Analysis of structural variations in a shallow estuarine deposit-feeding community

Changes in the structure of an estuarine, subtidal, benthic deposit-feeding community have been investigated. Three quantitative samples were taken within a grid 10 m on a side every four weeks from May, 1971 to July, 1973. Each sample was washed over a 250 μm sieve. Streblospio benedicti Webster, Capitella capitata (Fabricius), Heteromastus filiformis (Claparède), Potydora ligni Webster, and Paranais litoralis (Müller) were the five dominant species on the basis of their total abundance, percentage occurrence, and biological index value. Repeatable cycles in diversity were observed for Fager's scaled standard deviation and scaled information measure, as well as for Lloyd and Ghelardi's equitability, but not for the unsealed information theory measure. McNaughton's dominance index was strongly inversely correlated with all diversity measures. Graphical measures of lognormal skewness and normal kurtosis, as applied to Whittaker's dominance diversity curves, followed repeatable cycles, whereas normal skewness and lognormal kurtosis did not. A strong relationship between Fager's scaled standard deviation diversity, dominance, and the degree to which resources were being shared by the deposit-feeding segment of the community was suggested. A decrease in average niche width and average niche overlap was observed as the community developed during the period of strong larval recruitment.     

Distance-Based Functional Diversity Measures and Their Decomposition: A Framework Based on Hill Numbers

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.     

Unconstrained gene flow between populations of a widespread epiphytic lichen Usnea subfloridana (Parmeliaceae,Ascomycota) in Estonia

Few studies have investigated the genetic diversity of populations of common and widespread lichenized fungi using microsatellite markers, especially the relationships between different measures of genetic diversity and environmental heterogeneity. The main aim of our study was to investigate the population genetics of a widespread and mainly clonally reproducing Usnea subfloridana at the landscape scale, focusing on the comparison of lichen populations within hemiboreal forest stands. Particular attention has been paid to the genetic differentiation of lichen populations in two geographically distinct regions in Estonia and the relationships between forest characteristics and measures of genetic diversity. We genotyped 578 Usnea thalli from eleven lichen populations using seven specific fungal microsatellite markers. Measures of genetic diversity (allelic richness, Shannon's information index, Nei's unbiased genetic diversity, clonal diversity, the number of multilocus genotypes, the number of private alleles, and the minimum number of colonization events) were calculated and compared between Usnea populations. Shared haplotypes, gene flow and AMOVA analyses suggest that unconstrained gene flow and exchange of multilocus genotypes exist between the two geographically remote regions in Estonia. Stand age, mean circumference of the host tree, size of forest site and tree species composition did not show any significant influence on allelic richness, Shannon's information index, Nei's unbiased genetic diversity, clonal diversity, the number of private alleles, and the minimum number of colonization events of U. subfloridana populations. Therefore it was concluded that other factors of habitat heterogeneity could probably have a more significant effect on population genetics of U. subfloridana populations.     

Diversity indices: Which ones are admissible?

Many indices have been proposed for measuring diversity. If we demand that any index satisfy a few basic properties, including that it contain hierarchical components, then only the subset, {N_a for a > 0} of Hill's family need be considered. (This subset includes indices related to the Shannon-Wiener index, H′ = log N₁, and Simpson's index of concentration, λ = 1/N₂.) Ecological components can also be defined for any of these indices. Only N₂, however, can be used consistently to define local diversity and segregation components. These observations suggest that N₂ is the best, single measure of diversity, and that the only other index worth considering is N₁ .     

Models for the logarithmic species abundance distributions

Three models, developed by Karlin, McGregor and Ewens to describe evolving populations of selectively neutral genotypes, are shown to lead to various versions of Fisher's logarithmic series distribution for species abundance. Statistical inference procedures and measures of diversity which have been developed in one of the two contexts are therefore also applicable in the other context, and the paper reviews and extends these links. Some work of Fisher, Good and Rao is shown to be based on a faulty version of the logarithmic distribution, which, nevertheless, is a good approximation to a consistent version.     

Predicting productivity in tropical reservoirs: The roles of phytoplankton taxonomic and functional diversity

Primary productivity is intimately linked with biodiversity and ecosystem functioning. Much of what is known today about such relationship has been based on the manipulation of species richness. Other facets of biodiversity, such as functional diversity, have been neglected within this framework, particularly in freshwater systems. We assess the adequacy of different diversity measures, from species richness and evenness, to functional groups richness and functional diversity indices, to predict primary productivity in 19 tropical reservoirs of central Brazil, built to generate hydroelectric energy. We applied linear mixed models (and model selection based on the Akaike’s information criterion) to achieve our goal, using chlorophyll-a concentration as a surrogate for primary productivity. A total of 412 species were collected in this study. Overall we found a positive relation between productivity and diversity, with functional evenness representing the only exception. The most parsimonious models never included functional group classifications, with at least one continuous measure of functional diversity being present in many models. The best model included only species richness and explained 24.1% of variability in productivity. We therefore advise the use of species richness as an indicator of productivity in tropical freshwater environments. However, since the productivity–diversity relationship is known to be scale dependent, we recommend the use of continuous measures of functional diversity in future biodiversity and ecosystem functioning studies, in order to be certain that all functional differences between communities are being accounted for.     

