Probability Range in Damage Predictions as Related to Sampling Decisions

The risk involved in basing a nematode management decision on predicted crop loss is related to the uncertainty in the crop damage function and error in measuring nematode population density. The sampling intensity necessary to measure a nematode population with specified precision varies with population density. Since the density is unknown prior to sampling, optimum sampling intensity for a management decision is calculated for the economic threshold population level associated with the management cost. Population densities below the threshold are measured with greater precision than required; those above the threshold are less precisely measured, but invoke management. The approach described provides resolution to sampling strategies and allows assessment of the risk associated with the management decision.     

Single-cell behavior and population heterogeneity: solving an inverse problem to compute the intrinsic physiological state functions

The dynamics of isogenic cell populations can be described by cell population balance models that account for phenotypic heterogeneity. To utilize the predictive power of these models, however, we must know the rates of single-cell reaction and division and the bivariate partition probability density function. These three intrinsic physiological state (IPS) functions can be obtained by solving an inverse problem that requires knowledge of the phenotypic distributions for the overall cell population, the dividing cell subpopulation and the newborn cell subpopulation. We present here a robust computational procedure that can accurately estimate the IPS functions for heterogeneous cell populations. A detailed parametric analysis shows how the accuracy of the inverse solution is affected by discretization parameters, the type of non-parametric estimators used, the qualitative characteristics of phenotypic distributions and the unknown partitioning probability density function. The effect of finite sampling and measurement errors on the accuracy of the recovered IPS functions is also assessed. Finally, we apply the procedure to estimate the IPS functions of an E. coli population carrying an IPTG-inducible genetic toggle network. This study completes the development of an integrated experimental and computational framework that can become a powerful tool for quantifying single-cell behavior using measurements from heterogeneous cell populations.     

Estimating the optimal bottleneck ratio for experimental evolution: the burst-death model

Population bottlenecks are ubiquitous in nature, and are an inherent feature of the experimental protocol for many laboratory selection experiments. These bottlenecks can have profound effects on the rate and trajectory of evolution. In particular, there is a trade-off between sampling the population too frequently and imposing infrequent, but more severe, bottlenecks. In this paper we consider the effects of population bottlenecks, assuming a burst-death model for the life history of the organism under study. This model assumes that generation times are exponentially distributed and that at each generation, individuals in the population have a fixed number of offspring. The model also allows for a constant death rate between bottlenecks. We use this model to estimate the optimal bottleneck ratio, that is, the fraction of the population that should be sampled at each bottleneck in order to maximize the probability that beneficial mutations occur and are not lost. We find that the optimal ratio is roughly constant with respect to many of the model parameters, and that sampling about 20% of the population will maximize the rate of adaptation.     

Calculation of the minimum number of replicate spots required for detection of significant gene expression fold change in microarray experiments

MOTIVATION: We present statistical methods for determining the number of per gene replicate spots required in microarray experiments. The purpose of these methods is to obtain an estimate of the sampling variability present in microarray data, and to determine the number of replicate spots required to achieve a high probability of detecting a significant fold change in gene expression, while maintaining a low error rate. Our approach is based on data from control microarrays, and involves the use of standard statistical estimation techniques. RESULTS: After analyzing two experimental data sets containing control array data, we were able to determine the statistical power available for the detection of significant differential expression given differing levels of replication. The inclusion of replicate spots on microarrays not only allows more accurate estimation of the variability present in an experiment, but more importantly increases the probability of detecting genes undergoing significant fold changes in expression, while substantially decreasing the probability of observing fold changes due to chance rather than true differential expression.     

