An analytical framework for estimating aquatic species density from environmental DNA

Environmental DNA (eDNA) analysis of water samples is on the brink of becoming a standard monitoring method for aquatic species. This method has improved detection rates over conventional survey methods and thus has demonstrated effectiveness for estimation of site occupancy and species distribution. The frontier of eDNA applications, however, is to infer species density. Building upon previous studies, we present and assess a modeling approach that aims at inferring animal density from eDNA. The modeling combines eDNA and animal count data from a subset of sites to estimate species density (and associated uncertainties) at other sites where only eDNA data are available. As a proof of concept, we first perform a cross‐validation study using experimental data on carp in mesocosms. In these data, fish densities are known without error, which allows us to test the performance of the method with known data. We then evaluate the model using field data from a study on a stream salamander species to assess the potential of this method to work in natural settings, where density can never be known with absolute certainty. Two alternative distributions (Normal and Negative Binomial) to model variability in eDNA concentration data are assessed. Assessment based on the proof of concept data (carp) revealed that the Negative Binomial model provided much more accurate estimates than the model based on a Normal distribution, likely because eDNA data tend to be overdispersed. Greater imprecision was found when we applied the method to the field data, but the Negative Binomial model still provided useful density estimates. We call for further model development in this direction, as well as further research targeted at sampling design optimization. It will be important to assess these approaches on a broad range of study systems.     

A stochastic catch-effort method for estimating animal abundance

A method for estimating the size of a heavily exploited animal population from catch data and relative-harvest-effort data is presented. The method assumes a competing-risk model of adult deaths and captures that is similar to the hazard-regression model of Cox (1972, Journal of the Royal Statistical Society, Series B 34, 187-220). This model avoids making any assumptions about birth rates or juvenile mortality rates, and allows the user to incorporate an arbitrary number of time-dependent covariates into the natural and catch hazard functions. Estimates of the population's size, together with asymptotic error bounds and predictions of subsequent catches, are derived from maximum likelihood estimates of the parameters of the model. A simulation study is presented which indicates that this method is far more accurate than previously available catch-effort techniques. The method is illustrated with some fisheries data. A series of models is fitted to the data with the objective of improving the goodness of fit while maintaining biologic plausibility of the model. In this example a 68% reduction in the mean sum of squares for error is obtained and the accuracy of future catch predictions is greatly improved. This method is particularly appropriate for estimating the sizes of commercially exploited aquatic populations whose sizes are too large to make mark-recapture techniques feasible, and which are not amenable to line-transect techniques.     

An alternative method of estimating the cranial capacity of Olduvai Hominid 7

The cranial capacity of Olduvai Hominid 7 is estimated to be 690 cc, with a standard uncertainty range of 538 to 868 cc. The estimate is derived from a systematic consideration of the relationships between Bregma-Asterion chords and cranial capacities obtained from a large sample of Homo sapiens and Pan troglodytes and from available fossil hominids. The estimation technique is applicable to other characters and specimens.     

An alternative stochastic model of generation of oligodendrocytes in cell culture

According to our previous model, oligodendrocyte – type 2 (O-2A) astrocyte progenitor cells become competent for differentiation in vitro after they complete a certain number of critical mitotic cycles. After attaining the competency to differentiate, progenitor cells divide with fixed probability p in subsequent cycles. The number of critical cycles is random; analysis of data suggests that it varies from zero to two. The present paper presents an alternative model in which there are no critical cycles, and the probability that a progenitor cell will divide again decreases gradually to a plateau value as the number of completed mitotic cycles increases. In particular all progenitor cells have the ability to differentiate from the time of plating. The Kiefer-Wolfowitz procedure is used to fit the new model to experimental data on the clonal growth of purified O-2A progenitor cells obtained from the optic nerves of 7 day old rats. The new model is shown to fit the experimental data well, indicating that it is not possible to determine whether critical cycles exist on the basis of these experimental data. In contrast to the fit of the previous model, which suggested that the addition of thyroid hormone increased the limiting probability of differentiation as the number of mitotic cycles increases, the fit of the new model suggests that the addition of thyroid hormone has almost no effect on the limiting probability of differentiation. Received: 6 March 2000 / Revised version: 18 September 2000 / Published online: 30 April 2001     

