Diversity in biology: definitions, quantification and models

Unbiased estimation of sampling variance for Simpson's diversity index

Quantification of measurement uncertainty is crucial for robust scientific inference, yet accurate estimates of this uncertainty remain elusive for ecological measures of diversity. Here, we address this longstanding challenge by deriving a closed-form unbiased estimator for the sampling variance of Simpson's diversity index. In numerical tests the estimator consistently outperforms existing approaches, particularly for applications in which species richness exceeds sample size. We apply the estimator to quantify biodiversity loss in marine ecosystems and to demonstrate ligand-dependent contributions of T-cell-receptor chains to specificity, illustrating its versatility across fields. The novel estimator provides researchers with a reliable method for comparing diversity between samples, essential for quantifying biodiversity trends and making informed conservation decisions.

Surrogate modeling and control of medical digital twins

The vision of personalized medicine is to identify interventions that maintain or restore a person's health based on their individual biology. Medical digital twins, computational models that integrate a wide range of health-related data about a person and can be dynamically updated, are a key technology that can help guide medical decisions. Such medical digital twin models can be high-dimensional, multi-scale, and stochastic. To be practical for healthcare applications, they often need to be simplified into low-dimensional surrogate models that can be used for optimal design of interventions. This paper introduces surrogate modeling algorithms for the purpose of optimal control applications. As a use case, we focus on agent-based models (ABMs), a common model type in biomedicine for which there are no readily available optimal control algorithms. By deriving surrogate models that are based on systems of ordinary differential equations, we show how optimal control methods can be employed to compute effective interventions, which can then be lifted back to a given ABM. The relevance of the methods introduced here extends beyond medical digital twins to other complex dynamical systems.

Chaotic turnover of rare and abundant species in a strongly interacting model community

The composition of ecological communities varies not only between different locations but also in time. Understanding the fundamental processes that drive species toward rarity or abundance is crucial to assessing ecosystem resilience and adaptation to changing environmental conditions. In plankton communities in particular, large temporal fluctuations in species abundances have been associated with chaotic dynamics. On the other hand, microbial diversity is overwhelmingly sustained by a "rare biosphere" of species with very low abundances. We consider here the possibility that interactions within a species-rich community can relate both phenomena. We use a Lotka-Volterra model with weak immigration and strong, disordered, and mostly competitive interactions between hundreds of species to bridge single-species temporal fluctuations and abundance distribution patterns. We highlight a generic chaotic regime where a few species at a time achieve dominance but are continuously overturned by the invasion of formerly rare species. We derive a focal-species model that captures the intermittent boom-and-bust dynamics that every species undergoes. Although species cannot be treated as effectively uncorrelated in their abundances, the community's effect on a focal species can nonetheless be described by a time-correlated noise characterized by a few effective parameters that can be estimated from time series. The model predicts a nonunitary exponent of the power-law abundance decay, which varies weakly with ecological parameters, consistent with observation in marine protist communities. The chaotic turnover regime is thus poised to capture relevant ecological features of species-rich microbial communities.

Forecasting drug-overdose mortality by age in the United States at the national and county levels

The drug-overdose crisis in the United States continues to intensify. Fatalities have increased 5-fold since 1999 reaching a record high of 108,000 deaths in 2021. The epidemic has unfolded through distinct waves of different drug types, uniquely impacting various age, gender, race, and ethnic groups in specific geographical areas. One major challenge in designing interventions and efficiently delivering treatment is forecasting age-specific overdose patterns at the local level. To address this need, we develop a forecasting method that assimilates observational data obtained from the CDC WONDER database with an age-structured model of addiction and overdose mortality. We apply our method nationwide and to three select areas: Los Angeles County, Cook County, and the five boroughs of New York City, providing forecasts of drug-overdose mortality and estimates of relevant epidemiological quantities, such as mortality and age-specific addiction rates.

