Cajo ter Braak

Cajo ter Braak
Wageningen University & Research | WUR · Biometris, Department of Mathematical and Statistical Methods

Professor Emeritus

About

326
Publications
111,549
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Introduction
Cajo ter Braak works at the Biometris, Department of Mathematical and Statistical Methods, Wageningen University & Research. Cajo does research in Statistical ecology, Multivariate analysis and Bayesian computation. '

Publications

Publications (326)
Book
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The vegan package provides tools for descriptive community ecology. It has most basic functions of diversity analysis, community ordination and dissimilarity analysis. Most of its multivariate tools can be used for other data types as well. The functions in the vegan package contain tools for diversity analysis, ordination methods and tools for th...
Article
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In testing an overall null hypothesis, it does not matter whether to permute the response variables (Y) while keeping the predictors fixed or to permute the predictor variables (X) while keeping the response variables fixed. However, in weighted (univariate and multivariate) regression and in partial tests these options yield different results. Thi...
Preprint
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The Iberian Peninsula is characterised by a steep west-east moisture gradient today, reflecting the dominance of maritime influences along the Atlantic coast and more Mediterranean-type climate further east. Holocene pollen records from the Peninsula suggest that this gradient was less steep during the early to mid-Holocene, possibly reflecting the...
Article
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Bacteria are part of the insect gut system and influence many physiological traits of their host. Gut bacteria may even reduce or block the transmission of arboviruses in several species of arthropod vectors. Culicoides biting midges are important arboviral vectors of several livestock and wildlife diseases, yet limited information is available on...
Article
Aim Here we examine the functional profile of regional tree species pools across the latitudinal distribution of Neotropical moist forests, and test trait–climate relationships among local communities. We expected opportunistic strategies (acquisitive traits, small seeds) to be overrepresented in species pools further from the equator, but also in...
Article
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Aim High levels of nitrogen deposition have been responsible for important losses of plant species diversity. It is often assumed that reduction of ammonia and nitrogen oxide emissions will result in the recovery of the former biodiversity. In Western Europe, N deposition peaked between 1980 and 1988 and declined thereafter. In a 60‐year experiment...
Article
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Microbiome composition data collected through amplicon sequencing are count data on taxa in which the total count per sample (the library size) is an artefact of the sequencing platform and as a result such data are compositional. To avoid library size dependency, one common way of analyzing multivariate compositional data is to perform a principal...
Article
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To combat antimicrobial resistance (AMR), policymakers need an overview of evolution and trends of AMR in relevant animal reservoirs, and livestock is monitored by susceptibility testing of sentinel organisms such as commensal E. coli. Such monitoring data are often vast and complex and generates a need for outcome indicators that summarize AMR for...
Article
Quantitative reconstructions of past climates are an important resource for evaluating how well climate models reproduce climate changes. One widely used statistical approach for making such reconstructions from fossil biotic assemblages is weighted averaging partial least-squares regression (WA-PLS). There is however a known tendency for WA-PLS to...
Article
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Tripartite interactions among insect vectors, midgut bacteria, and viruses may determine the ability of insects to transmit pathogenic arboviruses. Here, we investigated the impact of gut bacteria on the susceptibility of Culicoides nubeculosus and Culicoides sonorensis biting midges for Schmallenberg virus, and of Aedes aegypti mosquitoes for Zika...
Data
This is the supplementary material of the paper "Double constrained ordination for assessing biological trait responses to multiple stressors: A case study with benthic macroinvertebrate communities" organized in a better way than at the publisher (https://doi.org/10.1016/j.scitotenv.2020.142171) . Notably, the zip file with R code for dc-CA contai...
Article
Full-text available
Benthic macroinvertebrate communities are used as indicators for anthropogenic stress in freshwater ecosystems. To better understand the relationship between anthropogenic stress and changes in macroinvertebrate community composition, it is important to understand how different stressors and species traits are associated, and how these associations...
