Metric Of Diversity Research Articles

Dietary Diversity Measures Derived from Food Frequency Methods Are Weak Proxies for Anthropometric Indicators of Child Nutrition in East Africa (P11-111-19)

ObjectivesThe 7-item child dietary diversity score (DDS) is used widely as a metric of dietary diversity (DD) for infant and young child feeding (IYCF) in low-middle income countries. Validation of the DDS was based on mean micronutrient density adequacy and not other measures of child nutrition. We aimed to develop a measure of DD more strongly associated with anthropometric indicators of child nutrition. MethodsWe used data from two Tanzanian surveys, IMMANA (n = 88; ages 6–23 mo.) and the Demographic and Health Survey (DHS) (n = 9,156; ages 6–59 mo.), and two Kenyan surveys, MAMA SASHA (n = 384; age 6–12 mo.) and DHS (n = 17,509; ages 6–59 mo.). For each survey, we calculated the DDS, minimum DD, a score using all 15 items found in the standard DHS, and a yes/no indicator of animal source food (ASF) consumption. In IMMANA and MAMA SASHA, we also used a count of all unique food items consumed and based each measure on both 24-hr and 7-day recall periods. Outcome indicators were stunting, wasting, and underweight as defined by WHO. We evaluated the performance of each DD measure in identifying child undernutrition by comparing the area under the ROC curve (AUC), and estimating odds ratios using logistic regression methods. AUC = 50% is no better than random assignment. Complex survey procedures were used in all analyses and alpha was set at 0.05. ResultsIn the DHS and MAMA SASHA data, all measures of DD had similar AUC values that did not exceed 61% when compared to the anthropometric indicators. In the IMMANA data, no measure exceeded 70% AUC for wasting, 64% for underweight, or 58% for stunting. For most DD measures, increasing the recall period to 7 days marginally improved its AUC (< 3%), while it decreased the AUC for wasting in the IMMANA data. The ASF indicator had a similar AUC to the DDS. In the Tanzania DHS, a higher DD, by all four measures, was associated with decreased odds of stunting, wasting, and underweight. In contrast, no measure of DD was associated with growth indicators for Kenya. The DD indicators based on the 15-item list and the count of unique foods were negatively associated with odds of wasting in the IMMANA data. ConclusionsIn two east African settings, measures of DD derived from existing food frequency questionnaires were weak proxies for measures of child undernutrition based on anthropometry. Funding SourcesInnovative Methods and Metrics for Agriculture and Nutrition Actions.

Phylogenetic and compositional diversity are governed by different rules: a study of fleas parasitic on small mammals in four biogeographic realms

We studied patterns of phylogenetic and compositional diversity of fleas parasitic on small mammals and asked whether these patterns are affected by environmental variation or evolutionary/historical processes. We considered environmental variation via both off‐host (air temperature, precipitation, the amount of green vegetation, latitude) and host‐associated (phylogenetic and species composition) environments. The indicators of evolutionary/historical processes were phylogenetic and compositional uniqueness estimated via phylogenetic or compositional, respectively, β‐diversity of either fleas or hosts. We found that phylogenetic uniqueness of flea assemblages was the main predictor of their phylogenetic diversity in all realms. In addition, host phylogenetic diversity and uniqueness played also some role in the Palearctic, whereas the effect of the off‐host environment was either extremely weak or absent. Compositional diversity of fleas was consistently affected by compositional diversity of hosts in all realms except the Neotropics. The effect of the off‐host environment on compositional flea diversity was substantial in all realms except the Palearctic. No effect of latitude on either metric of flea diversity was found. We conclude that phylogenetic diversity of fleas is driven mainly by evolutionary/historical processes, whereas drivers of their compositional diversity are associated with current ecological conditions.

Diversity and the Starting Salaries of Undergraduate Business School Students

We treat racial diversity of the student body at both the college of business and the institutional level as an input into the undergraduate business school productive process, and find that diversity is positively related to improved starting salary outcomes for college of business students. The effects are meaningful – a one standard deviation in increase in our metric of student racial diversity at the college level implies a seven-place increase in salary rank among the 90 schools for which we have data.

