Identifying predator-prey processes from time-series

The functional response is a key element in predator-prey models as well as in food chains and food webs. Classical models consider it as a function of prey abundance only. However, many mechanisms can lead to predator dependence, and there is increasing evidence for the importance of this dependence. Identification of the mathematical form of the functional response from real data is therefore a challenging task. In this paper we apply model-fitting to test if typical ecological predator-prey time series data, which contain both observation error and process error, can give some information about the form of the functional response. Working with artificial data (for which the functional response is known) we will show that with moderate noise levels, identification of the model that generated the data is possible. However, the noise levels prevailing in real ecological time-series can give rise to wrong identifications. We will also discuss the quality of parameter estimation by fitting differential equations to such time-series.     

Environmetric time-series analysis: modelling natural systems from experimental time-series data

Using the modelling of solute transport in flowing media as an example, this paper outlines the main aspects of a systematic approach to the modelling of natural systems from experimental time-series data. The objective of the approach, which exploits sophisticated methods of recursive parameter estimation, is to produce a parametrically efficient, data-based model which is both physically meaningful and statistically well defined. Although the proposed methodology has its origins in systems and control theory and may be unfamiliar to some natural scientists, it has been developed and refined for use with natural environmental systems over the past 20 years, and has wide application potential in areas such as biology and ecology. In this sense, the paper is intended to introduce the more general reader to the topic, in the hope that the tutorial review and practical examples will stimulate interest and encourage reference to the many publications cited in the paper. The practical examples are concerned with the modelling of pollutant dispersion in stream channels: phloem translocation and carbon partitioning in plants: and rainfall-streamflow modelling in a river catchment.     

Identifying and modelling environmental indicators for assessing population vulnerability to conflict using ground and satellite data

Conflicts may be directly responsible for the modification of features in the landscape by causing damage to built-up areas or to the environment. Landscape features may also be indirectly affected by conflict as the result of changes in the way of life of inhabitants and their use of natural resource. Conflict-induced changes in landuse features may thus be associated with changes in population vulnerability. This study focuses on the environmental indicators for population vulnerability, an important parameter contributing to risk assessment during and after conflict.These environmental indicators are first identified using field data and are then derived from satellite data. The satellite-derived indicators are used as model input to create a risk map for two areas in Northern Iraq that were targeted during the Anfal Campaigns in 1987 and 1988: Jafati Valley and the southern region of Dahuk. The satellite-driven model is further applied to three dates for the same study areas: 1987, 1989 and 2000–2001. The output describes the risk level within the region for each of the dates studied, and the changes which occurred in Northern Iraq as the result of the Anfal Campaigns.Results show that spatial-based hazard risk assessment is possible using environmental indicators derived from Earth Observation data. For conflict-driven changes in the Jafati Valley study area, there is an apparent change in human activity, manifested as a conversion from agricultural land to grassland, the harvesting of rural mountainous woodland and the net disappearance of built-up areas. For this study area affected by conflict, 86% of the regions where these land cover changes occur were labelled as being at risk according to the model output. In the second study area, 63% of the changes in land cover occur in the regions labelled as being most vulnerable. Further research on this second study site shows that the area was affected by climatic and economic factors rather than conflict.     

Inferences about information flow and dispersal for spatially extended population systems using time-series data

This work explores an information-theoretic approach to drawing inferences about coupling of spatially extended ecological populations based solely on time-series of abundances. The efficacy of the approach, time-delayed mutual information, was explored using a spatially extended predator-prey model system in which populations at different patches were coupled via diffusive movement. The approach identified the relative magnitude and direction of information flow resulting from animal movement between populations, the change in information flow as a function of distance separating populations, and the diffusive nature of the information flow. In addition, when the diffusive movement was eliminated from the model, mutual information correctly provided no evidence of information flow, even when population synchrony was generated by a common environmental driving function. Thus, for this model system, time-delayed mutual information was useful in discriminating between the Moran effect and animal movement as causes of population synchrony, as well as in characterizing dispersal in terms of direction, relative speed and diffusive nature.     

