A Single Compartment Quantal Response Model with a Renewal Type Input Process and IID Releases

We deal with a single compartment quantal response model, where unlike the previous models, which do not have any input after the administration of a single dose Z(0)=z at time t=0, we allow inputs of doses after time t=0. More precisely, the system uses the (s, S) input policy as in inventory models, and has IID releases. Also when the amount of dose in the subject reaches 0, there is a probability p to stop having input thereafter. Among other results, the probability that the subject never responds and the expressions for some quantities of interest are obtained.     

Outcomes of decades long installation of nest boxes for arboreal mammals in southern Australia

Nest boxes are commonly installed to support hollow‐using species where the abundance of hollow‐bearing trees is deficient. Recent studies have provided equivocal evidence about the effectiveness of nest box projects and have highlighted significant management costs associated with some projects. We document the functionality of 303 nest boxes installed across five different community‐led projects in southern Australia for periods of 10–25 years. As expected, we found that nest boxes lost functionality over time. However, 60% remained functional to support the Brush‐tailed Phascogale (Phascogale tapoatafa) and the Sugar Glider (Petaurus breviceps) after almost 20 years. Years installed, method of nest box attachment and tree species influenced whether boxes remained functional. Nest box construction material changed over time so could not be assessed specifically. When inspected in a single year, the Brush‐tailed Phascogale occupied 9% of functional boxes and another 48% contained their nests. The Sugar Glider occupied 15% of functional boxes and another 22% contained their nests. These values suggest the nest box installations were highly effective for these species, although more detailed study is needed to understand what contribution these installations have made to support the local populations. Maintenance of most nest boxes occurred twice a year in the first five years after installation, but many received no maintenance for periods of three years, and some 10–15 years, before our census. Our findings suggest that infrequent maintenance by community groups can sustain nest box projects over periods of several decades. Research into employing nest boxes as a management tool in Australia is still in its infancy. Further studies are needed to resolve factors that limit their effectiveness.     

Stochastic models of tumor growth and the probability of elimination by cytotoxic cells

The probability of tumor extinction due to the action of cytotoxic cell populations is investigated by several one dimensional stochastic models of the population growth and elimination processes of a tumor. The several models are made necessary by the nonlinearity of the processes and the different parameter ranges explored. The deterministic form of the model is where γ₀, k′₆ and k ₁ are positive constants. The parameter of most import is which determines the stability of the T = 0 equilibrium. With an initial tumor size of one, a (linear) branching process is used to estimate the extinction probability. However, in the case λ = 0 when the linearization of the deterministic model gives no information (T = 0 is actually unstable) the branching model is unsatisfactory. This makes necessary the utilization of a density-dependent branching process to approximate the population. Through scaling a diffusion limit is reached which enables one to again compute the probability of extinction. For populations away from one a sequence of density-dependent jump Markov processes are approximated by a sequence of diffusion processes. In limiting cases, the estimates of extinction correspond to that computed from the original branching process. Table 1 summarizes the results.     

Invasive cutleaf coneflower seeds cached in nest boxes: possibility of dispersal by a native rodent

Invasive species present serious problems for ecosystems and economies. One such species, the invasive cutleaf coneflower (Rudbeckia laciniata L.), has several modes of seed dispersal, namely autochory, anemochory, epizoochory, myrmecochory and anthropochory. Because we found caches of this invasive plant's seeds in two nest boxes, suggesting the possibility of synzoochory, we report here the details of the caches. In one of the boxes, many of the seeds were cached in autumn and eaten during the winter. Automatic sensor cameras directed at the boxes revealed that three rodent species and two avian species visited the boxes. The characteristics of the caches and the nest‐box visitors suggested that the small Japanese field mouse (Apodemus argenteus Temm.) was the animal most likely to have cached the seeds in the boxes.     

