Transcending data gaps: a framework to reduce inferential errors in ecological analyses

The analysis of functional diversity (FD) has gained increasing importance due to its generality and utility in ecology. In particular, patterns in the spatial distribution and temporal change of FD are being used to predict locations and functional groups that are immediately vulnerable to global changes. A major impediment to the accurate measurement of FD is the pervasiveness of missing data in trait datasets. While such prevalent data gaps can engender misleading inferences in FD analyses, we currently lack any practical guide to handle missing data in trait datasets. Here, we identify significant mismatches between true FD and values derived from datasets that contain missing data. We demonstrate that imputing missing data with a phylogeny‐informed approach reduces the risk of misinterpretation of FD patterns, and provides baseline information against which central questions in ecology can be evaluated.     

Filling the gap in functional trait databases: use of ecological hypotheses to replace missing data

Functional trait databases are powerful tools in ecology, though most of them contain large amounts of missing values. The goal of this study was to test the effect of imputation methods on the evaluation of trait values at species level and on the subsequent calculation of functional diversity indices at community level using functional trait databases. Two simple imputation methods (average and median), two methods based on ecological hypotheses, and one multiple imputation method were tested using a large plant trait database, together with the influence of the percentage of missing data and differences between functional traits. At community level, the complete‐case approach and three functional diversity indices calculated from grassland plant communities were included. At the species level, one of the methods based on ecological hypothesis was for all traits more accurate than imputation with average or median values, but the multiple imputation method was superior for most of the traits. The method based on functional proximity between species was the best method for traits with an unbalanced distribution, while the method based on the existence of relationships between traits was the best for traits with a balanced distribution. The ranking of the grassland communities for their functional diversity indices was not robust with the complete‐case approach, even for low percentages of missing data. With the imputation methods based on ecological hypotheses, functional diversity indices could be computed with a maximum of 30% of missing data, without affecting the ranking between grassland communities. The multiple imputation method performed well, but not better than single imputation based on ecological hypothesis and adapted to the distribution of the trait values for the functional identity and range of the communities. Ecological studies using functional trait databases have to deal with missing data using imputation methods corresponding to their specific needs and making the most out of the information available in the databases. Within this framework, this study indicates the possibilities and limits of single imputation methods based on ecological hypothesis and concludes that they could be useful when studying the ranking of communities for their functional diversity indices.     

A new statistical approach for assessing similarity of species composition with incidence and abundance data

The classic Jaccard and Sørensen indices of compositional similarity (and other indices that depend upon the same variables) are notoriously sensitive to sample size, especially for assemblages with numerous rare species. Further, because these indices are based solely on presence–absence data, accurate estimators for them are unattainable. We provide a probabilistic derivation for the classic, incidence‐based forms of these indices and extend this approach to formulate new Jaccard‐type or Sørensen‐type indices based on species abundance data. We then propose estimators for these indices that include the effect of unseen shared species, based on either (replicated) incidence‐ or abundance‐based sample data. In sampling simulations, these new estimators prove to be considerably less biased than classic indices when a substantial proportion of species are missing from samples. Based on species‐rich empirical datasets, we show how incorporating the effect of unseen shared species not only increases accuracy but also can change the interpretation of results.     

Assessing the Importance of Intraspecific Variability in Dung Beetle Functional Traits

Functional diversity indices are used to facilitate a mechanistic understanding of many theoretical and applied questions in current ecological research. The use of mean trait values in functional indices assumes that traits are robust, in that greater variability exists between than within species. While the assertion of robust traits has been explored in plants, there exists little information on the source and extent of variability in the functional traits of higher trophic level organisms. Here we investigated variability in two functionally relevant dung beetle traits, measured from individuals collected from three primary forest sites containing distinct beetle communities: body mass and back leg length. In doing so we too addressed the following questions: (i) what is the contribution of intra vs. interspecific differences in trait values; (ii) what sample size is needed to provide representative species mean trait values; and (iii) what impact does omission of intraspecific trait information have on the calculation of functional diversity (FD) indices from naturally assembled communities? At the population level, interspecific differences explained the majority of variability in measured traits (between 94% and 96%). In accordance with this, the error associated with calculating FD without inclusion of intraspecific variability was low, less than 20% in all cases. This suggests that complete sampling to capture intraspecific variance in traits is not necessary even when investigating the FD of small and/or naturally formed communities. To gain an accurate estimation of species mean trait values we encourage the measurement of 30–60 individuals and, where possible, these should be taken from specimens collected from the site of study.     

