We propose an integrated sampling, rarefaction, and extrapolation methodology to compare species richness of a set of communities based on samples of equal completeness (as measured by sample ...coverage) instead of equal size. Traditional rarefaction or extrapolation to equal-sized samples can misrepresent the relationships between the richnesses of the communities being compared because a sample of a given size may be sufficient to fully characterize the lower diversity community, but insufficient to characterize the richer community. Thus, the traditional method systematically biases the degree of differences between community richnesses. We derived a new analytic method for seamless coverage-based rarefaction and extrapolation. We show that this method yields less biased comparisons of richness between communities, and manages this with less total sampling effort. When this approach is integrated with an adaptive coverage-based stopping rule during sampling, samples may be compared directly without rarefaction, so no extra data is taken and none is thrown away. Even if this stopping rule is not used during data collection, coverage-based rarefaction throws away less data than traditional size-based rarefaction, and more efficiently finds the correct ranking of communities according to their true richnesses. Several hypothetical and real examples demonstrate these advantages.
Hill numbers or the effective number of species are increasingly used to quantify species diversity of an assemblage. Hill numbers were recently extended to phylogenetic diversity, which incorporates ...species evolutionary history, as well as to functional diversity, which considers the differences among species traits. We review these extensions and integrate them into a framework of attribute diversity (the effective number of entities or total attribute value) based on Hill numbers of taxonomic entities (species), phylogenetic entities (branches of unit-length), or functional entities (species-pairs with unit-distance between species). This framework unifies ecologists' measures of species diversity, phylogenetic diversity, and distance-based functional diversity. It also provides a unified method of decomposing these diversities and constructing normalized taxonomic, phylogenetic, and functional similarity and differentiation measures, including
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-assemblage phylogenetic or functional generalizations of the classic Jaccard, Sørensen, Horn, and Morisita-Horn indexes. A real example shows how this framework extracts ecological meaning from complex data.
Summary
The compositional complexity of an assemblage is not expressible as a single number; standard measures such as diversities (Hill numbers) and entropies (Rényi entropies and Tsallis entropies) ...vary in their order q which determines the measures' emphasis on rare or common species. Ranking and comparing assemblages depend on the choice of q. Rather than selecting one or a few measures to describe an assemblage, it is preferable to convey the complete story by presenting a continuous profile, a plot of diversity or entropy as a function of q ≥ 0. This makes it easy to visually compare the compositional complexities of multiple assemblages and to judge the evenness of the relative abundance distributions of the assemblages. In practice, the profile is plotted for all values of q from 0 to q = 3 or 4 (beyond which it generally changes little).
These profiles are usually generated by substituting species sample proportions into the complexity measures. However, this empirical approach typically underestimates the true profile for low values of q, because samples usually miss some of the assemblage's species due to under‐sampling. Although bias‐reduction methods exist for individual measures of order q = 0, 1 and 2, there has been no analytic method that unifies these bias‐corrected estimates into a continuous profile.
For incomplete sampling data, this work proposes a novel analytic method to obtain accurate, continuous, low‐bias diversity and entropy profiles with focus on low orders of q (0 ≤ q ≤ 3). Our approach is based on reformulating the diversity and entropy of any order q in terms of the successive discovery rates of new species with respect to sample size, that is the successive slopes of the species accumulation curve. A bootstrap method is applied to obtain approximate variances of our proposed profiles and to construct the associated confidence intervals.
Extensive simulations from theoretical models and real surveys show that the proposed profiles greatly reduce under‐sampling bias and have substantially lower bias and mean‐squared error than the empirical profile, especially for q ≤ 1. Our method is also extended to deal with incidence data.
Summary
Hill numbers (or the effective number of species) have been increasingly used to quantify the species/taxonomic diversity of an assemblage. The sample‐size‐ and coverage‐based integrations of ...rarefaction (interpolation) and extrapolation (prediction) of Hill numbers represent a unified standardization method for quantifying and comparing species diversity across multiple assemblages.
We briefly review the conceptual background of Hill numbers along with two approaches to standardization. We present an R package iNEXT (iNterpolation/EXTrapolation) which provides simple functions to compute and plot the seamless rarefaction and extrapolation sampling curves for the three most widely used members of the Hill number family (species richness, Shannon diversity and Simpson diversity). Two types of biodiversity data are allowed: individual‐based abundance data and sampling‐unit‐based incidence data.