A framework for estimating the sensitivity of eDNA surveys

Imperfect sensitivity, or imperfect detection, is a feature of all survey methods that needs to be accounted for when interpreting survey results. Detection of environmental DNA (eDNA) is increasingly being used to infer species distributions, yet the sensitivity of the technique has not been fully evaluated. Sensitivity, or the probability of detecting target DNA given it is present at a site, will depend on both the survey method and the concentration and dispersion of target DNA molecules at a site. We present a model to estimate target DNA concentration and dispersion at survey sites and to estimate the sensitivity of an eDNA survey method. We fitted this model to data from a species‐specific eDNA survey for Oriental weatherloach, Misgurnus anguillicaudatus, at three sites sampled in both autumn and spring. The concentration of target DNA molecules was similar at all three sites in autumn but much higher at two sites in spring. Our analysis showed the survey method had ≥95% sensitivity at sites where target DNA concentrations were ≥11 molecules per litre. We show how these data can be used to compare sampling schemes that differ in the number of field samples collected per site and number of PCR replicates per sample to achieve ≥95% sensitivity at a given target DNA concentration. These models allow researchers to quantify the sensitivity of eDNA survey methods to optimize the probability of detecting target species, and to compare DNA concentrations spatially and temporarily.     

Diagnostic measures for empirical likelihood of general estimating equations

We develop diagnostic measures for assessing the influence ofindividual observations when using empirical likelihood withgeneral estimating equations, and we use these measures to constructgoodness-of-fit statistics for testing possible misspecificationin the estimating equations. Our diagnostics include case-deletionmeasures, local influence measures and pseudo-residuals. Ourgoodness-of-fit statistics include the sum of local influencemeasures and the processes of pseudo-residuals. Simulation studiesare conducted to evaluate our methods, and real datasets areanalyzed to illustrate the use of our diagnostic measures andgoodness-of-fit statistics.     

Generalized method of moments for estimating parameters of stochastic reaction networks

Background

Discrete-state stochastic models have become a well-established approach to describe biochemical reaction networks that are influenced by the inherent randomness of cellular events. In the last years several methods for accurately approximating the statistical moments of such models have become very popular since they allow an efficient analysis of complex networks.

Results

We propose a generalized method of moments approach for inferring the parameters of reaction networks based on a sophisticated matching of the statistical moments of the corresponding stochastic model and the sample moments of population snapshot data. The proposed parameter estimation method exploits recently developed moment-based approximations and provides estimators with desirable statistical properties when a large number of samples is available. We demonstrate the usefulness and efficiency of the inference method on two case studies.

Conclusions

The generalized method of moments provides accurate and fast estimations of unknown parameters of reaction networks. The accuracy increases when also moments of order higher than two are considered. In addition, the variance of the estimator decreases, when more samples are given or when higher order moments are included.

     

Some further results from a stochastic fertility model for women

Any realistic model of human fertility should encompass the distributions and interactions of three time intervals a fecund married woman may experience repeatedly in her childbearing period: (1) waiting time for a conception, (2) gestation period, and (3) period of postpartum amenorrhea. Perrin & Sheps (1964) presented a model in which human reproduction is viewed as a Markov renewal process with a finite number of states. Das Gupta (1973b) presented a general probability model of fertility along the lines suggested by Perrin & Sheps which removes two limitations of their model. First, it does not assume that the distributions of durations of stay in the fertility states are independent of each other. Second, it allows us to study the effect of breast-feeding on demographic characteristics, such as interval between live births or birth rate. Results derived in Das Gupta (1973b) include the distributions of time intervals and the exact probabilities of different states at a particular time. The present paper includes additional results pertaining to the same general model, such as the distribution of number of conceptions in a fixed period of time, the distribution of time needed for a fixed number of conceptions, pregnancy rate and fertility rate, and the distribution of the time elapsed since last live birth. The general results are applied to specific models to obtain some known results.     