On the importance of intraspecific variability for the quantification of functional diversity

Functional diversity (FD) is a key facet of biodiversity used to address central questions in ecology. Despite recent methodological advances, FD remains a complex concept and no consensus has been reached either on how to quantify it, or on how it influences ecological processes. Here we define FD as the distribution of trait values within a community. When and how to account for intraspecific trait variability (ITV) when measuring FD remains one of the main current debates. It remains however unclear to what extent accounting for population‐level ITV would modify FD quantification and associated conclusions. In this paper, we address two critical questions: (1) How sensitive are different components of FD to the inclusion of population‐level ITV? (2) Does the omission of ITV obscure the understanding of ecological patterns? Using a mixture of empirical data and simulation experiments, we conducted a sensitivity analysis of four commonly used FD indices (community weighted mean traits, functional richness, Rao's quadratic entropy, Petchey and Gaston's FD index) and their relationships with environmental gradients and species richness, by varying both the extent (plasticity or not) and the structure (contingency to environmental gradient due to local adaptation) of population‐level ITV. Our results suggest that ITV may strongly alter the quantification of FD and the detection of ecological patterns. Our analysis highlights that 1) species trait values distributions within communities are crucial to the sensitivity to ITV, 2) ITV structure plays a major role in this sensitivity and 3) different indices are not evenly sensitive to ITV, the single‐trait FD from Petchey and Gaston being the most sensitive among the four metrics tested. We conclude that the effects of intraspecific variability in trait values should be more systematically tested before drawing central conclusions on FD, and suggest the use of simulation studies for such sensitivity analyses.     

Clade composition of a plant community indicates its phylogenetic diversity

Phylogenetic diversity quantification is based on indices computed from phylogenetic distances among species, which are derived from phylogenetic trees. This approach requires phylogenetic expertise and available molecular data, or a fully sampled synthesis‐based phylogeny. Here, we propose and evaluate a simpler alternative approach based on taxonomic coding. We developed metrics, the clade indices, based on information about clade proportions in communities and species richness of a community or a clade, which do not require phylogenies. Using vegetation records from herbaceous plots from Central Europe and simulated vegetation plots based on a megaphylogeny of vascular plants, we examined fit accuracy of our proposed indices for all dimensions of phylogenetic diversity (richness, divergence, and regularity). For real vegetation data, the clade indices fitted phylogeny‐based metrics very accurately (explanatory power was usually higher than 80% for phylogenetic richness, almost always higher than 90% for phylogenetic divergence, and often higher than 70% for phylogenetic regularity). For phylogenetic regularity, fit accuracy was habitat and species richness dependent. For phylogenetic richness and divergence, the clade indices performed consistently. In simulated datasets, fit accuracy of all clade indices increased with increasing species richness, suggesting better precision in species‐rich habitats and at larger spatial scales. Fit accuracy for phylogenetic divergence and regularity was unreliable at large phylogenetic scales, suggesting inadvisability of our method in habitats including many distantly related lineages. The clade indices are promising alternative measures for all projects with a phylogenetic framework, which can trade‐off a little precision for a significant speed‐up and simplification, such as macroecological analyses or where phylogenetic data is incomplete.     

Missing value imputation for microRNA expression data by using a GO-based similarity measure