Article
Full-text available
Microbial communities, which drive the major ecosystem functions, are composed by a wide range of interacting species. Understanding how microbial communities are structured and the underlying processes is a crucial task for interpreting ecosystem response to global change but it is challenging as microbial interactions cannot usually be directly o...
Article
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An amendment to this paper has been published and can be accessed via a link at the top of the paper.
Article
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The use of functional information in the form of species traits plays an important role in explaining biodiversity patterns and responses to environmental changes. Although relationships between species composition, their traits, and the environment have been extensively studied on a case-by-case basis, results are variable, and it remains unclear...
Article
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Alfalfa (Medicago sativa L.) silage (AS) is an important feedstuff in ruminant nutrition. However, its high non-protein nitrogen content often leads to poor ruminal nitrogen retention. Various pre-ensiling treatments differing with respect to dry matter concentrations, wilting intensities and sucrose addition have been previously shown to improve t...
Article
Urban rivers often function as sinks for various contaminants potentially placing the benthic communities at risk of exposure. We performed a comprehensive biological survey of the benthic macroinvertebrate and bacterial community compositions in six rivers from the suburb to the central urban area of Guangzhou city (South China), and evaluated the...
Article
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Introduction Attention deficit hyperactivity disorder (ADHD) is the most common childhood behavioural disorder, causing significant impediment to a child’s development. It is a complex disorder with numerous contributing (epi)genetic and environmental factors. Currently, treatment consists of behavioural and pharmacological therapy. However, ADHD m...
Article
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1.Statistical analysis of trait‐environment association is challenging owing to the lack of a common observation unit: Community weighted mean regression (CWMr) uses site points, multilevel models focus on species points, and the fourth‐corner correlation uses all species‐site combinations. This situation invites the development of new methods capa...
Article
The Eemian interglacial represents a natural experiment on how past vegetation with negligible human impact responded to amplified temperature changes compared to the Holocene. Here, we assemble 47 carefully selected Eemian pollen sequences from Europe to explore geographical patterns of (1) total compositional turnover and total variation for each...
Preprint
Full-text available
Statistical analysis of trait-environment association is challenging owing to the lack of a common observation unit: Community weighted mean regression (CWM) uses site points, multilevel models use species points, and the fourth corner correlation uses all species-site combinations. This situation invites the development of new methods capable of u...
Preprint
Full-text available
Statistical analysis of trait-environment association is challenging owing to the lack of a common observation unit: Community weighted mean regression (CWM) uses site points, multilevel models use species points, and the fourth corner correlation uses all species-site combinations. This situation invites the development of new methods capable of u...
Article
Full-text available
The fourth‐corner analysis aims to quantify and test for relationships between species traits and site‐specific environmental variables, mediated by site‐specific species abundances. Since there is no common unit of observation, the significance of the relationships is tested using a double permutation procedure (site‐based and species‐based). This...
Article
Full-text available
Question The community weighted means (CWM) approach is an easy way of analyzing trait‐environment association by regressing (or correlating) the mean trait per plot against an environmental variable and assessing the statistical significance of the slope or the associated correlation coefficient. However, the CWM approach does not yield valid test...
Article
Full-text available
Correspondence analysis with linear external constraints on both the rows and the columns has been mentioned in the ecological literature, but lacks full mathematical treatment and easily available algorithms and software. This paper fills this gap by defining the method as maximizing the fourth-corner correlation between linear combinations, by pr...
Article
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Ultrasonic vocalizations (USVs) are crucial in the social behavior of rats. We aim to relate USV rates of pairs of rats to individual activity in an automated home cage (PhenoTyper®) where USVs are recorded per pair and not per individual. We propose a composite link model approach to parametrize a mechanistic “sum‐of‐rates” model in which the pair...
Presentation
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Presentation summarizing 5 papers on trait-environment relations in ecology, L-shaped data or bipartite graphs. It starts with a description of the data, a simple loglinear (GLM) model and the Rao score test on interaction. This leads to the Legendre’s fourth-corner correlation and, for multi-trait, multi-environment problems, double constrained co...