From populations to networks: Relating diversity indices and frustration in signed graphs

Diversity indices of quadratic type, such as fractionalization and Simpson index, are measures of heterogeneity in a population. Even though they are univariate, they have an intrinsic bivariate interpretation as encounters among the elements of the population. In the paper, it is shown that this leads naturally to associate populations to weakly balanced signed networks. In particular, the frustration of such signed networks is shown to be related to fractionalization by a closed-form expression. This expression allows to simplify drastically the calculation of frustration for weakly balanced signed graphs.

Mathematical Characterization of Private and Public Immune Receptor Sequences

Diverse T and B cell repertoires play an important role in mounting effective immune responses against a wide range of pathogens and malignant cells. The number of unique T and B cell clones is characterized by T and B cell receptors (TCRs and BCRs), respectively. Although receptor sequences are generated probabilistically by recombination processes, clinical studies found a high degree of sharing of TCRs and BCRs among different individuals. In this work, we use a general probabilistic model for T/B cell receptor clone abundances to define "publicness" or "privateness" and information-theoretic measures for comparing the frequency of sampled sequences observed across different individuals. We derive mathematical formulae to quantify the mean and the variances of clone richness and overlap. Our results can be used to evaluate the effect of different sampling protocols on abundances of clones within an individual as well as the commonality of clones across individuals. Using synthetic and empirical TCR amino acid sequence data, we perform simulations to study expected clonal commonalities across multiple individuals. Based on our formulae, we compare these simulated results with the analytically predicted mean and variances of the repertoire overlap. Complementing the results on simulated repertoires, we derive explicit expressions for the richness and its uncertainty for specific, single-parameter truncated power-law probability distributions. Finally, the information loss associated with grouping together certain receptor sequences, as is done in spectratyping, is also evaluated. Our approach can be, in principle, applied under more general and mechanistically realistic clone generation models.

Probiotic supplementation during antibiotic treatment is unjustified in maintaining the gut microbiome diversity: a systematic review and meta-analysis

BACKGROUND

Probiotics are often used to prevent antibiotic-induced low-diversity dysbiosis, however their effect is not yet sufficiently summarized in this regard. We aimed to investigate the effects of concurrent probiotic supplementation on gut microbiome composition during antibiotic therapy.

METHODS

We performed a systematic review and meta-analysis of randomized controlled trials reporting the differences in gut microbiome diversity between patients on antibiotic therapy with and without concomitant probiotic supplementation. The systematic search was performed in three databases (MEDLINE (via PubMed), Embase, and Cochrane Central Register of Controlled Trials (CENTRAL)) without filters on 15 October 2021. A random-effects model was used to estimate pooled mean differences (MD) with 95% confidence intervals (CI). This review was registered on PROSPERO (CRD42021282983).

RESULTS

Of 11,769 identified articles, 15 were eligible in the systematic review and 5 in the meta-analyses. Quantitative data synthesis for Shannon (MD = 0.23, 95% CI: [(-)0.06-0.51]), Chao1 (MD = 11.59 [(-)18.42-41.60]) and observed OTUs (operational taxonomic unit) (MD = 17.15 [(-)9.43-43.73]) diversity indices revealed no significant difference between probiotic supplemented and control groups. Lacking data prevented meta-analyzing other diversity indices; however, most of the included studies reported no difference in the other reported α- and ß-diversity indices between the groups. Changes in the taxonomic composition varied across the eligible studies but tended to be similar in both groups. However, they showed a potential tendency to restore baseline levels in both groups after 3-8 weeks. This is the first meta-analysis and the most comprehensive review of the topic to date using high quality methods. The limited number of studies and low sample sizes are the main limitations of our study. Moreover, there was high variability across the studies regarding the indication of antibiotic therapy and the type, dose, and duration of antimicrobials and probiotics.

CONCLUSIONS

Our results showed that probiotic supplementation during antibiotic therapy was not found to be influential on gut microbiome diversity indices. Defining appropriate microbiome diversity indices, their standard ranges, and their clinical relevance would be crucial.