Missing values are commonly present in microarray data profiles. Instead of discarding genes or samples with incomplete expression level, missing values need to be properly imputed for accurate data analysis. The imputation methods can be roughly categorized as expression level-based and domain knowledge-based. The first type of methods only rely on expression data without the help of external data sources, while the second type incorporates available domain knowledge into expression data to improve imputation accuracy. In recent years, microRNA (miRNA) microarray has been largely developed and used for identifying miRNA biomarkers in complex human disease studies. Similar to mRNA profiles, miRNA expression profiles with missing values can be treated with the existing imputation methods. However, the domain knowledge-based methods are hard to be applied due to the lack of direct functional annotation for miRNAs. With the rapid accumulation of miRNA microarray data, it is increasingly needed to develop domain knowledge-based imputation algorithms specific to miRNA expression profiles to improve the quality of miRNA data analysis. We connect miRNAs with domain knowledge of Gene Ontology (GO) via their target genes, and define miRNA functional similarity based on the semantic similarity of GO terms in GO graphs. A new measure combining miRNA functional similarity and expression similarity is used in the imputation of missing values. The new measure is tested on two miRNA microarray datasets from breast cancer research and achieves improved performance compared with the expression-based method on both datasets. The experimental results demonstrate that the biological domain knowledge can benefit the estimation of missing values in miRNA profiles as well as mRNA profiles. Especially, functional similarity defined by GO terms annotated for the target genes of miRNAs can be useful complementary information for the expression-based method to improve the imputation accuracy of miRNA array data. Our method and data are available to the public upon request.     

Assessing among‐lineage variability in phylogenetic imputation of functional trait datasets

Phylogenetic imputation has recently emerged as a potentially powerful tool for predicting missing data in functional traits datasets. As such, understanding the limitations of phylogenetic modelling in predicting trait values is critical if we are to use them in subsequent analyses. Previous studies have focused on the relationship between phylogenetic signal and clade‐level prediction accuracy, yet variability in prediction accuracy among individual tips of phylogenies remains largely unexplored. Here, we used simulations of trait evolution along the branches of phylogenetic trees to show how the accuracy of phylogenetic imputations is influenced by the combined effects of 1) the amount of phylogenetic signal in the traits and 2) the branch length of the tips to be imputed. Specifically, we conducted cross‐validation trials to estimate the variability in prediction accuracy among individual tips on the phylogenies (hereafter ‘tip‐level accuracy’). We found that under a Brownian motion model of evolution (BM, Pagel't λ = 1), tip‐level accuracy rapidly decreased with increasing tip branch‐lengths, and only tips of approximately 10% or less of the total height of the trees showed consistently accurate predictions (i.e. cross‐validation R‐squared >0.75). When phylogenetic signal was weak, the effect of tip branch‐length was reduced, becoming negligible for traits simulated with λ < 0.7, where accuracy was in any case low. Our study shows that variability in prediction accuracy among individual tips of the phylogeny should be considered when evaluating the reliability of phylogenetically imputed trait values. To address this challenge, we describe a Monte Carlo‐based method that allows one to estimate the expected tip‐level accuracy of phylogenetic predictions for continuous traits. Our approach identifies gaps in functional trait datasets for which phylogenetic imputation performs poorly, and will help ecologists to design more efficient trait collection campaigns by focusing resources on lineages whose trait values are more uncertain.     

Shifts in mollusc traits following floodplain reconnection: Testing the response of functional diversity components

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Application of Multiple Imputation for Missing Values in Three-Way Three-Mode Multi-Environment Trial Data

It is a common occurrence in plant breeding programs to observe missing values in three-way three-mode multi-environment trial (MET) data. We proposed modifications of models for estimating missing observations for these data arrays, and developed a novel approach in terms of hierarchical clustering. Multiple imputation (MI) was used in four ways, multiple agglomerative hierarchical clustering, normal distribution model, normal regression model, and predictive mean match. The later three models used both Bayesian analysis and non-Bayesian analysis, while the first approach used a clustering procedure with randomly selected attributes and assigned real values from the nearest neighbour to the one with missing observations. Different proportions of data entries in six complete datasets were randomly selected to be missing and the MI methods were compared based on the efficiency and accuracy of estimating those values. The results indicated that the models using Bayesian analysis had slightly higher accuracy of estimation performance than those using non-Bayesian analysis but they were more time-consuming. However, the novel approach of multiple agglomerative hierarchical clustering demonstrated the overall best performances.     

