Some solutions to the multivariate Behrens-Fisher problem for dissimilarity-based analyses

The essence of the generalised multivariate Behrens–Fisher problem (BFP) is how to test the null hypothesis of equality of mean vectors for two or more populations when their dispersion matrices differ. Solutions to the BFP usually assume variables are multivariate normal and do not handle high‐dimensional data. In ecology, species' count data are often high‐dimensional, non‐normal and heterogeneous. Also, interest lies in analysing compositional dissimilarities among whole communities in non‐Euclidean (semi‐metric or non‐metric) multivariate space. Hence, dissimilarity‐based tests by permutation (e.g., PERMANOVA, ANOSIM) are used to detect differences among groups of multivariate samples. Such tests are not robust, however, to heterogeneity of dispersions in the space of the chosen dissimilarity measure, most conspicuously for unbalanced designs. Here, we propose a modification to the PERMANOVA test statistic, coupled with either permutation or bootstrap resampling methods, as a solution to the BFP for dissimilarity‐based tests. Empirical simulations demonstrate that the type I error remains close to nominal significance levels under classical scenarios known to cause problems for the un‐modified test. Furthermore, the permutation approach is found to be more powerful than the (more conservative) bootstrap for detecting changes in community structure for real ecological datasets. The utility of the approach is shown through analysis of 809 species of benthic soft‐sediment invertebrates from 101 sites in five areas spanning 1960 km along the Norwegian continental shelf, based on the Jaccard dissimilarity measure

Emergent synergistic lysosomal toxicity of chemical mixtures in molluscan blood cells (hemocytes)

The problem of effective assessment of risk posed by complex mixtures of toxic chemicals in the environment is a major challenge for government regulators and industry. The biological effect of the individual contaminants, where these are known, can be measured; but the problem lies in relating toxicity to the multiple constituents of contaminant cocktails. The objective of this study was to test the hypothesis that diverse contaminant mixtures may cause a greater toxicity than the sum of their individual parts, due to synergistic interactions between contaminants with different intracellular targets. Lysosomal membrane stability in hemocytes from marine mussels was used for in vitro toxicity tests; and was coupled with analysis using the isobole method and a linear additive statistical model. The findings from both methods have shown significant emergent synergistic interactions between environmentally relevant chemicals (i.e., polycyclic aromatic hydrocarbons, pesticides, biocides and a surfactant) when exposed to isolated hemocytes as a mixture of 3 & 7 constituents. The results support the complexity-based hypothesis that emergent toxicity occurs with increasing contaminant diversity, and raises questions about the validity of estimating toxicity of contaminant mixtures based on the additive toxicity of single components. Further experimentation is required to investigate the potential for interactive effects in mixtures with more constituents (e.g., 50 –100) at more environmentally realistic concentrations in order to test other regions of the model, namely, very low concentrations and high diversity. Estimated toxicant diversity coupled with tests for lysosomal damage may provide a potential tool for determining the toxicity of estuarine sediments, dredge spoil or contaminated soil

Contrasting arbuscular mycorrhizal communities colonizing different host plants show a similar response to a soil phosphorus concentration gradient

High soil phosphorus (P) concentration is frequently shown to reduce root colonization by arbuscular mycorrhizal (AM) fungi, but the influence of P on the diversity of colonizing AM fungi is uncertain. We used terminal restriction fragment length polymorphism (T-RFLP) of 18S rDNA and cloning to assess diversity of AM fungi colonizing maize (Zea mays), soybean (Glycene max) and field violet (Viola arvensis) at three time points in one season along a P gradient of 10–280 mg l−1 in the field. Percentage AM colonization changed between sampling time points but was not reduced by high soil P except in maize. There was no significant difference in AM diversity between sampling time points. Diversity was reduced at concentrations of P > 25 mg l−1, particularly in maize and soybean. Both cloning and T-RFLP indicated differences between AM communities in the different host species. Host species was more important than soil P in determining the AM community, except at the highest P concentration. Our results show that the impact of soil P on the diversity of AM fungi colonizing plants was broadly similar, despite the fact that different plants contained different communities. However, subtle differences in the response of the AM community in each host were evident

