The fixation probability of a beneficial allele in a population dividing by binary fission

We derive formulae for the fixation probability, P, of a rare benefical allele segregating in a population of fixed size which reproduces by binary fission, in terms of the selection coefficient for the beneficial allele, s. We find that an earlier result P 4s does not depend on the assumption of binary fission, but depends on an assumption about the ordering of events in the life cycle. We find that P 2s for mutations occurring during chromosome replication and P 2.8s for mutations occurring at random times between replication events.     

A symbolic framework for the description of tree architecture models

The system of tree architecture proposed by Hallé and Oldeman consists of 23 models named after botanists playing leading roles in elucidating tree architecture. This system gives no indication why other models do not occur. A symbolism is presented here which can serve as a shorthand in recording tree architectures without assumptions about models. and immediately interpretable. Using this symbolism to represent the models proposed by Hallé and Oldeman permits creation of general rules of tree architecture. some of which raise interesting theoretical questions. Two further tree models that might well be expected to exist and several which would not be expected. are described.     

On the survival probability of a slightly advantageous mutant gene in a multitype population: A multidimensional branching process model

The estimated survival probability of a slightly supercritical Galton-Watson process is generalized to a multitype branching process. The result is used to estimate the probability of initial success of a mutant gene whose effect on the individual carrier depends on the carrier's sex, class, etc. The probability of initial success is also estimated in a case where the effect of the mutation is manifested in terms of the distribution of types within one's progeny, e.g. in a case of a change in the sex ratio.     

An approach to the residence time distribution for stochastic multi-compartment models

Stochastic compartmental models are widely used in modeling processes such as drug kinetics in biological systems. This paper considers the distribution of the residence times for stochastic multi-compartment models, especially systems with non-exponential lifetime distributions. The paper first derives the moment generating function of the bivariate residence time distribution for the two-compartment model with general lifetimes and approximates the density of the residence time using the saddlepoint approximation. Then, it extends the distributional approach to the residence time for multi-compartment semi-Markov models combining the cofactor rule for a single destination and the analytic approach to the two-compartment model. This approach provides a complete specification of the residence time distribution based on the moment generating function and thus facilitates an easier calculation of high-order moments than the approach using the coefficient matrix. Applications to drug kinetics demonstrate the simplicity and usefulness of this approach.     

Moments of physiological transit time distributions and the time course of drug disposition in the body

Characterizing the tissue distribution kinetics of drugs by physiological and physico-chemical parameters and using a circulatory model the time course of blood concentration after intravenous injection is predicted for linear pharmacokinetic systems. The interrelationships between the first three (zero to second) moments of the distribution functions of organ transfer times, circulation times and residence times of drug molecules in the body are described. Utilizing literature data the model is applied to the analysis of lidocain kinetics in humans.     

Fixation of Strategies for an Evolutionary Game in Finite Populations

A stochastic evolutionary dynamics of two strategies given by 2x 2 matrix games is studied in finite populations. We focus on stochastic properties of fixation: how a strategy represented by a single individual wins over the entire population. The process is discussed in the framework of a random walk with site dependent hopping rates. The time of fixation is found to be identical for both strategies in any particular game. The asymptotic behavior of the fixation time and fixation probabilities in the large population size limit is also discussed. We show that fixation is fast when there is at least one pure evolutionary stable strategy (ESS) in the infinite population size limit, while fixation is slow when the ESS is the coexistence of the two strategies.     

A compact result for the time-dependent probability of fixation at a neutral locus

A result is derived, in the form of a sum, for the time-dependent probability of fixation of an unlinked neutral locus. The result captures many of the key features of the probability of fixation in a highly compact form. For ‘small’ times (t?4N_e) a single term of the sum accurately determines the time-dependent probability of fixation. This is in contrast to the well-known result of Kimura, which requires the contribution of many terms in a different sum, for ‘small’ times. Going beyond small times, an approximation is derived for the time-dependent probability of fixation which applies for all times when the initial relative allele frequency is small.     

Misconceptions and practical problems in the use of 15N soil enrichment techniques for estimating N2 fixation

The ¹⁵N methods are potentially accurate for measuring N₂ fixation in plants. The only problem with those methods is, how to ensure that the ¹⁵N/¹⁴N ratio in the plant accurately reflects the integrated ¹⁵N/¹⁴N ratio (R) in soil which is variable in time and with soil depth. However, the consequences of using an inappropriate reference plant vary with the level of N₂ fixation and the conditions under which the study was made. For example, the errors introduced into the values of N₂ fixation are higher at low levels of fixation, and decrease with increasing rates of fixation. At very high N₂ fixation rates, the errors are often insignificant. Also, the magnitude of error is proportional to the rate of decline of the ¹⁵N/¹⁴N ratio with time. Since N₂ fixation in most plants would be expected to below 60%, the question of how to select a good reference plant is still pertinent. In this paper, we have discussed some of the criteria to adopt in selecting reference plants, e.g. how to ensure that the reference plant is not fixing N₂, is absorbing most of its N from the same zone as the fixing plant, and in the same pattern with time, etc. In addition, we have discussed ¹⁵N labelling materials and methods that are likely to minimize any errors even when the fixing and reference plants don't match well in certain important criteria. The use of slow release ¹⁵N fertilizer or ¹⁵N labelled plant materials results in slow changes in the ¹⁵N/¹⁴N ratio of soil, and is strongly recommended. Where ¹⁵N inorganic fertilizers are used, the application of the fertilizer in small splits at various intervals is recommended over a one-time application. The problem with the reference crop, which has sometimes discouraged potential users of the ¹⁵N methods, is surmountable, as discussed in this paper.     