A method for estimating stochastic noise in large genetic regulatory networks

MOTIVATION: Genetic regulatory networks are often affected by stochastic noise, due to the low number of molecules taking part in certain reactions. The networks can be simulated using stochastic techniques that model each reaction as a stochastic event. As models become increasingly large and sophisticated, however, the solution time can become excessive; particularly if one wishes to determine the effect on noise of changes to a series of parameters, or the model structure. Methods are therefore required to rapidly estimate stochastic noise. RESULTS: This paper presents an algorithm, based on error growth techniques from non-linear dynamics, to rapidly estimate the noise characteristics of genetic networks of arbitrary size. The method can also be used to determine analytical solutions for simple sub-systems. It is demonstrated on a number of cases, including a prototype model of the galactose regulatory pathway in yeast. AVAILABILITY: A software tool which incorporates the algorithm is available for use as part of the stochastic simulation package Dizzy. It is available for download at http://labs.systemsbiology.net/bolouri/software/Dizzy/ CONTACT: dorrell@systemsbiology.org SUPPLEMENTARY INFORMATION: A conceptual model of the regulatory part of the galactose utilization pathway in yeast, used as an example in the paper, is available at http://labs.systemsbiology.net/bolouri/models/galconcept.dizzy     

A genome evolution-based framework for measures of originality for clades

To evaluate the originality of a species for determining its conservation priority, most indices use the branching pattern and the branch length of a phylogenetic tree to represent the diversification pattern and the number of characters. One limitation of these indices is their lack of consideration of the dynamic process, such as character changes and distribution along lineages during evolution. In this study, we propose a robust framework incorporating the underlying dynamic processes under a framework of genome evolution to model character changes and distribution along different lineages in a given phylogenetic tree. Our framework provides a more transparent modeling, instead of the simple surrogates of branching pattern and branch length previously employed. Nonrandom extinction has been found to be clustered within old and species-poor clades, thus it is desirable to combine the evaluation of originality of clades, which will provide a more complete picture and a useful tool for setting global conservation priorities. Using a phylogenetic tree consisting of 70 species of New World terrestrial Carnivora, we demonstrate that the index derived from our framework can discern the difference in originality of clades. Moreover, we demonstrate that the originality of clades and species in a tree changes with different scenarios of dynamic processes, which were neglected by previous indices. We find that the originality of clades should be one of the criteria for setting global conservation priorities.     

Scalable and flexible inference framework for stochastic dynamic single-cell models

Understanding the inherited nature of how biological processes dynamically change over time and exhibit intra- and inter-individual variability, due to the different responses to environmental stimuli and when interacting with other processes, has been a major focus of systems biology. The rise of single-cell fluorescent microscopy has enabled the study of those phenomena. The analysis of single-cell data with mechanistic models offers an invaluable tool to describe dynamic cellular processes and to rationalise cell-to-cell variability within the population. However, extracting mechanistic information from single-cell data has proven difficult. This requires statistical methods to infer unknown model parameters from dynamic, multi-individual data accounting for heterogeneity caused by both intrinsic (e.g. variations in chemical reactions) and extrinsic (e.g. variability in protein concentrations) noise. Although several inference methods exist, the availability of efficient, general and accessible methods that facilitate modelling of single-cell data, remains lacking. Here we present a scalable and flexible framework for Bayesian inference in state-space mixed-effects single-cell models with stochastic dynamic. Our approach infers model parameters when intrinsic noise is modelled by either exact or approximate stochastic simulators, and when extrinsic noise is modelled by either time-varying, or time-constant parameters that vary between cells. We demonstrate the relevance of our approach by studying how cell-to-cell variation in carbon source utilisation affects heterogeneity in the budding yeast Saccharomyces cerevisiae SNF1 nutrient sensing pathway. We identify hexokinase activity as a source of extrinsic noise and deduce that sugar availability dictates cell-to-cell variability.     

