Estimating a predator-prey dynamical model with the parameter cascades method

Summary .   Ordinary differential equations (ODEs) are widely used in ecology to describe the dynamical behavior of systems of interacting populations. However, systems of ODEs rarely provide quantitative solutions that are close to real field observations or experimental data because natural systems are subject to environmental and demographic noise and ecologists are often uncertain about the correct parameterization. In this article we introduce "parameter cascades" as an improved method to estimate ODE parameters such that the corresponding ODE solutions fit the real data well. This method is based on the modified penalized smoothing with the penalty defined by ODEs and a generalization of profiled estimation, which leads to fast estimation and good precision for ODE parameters from noisy data. This method is applied to a set of ODEs originally developed to describe an experimental predator–prey system that undergoes oscillatory dynamics. The new parameterization considerably improves the fit of the ODE model to the experimental data sets. At the same time, our method reveals that important structural assumptions that underlie the original ODE model are essentially correct. The mathematical formulations of the two nonlinear interaction terms (functional responses) that link the ODEs in the predator–prey model are validated by estimating the functional responses nonparametrically from the real data. We suggest two major applications of "parameter cascades" to ecological modeling: It can be used to estimate parameters when original data are noisy, missing, or when no reliable priori estimates are available; it can help to validate the structural soundness of the mathematical modeling approach.     

Joint model of recurrent events and a terminal event with time‐varying coefficients

Joint modeling of recurrent events and a terminal event has been studied extensively in the past decade. However, most of the previous works assumed constant regression coefficients. This paper proposes a joint model with time‐varying coefficients in both event components. The proposed model not only accommodates the correlation between the two type of events, but also characterizes the potential time‐varying covariate effects. It is especially useful for evaluating long‐term risk factors' effect that could vary with time. A Gaussian frailty is used to model the correlation between event times. The nonparametric time‐varying coefficients are modeled using cubic splines with penalty terms. A simulation study shows that the proposed estimators perform well. The model is used to analyze the readmission rate and mortality jointly for stroke patients admitted to Veterans Administration (VA) Hospitals.     

Estimating the Location and Time Course of Synaptic Input from Multi-Site Potential Recordings

A method is introduced that permits accurate and robust extraction of the location and time course of synaptic conductance from potentials recorded on either side of, and perhaps at some distance from, the synapse in question. It is shown that such data permits one to fully overcome the problems typically associated with lack of spaceclamp. The method does not presume anything about the nature of the time course and yet is applicable to branched, active cells receiving simultaneous input from a number of synapses.     

Using Penalized Splines to Model Age‐ and Season‐of‐Birth‐Dependent Effects of Childhood Mortality Risk Factors in Rural Burkina Faso

Several previous studies have identified risk factors for childhood mortality in high risk areas, such as Sub‐Saharan Africa. Among these are lifestyle factors related for example to nutrition or sanitation. Other factors are related to social class, ethnicity and poverty in general. Few studies have investigated a dependence of these factors by age and season of birth which is the focus in this study. We perform a survival analysis of 9121 children born between 1998 and 2001 in a rural area of western Burkina Faso. The whole population is under demographic surveillance since 1993. All cause mortality is used as the endpoint and follow‐up information until the age of five years is available. Recently developed spline regression methods are used for the analysis. Ethnic group, religion, age of mother, twin status, sex, and distance to next health center are used as covariates all of which having a clear effect on survival in standard Cox regression analysis. With penalized spline regression, a more detailed risk pattern is observed. Ethnicity is more related to death at early age, as well as age of mother. The effect of the risk factors considered also appear to be related with season of birth (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Oligonucleotide‐directed mutagenesis for precision gene editing

Differences in gene sequences, many of which are single nucleotide polymorphisms, underlie some of the most important traits in plants. With humanity facing significant challenges to increase global agricultural productivity, there is an urgent need to accelerate the development of these traits in plants. oligonucleotide‐directed mutagenesis (ODM), one of the many tools of Cibus’ Rapid Trait Development System ( RTDS ^?) technology, offers a rapid, precise and non‐transgenic breeding alternative for trait improvement in agriculture to address this urgent need. This review explores the application of ODM as a precision genome editing technology, with emphasis on using oligonucleotides to make targeted edits in plasmid, episomal and chromosomal DNA of bacterial, fungal, mammalian and plant systems. The process of employing ODM by way of RTDS technology has been improved in many ways by utilizing a fluorescence conversion system wherein a blue fluorescent protein (BFP) can be changed to a green fluorescent protein (GFP) by editing a single nucleotide of the BFP gene (CAC→TAC; H66 to Y66). For example, dependent on oligonucleotide length, applying oligonucleotide‐mediated technology to target the BFP transgene in Arabidopsis thaliana protoplasts resulted in up to 0.05% precisely edited GFP loci. Here, the development of traits in commercially relevant plant varieties to improve crop performance by genome editing technologies such as ODM, and by extension RTDS , is reviewed.     