Distributed parameter identification for a label-structured cell population dynamics model using CFSE histogram time-series data

In this work we address the problem of the robust identification of unknown parameters of a cell population dynamics model from experimental data on the kinetics of cells labelled with a fluorescence marker defining the division age of the cell. The model is formulated by a first order hyperbolic PDE for the distribution of cells with respect to the structure variable x (or z) being the intensity level (or the log₁₀-transformed intensity level) of the marker. The parameters of the model are the rate functions of cell division, death, label decay and the label dilution factor. We develop a computational approach to the identification of the model parameters with a particular focus on the cell birth rate α(z) as a function of the marker intensity, assuming the other model parameters are scalars to be estimated. To solve the inverse problem numerically, we parameterize α(z) and apply a maximum likelihood approach. The parametrization is based on cubic Hermite splines defined on a coarse mesh with either equally spaced a priori fixed nodes or nodes to be determined in the parameter estimation procedure. Ill-posedness of the inverse problem is indicated by multiple minima. To treat the ill-posed problem, we apply Tikhonov regularization with the regularization parameter determined by the discrepancy principle. We show that the solution of the regularized parameter estimation problem is consistent with the data set with an accuracy within the noise level in the measurements.      

An analysis of succession along an environmental gradient using data from a lawn

Differences in vegetation dynamics over a period of two years along an environmental gradient of shading on a lawn are examined. Communities (groups) recognized by numerical classification are correlated with degree of shading, season and differences between years by means of generalized linear model analysis. More of the variance is explained if environmental position is used instead of degree of shading as spatial distribution of a strongly competitive species (Trifolium repens) is confounded with shading. Transition probabilities are related to environmental position and season. Simulation with Markov matrices for each season and position demonstrate markedly different successions for different positions. These simulations have no predictive value however as accurate estimate of transition probabilities requires knowledge of the state of adjacent quadrats, i.e. individual observations of transition probabilities are not independent.Transition matrices are unlikely to be useful for predictive analysis of succession when spatial pattern is of significance in the community.We thank S. Kendall, S. Witts, A. Howard and C. Helman for their assistance with the data preparation and analysis, and R. Cunningham for advice on statistical analysis.     

Identifying inhibitory threshold values of repressing metabolites in CHO cell culture using multivariate analysis methods

Elevation of lactate, ammonia, osmolality, and carbon dioxide to inhibitory levels was reported to have adverse effects on cell growth and protein productivity in mammalian cell culture. Multivariate analysis methods were used to investigate the roles of these repressing metabolites in a fed-batch CHO cell culture for antibody fusion protein B1 (B1) production. Principal Factor Analysis methodology was applied to manufacturing-scale data of 112 cell culture runs, which identified threshold values of four repressing metabolites as follows: (1) ammonium levels above 5.1 mM inhibit cell growth; (2) both lactate and osmolality levels above 58 mM and 382 mOsm/kg affect cell viability; and (3) carbon dioxide levels at or above 111 mmHg reduce protein quality. These threshold values were then verified by simulations using Monod-type equations and Canonical Correlation. These results suggest that adverse effects on cell growth, productivity, and product quality may be minimized under the ideal cell culture condition, in which the peak values of all four repressing metabolites are maintained below the threshold values. This strategy was evaluated in 45 cell culture runs in 50-L bioreactors. Eight out of 45 runs were operated under the ideal condition, while the remaining 37 runs had at least one repressing metabolite with peak value at or above the threshold. In comparison to the remaining runs, the eight cell culture runs under the ideal condition had 17%, 40%, and 11% higher values in peak viable cell density, final B1 titer, and quality attribute, respectively. The unique methodology used in this study may be generally applicable in characterizing cell culture processes.     

Particle-verification for single-particle, reference-based reconstruction using multivariate data analysis and classification

As collection of electron microscopy data for single-particle reconstruction becomes more efficient, due to electronic image capture, one of the principal limiting steps in a reconstruction remains particle-verification, which is especially costly in terms of user input. Recently, some algorithms have been developed to window particles automatically, but the resulting particle sets typically need to be verified manually. Here we describe a procedure to speed up verification of windowed particles using multivariate data analysis and classification. In this procedure, the particle set is subjected to multi-reference alignment before the verification. The aligned particles are first binned according to orientation and are binned further by K-means classification. Rather than selection of particles individually, an entire class of particles can be selected, with an option to remove outliers. Since particles in the same class present the same view, distinction between good and bad images becomes more straightforward. We have also developed a graphical interface, written in Python/Tkinter, to facilitate this implementation of particle-verification. For the demonstration of the particle-verification scheme presented here, electron micrographs of ribosomes are used.     