Estimation of population allele frequencies from next‐generation sequencing data: pool‐versus individual‐based genotyping

Molecular markers produced by next‐generation sequencing (NGS) technologies are revolutionizing genetic research. However, the costs of analysing large numbers of individual genomes remain prohibitive for most population genetics studies. Here, we present results based on mathematical derivations showing that, under many realistic experimental designs, NGS of DNA pools from diploid individuals allows to estimate the allele frequencies at single nucleotide polymorphisms (SNPs) with at least the same accuracy as individual‐based analyses, for considerably lower library construction and sequencing efforts. These findings remain true when taking into account the possibility of substantially unequal contributions of each individual to the final pool of sequence reads. We propose the intuitive notion of effective pool size to account for unequal pooling and derive a Bayesian hierarchical model to estimate this parameter directly from the data. We provide a user‐friendly application assessing the accuracy of allele frequency estimation from both pool‐ and individual‐based NGS population data under various sampling, sequencing depth and experimental error designs. We illustrate our findings with theoretical examples and real data sets corresponding to SNP loci obtained using restriction site–associated DNA (RAD) sequencing in pool‐ and individual‐based experiments carried out on the same population of the pine processionary moth (Thaumetopoea pityocampa). NGS of DNA pools might not be optimal for all types of studies but provides a cost‐effective approach for estimating allele frequencies for very large numbers of SNPs. It thus allows comparison of genome‐wide patterns of genetic variation for large numbers of individuals in multiple populations.     

Referent sampling,family history and relative risk: the role of length-biased sampling

Familial risk of disease is often assessed using case control studies based on referent databases. A referent database is a collection of family histories of cases typically assembled as a result of one family member being diagnosed with disease. This sampling scheme is equivalent to sampling families proportional to their size. The larger the family, the greater the probability of finding the family in the referent registry. This phenomena is known as length-biased sampling. The consequence of this kind of sampling is to bias the regression estimate associated with family history. The estimate is typically inflated in comparison to what is true for the actual population.     

Estimation of the Optimal Statistical Quality Control Sampling Time Intervals Using a Residual Risk Measure

Background

An open problem in clinical chemistry is the estimation of the optimal sampling time intervals for the application of statistical quality control (QC) procedures that are based on the measurement of control materials. This is a probabilistic risk assessment problem that requires reliability analysis of the analytical system, and the estimation of the risk caused by the measurement error.

Methodology/Principal Findings

Assuming that the states of the analytical system are the reliability state, the maintenance state, the critical-failure modes and their combinations, we can define risk functions based on the mean time of the states, their measurement error and the medically acceptable measurement error. Consequently, a residual risk measure rr can be defined for each sampling time interval. The rr depends on the state probability vectors of the analytical system, the state transition probability matrices before and after each application of the QC procedure and the state mean time matrices. As optimal sampling time intervals can be defined those minimizing a QC related cost measure while the rr is acceptable. I developed an algorithm that estimates the rr for any QC sampling time interval of a QC procedure applied to analytical systems with an arbitrary number of critical-failure modes, assuming any failure time and measurement error probability density function for each mode. Furthermore, given the acceptable rr, it can estimate the optimal QC sampling time intervals.

Conclusions/Significance

It is possible to rationally estimate the optimal QC sampling time intervals of an analytical system to sustain an acceptable residual risk with the minimum QC related cost. For the optimization the reliability analysis of the analytical system and the risk analysis of the measurement error are needed.     

Comparison of asymptotic population growth rates with heterogeneous variances

This report explores how the heterogeneity of variances affects randomization tests used to evaluate differences in the asymptotic population growth rate, λ. The probability of Type I error was calculated in four scenarios for populations with identical λ but different variance of λ: (1) Populations have different projection matrices: the same λ may be obtained from different sets of vital rates, which gives room for different variances of λ. (2) Populations have identical projection matrices but reproductive schemes differ and fecundity in one of the populations has a larger associated variance. The two other scenarios evaluate a sampling artifact as responsible for heterogeneity of variances. The same population is sampled twice, (3) with the same sampling design, or (4) with different sampling effort for different stages. Randomization tests were done with increasing differences in sample size between the two populations. This implies additional differences in the variance of λ. The probability of Type I error keeps at the nominal significance level (α = .05) in Scenario 3 and with identical sample sizes in the others. Tests were too liberal, or conservative, under a combination of variance heterogeneity and different sample sizes. Increased differences in sample size exacerbated the difference between observed Type I error and the nominal significance level. Type I error increases or decreases depending on which population has a larger sample size, the population with the smallest or the largest variance. However, by their own, sample size is not responsible for changes in Type I errors.     

