Measuring temporal change in alpha diversity : a framework integrating taxonomic, phylogenetic and functional diversity and the iNEXT.3D standardization

Funding: This work is jointly supported by the Natural Environment Research Council, UK (NE/T004487/1 for AM and MD) and the Taiwan Ministry of Science and Technology under Contracts NERC-MOST 108-2923-M-007-003 (for AC and CC). AM and MD also acknowledge support from the Leverhulme Trust (RPG-2019-401).1. Biodiversity is a multifaceted concept covering different levels of organisation from genes to ecosystems. Biodiversity has at least three dimensions: (i) Taxonomic diversity (TD): a measure that is sensitive to the number and abundances of species. (ii) Phylogenetic diversity (PD): a measure that incorporates not only species abundances but also species evolutionary histories. (iii) Functional diversity (FD): a measure that considers not only species abundances but also species? traits. 2. We integrate the three dimensions of diversity under a unified framework of Hill numbers and their generalizations. Our TD quantifies the effective number of equally-abundant species, PD quantifies the effective total branch length, mean-PD (PD divided by tree depth) quantifies the effective number of equally-divergent lineages, and FD quantifies the effective number of equally-distinct virtual functional groups (or functional ?species?). Thus, TD, mean-PD and FD are all in the same units of species/lineage equivalents and can be meaningfully compared. 3. Like species richness, empirical TD, PD and FD based on sampling data, depend on sampling effort and sample completeness. For TD (Hill numbers), the iNEXT (interpolation and extrapolation) standardization was developed for standardizing sample size or sample completeness (as measured by sample coverage, the fraction of individuals that belong to the observed species) to make objective comparisons across studies. This paper extends the iNEXT method to the iNEXT.3D standardization to encompass all three dimensions of diversity via sample-size- and sample-coverage-based rarefaction and extrapolation under the unified framework. The asymptotic diversity estimates (i.e., sample size tends to infinity and sample coverage tends to unity) are also derived. In addition to individual-based abundance data, the proposed iNEXT.3D standardization is adapted to deal with incidence-based occurrence data. 4. We apply the integrative framework and the proposed iNEXT.3D standardization to measure temporal alpha-diversity changes for estuarine fish assemblage data spanning four decades. The influence of environmental drivers on diversity change are also assessed. Our analysis informs a mechanistic interpretation of biodiversity change in the three dimensions of diversity. The accompanying freeware, iNEXT.3D, developed during this project, facilitates all computation and graphics.PostprintPeer reviewe

Diversity from genes to ecosystems : a unifying framework to study variation across biological metrics and scales

This work was assisted through participation in “Next Generation Genetic Monitoring” Investigative Workshop at the National Institute for Mathematical and Biological Synthesis, sponsored by the National Science Foundation through NSF Award #DBI-1300426, with additional support from The University of Tennessee, Knoxville. Hawaiian fish community data were provided by the NOAA Pacific Islands Fisheries Science Center's Coral Reef Ecosystem Division (CRED) with funding from NOAA Coral Reef Conservation Program. O.E.G. was supported by the Marine Alliance for Science and Technology for Scotland (MASTS). A. C. and C. H. C. were supported by the Ministry of Science and Technology, Taiwan. P.P.-N. was supported by a Canada Research Chair in Spatial Modelling and Biodiversity. K.A.S. was supported by National Science Foundation (BioOCE Award Number 1260169) and the National Center for Ecological Analysis and Synthesis. All data used in this manuscript are available in DRYAD (https://doi.org/dx.doi.org/10.5061/dryad.qm288) and BCO-DMO (http://www.bco-dmo.org/project/552879).Biological diversity is a key concept in the life sciences and plays a fundamental role in many ecological and evolutionary processes. Although biodiversity is inherently a hierarchical concept covering different levels of organisation (genes, population, species, ecological communities and ecosystems), a diversity index that behaves consistently across these different levels has so far been lacking, hindering the development of truly integrative biodiversity studies. To fill this important knowledge gap we present a unifying framework for the measurement of biodiversity across hierarchical levels of organisation. Our weighted, information-based decomposition framework is based on a Hill number of order q = 1, which weights all elements in proportion to their frequency and leads to diversity measures based on Shannon’s entropy. We investigated the numerical behaviour of our approach with simulations and showed that it can accurately describe complex spatial hierarchical structures. To demonstrate the intuitive and straightforward interpretation of our diversity measures in terms of effective number of components (alleles, species, etc.) we applied the framework to a real dataset on coral reef biodiversity. We expect our framework will have multiple applications covering the fields of conservation biology, community genetics, and eco-evolutionary dynamics.Publisher PDFPeer reviewe

Quantifying sample completeness and comparing diversities among assemblages.