Multi-Platform News Use and Political Participation Across Age Groups: Toward a Valid Metric of Platform Diversity and Its Effects

News consumption in today’s media environment is increasingly characterized by reliance on multiple platforms: People now get their news from the web, television, radio, and various social media. Employing a nationally representative survey from the United States, this study develops an index of multi-platform news use. The index is validated by testing age group differences in the way people participate in politics. Results show that Millennials are more likely to rely on multiple platforms for news. Multi-platform news is also positively related to alternative modes of political engagement. Results are discussed in light of generational shifts in political behavior.

Variant antigen repertoires in Trypanosoma congolense populations and experimental infections can be profiled from deep sequence data using universal protein motifs.

African trypanosomes are vector-borne hemoparasites of humans and animals. In the mammal, parasites evade the immune response through antigenic variation. Periodic switching of the variant surface glycoprotein (VSG) coat covering their cell surface allows sequential expansion of serologically distinct parasite clones. Trypanosome genomes contain many hundreds of VSG genes, subject to rapid changes in nucleotide sequence, copy number, and chromosomal position. Thus, analyzing, or even quantifying, VSG diversity over space and time presents an enormous challenge to conventional techniques. Indeed, previous population genomic studies have overlooked this vital aspect of pathogen biology for lack of analytical tools. Here we present a method for analyzing population-scale VSG diversity in Trypanosoma congolense from deep sequencing data. Previously, we suggested that T. congolense VSGs segregate into defined “phylotypes” that do not recombine. In our data set comprising 41 T. congolense genome sequences from across Africa, these phylotypes are universal and exhaustive. Screening sequence contigs with diagnostic protein motifs accurately quantifies relative phylotype frequencies, providing a metric of VSG diversity, called the “variant antigen profile.” We applied our metric to VSG expression in the tsetse fly, showing that certain, rare VSG phylotypes may be preferentially expressed in infective, metacyclic-stage parasites. Hence, variant antigen profiling accurately and rapidly determines the T. congolense VSG gene and transcript repertoire from sequence data, without need for manual curation or highly contiguous sequences. It offers a tractable approach to measuring VSG diversity across strains and during infections, which is imperative to understanding the host–parasite interaction at population and individual scales.

Nonpareil 3: Fast Estimation of Metagenomic Coverage and Sequence Diversity.

Estimations of microbial community diversity based on metagenomic data sets are affected, often to an unknown degree, by biases derived from insufficient coverage and reference database-dependent estimations of diversity. For instance, the completeness of reference databases cannot be generally estimated since it depends on the extant diversity sampled to date, which, with the exception of a few habitats such as the human gut, remains severely undersampled. Further, estimation of the degree of coverage of a microbial community by a metagenomic data set is prohibitively time-consuming for large data sets, and coverage values may not be directly comparable between data sets obtained with different sequencing technologies. Here, we extend Nonpareil, a database-independent tool for the estimation of coverage in metagenomic data sets, to a high-performance computing implementation that scales up to hundreds of cores and includes, in addition, a k-mer-based estimation as sensitive as the original alignment-based version but about three hundred times as fast. Further, we propose a metric of sequence diversity (Nd ) derived directly from Nonpareil curves that correlates well with alpha diversity assessed by traditional metrics. We use this metric in different experiments demonstrating the correlation with the Shannon index estimated on 16S rRNA gene profiles and show that Nd additionally reveals seasonal patterns in marine samples that are not captured by the Shannon index and more precise rankings of the magnitude of diversity of microbial communities in different habitats. Therefore, the new version of Nonpareil, called Nonpareil 3, advances the toolbox for metagenomic analyses of microbiomes. IMPORTANCE Estimation of the coverage provided by a metagenomic data set, i.e., what fraction of the microbial community was sampled by DNA sequencing, represents an essential first step of every culture-independent genomic study that aims to robustly assess the sequence diversity present in a sample. However, estimation of coverage remains elusive because of several technical limitations associated with high computational requirements and limiting statistical approaches to quantify diversity. Here we described Nonpareil 3, a new bioinformatics algorithm that circumvents several of these limitations and thus can facilitate culture-independent studies in clinical or environmental settings, independent of the sequencing platform employed. In addition, we present a new metric of sequence diversity based on rarefied coverage and demonstrate its use in communities from diverse ecosystems.