Detection of a colonizing, aquatic, non-indigenous species

Detecting the presence of rare species has interested ecologists and conservation biologists for many years. A particularly daunting application of this problem pertains to the detection of non-indigenous species (NIS) as they colonize new ecosystems. Ethical issues prevent experimental additions of NIS to most natural systems to explore the relationship between sampling intensity and the detection probability of a colonizing NIS. Here we examine this question using a recently introduced water flea, Cercopagis pengoi , in Lake Ontario. The species has biphasic population development, with sexually-produced 'spring morphs' developing prior to parthenogenetically-produced 'typical' morphs. Thus, this biphasic morphology allows distinction between new colonists (spring morphs) from subsequent generations. We repeatedly sampled Hamilton Harbour, Lake Ontario for the presence of both spring and typical morphs. Probability of detection was positively related to both the number of samples taken and animal density in the lake; however, even highly intensive sampling (100 samples) failed to detect the species in early spring when densities were very low. Spatial variation was greatest when densities of Cercopagis were intermediate to low. Sub-sampling, which increased space between adjacent samples, significantly decreased the number of samples required to reach greater, calculated detection probabilities on these dates. Typical sampling protocols for zooplankton have a low probability (< 0.2) of detecting the species unless population density is high. Results of this study suggest that early detection of colonizing, aquatic NIS may be optimized through use of a risk-based sampling design, combined with high sampling intensity in areas deemed most vulnerable to invasion, rather than less intensive sampling at a wider array of sites.     

Estimating the abundance of burrow‐nesting species through the statistical analysis of combined playback and visual surveys

The conservation of elusive species relies on our ability to obtain unbiased estimates of their abundance trends. Many species live or breed in cavities, making it easy to define the search units (the cavity) yet hard to ascertain their occupancy. One such example is that of certain colonial seabirds like petrels and shearwaters, which occupy burrows to breed. In order to increase the chances of detection for these types of species, their sampling can be done using two independent methods to check for cavity occupancy: visual inspection, and acoustic response to a playback call. This double‐detection process allows us to estimate the probability of burrow occupancy by accounting for the probability of detection associated with each method. Here we provide a statistical framework to estimate the occupancy and population size of burrow‐dwelling species. We show how to implement the method using both maximum likelihood and Bayesian approaches, and test its precision and bias using simulated datasets. We subsequently illustrate how to extend the method to situations where two different species may occupy the burrows, and apply it to a dataset on wedge‐tailed shearwaters Puffinus pacificus and tropical shearwaters P. bailloni on Aride Island, Seychelles. The simulations showed that the single‐species model performed well in terms of error and bias except when detection probabilities and occupancies were very low. The two‐species model applied to shearwaters showed that detection probabilities were highly heterogeneous. The population sizes of wedge‐tailed and tropical shearwaters were estimated at 13 716 (95% CI: 12 909–15 874) and 25 550 (23 667–28 777) pairs respectively. The advantages of formulating the call‐playback sampling method statistically is that it provides a framework to calculate uncertainty in the estimates and model assumptions. This method is applicable to a variety of cavity‐dwelling species where two methods can be used to detect cavity occupancy.     