Phylogenetic diversity measures based on Hill numbers

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.     

Computing additive beta-diversity from presence and absence scores: a critique and alternative parameters

Whittaker first proposed to measure the variation in species composition among plots or beta-diversity as the ratio between regional diversity (gamma-diversity) and average local diversity (alpha-diversity). More recently, an alternative way of partitioning diversity for which beta-diversity is obtained as the difference between gamma-diversity and average alpha-diversity has become very popular for linking the structure of species assemblages to ecosystem functioning in a spatially explicit manner. Unfortunately, additive beta-diversity computed from species presences and absences suffers from the major drawback of being dependent on regional species richness. For instance, if the separation between beta-diversity and gamma-diversity is incomplete, so that variation in species composition is affected by species richness, then differences in beta-diversity values among different sets of plots could reflect differences in the species count rather than any fundamental difference in species composition among the plots. Based on the above observation, in this paper I will first propose a basic requirement for beta-diversity measures that adequately captures our intuitive notion of independence of species richness. Next, I will show that additive beta-diversity computed from species presence and absence scores can be interpreted within the framework of fuzzy set theory. Finally, based on this unusual "fuzzy" interpretation of additive beta-diversity, I will introduce two families of parametric beta-diversity measures whose members have varying sensitivities to the presence of rare and frequent species.     

A formalization of consensus index methods

A consensus in dex method comprises a consensus method and a consensus index that are defined on a common set of objects (e.g. classifications). For each profile of objects, the consensus method returns a consensus object representing information or structure shared among profile objects, while the consensus index returns a quantitative measure of agreement among profile objects. Since the relationship between consensus method and consensus index is poorly understood, we propose simple axioms prescribing it in the most general terms. Many taxonomic consensus index methods violate these axioms because their consensus indices measure consensus object invariants rather than profile agreement. We propose paradigms to obtain consensus index methods that measure agreement and satisfy the axioms. These paradigms salvage concepts underlying consensus index methods violating the axioms. This work was supported in part by the Faculty of Science at Memorial University of Newfoundland, and by the Natural Sciences and Engineering Research Council of Canada Under Grant A-4142.     

On the Apportionment of Population Structure

Measures of population differentiation, such as F_ST, are traditionally derived from the partition of diversity within and between populations. However, the emergence of population clusters from multilocus analysis is a function of genetic structure (departures from panmixia) rather than of diversity. If the populations are close to panmixia, slight differences between the mean pairwise distance within and between populations (low F_ST) can manifest as strong separation between the populations, thus population clusters are often evident even when the vast majority of diversity is partitioned within populations rather than between them. For any given F_ST value, clusters can be tighter (more panmictic) or looser (more stratified), and in this respect higher F_ST does not always imply stronger differentiation. In this study we propose a measure for the partition of structure, denoted E_ST, which is more consistent with results from clustering schemes. Crucially, our measure is based on a statistic of the data that is a good measure of internal structure, mimicking the information extracted by unsupervised clustering or dimensionality reduction schemes. To assess the utility of our metric, we ranked various human (HGDP) population pairs based on F_ST and E_ST and found substantial differences in ranking order. E_ST ranking seems more consistent with population clustering and classification and possibly with geographic distance between populations. Thus, E_ST may at times outperform F_ST in identifying evolutionary significant differentiation.     

Negative relationships between species richness and evenness render common diversity indices inadequate for assessing long-term trends in butterfly diversity

Species richness and evenness, the two principle components of species diversity, are frequently used to describe variation in species assemblages in space and time. Compound indices, including variations of both the Shannon–Wiener index and Simpson’s index, are assumed to intelligibly integrate species richness and evenness into all-encompassing measures. However, the efficacy of compound indices is disputed by the possibility of inverse relationships between species richness and evenness. Past studies have assessed relationships between various diversity measures across survey locations for a variety of taxa, often finding species richness and evenness to be inversely related. Butterflies are one of the most intensively monitored taxa worldwide, but have been largely neglected in such studies. Long-term butterfly monitoring programs provide a unique opportunity for analyzing how trends in species diversity relate to habitat and environmental conditions. However, analyzing trends in butterfly diversity first requires an assessment of the applicability of common diversity measures to butterfly assemblages. To accomplish this, we quantified relationships between butterfly diversity measures estimated from 10 years of butterfly population data collected in the North Saskatchewan River Valley in Edmonton, Alberta, Canada. Species richness and evenness were inversely related within the butterfly assemblage. We conclude that species evenness may be used in conjunction with richness to deepen our understandings of assemblage organization, but combining these two components within compound indices does not produce measures that consistently align with our intuitive sense of species diversity.     

