Entropy and the species accumulation curve: a novel entropy estimator via discovery rates of new species

Ecological setting of phlebotomine sand flies in the Republic of Kosovo

Sand flies (Diptera, Psychodidae) are the principal vectors of Leishmania spp., the causative agents of leishmaniasis, as well as phleboviruses. In the Balkans, the endemicity and spreading of sand fly-borne diseases are evident, particularly in the Republic of Kosovo, a country with a predominantly humid continental climate. To date, understanding the drivers behind the spatial structure and diversity patterns of sand fly communities in humid continental regions remains limited. Therefore, elucidating the geographical and ecological factors contributing to the presence of potential vector species in the country is crucial. We aimed to enhance our understanding of factors influencing sand fly occurrence in cool and wet wintering humid continental areas, which could serve as a model for other countries with similar climatic conditions. Therefore, we assessed the currently known sand fly fauna through detailed environmental analyses, including Voronoi tessellation patterns, entropy calculations, Principal Coordinate and Component Analyses, Hierarchical Clustering, Random Trees, and climatic suitability patterns. Notable differences in the ecological tolerance of the species were detected, and the most important climatic features limiting sand fly presence were wind speed and temperature seasonality. Sand flies were observed to prefer topographical environments with little roughness, and the modelled climatic suitability values indicated that, dominantly, the western plain regions of Kosovo harbour the most diverse sand fly fauna; and are the most threatened by sand fly-borne diseases. Phlebotomus neglectus and P. perfiliewi, both confirmed vectors for L. infantum and phleboviruses, were identified as two main species with vast distribution in Kosovo. Contrary to this, most other present species are relatively sparse and restricted to temperate rather than humid continental regions. Our findings reveal a diverse potential sand fly fauna in Kosovo, indicating the need for tailored strategies to address varying risks across the country's western and eastern regions in relation to leishmaniasis control amidst changing environmental conditions.

A Comparative Analysis of Discrete Entropy Estimators for Large-Alphabet Problems

This paper presents a comparative study of entropy estimation in a large-alphabet regime. A variety of entropy estimators have been proposed over the years, where each estimator is designed for a different setup with its own strengths and caveats. As a consequence, no estimator is known to be universally better than the others. This work addresses this gap by comparing twenty-one entropy estimators in the studied regime, starting with the simplest plug-in estimator and leading up to the most recent neural network-based and polynomial approximate estimators. Our findings show that the estimators' performance highly depends on the underlying distribution. Specifically, we distinguish between three types of distributions, ranging from uniform to degenerate distributions. For each class of distribution, we recommend the most suitable estimator. Further, we propose a sample-dependent approach, which again considers three classes of distribution, and report the top-performing estimators in each class. This approach provides a data-dependent framework for choosing the desired estimator in practical setups.

Integration of polygenic and gut metagenomic risk prediction for common diseases

Multiomics has shown promise in noninvasive risk profiling and early detection of various common diseases. In the present study, in a prospective population-based cohort with ~18 years of e-health record follow-up, we investigated the incremental and combined value of genomic and gut metagenomic risk assessment compared with conventional risk factors for predicting incident coronary artery disease (CAD), type 2 diabetes (T2D), Alzheimer disease and prostate cancer. We found that polygenic risk scores (PRSs) improved prediction over conventional risk factors for all diseases. Gut microbiome scores improved predictive capacity over baseline age for CAD, T2D and prostate cancer. Integrated risk models of PRSs, gut microbiome scores and conventional risk factors achieved the highest predictive performance for all diseases studied compared with models based on conventional risk factors alone. The present study demonstrates that integrated PRSs and gut metagenomic risk models improve the predictive value over conventional risk factors for common chronic diseases.

Diversity of an Odonata assemblage from a tropical dry forest in San Buenaventura, Jalisco, Mexico (Insecta, Odonata)

Background

The patterns of richness, diversity, and abundance of an odonate assemblage from San Buenaventura, Jalisco are presented here. A total of 1087 specimens from seven families, 35 genera and 66 species were obtained through monthly samplings of five days each during a period of one year. Libellulidae was the most diverse family (28 species), followed by Coenagrionidae (21), Gomphidae (7), Aeshnidae (6), Calopterygidae (2), Lestidae (1) and Platystictidae (1). Argia was the most speciose genus. The highest species richness and Shannon diversity were found during August and September, whereas the highest abundance was observed in June and the highest Simpson diversity was recorded in September - all of which were associated with the rainy season. The highest values of phylogenetic diversity were found from June to October. The different diversity facets of this assemblage were positively correlated with precipitation and minimum temperature, whereas maximum temperature showed no influence. In addition, we found that this odonate diversity was higher than most Mexican localities with tropical dry forest (TDF) studied.

New information

We continue our efforts to describe the patterns of richness, diversity and abundance of some insect groups associated with the tropical dry forest ecosystem in Mexico, following a latitudinal gradient of the distribution of this ecosystem in the country. Our emphasis here was to evaluate the spatial and temporal patterns of richness and diversity of an Odonata assemblage from Jalisco, Mexico.

Entropy Estimators for Markovian Sequences: A Comparative Analysis

Entropy estimation is a fundamental problem in information theory that has applications in various fields, including physics, biology, and computer science. Estimating the entropy of discrete sequences can be challenging due to limited data and the lack of unbiased estimators. Most existing entropy estimators are designed for sequences of independent events and their performances vary depending on the system being studied and the available data size. In this work, we compare different entropy estimators and their performance when applied to Markovian sequences. Specifically, we analyze both binary Markovian sequences and Markovian systems in the undersampled regime. We calculate the bias, standard deviation, and mean squared error for some of the most widely employed estimators. We discuss the limitations of entropy estimation as a function of the transition probabilities of the Markov processes and the sample size. Overall, this paper provides a comprehensive comparison of entropy estimators and their performance in estimating entropy for systems with memory, which can be useful for researchers and practitioners in various fields.

Transcriptional immunogenomic analysis reveals distinct immunological clusters in paediatric nervous system tumours

BACKGROUND

Cancer immunotherapies including immune checkpoint inhibitors and Chimeric Antigen Receptor (CAR) T-cell therapy have shown variable response rates in paediatric patients highlighting the need to establish robust biomarkers for patient selection. While the tumour microenvironment in adults has been widely studied to delineate determinants of immune response, the immune composition of paediatric solid tumours remains relatively uncharacterized calling for investigations to identify potential immune biomarkers.

