In the deep end: pooling data and other statistical challenges of zoo and aquarium research

Zoo and aquarium research presents many logistic challenges, including extremely small sample sizes and lack of independent data points, which lend themselves to the misuse of statistics. Pseudoreplication and pooling of data are two statistical problems common in research in the biological sciences. Although the prevalence of these and other statistical miscues have been documented in other fields, little attention has been paid to the practice of statistics in the field of zoo biology. A review of articles published in the journal Zoo Biology between 1999–2004 showed that approximately 40% of the 146 articles utilizing inferential statistics during that span contained some evidence of pseudoreplication or pooling of data. Nearly 75% of studies did not provide degrees of freedom for all statistics and approximately 20% did not report test statistic values. Although the level of pseudoreplication in this dataset is not outside the levels found in other branches of biology, it does indicate the challenges of dealing with appropriate data analysis in zoo and aquarium studies. The standardization of statistical techniques to deal with the methodological challenges of zoo and aquarium populations can help advance zoo research by guiding the production and analysis of applied studies. This study recommends techniques for dealing with these issues, including complete disclosure of data manipulation and reporting of statistical values, checking and control for institutional effects in statistical models, and avoidance of pseudoreplicated observations. Additionally, zoo biologists should seek out other models such as hierarchical or factorial models or randomization tests to supplement their repertoire of t‐tests and ANOVA. These suggestions are intended to stimulate conversation and examination of the current use of statistics in zoo biology in an effort to develop more consistent requirements for publication. Zoo Biol 0:1–14, 2006. © 2006 Wiley‐Liss, Inc.     

Exploring patterns of interspecific variation in quantitative traits using sequential phylogenetic eigenvector regressions

A number of metrics have been developed for estimating phylogenetic signal in data and to evaluate correlated evolution, inferring broad-scale evolutionary and ecological processes. Here, we proposed an approach called phylogenetic signal-representation (PSR) curve, built upon phylogenetic eigenvector regression (PVR). In PVR, selected eigenvectors extracted from a phylogenetic distance matrix are used to model interspecific variation. In the PSR curve, sequential PVR models are fitted after successively increasing the number of eigenvectors and plotting their R(2) against the accumulated eigenvalues. We used simulations to show that a linear PSR curve is expected under Brownian motion and that its shape changes under alternative evolutionary models. The PSR area, expressing deviations from Brownian motion, is strongly correlated (r= 0.873; P < 0.01) with Blomberg's K-statistics, so nonlinear PSR curves reveal if traits are evolving at a slower or higher rate than expected by Brownian motion. The PSR area is also correlated with phylogenetic half-life under an Ornstein-Uhlenbeck process, suggesting how both methods describe the shape of the relationship between interspecific variation and time since divergence among species. The PSR curve provides an elegant exploratory method to understand deviations from Brownian motion, in terms of acceleration or deceleration of evolutionary rates occurring at large or small phylogenetic distances.     

Dispersal ability of marked,irradiated olive fruit flies [Bactrocera oleae (Rossi) (Diptera: Tephritidae)] in arid regions

The dispersal of marked, irradiated olive fruit flies originating from a hybrid laboratory strain was studied in an olive groove located in the arid regions of southern Israel. Release–recapture experiments (eight in total) were conducted throughout a period of 5 months (July–December 2008). In each experiment, ca. 5000 flies were released. Recapture of flies was conducted using a grid of 30 yellow sticky traps set in expanding semicircles from the centre of release. Service of traps was conducted 3 and 15 days after the release. Fly quality and adult food type (only sucrose and protein + sucrose) before release was also investigated. Results point at an average dispersal distance of marked, irradiated olive flies of ca. 50 m. Pre‐release adult diet did not affect dispersal ability. Fly recovery averaged ca. 3.5% during summer and ca. 1.5% during autumn. Most of the recovery concentrated during the first 3 days after releases, suggesting low survival of the released flies afterwards. As inferred from circular statistics, direction of dispersal was non‐random with a significant directionality to the north‐west. Results are discussed in view of environmental temperatures and wind direction.     

Spatial variability of the plankton trophic interaction in the North Sea: a new feature after the early 1970s

Traditionally, marine ecosystem structure was thought to be bottom‐up controlled. In recent years, a number of studies have highlighted the importance of top‐down regulation. Evidence is accumulating that the type of trophic forcing varies temporally and spatially, and an integrated view – considering the interplay of both types of control – is emerging. Correlations between time series spanning several decades of the abundances of adjacent trophic levels are conventionally used to assess the type of control: bottom‐up if positive or top‐down if this is negative. This approach implies averaging periods which might show time‐varying dynamics and therefore can hide part of this temporal variability. Using spatially referenced plankton information extracted from the Continuous Plankton Recorder, this study addresses the potential dynamic character of the trophic structure at the planktonic level in the North Sea by assessing its variation over both temporal and spatial scales. Our results show that until the early‐1970s a bottom‐up control characterized the base of the food web across the whole North Sea, with diatoms having a positive and homogeneous effect on zooplankton filter‐feeders. Afterwards, different regional trophic dynamics were observed, in particular a negative relationship between total phytoplankton and zooplankton was detected off the west coast of Norway and the Skagerrak as opposed to a positive one in the southern reaches. Our results suggest that after the early 1970s diatoms remained the main food source for zooplankton filter‐feeders east of Orkney–Shetland and off Scotland, while in the east, from the Norwegian Trench to the German Bight, filter‐feeders were mainly sustained by dinoflagellates.     