Stability of production and plant species diversity in managed grasslands: A retrospective study

Plant biodiversity theory suggests that increased plant species diversity contributes to the stability of ecosystems. In managed grasslands, such as pastures, greater stability of herbage production would be beneficial. In this retrospective study, I used data from three reports from the 1930s, 1940s, and 1960s to determine whether increasing mixture complexity contributed to yield stability with time. Yield data from a total of 175 mixtures of grasses and legumes (two to seven species per mixture) in experiments of 3–6 year duration in Connecticut, Pennsylvania, and Utah, USA, were used in the analysis. Regression was used to examine relationships among herbage yield, stability of yield [measured as the interannual coefficient of variation (CV)], and diversity measures [Shannon diversity index (H), species richness (S), and evenness (J)]. In several instances there was no relationship between herbage yield or yield stability and the complexity (number of species) of the mixture. In one experiment, the proportion of legume in the sward seemed to be the controlling factor regarding herbage yield and yield stability. Monocultures and binary mixtures frequently had the highest interannual CV (e.g., less yield stability) than more complex mixtures. Within forage mixtures, however, there was no consistent relationship between herbage yield or yield stability and measures of species diversity. Species identity and composition of forage mixtures may be more important determinants of herbage yield than simply the number of species.     

Probability of same genotype or of graft compatibility, importance of the distribution of gene frequencies

Resemblance between relatives may be considered at the phenotypic level; the question is to then measure the relation between the intensity or the nature of their kinship and the similarity of their visible features. It may also be considered on the genetic level; the question is to then know to what extent the kinship involves the possession of the same genes.This problem is far from being academic; it may have medical implications. Graft compatibility requires that the genes present in the donor's genotype be present in the recipient's genotype (if not, the donor's genes control the formation of antigenic substances against which the recipient is able to produce antibodies which cause rejection), or even that the donor's and recipient's genotypes are the same (particularly for marrow graft).For two given individuals, the probability of graft compatibility clearly depends on the number of loci involved, the number and frequencies of the alleles, and the parental relationship of the individuals.Limiting our reasoning to the case where the reject process is dependent on only one locus, we show herein how the knowledge of genealogies, as complicated as they may be, allows us to determine this probability as a function of genes frequencies. These frequencies, however, are often unknown. We compare the probabilities of compatibility resulting from various hypotheses on genes repartition.     

Fast Computations for Measures of Phylogenetic Beta Diversity

For many applications in ecology, it is important to examine the phylogenetic relations between two communities of species. More formally, let ?? be a phylogenetic tree and let A and B be two samples of its tips, representing the examined communities. We want to compute a value that expresses the phylogenetic diversity between A and B in ??. There exist several measures that can do this; these are the so-called phylogenetic beta diversity (β-diversity) measures. Two popular measures of this kind are the Community Distance (CD) and the Common Branch Length (CBL). In most applications, it is not sufficient to compute the value of a beta diversity measure for two communities A and B; we also want to know if this value is relatively large or small compared to all possible pairs of communities in ?? that have the same size. To decide this, the ideal approach is to compute a standardised index that involves the mean and the standard deviation of this measure among all pairs of species samples that have the same number of elements as A and B. However, no method exists for computing exactly and efficiently this index for CD and CBL. We present analytical expressions for computing the expectation and the standard deviation of CD and CBL. Based on these expressions, we describe efficient algorithms for computing the standardised indices of the two measures. Using standard algorithmic analysis, we provide guarantees on the theoretical efficiency of our algorithms. We implemented our algorithms and measured their efficiency in practice. Our implementations compute the standardised indices of CD and CBL in less than twenty seconds for a hundred pairs of samples on trees with 7 ⋅ 10⁴ tips. Our implementations are available through the R package PhyloMeasures.     

Further remarks on Darwinian selection and “altruism”

In a recent note, Maynard Smith (Theor. Pop. Biol., in press) has claimed that there are certain difficulties in applying the method developed by us (Theor. Pop. Biol.14, 268–280) which incorporates the evolution of altruism into the population genetic theory of frequency-dependent selection. Of the four examples presented by Maynard Smith, the case of alarm calls was shown to have a natural expression in our multiplicative framework, and to produce conclusions different from those expected under the usual additive assumptions. We show here that the examples of the sterile worker, and of parental care are both simply expressible in terms of our conditional probability approach. The fourth example, the case of incest taboos, will be discussed elsewhere. Using Maynard Smith's examples important differences between the results for the additive and multiplicative fitness constructions are revealed. It is concluded that the heuristic approach using “inclusive fitness” offers no substantive advantages over exact population genetic modelling.     