METHODS

To inform immunotherapy approaches in paediatric cancers with embryonal origin, we performed an immunogenomic analysis of RNA-seq data from 925 treatment-naïve paediatric nervous system tumours (pedNST) spanning 12 cancer types from three publicly available data sets.

RESULTS

Within pedNST, we uncovered four broad immune clusters: Paediatric Inflamed (10%), Myeloid Predominant (30%), Immune Neutral (43%) and Immune Desert (17%). We validated these clusters using immunohistochemistry, methylation immune inference and segmentation analysis of tissue images. We report shared biology of these immune clusters within and across cancer types, and characterization of specific immune cell frequencies as well as T- and B-cell repertoires. We found no associations between immune infiltration levels and tumour mutational burden, although molecular cancer entities were enriched within specific immune clusters.

CONCLUSIONS

Given the heterogeneity of immune infiltration within pedNST, our findings suggest personalized immunogenomic profiling is needed to guide selection of immunotherapeutic strategies.

Low-probability states, data statistics, and entropy estimation

A fundamental problem in the analysis of complex systems is getting a reliable estimate of the entropy of their probability distributions over the state space. This is difficult because unsampled states can contribute substantially to the entropy, while they do not contribute to the maximum likelihood estimator of entropy, which replaces probabilities by the observed frequencies. Bayesian estimators overcome this obstacle by introducing a model of the low-probability tail of the probability distribution. Which statistical features of the observed data determine the model of the tail, and hence the output of such estimators, remains unclear. Here we show that well-known entropy estimators for probability distributions on discrete state spaces model the structure of the low-probability tail based largely on a few statistics of the data: the sample size, the maximum likelihood estimate, the number of coincidences among the samples, and the dispersion of the coincidences. We derive approximate analytical entropy estimators for undersampled distributions based on these statistics, and we use the results to propose an intuitive understanding of how the Bayesian entropy estimators work.

Light availability and plant shade tolerance modify plant-microbial interactions and feedbacks in subtropical trees

Plant-soil feedbacks (PSFs) are an important mechanism of species coexistence in forest communities. However, evidence remains limited for how light availability regulates PSFs in species with different shade tolerance via changes in plant-microbial interactions. Here we tested in a glasshouse experiment how PSFs changed as a function of light availability and tree shade tolerance. Soil bacterial and fungal communities were profiled using the 16S rRNA and ITS2 gene sequencing, respectively. Under low light, individual PSFs were positively related to shade tolerance, while the least shade-tolerant species produced the most positive PSFs under high light. Pairwise PSFs between species with contrasting shade tolerance were strongly positive under high light but negative under low light, thereby promoting the dominance of less shade-tolerant species in forest gaps and species coexistence under closed canopy, respectively. Under high light, PSFs were related to soil microbial composition and diversity, with the relative abundance of arbuscular mycorrhizal fungi being the primary driver of PSFs. Under low light, none of soil microbial properties were significantly related to PSFs. These findings indicate PSFs and plant shade tolerance interact to promote species coexistence and improve our understanding of how soil microbes contribute to variation in PSFs.

Alien insect dispersal mediated by the global movement of commodities

Globalization and economic growth are recognized as key drivers of biological invasions. Alien species have become a feature of almost every biological community worldwide, and rates of new introductions continue to rise as the movement of people and goods accelerates. Insects are among the most numerous and problematic alien organisms, and are mainly introduced unintentionally with imported cargo or arriving passengers. However, the processes occurring prior to insect introductions remain poorly understood. We used a unique dataset of 1,902,392 border interception records from inspections at air, land, and maritime ports in Australia, New Zealand, Europe, Japan, USA, and Canada to identify key commodities associated with insect movement through trade and travel. In total, 8939 species were intercepted, and commodity association data were available for 1242 species recorded between 1960 and 2019. We used rarefaction and extrapolation methods to estimate the total species richness and diversity associated with different commodity types. Plant and wood products were the main commodities associated with insect movement across cargo, passenger baggage, and international mail. Furthermore, certain species were mainly associated with specific commodities within these, and other broad categories. More closely related species tended to share similar commodity associations, but this occurred largely at the genus level rather than within orders or families. These similarities within genera can potentially inform pathway management of new alien species. Combining interception records across regions provides a unique window into the unintentional movement of insects, and provides valuable information on establishment risks associated with different commodity types and pathways.

Assessing tree species diversity in forest ecosystems: A new approach

The significance of biodiversity research is to understand the structure and function of the community, and then to protect and monitor the community. The metric of biodiversity is the base of biodiversity conservation. Species richness and evenness are the most common descriptors of biodiversity. Whether it is diversity information measure, probability measure or geometric measure, they all express the combination of species richness and evenness in different ways. This study presents a new biologically meaningful measure of species diversity, which evaluates species richness and evenness independently, designated as DRE. The novelty of our method is to use “absolute discrepancy” to express the dissimilarity between the observed community and the uniform distribution community with the same species composition and same abundance of each species, and then measure the species evenness. The logarithmic transformation of the species number is used to measure species richness with values ranging between 0 and 1. We test the performance of this measure using simulated data and observations of natural and planted forests in different climatic zones. The results showed that the new diversity index (DRE) has superior statistical qualities compared with the traditional indices. Especially, in extremely uneven communities, the new measure describes the causes of diversity changes than the traditional DRE. In addition, DRE is more sensitive to the abundance changes of rare species in the simulated community, and the interpretation of the results is more intuitive and meaningful. It is an improved method to evaluate the species diversity of any ecosystem.

Integration of TAM Model of Consumers’ Intention to Adopt Cryptocurrency Platform in Thailand: The Mediating Role of Attitude and Perceived Risk

The purpose of this paper was to propose a model that examined a study adopting the technology acceptance model with additional constructs (i.e., innovativeness) and the mediating role of attitude and perceived risk to use the cryptocurrency platform in Thailand. The data were collected through a questionnaire-based survey (456 usable responses) from consumers in Thailand. A two-step SEM approach (i.e., a measurement model and a structural model) was used to analyze the data. The findings showed a significant positive influence of perceived usefulness, perceived ease of use, innovativeness, attitude, perceived risk, and cryptocurrency platform adoption. Moreover, attitude mediated the relationship between perceived usefulness, perceived ease of use, innovativeness, and cryptocurrency platform adoption. Overall, our results showed that the model of perceived usefulness, perceived ease of use, and innovativeness explained 62.9% of the variance in the intention to use the cryptocurrency platform in Thailand. Our study has contributed to the technology acceptance model and highlighted its effectiveness in explaining the adoption of the cryptocurrency platform in Thailand.