A model for the spread of an epidemic

A temporally continuous and spatially discrete stochastic model for the spread of an epidemic within some set of holdings is constructed. A recursion formula is given for the probability that a certain set of holdings is infected at a certain moment. Moreover, under an additional condition (which will always be satisfied in practice) a formula for the expected value and the variance of the moment when a certain holding is infected the first time is given.     

A comparison of persistence-time estimation for discrete and continuous stochastic population models that include demographic and environmental variability

A discrete-time Markov chain model, a continuous-time Markov chain model, and a stochastic differential equation model are compared for a population experiencing demographic and environmental variability. It is assumed that the environment produces random changes in the per capita birth and death rates, which are independent from the inherent random (demographic) variations in the number of births and deaths for any time interval. An existence and uniqueness result is proved for the stochastic differential equation system. Similarities between the models are demonstrated analytically and computational results are provided to show that estimated persistence times for the three stochastic models are generally in good agreement when the models satisfy certain consistency conditions.     

Illustration of some limits of the Markov assumption for transition between groups in models of spread of an infectious pathogen in a structured herd

In epidemic models concerning a structured population, sojourn times in a group are usually described by an exponential distribution. For livestock populations, realistic distributions may be preferred for group changes (e.g. depending on sojourn time). We illustrated the effect on pathogen spread of the use of an exponential distribution, instead of the true distribution of the transition time, between groups for a population separated into two groups (youngstock, adults) when this true distribution is a triangular one. Concerning the epidemic process, two assumptions were defined: one type of excreting animal (SIR model), and two types of excreting animals (transiently or persistently infected animals). The study was conducted with two indirect-transmission levels between groups. Among the adults, the epidemic size and the last infection time were significantly different. For persistence, epidemic sizes (in the entire population and in youngstock) and first infection time, results varied according to models (excretion assumption, indirect-transmission level).     

Cloning of the gene for phosphoenolpyruvate carboxylase from Azotobacter chroococcum, an enzyme important in aerobic nitrogen fixation

Summary Azotobacter chroococcum Fos 189 is a Tn1-induced mutant which, unlike the parent strain MCD1, does not fix nitrogen in air when provided with glucose or pyruvate as sole carbon sources. Fos 189 showed 5% of parental activity for phosphoenolpyruvate carboxylase though PEP synthetase activity was normal. The A. chroococcum phosphoenolpyruvate carboxylase (ppc) gene was isolated after complementation of an appropriate Escherichia coli mutant using a broad host range gene bank prepared from A. chroococcum genomic DNA. The gene was localised by transposon mutagenesis and subcloning on a minimum DNA fragment of 6.6 kb. Broad host range plasmids containing the A. chroococcum ppc gene complemented the mutation in Fos 189 thereby restoring aerotolerant nitrogen fixation.     

Investigating the potential of Bacillus subtilis α‐amylase as a pressure‐temperature‐time indicator for high hydrostatic pressure pasteurization processes

The potential of Bacillus subtilis α‐amylase (BSA) as a pressure‐temperature‐time indicator (pTTI) for high pressure pasteurization processing (400–600 MPa; T_i 10–40°C; 1–15 min) was investigated. A stepwise approach was followed for the development of an enzyme‐based, extrinsic, isolated pTTI. First, based on literature data on the pressure stability, BSA was selected as a candidate indicator. Next to the accuracy and ease of the measurement of the indicator's response (residual activity) to the pressure treatment, the storage and handling stability of BSA at atmospheric pressure was verified. Second, the stability of BSA at a constant temperature (T) and time in function of pressure (p) was investigated. Solvent engineering was used to shift the inactivation window of BSA in the processing range of interest. Third, the enzyme (1 g/L BSA—MES 0.05 M pH 5.0) was kinetically calibrated under isobaric‐isothermal conditions. Time dependent changes in activity could be modeled best by a first‐order model. Except for low pressures and high temperatures, a synergistic effect between pressure and temperature could be observed. Based on the model selected to describe the combined p,T‐dependency of the inactivation rate constant, an elliptically shaped isorate contour plot could be constructed, illustrating the processing range where BSA can be used to demonstrate temperature gradients. Fourth, the validity of the kinetic model was tested successfully under dynamic conditions similar to those used in food industry. Finally, the indicator was found suitable to demonstrate nonuniformity in two‐sectional planes of a vertical, single vessel system. © 2009 American Institute of Chemical Engineers. Biotechnol. Prog., 2009     