Changing Land Use a Threat to Surface Water Quality: a Vulnerability Assessment Approach in Zanjanroud Watershed, Central Iran

Maintaining the quality of surface water resources as one of the most vital water supplies has always been at the center of global concerns. A set of manifest and latent factors have yet been identified by researchers worldwide that are subject to affect the quality of surface water. Among which, the effect of land use change, due to a spatial and temporal complexity, is often not easily verifiable. The present study attempts to offer an index-based model to quantify vulnerability of surface water resources in a semi arid basin in central Iran against land use changes. For this, water quality data including Na, K, Mg, Ca, Sodium Adsorption Ratio (SAR), total anions (Sum. A), SO4, Cl, HCO3, EC, TDS, and pH were collected from hydrometric stations over a period of 26 years (1987‒2013). In order to detect land use changes, the land use maps of the years 1987, 1998, 2002, 2009, and 2013 were prepared from TM satellite images using supervised classification method. At next step, changing patterns of different land uses were traced by Shanon’s Diversity Index (SHDI) as a metric of patch diversity indicating diversity and heterogeneity of a landscape over time. Relationship between the SHDI values and water quality indicators revealed the impact of land use changes on quality of surface water resources. Statistical analysis confirmed a significant relationship between nine water quality factors and water discharge in the basin during the study period. From 1998 to 2009, the greatest changes were visible in the total anions, Ca, SO4, and HCO3. These parameters along with salinity were increasing in almost all sub-basins. According to the results, conversion of poor rangelands to rain fed agriculture fields is the most apparent land use change occurred in the study area over the study period. In 1987, SHDI as an indicator of the diversity and changes in the basin, showed a significant relationship with good rangelands (R2 =–0.835). This indicates that fragmentation of the entire watershed area was initiated in 1987, which reached its peak in 2013. Generally speaking, urbanization, poor rangeland, and irrigated agriculture were recognized as three influential land uses adversely affect the water quality in the study area.

Decomposing functional diversity

Summary One aspect of biodiversity, functional diversity, reflects the functional role of species within a community as measured by species characteristics. We present a new metric, functional trait dispersion, based on the concept of species distinctiveness measured as the distance among species in the multidimensional space defined by trait values. This metric can be decomposed into components of species richness, functional evenness and mean dispersion, and into parts that measure diversity within and among subgroups. Using an appropriate distance measure, mean dispersion (M′) is calculated as the average distance among all possible pairs of species. Functional evenness [qE(T)] is derived from Hill diversity based on the proportional distances between pairs of species and species richness (S). Functional trait dispersion [qD(TM)] is then computed as 1 + (S−1) × qE(T) × M′. It has a range of [1,S] and measures the effective number of functionally distinct species for a given level of species dispersion. Using constructed data, we demonstrate that qD(TM) captures appropriate ecological properties such that a community with greater species richness, greater dispersal in trait space or greater mean dispersion has greater functional diversity. Functional trait dispersion can also provide measures of within‐community dispersion and the effective number of functionally distinctive compartments (groups of communities with similar functional structure). Using empirical data of bats along an elevational gradient in Peru, we demonstrate that functional trait dispersion and its components provide insights about gradients of biodiversity. Functional trait dispersion comports to reasonable criteria for a metric of functional diversity and can be decomposed in a variety of ways that facilitate understanding of patterns of variation. Other metrics of functional diversity neither integrate all three diversity components, nor can many be decomposed into variation within and among subgroups. Because functional trait dispersion measures properties of distance and the effective number of functionally distinct species, it can be used in conjunction with other biodiversity metrics that are based on species identity, abundance or phylogenetic relatedness to inform management and the preservation of biodiversity.

Phylogenetic regionalization of marine plants reveals close evolutionary affinities among disjunct temperate assemblages

While our knowledge of species distributions and diversity in the terrestrial biosphere has increased sharply over the last decades, we lack equivalent knowledge of the marine world. Here, we use the phylogenetic tree of seagrasses along with their global distributions and a metric of phylogenetic beta diversity to generate a phylogenetically-based delimitation of marine phytoregions (phyloregions). We then evaluate their evolutionary affinities and explore environmental correlates of phylogenetic turnover between them. We identified 11 phyloregions based on the clustering of phylogenetic beta diversity values. Most phyloregions can be classified as either temperate or tropical, and even geographically disjunct temperate regions can harbor closely related species assemblages. Geographic differences in sea surface temperatures account for more phylogenetic turnover than either water salinity or bathymetry. We also found a strong temperate-tropical gradient in evolutionary distinctiveness, with temperate phyloregions being the most evolutionarily unique. Our results highlight differences between the marine and terrestrial worlds, and suggest that the interplay between long-distance dispersal and phylogenetic niche conservatism played a central role in determining the contemporary distributions of seagrasses worldwide.