Strong floristic distinctiveness across Neotropical successional forests

Forests that regrow naturally on abandoned fields are important for restoring biodiversity and ecosystem services, but can they also preserve the distinct regional tree floras? Using the floristic composition of 1215 early successional forests (≤20 years) in 75 human-modified landscapes across the Neotropic realm, we identified 14 distinct floristic groups, with a between-group dissimilarity of 0.97. Floristic groups were associated with location, bioregions, soil pH, temperature seasonality, and water availability. Hence, there is large continental-scale variation in the species composition of early successional forests, which is mainly associated with biogeographic and environmental factors but not with human disturbance indicators. This floristic distinctiveness is partially driven by regionally restricted species belonging to widespread genera. Early secondary forests contribute therefore to restoring and conserving the distinctiveness of bioregions across the Neotropical realm, and forest restoration initiatives should use local species to assure that these distinct floras are maintained.

On Generalized Schürmann Entropy Estimators

We present a new class of estimators of Shannon entropy for severely undersampled discrete distributions. It is based on a generalization of an estimator proposed by T. Schürmann, which itself is a generalization of an estimator proposed by myself.For a special set of parameters, they are completely free of bias and have a finite variance, something which is widely believed to be impossible. We present also detailed numerical tests, where we compare them with other recent estimators and with exact results, and point out a clash with Bayesian estimators for mutual information.

Inferring a Property of a Large System from a Small Number of Samples

Inferring the value of a property of a large stochastic system is a difficult task when the number of samples is insufficient to reliably estimate the probability distribution. The Bayesian estimator of the property of interest requires the knowledge of the prior distribution, and in many situations, it is not clear which prior should be used. Several estimators have been developed so far in which the proposed prior us individually tailored for each property of interest; such is the case, for example, for the entropy, the amount of mutual information, or the correlation between pairs of variables. In this paper, we propose a general framework to select priors that is valid for arbitrary properties. We first demonstrate that only certain aspects of the prior distribution actually affect the inference process. We then expand the sought prior as a linear combination of a one-dimensional family of indexed priors, each of which is obtained through a maximum entropy approach with constrained mean values of the property under study. In many cases of interest, only one or very few components of the expansion turn out to contribute to the Bayesian estimator, so it is often valid to only keep a single component. The relevant component is selected by the data, so no handcrafted priors are required. We test the performance of this approximation with a few paradigmatic examples and show that it performs well in comparison to the ad-hoc methods previously proposed in the literature. Our method highlights the connection between Bayesian inference and equilibrium statistical mechanics, since the most relevant component of the expansion can be argued to be that with the right temperature.

Detecting structured repetition in child-surrounding speech: Evidence from maximally diverse languages

Caretakers tend to repeat themselves when speaking to children, either to clarify their message or to redirect wandering attention. This repetition also appears to support language learning. For example, words that are heard more frequently tend to be produced earlier by young children. However, pure repetition only goes so far; some variation between utterances is necessary to support acquisition of a fully productive grammar. When individual words or morphemes are repeated, but embedded in different lexical and syntactic contexts, the child has more information about how these forms may be used and combined. Corpus analysis has shown that these partial repetitions frequently occur in clusters, which have been coined variation sets. More recent research has introduced algorithms that can extract these variation sets automatically from corpora with the goal of measuring their relative prevalence across ages and languages. Longitudinal analyses have revealed that rates of variation sets tend to decrease as children get older. We extend this research in several ways. First, we consider a maximally diverse sample of languages, both genealogically and geographically, to test the generalizability of developmental trends. Second, we compare multiple levels of repetition, both words and morphemes, to account for typological differences in how information is encoded. Third, we consider several additional measures of development to account for deficiencies in age as a measure of linguistic aptitude. Fourth, we examine whether the levels of repetition found in child-surrounding speech is greater or less than what would have been expected by chance. This analysis produced a new measure, redundancy, which captures how repetitive speech is on average given how repeititive it could have been. Fifth, we compare rates of repetition in child-surrounding and adult-directed speech to test whether variation sets are especially prevalent in child-surrounding speech. We find that (1) some languages show increases in repetition over development, (2) true estimates of variation sets are generally lower than or equal to random baselines, (3) these patterns are largely convergent across developmental indices, and (4) adult-directed speech is reliably less redundant, though in some cases more repetitive, than child-surrounding speech. These results are discussed with respect to features of the corpora, typological properties of the languages, and differential rates of change in repetition and redundancy over children's development.

Word Order Variation is Partially Constrained by Syntactic Complexity

Previous work suggests that when speakers linearize syntactic structures, they place longer and more complex dependents further away from the head word to which they belong than shorter and simpler dependents, and that they do so with increasing rigidity the longer expressions get, for example, longer objects tend to be placed further away from their verb, and with less variation. Current theories of sentence processing furthermore make competing predictions on whether longer expressions are preferentially placed as early or as late as possible. Here we test these predictions using hierarchical distributional regression models that allow estimates of word order and word order variation at the level of individual dependencies in corpora from 71 languages, while controlling for confounding effects from the type of dependency (e.g., subject vs. object), and the type of clause (main vs. subordinate) involved as well as from trends that are characteristic of individual languages, language families, and language contact areas. Our results show the expected correlations of length with position and variation only for two out of six dependency types (obliques and nominal modifiers) and no difference between clause types. These findings challenge received theories of across‐the‐board effects of complexity on word order and word order variation and call for theoretical models that relativize effects to specific kinds of syntactic structures and dependencies.