Simulation of a multicolumn recirculated packed bed reactor (MRPBR) for penicillin acylase

Enzyme reactors for the industrial hydrolysis of penicillin are analyzed in terms of biocatalyst stability to pH. A multicolumn system with packed beds placed in parallel and operating under recirculating conditions is proposed as an adequate reactor for this process. The system is studied both experimentally and with the aid of a simulation program.List of Symbols A transversal area (cm²) - C _A ammonia concentration in the reaction mixture (M) - C ₁ concentration of KH₂PO₄ in buffer (M) - C ₂ concentration of K₂HPO₄ in buffer (M) - d _p biocatalyst diameter (cm) - E enzyme or biocatalyst concentration (gcat l^–1) - K _APA APA non competitive inhibition constant (M) - K _IS excess substrate inhibition constant (M) - Km constant Michaelis-Menten (M) - K _PAA PAA competitive inhibition constant (M) - Q recirculation flow rate (cm³ min^–1) - Q _T recirculation flow rate per column (cm³ min^–1) - Re Reynolds number - S _E substrate concentration entering the neutralization tank (M) - S ₀ initial substrate concentration (M) - S _T substrate concentration in neutralization tank (M) - t time (min) - v _i initial reactor rate (mol min^–1 gcat^–1) - V _s superficial velocity (cm seg^–1) - V _T volume of neutralization tank (cm³) - X _E substrate conversion entering tank - X _T substrate conversion in neutralization tank - X conversion - Z reactor length (cm) - z axial position in reactor (cm) - z ^* non-dimensional axial position in reactor - biocatalyst's density (gcat cm^–3) - p pressure drop in the packed-bed reactor     

A Bayesian Approach to Surrogacy Assessment Using Principal Stratification in Clinical Trials

Summary A surrogate marker (S) is a variable that can be measured earlier and often more easily than the true endpoint (T) in a clinical trial. Most previous research has been devoted to developing surrogacy measures to quantify how well S can replace T or examining the use of S in predicting the effect of a treatment (Z). However, the research often requires one to fit models for the distribution of T given S and Z. It is well known that such models do not have causal interpretations because the models condition on a postrandomization variable S. In this article, we directly model the relationship among T, S, and Z using a potential outcomes framework introduced by Frangakis and Rubin (2002, Biometrics 58 , 21–29). We propose a Bayesian estimation method to evaluate the causal probabilities associated with the cross‐classification of the potential outcomes of S and T when S and T are both binary. We use a log‐linear model to directly model the association between the potential outcomes of S and T through the odds ratios. The quantities derived from this approach always have causal interpretations. However, this causal model is not identifiable from the data without additional assumptions. To reduce the nonidentifiability problem and increase the precision of statistical inferences, we assume monotonicity and incorporate prior belief that is plausible in the surrogate context by using prior distributions. We also explore the relationship among the surrogacy measures based on traditional models and this counterfactual model. The method is applied to the data from a glaucoma treatment study.     

Experimentally increased nest temperature affects body temperature,growth and apparent survival in blue tit nestlings

The thermal environment experienced by birds during early postembryonic development may be an important factor shaping growth and survival. However, few studies have directly manipulated nest temperature (T _n) during the nestling phase, and none have measured the consequences of experimental heat stress on nestlings’ body temperature (T _b). It is therefore not known to what extent any fitness consequences of development in a thermally challenging environment arise as a direct, or indirect, effect of heat stress. We, therefore, studied how experimentally increased T _n affected T _b in 8–12 d old blue tit Cyanistes caeruleus nestlings, to investigate if increased thermoregulatory demands to maintain normothermic T _b influenced nestling growth and apparent long‐term survival. Nestlings in heated nest‐boxes had significantly higher T _b compared to unheated nestlings during most of the experimental period. Yet, despite facing T _n  50°C (as measured in the bottom of the nest cup below the nestlings), the highest nestling T _b recorded was 43.8°C with nestlings showing evidence of controlled facultative hyperthermia without any increased nestling mortality in heated nests. However, body mass gain was lower in these nestlings compared to nestlings from control nest‐boxes. Contrary to our prediction, a larger proportion of nestlings from heated nest‐boxes were recaptured during their first winter, or subsequently recruited into the breeding population as first‐ or second‐year breeders. This result should, however, be treated with caution because of low recapture rates. This study highlights the importance of the thermal environment during nestling development, and its role in shaping both growth patterns and possibly also apparent survival.     