Reduced rank hazard regression with fixed and time‐varying effects of the covariates

Modelling survival data from long‐term follow‐up studies presents challenges. The commonly used proportional hazards model should be extended to account for dynamic behaviour of the effects of fixed covariates. This work illustrates the use of reduced rank models in survival data, where some of the covariate effects are allowed to behave dynamically in time and some as fixed. Time‐varying effects of the covariates can be fitted by using interactions of the fixed covariates with flexible transformations of time based on b‐splines. To avoid overfitting, a reduced rank model will restrict the number of parameters, resulting in a more sensible fit to the data. This work presents the basic theory and the algorithm to fit such models. An application to breast cancer data is used for illustration of the suggested methods.     

Inference for epidemic models with time‐varying infection rates: Tracking the dynamics of oak processionary moth in the UK

1. Invasive pests pose a great threat to forest, woodland, and urban tree ecosystems. The oak processionary moth (OPM) is a destructive pest of oak trees, first reported in the UK in 2006. Despite great efforts to contain the outbreak within the original infested area of South‐East England, OPM continues to spread.
2. Here, we analyze data consisting of the numbers of OPM nests removed each year from two parks in London between 2013 and 2020. Using a state‐of‐the‐art Bayesian inference scheme, we estimate the parameters for a stochastic compartmental SIR (susceptible, infested, and removed) model with a time‐varying infestation rate to describe the spread of OPM.
3. We find that the infestation rate and subsequent basic reproduction number have remained constant since 2013 (with R0 between one and two). This shows further controls must be taken to reduce R0 below one and stop the advance of OPM into other areas of England.
4. Synthesis. Our findings demonstrate the applicability of the SIR model to describing OPM spread and show that further controls are needed to reduce the infestation rate. The proposed statistical methodology is a powerful tool to explore the nature of a time‐varying infestation rate, applicable to other partially observed time series epidemic data.

     

Filamentous fungal characterizations by matrix‐assisted laser desorption/ionization time‐of‐flight mass spectrometry

Matrix‐assisted laser desorption/ionization time‐of‐flight intact cell mass spectrometry (MALDI‐TOF ICMS) is coming of age for the identification and characterization of fungi. The procedure has been used extensively with bacteria. UV‐absorbing matrices function as energy mediators that transfer the absorbed photoenergy from an irradiation source to the surrounding sample molecules, resulting in minimum fragmentation. A surprisingly high number of fungal groups have been studied: (i) the terverticillate penicillia, (ii) aflatoxigenic, black and other aspergilli, (iii) Fusarium, (iv) Trichoderma, (iv) wood rotting fungi (e.g. Serpula lacrymans) and (v) dermatophytes. The technique has been suggested for optimizing quality control of fungal Chinese medicines (e.g. Cordyceps). MALDI‐TOF ICMS offers advantages over PCR. The method is now used in taxonomic assessments (e.g. Trichoderma) as distinct from only strain characterization. Low and high molecular mass natural products (e.g. peptaibols) can be analysed. The procedure is rapid and requires minimal pretreatment. However, issues of reproducibility need to be addressed further in terms of strains of species tested and between run variability. More studies into the capabilities of MALDI‐TOF ICMS to identify fungi are required.     

Stochastic models for inferring genetic regulation from microarray gene expression data

Microarray expression profiles are inherently noisy and many different sources of variation exist in microarray experiments. It is still a significant challenge to develop stochastic models to realize noise in microarray expression profiles, which has profound influence on the reverse engineering of genetic regulation. Using the target genes of the tumour suppressor gene p53 as the test problem, we developed stochastic differential equation models and established the relationship between the noise strength of stochastic models and parameters of an error model for describing the distribution of the microarray measurements. Numerical results indicate that the simulated variance from stochastic models with a stochastic degradation process can be represented by a monomial in terms of the hybridization intensity and the order of the monomial depends on the type of stochastic process. The developed stochastic models with multiple stochastic processes generated simulations whose variance is consistent with the prediction of the error model. This work also established a general method to develop stochastic models from experimental information.     