Addressing challenges in non invasive capture-recapture based estimates of small populations: a pilot study on the Apennine brown bear

It is often difficult to determine optimal sampling design for non-invasive genetic sampling, especially when dealing with rare or elusive species depleted of genetic diversity. To address this problem, we ran a hair-snag pilot study on the remnant Apennine brown bear population. We used occupancy models to estimate the performance of an improved field protocol, a meta-analysis approach to indirectly model capture probability, and simulations to evaluate the effect of genotyping errors on the accuracy of capture-recapture population estimates. In spring 2007 we collected 70 bear hair samples in 15 5 × 5 km cells, using 5 10-day trapping sessions. Bear detectability was higher in 2007 than in a previous attempt on the same population in 2004, reflecting improved field protocols and sampling design. However, individual capture probability was 0.136 (95% CI = 0.120–0.152), still below the minimum requirements of capture-mark-recapture closed population models. We genotyped hair samples (n = 63) at 9 microsatellite loci, obtaining 94% Polymerase Chain Reaction success, and 13 bear genotypes. Estimated P_IDsib was 0.00594, and per-genotype error rate was 0.13, corresponding to a 99% probability of correct individual identification. Simulation studies showed that the effect of non-corrected or filtered genetic errors on the accuracy of population estimates was negligible only when individual capture probability was >0.2. Our results underline how the interaction among field protocols, sampling strategies and genotyping errors may affect the accuracy of DNA-based estimates of small and genetically depleted populations, and warned us about the feasibility of a survey using only traditional hair-snag sampling. In this and similar cases, indications from pilot studies can provide cost-effective means to evaluate the efficiency of designed sampling and modelling procedures.     

The labelled mitosis curve for a population consisting of fast and slowly cycling cells

In studies of tumour growth, and particularly of tumour treatment with phase-specific chemotherapeutic agents, the fraction labelled mitosis technique is frequently used to estimate the kinetic properties of the cell population making up the tumour. We show here that the FLM technique is in principle very insensitive to the behaviour of slowly cycling cells, even if these constitute a large proportion of the total cell population. Furthermore, since the rate of DNA synthesis is frequently lower in slowly growing cells than in those growing rapidly, there is a higher probability of labelling error associated with the former cells. In view of these theoretical and experimental considerations, it is suggested that considerable caution be used when applying the FLM technique to heterogeneous cell populations such as those of solid tumours.     

Evolutionary rescue under demographic and environmental stochasticity

Populations suffer two types of stochasticity: demographic stochasticity, from sampling error in offspring number, and environmental stochasticity, from temporal variation in the growth rate. By modelling evolution through phenotypic selection following an abrupt environmental change, we investigate how genetic and demographic dynamics, as well as effects on population survival of the genetic variance and of the strength of stabilizing selection, differ under the two types of stochasticity. We show that population survival probability declines sharply with stronger stabilizing selection under demographic stochasticity, but declines more continuously when environmental stochasticity is strengthened. However, the genetic variance that confers the highest population survival probability differs little under demographic and environmental stochasticity. Since the influence of demographic stochasticity is stronger when population size is smaller, a slow initial decline of genetic variance, which allows quicker evolution, is important for population persistence. In contrast, the influence of environmental stochasticity is population-size-independent, so higher initial fitness becomes important for survival under strong environmental stochasticity. The two types of stochasticity interact in a more than multiplicative way in reducing the population survival probability. Our work suggests the importance of explicitly distinguishing and measuring the forms of stochasticity during evolutionary rescue.     

Risk-targeted selection of agricultural holdings for post-epidemic surveillance: estimation of efficiency gains

Current post-epidemic sero-surveillance uses random selection of animal holdings. A better strategy may be to estimate the benefits gained by sampling each farm and use this to target selection. In this study we estimate the probability of undiscovered infection for sheep farms in Devon after the 2001 foot-and-mouth disease outbreak using the combination of a previously published model of daily infection risk and a simple model of probability of discovery of infection during the outbreak. This allows comparison of the system sensitivity (ability to detect infection in the area) of arbitrary, random sampling compared to risk-targeted selection across a full range of sampling budgets. We show that it is possible to achieve 95% system sensitivity by sampling, on average, 945 farms with random sampling and 184 farms with risk-targeted sampling. We also examine the effect of ordering samples by risk to expedite return to a disease-free status. Risk ordering the sampling process results in detection of positive farms, if present, 15.6 days sooner than with randomly ordered sampling, assuming 50 farms are tested per day.     