We develop a novel class of measures to quantify sample completeness of a biological survey. The class of measures is parameterized by an order q ≥ 0 to control for sensitivity to species relative abundances. When q = 0, species abundances are disregarded and our measure reduces to the conventional measure of completeness, that is, the ratio of the observed species richness to the true richness (observed plus undetected). When q = 1, our measure reduces to the sample coverage (the proportion of the total number of individuals in the entire assemblage that belongs to detected species), a concept developed by Alan Turing in his cryptographic analysis. The sample completeness of a general order q ≥ 0 extends Turing's sample coverage and quantifies the proportion of the assemblage's individuals belonging to detected species, with each individual being proportionally weighted by the (q − 1)th power of its abundance. We propose the use of a continuous profile depicting our proposed measures with respect to q ≥ 0 to characterize the sample completeness of a survey. An analytic estimator of the diversity profile and its sampling uncertainty based on a bootstrap method are derived and tested by simulations. To compare diversity across multiple assemblages, we propose an integrated approach based on the framework of Hill numbers to assess (a) the sample completeness profile, (b) asymptotic diversity estimates to infer true diversities of entire assemblages, (c) non‐asymptotic standardization via rarefaction and extrapolation, and (d) an evenness profile. Our framework can be extended to incidence data. Empirical data sets from several research fields are used for illustration.publishedVersionPaid Open Acces

Rarefaction and extrapolation with beta diversity under a framework of Hill numbers : the iNEXT.beta3D standardization

This work isjointly supported by the Natural Environment Research Council, UK and the Taiwan Ministry of Science and Technology under Contracts NERC-MOST 108-2923-M-007-003 and NE/T004487/1. AEM also acknowledges the Leverhulme Trust (RPG-2019-402). Support for the establishment and monitoring of permanent plots in Costa Rican forests was provided by grants from the Andrew W. Mellon Foundation, the US National Science Foundation (NSF DEB-0424767, NSF DEB-0639393 and NSF DEB-1147429), US NASA Terrestrial Ecology Program, and the University of Connecticut Research Foundation. MD is supported by a Leverhulme Trust Research Centre - the Leverhulme Centre for Anthropocene Biodiversity (RC-2018-021). L.F.S.M. was supported by the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) grant 307984/2022-2.Based on sampling data, we propose a rigorous standardization method to measure and compare beta diversity across datasets. Here beta diversity, which quantifies the extent of among-assemblage differentiation, relies on Whittaker's original multiplicative decomposition scheme, but we use Hill numbers for any diversity order q ≥ 0. Richness-based beta diversity (q = 0) quantifies the extent of species identity shift, whereas abundance-based (q > 0) beta diversity also quantifies the extent of difference among assemblages in species abundance. We adopt and define the assumptions of a statistical sampling model as the foundation for our approach, treating sampling data as a representative sample taken from an assemblage. The approach makes a clear distinction between the theoretical assemblage level (unknown properties/parameters of the assemblage) and the sampling data level (empirical/observed statistics computed from data). At the assemblage level, beta diversity for N assemblages reflects the interacting effect of the species abundance distribution and spatial/temporal aggregation of individuals in the assemblage. Under independent sampling, observed beta (= gamma/alpha) diversity depends not only on among-assemblage differentiation but also on sampling effort/completeness, which in turn induces dependence of beta on alpha and gamma diversity. How to remove the dependence of richness-based beta diversity on its gamma component (species pool) has been intensely debated. Our approach is to standardize gamma and alpha based on sample coverage (an objective measure of sample completeness). For a single assemblage, the iNEXT method was developed, through interpolation (rarefaction) and extrapolation with Hill numbers, to standardize samples by sampling effort/completeness. Here we adapt the iNEXT standardization to alpha and gamma diversity, that is, alpha and gamma diversity are both assessed at the same level of sample coverage, to formulate standardized, coverage-based beta diversity. This extension of iNEXT to beta diversity required the development of novel concepts and theories, including a formal proof and simulation-based demonstration that the resulting standardized beta diversity removes the dependence of beta diversity on both gamma and alpha values, and thus reflects the pure among-assemblage differentiation. The proposed standardization is illustrated with spatial, temporal, and spatiotemporal datasets, while the freeware iNEXT.beta3D facilitates all computations and graphics.Publisher PDFPeer reviewe