Patterns of morphological traits shaping the feeding guilds in the intertidal mudflat fishes of the Indian Sundarbans

Broad-scale patterns of resource utilization and the corresponding morphological evolution is a result of an integral relationship among form and function. In addition, there is also an inherent role of the latter in determining species co-interaction and assemblage pattern that forms an integral aspect of ecological research. The present study aimed to evaluate the ecomorphological relationship among 37 fish species inhabiting the intertidal mudflats of the Indian Sundarbans by outlining the following objectives: (i) identifying and characterizing feeding guilds/groups and (ii) understanding the inter-relationship between morphometry with (a) the established feeding guild classifications and (b) observed prey taxa (that characterizes these feeding groups) for determining the role of morphometry in prey acquisition followed by (iii) the evaluation of their potential phylogenetic convergence among the species. For the first objective, two approaches for feeding guild classification were made (3-Guild and 8-Guild) for assessing the prediction accuracy of morphological characters in identifying the different guilds. While the former was based on troph values, the latter classification mode relied on the similarities in diet composition among the different fish species. For addressing the second objective, we employed two different models namely, linear discriminant (LDA) and redundancy analysis (RDA). While the LDA model tested the prediction accuracy of morphological traits in classifying the different feeding guilds, RDA was applied to model the correlation between the morphological traits and the prey categories. In the LDA model, morphological characters showed higher accuracy (78.4%) in classifying three feeding groups rather than eight feeding groups (73%). Following this, the RDA model (explaining 79.78% of constrained variance) showed gill raker intensity, protrusion length, head depth, caudal peduncle, eye diameter and inter-orbital distance to be highly associated with selection of specific prey types by species, thereby characterizing a particular feeding guild. However, generalized linear models testing for correlation between troph value and feeding groups showed substantial variation (90.35%) in the dietary index being explained by the 8-Guild classification. Hence, our study maintains the assumption that broad morphological differentiation acts as one of the underlying processes resulting in dietary variations that results in the varying modes of resource utilization by the coexisting species, thereby determining the structure of a trophic guild. Furthermore, it also suggests that in terms of prey abundance or selectivity, the 8-Guild model is much more conducive in representing the feeding habits of the species while the morphological traits reflected a relatively broader scheme of classification, (i.e., 3-Guild model) with certain traits being phylogenetically conserved within these groups.

Undersampling correction methods to control γ-dependence for comparing β-diversity between regions

Measures of β-diversity are known to be biased by differences in γ-diversity (i.e., γ-dependence), making it challenging to compare β-diversity across regions. Undersampling corrections have been designed to reduce effects of γ-dependence on β-diversity arising from the problem of incomplete sampling. However, no study has systematically tested the effectiveness of these corrections or examined how well they reflect β-diversity patterns across ecological gradients. Here, we conduct these tests by comparing two undersampling corrections with the widely used individual-based null model approach, using both simulated communities along an ecological gradient and empirical data across a wide range of γ-diversity and sample sizes. We found that undersampling corrections using diversity accumulation curves were more effective than the null-model approaches in removing γ-dependence. In particular, the corrected β-Shannon diversity index was least dependent on γ-diversity, and was the most reflective of the β-diversity pattern along a simulated ecological gradient. Moreover, a corrected Jaccard-Chao index applied to null model results removed γ-dependence more effectively than either the correction alone or the null model alone. Undersampling corrections are effective tools for removing γ-dependence bias, thus facilitating comparisons of β-diversity across regions.

Arbuscular Mycorrhizal Fungal Assemblages in Conservation Unit of Atlantic Forest Areas Under Native Vegetation and Natural Regeneration

Arbuscular mycorrhizal fungi (AMF) play an important role in the dynamic of plant community in the south American Atlantic Rainforest biome. Even in protected areas, this biome is under several anthropic impacts, which can cause shifts in the soil microbiota, including AMF. This study aimed to determine the structure and composition of AMF community in areas of native Atlantic Forest and in natural regeneration and to identify which abiotic factors are influencing this community in these areas. Soil samples were collected at Monte Pascoal National and Historical Park, in Southern Bahia, in native and natural regeneration areas of Atlantic Forest in two seasons (rainy and dry). Greater number of glomerospores and richness and diversity of AMF were found in the area under regeneration, with differences between seasons being observed only for the number of glomerospores. Seventy-seven species of AMF were recorded, considering all areas and seasons, with Acaulospora and Glomus being the most representative genera. Greater abundance of species of the genera Acaulospora, Claroideoglomus, and Septoglomus was found in the regeneration area. The AMF community differed between the study areas, but not between seasons, with soil attributes (pH, K, Al, Mg, m, and clay) structuring factors for this difference in the AMF community. Atlantic Forest areas in natural regeneration and the soil edaphic factors provide changes in the structure and composition of the AMF community, increasing the richness and diversity of these fungi in conservation units.

Selecting an Effective Entropy Estimator for Short Sequences of Bits and Bytes with Maximum Entropy

Entropy makes it possible to measure the uncertainty about an information source from the distribution of its output symbols. It is known that the maximum Shannon's entropy of a discrete source of information is reached when its symbols follow a Uniform distribution. In cryptography, these sources have great applications since they allow for the highest security standards to be reached. In this work, the most effective estimator is selected to estimate entropy in short samples of bytes and bits with maximum entropy. For this, 18 estimators were compared. Results concerning the comparisons published in the literature between these estimators are discussed. The most suitable estimator is determined experimentally, based on its bias, the mean square error short samples of bytes and bits.

Patterns of richness, diversity and abundance of an odonate assemblage from a tropical dry forest in the Santiago Dominguillo Region, Oaxaca, México (Insecta: Odonata)

A study on the patterns of richness, diversity and abundance of the Odonata from Santiago Dominguillo, Oaxaca is presented here. A total of 1601 specimens from six families, 26 genera and 50 species were obtained through monthly samplings of five days each. Libellulidae was the most diverse family (21 species), followed by Coenagrionidae (19), Gomphidae (4) and Calopterygidae (3). The Lestidae, Platystictidae and Aeshnidae families were the less diverse, with only one species each. Argia was the most speciose genus with 11 species, followed by Enallagma, Hetaerina, Erythrodiplax and Macrothemis with three species each and Phyllogomphoides, Brechmorhoga, Dythemis, Erythemis and Orthemis with two species each. The remaining 17 genera had one species each. Argiapipila Calvert, 1907 and Leptobasisvacillans Hagen in Selys, 1877 were recorded for the first time for the state of Oaxaca. We also analysed the temporal patterns of taxonomic and phylogenetic divergence for the Santiago Dominguillo Odonata assemblage: the Shannon diversity value throughout the year was 21.07 effective species, while the Simpson diversity was 13.17. In general, the monthly phylogenetic divergence was higher than expected for taxonomic distinctness, and lesser for average taxonomic distinctness. Monthly diversity, evenness and taxonomic divergence showed significant positive correlations (from moderate to strong) with monthly precipitation values. The analysis of our results, however, indicates that an increase in rainfall not only influences the temporal diversity of species, but also the identity of supraspecific taxa that constitute those temporal assemblages, i.e. there is an increase in temporal phylogenetic divergence.