Fine-Scale Ecological and Genetic Population Structure of Two Whitefish (Coregoninae) Species in the Vicinity of Industrial Thermal Emissions.

Thermal pollution from industrial processes can have negative impacts on the spawning and development of cold-water fish. Point sources of thermal effluent may need to be managed to avoid affecting discrete populations. Correspondingly, we examined fine-scale ecological and genetic population structure of two whitefish species (Coregonus clupeaformis and Prosopium cylindraceum) on Lake Huron, Canada, in the immediate vicinity of thermal effluent from nuclear power generation. Niche metrics using δ13C and δ15N stable isotopes showed high levels of overlap (48.6 to 94.5%) in resource use by adult fish captured in areas affected by thermal effluent compared to nearby reference locations. Isotopic niche size, a metric of resource use diversity, was 1.3- to 2.8-fold higher than reference values in some thermally affected areas, indicative of fish mixing. Microsatellite analyses of genetic population structure (Fst, STRUCTURE and DAPC) indicated that fish captured at all locations in the vicinity of the power plant were part of a larger population extending beyond the study area. In concert, ecological and genetic markers do not support the presence of an evolutionarily significant unit in the vicinity of the power plant. Thus, future research should focus on the potential impacts of thermal emissions on development and recruitment.

A novel phylogenetic regionalization of phytogeographical zones of southern Africa reveals their hidden evolutionary affinities

AbstractAimAlthough existing bioregional classification schemes often consider the compositional affinities within regional biotas, they do not typically incorporate phylogenetic information explicitly. Because phylogeny captures information on the evolutionary history of taxa, it provides a powerful tool for delineating biogeographical boundaries and for establishing relationships among them. Here, we present the first vegetation delineation of the woody flora of southern Africa based upon evolutionary relationships.LocationSouthern Africa.MethodsWe used a published time‐calibrated phylogenetic tree for 1400 woody plant species along with their geographical distributions and a metric of phylogenetic beta diversity to generate a phylogenetic delineation of the woody vegetation of southern Africa. We then explored environmental correlates of phylogenetic turnover between them, and the evolutionary distinctiveness of the taxa within them.ResultsWe identified 15 phylogenetically distinct biogeographical units, here referred to as phyloregions. The largest phyloregion broadly overlaps with Savanna vegetation, while the phyloregion overlapping with the south‐western portion of the Fynbos biome is the most evolutionarily distinct. Potential evapotranspiration and mean annual temperature differ significantly among phyloregions and correlate with patterns of phylogenetic beta diversity between them. Our phylogeny‐based delimitation of southern Africa's woody vegetation broadly matches currently recognized phytogeographical classifications, but also highlights parts of the Namib Karoo and Greater Limpopo Transfrontier Park as distinct, but previously under‐recognized biogeographical units.Main conclusionsOur analysis provides new insights into the structure and phylogenetic relationships among the woody flora of southern Africa. We show that evolutionary affinities differentiate phyloregions closely resembling existing vegetation classifications, yet also identify ‘cryptic’ phyloregions that are as evolutionarily distinct as some of the recognized African vegetation types.

The Leinster and Cobbold indices improve inferences about microbial diversity

Abstract An increasing number of ecological studies compare the diversity of microbial taxa along environmental gradients or between imposed treatments. Estimates are often based on analysis-of-variance of taxon-richness inferred from pyrosequencing data. We conducted a reanalysis of three 454-pyrosequencing studies on arbuscular-mycorrhizal-fungal diversity to evaluate the suitability of using the Leinster and Cobbold diversity-indices (LCdis) to assess diversity. We expected that the potential of LCdis to consider phylogenic relationships could resolve problems arising from ambiguous species-delineation in microbial-systems. Our reanalysis showed that comparisons between studies differing considerably in sequencing depth may be risky. Moreover, we show that LCdis not only reproduce the results of analyses of variance but can also resolve issues connected to variation in sequence read number, while additionally representing a less conservative metric of diversity than analysis-of-variance of taxa-richness. Based on these results we advocate the use of inclusive diversity indices in ecological studies targeting microbial communities.

Analysis of Plasmodium falciparum diversity in natural infections by deep sequencing.