Advances in antibody discovery from human BCR repertoires

Antibodies make up an important and growing class of compounds used for the diagnosis or treatment of disease. While traditional antibody discovery utilized immunization of animals to generate lead compounds, technological innovations have made it possible to search for antibodies targeting a given antigen within the repertoires of B cells in humans. Here we group these innovations into four broad categories: cell sorting allows the collection of cells enriched in specificity to one or more antigens; BCR sequencing can be performed on bulk mRNA, genomic DNA or on paired (heavy-light) mRNA; BCR repertoire analysis generally involves clustering BCRs into specificity groups or more in-depth modeling of antibody-antigen interactions, such as antibody-specific epitope predictions; validation of antibody-antigen interactions requires expression of antibodies, followed by antigen binding assays or epitope mapping. Together with innovations in Deep learning these technologies will contribute to the future discovery of diagnostic and therapeutic antibodies directly from humans.

Coalescent dynamics of planktonic communities

Planktonic communities are extremely diverse and include a vast number of rare species. The dynamics of these rare species is best described by individual-based models. However, individual-based approaches to planktonic diversity face substantial difficulties, due to the large number of individuals required to make realistic predictions. In this paper, we study the diversity of planktonic communities by means of a spatial coalescence model that incorporates transport by oceanic currents. As a main advantage, our approach requires simulating a number of individuals equal to the size of the sample one is interested in, rather than the size of the entire community. By theoretical analysis and simulations, we explore the conditions upon which our coalescence model is equivalent to individual-based dynamics. As an application, we use our model to predict the impact of chaotic advection by oceanic currents on biodiversity. We conclude that the coalescent approach permits one to simulate marine microbial communities much more efficiently than with individual-based models.

Diversity strengthens competing teams

How does the composition of a collection of individuals affect its outcome in competition with other collections of individuals? Assuming that individuals can be different, we develop a model to interpolate between individual-level interactions and collective-level consequences. Rooted in theoretical mathematics, the model is not constrained to any specific context. Potential applications include research, education, sports, politics, ecology, agriculture, algorithms and finance. Our first main contribution is a game theoretic model that interpolates between the internal composition of an ensemble of individuals and the repercussions for the ensemble as a whole in competition with others. The second main contribution is the rigorous identification of all equilibrium points and strategies. These equilibria suggest a mechanistic underpinning for biological and physical systems to tend towards increasing diversity due to the strength it imparts to the system in competition with others.

Quantifying information of intracellular signaling: progress with machine learning

Cells convey information about their extracellular environment to their core functional machineries. Studying the capacity of intracellular signaling pathways to transmit information addresses fundamental questions about living systems. Here, we review how information-theoretic approaches have been used to quantify information transmission by signaling pathways that are functionally pleiotropic and subject to molecular stochasticity. We describe how recent advances in machine learning have been leveraged to address the challenges of complex temporal trajectory datasets and how these have contributed to our understanding of how cells employ temporal coding to appropriately adapt to environmental perturbations.

Phenotypic Diversity in Wild and Cultivated Date Palm (Phoenix, Arecaceae): Quantitative Analysis Using Information Theory