Retrieving a mitogenomic mammal tree using composite taxa

Supermatrices are often characterized by a large amount of missing data. One possible approach to minimize such missing data is to create composite taxa. These taxa are formed by sampling sequences from different species in order to obtain a composite sequence that includes a maximum number of genes. Although this approach is increasingly used, its accuracy has rarely been tested and some authors prefer to analyze incomplete supermatrices by coding unavailable sequences as missing. To further validate the composite taxon approach, it was applied to complete mitochondrial matrices of 102 mammal species representing 93 families with varying amount of missing data. On average, missing data and composite matrices showed similar congruence to model trees obtained from the complete sequence matrix. As expected, the level of congruence to model trees decreased as missing data increased, with both approaches. We conclude that the composite taxon approach is worth considering in a phylogenomic context since it performs well and reduces computing time when compared to missing data matrices.     

Functional diversity changes during tropical forest succession

Functional diversity (FD) ‘those components of biodiversity that influence how an ecosystem operates or functions’ is a promising tool to assess the effect of biodiversity loss on ecosystem functioning. FD has received ample theoretical attention, but empirical studies are limited. We evaluate changes in species richness and FD during tropical secondary forest succession after shifting cultivation in Mexico. We also test whether species richness is a good predictor of FD. FD was calculated based on a combination of nine functional traits, and based on two individual traits important for primary production (specific leaf area) and carbon sequestration (wood density). Stand basal area was a good predictor of successional changes in diversity and FD, in contrast to fallow age. Incidence-based FD indices increased logarithmically with stand basal area, but FD weighted by species’ importance values lacked pattern with succession. Species richness and diversity are strong predictors of FD when all traits were considered; linear relationships indicate that all species are equally functionally complementary, suggesting there is little functional redundancy. In contrast, when FD was calculated for individual traits and weighted for abundances, species richness may underestimate FD.Selection of functional trait(s) critically determines FD, with large consequences for studies relating biodiversity to ecosystem functioning. Careful consideration of the traits required to capture the ecosystem process of interest is thus essential.     

Loss of functional diversity under land use intensification across multiple taxa

Land use intensification can greatly reduce species richness and ecosystem functioning. However, species richness determines ecosystem functioning through the diversity and values of traits of species present. Here, we analyze changes in species richness and functional diversity (FD) at varying agricultural land use intensity levels. We test hypotheses of FD responses to land use intensification in plant, bird, and mammal communities using trait data compiled for 1600+ species. To isolate changes in FD from changes in species richness we compare the FD of communities to the null expectations of FD values. In over one-quarter of the bird and mammal communities impacted by agriculture, declines in FD were steeper than predicted by species number. In plant communities, changes in FD were indistinguishable from changes in species richness. Land use intensification can reduce the functional diversity of animal communities beyond changes in species richness alone, potentially imperiling provisioning of ecosystem services.     

Functional traits composition predict macrophytes community productivity along a water depth gradient in a freshwater lake

Functional trait composition of plant communities has been proposed as a helpful key for understanding the mechanisms of biodiversity effects on ecosystem functioning. In this study, we applied a step‐wise modeling procedure to test the relative effects of taxonomic diversity, functional identity, and functional diversity on macrophytes community productivity along water depth gradient. We sampled 42 plots and 1513 individual plants and measured 16 functional traits and abundance of 17 macrophyte species. Results showed that there was a significant decrease in taxonomic diversity, functional identity (i.e., stem dry mass content, leaf [C] and leaf [N]), and functional diversity (i.e., floating leaf, mean Julian flowering date and rooting depth) with increasing water depth. For the multiple‐trait functional diversity (FD) indices, functional richness decreased, while functional divergence increased with water depth gradient. Macrophyte community productivity was strongly determined by functional trait composition within community, but not significantly affected by taxonomic diversity. Community‐weighted means (CWM) showed a two times higher explanatory power relative to FD indices in determining variations in community productivity. For nine of sixteen traits, CWM and FD showed significant correlations with community productivity, although the strength and direction of those relations depended on selected trait. Furthermore, functional composition in a community affected productivity through either additive or opposite effects of CWM and FD, depending on the particular traits being considered. Our results suggested both mechanisms of mass ratio and niche complementarity can operate simultaneously on variations in community productivity, and considering both CWM and FD would lead to a more profound understanding of traits–productivity relationships.     

