Parameters measured with Cytobuoy are partially redundant, since many morphological and FL descriptors are cross-correlated. Therefore, the choice of measured parameters represents the first critical decision step in the process of defining BD measures (Figure 2). A first assessment of traits based on correlation and ecological relevance is required in order to extract a number of robust descriptors for individual particles. Fortunately, phytoplankton is a classical model in ecology and evolution, and detailed knowledge about its most relevant ecological traits exists, which can also be relatively easily validated with microscopic analysis. In particular, cell size and shape (which influence motility and nutrient uptake through surface-to-volume ratio), and photosynthetic performance (driven by pigment type and concentration), are key phytoplankton traits, affecting growth, metabolism, access to resources, and susceptibility to grazing (Litchman and Klausmeier, 2008). Previous work has shown that a number of size- and pigment-related parameters monitored by Cytobuoy analysis are ecologically meaningful, responding to changes in nutrient levels, temperature, and abundance of zooplankton grazers (Pomati et al., 2011, 2013). Many of these focal traits, such as size and pigment content, also appeared to be under selection by environmental filters and species interactions, determining changes in population dynamics and phytoplankton community functioning (Pomati and Nizzetto, 2013; Pomati et al., 2013).

With individual-based data such as SFC's, conventional ecological measures of BD are not directly applicable. One possible approach is to define groups based on some key traits or on a set of linear combinations of all traits (for example, principal components) (Pomati et al., 2011, 2013) (Figure 2). In this context, we suggest to utilize a set of defined and well understood phytoplankton traits for studying BD changes, rather than principal components (which would be specific to the dataset), in order to allow for comparison of results across studies. A classification of phytoplankton into categories based on morphological characters has shown to offer good prospects in terms of objectivity, reproducibility, functional properties, and prediction (Kruk et al., 2010). In order to create functional categories of organisms, different approaches have been proposed for clustering SFC datasets (Caillault et al., 2009; Malkassian et al., 2011; Pomati et al., 2011, 2013). Groups obtained by statistical clustering seem to retain meaningful ecological information, since SFC-based clusters and associated traits have shown distinct diurnal and seasonal dynamics (Thyssen et al., 2008b, 2011; Pomati et al., 2011). Additionally, the total abundance within these categories can be tracked and characterized by conventional species-based metrics (such as richness, evenness and diversity indices) (Figure 2). In previous work, we have found that patterns of Cytobuoy-derived functional groups were comparable to those of identified phytoplankton taxa, both with regards to alpha- and beta-diversity measures (Pomati et al., 2013).

We also noted that the identity (and abundance) of Cytobuoy-derived functional groups did not fully reflect the identity (and abundance) of microscopically defined taxonomic groups (Pomati et al., 2011, 2013). Several species can in fact map into one functional category (in case they share similar morphology) and individuals of the same species can be assigned to different groups (single cells vs. colonies, for example), hampering our ability to fully interpret the observed ecological dynamics. This phenomenon can also be explained by the much larger volumes analyzed by traditional microscopic methods for the analysis of phytoplankton (hundreds of mL) compared to those sampled by automated SFC (few mL). The likelihood to count large particles is higher in microscopic-based methods, while small cells are more efficiently counted by flow-cytometry. To account for this different resolution of flow-cytometry across the range of phytoplankton abundances and sizes it is possible to perform two separate protocols in SFC to analyze small (and abundant) particles on one side, and large (and rare) particles on the other side. This approach has the limitation of not providing a single comprehensive description of the phytoplankton community in terms of the distribution of organisms in the multi-dimensional trait-space and their relative abundance. Such a structure carries important information about the ecological and evolutionary processes that have shaped the community, and should be the target (see below) of trait-diversity indices. The alternative strategy is to calibrate sampling protocols in order to retain only particles above the analytical scanning limit (1 μm) and sample volumes larger enough to acquire sufficient information about the characteristics of both small and large particles and cover the widest possible trait-diversity of the phytoplankton. This approach has the limitation of losing information about pico-plankton smaller than 1 μm, but retains the actual community structure in terms of relative abundance of organisms and their descriptors in the multidimensional trait-space.

