength were examined in stems of two congeneric pairs of co-occurring chaparral shrubs. First, since previously published results indicated that Adenostoma sparsifolium (Rosaceae) had greater specific conductivity (k _s or hydraulic conductivity per xylem transverse area) than A. fasciculatum, it was hypothesized that A. sparsifolium would have greater vessel lumen area per square millimeter of xylem area, and less mechanical strength, than A. fasciculatum. Secondly, since Ceanothus megacarpus (Rhamnaceae) is a non-sprouter (unable to sprout from the root crown following fire or other major disturbance) whereas C. spinosus is a sprouter and thus able to form new stems following disturbance, it was hypothesized that C. megacarpus would have greater mechanical strength, but lower k _s, than C. spinosus. Both hypotheses were supported. Based upon computer-aided image analyses, A. sparsifolum had significantly higher mean and maximum vessel diameters (16.4, 40.5 vs. 14.6, 35.7 μm), a 34% greater percent vessel lumen area, and a two-fold greater measured and theoretical k _s than A. fasciculatum. This corresponded to 14% lower stem density (wet weight/volume) and less mechanical strength, with a 37% lower modulus of elasticity (MOE) and a 30% lower modulus of rupture (MOR) than A. fasciculatum. Similarly, C.␣spinosus had a significantly higher maximum vessel diameter (52.7 vs. 41.8 μm) and a 92% higher theoretical k _s (and 43% higher measured k _s) than C. megacarpus. This corresponded to a 9% lower stem density and 20% lower MOR than for C. megacarpus. Thus, at least within these two congeneric pairs of chaparral shrubs growing together in the same habitat, there may be tradeoffs between mechanical strength and conductive efficiency of the stem xylem which correspond to differences in transport physiology and life history traits of sprouter versus non-sprouter species.     

Analysis of a mathematical model for the growth of tumors

 In this paper we study a recently proposed model for the growth of a nonnecrotic, vascularized tumor. The model is in the form of a free-boundary problem whereby the tumor grows (or shrinks) due to cell proliferation or death according to the level of a diffusing nutrient concentration. The tumor is assumed to be spherically symmetric, and its boundary is an unknown function r=s(t). We concentrate on the case where at the boundary of the tumor the birth rate of cells exceeds their death rate, a necessary condition for the existence of a unique stationary solution with radius r=R ₀ (which depends on the various parameters of the problem). Denoting by c the quotient of the diffusion time scale to the tumor doubling time scale, so that c is small, we rigorously prove that (i) lim inf _t→∞ s(t)>0, i.e. once engendered, tumors persist in time. Indeed, we further show that (ii) If c is sufficiently small then s(t)→R ₀ exponentially fast as t→∞, i.e. the steady state solution is globally asymptotically stable. Further, (iii) If c is not “sufficiently small” but is smaller than some constant γ determined explicitly by the parameters of the problem, then lim sup _t→∞ s(t)<∞; if however c is “somewhat” larger than γ then generally s(t) does not remain bounded and, in fact, s(t)→∞ exponentially fast as t→∞. Received: 25 February 1998 / Revised version: 30 April 1998     

The production of xylitol from d-xylose by fermentation with Hansenula polymorpha

We have analysed the influence of the initial pH of the medium and the quantity of aeration provided during the batch fermentation of solutions of d-xylose by the yeast Hansenula polymorpha (34438 ATCC). The initial pH was altered between 3.5 and 6.5 whilst aeration varied between 0.0 and 0.3 vvm. The temperature was kept at 30 °C during all the experiments. Hansenula polymorpha is known to produce high quantities of xylitol and low quantities of ethanol. The most favourable conditions for the growth of xylitol turned out to be: an initial pH of between 4.5 and 5.5 and the aeration provided by the stirring vortex alone. Thus, at an initial pH of 5.5, the maximum specific production rate (μ_m) was 0.41 h⁻¹, the overall biomass yield (Y _x/s ^G) was 0.12 g g⁻¹, the specific d-xylose-consumption rate (q _s ) was 0.075 g g⁻¹ h⁻¹ (for t = 75 h), the specific xylitol-production rate (q _Xy ) was 0.31 g g⁻¹ h⁻¹ (for t = 30 h) and the overall yields of ethanol (Y _E/s ^G) and xylitol (Y _Xy/s ^G) were 0.017 and 0.61 g g⁻¹ respectively. Both q _s and q _Xy decreased during the course of the experiments once the exponential growth phase had finished. Received: 26 March 1998 / Received revision: 30 June 1998 / Accepted: 2 July 1998     