Cavity type influences abundance of nest-dwelling avian blow flies: an experiment with tree swallows

1. Diverse assemblages of blood-feeding parasitic arthropods occupy the nests of birds, and nest temperature and humidity can strongly influence the population dynamics of these ectoparasites, with important implications for parasite–host relationships. 2. This study used two types of nest box that differed in internal microclimates, one constructed of plywood and the other constructed of boles of aspen (Populus tremuloides Michx.), more closely replicating natural cavities, to examine how nest microclimate affects the prevalence and abundance of nest-dwelling larval blow flies (Protocalliphora and Trypocalliphora spp.) in nests of tree swallows (Tachycineta bicolor Vieillot, 1808). 3. Based on known microclimatic differences between the box types and responses of larval blow flies to different temperatures, it was predicted that the microclimate of plywood boxes would be more favourable for growth and development of larval blow flies, and therefore have higher abundance, and possibly higher prevalence, of larval blow flies. 4. Plywood nest boxes had higher abundance, but not prevalence, of larval blow flies compared with aspen boxes at two different geographical locations in Canada. Nest composition also differed between box types, particularly at one site, where aspen boxes contained more nesting material (grass and feathers) than did plywood boxes. 5. Although it seems probable that microclimate was driving the differences between box types in abundance of larval blow flies, several additional explanations are discussed. These findings may have implications for conservation efforts, particularly those where nest boxes are used to aid in the recovery of declining bird populations.     

Ectoparasites,nest site choice and breeding success in the pied flycatcher

It has recently been suggested that nest box studies might bias the measurement of behavioural and life-history traits, because the removal of old nests may reduce the load of ectoparasites. This experimental artefact may have notable effects on nest site choice and breeding success in cavity-breeding birds. We tested (i) if pied flycatchers Ficedula hypoleuca prefer clean nest boxes and (ii) if old nest material affects the number of parasites and the breeding success of pied flycatchers. In the first experiment we offered birds one cleaned nest box and one nest box with old nest material from the previous year. The two nest boxes were placed in very similar sites near each other. In this experiment all pied flycatchers clearly preferred dirty nest boxes. In the second part of the study we distributed clean nest boxes and dirty ones on the same study area. After breeding was over we counted the number of fleas Ceratophyllus gallinae in the nest material. This flea species was the most abundant and probably the most hazardous parasite in the nests. Surprisingly, we found that there were significantly more fleas in the nest boxes with nests of the current year only than in the boxes with nests of both current and previous year. This might explain the preference for the dirty boxes. However, our results do not indicate that the number of fleas affects breeding success in the pied flycatcher.     

Multipoint linkage analysis in X-linked Alport syndrome

Summary In order to localize the gene for the X-linked form of Alport syndrome (ATS) more precisely, we performed restriction fragment length polymorphism analysis with nine different X-chromosomal DNA markers in 107 members of twelve Danish families segregating for classic ATS or progressive hereditary nephritis without deafness. Two-point linkage analysis confirmed close linkage to the markers DXS17(S21) (Z _max = 4.44 at = 0.04), DXS94(pXG-12) (Z _max=8.07 at =0.04), and DXS101(cX52.5) (Z _max=6.04 at =0.00), and revealed close linkage to two other markers: DXS88(pG3-1) (Z _max =6.36 at =0.00) and DXS11(p22–33) (z _max=3.45 at =0.00). Multipoint linkage analysis has mapped the gene to the region between the markers DXS17 and DXS94, closely linked to DXS101. By taking into account the consensus map and results from other studies, the most probable order of the loci is: DXYS1(pDP34)-DXS3(p19-2)-DXS17-(ATS, DXS101)-DXS94-DXS11-DXS42(p43-15)-DXS51(52A). DXS88 was found to be located between DXS17 and DXS42, but the order in relation to the ATS locus and the other markers used in this study could not be determined.     

When and where was the most recent common ancestor?