Several applications of the iNEXT packages are reviewed: (i) Non‐asymptotic analysis: comparison of diversity estimates for equally large or equally complete samples. (ii) Asymptotic analysis: comparison of estimated asymptotic or true diversities. (iii) Assessment of sample completeness (sample coverage) across multiple samples. (iv) Comparison of estimated point diversities for a specified sample size or a specified level of sample coverage.
Two examples are demonstrated, using the data (one for abundance data and the other for incidence data) included in the package, to illustrate all R functions and graphical displays.
Hill numbers (or the "effective number of species") are increasingly used to characterize species diversity of an assemblage. This work extends Hill numbers to incorporate species pairwise functional ...distances calculated from species traits. We derive a parametric class of functional Hill numbers, which quantify "the effective number of equally abundant and (functionally) equally distinct species" in an assemblage. We also propose a class of mean functional diversity (per species), which quantifies the effective sum of functional distances between a fixed species to all other species. The product of the functional Hill number and the mean functional diversity thus quantifies the (total) functional diversity, i.e., the effective total distance between species of the assemblage. The three measures (functional Hill numbers, mean functional diversity and total functional diversity) quantify different aspects of species trait space, and all are based on species abundance and species pairwise functional distances. When all species are equally distinct, our functional Hill numbers reduce to ordinary Hill numbers. When species abundances are not considered or species are equally abundant, our total functional diversity reduces to the sum of all pairwise distances between species of an assemblage. The functional Hill numbers and the mean functional diversity both satisfy a replication principle, implying the total functional diversity satisfies a quadratic replication principle. When there are multiple assemblages defined by the investigator, each of the three measures of the pooled assemblage (gamma) can be multiplicatively decomposed into alpha and beta components, and the two components are independent. The resulting beta component measures pure functional differentiation among assemblages and can be further transformed to obtain several classes of normalized functional similarity (or differentiation) measures, including N-assemblage functional generalizations of the classic Jaccard, Sørensen, Horn and Morisita-Horn similarity indices. The proposed measures are applied to artificial and real data for illustration.
Celotno besedilo
Dostopno za:
DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, SIK, UILJ, UKNU, UL, UM, UPUK
We propose a parametric class of phylogenetic diversity (PD) measures that are sensitive to both species abundance and species taxonomic or phylogenetic distances. This work extends the conventional ...parametric species-neutral approach (based on ‘effective number of species’ or Hill numbers) to take into account species relatedness, and also generalizes the traditional phylogenetic approach (based on ‘total phylogenetic length’) to incorporate species abundances. The proposed measure quantifies ‘the mean effective number of species’ over any time interval of interest, or the ‘effective number of maximally distinct lineages’ over that time interval. The product of the measure and the interval length quantifies the ‘branch diversity’ of the phylogenetic tree during that interval. The new measures generalize and unify many existing measures and lead to a natural definition of taxonomic diversity as a special case. The replication principle (or doubling property), an important requirement for species-neutral diversity, is generalized to PD. The widely used Rao's quadratic entropy and the phylogenetic entropy do not satisfy this essential property, but a simple transformation converts each to our measures, which do satisfy the property. The proposed approach is applied to forest data for interpreting the effects of thinning.
There have been intense debates about the decomposition of regional diversity (gamma) into its within-community component (alpha) and between-community component (beta). Although a recent
Ecology
...Forum achieved consensus in the use of "numbers equivalents" (Hill numbers) as the proper choice of diversity measure, three related major issues were still left unresolved. (1) What is the precise meaning of the "independence" or "statistical independence" of alpha diversity and beta diversity? (2) Which partitioning (additive vs. multiplicative) should be used for a given application? (3) What is the proper formula for alpha diversity, as there are two formulas in the literature? This paper proposes a possible resolution to each of these issues. For the first issue, we clarify the definitions of "independence" and "statistical independence" from two perspectives so that confusion about this issue can be cleared up. We also discuss the causes of dependence, so that the dependence relationship between any two diversity components in both partitioning schemes can be rigorously justified by theory and also intuitively understood by simulation. For the second issue, both multiplicative and additive beta diversities based on Hill numbers are useful measures and quantify different aspects of communities. However, neither can be directly applied to compare relative compositional similarity or differentiation across multiple regions with different numbers of communities because multiplicative beta diversity depends on the number of communities, and additive beta diversity additionally depends on alpha (equivalently, on gamma). Such dependences should be removed. We propose transformations to remove these dependences, and we show that the transformed multiplicative beta and additive beta both lead to the same classes of measures, which are always in a range of 0, 1 and thus can be used to compare relative similarity or differentiation among communities across multiple regions. These similarity measures include multiple-community generalizations of the Sørenson, Jaccard, Horn, and Morisita-Horn measures. For the third issue, we present some observations including a finding about which alpha formula produces independent alpha and beta components. These may help to resolve the choice of a proper formula for alpha diversity. Some related issues are also briefly discussed.