Model-free model elimination: A new step in the model-free dynamic analysis of NMR relaxation data

Model-free analysis is a technique commonly used within the field of NMR spectroscopy to extract atomic resolution, interpretable dynamic information on multiple timescales from the R ₁, R ₂, and steady state NOE. Model-free approaches employ two disparate areas of data analysis, the discipline of mathematical optimisation, specifically the minimisation of a χ² function, and the statistical field of model selection. By searching through a large number of model-free minimisations, which were setup using synthetic relaxation data whereby the true underlying dynamics is known, certain model-free models have been identified to, at times, fail. This has been characterised as either the internal correlation times, τ _e , τ _f , or τ _s , or the global correlation time parameter, local τ _m , heading towards infinity, the result being that the final parameter values are far from the true values. In a number of cases the minimised χ² value of the failed model is significantly lower than that of all other models and, hence, will be the model which is chosen by model selection techniques. If these models are not removed prior to model selection the final model-free results could be far from the truth. By implementing a series of empirical rules involving inequalities these models can be specifically isolated and removed. Model-free analysis should therefore consist of three distinct steps: model-free minimisation, model-free model elimination, and finally model-free model selection. Failure has also been identified to affect the individual Monte Carlo simulations used within error analysis. Each simulation involves an independent randomised relaxation data set and model-free minimisation, thus simulations suffer from exactly the same types of failure as model-free models. Therefore, to prevent these outliers from causing a significant overestimation of the errors the failed Monte Carlo simulations need to be culled prior to calculating the parameter standard deviations.     

Oxygen transfer to slurries treated in a rotating drum operated at atmospheric pressure

The objective of this work was to determine (1) the effect of rotational speed (N) and lifters on the oxygen transfer coefficient (k _L) of a mineral solution and (2) the effect of solids concentration of a slurry soil-mineral solution on k _L, at a fixed value N (0.25 s⁻¹); in both cases the treatment was carried out in an aerated rotating drum reactor (RDR) operated at atmospheric pressure. First, the k _L for the mineral solution was in the range 6.38 × 10⁻⁴–7.69 × 10⁻⁴ m s⁻¹, which was of the same order of magnitude as those calculated for closed rotating drums supplied with air flow. In general, k _L of RDR implemented with lifters was superior or equal to that of RDR without lifters. For RDR implemented with lifters, k _L increased with N in the range 6.65 × 10⁻⁴–10.51 × 10⁻⁴ m s⁻¹, whereas k _L of RDR without lifters first increased with N up to N = 0.102 s⁻¹, and decreased beyond this point. Second, regarding soil slurry experiments, an abrupt fall of k _L (ca. 50%) at low values of the solid concentration (C _v) and an asymptotic pattern at high C _v were observed at N = 0.25 s⁻¹. These results suggest that mass transfer phenomena were commanded by the slurry properties and a semi-empirical equation of the form Sh = f(Re, Sc) seems to corroborate this finding.     

