Statistical properties of population differentiation estimators under stepwise mutation in a finite island model.

Microsatellite loci mutate at an extremely high rate and are generally thought to evolve through a stepwise mutation model. Several differentiation statistics taking into account the particular mutation scheme of the microsatellite have been proposed. The most commonly used is R(ST) which is independent of the mutation rate under a generalized stepwise mutation model. F(ST) and R(ST) are commonly reported in the literature, but often differ widely. Here we compare their statistical performances using individual-based simulations of a finite island model. The simulations were run under different levels of gene flow, mutation rates, population number and sizes. In addition to the per locus statistical properties, we compare two ways of combining R(ST) over loci. Our simulations show that even under a strict stepwise mutation model, no statistic is best overall. All estimators suffer to different extents from large bias and variance. While R(ST) better reflects population differentiation in populations characterized by very low gene-exchange, F(ST) gives better estimates in cases of high levels of gene flow. The number of loci sampled (12, 24, or 96) has only a minor effect on the relative performance of the estimators under study. For all estimators there is a striking effect of the number of samples, with the differentiation estimates showing very odd distributions for two samples.

Analysis of a finite volume method for a cross-diffusion model in population dynamics

The main goal of this paper is to propose a convergent finite volume method for a reactionâeuro"diffusion system with cross-diffusion. First, we sketch an existence proof for a class of cross-diffusion systems. Then the standard two-point finite volume fluxes are used in combination with a nonlinear positivity-preserving approximation of the cross-diffusion coefficients. Existence and uniqueness of the approximate solution are addressed, and it is also shown that the scheme converges to the corresponding weak solution for the studied model. Furthermore, we provide a stability analysis to study pattern-formation phenomena, and we perform two-dimensional numerical examples which exhibit formation of nonuniform spatial patterns. From the simulations it is also found that experimental rates of convergence are slightly below second order. The convergence proof uses two ingredients of interest for various applications, namely the discrete Sobolev embedding inequalities with general boundary conditions and a space-time $L^1$ compactness argument that mimics the compactness lemma due to Kruzhkov. The proofs of these results are given in the Appendix.

An expression of mixed animal model equations to account for different means and variances in the base population

This paper presents a general expression to predict breeding values using animal models when the base population is selected, i.e. the means and variances of breeding values in the base generation differ among individuals. Rules for forming the mixed model equations are also presented. A numerical example illustrates the procedure.

A Population-Based Model to Consider the Effect of Seasonal Variation on Serum 25(OH)D and Vitamin D Status.

Background. We elaborated a model that predicts the centiles of the 25(OH)D distribution taking into account seasonal variation. Methods. Data from two Swiss population-based studies were used to generate (CoLaus) and validate (Bus Santé) the model. Serum 25(OH)D was measured by ultra high pressure LC-MS/MS and immunoassay. Linear regression models on square-root transformed 25(OH)D values were used to predict centiles of the 25(OH)D distribution. Distribution functions of the observations from the replication set predicted with the model were inspected to assess replication. Results. Overall, 4,912 and 2,537 Caucasians were included in original and replication sets, respectively. Mean (SD) 25(OH)D, age, BMI, and % of men were 47.5 (22.1) nmol/L, 49.8 (8.5) years, 25.6 (4.1) kg/m(2), and 49.3% in the original study. The best model included gender, BMI, and sin-cos functions of measurement day. Sex- and BMI-specific 25(OH)D centile curves as a function of measurement date were generated. The model estimates any centile of the 25(OH)D distribution for given values of sex, BMI, and date and the quantile corresponding to a 25(OH)D measurement. Conclusions. We generated and validated centile curves of 25(OH)D in the general adult Caucasian population. These curves can help rank vitamin D centile independently of when 25(OH)D is measured.