Until now, decomposition of abundance-sensitive gamma (regional) phylogenetic diversity measures into alpha and beta (within- and between-group) components has been based on an additive partitioning ...of phylogenetic generalized entropies, especially Rao's quadratic entropy. This additive approach led to a phylogenetic measure of differentiation between assemblages: (gamma − alpha)/gamma. We show both empirically and theoretically that this approach inherits all of the problems recently identified in the additive partitioning of non-phylogenetic generalized entropies. When within-assemblage (alpha) quadratic entropy is high, the additive beta and the differentiation measure (gamma − alpha)/gamma always tend to zero (implying no differentiation) regardless of phylogenetic structures and differences in species abundances across assemblages. Likewise, the differentiation measure based on the phylogenetic generalization of Shannon entropy always approaches zero whenever gamma phylogenetic entropy is high. Such critical flaws, inherited from their non-phylogenetic parent measures (Gini-Simpson index and Shannon entropy respectively), have caused interpretational problems. These flaws arise because phylogenetic generalized entropies do not obey the replication principle, which ensures that the diversity measures are linear with respect to species addition or group pooling. Furthermore, their complete partitioning into independent components is not additive (except for phylogenetic entropy). Just as in the non-phylogenetic case, these interpretational problems are resolved by using phylogenetic Hill numbers that obey the replication principle. Here we show how to partition the phylogenetic gamma diversity based on Hill numbers into independent alpha and beta components, which turn out to be multiplicative. The resulting phylogenetic beta diversity (ratio of gamma to alpha) measures the effective number of completely phylogenetically distinct assemblages. This beta component measures pure differentiation among assemblages and thus can be used to construct several classes of similarity or differentiation measures normalized onto the range 0, 1. We also propose a normalization to fix the traditional additive phylogenetic similarity and differentiation measures, and we show that this yields the same similarity and differentiation measures we derived from multiplicative phylogenetic diversity partitioning. We thus can achieve a consensus on phylogenetic similarity and differentiation measures, including
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-assemblage phylogenetic generalizations of the classic Jaccard, Sørensen, Horn, and Morisita-Horn measures. Hypothetical and real examples are used for illustration.
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.
A unified approach to quantifying sample completeness of a biological survey and comparing diversity among assemblages is proposed and applied to four contrasting field data examples. We propose a four‐step procedure that links sample completeness, diversity estimation, rarefaction and extrapolation, and evenness in a fully integrated approach.
The evolutionary split between gymnosperms and angiosperms has far‐reaching implications for the current communities colonizing trees. The inherent characteristics of dead wood include its role as a ...spatially scattered habitat of plant tissue, transient in time. Thus, local assemblages in deadwood forming a food web in a necrobiome should be affected not only by dispersal ability but also by host tree identity, the decay stage and local abiotic conditions. However, experiments simultaneously manipulating these potential community drivers in deadwood are lacking. To disentangle the importance of spatial distance and microclimate, as well as host identity and decay stage as drivers of local assemblages, we conducted two consecutive experiments, a 2‐tree species and 6‐tree species experiment with 80 and 72 tree logs, respectively, located in canopy openings and under closed canopies of a montane and a lowland forest. We sampled saproxylic beetles, spiders, fungi and bacterial assemblages from logs. Variation partitioning for community metrics based on a unified framework of Hill numbers showed consistent results for both studies: host identity was most important for sporocarp‐detected fungal assemblages, decay stage and host tree for DNA‐detected fungal assemblages, microclimate and decay stage for beetles and spiders and decay stage for bacteria. Spatial distance was of minor importance for most taxa but showed the strongest effects for arthropods. The contrasting patterns among the taxa highlight the need for multi‐taxon analyses in identifying the importance of abiotic and biotic drivers of community composition. Moreover, the consistent finding of microclimate as the primary driver for saproxylic beetles compared to host identity shows, for the first time that existing evolutionary host adaptions can be outcompeted by local climate conditions in deadwood.
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