Current approaches employed for BD research using SFC data have two main scientific limitations. First, they require statistical clustering or artificial neural networks to construct functional groups (Boddy et al., 2001), and these final categories may not have a general ecological interpretation. Each different method suffers from arbitrary decision steps that may critically affect the outcomes in terms of BD metrics, through identity and abundance of resulting formed groups (Figure 2) (Petchey and Gaston, 2006). Second, SFC data do not yet fully exploit the rich individual-based description of communities embedded within the datasets and described above. Individual-based SFC data are in the form of high-dimensional multivariate distributions of phytoplankton descriptors, which have variable strength as predictors of the relevant target processes. As reviewed in section An Individual Trait-Based Perspective to BD-EF Research, there is an emerging consensus that the composition and distribution of continuous measurable functional traits, i.e., FD, is a better predictor of EF, stability and adaptive capacity of the system compared to richness or evenness of groups of organisms (Norberg et al., 2001; Naeem and Wright, 2003; Norberg, 2004; Hillebrand and Matthiessen, 2009; Reiss et al., 2009). Below we review the available metrics that directly take into account the full range of multiple trait variation for quantifying FD for each given community (Mouchet et al., 2010; Schleuter et al., 2010). Most FD metrics and indices have rarely or never been applied to individual level data, used in empirical studies, or tested for their temporal and spatial relationships with important community processes. We argue that SFC data represent a unique opportunity to experiment and develop individual-level FD metrics.

Published functional metrics are based either on single or multiple traits. One-dimensional indices account for selection on single traits by EC, and have been successfully utilized to test hypotheses on the processes that determine diversity, identity, and abundance of co-occurring species. This approach allows a direct link to classic ecological theory: responses in the distribution of single traits at the community level (convergence on similar values, reduction of trait range, clustered patterns, evenly spaced traits) can help inferring mechanisms such as environmental filtering, competitive exclusion of some species, grazing/predation/parasitism by specialists or generalists, competition for resources (Macarthur and Levins, 1967; Chesson and Kuang, 2008; Kraft et al., 2008; Cornwell and Ackerly, 2009; Ingram and Shurin, 2009; Kraft and Ackerly, 2010; Paine et al., 2011; Pomati et al., 2013). For example, species co-occurrence patterns can be partially explained by habitat filtering, niche partitioning and stabilizing processes (Kraft and Ackerly, 2010), and even different trophic groups seem to be reciprocally linked by the response of single morphological traits to ecosystem management (Moretti et al., 2013). A single trait approach, however, does not afford an comprehensive view of species differences in potentially important functional traits, which may affect functioning directly or indirectly (Suding et al., 2008). Additionally, when studying niche complementarity, results based on a single trait are biased toward finding functional redundancy among species, because functional niches that are distinct in a multi-dimensional functional space could appear as overlapping when only a trait (dimension) is considered (Rosenfeld, 2002; Mouchet et al., 2010).

Metrics based on multiple traits allow a more comprehensive view of differences among taxa, and potentially among individuals. A multi-dimensional trait approach is common in ecological morphometrics, classical ecology, evolutionary genetics and evolutionary ecology, where it is used to illustrate differences between biological entities (e.g., morphs, niches, genotypes, and life-history strategies). Multiple trait metrics should theoretically offer a better link to ecosystem function, because the community contribution to ecosystem processes results from the combination of all traits of species or individuals (Suding et al., 2008; Reiss et al., 2009). The use of complementary multiple trait metrics has recently been proposed as a powerful framework for detecting responses to disturbance, and to relate them to ecological theory (Mouillot et al., 2013). For instance, multi-dimensional FD provided support for the physiological tolerance hypothesis in plant communities (Currie et al., 2004), which represents a specific case of assembly through environmental filtering (Cornwell and Ackerly, 2009), suggesting that increased species richness in favorable climatic conditions is a consequence of availability of a wider range of functional traits (Spasojevic et al., 2014). We argue that FD indices based on multiple traits are better suited for linking BD metrics to EC and EF using individual-based data. This is especially true if we consider that a multi-dimensional approach still allows to separately consider single trait responses, while one-dimensional indices lack the evaluation of individual differences in a multi-dimensional trait space.