The first survey of Cystobasidiomycete yeasts in the lichen genus Cladonia; with the description of Lichenozyma pisutiana gen. nov., sp. nov.

The view of lichens as a symbiosis only between a mycobiont and a photobiont has been challenged by discoveries of diverse associated organisms. Specific basidiomycete yeasts in the cortex of a range of macrolichens were hypothesized to influence the lichens' phenotype. The present study explores the occurrence and diversity of cystobasidiomycete yeasts in the lichen genus Cladonia. We obtained seven cultures and 56 additional sequences using specific primers from 27 Cladonia species from all over Europe and performed phylogenetic analyses based on ITS, LSU and SSU rDNA loci. We revealed yeast diversity distinct from any previously reported. Representatives of Cyphobasidiales, Microsporomycetaceae and of an unknown group related to Symmetrospora have been found. We present evidence that the Microsporomycetaceae contains mainly lichen-associated yeasts. Lichenozyma pisutiana is circumscribed here as a new genus and species. We report the first known associations between cystobasidiomycete yeasts and Cladonia (both corticate and ecorticate), and find that the association is geographically widespread in various habitats. Our results also suggest that a great diversity of lichen associated yeasts remains to be discovered.     

The use of species abundance estimates in marine benthic studies

The application of species abundance estimates, commonly used in terrestrial plant ecology, to marine benthic dredge data is advocated. Two possible scales were tested for their ability to measure adequately the structure of an assemblage by computing measures of evenness diversity McNaughton's dominance index, and Morisita's index of dispersion using both real counts obtained from grab samples and these counts transformed into the two respective abundance estimates. It is concluded that species abundance estimators, when applied to grab or dredge data result in significant savings in sample processing time with only a minimal loss of information about assemblage structure.     

Measuring beta‐diversity from taxonomic similarity

Question: The utility of beta (β‐) diversity measures that incorporate information about the degree of taxonomic (dis)similarity between species plots is becoming increasingly recognized. In this framework, the question for this study is: can we define an ecologically meaningful index of β‐diversity that, besides indicating simple species turnover, is able to account for taxonomic similarity amongst species in plots? Methods: First, the properties of existing measures of taxonomic similarity measures are briefly reviewed. Next, a new measure of plot‐to‐plot taxonomic similarity is presented that is based on the maximal common subgraph of two taxonomic trees. The proposed measure is computed from species presences and absences and include information about the degree of higher‐level taxonomic similarity between species plots. The performance of the proposed measure with respect to existing coefficients of taxonomic similarity and the coefficient of Jaccard is discussed using a small data set of heath plant communities. Finally, a method to quantify β‐diversity from taxonomic dissimilarities is discussed. Results: The proposed measure of taxonomic β‐diversity incorporates not only species richness, but also information about the degree of higher‐order taxonomic structure between species plots. In this view, it comes closer to a modern notion of biological diversity than more traditional measures of β‐di‐versity. From regression analysis between the new coefficient and existing measures of taxonomic similarity it is shown that there is an evident nonlinearity between the coefficients. This nonlinearity demonstrates that the new coefficient measures similarity in a conceptually different way from previous indices. Also, in good agreement with the findings of previous authors, the regression between the new index and the Jaccard coefficient of similarity shows that more than 80% of the variance of the former is explained by the community structure at the species level, while only the residual variance is explained by differences in the higher‐order taxonomic structure of the species plots. This means that a genuine taxonomic approach to the quantification of plot‐to‐plot similarity is only needed if we are interested in the residual system's variation that is related to the higher‐order taxonomic structure of a pair of species plots.     

Abstract representations of biological systems in supercategories

An abstract representation of biological systems from the standpoint of the theory of supercategories is presented. The relevance of such representations forG-relational biologies is suggested. In section A the basic concepts of our representation, that is class, system, supercategory and measure are introduced. Section B is concerned with the mathematical representation starting with some axioms and principles which are natural extensions of the current abstract representations in biology. Likewise, some extensions of the principle of adequate design are introduced in section C. Two theorems which present the connection between categories and supercategories are proved. Two other theorems concerning the dynamical behavior of biological and biophysical systems are derived on the basis of the previous considerations. Section D is devoted to a general study of oscillatory behavior in enzymic systems, some general quantitative relations being derived from our representation. Finally, the relevance of these results for a quantum theoretic approach to biology is discussed.