Species packing and the latitudinal gradient in beta-diversity

The decline in species richness at higher latitudes is among the most fundamental patterns in ecology. Whether changes in species composition across space (beta-diversity) contribute to this gradient of overall species richness (gamma-diversity) remains hotly debated. Previous studies that failed to resolve the issue suffered from a well-known tendency for small samples in areas with high gamma-diversity to have inflated measures of beta-diversity. Here, we provide a novel analytical test, using beta-diversity metrics that correct the gamma-diversity and sampling biases, to compare beta-diversity and species packing across a latitudinal gradient in tree species richness of 21 large forest plots along a large environmental gradient in East Asia. We demonstrate that after accounting for topography and correcting the gamma-diversity bias, tropical forests still have higher beta-diversity than temperate analogues. This suggests that beta-diversity contributes to the latitudinal species richness gradient as a component of gamma-diversity. Moreover, both niche specialization and niche marginality (a measure of niche spacing along an environmental gradient) also increase towards the equator, after controlling for the effect of topographical heterogeneity. This supports the joint importance of tighter species packing and larger niche space in tropical forests while also demonstrating the importance of local processes in controlling beta-diversity.

SARS-CoV-2 outbreak in a tri-national urban area is dominated by a B.1 lineage variant linked to a mass gathering event

The first case of SARS-CoV-2 in Basel, Switzerland was detected on February 26th 2020. We present a phylogenetic study to explore viral introduction and evolution during the exponential early phase of the local COVID-19 outbreak from February 26th until March 23rd. We sequenced SARS-CoV-2 naso-oropharyngeal swabs from 746 positive tests that were performed at the University Hospital Basel during the study period. We successfully generated 468 high quality genomes from unique patients and called variants with our COVID-19 Pipeline (COVGAP), and analysed viral genetic diversity using PANGOLIN taxonomic lineages. To identify introduction and dissemination events we incorporated global SARS-CoV-2 genomes and inferred a time-calibrated phylogeny. Epidemiological data from patient questionnaires was used to facilitate the interpretation of phylogenetic observations. The early outbreak in Basel was dominated by lineage B.1 (83·6%), detected first on March 2nd, although the first sample identified belonged to B.1.1. Within B.1, 68·2% of our samples fall within a clade defined by the SNP C15324T ('Basel cluster'), including 157 identical sequences at the root of the 'Basel cluster', some of which we can specifically trace to regional spreading events. We infer the origin of B.1-C15324T to mid-February in our tri-national region. The other genomes map broadly over the global phylogenetic tree, showing several introduction events from and/or dissemination to other regions of the world via travellers. Family transmissions can also be traced in our data. A single lineage variant dominated the outbreak in the Basel area while other lineages, such as the first (B.1.1), did not propagate. A mass gathering event was the predominant initial source of cases, with travel returners and family transmissions to a lesser extent. We highlight the importance of adding specific questions to epidemiological questionnaires, to obtain data on attendance of large gatherings and their locations, as well as travel history, to effectively identify routes of transmissions in up-coming outbreaks. This phylogenetic analysis in concert with epidemiological and contact tracing data, allows connection and interpretation of events, and can inform public health interventions. Trial Registration: ClinicalTrials.gov NCT04351503.

More than one million barriers fragment Europe's rivers

Rivers support some of Earth's richest biodiversity¹ and provide essential ecosystem services to society², but they are often fragmented by barriers to free flow³. In Europe, attempts to quantify river connectivity have been hampered by the absence of a harmonized barrier database. Here we show that there are at least 1.2 million instream barriers in 36 European countries (with a mean density of 0.74 barriers per kilometre), 68 per cent of which are structures less than two metres in height that are often overlooked. Standardized walkover surveys along 2,715 kilometres of stream length for 147 rivers indicate that existing records underestimate barrier numbers by about 61 per cent. The highest barrier densities occur in the heavily modified rivers of central Europe and the lowest barrier densities occur in the most remote, sparsely populated alpine areas. Across Europe, the main predictors of barrier density are agricultural pressure, density of river-road crossings, extent of surface water and elevation. Relatively unfragmented rivers are still found in the Balkans, the Baltic states and parts of Scandinavia and southern Europe, but these require urgent protection from proposed dam developments. Our findings could inform the implementation of the EU Biodiversity Strategy, which aims to reconnect 25,000 kilometres of Europe's rivers by 2030, but achieving this will require a paradigm shift in river restoration that recognizes the widespread impacts caused by small barriers.

Upscaling Statistical Patterns from Reduced Storage in Social and Life Science Big Datasets

Recent technological and computational advances have enabled the collection of data at an unprecedented rate. On the one hand, the large amount of data suddenly available has opened up new opportunities for new data-driven research but, on the other hand, it has brought into light new obstacles and challenges related to storage and analysis limits. Here, we strengthen an upscaling approach borrowed from theoretical ecology that allows us to infer with small errors relevant patterns of a dataset in its entirety, although only a limited fraction of it has been analysed. In particular we show that, after reducing the input amount of information on the system under study, by applying our framework it is still possible to recover two statistical patterns of interest of the entire dataset. Tested against big ecological, human activity and genomics data, our framework was successful in the reconstruction of global statistics related to both the number of types and their abundances while starting from limited presence/absence information on small random samples of the datasets. These results pave the way for future applications of our procedure in different life science contexts, from social activities to natural ecosystems.

The dynamics of negative stereotypes as revealed by tweeting behavior in the aftermath of the Charlie Hebdo terrorist attack

We describe the evolution of a stereotype as it emerged in tweets about the Charlie Hebdo terrorist attack in Paris in early 2015. Our focus is on terms associated with the Muslim community and the Islamic world. The data (400k tweets) were collected via Twitter streaming API and consisted of tweets that contained at least one of 16 hashtags associated with the Charlie Hebdo attack (e.g., #JeSuisCharlie, #IAmCharlie, #ParisAttacks), collected between January 14th and February 9th. From these data, we generated pairwise co-occurrence frequencies between key words such as “Islam”, “Muslim(s)”, “Arab(s)”, and “The Prophet” and possible associates such as: “terrorism”, “terror”, “terrorist(s)”, “kill(ed)”, “free”, “freedom” and “love”. We use changes in frequency of co-occurring words to define ways in which acute negative and positive stereotypes towards Muslims and Islam arise and evolve in three phases during the period of interest. We identify a positively-valenced backlash in a subset of tweets associated with the “origins of Islam”. Results depict the emergence and transformation of implicit online stereotypes related to Islam from naturally occurring social media data and how pro-as well as anti-Islam online small-world networks evolve in response to a terrorist attack.