Malaria elimination strategies require surveillance of the parasite population for genetic changes that demand a public health response, such as new forms of drug resistance. 1,2 Here we describe methods for large-scale analysis of genetic variation in Plasmodium falciparum by deep sequencing of parasite DNA obtained from the blood of patients with malaria, either directly or after short term culture. Analysis of 86,158 exonic SNPs that passed genotyping quality control in 227 samples from Africa, Asia and Oceania provides genome-wide estimates of allele frequency distribution, population structure and linkage disequilibrium. By comparing the genetic diversity of individual infections with that of the local parasite population, we derive a metric of within-host diversity that is related to the level of inbreeding in the population. An open-access web application has been established for exploration of regional differences in allele frequency and of highly differentiated loci in the P. falciparum genome.

Modelling the impact of acute infection dynamics on the accumulation of HIV-1 mutations

Events over the past year have brought hope and have re-energized the interest in targeting pre-infection or early infection period with preventative or therapeutic interventions such as vaccines and pre-exposure prophylaxis (PrEP). In breakthrough infections, the incidence, long term prognosis and clinical significance of early infection events is not well understood but it is possible that these early events may be crucial in determining the subsequent course of disease. We use a branching process model in a deterministically varying environment to explore how the dynamics of early infection affects the accumulation of mutations which lay the seeds for long term evolution of drug resistance and immune system evasion. We relate this exploration to regimes of impact, on diversity, of tropical interventions strategies such as PrEP and vaccines. As a metric of diversity we compute the probability of existence of particular genomes which potentially arise. Using several model scenarios, we demonstrate various regimes of ‘response’ of evolution to ‘intervention’. Transient effects of therapeutic interventions early in infection that impose a fitness cost on early viruses can significantly reduce the probability of diversity later during the chronic state of infection. This stands in contrast to the concern that early selective pressure may increase the probability of later existence of drug resistance mutations, for example. The branching process paradigm offers the ability to efficiently compute important indicators of viral diversity, in a framework with a modest number of simplifying assumptions, without simulating the full range of individual level scenarios. These models may be useful to illustrate the impact of vaccines and PrEP on viral evolution in the case of breakthrough infection. They also suggest that new measures of viral diversity which correlate to prognosis should be sought in trials for PrEP and vaccines.

The effect of biodiversity on tree productivity: from temperate to boreal forests

ABSTRACTAim An important issue regarding biodiversity concerns its influence on ecosystem functioning. Experimental work has led to the proposal of mechanisms such as niche complementarity. However, few attempts have been made to confirm these in natural systems, especially in forests. Furthermore, one of the most interesting unresolved questions is whether the effects of complementarity on ecosystem functioning (EF) decrease in favour of competitive exclusions over an increasing productivity gradient. Using records from permanent forest plots, we asked the following questions. (1) Is tree productivity positively related to diversity? (2) Does the effect of diversity increase in less productive forests? (3) What metric of diversity (e.g. functional or phylogenetic diversity) better relates to tree productivity?Location Temperate, mixed and boreal forests of eastern Canada.Methods Over 12,000 permanent forest plots, from temperate to boreal forests, were used to test our hypotheses in two steps. (1) Stepwise regressions were used to identify the best explanatory variables for tree productivity. (2) The selected climatic and environmental variables, as well as density and biodiversity indices, were included in a structural equation model where links (paths) between covarying variables are made explicit, making structural equation modelling the best tool to explore such complicated causal networks.Results This is the first large‐scale demonstration of a strong, positive and significant effect of biodiversity on tree productivity with control for climatic and environmental conditions. Important differences were noted between the two forest biomes investigated.Main conclusions We show for the first time that complementarity may be less important in temperate forests growing in a more stable and productive environment where competitive exclusion is the most probable outcome of species interactions, whereas in the more stressful environment of boreal forests, beneficial interactions between species may be more important. The present work is also a framework for the analysis of large datasets in biodiversity–ecosystem functioning (B‐EF) research.