The quantitative study of genetic diversity requires tools to describe quantitatively and in parallel the whole phenotypic diversity in order to produce meaningful comparisons. The genus Phoenix offers examples of species with very different levels of diversity or heterogeneity. Within Phoenix, date palm (Phoenix dactylifera L.) is a major food crop of global relevance. The concept of information entropy was introduced by Claude Shannon; although initially intended to evaluate data communication systems, it has been used to measure biodiversity in terms of richness, evenness and dominance. In the present work, we will use it to describe heterogeneity within the different taxonomic units in the genus Phoenix. The description of the Phoenix morphological diversity in the present work is based on 596 accessions or populations belonging to 43 mutually exclusive taxonomic units (species, subspecies, varieties, landrace groups and hybrids). As Phoenix is a dioecious palm genus, female and male individuals are described separately. Each accession or sample is described using 116 characters totaling 449 states. The Shannon information entropy index allows the quantitative representation of the different levels of heterogeneity in the various taxonomic units of the genus Phoenix. Morphology, consistency and coloration of fruit and seed, followed by the inflorescences and female flowers, comprise the taxonomic characters that contribute the most to heterogeneity. Vegetative characters contribute less than the characters of the reproductive organs as a whole. Phoenix dactylifera and related Mediterranean and Macaronesian taxa present the maximum heterogeneity. Immediately afterwards we find P. loureiroi and, behind, the group of P. pusilla. At the lower limit of heterogeneity, we find species restricted in their distribution area: P. rupicola, P. theophrasti, P. roebelenii and P. acaulis. Phoenix dactylifera conforms to a complex of landraces and cultivars that coexist as phenotypically well-defined geographical groups with numerous intermediate forms and the long-distance translocation of otherwise local cultivars. This results in high heterogeneity. For the western and eastern groups of Phoenix dactylifera, it is extremely difficult to find a set of well-defined differential characters. However, some of the variables analyzed here allow us to propose a set of their respective syndromes. The high phenotypic heterogeneity in various Phoenix species is related to the genetic diversity, age and ancestry of different taxa, hybridization events and introgressions prior to domestication, and selective pressures after domestication and, again, interspecific crosses after domestication.

A statistical model of COVID-19 testing in populations: effects of sampling bias andtesting errors

We develop a statistical model for the testing of disease prevalence in a population. The model assumes a binary test result, positive or negative, but allows for biases in sample selection and both type I (false positive) and type II (false negative) testing errors. Our model also incorporates multiple test types and is able to distinguish between retesting and exclusion after testing. Our quantitative framework allows us to directly interpret testing results as a function of errors and biases. By applying our testing model to COVID-19 testing data and actual case data from specific jurisdictions, we are able to estimate and provide uncertainty quantification of indices that are crucial in a pandemic, such as disease prevalence and fatality ratios. This article is part of the theme issue 'Data science approach to infectious disease surveillance'.

Clonal dominance in excitable cell networks

Clonal dominance arises when the descendants (clones) of one or a few founder cells contribute disproportionally to the final structure during collective growth [1-8]. In contexts such as bacterial growth, tumorigenesis, and stem cell reprogramming [2-4], this phenomenon is often attributed to pre-existing propensities for dominance, while in stem cell homeostasis, neutral drift dynamics are invoked [5,6]. The mechanistic origin of clonal dominance during development, where it is increasingly documented [1,6-8], is less understood. Here, we investigate this phenomenon in the Drosophila melanogaster follicle epithelium, a system in which the joint growth dynamics of cell lineage trees can be reconstructed. We demonstrate that clonal dominance can emerge spontaneously, in the absence of pre-existing biases, as a collective property of evolving excitable networks through coupling of divisions among connected cells. Similar mechanisms have been identified in forest fires and evolving opinion networks [9-11]; we show that the spatial coupling of excitable units explains a critical feature of the development of the organism, with implications for tissue organization and dynamics [1,12,13].

A new diversity index

We introduce here a new index of diversity based on consideration of reasonable propositions that such an index should have in order to represent diversity. The behaviour of the index is compared with that of the Gini-Simpson diversity index, and is found to predict more realistic values of diversity for small communities, in particular when each species is equally represented and for small communities. The index correctly provides a measure of true diversity that is equal to the species richness across all values of species and organism numbers when all species are equally represented, as well as Hill's more stringent 'doubling' criterion when they are not. In addition, a new graphical interpretation is introduced that permits a straightforward visual comparison of pairs of indices across a wide range within a parameter space based on species and organism numbers.