Article
An environmental risk assessment for the introduction of genetically modified crops includes assessing the consequences for biodiversity. In this study arthropod biodiversity was measured using pitfall traps in potato agro-ecosystems in Ireland and The Netherlands over two years. We tested the impact of site, year, potato genotype, and fungicide ma...
Article
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Leaves are the major component of terrestrial litter input into aquatic systems. Leaves are distributed by the flow, accumulate in low flow areas and form patches. In natural streams, stable leaf patches form around complex structures, such as large woody debris. Until now, little is known about flow conditions under which leaf patches persist. Thi...
Article
Full-text available
Ecologists wish to understand the role of traits of species in determining where each species occurs in the environment. For this, they wish to detect associations between species traits and environmental variables from three data tables, species count data from sites with associated environmental data and species trait data from data bases. These...
Article
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Principal response curves analysis (PRC) is widely applied to experimental multivariate longitudinal data for the study of time-dependent treatment effects on the multiple outcomes or response variables (RVs). Often, not all of the RVs included in such a study are affected by the treatment and RV-selection can be used to identify those RVs and so g...
Article
Full-text available
Statistical testing of trait-environment association from data is a challenge as there is no common unit of observation: the trait is observed on species, the environment on sites and the mediating abundance on species-site combinations. A number of correlation-based methods, such as the community weighted trait means method (CWM), the fourth-corne...
Data
The simulation models Mathematical description of the Gaussian response model and log-linear model used in the simulation.
Data
Annotated R-functions and scripts Description of the R functions and script with example output.
Data
Diagnostic plot Dunn-Smith residuals of the model ‘site+species+species:Snow’ against the fitted values in the aravo data set.
Data
Why does site-based statistical testing in a GLM fail?
Data
R-files The zip contains three R-files. The file trait_env_Type_I_error_examples.R is the driver script, the other contain functions as explained in Article S2.
Article
Full-text available
The process of macroinvertebrate drift in streams is characterized by dislodgement, drift distance and subsequent return to the bottom. While dislodgement is well studied, the fate of drifting organisms is poorly understood, especially concerning Trichoptera. Therefore, the aim of the present study was to determine the ability of six case-building...
Article
Full-text available
Establishing trait-environment relationships has become routine in community ecology. Here, we demonstrate that the Community Weighted Means correlation (CWM) and its parallel approach in linking trait variation to the environment, the Species Niche Centroid correlation (SNC), have important shortcomings, arguing against their continuing applicatio...
Article
Quantitative insight into species differences in risk assessment is expected to reduce uncertainty and variability related to extrapolation from animals to humans. This paper explores quantification and comparison of gene expression data between tissues and species from intervention studies with isoflavones. Gene expression data from peripheral blo...
Article
Full-text available
There is a growing need for good environmental risk assessment of engineered nanoparticles (ENPs). Environmental risk assessment of ENPs has been hampered by lack of data and knowledge about ENPs, their environmental fate and their toxicity. This leads to uncertainty in the risk assessment. To effectively deal with uncertainty in the risk assessmen...
Article
Full-text available
The ecosystem services (EcoS) concept is being used increasingly to attach values to natural systems and the multiple benefits they provide to human societies. Ecosystem processes or functions only become EcoS if they are shown to have social and/or economic value. This should assure an explicit connection between the natural and social sciences, b...
Article
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Estimating the risk, P(X > Y), in probabilistic environmental risk assessment of nanoparticles is a problem when confronted by potentially small risks and small sample sizes of the exposure concentration X and/or the effect concentration Y. This is illustrated in the motivating case study of aquatic risk assessment of nano-Ag. A non-parametric esti...
Article
Both environmental filtering and dispersal filtering are known to influence plant species distribution patterns and biodiversity. Particularly in dynamic habitats, however, it remains unclear whether environmental filtering (stimulated by stressful conditions) or dispersal filtering (during recolonization events) dominates in community assembly, or...