The configuration of the seminal roots ofTriticum aestivum L. (Poaceae)

The seminal root system of wheat (Triticum aestivum L.) is composed of the primary seminal root, the first pair of seminal roots, and the second pair of seminal roots, which are known to grow in different directions. The direction of root growth, which can be expressed by ϑ (the angle between the root and the plumb line) and φ (the angle between the root and a vertical plane including the primary seminal root), was studied with special attention to the latter. It was measured on seedlings grown in a small hemispherical soil-filled mesh basket. There were varietal differences in the φ of the first pair of roots (φ_f) and in the φ of the second pair of roots (φ_s). (φ_f) and (φ_s) were significantly correlated. The mean distance (MD), a measure to evaluate the efficiency of root spacing, was correlated with the difference between (φ_f) and (φ_s). Neither experimentally applied low soil water potential nor the excision of the primary seminal root affected φ. When the grain was sown vertically with the tip of the embryo pointing downwards, it was found that the growth movement into a direction different from the plumb line and (φ_s) was greatly modified. it is suggested that certain internal mechanisms, possibly involving gravitropic reactions, are operating to control the direction of root growth. The significance of root growth direction at the seedling stage is discussed.     

Inhibition by light of CO2 evolution from dark respiration: Comparison of two gas exchange methods

Two approaches to determine the fraction (μ) of mitochondrial respiration sustained during illumination by measuring CO₂ gas exchange are compared. In single leaves, the respiration rate in the light (`day respiration' rate R<sub>d</sub>) is determined as the ordinate of the intersection point of A–c<sub>i</sub> curves at various photon flux densities and compared with the CO<sub>2</sub> evolution rate in darkness (`night respiration' rate R_n). Alternatively, using leaves with varying values of CO₂ compensation concentration (Γ), intracellular resistance (r_i) and R_n, an average number for μ can be derived from the linear regression between Γ and the product r_iċR_n. Both methods also result in a number c* for that intercellular CO₂ concentration at which net CO₂ uptake rate is equal to –R_d. c* is an approximate value of the photocompensation point Γ* (Γ in the absence of mitochondrial respiration), which is related to the CO₂/O₂ specificity factor of Rubisco S_c/o. The presuppositions and limitations for application of both approaches are discussed. In leaves of Nicotiana tabacum, at 22 °C, single leaf measurements resulted in mean values of μ = 0.71 and c_* = 34 μmol mol⁻¹. At the photosynthetically active photon flux density of 960 μmol quanta m⁻² s⁻¹, nearly the same numbers were derived from the linear relationship between Γ and r_iċR_n. c* and R_d determined by single leaf measurements varied between 31 and 41 μmol mol⁻¹ and between 0.37 and 1.22 μmol m⁻² s⁻¹, respectively. A highly significant negative correlation between c* and R_d was found. From the regression equation we obtained estimates for Γ* (39 μmol mol⁻¹), S_c/o (96.5 mol mol⁻¹) and the mesophyll CO₂ transfer resistance (7.0 mol⁻¹ m² s). This revised version was published online in June 2006 with corrections to the Cover Date.     

A theoretical model for the control mechanisms in biochemical reactions

A mathematical representation for the analysis of control mechanisms in biochemical reactions is presented. First, the theoretical concept of concentration in biological systems is developed. Then a system consisting of two functions λ and τ is constructed as a network of single output automata. The range of λ is taken to be formed by a set of twostates qualitatively different from the “repair function” Φ _f of a mappingf: A→B in the stimulated Φ¹ and unstimulated state Φ⁰. Likewise, the range of τ is formed by the set δ={f ^o ,f ¹} wheref ¹ means the mappingf in its stimulated state andf ^o in the unstimulated one. It is demonstrated that the mathematical structure described acts as a control mechanism over thef and Φ _f , so that two biochemical components,A→B, are transformed at a controlled rate. Some of the biological applications of this model are briefly examined. The Jacob-Monod model, the enzymatic adaptation phenomenon, and the “rheon unit” hypothesis are discussed within our framework. Eventually, a concrete model for the RNA-polymerase mechanism, based on the above discussion, is presented.     

A note on imitative behavior

In a preceding paper (Bull. Math. Biophysics,27, 175–185) the distribution function ofφ=ɛ ₁-ɛ ₂,—the difference of excitations in the two mutually inhibiting centers, has been derived in terms of the distribution functionsf ₁(ɛ ₁) andf ₂(ɛ ₂) of the two excitations. In the present note some properties of the distribution functionf(ϕ) in terms of the propertiesf ₁(ɛ ₁) andf ₂(ɛ ₂) are derived.     