Analysis of similarities (ANOSIM) for 3‐way designs

Analysis of similarities (ANOSIM) is a robust non-parametric hypothesis-testing framework for differences in resemblances among groups of samples. To date, the generalisation and use of ANOSIM to analyse various 2-way nested and crossed designs with unordered or ordered factors has been described. This paper describes how the 2-way tests may be extended and modified for the analysis of 3-way designs, including the introduction of a different type of constrained permutation procedure for a design in which one factor is nested in another and crossed with a third. The construction of 3-way tests using the generalised statistic in various nested and crossed designs, with or without ordered factors, and with or without replication, is described. Applications of the new tests to ecological data are demonstrated using three marine examples. They are as follows: a study of changes in fish diet for fish of increasing size sampled in different locations at different times (a 3-way fully crossed design with ordered factors); a hierarchical spatial study of the fauna inhabiting kelp holdfasts (a 3- way fully nested design with unordered factors); and a study of infaunal macrobenthos in which sites within areas were resampled over a long time series (a design in which sites are nested in areas but crossed with years, both latter factors potentially being ordered). The magnitudes of the ANOSIM statistics provide information about relative effect sizes (accounting for other factors), which is often a focus for multifactorial designs. Though the described ANOSIM tests do not provide parallels for all the range of 3-way mixed-factor designs possible in ANOVA (and its multivariate semi-parametric counterpart PERMANOVA), it is seen that for nested factors these ANOSIM tests parallel the matching PERMANOVA random-effects models, and not their fixed-effects counterparts, thus allowing the same broader inference about the space from which these random factor levels are drawn

Analysis of similarities (ANOSIM) for 2‐way layouts using a generalised ANOSIM statistic, with comparative notes on Permutational Multivariate Analysis of Variance (PERMANOVA)

In the study of multivariate data, for example of change in ecological communities, ANOSIM is a robust non-parametric hypothesis-testing framework for differences in resemblances among groups of samples. RELATE is a non-parametric Mantel test of the hypothesis of no relationship between two resemblance matrices. Details are given of the explicit link between the RELATE statistic, a Spearman rank correlation (ρ) between corresponding elements in the two resemblance matrices, and the ANOSIM statistic R, a scaled contrast between the among- and within-group ranks. It is seen that R can equivalently be defined as the slope of the linear regression of ranked resemblances from observations against ranked distances among samples, the latter from a simple model matrix assigning the values 1 and 0 to between- and within-group distances, respectively. Re-defining this model matrix to represent ordered distances among groups leads naturally to a generalised ANOSIM statistic, RO, suitable for testing, for example, ordered factor levels in space or time, or an environmental or pollution gradient. Two variants of the generalised ANOSIM statistic are described, namely ROc where there are replicates within groups, and ROs where there are only single samples (no replicates) within groups, for which an ANOSIM test was not previously available. Three marine ecological examples using ANOSIM to analyse an ordered factor in one-way designs are provided. These are: (1) changes in macrofaunal composition with increasing distance from an oil rig; (2) differences in phytal meiofaunal community composition with increasing macroalgal complexity; and (3) changes in average community composition of free-living nematodes along a long-term heavy metal gradient. Incorporating knowledge of an ordering structure is seen to provide more focussed, and thus stronger, ANOSIM tests, but inevitably risks losing power if that prior knowledge is incorrect or inappropriate

Clustering in non-parametric multivariate analyses.

Non-parametric multivariate analyses of complex ecological datasets are widely used. Following appropriate pre-treatment of the data inter-sample resemblances are calculated using appropriate measures. Ordination and clustering derived from these resemblances are used to visualise relationships among samples (or variables). Hierarchical agglomerative clustering with group-average (UPGMA) linkage is often the clustering method chosen. Using an example dataset of zooplankton densities from the Bristol Channel and Severn Estuary, UK, a range of existing and new clustering methods are applied and the results compared. Although the examples focus on analysis of samples, the methods may also be applied to species analysis. Dendrograms derived by hierarchical clustering are compared using cophenetic correlations, which are also used to determine optimum in flexible beta clustering. A plot of cophenetic correlation against original dissimilarities reveals that a tree may be a poor representation of the full multivariate information. UNCTREE is an unconstrained binary divisive clustering algorithm in which values of the ANOSIM R statistic are used to determine (binary) splits in the data, to form a dendrogram. A form of flat clustering, k-R clustering, uses a combination of ANOSIM R and Similarity Profiles (SIMPROF) analyses to determine the optimum value of k, the number of groups into which samples should be clustered, and the sample membership of the groups. Robust outcomes from the application of such a range of differing techniques to the same resemblance matrix, as here, result in greater confidence in the validity of a clustering approach

A generalised analysis of similarities (ANOSIM) statistic for designs with ordered factors