Leveraging Experimental Strategies to Capture Different Dimensions of Microbial Interactions

Microorganisms are a fundamental part of virtually every ecosystem on earth. Understanding how collectively they interact, assemble, and function as communities has become a prevalent topic both in fundamental and applied research. Owing to multiple advances in technology, answering questions at the microbial system or network level is now within our grasp. To map and characterize microbial interaction networks, numerous computational approaches have been developed; however, experimentally validating microbial interactions is no trivial task. Microbial interactions are context-dependent, and their complex nature can result in an array of outcomes, not only in terms of fitness or growth, but also in other relevant functions and phenotypes. Thus, approaches to experimentally capture microbial interactions involve a combination of culture methods and phenotypic or functional characterization methods. Here, through our perspective of food microbiologists, we highlight the breadth of innovative and promising experimental strategies for their potential to capture the different dimensions of microbial interactions and their high-throughput application to answer the question; are microbial interaction patterns or network architecture similar along different contextual scales? We further discuss the experimental approaches used to build various types of networks and study their architecture in the context of cell biology and how they translate at the level of microbial ecosystem.

A statistical model of COVID-19 testing in populations: effects of sampling bias and testing errors

We develop a statistical model for the testing of disease prevalence in a population. The model assumes a binary test result, positive or negative, but allows for biases in sample selection and both type I (false positive) and type II (false negative) testing errors. Our model also incorporates multiple test types and is able to distinguish between retesting and exclusion after testing. Our quantitative framework allows us to directly interpret testing results as a function of errors and biases. By applying our testing model to COVID-19 testing data and actual case data from specific jurisdictions, we are able to estimate and provide uncertainty quantification of indices that are crucial in a pandemic, such as disease prevalence and fatality ratios.

The diversity of commercially available ale and lager yeast strains and the impact of brewer's preferential yeast choice on the fermentative beer profiles

Yeasts from the species Saccharomyces cerevisiae (ale yeast) and Saccharomyces pastorianus (lager yeast) are the main component of beer fermentation. It is known that different beer categories depend on the use of specific ale or lager strains, where the yeast imprints its distinctive fermentative profile to the beer. Despite this, there are no studies reporting how diverse, rich, and homogeneous the beer categories are in terms of commercially available brewing yeast strains. In this work, the diversity, richness, and evenness of different beer categories and commercial yeast strains available for brewing were evaluated by applying quantitative concepts of diversity analysis in a sample of 119,189 beer recipes. For this purpose, the frequency of ale or lager and dry or liquid yeast formulations usage was accessed and its correlation with the number of yeast strains, recipes, lowest and highest values of original and final gravity, international bitter units, and alcohol by volume were analyzed. A statistical framework was applied for comparing the lowest and highest fermentation temperature as well as the attenuation percentage for ale and lager yeasts strains in both dry and liquid formulations. Additionally, the brewer's preferential use of a specific brewing yeast strain in comparison to all different yeast strains reported for a beer category was estimated. The results indicated that many beer categories are preferentially fermented with dry yeast formulations instead of liquid yeasts, despite the high number of available liquid yeast formulations. Finally, the preferential use of specific yeast formulations drives the fermentative diversity of a beer category, showing that many yeast strains are potentially and industrially underexplored.

The great divide: drivers of polarization in the US public

Many democratic societies have become more politically polarized, with the U.S. being the main example. The origins of this phenomenon are still not well-understood and subject to debate. To provide insight into some of the mechanisms underlying political polarization, we develop a mathematical framework and employ Bayesian Markov chain Monte-Carlo (MCMC) and information-theoretic concepts to analyze empirical data on political polarization that has been collected by Pew Research Center from 1994 to 2017. Our framework can capture the evolution of polarization in the Democratic- and Republican-leaning segments of the U.S. public and allows us to identify its drivers. Our empirical and quantitative evidence suggests that political polarization in the U.S. is mainly driven by strong political/cultural initiatives in the Democratic party.

ELECTRONIC SUPPLEMENTARY MATERIAL

The online version of this article (10.1140/epjds/s13688-020-00249-4) contains supplementary material.