Arthropod Communities in Urban Agricultural Production Systems under Different Irrigation Sources in the Northern Region of Ghana

Urban and peri-urban agricultural (UPA) production systems in West African countries do not only mitigate food and financial insecurity, they may also foster biodiversity of arthropods and partly compensate for structural losses of natural environments. However, management practices in UPA systems like irrigation may also contribute to disturbances in arthropod ecology. To fill knowledge gaps in the relationships between UPA management and arthropod populations, we compared arthropods species across different irrigation sources in Tamale. During a 72-h sampling period, 14,226 arthropods were caught with pitfall traps and pan traps from 36 fields. These specimens comprised 13 orders, 103 families, 264 genera, and 329 taxa (243 identified species, 86 unidentified species) and categorized into five feeding guilds (carnivores, decomposers, herbivores, omnivores, and pollinators). Species richness, species accumulation curves, and diversity functions (richness, evenness, and dispersion) were calculated to characterize the arthropod community. Non-metric multidimensional scaling was applied to examine structural similarity of arthropod communities among sites. To account for the effects of soil-related data, we furthermore applied a redundancy analysis. Arthropods grouped according to the irrigation water source, whereby the dipterans were most dominant under wastewater conditions. Here, particularly the eye gnat, Hippelates pusio, a disease-causing vector for humans, accounted for the dipterans. The occurrence of three alien ant species suggested community shifts through invasive species, while the occurrence of seven ant species (at least one ant species occurred under each water source) that form mutualistic relationships with aphids highlighted future risks of aphid pest outbreak. Future studies on these taxa should specifically target their ecological and economic effects and potential countermeasures.

Shannon diversity index: a call to replace the original Shannon's formula with unbiased estimator in the population genetics studies

BACKGROUND

The Shannon diversity index has been widely used in population genetics studies. Recently, it was proposed as a unifying measure of diversity at different levels-from genes and populations to whole species and ecosystems. The index, however, was proven to be negatively biased at small sample sizes. Modifications to the original Shannon's formula have been proposed to obtain an unbiased estimator.

METHODS

In this study, the performance of four different estimators of Shannon index-the original Shannon's formula and those of Zahl, Chao and Shen and Chao et al.-was tested on simulated microsatellite data. Both the simulation and analysis of the results were performed in the R language environment. A new R function was created for the calculation of all four indices from the genind data format.

RESULTS

Sample size dependence was detected in all the estimators analysed; however, the deviation from parametric values was substantially smaller in the derived measures than in the original Shannon's formula. Error rate was negatively associated with population heterozygosity. Comparisons among loci showed that fast-mutating loci were less affected by the error, except for the original Shannon's estimator which, in the smallest sample, was more strongly affected by loci with a higher number of alleles. The Zahl and Chao et al. estimators performed notably better than the original Shannon's formula.

CONCLUSION

The results of this study show that the original Shannon index should no longer be used as a measure of genetic diversity and should be replaced by Zahl's unbiased estimator.

Estimating diversity in networked ecological communities

Comparing ecological communities across environmental gradients can be challenging, especially when the number of different taxonomic groups in the communities is large. In this setting, community-level summaries called diversity indices are widely used to detect changes in the community ecology. However, estimation of diversity indices has received relatively little attention from the statistical community. The most common estimates of diversity are the maximum likelihood estimates of the parameters of a multinomial model, even though the multinomial model implies strict assumptions about the sampling mechanism. In particular, the multinomial model prohibits ecological networks, where taxa positively and negatively co-occur. In this article, we leverage models from the compositional data literature that explicitly account for co-occurrence networks and use them to estimate diversity. Instead of proposing new diversity indices, we estimate popular diversity indices under these models. While the methodology is general, we illustrate the approach for the estimation of the Shannon, Simpson, Bray–Curtis, and Euclidean diversity indices. We contrast our method to multinomial, low-rank, and nonparametric methods for estimating diversity indices. Under simulation, we find that the greatest gains of the method are in strongly networked communities with many taxa. Therefore, to illustrate the method, we analyze the microbiome of seafloor basalts based on a 16S amplicon sequencing dataset with 1425 taxa and 12 communities.

Diversity in biology: definitions, quantification and models

Diversity indices are useful single-number metrics for characterizing a complex distribution of a set of attributes across a population of interest. The utility of these different metrics or sets of metrics depends on the context and application, and whether a predictive mechanistic model exists. In this topical review, we first summarize the relevant mathematical principles underlying heterogeneity in a large population, before outlining the various definitions of 'diversity' and providing examples of scientific topics in which its quantification plays an important role. We then review how diversity has been a ubiquitous concept across multiple fields, including ecology, immunology, cellular barcoding experiments, and socioeconomic studies. Since many of these applications involve sampling of populations, we also review how diversity in small samples is related to the diversity in the entire population. Features that arise in each of these applications are highlighted.

Analysis of the Whole CDR3 T Cell Receptor Repertoire after Hematopoietic Stem Cell Transplantation in 2 Clinical Cohorts

A major cause of morbidity and mortality for patients who undergo hematologic stem cell transplantation (HSCT) is acute graft-versus-host disease (aGVHD), a mostly T cell-mediated disease. Examination of the T cell receptor (TCR) repertoire of HSCT recipients and the use of next-generation nucleotide sequencing have raised the question of whether features of TCR repertoire reconstitution might reproducibly associate with aGVHD. We hypothesized that the peripheral blood TCR repertoire of patients with steroid-nonresponsive aGVHD would be less diverse. We also hypothesized that patients with GVHD who shared HLA might also share common clones at the time of GVHD diagnosis, thereby potentially providing potential clinical indicators for treatment stratification. We further hypothesized that HSCT recipients with the same HLA mismatch might share a more similar TCR repertoire based on a potentially shared focus of alloreactive responses. We studied 2 separate patient cohorts and 2 separate platforms for measuring TCR repertoire. The first cohort of patients was from a multicenter Phase III randomized double-blinded clinical trial of patients who developed aGVHD (NCT01002742). The second cohort comprised samples from biobanks from 2 transplantation centers and the Center for International Blood and Marrow Transplant Research of patients who underwent mismatched HSCT. There were no statistically significant differences in the TCR diversity of steroid responders and nonresponders among patients with aGVHD on the day of diagnosis. Most clones in the repertoire were unique to each patient, but a small number of clones were found to be both exclusive to and shared among aGVHD nonresponders. We were also able to show a strong correlation between the presence of Vβ20 and Vβ29 and steroid responsiveness. Using the Bhattacharya coefficient, those patients who shared the same HLA mismatch were shown to be no more similar to one another than to those who had a completely different mismatch. Using 2 separate clinical cohorts and 2 separate platforms for analyzing the TCR repertoire, we have shown that the sampled human TCR repertoire is largely unique to each patient but contains glimmers of common clones of subsets of clones based on responsiveness to steroids in aGVHD on the day of diagnosis. These studies are informative for future strategies to assess for reproducible TCR responses in human alloreactivity and possible markers of GVHD responsiveness to therapy.