Co‐variation between the intensity of behavioural manipulation and parasite development time in an acanthocephalan–amphipod system

Pomphorhynchus laevis, a fish acanthocephalan parasite, manipulates the behaviour of its gammarid intermediate host to increase its trophic transmission to the definitive host. However, the intensity of behavioural manipulation is variable between individual gammarids and between parasite populations. To elucidate causes of this variability, we compared the level of phototaxis alteration induced by different parasite sibships from one population, using experimental infections of Gammarus pulex by P. laevis. We used a naive gammarid population, and we carried out our experiments in two steps, during spring and winter. Moreover, we also investigated co‐variation between phototaxis (at different stages of infection, ‘young’ and ‘old cystacanth stage’) and two other fitness‐related traits, infectivity and development time. Three main parameters could explain the parasite intra‐population variation in behavioural manipulation. The genetic variation, suggested by the differences between parasite families, was lower than the variation owing to an (unidentified) environmental factor. Moreover, a correlation was found between development rate and the intensity of behavioural change, the fastest growing parasites being unable to induce rapid phototaxis reversal. This suggests that parasites cannot optimize at the same time these two important parameters of their fitness, and this could explain a part of the variation observed in the wild.     

A transient expression assay for the in planta efficacy screening of an antimicrobial peptide against grapevine bacterial pathogens

Aims: Natural and synthetic antimicrobial peptides (AMPs) are of increasing interest as potential resistance conferring elements in plants against pathogen infection. The efficacy of AMPs against pathogens is prescreened by in vitro assays, and promising AMP candidates are introduced as transgenes into plants. As in vitro and in planta environments differ, a prescreening procedure of the AMP efficacy in the plant environment is desired. Here, we report the efficacy of the purified synthetic peptide D4E1 against the grapevine‐infecting bacterial pathogens Agrobacterium vitis and Xylophilus ampelinus in vitro and describe for the first time an in planta prescreening procedure based on transiently expressed D4E1. Methods and Results: The antimicrobial effect of D4E1 against Ag. vitis and X. ampelinus was shown by a reduction in colony‐forming units in vitro in a traditional plate‐based assay and by a reduction in bacterial titres in planta as measured by quantitative real‐time PCR (qPCR) in grapevine leaves transiently expressing D4E1. A statistically significant reduction in titre was shown for X. ampelinus, but for Ag. vitis, a significant reduction in titre was only observed in a subset of plants. Conclusions: The titres of both grapevine‐infecting bacterial pathogens were reduced in an in vitro assay and for X. ampelinus in an in planta assay by D4E1 application. This widens the applicability of D4E1 as a potential resistance‐enhancing element to additional pathogens and in a novel plant species. Significance and Impact of the Study: D4E1 is a promising candidate to confer enhanced resistance against the two tested grapevine bacterial pathogens, and the applied transient expression system proved to be a valuable tool for prescreening of D4E1 efficacy in an in planta environment. The described prescreening procedure can be used for other AMPs and might be adapted to other plant species and pathogens before the expensive and tedious development of stably transgenic lines is started.     

Establishment of an efficient multiplex real‐time PCR assay for human papillomavirus genotyping in cervical cytology specimens: comparison with hybrid capture II

J.‐H. Lee, N.‐W. Lee, S.‐W. Hong, Y.‐S. Nam, J.‐W. Choi and Y.‐S. Kim Establishment of an efficient multiplex real‐time PCR assay for human papillomavirus genotyping in cervical cytology specimens: comparison with hybrid capture II Objective: To establish an efficient multiplex real‐time PCR assay for 15 human papillomavirus (HPV) genotypes, we designed multiplexing parameters and compared our PCR system with the hybrid capture (HC) II test using cervical cytology samples. Methods: For preventing cross‐reactive amplifications, variable HPV genes (E1, E2, E6, E7 and L1) were targeted. The melting temperatures of all primers and probes, and the size of the PCR product were optimized for the multiplex PCR. Our PCR system was compared with the HC II assays in the detection and genotyping of HPV infection using 173 cytology smears. Discordant cases between the two assays were verified by direct HPV DNA sequencing. Results: Of 173 women, 93 (53.8%) were HPV‐positive by the HC II assay and/or the multiplex real‐time PCR assay. The HPV genotypes were determined in 92 (98.9%) of 93 cases by the multiplex real‐time PCR and/or DNA sequencing. The agreement rate between multiplex PCR and HC II methods was 91.9% (kappa = 0.84). Although the sample size of this study needs to be increased to have epidemiological significance, multiple infections and HPV 16 were the predominant type. HPV 58, 52 and 18 accounted for 25% of HPV infections. HPV 52, 58 and 31 constituted 30% of CIN 2/3. Conclusion: The multiplex real‐time PCR system shows a good and reliable clinical performance. This in house PCR assay is fast and cost‐effective for HPV genotyping and the detection of HPV co‐infection in the post‐HPV vaccination era.