 The structured coalescent is investigated for single-locus, digenic samples in the diffusion limit of the unidimensional stepping-stone model for homogeneous, isotropic migration and random genetic drift. Let T denote the scaled time to the most recent common ancestor (MRCA) of the two genes, and let Z designate the scaled deviation of the position of the MRCA from the average position of the two genes. The joint probability density of T and Z is evaluated explicitly. Both the marginal and conditional distributions of T have infinite expectation, as does the marginal distribution of Z. Conditioned on T = τ, the distribution of Z is Gaussian with mean zero and variance 2τ. The main results are extended to anisotropic migration. The results establish the existence of and define in the diffusion limit a retrospective stochastic process for digenic samples in one spatial dimension. Received: 1 May 2001 / Revised version: 2 September 2001 / Published online: 8 February 2002     

Zur Genetik Der Trikotylie

Zusammenfassung Die Interpretation der Selektionsversuche von Hugo de Vries an trikotylen Rassen ergibt, daß dem Merkmal trikotyl zwei oder drei Genpaare zugrunde liegen. Zur Realisation des Merkmals ist zunächst ein Genpaar tt verantwortlich, dessen Wirkung von der Art des Vorhandenseins der Zusatzgene Z ₁, Z ₂, bzw. z ₁, z ₂ abhängig ist. tt Z ₁ Z ₁ Z ₂ Z ₂-Individuen haben die geringste Möglichkeit zur Entfaltung der Trikotylieanlage, tt z ₁ z ₁ z ₂ z ₂-Individuen die größte.Die eigenen Untersuchungen ergeben eine außergewöhnlich starke Abhängigkeit des Merkmalsunterschieds di-trikotyl von äußeren Bedingungen. Verläuft die Embryoentwicklung unter Herbstbedingungen, so werden 20% Trikotyle gegenüber 0,5% unter Sommerbedingungen gebildet. Durch Entblätterung der Pflanzen im Sommer lassen sich ebenfalls hohe Prozentsätze von Trikotylen erzeugen. Damit wird gezeigt, daß Nahrungsmangel während der Embryobildung der die Trikotylie begünstigende Außenfaktor ist. Er bewirkt, daß der Umschlagspunkt, bei dem sich eine Anlage für Trikotylie entfalten kann, eher erreicht wird als bei normaler Ernährung. Die Wirkung der Trikotyliegene läßt sich als Herabsetzung des Umschlagspunktes auffassen, sodaß unter Normalbedingungen die Entwicklung zur Trikotylie begünstigt ist.Die Realisation der Trikotylie stellt einen Grenzfall zur echten alternativen Modifikabilität dar, indem zwischen den beiden Maxima mit di- und trikotylen auch Hemiformen auftreten. Ihre Zahl bleibt stets gering, wie auch immer die beiden Maxima durch Änderung der Gengrundlage oder der äußeren Bedingungen wechselseitig erhöht und erniedrigt werden mögen.     

Modelling and off line optimization of batch gluconic acid fermentation

Summary The role of mathematical modelling and off line optimization for a batch fermentation process is described. The fermentation of gluconic acid by Acetobacter suboxydans ATCC 621 was studied. The model is based on a series of batch experiments in which the temperature was the only variable. The differential equations of the models were derived from these experiments to give the kinetic parameters and the parametric models varying with the temperature. The fermentation was optimized using Pontryagin's maximum principle. This gave the temperature profile of fermentation.Abbreviations x, g, l, S, c, P The concentration of cell mass, glucose, lactone, gluconic acid, 5-ketogluconic acid and total acidic products respectively - r₁, r₂ E₁ or E₂ enzyme in complex/total E₁ or E₂ enzyme content - a, b E₁ and E₂ enzyme content of unit quantity of biomass - k_i and K_j Rate constants - _max Maximum specific growth rate - y_x z₁=r₁x z₂=r₂x Yield coefficient of biomass with respect to growth on glucose - z₁ r₁x - z₂ r₂x     