Monitoring long-term spatial and temporal trends of the infaunal community characteristics along the shallow waters of the Mediterranean coast of Israel

Sandy sediment and its infauna were annually sampled along the shallow waters of the Israeli coast during the 2005-2016 period, as a part of the Israeli National Environmental Program framework, aiming to detect anthropogenic interference in that province by monitoring changes in the species composition, abundance, and diversity of the infaunal communities and in accompanied abiotic parameters: the levels of total organic carbon and a series of heavy metals and the site-specific grain size distribution. The > 250-μm fraction of the fauna was segregated from the sampled sediment and was identified to species or higher taxonomic level. Three spatial biotopes were determined based on their unique faunal composition, Haifa Bay, Haifa harbor, and the southern coast. Species homogeneity among samples of each biotope was evaluated. Temporal and spatial changes of the species composition, abundance, and diversity were calculated for each biotope, mostly revealing random annual fluctuations. Only two minor temporal trends were observed: two spatially identical and temporally different faunal communities in the southern coast biotope, distinguishing the 2005-2007 and 2008-2016 periods, and a slight increase in the number of species across time in the two Haifa Bay provinces. Total organic carbon was highly correlated to the faunal composition with the highest organic carbon levels in the Haifa harbor biotope. The biotopes' mutually occurring abundant species were sufficient to determine biotope borders and the contribution of intermittently sampled rare species, including the zoogeographically Indo-Pacific originated ones was feeble, important only to identify species migration and faunistics. Practically, three sampling sites along the Israeli shallow soft substrate, corresponding to the defined spatial biotopes, are sufficient to monitor the effect of environmental changes. Seasonal sampling twice a year is recommended as well as more accurate species identification using molecular taxonomy.

Microbes and macro-invertebrates show parallel β-diversity but contrasting α-diversity patterns in a marine natural experiment

Documenting ecological patterns across spatially, temporally and taxonomically diverse ecological communities is necessary for a general understanding of the processes shaping biodiversity. A major gap in our understanding remains the comparison of diversity patterns across a broad spectrum of evolutionarily and functionally diverse organisms, particularly in the marine realm. Here, we aim to narrow this gap by comparing the diversity patterns of free-living microbes and macro-invertebrates across a natural experiment provided by the marine lakes of Palau: geographically discrete and environmentally heterogeneous bodies of seawater with comparable geological and climatic history, and a similar regional species pool. We find contrasting patterns of α-diversity but remarkably similar patterns of β-diversity between microbial and macro-invertebrate communities among lakes. Pairwise dissimilarities in community composition among lakes are positively correlated between microbes and macro-invertebrates, and influenced to a similar degree by marked gradients in oxygen concentration and salinity. Our findings indicate that a shared spatio-temporal and environmental context may result in parallel patterns of β-diversity in microbes and macro-invertebrates, in spite of key trait differences between these organisms. This raises the possibility that parallel processes also influence transitions among regional biota across the tree of life, at least in the marine realm.

Molecular Heterogeneity in Large-Scale Biological Data: Techniques and Applications

High-throughput sequencing technologies have evolved at a stellar pace for almost a decade and have greatly advanced our understanding of genome biology. In these sampling-based technologies, there is an important detail that is often overlooked in the analysis of the data and the design of the experiments, specifically that the sampled observations often do not give a representative picture of the underlying population. This has long been recognized as a problem in statistical ecology and in the broader statistics literature. In this review, we discuss the connections between these fields, methodological advances that parallel both the needs and opportunities of large-scale data analysis, and specific applications in modern biology. In the process we describe unique aspects of applying these approaches to sequencing technologies, including sequencing error, population and individual heterogeneity, and the design of experiments.

A comprehensive assessment of stream fragmentation in Great Britain

Artificial barriers are one of the main threats to river ecosystems, resulting in habitat fragmentation and loss of connectivity. Yet, the abundance and distribution of most artificial barriers, excluding high-head dams, is poorly documented. We provide a comprehensive assessment of the distribution and typology of artificial barriers in Great Britain, and estimate for the first time the extent of river fragmentation. To this end, barrier data were compiled from existing databases and were ground-truthed by field surveys in England, Scotland and Wales to derive a correction factor for barrier density across Great Britain. Field surveys indicate that existing barrier databases underestimate barrier density by 68%, particularly in the case of low-head structures (<1 m) which are often missing from current records. Field-corrected barrier density estimates ranged from 0.48 barriers/km in Scotland to 0.63 barriers/km in Wales, and 0.75 barriers/km in England. Corresponding estimates of stream fragmentation by weirs and dams only, measured as mean barrier-free length, were 12.30 km in Scotland, 6.68 km in Wales and 5.29 km in England, suggesting the extent of river modification differs between regions. Our study indicates that 97% of the river network in Great Britain is fragmented and <1% of the catchments are free of artificial barriers.

Estimating the Mutual Information between Two Discrete, Asymmetric Variables with Limited Samples

Determining the strength of nonlinear, statistical dependencies between two variables is a crucial matter in many research fields. The established measure for quantifying such relations is the mutual information. However, estimating mutual information from limited samples is a challenging task. Since the mutual information is the difference of two entropies, the existing Bayesian estimators of entropy may be used to estimate information. This procedure, however, is still biased in the severely under-sampled regime. Here, we propose an alternative estimator that is applicable to those cases in which the marginal distribution of one of the two variables—the one with minimal entropy—is well sampled. The other variable, as well as the joint and conditional distributions, can be severely undersampled. We obtain a consistent estimator that presents very low bias, outperforming previous methods even when the sampled data contain few coincidences. As with other Bayesian estimators, our proposal focuses on the strength of the interaction between the two variables, without seeking to model the specific way in which they are related. A distinctive property of our method is that the main data statistics determining the amount of mutual information is the inhomogeneity of the conditional distribution of the low-entropy variable in those states in which the large-entropy variable registers coincidences.