A practical validation approach for virus titer testing of avian infectious bursal disease live vaccine according to current regulatory guidelines

The method for virus titer determination of avian infectious bursal disease (IBD) live vaccine, developed long before regulatory validation guidelines is a cell culture based biological assay intended for use in vaccine release testing.The aim of our study was to perform a validation, based on fit-for-purpose principle, of an old 50% tissue culture infectious dose (TCID₅₀) method according to Guidelines of the International Cooperation on Harmonization of Technical Requirements for Registration of Veterinary Medicinal Products (VICH).This paper addresses challenges and discusses some key aspects that should be considered when validating biological methods. A different statistical approach and non-parametric statistics was introduced in validation protocol in order to derive useful information from experimental data. This approach is applicable for a wide range of methods.In conclusion, the previous virus titration method had showed to be precise, accurate, linear, robust and in accordance with current regulatory standards, which indicates that there is no need for additional re-development or upgrades of the method for its suitability for intended use.     

Forecasting species ranges by statistical estimation of ecological niches and spatial population dynamics

Aim The study and prediction of species–environment relationships is currently mainly based on species distribution models. These purely correlative models neglect spatial population dynamics and assume that species distributions are in equilibrium with their environment. This causes biased estimates of species niches and handicaps forecasts of range dynamics under environmental change. Here we aim to develop an approach that statistically estimates process‐based models of range dynamics from data on species distributions and permits a more comprehensive quantification of forecast uncertainties. Innovation We present an approach for the statistical estimation of process‐based dynamic range models (DRMs) that integrate Hutchinson's niche concept with spatial population dynamics. In a hierarchical Bayesian framework the environmental response of demographic rates, local population dynamics and dispersal are estimated conditional upon each other while accounting for various sources of uncertainty. The method thus: (1) jointly infers species niches and spatiotemporal population dynamics from occurrence and abundance data, and (2) provides fully probabilistic forecasts of future range dynamics under environmental change. In a simulation study, we investigate the performance of DRMs for a variety of scenarios that differ in both ecological dynamics and the data used for model estimation. Main conclusions Our results demonstrate the importance of considering dynamic aspects in the collection and analysis of biodiversity data. In combination with informative data, the presented framework has the potential to markedly improve the quantification of ecological niches, the process‐based understanding of range dynamics and the forecasting of species responses to environmental change. It thereby strengthens links between biogeography, population biology and theoretical and applied ecology.     

Causal inference in biomolecular pathways using a Bayesian network approach and an Implicit method

We introduce here the concept of Implicit networks which provide, like Bayesian networks, a graphical modelling framework that encodes the joint probability distribution for a set of random variables within a directed acyclic graph. We show that Implicit networks, when used in conjunction with appropriate statistical techniques, are very attractive for their ability to understand and analyze biological data. Particularly, we consider here the use of Implicit networks for causal inference in biomolecular pathways. In such pathways, an Implicit network encodes dependencies among variables (proteins, genes), can be trained to learn causal relationships (regulation, interaction) between them and then used to predict the biological response given the status of some key proteins or genes in the network. We show that Implicit networks offer efficient methodologies for learning from observations without prior knowledge and thus provide a good alternative to classical inference in Bayesian networks when priors are missing. We illustrate our approach by an application to simulated data for a simplified signal transduction pathway of the epidermal growth factor receptor (EGFR) protein.     

Summary statistics of neutral mutations in longitudinal DNA samples

Longitudinal samples of DNA sequences are the DNA sequences sampled from the same population at different time points. For fast evolving organisms, e.g. RNA virus, these kind of samples have increasingly been used to study the evolutionary process in action. Longitudinal samples provide some interesting new summary statistics of genetic variation, such as the frequency of mutation of size i in one sample and size j in another, the average number of mutations accumulated since the common ancestor of two sequences each from a different sample, and number of private, shared and fixed mutations within samples. To make the results more applicable, we used in this study a general two-sample model, which assumes two longitudinal samples were taken from the same measurably evolving population. Inspired by the HIV study, we also studied a two-sample-two-stage model, which is a special case of two-sample model and assumes a treatment after the first sampling instantaneously changes the population size. We derived the formulas for calculating statistical properties, e.g. expectations, variances and covariances, of these new summary statistics under the two models. Potential applications of these results were discussed.     

Individualism in plant populations: using stochastic differential equations to model individual neighbourhood-dependent plant growth

We study individual plant growth and size hierarchy formation in an experimental population of Arabidopsis thaliana, within an integrated analysis that explicitly accounts for size-dependent growth, size- and space-dependent competition, and environmental stochasticity. It is shown that a Gompertz-type stochastic differential equation (SDE) model, involving asymmetric competition kernels and a stochastic term which decreases with the logarithm of plant weight, efficiently describes individual plant growth, competition, and variability in the studied population. The model is evaluated within a Bayesian framework and compared to its deterministic counterpart, and to several simplified stochastic models, using distributional validation. We show that stochasticity is an important determinant of size hierarchy and that SDE models outperform the deterministic model if and only if structural components of competition (asymmetry; size- and space-dependence) are accounted for. Implications of these results are discussed in the context of plant ecology and in more general modelling situations.