Modelling time‐varying low‐temperature‐induced mortality rates for pupae of Tuta absoluta (Gelechiidae,Lepidoptera)

In a series of laboratory experiments, acclimated pupae of Tuta absoluta were exposed to various constant low temperatures in order to estimate their maximum survival times (Kaplan–Meier, Lt_99.99). A Weibull function was fitted to the data points, describing maximum survival time as a function of temperature. In another experiment at ?6°C, the progress of mortality increasing with exposure time was identified. These values were fitted by a sigmoidal function converging asymptotically to 100% mortality for very long exposure times. Analysing mortality data from the maximum survival experiment by a generalized linear model showed a significant common slope parameter (p < .001) that reveals parallelism of the survival curves at each temperature if a log time axis is used. These curves appear stretched (time scaled) if plotted with a nonlogarithmic time axis. By combining these mathematical relations, it was possible to calculate a species‐specific ‘mortality surface’ which exhibits mortalities, depending on temperature and duration of exposure. In order to accumulate hourly mortalities for courses of varying temperatures, an algorithm was developed which yields mortality values from that surface taking into account the attained mortality level. In validation experiments, recorded mortalities were compared against modelled mortalities. Prediction of mortality was partially supported by the model, but pupae experiencing intensely fluctuating temperatures showed decreased mortality, probably caused by rapid cold hardening during exposure. Despite this observation, mortality data converged to distinct levels very close to 100% depending on the intensity of temperature fluctuations that were characteristic for different types of experiments. The highest mortality limit occurred at intensely fluctuating temperatures in laboratory experiments. This constituted a benchmark that was not reached under various field conditions. Thus, it was possible to identify temperature limits for the extinction of field populations of Tuta absoluta pupae.     

Cox proportional hazards models with left truncation and time‐varying coefficient: Application of age at event as outcome in cohort studies

When analyzing time‐to‐event cohort data, two different ways of choosing a time scale have been discussed in the literature: time‐on‐study or age at onset of disease. One advantage of choosing the latter is interpretability of the hazard ratio as a function of age. To handle the analysis of age at onset in a principled manner, we present an analysis of the Cox Proportional Hazards model with time‐varying coefficient for left‐truncated and right‐censored data. In the analysis of Northern Manhattan Study (NOMAS) with age at onset of stroke as outcome, we demonstrate that well‐established risk factors may be important only around a certain age span and less established risk factors can have a strong effect in a certain age span.     

Using time‐of‐detection to evaluate detectability assumptions in temporally replicated aural count indices: an example with Ring‐necked Pheasants

ABSTRACT The validity of treating counts as indices to abundance is based on the assumption that the expected detection probability, E(p), is constant over time or comparison groups or, more realistically, that variation in p is small relative to variation in population size that investigators seek to detect. Unfortunately, reliable estimates of E(p) and var(p) are lacking for most index methods. As a case study, we applied the time‐of‐detection method to temporally replicated (within season) aural counts of crowing male Ring‐necked Pheasants (Phasianus colchicus) at 18 sites in southern Minnesota in 2007 to evaluate the detectability assumptions. More specifically, we used the time‐of‐detection method to estimate E(p) and var(p), and then used these estimates in a Monte Carlo simulation to evaluate bias‐variance tradeoffs associated with adjusting count indices for imperfect detection. The estimated mean detection probability in our case study was 0.533 (SE = 0.030) and estimated spatial variation in E(p) was 0.081 (95% CI: 0.057–0.126). On average, both adjusted (for) and unadjusted counts of crowing males qualitatively described the simulated relationship between pheasant abundance and grassland abundance, but the bias‐variance tradeoff was smaller for adjusted counts (MSE = 0.003 vs. 0.045, respectively). Our case study supports the general recommendation to use, whenever feasible, formal population‐estimation procedures (e.g., mark‐recapture, distance sampling, double sampling) to account for imperfect detection. However, we caution that interpreting estimates of absolute abundance can be complicated, even if formal estimation methods are used. For example, the time‐of‐detection method was useful for evaluating detectability assumptions in our case study and the method could be used to adjust aural count indices for imperfect detection. Conversely, using the time‐of‐detection method to estimate absolute abundances in our case study was problematic because the biological populations and sampling coverage could not be clearly delineated. These estimation and inference challenges may also be important in other avian surveys that involve mobile species (whose home ranges may overlap several sampling sites), temporally replicated counts, and inexact sampling coverage.