Integrative modelling of animal movement: incorporating in situ habitat and behavioural information for a migratory marine predator

A fundamental goal in animal ecology is to quantify how environmental (and other) factors influence individual movement, as this is key to understanding responsiveness of populations to future change. However, quantitative interpretation of individual-based telemetry data is hampered by the complexity of, and error within, these multi-dimensional data. Here, we present an integrative hierarchical Bayesian state-space modelling approach where, for the first time, the mechanistic process model for the movement state of animals directly incorporates both environmental and other behavioural information, and observation and process model parameters are estimated within a single model. When applied to a migratory marine predator, the southern elephant seal (Mirounga leonina), we find the switch from directed to resident movement state was associated with colder water temperatures, relatively short dive bottom time and rapid descent rates. The approach presented here can have widespread utility for quantifying movement–behaviour (diving or other)–environment relationships across species and systems.     

Sensitivity of Bayes estimators to hyper-parameters with an application to maximum yield from fisheries

Priors are seldom unequivocal and an important component of Bayesian modeling is assessment of the sensitivity of the posterior to the specified prior distribution. This is especially true in fisheries science where the Bayesian approach has been promoted as a rigorous method for including existing information from previous surveys and from related stocks or species. These informative priors may be highly contested by various interest groups. Here, formulae for the first and second derivatives of Bayes estimators with respect to hyper-parameters of the joint prior density are given. The formula for the second derivative provides a correction to a previously published result. The formulae are shown to reduce to very convenient and easily implemented forms when the hyper-parameters are for exponential family marginal priors. For model parameters with such priors it is shown that the ratio of posterior variance to prior variance can be interpreted as the sensitivity of the posterior mean to the prior mean. This methodology is applied to a nonlinear state-space model for the biomass of South Atlantic albacore tuna and sensitivity of the maximum sustainable yield to the prior specification is examined.     

Stochastic models of neuronal dynamics

Cortical activity is the product of interactions among neuronal populations. Macroscopic electrophysiological phenomena are generated by these interactions. In principle, the mechanisms of these interactions afford constraints on biologically plausible models of electrophysiological responses. In other words, the macroscopic features of cortical activity can be modelled in terms of the microscopic behaviour of neurons. An evoked response potential (ERP) is the mean electrical potential measured from an electrode on the scalp, in response to some event. The purpose of this paper is to outline a population density approach to modelling ERPs.We propose a biologically plausible model of neuronal activity that enables the estimation of physiologically meaningful parameters from electrophysiological data. The model encompasses four basic characteristics of neuronal activity and organization: (i) neurons are dynamic units, (ii) driven by stochastic forces, (iii) organized into populations with similar biophysical properties and response characteristics and (iv) multiple populations interact to form functional networks. This leads to a formulation of population dynamics in terms of the Fokker-Planck equation. The solution of this equation is the temporal evolution of a probability density over state-space, representing the distribution of an ensemble of trajectories. Each trajectory corresponds to the changing state of a neuron. Measurements can be modelled by taking expectations over this density, e.g. mean membrane potential, firing rate or energy consumption per neuron. The key motivation behind our approach is that ERPs represent an average response over many neurons. This means it is sufficient to model the probability density over neurons, because this implicitly models their average state. Although the dynamics of each neuron can be highly stochastic, the dynamics of the density is not. This means we can use Bayesian inference and estimation tools that have already been established for deterministic systems. The potential importance of modelling density dynamics (as opposed to more conventional neural mass models) is that they include interactions among the moments of neuronal states (e.g. the mean depolarization may depend on the variance of synaptic currents through nonlinear mechanisms).Here, we formulate a population model, based on biologically informed model-neurons with spike-rate adaptation and synaptic dynamics. Neuronal sub-populations are coupled to form an observation model, with the aim of estimating and making inferences about coupling among sub-populations using real data. We approximate the time-dependent solution of the system using a bi-orthogonal set and first-order perturbation expansion. For didactic purposes, the model is developed first in the context of deterministic input, and then extended to include stochastic effects. The approach is demonstrated using synthetic data, where model parameters are identified using a Bayesian estimation scheme we have described previously.     