Development of a population-based cost-effectiveness model of chronic graft versus host disease in Spain

Chronic graft-versus-host disease (cGvHD) is the leading cause of late nonrelapse mortality (transplant-related mortality) after hematopoietic stem cell transplant. Given that there are a wide range of treatment options for cGvHD, assessment of the associated costs and efficacy can help clinicians and health care providers allocate health care resources more efficiently. OBJECTIVE: The purpose of this study was to assess the cost-effectiveness of extracorporeal photopheresis (ECP) compared with rituximab (Rmb) and with imatinib (Imt) in patients with cGvHD at 5 years from the perspective of the Spanish National Health System. METHODS: The model assessed the incremental cost-effectiveness/utility ratio of ECP versus Rmb or Imt for 1000 hypothetical patients by using microsimulation cost-effectiveness techniques. Model probabilities were obtained from the literature. Treatment pathways and adverse events were evaluated taking clinical opinion and published reports into consideration. Local data on costs (2010 Euros) and health care resources utilization were validated by the clinical authors. Probabilistic sensitivity analyses were used to assess the robustness of the model. RESULTS: The greater efficacy of ECP resulted in a gain of 0.011 to 0.024 quality-adjusted life-year in the first year and 0.062 to 0.094 at year 5 compared with Rmb or Imt. The results showed that the higher acquisition cost of ECP versus Imt was compensated for at 9 months by greater efficacy; this higher cost was partially compensated for ( 517) by year 5 versus Rmb. After 9 months, ECP was dominant (cheaper and more effective) compared with Imt. The incremental cost-effectiveness ratio of ECP versus Rmb was 29,646 per life-year gained and 24,442 per quality-adjusted life-year gained at year 2.5. Probabilistic sensitivity analysis confirmed the results. The main study limitation was that to assess relative treatment effects, only small studies were available for indirect comparison. CONCLUSION: ECP as a third-line therapy for cGvHD is a more cost-effective strategy than Rmb or Imt.

A new model for the population pharmacokinetics of didanosine in healthy subjects

Didanosine (ddI) is a component of highly active antiretroviral therapy drug combinations, used especially in resource-limited settings and in zidovudine-resistant patients. The population pharmacokinetics of ddI was evaluated in 48 healthy volunteers enrolled in two bioequivalence studies. These data, along with a set of co-variates, were the subject of a nonlinear mixed-effect modeling analysis using the NONMEM program. A two-compartment model with first order absorption (ADVAN3 TRANS3) was fitted to the serum ddI concentration data. Final pharmacokinetic parameters, expressed as functions of the co-variates gender and creatinine clearance (CL CR), were: oral clearance (CL = 55.1 + 240 x CL CR + 16.6 L/h for males and CL = 55.1 + 240 x CL CR for females), central volume (V2 = 9.8 L), intercompartmental clearance (Q = 40.9 L/h), peripheral volume (V3 = 62.7 + 22.9 L for males and V3 = 62.7 L for females), absorption rate constant (Ka = 1.51/h), and dissolution time of the tablet (D = 0.43 h). The intraindividual (residual) variability expressed as coefficient of variation was 13.0%, whereas the interindividual variability of CL, Q, V3, Ka, and D was 20.1, 75.8, 20.6, 18.9, and 38.2%, respectively. The relatively high (>30%) interindividual variability for some of these parameters, observed under the controlled experimental settings of bioequivalence trials in healthy volunteers, may result from genetic variability of the processes involved in ddI absorption and disposition.

Male gonadal function, prolactin secretion and lactotroph population in an experimental model of cirrhosis

Liver cirrhosis, a highly prevalent chronic disease, is frequently associated with endocrine dysfunctions, notably in the gonadal axis. We evaluated lactotroph population by immunohistochemistry, gonadotropins and prolactin by immunoradiometric assay and testosterone and estradiol by radioimmunoassay in adult male Wistar rats with cirrhosis induced by carbon tetrachloride. No significant difference in mean ± SEM percentages of lactotrophs was found between cirrhotic animals and controls (N = 12, mean 18.95 ± 1.29%). Although there was no significant difference between groups in mean serum levels of prolactin (control: 19.2 ± 4 ng/mL), luteinizing hormone (control: 1.58 ± 0.43 ng/mL), follicle-stimulating hormone (control: 19.11 ± 2.28 ng/mL), estradiol (control: 14.65 ± 3.22 pg/mL), and total testosterone (control: 138.41 ± 20.07 ng/dL), 5 of the cirrhotic animals presented a hormonal profile consistent with hypogonadism, all of them pointing to a central origin of this dysfunction. Four of these animals presented high levels of estradiol and/or prolactin, with a significant correlation between these two hormones in both groups (r = 0.54; P = 0.013). It was possible to detect the presence of central hypogonadism in this model of cirrhotic animals. The hyperestrogenemia and hyperprolactinemia found in some hypogonadal animals suggest a role in the genesis of hypogonadism, and in the present study they were not associated with lactotroph hyperplasia.