Biological Properties of Acidic Cosmetic Water from Seawater

This current work was to investigate the biological effects of acidic cosmetic water (ACW) on various biological assays. ACW was isolated from seawater and demonstrated several bio-functions at various concentration ranges. ACW showed a satisfactory effect against Staphylococcus aureus, which reduced 90% of bacterial growth after a 5-second exposure. We used cultured human peripheral blood mononuclear cells (PBMCs) to test the properties of ACW in inflammatory cytokine release, and it did not induce inflammatory cytokine release from un-stimulated, normal PBMCs. However, ACW was able to inhibit bacterial lipopolysaccharide (LPS)-induced inflammatory cytokine TNF-α released from PBMCs, showing an anti-inflammation potential. Furthermore, ACW did not stimulate the rat basophilic leukemia cell (RBL-2H3) related allergy response on de-granulation. Our data presented ACW with a strong anti-oxidative ability in a superoxide anion radical scavenging assay. In mass spectrometry information, magnesium and zinc ions demonstrated bio-functional detections for anti-inflammation as well as other metal ions such as potassium and calcium were observed. ACW also had minor tyrosinase and melanin decreasing activities in human epidermal melanocytes (HEMn-MP) without apparent cytotoxicity. In addition, the cell proliferation assay illustrated anti-growth and anti-migration effects of ACW on human skin melanoma cells (A375.S2) indicating that it exerted the anti-cancer potential against skin cancer. The results obtained from biological assays showed that ACW possessed multiple bioactivities, including anti-microorganism, anti-inflammation, allergy-free, antioxidant, anti-melanin and anticancer properties. To our knowledge, this was the first report presenting these bioactivities on ACW

Hill-Chao numbers allow decomposing gamma multifunctionality into alpha and beta components

Biodiversity-ecosystem functioning (BEF) research has provided strong evidence and mechanistic underpinnings to support positive effects of biodiversity on ecosystem functioning, from single to multiple functions. This research has provided knowledge gained mainly at the local alpha scale (i.e. within ecosystems), but the increasing homogenization of landscapes in the Anthropocene has raised the potential that declining biodiversity at the beta (across ecosystems) and gamma scales is likely to also impact ecosystem functioning. Drawing on biodiversity theory, we propose a new statistical framework based on Hill-Chao numbers. The framework allows decomposition of multifunctionality at gamma scales into alpha and beta components, a critical but hitherto missing tool in BEF research; it also allows weighting of individual ecosystem functions. Through the proposed decomposition, new BEF results for beta and gamma scales are discovered. Our novel approach is applicable across ecosystems and connects local- and landscape-scale BEF assessments from experiments to natural settings

Asymmetric Origin for Gravitino Relic Density in the Hybrid Gravity-Gauge Mediated Supersymmetry Breaking

We propose the hybrid gravity-gauge mediated supersymmetry breaking where the gravitino mass is about several GeV. The strong constraints on supersymmetry viable parameter space from the CMS and ATLAS experiments at the LHC can be relaxed due to the heavy colored supersymmetric particles, and it is consistent with null results in the dark matter (DM) direct search experiments such as XENON100. In particular, the possible maximal flavor and CP violations from the relatively small gravity mediation may naturally account for the recent LHCb anomaly. In addition, because the gravitino mass is around the asymmetric DM mass, we propose the asymmetric origin of the gravitino relic density and solve the cosmological coincident problem on the DM and baryon densities \Omega_{\rm DM}:\Omega_{B}\approx 5:1. The gravitino relic density arises from asymmetric metastable particle (AMP) late decay. However, we show that there is no AMP candidate in the minimal supersymmetric Standard Model (SM) due to the robust gaugino/Higgsino mediated wash-out effects. Interestingly, AMP can be realized in the well motivated supersymmetric SMs with vector-like particles or continuous U(1)_R symmetry. Especially, the lightest CP-even Higgs boson mass can be lifted in the supersymmetric SMs with vector-like particles.Comment: RevTex4, 21 pages, 1 figure, minor corrections, JHEP versio

R code for "A species richness estimator for sample-based incidence data sampled without replacement"

<p>The attached file includes the R code for constructing the figures and tables in the manuscript: "A species richness estimator for sample-based incidence data sampled without replacement." </p> <p>There are four main functions in the .txt file.</p> <ol> <li>SWOR_MLE(data,t,tt): output is the MLE of richness and its standard error.</li> <li>SWOR_Chao2(data,t,tt): output is wChao2 (Without-replacement-based Chao2) and its standard error. </li> <li>SWOR_NEW(data,t,tt): output is the newly proposed richness estimate and its standard error.</li> <li>WOR_Chao2(data,t): output is the Chao2 (With replacement) and its standard error.</li> </ol> <p>The inputs in each function:</p> <ol> <li>"data" is a numerical vector: the frequencies of species in the sample-based incidence data (the number of plots that species detected).</li> <li>"t" is the number of plots sampled in the sample.</li> <li>"tt" is the total number of plots in the region. </li> </ol> <p> </p&gt