Osmotic water permeability of plasma and vacuolar membranes in protoplasts II. Theoretical basis

Water permeability of the plasma membrane (PM) and the vacuolar membrane (VM) is important for intracellular and transcellular water movement in plants, because mature plant cells have large central vacuoles. We have developed a new method for measuring the osmotic water permeability of the PM and VM (P _f1 and P _f2, respectively) in individual plant cells. Here, the theoretical basis and procedure of the method are discussed. Protoplasts isolated from higher plant tissues are used to measure P _f1 and P _f2. Because of the semi-permeability (selective permeability) of cellular membranes, protoplasts swell or shrink under hypotonic or hypertonic conditions. A theoretical three-compartment model is presented for simulating time-dependent volume changes in the vacuolar and cytoplasmic spaces in a protoplast during osmotic excursions. The model describes the theoretical relationships between P _f1, P _f2 and the bulk osmotic water permeability of protoplasts (P _f(bulk)). The procedure for measuring the osmotic water permeability is: (1) P _f(bulk) is calculated from the time when half of the total change in protoplast volume is completed, by assuming that the protoplast has a single barrier to water movement across it (two-compartment model); (2) P _f2 of vacuoles isolated from protoplasts is obtained in the same manner; and (3) P _f1 is determined from P _f(bulk) and P _f2 according to the three-compartment model. The theoretical relationship between P _fl (m s⁻¹) and L _Pl (hydraulic conductivity, l=1, 2) (m s⁻¹ Pa⁻¹) is also discussed. Electronic supplementary material Supplementary material is available in the online version of this article at and is accessible for authorised users. Tsuneo Kuwagata and Mari Murai-Hatano contributed equally to the paper.     

On the average cellular volume in synchronized cell populations

As was done by Sinclair and Ross (1969(, we consider a cellular population that consists initially (at time zero) ofN ₀ newborn cells, all with the same volumev _o. It is assumed that the occurrence of cell division is determined only by a cell’s age, and not by its volume. The frequency function of interdivision times, τ, is denoted byf(τ). If cell death is negligible, the expected number of cells,N(t), will increase according to the laws of a simple age-dependent branching process. The expression forN(t) is obtained as a sum over all generations; thevth term of this sum, in turn, is a multiple convolution integral, reflecting the life history ofvth generation cells (i.e., the lengths of thev successive interdivision periods plus the age of the cell at timet). Assuming that cell volume is a given function of cell age, e.g., linear or exponential, and that cellular volume is exactly halved at each division, it is possible to calculate the volume of a cell with a given life history, and thus the average cellular volume of the whole population as a function of time. If at time zero the volumes differ from cell to cell, the final equation must be modified by averaging over initial volumes. In the case of linear volume increase with age, a very simple asymptotic expression is found for the average cellular volume ast→∞. The case of exponential volume increase with age also leads to a simple asymptotic formula, but the resulting volume distribution is unstable. The mean cellular volume at birth and the second moment of the volume distribution can be calculated in a similar manner. Work supported by the U.S. Atomic Energy Commission.     

Kinetics of Ca2+- and ATP-dependent, voltage-controlled anion conductance in the plasma membrane of mesophyll cells of Pisum sativum

Whole-cell patch-clamp techniques were used to measure anion currents through the plasma membrane of protoplasts of mesophyll cells of expanding pea (Pisum sativum L.) leaves. Voltage-induced changes of the currents could be modelled with single exponential activation and deactivation kinetics. The anion currents were activated at negative membrane potentials. The time constant of activation, τ_act, increased from 145 ms at −140 mV to 380 ms at −20 mV. A Boltzmann fit to the activation curve, n_∞ (ΔG_Vm/ΔG_max), yielded a half-activation voltage of +27 mV. Opening and closing rate constants, α and β respectively, were calculated from the values of τ and n_∞. The currents depended on the presence of cytoplasmic Ca²⁺ concentrations higher than 10⁻⁶ M. Including 3 mM MgATP in the intracellular solution resulted in a voltage-dependent inactivation of the anion current. The conductance-voltage relation resulting from the voltage-dependent activation and inactivation had a maximum at about −25 mV. The relations of the current in pea are discussed with respect to the anion currents in guard cells and suspension-cultured tobacco cells, and its possible role in growing leaf cells. Received: 1 March 1996 / Accepted: 16 September 1996     