Disentangling community functional components in a litter‐macrodetritivore model system reveals the predominance of the mass ratio hypothesis

Recent investigations have shown that two components of community trait composition are important for key ecosystem processes: (i) the community‐weighted mean trait value (CWM), related to the mass ratio hypothesis and dominant trait values in the community, and (ii) functional diversity (FD), related to the complementarity hypothesis and the divergence of trait values. However, no experiments controlling for the inherent dependence between CWM and FD have been conducted so far. We used a novel experimental framework to disentangle the unique and shared effects of CWM and FD in a leaf litter‐macrodetritivore model system. We manipulated isopod assemblages varying in species number, CWM and FD of litter consumption rate to test the relative contribution of these community parameters in the decomposition process. We showed that CWM, but also the combination of CWM and FD, is a main factor controlling litter decomposition. When we tested individual biodiversity components separately, CWM of litter consumption rate showed a significant effect on decomposition, while FD and species richness alone did not. Our study demonstrated that (i) trait composition rather than species diversity drives litter decomposition, (ii) dominant trait values in the community (CWM) play a chief role in driving ecosystem processes, corroborating the mass ratio hypothesis, and (iii) trait dissimilarity can contribute in modulating the overall biodiversity effects. Future challenge is to assess whether the generality of our finding, that is, that dominant trait values (CWM) predominate over trait dissimilarity (FD), holds for other ecosystem processes, environmental conditions and different spatial and temporal scales.     

Community trait response to environment: disentangling species turnover vs intraspecific trait variability effects

Ecological communities and their response to environmental gradients are increasingly being described by various measures of trait composition. Aggregated trait averages (i.e. averages of trait values of constituent species, weighted by species proportions) are popular indices reflecting the functional characteristics of locally dominant species. Because the variation of these indices along environmental gradients can be caused by both species turnover and intraspecific trait variability, it is necessary to disentangle the role of both components to community variability. For quantitative traits, trait averages can be calculated from ‘fixed’ trait values (i.e. a single mean trait value for individual species used for all habitats where the species is found) or trait values for individual species specific to each plot, or habitat, where the species is found. Changes in fixed averages across environments reflect species turnover, while changes in specific traits reflect both species turnover and within‐species variability in traits. Here we suggest a practical method (accompanied by a set of R functions) that, by combining ‘fixed’ and ‘specific averages’, disentangles the effect of species turnover, intraspecific trait variability, and their covariation. These effects can be further decomposed into parts ascribed to individual explanatory variables (i.e. treatments or environmental gradients considered). The method is illustrated with a case study from a factorial mowing and fertilization experiment in a meadow in South Bohemia. Results show that the variability decomposition differs markedly among traits studied (height, Specific Leaf Area, Leaf N, P, C concentrations, leaf and stem dry matter content), both according to the relative importance of species turnover and intraspecific variability, and also according to their response to experimental factors. Both the effect of intraspecific trait variability and species turnover must be taken into account when assessing the functional role of community trait structure. Neglecting intraspecific trait variability across habitats often results in underestimating the response of communities to environmental changes.     

Distribution models of estuarine fish species: The effect of sampling bias,species ecology and threshold selection on models' accuracy

Species distribution models (SDMs) relate presence/absence data to environmental variables, allowing to predict species environmental requirements and potential distribution. They have been increasingly used in fields such as ecology, biogeography and evolution, and often support conservation priorities and strategies. Thus, it becomes crucial to understand how trustworthy and reliable their predictions are. Different approaches, such as using ensemble methods (combining forecasts of different single models), or applying the most suitable threshold to transform continuous probability maps into species presences or absences, have been used to reduce model-based uncertainty. Taking into account the influence of biased sampling imprecision in species location, small datasets and species ecological characteristics, may also help to detect and compensate for uncertainty in the model building process. To investigate the effect of applying an ensemble approach, several threshold selection criteria and different datasets representing seasonal and spatial sampling bias, on models' accuracy, SDMs were built for four estuarine fish species with distinct use of the estuarine systems. Overall, predictions obtained with the ensemble approach were more accurate. Variability in accuracy metrics obtained with the nine threshold selection criteria applied was more pronounced for species with low prevalence and when sensitivity was calculated. Higher values of accuracy measures were registered with the threshold that maximizes the sum of sensitivity and specificity, and the threshold where the predicted prevalence equals the observed, whereas the 0.5 cut-off was unreliable, originating the lowest values for these metrics. Accuracy of models created from a spatially biased sampling was overall higher than accuracy of models created with a seasonally biased sampling or with the multi-year database created and this pattern was consistently obtained for marine migrant species, which use estuaries as nursery areas, presenting a seasonally and regular use of these ecosystems. The ecological dependence between these fish species and estuaries may add difficulties in the model building process, and needs to be taken into account, to improve their accuracy. The present study highlights the need for a thorough analysis of the critical underlying issues of the complete model building process to predict the distribution of estuarine fish species, due to the particular and dynamic nature of these ecosystems.     