Two-level Bayesian interaction analysis for survival data incorporating pathway information

Genetic interactions play an important role in the progression of complex diseases, providing explanation of variations in disease phenotype missed by main genetic effects. Comparatively, there are fewer studies on survival time, given its challenging characteristics such as censoring. In recent biomedical research, two-level analysis of both genes and their involved pathways has received much attention and been demonstrated as more effective than single-level analysis. However, such analysis is usually limited to main effects. Pathways are not isolated, and their interactions have also been suggested to have important contributions to the prognosis of complex diseases. In this paper, we develop a novel two-level Bayesian interaction analysis approach for survival data. This approach is the first to conduct the analysis of lower-level gene–gene interactions and higher-level pathway–pathway interactions simultaneously. Significantly advancing from the existing Bayesian studies based on the Markov Chain Monte Carlo (MCMC) technique, we propose a variational inference framework based on the accelerated failure time model with effective priors to accommodate two-level selection as well as censoring. Its computational efficiency is much desirable for high-dimensional interaction analysis. We examine performance of the proposed approach using extensive simulation. The application to TCGA melanoma and lung adenocarcinoma data leads to biologically sensible findings with satisfactory prediction accuracy and selection stability.     

The use of approximate Bayesian computation in conservation genetics and its application in a case study on yellow-eyed penguins

The inference of demographic parameters from genetic data has become an integral part of conservation studies. A group of Bayesian methods developed originally in population genetics, known as approximate Bayesian computation (ABC), has been shown to be particularly useful for the estimation of such parameters. These methods do not need to evaluate likelihood functions analytically and can therefore be used even while assuming complex models. In this paper we describe the ABC approach and identify specific parts of its algorithm that are being the subject of intensive studies in order to further expand its usability. Furthermore, we discuss applications of this Bayesian algorithm in conservation studies, providing insights on the potentialities of these tools. Finally, we present a case study in which we use a simple Isolation-Migration model to estimate a number of demographic parameters of two populations of yellow-eyed penguins (Megadyptes antipodes) in New Zealand. The resulting estimates confirm our current understanding of M. antipodes dynamic, demographic history and provide new insights into the expansion this species has undergone during the last centuries.     

Detecting and estimating density dependence in wildlife populations

We review methods for detecting and assessing the strength of density dependence based on 2 types of approaches: surveys of population size and studies of life history traits, in particular demographic parameters. For the first type of studies, methods neglecting uncertainty in population size should definitely be abandoned. Bayesian approaches to simple state-space models accounting for uncertainty in population size are recommended, with some caution because of numerical difficulties and risks of model misspecification. Realistic state-space models incorporating features such as environmental covariates, age structure, etc., may lack power because of the shortness of the time series and the simultaneous presence of process and sampling variability. In all cases, complementing the population survey data with some external information, with priority on the intrinsic growth rate, is highly recommended. Methods for detecting density dependence in life history traits are generally conservative (i.e., tend to underestimate the strength of density dependence). Among approaches to correct for this effect, the state-space formulation of capture–recapture models is again the most promising. Foreseeable developments will exploit integrated monitoring combining population size surveys and individual longitudinal data in refined state-space models, for which a Bayesian approach is the most straightforward statistical treatment. One may thus expect an integration of various types of models that will make it possible to look at density dependence as a complex biological process interacting with other processes rather than in terms of a simple equation; modern statistical and modeling tools make such a synthesis within reach. © 2012 The Wildlife Society.     

Transient responses of a modeled bursting neuron: analysis with equilibrium and averaged nullclines

We utilized a state-space approach to study the dynamics of a modeled bursting neuron consisting of 11 state variables. Such an approach may be used on a high-order system when a small number of variables are rate-limiting and dominate the dynamics of the model. Calculation of equilibrium and averaged nullclines and saddle-node bifurcations of the full and reduced models provided measures that indicated the transition between silence and spiking and the dynamics of the system during both the silent and spiking phases of the burst cycle. The relative stability of tonic beating solutions in the presence and absence of 5-HT was calculated in the state-space of the slow variables and related to specific biophysical mechanisms. The results were compared with similar simulations performed in Butera et al. (1995) which utilized a current-voltage (I-V)-based method for analysis. While the state-space method is sometimes more difficult to link to specific biophysical mechanisms, it offers a wider portrait of the dynamics of the system. In contrast, the use of I-V plots offers a direct relationship to biophysical processes, but provides no information on the dynamics of non-voltage-dependent processes such as Ca. Received: 6 December 1996 / Accepted in revised form: 1 July 1997     

Development of a variational scheme for model inversion of multi-area model of brain. Part I: simulation evaluation

We previously developed an integrated model of the brain within a single cortical area for functional Magnetic Resonance Imaging (fMRI), electroencephalography (EEG), and magnetoencephalography (MEG) using an extended neural mass model (ENMM). We then extended ENMM from a single-area to a multi-area model to develop a neural mass model of the entire brain. To this end, we derived a nonlinear state-space representation of the multi-area model. In Parts I and II of these two companion papers (henceforth called Part I and Part II), we develop and evaluate a variational Bayesian expectation maximization (VBEM) method to estimate parameters of multi-area ENMM (MEN) using E/MEG data. In Part I, we derive a state-space representation of MEN and use VBEM method for model inversion (parameter estimation). We evaluate and validate performance of VBEM method for model inversion of MEN using simulation studies in various signal-to-noise ratios. Details of VBEM method are presented in Part II. The proposed approach provides a useful technique for analyzing effective connectivity using non-invasive EEG and MEG methods.     