First Experimental Assessment of Protein Intrinsic Disorder Involvement in an RNA Virus Natural Adaptive Process

Intrinsic disorder (ID) in proteins is defined as a lack of stable structure in physiological conditions. Intrinsically disordered regions (IDRs) are highly abundant in some RNA virus proteomes. Low topological constraints exerted on IDRs are expected to buffer the effect of numerous deleterious mutations and could be related to the remarkable adaptive potential of RNA viruses to overcome resistance of their host. To experimentally test this hypothesis in a natural pathosystem, a set of four variants of Potato virus Y (PVY; Potyvirus genus) containing various ID degrees in the Viral genome-linked (VPg) protein, a key determinant of potyvirus adaptation, was designed. To estimate the ID contribution to the VPg-based PVY adaptation, the adaptive ability of the four PVY variants was monitored in the pepper host (Capsicum annuum) carrying a recessive resistance gene. Intriguingly, the two mutants with the highest ID content displayed a significantly higher ability to restore infection in the resistant host, whereas the less intrinsically disordered mutant was unable to restore infection. The role of ID on virus adaptation may be due either to a larger exploration of evolutionary pathways or the minimization of fitness penalty caused by resistance-breaking mutations. This pioneering study strongly suggests the positive impact of ID in an RNA virus adaptive capacity.

Urbanization as a driver of taxonomic, functional, and phylogenetic diversity losses in bird communities

Urbanization is one of the most important threats to biodiversity worldwide, as it drives declines in species diversity, functional diversity, and phylogenetic diversity and increases functional redundancy among species. We estimated taxonomic, functional, and phylogenetic diversities, as well as the abundance of several functional groups, in bird communities from a town in east-central Argentina in 1985–1986 and 30 years after (2015–2016). In 1985–1986, we found that taxonomic diversity (abundance, species richness, and alpha diversity), functional richness, and basal phylogenetic diversity were negatively related to building cover, whereas terminal phylogenetic diversity showed a positive relationship with building cover. Moreover, the abundance of specialized functional groups (ground, aerial, and foliage insectivores; nectarivores/insectivores; ground/canopy and ground granivores) decreased with increased building cover, whereas the reverse pattern for the abundance of generalists (medium-sized/large and small omnivores) was found. In 2015–2016, by contrast, taxonomic, functional, and phylogenetic diversities were not related to building cover. Our results not only support the hypothesis that urbanization affects the potential number of ecosystem functions, but also that this relationship may change through time. Given the accelerated rate of urbanization worldwide, an integrative approach between different facets of biodiversity is promoted to gain insight into the response of bird communities in urban environments.

Effects of Sample Size and Full Sibs on Genetic Diversity Characterization: A Case Study of Three Syntopic Iberian Pond-Breeding Amphibians

Accurate characterization of genetic diversity is essential for understanding population demography, predicting future trends and implementing efficient conservation policies. For that purpose, molecular markers are routinely developed for nonmodel species, but key questions regarding sampling design, such as calculation of minimum sample sizes or the effect of relatives in the sample, are often neglected. We used accumulation curves and sibship analyses to explore how these 2 factors affect marker performance in the characterization of genetic diversity. We illustrate this approach with the analysis of an empirical dataset including newly optimized microsatellite sets for 3 Iberian amphibian species: Hyla molleri, Epidalea calamita, and Pelophylax perezi. We studied 17-21 populations per species (total n = 547, 652, and 516 individuals, respectively), including a reference locality in which the effect of sample size was explored using larger samples (77-96 individuals). As expected, FIS and tests for Hardy-Weinberg equilibrium and linkage disequilibrium were affected by the presence of full sibs, and most initially inferred disequilibria were no longer statistically significant when full siblings were removed from the sample. We estimated that to obtain reliable estimates, the minimum sample size (potentially including full sibs) was close to 20 for expected heterozygosity, and between 50 and 80 for allelic richness. Our pilot study based on a reference population provided a rigorous assessment of marker properties and the effects of sample size and presence of full sibs in the sample. These examples illustrate the advantages of this approach to produce robust and reliable results for downstream analyses.

Monitoring Temporal Variation to Assess Changes in the Structure of Subtropical Atlantic Forest Butterfly Communities

The study of fauna through long-term surveys is important in unveiling how temporal patterns shape the structure of communities in tropical habitats. The butterfly assemblage of the subtropical Atlantic Forest may be considered highly diverse and shows changes in diversity and composition over time, highlighting the importance of long-term inventories. This work assessed temporal diversity patterns in the distribution and composition of butterfly assemblages in an Atlantic Forest site in southern Brazil using combined data from three years of standardized sampling with entomological nets, increasing the knowledge on this group in the Neotropics for monitoring and conservation. The butterfly fauna was analyzed in terms of richness, abundance, and composition. The inventories reached 401 species, with 14,442 butterfly individuals sampled. All the diversity parameters evaluated show significant differences between the first year of sampling compared to the second and third years. The latter had higher values of richness and abundance, followed by the first and second years. Hesperiidae was the richest family, followed by Nymphalidae and Lycaenidae, indicating a good representation of the assemblage as a whole. The results of this work are important for developing conservation programs in the Atlantic Forest and other forested environments in the neotropics, especially concerning reliable diversity assessments for the monitoring and management of protected areas. Decision making and public policy might also benefit from knowledge on temporal patterns of diversity regarding the maintenance of native habitats and integrity of biomes and their associated fauna.

Environment-induced changes in selective constraints on social learning during the peopling of the Americas

The weaponry technology associated with Clovis and related Early Paleoindians represents the earliest well-defined evidence of humans in Pleistocene North America. We assess the technological diversity of these fluted stone points found at archaeological sites in the western and eastern halves of North America by employing statistical tools used in the quantification of ecological biodiversity. Our results demonstrate that the earliest hunters in the environmentally heterogeneous East used a more diverse set of points than those in the environmentally homogenous West. This and other evidence shows that environmental heterogeneity in the East promoted the relaxation of selective constraints on social learning and increased experimentation with point designs.

The generalized Simpson's entropy is a measure of biodiversity

Modern measures of diversity satisfy reasonable axioms, are parameterized to produce diversity profiles, can be expressed as an effective number of species to simplify their interpretation, and come with estimators that allow one to apply them to real-world data. We introduce the generalized Simpson’s entropy as a measure of diversity and investigate its properties. We show that it has many useful features and can be used as a measure of biodiversity. Moreover, unlike most commonly used diversity indices, it has unbiased estimators, which allow for sound estimation of the diversity of poorly sampled, rich communities.