Osmotic water permeability of plasma and vacuolar membranes in protoplasts I. High osmotic water permeability in radish ( Raphanus sativus ) root cells as measured by a new method

Intra- and transcellular water movements in plants are regulated by the water permeability of the plasma membrane (PM) and vacuolar membrane (VM) in plant cells. In the present study, we investigated the osmotic water permeability of both PM (P _f1) and VM (P _f2), as well as the bulk osmotic water permeability of a protoplast (P _f(bulk)) isolated from radish (Raphanus sativus) roots. The values of P _f(bulk) and P _f2 were determined from the swelling/shrinking rate of protoplasts and isolated vacuoles under hypo- or hypertonic conditions. In order to minimize the effect of unstirred layer, we monitored dropping or rising protoplasts (vacuoles) in sorbitol solutions as they swelled or shrunk. P _f1 was calculated from P _f(bulk) and P _f2 by using the ‘three-compartment model’, which describes the theoretical relationship between P _f1, P _f2 and P _f(bulk) (Kuwagata and Murai-Hatano in J Plant Res, 2007). The time-dependent changes in the volume of protoplasts and isolated vacuoles fitted well to the theoretical curves, and solute permeation of PM and VM was able to be neglected for measuring the osmotic water permeability. High osmotic water permeability of more than 500 μm s⁻¹, indicating high activity of aquaporins (water channels), was observed in both PM and VM in radish root cells. This method has the advantage that P _f1 and P _f2 can be measured accurately in individual higher plant cells. Electronic supplementary material Supplementary material is available in the online version of this article at and is accessible for authorized users. It includes four appendices, four tables and two figures. Mari Murai-Hatano and Tsuneo Kuwagata contributed equally to the paper. An erratum to this article is available at .     

The turbidity maximum in the Tamar estuary

Many estuaries of medium to high tidal range exhibit an accumulation of fine cohesive material in their upper reaches in the region of the limit of saline intrusion. Much, or all, of this material is suspended each tidal cycle and the entire region undergoes a seasonal variation which appears to depend on fluvial input. Two factors which are throught to influence the formation and maintenance of turbidity maxima are the differing magnitudes of the bed shear stress (τ₀) on flood and ebb tides and the large vertical density gradient which developes on the ebb tide. Crucial to the importance of the first factor is that τ₀ exceeds a critical value, at which erosion occurs, for a greater period on the flood than on the ebb. The effect of the density gradient is that upward propagation of bed generated eddies is inhibited and the sediment is not transported into the upper part of the flow where it will be most effectively transported. It is not clear which, if either, of these mechanisms is dominant. Data consisting of vertical profiles of velocity, salinity and suspended solids were collected at four stations in the Tamar estuary during a high range tidal cycle. One station, at which the depth mean salinity (S _d ) varied from 0.0 to ∼ 12.0‰, was occupied permanently. The other stations were occupied such that data were collected asS _d varied in the range 0.0 to ∼ 4.0‰. In this way each station was occupied for a period of time on the ebb and flood tide. Observations show that during the early ebb, when the flow is relatively deep and slow, stratification persist untilS _d ∼ 0.0‰ and that no significant transport occurs while the flow is saline but that there is a rapid increase in suspended solids concentrations after this time. During the later ebb the shallower faster flow allowed the density gradient to be erode and significant transport was observed atS _d ∼ 5.0‰. On the flood tide the flow in the low salinity region is well-mixed troughout. Computation of the fluxes and total transport per unit breath of estuary show that on the ebb tide the quantity of solid material being transported by the low salinity (0–3‰) region remains nearly constant as this region of the flow is advebted seaward. On the flood tide, however, as the same region is advected landward the quantity of material being transported increases. It is concluded that in the Tamar estuary the early ebb tide stratification contributed to the formation and maintenance of a turbidity maximum which is strongly associated with the low salinity region of the flow. It is also speculated that the differences in the ebb and flood tide transport are caused by differences in the availability of mobile material on the bed at different stages of the tidal cycle.     