Improving Aquatic Warbler Population Assessments by Accounting for Imperfect Detection

Monitoring programs designed to assess changes in population size over time need to account for imperfect detection and provide estimates of precision around annual abundance estimates. Especially for species dependent on conservation management, robust monitoring is essential to evaluate the effectiveness of management. Many bird species of temperate grasslands depend on specific conservation management to maintain suitable breeding habitat. One such species is the Aquatic Warbler (Acrocephalus paludicola), which breeds in open fen mires in Central Europe. Aquatic Warbler populations have so far been assessed using a complete survey that aims to enumerate all singing males over a large area. Because this approach provides no estimate of precision and does not account for observation error, detecting moderate population changes is challenging. From 2011 to 2013 we trialled a new line transect sampling monitoring design in the Biebrza valley, Poland, to estimate abundance of singing male Aquatic Warblers. We surveyed Aquatic Warblers repeatedly along 50 randomly placed 1-km transects, and used binomial mixture models to estimate abundances per transect. The repeated line transect sampling required 150 observer days, and thus less effort than the traditional ‘full count’ approach (175 observer days). Aquatic Warbler abundance was highest at intermediate water levels, and detection probability varied between years and was influenced by vegetation height. A power analysis indicated that our line transect sampling design had a power of 68% to detect a 20% population change over 10 years, whereas raw count data had a 9% power to detect the same trend. Thus, by accounting for imperfect detection we increased the power to detect population changes. We recommend to adopt the repeated line transect sampling approach for monitoring Aquatic Warblers in Poland and in other important breeding areas to monitor changes in population size and the effects of habitat management.     

Assessing anostracan (Crustacea: Branchiopoda) cyst bank size: An attempt at a standardized method

Egg (cyst) banks play a fundamental role in the survival strategy of the hydrobionts of temporary pools. Therefore a quantitative estimate, as accurate as possible, of their size is the starting point for all the possible considerations concerning the life history of the inhabiting populations. We describe here, in some details, a sampling procedure to evaluate the number of cysts laid by the anostracan Chirocephalus ruffoi Cottarelli & Mura, 1984, in an experimental pool and we show that this procedure results in a good estimate of the cyst bank consistency. A pool 150 cm in diameter was divided into five concentrical rings, 13 cm apart from each other, and a central core (with a 10 cm radius). The number of samples needed to obtain an accurate estimate was calculated by taking into account that, to perform uniform sampling, the total volume of the samples must be proportional to the volume of the pool bed in each ring. The number of cysts in each of the rings was then estimated by considering the mean of the experimental results of a previous study (61 core samples along six transects across the pool itself), multiplied by the number of samples ideally performed in each sector. Evaluating the cyst bank size by the above method resulted in an estimate with an error of only 4% compared to the real cyst bank size. We also show that the number of samples needed can significantly be reduced, with an error on the total number of cysts that can be controlled. This result, that follows from statistical considerations on the confidence interval for the mean, allows us to obtain a general sampling procedure that can be applied to statistically comparable pools.     

Wind Power Error Estimation in Resource Assessments

Estimating the power output is one of the elements that determine the techno-economic feasibility of a renewable project. At present, there is a need to develop reliable methods that achieve this goal, thereby contributing to wind power penetration. In this study, we propose a method for wind power error estimation based on the wind speed measurement error, probability density function, and wind turbine power curves. This method uses the actual wind speed data without prior statistical treatment based on 28 wind turbine power curves, which were fitted by Lagrange''s method, to calculate the estimate wind power output and the corresponding error propagation. We found that wind speed percentage errors of 10% were propagated into the power output estimates, thereby yielding an error of 5%. The proposed error propagation complements the traditional power resource assessments. The wind power estimation error also allows us to estimate intervals for the power production leveled cost or the investment time return. The implementation of this method increases the reliability of techno-economic resource assessment studies.     