In the study of multivariate data, for example of change in ecological communities, ANOSIM is a robust non-parametric hypothesis-testing framework for differences in resemblances among groups of samples. RELATE is a non-parametric Mantel test of the hypothesis of no relationship between two resemblance matrices. Details are given of the explicit link between the RELATE statistic, a Spearman rank correlation (ρ) between corresponding elements in the two resemblance matrices, and the ANOSIM statistic R, a scaled contrast between the among- and within-group ranks. It is seen that R can equivalently be defined as the slope of the linear regression of ranked resem�blances from observations against ranked distances among samples, the latter from a simple model matrix assigning the values 1 and 0 to between- and within-group distances, respectively. Re-defining this model matrix to represent ordered distances among groups leads naturally to a generalised ANOSIM statistic, RO, suitable for testing, for example, ordered factor levels in space or time, or an environmental or pollution gradient. Two variants of the generalised ANOSIM statistic are described, namely ROc where there are replicates within groups, and ROs where there are only single samples (no replicates) within groups, for which an ANOSIM test was not previously available. Three marine ecological examples using ANOSIM to analyse an ordered factor in one-way designs are provided. These are: (1) changes in macrofaunal composition with increasing distance from an oil rig; (2) differences in phytal meiofaunal community composition with increasing macroalgal complexity; and (3) changes in average community composition of free-living nematodes along a long-term heavy metal gradient. Incorporating knowledge of an ordering structure is seen to provide more focussed, and thus stronger, ANOSIM tests, but inevitably risks losing power if that prior knowledge is incorrect or inappropriat

Addressing Comorbidities in People with Parkinson’s Disease: Considerations From An Expert Panel

In the UK, guidance exists to aid clinicians and patients deciding when treatment for Parkinson’s disease (PD) should be initiated and which therapies to consider. National Institute for Health and Care Excellence (NICE) guidance recommends that before starting PD treatment clinicians should discuss the following: the patient’s individual clinical circumstances; lifestyle; preferences; needs and goals; as well as the potential benefits and harms of the different drug classes. Individualization of medicines and management in PD significantly improves patients’ outcomes and quality of life. This article aims to provide simple and practical guidance to help clinicians address common, but often overlooked, co-morbidities. A multi-disciplinary group of PD experts discussed areas where clinical care can be improved by addressing commonly found co-morbidities in people with Parkinson’s (PwP) based on clinical experience and existing literature, in a roundtable meeting organized and funded by Bial Pharma UK Ltd. The experts identified four core areas (bone health, cardiovascular risk, anticholinergic burden, and sleep quality) that, if further standardized may improve treatment outcomes for PwP patients. Focusing on anticholinergic burden, cardiac risk, sleep, and bone health could offer a significant contribution to personalizing regimes for PwP and improving overall patient outcomes. Within this opinion-based paper, the experts offer a list of guiding factors to help practitioners in the management of PwP

Evolution of oligomeric state through allosteric pathways that mimic ligand binding.

Evolution and design of protein complexes are almost always viewed through the lens of amino acid mutations at protein interfaces. We showed previously that residues not involved in the physical interaction between proteins make important contributions to oligomerization by acting indirectly or allosterically. In this work, we sought to investigate the mechanism by which allosteric mutations act, using the example of the PyrR family of pyrimidine operon attenuators. In this family, a perfectly sequence-conserved helix that forms a tetrameric interface is exposed as solvent-accessible surface in dimeric orthologs. This means that mutations must be acting from a distance to destabilize the interface. We identified 11 key mutations controlling oligomeric state, all distant from the interfaces and outside ligand-binding pockets. Finally, we show that the key mutations introduce conformational changes equivalent to the conformational shift between the free versus nucleotide-bound conformations of the proteins.This is the accepted manuscript. The final version is available from AAAS at http://www.sciencemag.org/content/346/6216/1254346.abstract

Wanted dead or alive : high diversity of macroinvertebrates associated with living and ’dead’ Posidonia oceanica matte

The Mediterranean endemic seagrass Posidonia oceanica forms beds characterised by a dense leaf canopy and a thick root-rhizome ‘matte’. Death of P. oceanica shoots leads to exposure of the underlying matte, which can persist for many years, and is termed ‘dead’ matte. Traditionally, dead matte has been regarded as a degraded habitat. To test whether this assumption was true, the motile macroinvertebrates of adjacent living (with shoots) and dead (without shoots) matte of P. oceanica were sampled in four different plots located at the same depth (5–6 m) in Mellieha Bay, Malta (central Mediterranean). The total number of species and abundance were significantly higher (ANOVA; P<0.05 and P<0.01, respectively) in the dead matte than in living P. oceanica matte, despite the presence of the foliar canopy in the latter. Multivariate analysis (MDS) clearly showed two main groups of assemblages, corresponding to the two matte types. The amphipods Leptocheirus guttatus and Maera grossimana, and the polychaete Nereis rava contributed most to the dissimilarity between the two different matte types. Several unique properties of the dead matte contributing to the unexpected higher number of species and abundance of motile macroinvertebrates associated with this habitat are discussed. The findings have important implications for the conservation of bare P. oceanica matte, which has been generally viewed as a habitat of low ecological value.peer-reviewe