Vapor Phase Deposition, Structure, and Plasmonic Properties of Polymer-Based Composites Containing Ag–Cu Bimetallic Nanoparticles

Nanocomposite (NC) thin films with noble metal nanoparticles embedded in a dielectric material show very attractive plasmonic properties due to dielectric and quantum confinement effects. For single component nanoparticles (NPs), the plasmon resonance frequency can only be tuned in a narrow range. Much interest aroused in bimetallic nanoparticles (BNPs), however many wet chemical approaches do not allow large variation of the NP alloy composition and filling factor. Here, we report a vapor phase co-deposition method to produce polymer–metal NCs with embedded Ag_1 − x Cu _x alloy particles. The method allows production of NPs with controlled alloy composition (x), metal filling (f) and nanostructure in a protecting Teflon AF matrix. The nanostructure size and shape were characterized by transmission electron microscope. Energy dispersive X-ray spectroscopy was used to determine x and f. The optical properties and the position of surface plasmon resonances were studied by UV–Vis spectroscopy. The plasmon resonances can be tuned over a large range of the visible spectrum associated with the change in x, f, and nanostructure. For low filling factors and small particle sizes, only one resonance peak was observed. This is attributed to enhanced miscibility at the nanoscale. Double plasmon resonances were seen for larger particle sizes in accord with phase separation expected from the bulk phase diagram and were explained in terms of the formation of core-shell structures with Cu core and Ag shell. Changes upon annealing at 200 °C are also reported.     

Growth and production of the bivalve <Emphasis Type="Italic">Macoma balthica</Emphasis> (Linnaeus, 1758) (Cardiida: Tellinidae) in the southeastern part of the Baltic Sea

The growth and production of the Baltic clam Macoma balthica in the southeastern part of the Baltic Sea were studied. The shell length of M. balthica reached 23.5 mm, the maximum age was 13+ years. The linear growth was described by the von Bertalanffy equation for shallow-water area (depths 9–40 m): L _τ = 23.99(1 − e ^{−0.1293(τ − (−0.9578))}), and for the deep-water area (41–81 m): L _τ = 20.61(1 − e ^{−0.1813(τ − (−0.5608))}). The annual production was lower (25.35 ± 1.72 kJ/m²) in the shallow-water area than in the deep-water area (71.23 ± 4.48 kJ/m²), with values of P _s /B ratio 0.44 and 0.38, respectively.     

Characterization of the cadmium complex of peptide 49–61: a putative nucleation center for cadmium-induced folding in rabbit liver metallothionein IIA