A simple alternative to line transects of nests for estimating orangutan densities

We conducted a validation of the line transect technique to estimate densities of orangutan (Pongo pygmaeus) nests in a Bornean swamp forest, and compared these results with density estimates based on nest counts in plots and on female home ranges. First, we examined the accuracy of the line transect method. We found that the densities based on a pass in both directions of two experienced pairs of observers was 27% below a combined sample based on transect walks by eight pairs of observers, suggesting that regular line-transect densities may seriously underestimate true densities. Second, we compared these results with those obtained by nest counts in 0.2-ha plots. This method produced an estimated 15.24 nests/ha, as compared to 10.0 and 10.9, respectively, by two experienced pairs of observers who walked a line transect in both directions. Third, we estimated orangutan densities based on female home range size and overlap and the proportion of females in the population, which produced a density of 4.25–4.5 individuals/km² . Converting nest densities into orangutan densities, using locally estimated parameters for nest production rate and proportion of nest builders in the population, we found that density estimates based on the line transect results of the most experienced pairs on a double pass were 2.82 and 3.08 orangutans/km², based on the combined line transect data are 4.04, and based on plot counts are 4.30. In this swamp forest, plot counts therefore give more accurate estimates than do line transects. We recommend that this new method be evaluated in other forest types as well.     

A comparison of metrics for estimating phylogenetic signal under alternative evolutionary models

Several metrics have been developed for estimating phylogenetic signal in comparative data. These may be important both in guiding future studies on correlated evolution and for inferring broad-scale evolutionary and ecological processes (e.g., phylogenetic niche conservatism). Notwithstanding, the validity of some of these metrics is under debate, especially after the development of more sophisticated model-based approaches that estimate departure from particular evolutionary models (i.e., Brownian motion). Here, two of these model-based metrics (Blomberg’s K-statistics and Pagel’s λ) are compared with three statistical approaches [Moran’s I autocorrelation coefficient, coefficients of determination from the autoregressive method (ARM), and phylogenetic eigenvector regression (PVR)]. Based on simulations of a trait evolving under Brownian motion for a phylogeny with 209 species, we showed that all metrics are strongly, although non-linearly, correlated to each other. Our analyses revealed that statistical approaches provide valid results and may be still particularly useful when detailed phylogenies are unavailable or when trait variation among species is difficult to describe by more standard Brownian or O-U evolutionary models.     

A technique for estimating maximum harvesting effort in a stochastic fishery model

Exploitation of biological resources and the harvest of population species are commonly practiced in fisheries, forestry and wild life management. Estimation of maximum harvesting effort has a great impact on the economics of fisheries and other bio-resources. The present paper deals with the problem of a bioeconomic fishery model under environmental variability. A technique for finding the maximum harvesting effort in fluctuating environment has been developed in a two-species competitive system, which shows that under realistic environmental variability the maximum harvesting effort is less than what is estimated in the deterministic model. This method also enables us to find out the safe regions in the parametric space for which the chance of extinction of the species is minimized. A real life fishery problem has been considered to obtain the inaccessible parameters of the system in a systematic way. Such studies may help resource managers to get an idea for controlling the system.     

A stochastic downhill search algorithm for estimating the local false discovery rate

Screening for differential gene expression in microarray studies leads to difficult large-scale multiple testing problems. The local false discovery rate is a statistical concept for quantifying uncertainty in multiple testing. We introduce a novel estimator for the local false discovery rate that is based on an algorithm which splits all genes into two groups, representing induced and noninduced genes, respectively. Starting from the full set of genes, we successively exclude genes until the gene-wise p-values of the remaining genes look like a typical sample from a uniform distribution. In comparison to other methods, our algorithm performs compatibly in detecting the shape of the local false discovery rate and has a smaller bias with respect to estimating the overall percentage of noninduced genes. Our algorithm is implemented in the Bioconductor compatible R package TWILIGHT version 1.0.1, which is available from http://compdiag.molgen.mpg.de/software or from the Bioconductor project at http://www.bioconductor.org.