Exploring the drivers of wildlife population dynamics from insufficient data by Bayesian model averaging

A long-standing interest in ecology and wildlife management is to find drivers of wildlife population dynamics because it is crucial for implementing the effective wildlife management. Recent studies have demonstrated the usefulness of state-space modeling for this purpose, but we often confront the lack of the necessary time-series data. This is particularly common in wildlife management because of limited funds or early stage of data collection. In this study, we proposed a Bayesian model averaging technique in a state-space modeling framework for identifying the drivers of wildlife population dynamics from limited data. To exemplify the utility of Bayesian model averaging for wildlife management, we illustrate here the population dynamics of wild boars Sus scrofa in Chiba prefecture, central Japan. Despite the fact that our data are limited in both temporal and spatial resolution, Bayesian model averaging revealed the potential influence of bamboo forests and abandoned agricultural fields on wild boar population dynamics, and largely enhanced model predictability compared to the full model. Although Bayesian model averaging is not commonly used in ecology and wildlife management, our case study demonstrated that it may help to find influential drivers of wildlife population dynamics and develop a better management plan even from limited time-series data.     

Inhibition of L-lactate: cytochrome-c reductase (flavocytochrome b2) by product binding to the semiquinone transient. Loss of reactivity towards monoelectronic acceptors

Pyruvate has previously been shown to slow down the rate of intramolecular electron transfer from the flavosemiquinone (Fs) to the cytochrome b2 moiety of flavocytochrome b2 [Tegoni, M., Silvestrini, M. C., Labeyrie, F. & Brunori, M. (1984) Eur. J. Biochem. 140, 39-45] and to stabilize markedly the Fs state of the prosthetic flavin, relative to the oxidized (Fo) and the reduced (Fh) states [Tegoni, M., Janot, J. M. & Labeyrie, F. (1986) Eur. J. Biochem. 155, 491-503]. In the present study, we have determined the dissociation constants of pyruvate for the three redox forms of the prosthetic flavin and demonstrated that the Fs-pyruvate complex is actually much more stable than the Fo-pyruvate and Fh-pyruvate complexes. The inhibition produced by pyruvate has been characterized under steady-state conditions using both ferricytochrome c and ferricyanide as external acceptor. A detailed analysis and simulations of the suitable reaction scheme, taking into consideration all data from rapid kinetic studies of partial reactions previously published, show that the experimental noncompetitive inhibition results from the sum of a competitive effect due to binding of pyruvate to Fo and an uncompetitive effect due to binding to the Fs intermediate in a dead-end complex. Pyruvate binding to the semiquinone transient results in a marked loss of the reactivity of this donor in electron transfers to its specific partner, the cytochrome b2 present in the same active site, as to ferricyanide, an external acceptor. A critical evaluation of the parameters involved in the control of such reactivities is presented.     

Bovine plasminogen activator inhibitor 1: specificity determinations and comparison of the active, latent, and guanidine-activated forms

The plasminogen activator inhibitor 1 (PAI-1) synthesized and released by cultured bovine aortic endothelial cells is present in conditioned medium in a latent form that can be activated by guanidine hydrochloride [Hekman, C. M., & Loskutoff, D. J. (1985) J. Biol. Chem. 260, 11581-11587]. The purified, guanidine-activated PAI-1 was shown to inhibit both plasmin and trypsin in a dose- and time-dependent manner. Second-order rate constants for these interactions were calculated to be 6.6 X 10(5) and 7.0 X 10(6) M-1 s-1 for plasmin and trypsin, respectively. Experiments were conducted to compare the inherently active and the guanidine-activated forms of PAI-1. The two active forms had similar kinetic parameters for interaction with urokinase (Kd, 0.3 pM; kassoc, 1.5 X 10(8) M-1 s-1) and were both inactivated upon treatment with acid or base and by incubation at 37 degrees C. The latent form was relatively stable when incubated under similar conditions. The decrease in PAI-1 activity upon incubation at 37 degrees C was partially restored by a second treatment with guanidine hydrochloride. However, the degree of recovery decreased as a function of incubation time at 37 degrees C. These data suggest that active and guanidine-activated PAI-1 represent a single form of PAI-1. Incubation of this form at 37 degrees C yields two distinct populations of inactive PAI-1, one capable of reactivation and another that appears to be irreversibly inactivated.     