A Demographic Model to Evaluate Population Declines in the Endangered Streaked Horned Lark

The Streaked Horned Lark (Eremophila alpestris strigata) is listed as endangered by the State of Washington, USA and by Canada under the Species at Risk Act and is also classified as a federal candidate for listing under the Endangered Species Act in the USA. A substantial portion of Streaked Horned Lark habitat has been lost or degraded, and range contraction has occurred in Oregon, Washington, and British Columbia. We estimate the vital rates (fecundity, adult and juvenile survival) and population growth rate (λ) for Streaked Horned Larks breeding in Washington, USA and conduct a Life-Stage Simulation Analysis (LSA) to evaluate which vital rate has the greatest influence on λ. We simulated changes in the three vital rates to examine how much they would need to be adjusted either independently or in concert to achieve a stable Streaked Horned Lark population (λ = 1). We also evaluated which fecundity component (the number of fledglings per egg laid or renesting interval) had the greatest impact on λ. The estimate of population growth suggests that Streaked Horned Larks in Washington are declining rapidly (λ = 0.62 ± 0.10) and that local breeding sites are not sustainable without immigration. The LSA results indicate that adult survival had the greatest influence on λ, followed by juvenile survival and fecundity. However, increases in vital rates led to λ = 1 only when adult survival was raised from 0.47 to 0.85, juvenile survival from 0.17 to 0.58, and fecundity from 0.91 to 3.09. Increases in breeding success and decreases in the renesting interval influenced λ similarly; however, λ did not reach 1 even when breeding success was raised to 100% or renesting intervals were reduced to 1 day. Only when all three vital rates were increased simultaneously did λ approach 1 without requiring highly unrealistic increases in each vital rate. We conclude that conservation activities need to target all or multiple vital rates to be successful. The baseline data presented here and subsequent efforts to manage Streaked Horned Larks will provide valuable information for management of other declining Horned Lark subspecies and other grassland songbirds across North America.

The effects of environmental perturbation and measurement error on estimates of the shape parameter in the theta-logistic model of population regulation

The theta-logistic is a widely used generalisation of the logistic model of regulated biological processes which is used in particular to model population regulation. Then the parameter theta gives the shape of the relationship between per-capita population growth rate and population size. Estimation of theta from population counts is however subject to bias, particularly when there are measurement errors. Here we identify factors disposing towards accurate estimation of theta by simulation of populations regulated according to the theta-logistic model. Factors investigated were measurement error, environmental perturbation and length of time series. Large measurement errors bias estimates of theta towards zero. Where estimated theta is close to zero, the estimated annual return rate may help resolve whether this is due to bias. Environmental perturbations help yield unbiased estimates of theta. Where environmental perturbations are large, estimates of theta are likely to be reliable even when measurement errors are also large. By contrast where the environment is relatively constant, unbiased estimates of theta can only be obtained if populations are counted precisely Our results have practical conclusions for the design of long-term population surveys. Estimation of the precision of population counts would be valuable, and could be achieved in practice by repeating counts in at least some years. Increasing the length of time series beyond ten or 20 years yields only small benefits. if populations are measured with appropriate accuracy, given the level of environmental perturbation, unbiased estimates can be obtained from relatively short censuses. These conclusions are optimistic for estimation of theta. (C) 2008 Elsevier B.V All rights reserved.

A bagging-based correction for the mixture model estimator of population size

Estimation of a population size by means of capture-recapture techniques is an important problem occurring in many areas of life and social sciences. We consider the frequencies of frequencies situation, where a count variable is used to summarize how often a unit has been identified in the target population of interest. The distribution of this count variable is zero-truncated since zero identifications do not occur in the sample. As an application we consider the surveillance of scrapie in Great Britain. In this case study holdings with scrapie that are not identified (zero counts) do not enter the surveillance database. The count variable of interest is the number of scrapie cases per holding. For count distributions a common model is the Poisson distribution and, to adjust for potential heterogeneity, a discrete mixture of Poisson distributions is used. Mixtures of Poissons usually provide an excellent fit as will be demonstrated in the application of interest. However, as it has been recently demonstrated, mixtures also suffer under the so-called boundary problem, resulting in overestimation of population size. It is suggested here to select the mixture model on the basis of the Bayesian Information Criterion. This strategy is further refined by employing a bagging procedure leading to a series of estimates of population size. Using the median of this series, highly influential size estimates are avoided. In limited simulation studies it is shown that the procedure leads to estimates with remarkable small bias.