Generalised Extreme Value Distributions Provide a Natural Hypothesis for the Shape of Seed Mass Distributions

Among co-occurring species, values for functionally important plant traits span orders of magnitude, are uni-modal, and generally positively skewed. Such data are usually log-transformed “for normality” but no convincing mechanistic explanation for a log-normal expectation exists. Here we propose a hypothesis for the distribution of seed masses based on generalised extreme value distributions (GEVs), a class of probability distributions used in climatology to characterise the impact of event magnitudes and frequencies; events that impose strong directional selection on biological traits. In tests involving datasets from 34 locations across the globe, GEVs described log10 seed mass distributions as well or better than conventional normalising statistics in 79% of cases, and revealed a systematic tendency for an overabundance of small seed sizes associated with low latitudes. GEVs characterise disturbance events experienced in a location to which individual species’ life histories could respond, providing a natural, biological explanation for trait expression that is lacking from all previous hypotheses attempting to describe trait distributions in multispecies assemblages. We suggest that GEVs could provide a mechanistic explanation for plant trait distributions and potentially link biology and climatology under a single paradigm.     

Response of ant functional composition to fire

Little is known about the impact of disturbances on functional diversity and the long‐term provisioning of ecosystem services, especially in animals. In this work we analyze the effect of wildfire on the functional composition of Mediterranean ant communities. In particular, we asked whether a) fire changes functional composition (mean and dissimilarity of trait values) at the community level; and b) such fire‐induced functional modification is driven by changes in the relative abundance‐dominance of species or by a replacement of species with different traits. We sampled ant communities in burned and unburned plots along 22 sites in a western Mediterranean region, and we computed two complementary functional trait composition indices (‘trait average’ and ‘trait dissimilarity’) for 12 functional traits (related to resource exploitation, social structure and reproduction) and with two different datasets varying in the way species abundance is considered (i.e. abundance and occurrence data). Our results suggest a set of functional responses that seem to be related to direct mortality by fire as well as to indirect fire‐induced modifications in environmental conditions relevant for ants. Trait average of colony size, worker size, worker polymorphism and the ratio between queen and worker size, as well as the trait dissimilarity of the proportion of behaviorally dominant species and of liquid food consumption, and overall functional diversity, were higher in burned than in unburned areas. Interestingly, different patterns arise when comparing results from abundance and occurrence data. While the response to fire in trait averages is quite similar, in the case of trait dissimilarity, the higher values in response to fire are much more marked when considering occurrence rather than abundance data. Our results suggest that changes in trait average are driven at the same time by replacement of species with different traits and by changes in the relative abundance‐dominance of species, while fire promotes a higher diversity of functions that is primarily driven by rare species that are functionally unique. Overall, we observed major fire‐induced changes in functional composition in Mediterranean ant communities that might have relevant consequences for ecosystem processes and services.     

Non-linear PCA: a missing data approach

MOTIVATION: Visualizing and analysing the potential non-linear structure of a dataset is becoming an important task in molecular biology. This is even more challenging when the data have missing values. RESULTS: Here, we propose an inverse model that performs non-linear principal component analysis (NLPCA) from incomplete datasets. Missing values are ignored while optimizing the model, but can be estimated afterwards. Results are shown for both artificial and experimental datasets. In contrast to linear methods, non-linear methods were able to give better missing value estimations for non-linear structured data.Application: We applied this technique to a time course of metabolite data from a cold stress experiment on the model plant Arabidopsis thaliana, and could approximate the mapping function from any time point to the metabolite responses. Thus, the inverse NLPCA provides greatly improved information for better understanding the complex response to cold stress. CONTACT: scholz@mpimp-golm.mpg.de.