Incorporating movement into models of grey seal population dynamics

1. One of the most difficult problems in developing spatially explicit models of population dynamics is the validation and parameterization of the movement process. We show how movement models derived from capture-recapture analysis can be improved by incorporating them into a spatially explicit metapopulation model that is fitted to a time series of abundance data. 2. We applied multisite capture-recapture analysis techniques to photo-identification data collected from female grey seals at the four main breeding colonies in the North Sea between 1999 and 2001. The best-fitting movement models were then incorporated into state-space metapopulation models that explicitly accounted for demographic and observational stochasticity. 3. These metapopulation models were fitted to a 20-year time series of pup production data for each colony using a Bayesian approach. The best-fitting model, based on the Akaike Information Criterion (AIC), had only a single movement parameter, whose confidence interval was 82% less than that obtained from the capture-recapture study, but there was some support for a model that included an effect of distance between colonies. 4. The state-space modelling provided improved estimates of other demographic parameters. 5. The incorporation of movement, and the way in which it was modelled, affected both local and regional dynamics. These differences were most evident as colonies approached their carrying capacities, suggesting that our ability to discriminate between models should improve as the length of the grey seal time series increases.     

Development of a variational scheme for model inversion of multi-area model of brain. Part II: VBEM method

In Part I and Part II of these two companion papers (henceforth called Part I and Part II), we develop and evaluate a variational Bayesian expectation maximization (VBEM) method for model inversion of our multi-area extended neural mass model (MEN). In this paper, we develop the VBEM method to estimate posterior distributions of parameters of MEN. We choose suitable prior distributions for the model parameters in order to use properties of a conjugate-exponential model in implementing VBEM. Consequently, VBEM leads to analytically tractable forms. The proposed VBEM algorithm starts with initialization and consists of repeated iterations of a variational Bayesian expectation step (VB E-step) and a variational Bayesian maximization step (VB M-step). Posterior distributions of the model parameters are updated in the VB M-step. Distribution of the hidden state is updated in the VB E-step. We develop a variational extended Kalman smoother (VEKS) to infer the distribution of the hidden state in the VB E-step and derive the forward and backward passes of VEKS, analogous to the Kalman smoother. In Part I, we evaluate and validate the VBEM method using simulation studies.     

Bayesian Analysis of Composite Quantile Regression

This paper introduces a Bayesian approach for composite quantile regression employing the skewed Laplace distribution for the error distribution. We use a two-level hierarchical Bayesian model for coefficient estimation and future selection which assumes a prior distribution that favors sparseness. An efficient Gibbs sampling algorithm is developed to update the unknown quantities from the posteriors. The proposed approach is illustrated via simulation studies and two real datasets. Results indicate that the proposed approach performs quite good in comparison to the other approaches.     

Bayesian model adequacy and choice in phylogenetics

Bayesian inference is becoming a common statistical approach to phylogenetic estimation because, among other reasons, it allows for rapid analysis of large data sets with complex evolutionary models. Conveniently, Bayesian phylogenetic methods use currently available stochastic models of sequence evolution. However, as with other model-based approaches, the results of Bayesian inference are conditional on the assumed model of evolution: inadequate models (models that poorly fit the data) may result in erroneous inferences. In this article, I present a Bayesian phylogenetic method that evaluates the adequacy of evolutionary models using posterior predictive distributions. By evaluating a model's posterior predictive performance, an adequate model can be selected for a Bayesian phylogenetic study. Although I present a single test statistic that assesses the overall (global) performance of a phylogenetic model, a variety of test statistics can be tailored to evaluate specific features (local performance) of evolutionary models to identify sources failure. The method presented here, unlike the likelihood-ratio test and parametric bootstrap, accounts for uncertainty in the phylogeny and model parameters.     