Conservation in a cup of water: estimating biodiversity and population abundance from environmental DNA

Three mantras often guide species and ecosystem management: (i) for preventing invasions by harmful species, ‘early detection and rapid response’; (ii) for conserving imperilled native species, ‘protection of biodiversity hotspots’; and (iii) for assessing biosecurity risk, ‘an ounce of prevention equals a pound of cure.’ However, these and other management goals are elusive when traditional sampling tools (e.g. netting, traps, electrofishing, visual surveys) have poor detection limits, are too slow or are not feasible. One visionary solution is to use an organism’s DNA in the environment (eDNA), rather than the organism itself, as the target of detection. In this issue of Molecular Ecology, Thomsen et al. (2012) provide new evidence demonstrating the feasibility of this approach, showing that eDNA is an accurate indicator of the presence of an impressively diverse set of six aquatic or amphibious taxa including invertebrates, amphibians, a fish and a mammal in a wide range of freshwater habitats. They are also the first to demonstrate that the abundance of eDNA, as measured by qPCR, correlates positively with population abundance estimated with traditional tools. Finally, Thomsen et al. (2012) demonstrate that next‐generation sequencing of eDNA can quantify species richness. Overall, Thomsen et al. (2012) provide a revolutionary roadmap for using eDNA for detection of species, estimates of relative abundance and quantification of biodiversity.     

An interactive multivariate analysis of FCM data

The procedure and results of the interactive multivariate analysis of FCM data are described. Using principal-components analysis, cluster analysis, and interactive maneuvers, this procedure facilitates an effective data compression from a four-dimensional space into two-dimensional space, then allows cluster separation. The procedure is especially effective for separating clusters, which are degenerated in the usual scattergrams. Programs were mostly written in C language on MS-DOS and were tested on four-dimensional analysis of the blood cells, which resulted in a successful separation of the degenerated clusters.     

Regression analysis of multivariate panel count data

We consider panel count data which are frequently obtained in prospective studies involving recurrent events that are only detected and recorded at periodic assessment times. The data take the form of counts of the cumulative number of events detected at each inspection time, along with explanatory covariates. Examples arise in diverse areas such as epidemiological studies, medical follow-up studies, reliability studies, and tumorigenicity experiments. This article is concerned with regression analysis of multivariate panel count data which arise if more than one type of recurrent event is of interest and individuals are only observed intermittently. We present a class of marginal mean models which leave the dependence structures for related types of recurrent events completely unspecified. Estimating equations are developed for regression parameters, and the resulting estimates are shown to be consistent and asymptotically normal. Simulation studies show that the proposed estimation procedures work well for practical situations. The methodology is applied to a motivating study of patients with psoriatic arthritis in which the events of interest are the onset of joint damage according to 2 different criteria.     

Ensemble learning of genetic networks from time-series expression data

MOTIVATION: Inferring genetic networks from time-series expression data has been a great deal of interest. In most cases, however, the number of genes exceeds that of data points which, in principle, makes it impossible to recover the underlying networks. To address the dimensionality problem, we apply the subset selection method to a linear system of difference equations. Previous approaches assign the single most likely combination of regulators to each target gene, which often causes over-fitting of the small number of data. RESULTS: Here, we propose a new algorithm, named LEARNe, which merges the predictions from all the combinations of regulators that have a certain level of likelihood. LEARNe provides more accurate and robust predictions than previous methods for the structure of genetic networks under the linear system model. We tested LEARNe for reconstructing the SOS regulatory network of Escherichia coli and the cell cycle regulatory network of yeast from real experimental data, where LEARNe also exhibited better performances than previous methods. AVAILABILITY: The MATLAB codes are available upon request from the authors.     

The multivariate analysis of dermatoglyphics in population systematics

In this paper a multivariate analysis of dermatoglyphics was carried out. The following traits were used: pattern intensity on fingers, average of main line D terminations and frequencies of patterns in the five configurational areas of the palm. Firstly a cluster analysis is produced and completed with a principal components analysis. The results of both studies show clear agreement. The main conclusion is: the multivariate analysis of dermatoglyphics displays several groups of populations, which with the peculiarities pointed out in the paper, are in concordance with the classical racial stocks.     

Studying and modelling dynamic biological processes using time-series gene expression data

Biological processes are often dynamic, thus researchers must monitor their activity at multiple time points. The most abundant source of information regarding such dynamic activity is time-series gene expression data. These data are used to identify the complete set of activated genes in a biological process, to infer their rates of change, their order and their causal effects and to model dynamic systems in the cell. In this Review we discuss the basic patterns that have been observed in time-series experiments, how these patterns are combined to form expression programs, and the computational analysis, visualization and integration of these data to infer models of dynamic biological systems.