Factors affecting electrical impedance of internodal stem sections

A sample holder was designed and built to facilitate measuring the magnitude and phase angle of the electrical impedance of internodal stem sections from Cornus stolonifera Michx. A nonpolarizing, electrically conducting manganese dioxidecarbon paste used between the stem sample and the electrodes of the sample holder allowed measurement of impedance at frequencies from 50 hertz to 500 kilohertz without electrode polarization or electrical interference. The impedance magnitude was linearly dependent on the sample length, but this dependence was minimized by computing a normalized impedance magnitude. The normalized impedance magnitude (Z_nf) was calculated using the impedance magnitude (Z) at any specified frequency (f) and the impedance magnitude at 500 kilohertz (Z_{500 khz}) in the following formula: Z_nf = (Z - Z_{500 khz})/Z_{500 khz}. The normalized impedance magnitude was sensitive to injury produced by boiling and peeling the sample. Electrical impedance measurements on the bark and wood separately demonstrated that they have different electrical properties.     

Inference for an age-dependent,multitype branching-process model of mast cells

We consider an age-dependent, multitype model for the growth of mast cells in culture. After a colony of cells is established by an initiator type, the two possible types of cells are resting and proliferative. Using novel inferential procedures, we estimate the generation-time distribution and the offspring distribution of proliferative cells, and the waiting-time distribution of resting cells.List of Notations B _i cumulative distribution function for the time until branching of a cell of type i - b _i probability density function for the time until branching of a cell of type i - b _i b _i (1–D _i ) - D _i cumulative distribution function for the time until death of a cell of type i - d _i probability density function for the time until death of a cell of type i - probability density function of a gamma distribution - G _i cumulative distribution function for the lifetime of a cell of type i - G _1*2 Convolution of G ₁ and G ₂ - ¯G _i 1–G _i - g _i probability density function for the lifetime of a cell of type i - L _i likelihood of a history of type i - m average number of proliferative daughters produced by dividing cells - M _ij (t) the expected number of type-j cells in a colony at time t if that colony began at time 0 with one type-i cell - M _i+ (t) M _i0 (t) + M _i 1(t) + M _i 2(t) - p _rs probability that a dividing cell produces r proliferative and s resting daughters - t _i times defining colony histories. See IV.2.1 - T ₀ time to division of an initiator cell - T ₁, T ₂ times from birth to division of the two daughters of an initiator cell - T ₍₁₎, T ₍₂₎ order statistics of T ₁ and T ₂ - minimum value of a gamma distribution - scale parameter of a gamma distribution or of an exponential distribution - probability per unit time of death for proliferative and resting cells - _rs expected value of p _rs when there is heterogeneity - shape parameter of a gamma distribution     

Incident radiation and the allocation of nitrogen within Arctic plant canopies: implications for predicting gross primary productivity

Arctic vegetation is characterized by high spatial variability in plant functional type (PFT) composition and gross primary productivity (P). Despite this variability, the two main drivers of P in sub‐Arctic tundra are leaf area index (L_T) and total foliar nitrogen (N_T). L_T and N_T have been shown to be tightly coupled across PFTs in sub‐Arctic tundra vegetation, which simplifies up‐scaling by allowing quantification of the main drivers of P from remotely sensed L_T. Our objective was to test the L_T–N_T relationship across multiple Arctic latitudes and to assess L_T as a predictor of P for the pan‐Arctic. Including PFT‐specific parameters in models of L_T–N_T coupling provided only incremental improvements in model fit, but significant improvements were gained from including site‐specific parameters. The degree of curvature in the L_T–N_T relationship, controlled by a fitted canopy nitrogen extinction co‐efficient, was negatively related to average levels of diffuse radiation at a site. This is consistent with theoretical predictions of more uniform vertical canopy N distributions under diffuse light conditions. Higher latitude sites had higher average leaf N content by mass (N_M), and we show for the first time that L_T–N_T coupling is achieved across latitudes via canopy‐scale trade‐offs between N_M and leaf mass per unit leaf area (L_M). Site‐specific parameters provided small but significant improvements in models of P based on L_T and moss cover. Our results suggest that differences in L_T–N_T coupling between sites could be used to improve pan‐Arctic models of P and we provide unique evidence that prevailing radiation conditions can significantly affect N allocation over regional scales.     