 The synthetic peptide fragment containing residues 49–61 of rabbit liver metallothionein II (MT-II) (Ac-Ile-Cys-Lys-Gly-Ala-Ser-Asp-Lys-Cys-Ser-Cys-Cys-Ala-COOH), which includes the only sequential four cysteines bound to the same metal ion in Cd₇MT, forms a stable, monomeric Cd-peptide complex with 1 : 1 stoichiometry (Cd:peptide) via Cd-thiolate interactions. This represents the first synthesis of a single metal-binding site of MT independent of the domains. The ¹¹¹Cd NMR chemical shift at 716 ppm indicates that the ¹¹¹Cd²⁺ in the metal site is terminally coordinated to four side-chain thiolates of the cysteine residues. The pH of half dissociation for this Cd-peptide derivative, ∼3.3, demonstrates an affinity similar to that for Cd₇MT. Molecular mechanics calculations show that the thermodynamically most stable folding for this isolated Cd²⁺ center has the same counterclockwise chirality (Λ or S) observed in the native holo-protein. These properties are consistent with its proposed role as a nucleation center for cadmium-induced protein folding. However, the kinetic reactivity of the CdS₄ structure toward 5,5′-dithiobis(5-nitrobenzoate) (DTNB) and EDTA is greatly increased compared to the complete cluster (α-domain or holo-protein). The rate law for the reaction with DTNB is rate=(k _uf +k _1,f +k _2,f [DTNB])[peptide], where k _uf=0.15 s^–1, k _1,f=2.59×10^–3s^–1, and k _2,f=0.88 M^–1s^–1. The ultrafast step (uf), observable only by stopped-flow measurement, is unprecedented for mammalian (M₇MT) and crustacean (M₆MT) holo-proteins or the isolated domains. The accommodation of other metal ions by the peptide indicates a rich coordination chemistry, including stoichiometries of M-peptide for Hg²⁺, Cd²⁺, and Zn²⁺, M₂-peptide for Hg²⁺ and Au⁺, and (Et₃PAu)₂-peptide. Received: 9 December 1998 / Accepted: 20 May 1999     

Fixation of beneficial mutations in the presence of epistatic interactions

We investigate the effect of deleterious mutations on the process of fixation of new advantageous mutants in an asexual population. In particular we wish to study the dependence of the process on the strength of the deleterious mutations. We suppose the existence of epistatic interaction between the genes. We study the model by means of branching process theory and also by numerical simulations. Our results show the occurrence of two distinct regimes of behavior for the probability of fixation of these variants. The occurrence of either regime depends on the ratio between the selective advantage of the beneficial mutation s _b and on the selective parameter for deleterious mutations s _b . In the former, which takes place for s _b /s _d ≲ 1, the probability of fixation increases with the epistasis parameter α, whereas for s _b /s _d ≫ 1 the probability of fixation is a complex function of α and the mutation rate U. Surprisingly, we find that for the multiplicative landscape (α = 1) the probability of fixation P _fix is given by where π (s _b ) is the probability of fixation for the two-allele model in the absence of mutations as calculated by Haldane (1927, Proc. Camb. Phil. Soc., 26, 220–230) and Kimura (1962, Genetics, 47, 713–719).     

Kinetics of Sulfate Reduction in a Coastal Aquifer Contaminated with Petroleum Hydrocarbons

An integrated field and laboratory study was conducted to quantify the effect of environmental determinants on the activity of sulfate reducers in a freshwater aquifer contaminated with petroleum hydrocarbons (PHC). Within the contaminated zone, PHC-supported in␣situ sulfate reduction rates varied from 11.58±3.12 to 636±53 nmol cm⁻³ d⁻¹ and a linear increase (R ²=0.98) in reduction rate was observed with increasing in situ sulfate concentrations suggesting sulfate limitation. Half-saturation concentration (K _s) for sulfate reduction coupled to PHC mineralization was determined for the first time. At two different sites within the␣aquifer, maximum sulfate reduction rate under␣non-limiting conditions (R _max) was 5,000 nmol cm⁻³ d⁻¹, whereas the retrieved K _s values were 3.5 and 7.5 mM, respectively. The K _s values are the highest ever reported from a natural environment. Furthermore, the K _s values were significantly higher than in situ sulfate concentrations confirming sulfate limited growth. On addition of lactate and formate, sulfate reduction rate increased indicating that reactivity and bioavailability of organic substrate may also have played a role in rate inhibition in certain parts of the aquifer. Experiments with sulfide amendments show statistically minor decrease in sulfate reduction rates on addition of sulfide and analogous increase in sulfide toxicity with increasing sulfide concentrations (0.5–10 mM) was not apparent.     

Hierarchical Classification I: Single-Linkage Method

This is the first part of a survey of hierarchical clustering algorithms using joining methods: the Single-Linkage algorithm. Complete-Linkage and general algorithms defined by d(A_i, B) = = α,d(A_i, A_r)±α_sd(A_i, A_s)±βd(A_r, A_s) will be discussed in two subsequent papers.