The determination of total nitrogen and total phosphorus concentrations in freshwaters from land use, stock headage and population data: testing of a model for use in conservation and water quality management

1. Nutrient concentrations (particularly N and P) determine the extent to which water bodies are or may become eutrophic. Direct determination of nutrient content on a wide scale is labour intensive but the main sources of N and P are well known. This paper describes and tests an export coefficient model for prediction of total N and total P from: (i) land use, stock headage and human population; (ii) the export rates of N and P from these sources; and (iii) the river discharge. Such a model might be used to forecast the effects of changes in land use in the future and to hindcast past water quality to establish comparative or baseline states for the monitoring of change. 2. The model has been calibrated against observed data for 1988 and validated against sets of observed data for a sequence of earlier years in ten British catchments varying from uplands through rolling, fertile lowlands to the flat topography of East Anglia. 3. The model predicted total N and total P concentrations with high precision (95% of the variance in observed data explained). It has been used in two forms: the first on a specific catchment basis; the second for a larger natural region which contains the catchment with the assumption that all catchments within that region will be similar. Both models gave similar results with little loss of precision in the latter case. This implies that it will be possible to describe the overall pattern of nutrient export in the UK with only a fraction of the effort needed to carry out the calculations for each individual water body. 4. Comparison between land use, stock headage, population numbers and nutrient export for the ten catchments in the pre-war year of 1931, and for 1970 and 1988 show that there has been a substantial loss of rough grazing to fertilized temporary and permanent grasslands, an increase in the hectarage devoted to arable, consistent increases in the stocking of cattle and sheep and a marked movement of humans to these rural catchments. 5. All of these trends have increased the flows of nutrients with more than a doubling of both total N and total P loads during the period. On average in these rural catchments, stock wastes have been the greatest contributors to both N and P exports, with cultivation the next most important source of N and people of P. Ratios of N to P were high in 1931 and remain little changed so that, in these catchments, phosphorus continues to be the nutrient most likely to control algal crops in standing waters supplied by the rivers studied.

Experimental evidence and model explanation for cell population characteristics modification when applying sequential photodynamic therapy

We present experimental evidence of the existence of cell variability in terms of threshold light dose for Hep G2 (liver cancer cells) cultured. Using a theoretical model to describe the effects caused by successive photodynamic therapy (PDT) sessions, and based on the consequences of a partial response we introduce the threshold dose distribution concept within a tumor. The experimental model consists in a stack of flasks, and simulates subsequent layers of a tissue exposed to PDT application. The result indicates that cells from the same culture could respond in different ways to similar PDT induced-damages. Moreover, the consequence is a partial killing of the cells submitted to PDT, and the death fraction decreased at each in vitro PDT session. To demonstrate the occurrence of cell population modification as a response to PDT, we constructed a simple theoretical model and assumed that the threshold dose distribution for a cell population of a tumor is represented by a modified Gaussian distribution.

Predicting random effects with an expanded finite population mixed model

Prediction of random effects is an important problem with expanding applications. In the simplest context, the problem corresponds to prediction of the latent value (the mean) of a realized cluster selected via two-stage sampling. Recently, Stanek and Singer [Predicting random effects from finite population clustered samples with response error. J. Amer. Statist. Assoc. 99, 119-130] developed best linear unbiased predictors (BLUP) under a finite population mixed model that outperform BLUPs from mixed models and superpopulation models. Their setup, however, does not allow for unequally sized clusters. To overcome this drawback, we consider an expanded finite population mixed model based on a larger set of random variables that span a higher dimensional space than those typically applied to such problems. We show that BLUPs for linear combinations of the realized cluster means derived under such a model have considerably smaller mean squared error (MSE) than those obtained from mixed models, superpopulation models, and finite population mixed models. We motivate our general approach by an example developed for two-stage cluster sampling and show that it faithfully captures the stochastic aspects of sampling in the problem. We also consider simulation studies to illustrate the increased accuracy of the BLUP obtained under the expanded finite population mixed model. (C) 2007 Elsevier B.V. All rights reserved.