ON THE EXISTENCE OF A Go-PHASE IN THE CELL CYCLE

The model is based on the assumption that the cell cycle contains a G_o-phase which cells leave randomly with a constant probability per unit time, γ. After leaving the G_o-phase, the cells enter the C-phase which ends with cell division. The C-phase and its constituent phases, the‘true’G₁-phase, the S-phase, the G₂-phase and mitosis are assumed to have constant durations of T, T₁T_s, T₂ and T_m, respectively. For renewal tissue it is assumed that the probability per unit time of being lost from the population is a constant for all cells irrespective of their position in the cycle. The labelled mitosis curve and labelling index for continuous labelling are derived in terms of γ, T, and T_s. The model generates labelled mitosis curves which damp quickly and reach a constant value of twice the initial labelling index, if the mean duration of the G_o-phase is sufficiently long. It is shown that the predicted labelled mitosis and continuous labelling curves agree reasonably well with the experimental curves for the hamster cheek pouch if T has a value of about 60 hr. Data are presented for the rat dorsal epidermis which support the assumption that there is a constant probability per unit time of a cell being released from the Go-phase.     

A revised model for the control of fatty acid synthesis by master regulator Spo0A in Bacillus subtilis

In starving Bacillus subtilis cells, the accDA operon encoding two subunits of the essential acetyl‐CoA carboxylase (ACC) has been proposed to be tightly regulated by direct binding of the master regulator Spo0A to a cis element (0A box) in the promoter region. When the 0A box is mutated, biofilm formation and sporulation have been reported to be impaired. Here, we present evidence that two 0A boxes, one previously known (0A‐1) and another newly discovered (0A‐2) in the accDA promoter region are positively and negatively regulated by Spo0A～P respectively. Cells with mutated 0A boxes experience slight delays in sporulation, but eventually sporulate with high efficiency. In contrast, cells harboring a single mutated 0A‐2 box are deficient for biofilm formation, while cells harboring either a mutated 0A‐1 box or both mutated 0A boxes form biofilms. We further show that the essential ACC enzyme localizes on or near the cell membrane by directly observing a functional GFP fusion to one of the enzyme's subunits. Collectively, we propose a revised model in which accDA is primarily transcribed by a major σ^A‐RNA polymerase, while Spo0A～P plays an additional role in the fine‐tuning of accDA expression upon starvation to support proper biofilm formation and sporulation.     

Relationships between individual‐tree mortality and water‐balance variables indicate positive trends in water stress‐induced tree mortality across North America

Accounting for water stress‐induced tree mortality in forest productivity models remains a challenge due to uncertainty in stress tolerance of tree populations. In this study, logistic regression models were developed to assess species‐specific relationships between probability of mortality (P_m) and drought, drawing on 8.1 million observations of change in vital status (m) of individual trees across North America. Drought was defined by standardized (relative) values of soil water content (W_s,z) and reference evapotranspiration (ET_r,z) at each field plot. The models additionally tested for interactions between the water‐balance variables, aridity class of the site (AC), and estimated tree height (h). Considering drought improved model performance in 95 (80) per cent of the 64 tested species during calibration (cross‐validation). On average, sensitivity to relative drought increased with site AC (i.e. aridity). Interaction between water‐balance variables and estimated tree height indicated that drought sensitivity commonly decreased during early height development and increased during late height development, which may reflect expansion of the root system and decreasing whole‐plant, leaf‐specific hydraulic conductance, respectively. Across North America, predictions suggested that changes in the water balance caused mortality to increase from 1.1% yr^?1 in 1951 to 2.0% yr^?1 in 2014 (a net change of 0.9 ± 0.3% yr^?1). Interannual variation in mortality also increased, driven by increasingly severe droughts in 1988, 1998, 2006, 2007 and 2012. With strong confidence, this study indicates that water stress is a common cause of tree mortality. With weak‐to‐moderate confidence, this study strengthens previous claims attributing positive trends in mortality to increasing levels of water stress. This ‘learn‐as‐we‐go’ approach – defined by sampling rare drought events as they continue to intensify – will help to constrain the hydraulic limits of dominant tree species and the viability of boreal and temperate forest biomes under continued climate change.