Mathematical modeling of heat and water transport in human respiratory tract

Excessive heat and water losses from the airways are stimuli to asthma. To study heat and water vapor transport in the human respiratory tract, a time-dependent model, based on a single differential equation with an analytical solution, was developed that could predict the intra-airway temperatures and water vapor contents. The key feature is the dependence of the temperature and water vapor along the respiratory tract as a function of the air residence time at each location. The model assumes disturbed laminar flow leading to enhanced transport mechanisms and wall temperature profiles modeled according to experimental data (E. R. McFadden, Jr., B. M. Pichurko, H. F. Bowman, E. Ingenito, S. Burns, N. Dowling, and J. Soloway. J. Appl. Physiol. 58: 564-570, 1985). It predicts that 1) the air equilibrates with the wall before it reaches body conditions (37 degrees C, 99.5% relative humidity); 2) conditioning of the inspired air involves several generations, with the number depending on the respiratory conditions; and 3) the walls of the upper airways are unsaturated, although it is difficult to judge at this state the depth of the respiratory tract affected.     

Trypanosoma cruzi: characterization of an intracellular epimastigote-like form.

Almeida-de-Faria, M., Freymüller, E., Colli, W., and Alves, M. J. M. 1999. Trypanosoma cruzi: Characterization of an intracellular epimastigote-like form. Experimental Parasitology 92, 263-274. A detailed study of transient epimastigote-like forms as intermediates in the differentiation of Trypanosoma cruzi amastigotes to trypomastigotes inside the host cell cytoplasm was undertaken using the CL-14 clone grown in cells maintained at 33 degrees C. Several parameters related to these forms have been compared with epimastigotes and other stages of the parasite. Consequently, the designation of intracellular epimastigotes is proposed for these forms. Despite being five times shorter (5.4 +/- 0.7 micrometer) than the extracellular epimastigote (25.2 +/- 2.1 micrometer), the overall morphology of the intracellular epimastigote is very similar to a bona fide epimastigote, when cell shape, position, and general aspect of organelles are compared by transmission electron microscopy. Epimastigotes from both sources are lysed by human complement and bind to DEAE-cellulose, in contrast to amastigotes and trypomastigote forms. A monoclonal antibody (3C5) reacts with both epimastigotes either isolated from axenic media or intracellular and very faintly with amastigotes, but not with trypomastigotes. Some differences of a quantitative nature are apparent between the two epimastigote forms when reactivities with lectins or stage-specific antibodies are compared, revealing the transient nature of the intracellular epimastigote. The epitope recognized by 3C5 monoclonal antibody reacts slightly more intensely with extracellular than with intracellular epimastigotes, as detected by immunoelectron microscopy. Also a very faint reaction of the intracellular epimastigotes was observed with monoclonal antibody 2C2, an antibody which recognizes a glycoprotein specific for the amastigote stage. Biological parameters as growth curves in axenic media and inhability to invade nonphagocytic tissue-cultured cells are similar in the epimastigotes from both origins. It is proposed that the epimastigote-like forms are an obligatory transitional stage in the transformation of amastigotes to trypomastigotes with a variable time of permanency in the host cell cytoplasm depending on environmental conditions.     

A data-assimilation approach to predict population dynamics during epithelial-mesenchymal transition

Epithelial-mesenchymal transition (EMT) is a biological process that plays a central role in embryonic development, tissue regeneration, and cancer metastasis. Transforming growth factor-β (TGFβ) is a potent inducer of this cellular transition, comprising transitions from an epithelial state to partial or hybrid EMT state(s), to a mesenchymal state. Recent experimental studies have shown that, within a population of epithelial cells, heterogeneous phenotypical profiles arise in response to different time- and TGFβ dose-dependent stimuli. This offers a challenge for computational models, as most model parameters are generally obtained to represent typical cell responses, not necessarily specific responses nor to capture population variability. In this study, we applied a data-assimilation approach that combines limited noisy observations with predictions from a computational model, paired with parameter estimation. Synthetic experiments mimic the biological heterogeneity in cell states that is observed in epithelial cell populations by generating a large population of model parameter sets. Analysis of the parameters for virtual epithelial cells with biologically significant characteristics (e.g., EMT prone or resistant) illustrates that these sub-populations have identifiable critical model parameters. We perform a series of in silico experiments in which a forecasting system reconstructs the EMT dynamics of each virtual cell within a heterogeneous population exposed to time-dependent exogenous TGFβ dose and either an EMT-suppressing or EMT-promoting perturbation. We find that estimating population-specific critical parameters significantly improved the prediction accuracy of cell responses. Thus, with appropriate protocol design, we demonstrate that a data-assimilation approach successfully reconstructs and predicts the dynamics of a heterogeneous virtual epithelial cell population in the presence of physiological model error and parameter uncertainty.