Gene Conversion at the Gray Locus of SORDARIA FIMICOLA: Fit of the Experimental Data to a Hybrid DNA Model of Recombination

A hybrid DNA (hDNA) model of recombination has been algebraically formulated, which allows the prediction of frequencies of postmeiotic segregation and conversion of a given allele and their probability of being associated with a crossing over. The model considered is essentially the "Aviemore model." In contrast to some other interpretations of recombination, it states that gene conversion can only result from the repair of heteroduplex hDNA, with postmeiotic segregation resulting from unrepaired heteroduplexes. The model also postulates that crossing over always occurs distally to the initiation site of the hDNA. Eleven types of conversion and postmeiotic segregation with or without associated crossover were considered. Their theoretical frequencies are given by 11 linear equations with ten variables, four describing heteroduplex repair, four giving the probability of hDNA formation and its topological properties and two giving the probability that crossing over occurs at the left or right of the converting allele. Using the experimental data of Kitani and coworkers on conversion at the six best studied gray alleles of Sordaria fimicola, we found that the model considered fit the data at a P level above or very close (allele h4) to the 5% level of sampling error provided that the hDNA is partly asymmetric. The best fitting solutions are such that the hDNA has an equal probability of being formed on either chromatid or, alternatively, that both DNA strands have the same probability of acting as the invading strand during hDNA formation. The two mismatches corresponding to a given allele are repaired with different efficiencies. Optimal solutions are found if one allows for repair to be more efficient on the asymmetric hDNA than on the symmetric one. In the case of allele g1, our data imply that the direction of repair is nonrandom with respect to the strand on which it occurs.     

A semiparametric empirical likelihood method for biased sampling schemes with auxiliary covariates

We consider a semiparametric inference procedure for data from epidemiologic studies conducted with a two-component sampling scheme where both a simple random sample and multiple outcome- or outcome-/auxiliary-dependent samples are observed. This sampling scheme allows the investigators to oversample certain subpopulations believed to have more information about the regression model while still gaining insights about the underlying population through the simple random sample. We focus on settings where there is no additional information about the parent cohort and the sampling probability is nonidentifiable. We motivate our problem with an ongoing study to assess the association between the mutation level of epidermal growth factor receptor (EGFR) and the antitumor response to EGFR-targeted therapy among nonsmall cell lung cancer patients. The proposed method applies to both binary and multicategorical outcome data and allows an arbitrary link function in the framework of generalized linear models. Simulation studies show that the proposed estimator has nice small sample properties. The proposed method is illustrated with a data example.     

Combining band recovery data and Pollock's robust design to model temporary and permanent emigration

Capture-recapture models are widely used to estimate demographic parameters of marked populations. Recently, this statistical theory has been extended to modeling dispersal of open populations. Multistate models can be used to estimate movement probabilities among subdivided populations if multiple sites are sampled. Frequently, however, sampling is limited to a single site. Models described by Burnham (1993, in Marked Individuals in the Study of Bird Populations, 199-213), which combined open population capture-recapture and band-recovery models, can be used to estimate permanent emigration when sampling is limited to a single population. Similarly, Kendall, Nichols, and Hines (1997, Ecology 51, 563-578) developed models to estimate temporary emigration under Pollock's (1982, Journal of Wildlife Management 46, 757-760) robust design. We describe a likelihood-based approach to simultaneously estimate temporary and permanent emigration when sampling is limited to a single population. We use a sampling design that combines the robust design and recoveries of individuals obtained immediately following each sampling period. We present a general form for our model where temporary emigration is a first-order Markov process, and we discuss more restrictive models. We illustrate these models with analysis of data on marked Canvasback ducks. Our analysis indicates that probability of permanent emigration for adult female Canvasbacks was 0.193 (SE = 0.082) and that birds that were present at the study area in year i - 1 had a higher probability of presence in year i than birds that were not present in year i - 1.