Some mathematical aspects in the calculation of indices can be simplified when dealing with traits measured at the individual level using SFC. For example, we suggest not to consider those indices that integrate mathematical methods for separating intra- from interspecific trait differences (Schleuter et al., 2010), since individual-based data already combine both hierarchical levels. In addition, we suggest to exclude indices that need and assume trait frequency distributions or other data necessarily aggregated at the species level, because in SFC data every single individual represent a unique combination of traits and the process of categorizing would cause unavoidable loss of potentially important information (Table 1). Finally, we consider only the indices that have been designed to deal with traits that are continuous or expressed as proportions (i.e., not nominal, ordinal or binary traits), as for SFC measurements such as size and FL typically belong to this kind (Table 1).

Individual-based SFC datasets, especially if collected automatically with high spatial or temporal resolution, are generally extremely large. One possible way to solve this problem would be develop efficient subsampling algorithms, able to reduce the amount of data points maintaining the topology of data in a multi-dimensional space and the relative abundance of organisms. Suitable FD indices should however be computationally efficient. It could be convenient, for example, to avoid the calculation of distances and functional dendrograms among individuals (Petchey and Gaston, 2002). These require computation of metrics of similarity/dissimilarly among all data points and construction of topologies that become intractable for normal computers given the very large matrices (Table 1). The limitation of such approach becomes even more relevant when it's necessary to compare different samples (communities) across space and time, since for this purpose it is generally necessary to build an overall distance matrix and functional dendrogram merging all samples in a single dataset. Considering that it would also be desirable to minimize the number of arbitrary and critical decision steps in calculating FD indices (Figure 2), we argue that the best FD measures should also be robust toward possible methodological issues.

Since we seek to understand links between EC, BD dynamics and EF, we do not necessarily have to consider indices that incorporate a standard null model correction (Table 1) (Mason et al., 2013). Indeed, randomization of matrices may not be the best null approach in many cases since neutral (stochastic) processes may not generate strictly random patterns (Bell, 2005). Suitable indices to study FD and EF should rather allow their application to individual-based neutral models that simulate stochastic processes, such as dispersal of individuals, demography (birth, death, and reproduction) and ecological drift (Allouche and Kadmon, 2009; Jabot, 2010; Vanpeteghem and Haegeman, 2010).

Some BD indices represent a combination of different components of FD. FD_var (Mason et al., 2003), Rao coefficient (Rao, 1982; Botta-Dukát, 2005), and FDis (Laliberté and Legendre, 2010) combine measures of functional richness and divergence (Mason et al., 2013). In order to adequately describe and understand individual-level FD, however, each one of the ideally suitable multi-trait indices should measure one of the three different components of FD: richness, evenness, and divergence (Mason et al., 2005). In the most ideal case, these components are independent to each other (orthogonal). Additional components of FD have been suggested (Podani et al., 2013), they however do not apply to potential individual level trait data. FD components such as combinatory functional diversity (CFD) or functional heterogeneity (FH) only concern trait combinations in the context of nominal traits (i.e., non-quantitative traits coded into categories by discrete numbers), while we focus on continuous high-resolution data (Table 1). Another metric, though not effectively being a FD index, could be useful in characterizing communities in a multi-dimensional trait space. The functional identity (multi-trait analogous of community weighted mean CWM; Table 1) represents the centroid (coordinates) of a trait distribution in multi-dimensional functional space (Garnier et al., 2004; Spasojevic and Suding, 2012; Mouillot et al., 2013). With centroid coordinates information it is possible to detect a uniform translation of all data points in space, case in which FD indices of richness, evenness, and divergence are not supposed to change. However we argue that, at least in the context of multi-dimensional individual trait data, most of the changes in community functional structure would be reflected in functional richness, evenness and divergence.