Article
Full-text available
Insight into risks of nanotechnology and the use of nanoparticles is an essential condition for the social acceptance and safe use of nanotechnology. One of the problems with which the risk assessment of nanoparticles is faced is the lack of data, resulting in uncertainty in the risk assessment. We attempt to quantify some of this uncertainty by ex...
Article
Full-text available
In this paper, we reflect on a number of aspects of ordination methods: how should absences be treated in ordination and how do model-based methods, including Gaussian ordination and methods using generalized linear models, relate to the usual least-squares (eigenvector) methods based on (log−) transformed data. We defend detrended correspondence a...
Article
Recruitment processes are critical components of a plant's life cycle. However, in comparison with later stages in the plant life cycle (e.g. competition among adults), relatively little is known about their contribution to the regulation of plant species distribution. Particularly, little is known about the individual contributions of the three ma...
Article
Full-text available
Mesocosm experiments that study the ecological impact of chemicals are often analysed using the multivariate method 'Principal Response Curves' (PRCs). Recently, the extension of generalised linear models (GLMs) to multivariate data was introduced as a tool to analyse community data in ecology. Moreover, data aggregation techniques that can be anal...
Article
Full-text available
Both environmental filtering and dispersal filtering are known to influence plant species distribution patterns and biodiversity. Particularly in dynamic habitats, however, it remains unclear whether environmental filtering (stimulated by stressful conditions) or dispersal filtering (during recolonization events) dominates in community assembly, or...
Article
The number of perennial low-order lowland streams likely to experience intermittent flow is predicted to increase in north-western Europe. To understand the effects of such a change on macroinvertebrates, a field experiment was carried out in a currently perennial sandy lowland stream.Using a before–after control–impact design, the flow regime was...
Conference Paper
Full-text available
La agricultura se ha intensificado asociada a una mayor dependencia de los combustibles fósiles (agroquímicos, mecanización, riego), comprometiendo su sostenibilidad. Las rotaciones de cultivos son claves para mejorar la sostenibilidad de los sistemas de producción. El diseño de las rotaciones es un proceso complejo que conjuga diversos objetivos,...
Article
Full-text available
Multi-parameter models in systems biology are typically 'sloppy': some parameters or combinations of parameters may be hard to estimate from data, whereas others are not. One might expect that parameter uncertainty automatically leads to uncertain predictions, but this is not the case. We illustrate this by showing that the prediction uncertainty o...
Article
Full-text available
In this paper we attempt to explain observed niche differences among species (i.e. differences in their distribution along environmental gradients) by differences in trait values (e.g. volume) in phytoplankton communities. For this, we propose the trait-modulated Gaussian logistic model in which the niche parameters (optimum, tolerance and maximum)...
Article
Autonomous navigation of field robots in an agricultural environment is a difficult task due to the inherent uncertainty in the environment. The drawback of existing systems is the lack of robustness to these uncertainties. In this study we propose a vision-based navigation method to address these problems. The focus is on navigation through a maiz...
Article
Assessing trait responses to environmental gradients requires the simultaneous analysis of the information contained in three tables: L (species distribution across samples), R (environmental characteristics of samples), and Q (species traits). Among the available methods, the so-called fourth-corner and RLQ methods are two appealing alternatives t...
Article
Full-text available
Recurrent Clostridium difficile infection (CDI) can be effectively treated by infusion of a healthy donor faeces suspension. However, it is unclear what factors determine treatment efficacy. By using a phylogenetic microarray platform, we assessed composition, diversity and dynamics of faecal microbiota before, after and during follow-up of the tra...
Article
Autonomous navigation of robots in an agricultural environment is a difficult task due to the inherent uncertainty in the environment. Many existing agricultural robots use computer vision and other sensors to supplement Global Positioning System (GPS) data when navigating. Vision based methods are sensitive to ambient lighting conditions. This is...