Diversity of Interactions: A Metric for Studies of Biodiversity

ABSTRACTMultitrophic interactions play key roles in the origin and maintenance of species diversity, and the study of these interactions has contributed to important theoretical advances in ecology and evolutionary biology. Nevertheless, most biodiversity inventories focus on static species lists, and prominent theories of diversity still ignore trophic interactions. The lack of a simple interaction metric that is analogous to species richness is one reason why diversity of interactions is not examined as a response or predictor variable in diversity studies. Using plant–herbivore–enemy trophic chains as an example, we develop a simple metric of diversity in which richness, diversity indices (e.g., Simpson's 1/D), and rarefaction diversity are calculated with links as the basic unit rather than species. Interactions include all two‐link (herbivore–plant and enemy–herbivore) and three‐link (enemy–herbivore–plant) chains found in a study unit. This metric is different from other indices, such as traditional diversity measures, connectivity and interaction diversity in food‐web studies, and the diversity of interaction index in behavioral studies, and it is easier to compute. Using this approach to studying diversity provides novel insight into debates about neutrality and correlations between diversity, stability, productivity, and ecosystem services.

Lichen community change in response to succession in aspen forests of the southern Rocky Mountains

In western North America, quaking aspen ( Populus tremuloides) is the most common hardwood in montane landscapes. Fire suppression, grazing and wildlife management practices, and climate patterns of the past century are all potential threats to aspen coverage in this region. If aspen-dependent species are losing habitat, this raises concerns about their long-term viability. Though lichens have a rich history as air pollution indicators, we believe that they may also be useful as a metric of community diversity associated with habitat change. We established 47 plots in the Bear River Range of northern Utah and southern Idaho to evaluate the effects of forest succession on epiphytic macrolichen communities. Plots were located in a narrow elevational belt (2134–2438 m) to minimize the known covariant effects of elevation and moisture on lichen communities. Results show increasing total lichen diversity and a decrease in aspen-dependent species as aspen forests succeed to conifer cover types. The interactive roles of stand aspect, basal area and cover of dominant trees, stand age, aspen bark scars, and recent tree damage were examined as related to these trends. We developed an aspen index score based on lichens showing an affinity for aspen habitat ( Phaeophyscia nigricans, Physcia tenella, Xanthomendoza fulva, Xanthomendoza galericulata) and found a significant negative relationship between the index and successional progression. Indicator species analysis showed the importance of all stages of aspen-conifer succession for lichen community diversity and highlighted the decline of aspen-dependent species with advancing succession. We present a landscape-level community analysis of lichens in the context of a conceptual model for aspen succession for the southern Rocky Mountains. We conclude that while total number of lichen species increases with succession, aspen-dependent species cover and richness will decline. In this way, epiphytic lichens communities may constitute an effective indicator of community-level diversity in for aspen-dependent species at-large.

The role of habitat connectivity and landscape geometry in experimental zooplankton metacommunities

Theory predicts that inter‐patch dispersal rates and patterns of patch heterogeneity both have the potential to alter patterns of local and regional species diversity. To test this, we manipulated both rates of habitat connectivity and the geometric arrangement of habitat heterogeneity within regions of experimental zooplankton communities. We found no effects of habitat geometry on any metric of species diversity or composition. Additionally, we found no effect of habitat connectivity rate on local species diversity. We did, however, find that increasing connectivity led to a decrease in regional diversity, as well as an increase in the percent similarity of local communities within regions. Of all of the species in these communities, the relatively large cladoceran Ceriodaphnia reticulata significantly responded to the treatments, and had a higher probability of achieving high densities when connectance was high. As such, we suggest that this species played a large role in driving the increased local community similarity and decreased regional species richness as connectivity increased. These findings are in opposition to previous experimental studies of metacommunities, but support the notion that increased connectance among local patches may decrease regional diversity when patches are heterogeneous.

Hierarchic Social Entropy: An Information Theoretic Measure of Robot Group Diversity

As research expands in multiagent intelligent systems, investigators need new tools for evaluating the artificial societies they study. It is impossible, for example, to correlate heterogeneity with performance in multiagent robotics without a quantitative metric of diversity. Currently diversity is evaluated on a bipolar scale with systems classified as either heterogeneous or homogeneous, depending on whether any of the agents differ. Unfortunately, this labeling doesn't tell us much about the extent of diversity in heterogeneous teams. How can it be determined if one system is more or less diverse than anotherq Heterogeneity must be evaluated on a continuous scale to enable substantive comparisons between systems. To enable these types of comparisons, we introduce: (1) a continuous measure of robot behavioral difference, and (2) hierarchic social entropy, an application of Shannon's information entropy metric to robotic groups that provides a continuous, quantitative measure of robot team diversity. The metric captures important components of the meaning of diversity, including the number and size of behavioral groups in a society and the extent to which agents differ. The utility of the metrics is demonstrated in the experimental evaluation of multirobot soccer and multirobot foraging teams.