Functional richness is the total amount of space occupied by all taxa of a community in the multi-dimensional trait space. An ideal richness index should be able to take into account and exclude gaps in trait distribution. In other words, trait richness approximates as accurately as possible the multi-dimensional space effectively occupied by the community, rather than a simple trait range. Nevertheless, very different estimates of functional richness have been proposed, such as the volume of the minimal convex hull containing all taxa within the multi-dimensional space (Cornwell et al., 2006; Villéger et al., 2008), the total branch length of a dendrogram calculated according to distances between taxa in the trait space (Petchey and Gaston, 2002) or simply the number of functional groups represented by taxa in a community (Petchey and Gaston, 2006).

Functional evenness is a measure of how evenly taxa are distributed within the trait space. While different one-dimensional indices have been proposed for even spacing of traits, e.g., E_var (Smith and Wilson, 1996; Mason et al., 2005), FRO (functional regularity) (Mouillot et al., 2005) and SDNN/SDNNr/SDNDr (based on the standard deviation of nearest or successive neighbor distance) (Kraft and Ackerly, 2010), only one multi-dimensional index of functional evenness based on quantitative data exist (Table 1). FEve measures the regularity in the distribution of taxa within the multi-dimensional functional space, calculating a network that links all the points with the minimum sum of branch lengths (minimum spanning tree) (Villéger et al., 2008).

Functional divergence measures how spread-out taxa are in the multi-dimensional trait space. For its estimation several approaches are possible. FDiv quantifies how single taxa distances to the centroid of a trait distribution in the multi-dimensional space deviate from the overall mean distance (Villéger et al., 2008). The Rao coefficient is the total distance between each pair of taxa in a trait distance matrix (Rao, 1982; Botta-Dukát, 2005; Ricotta and Moretti, 2011), while FDis (functional dispersion) measures the mean distance of taxa to the centroid of a trait distribution in a multi-dimensional space (Laliberté and Legendre, 2010; Mouillot et al., 2013).

We suggest that to study EC-BD-EF relationships in general, it is necessary to select a set of FD indices that are able to account for physiological, ecological, and evolutionary components of BD change. Specifically, for individual-based data such as SFC, FD indices should describe changes in the structure of multi-dimensional trait space, where each coordinate axis corresponds to a measured trait and each point represents an individual organism. This representation of BD is analogous to Hutchinsonian niche hypervolume, where species are points in a multi-dimensional space defined by environmental parameters (Hutchinson, 1957). Our proposed approach, therefore, expands the functional niche definition by Rosenfeld (2002), where niche axes are represented by ecological processes that are in fact related to morphological and physiological attributes of individuals (Rosenfeld, 2002).

According to these considerations and those explained in the previous section, we identify FRic, FEve, and three indices of functional divergence (FDiv, FDis, and Rao coefficient) as the most promising existing FD indices for application to individual-based SFC data (Table 1). Their definition (presented earlier) and interpretation can easily be adapted to fit individuals instead of species. It is important to note that trait divergence of individual-based data can potentially be interpreted in the context of evolutionary adaptation: single individuals or groups of similar individuals that diverge from the centroid of the trait distribution can be thought to reflect combinations of traits under selection. Over time such trait divergence processes illustrate evolutionary trajectories that target populations express as a response to an ongoing EC. On the contrary, the widely used species mean traits do not allow to detect differences and changes at the phenotypic level where evolution effectively works, namely in diverging alternative strategies and phenotypes at the individual level.

FRic, FEve, FDiv, FDis, Rao coefficient are based on the objective position of every individual organism (point) within a multi-dimensional trait space. Therefore, these indices do not require a processes of categorization, they allow the use of raw data, and restrict the number of critical decision steps in calculating BD measures (Table 1, Figure 2). As they also do not require calculation of large relative distance matrices among data points or functional dendrograms (Table 1), these indices are directly computable for each sample separately and comparable among samples. These indices and associated functions are freely available for use and calculation using the open source programming language R (R-Development-Core-Team, 2014) through the FD package (Laliberté and Legendre, 2010). Our preliminary assessment suggests that they are computationally tractable even for very large high-frequency individual-based SFC datasets (Table 1).

Both the Rao coefficient and FDis seem to embed a mixture of functional divergence and functional trait richness (Mason et al., 2013). From a theoretical point of view, FDiv, FDis, and Rao coefficient could all be suitable for application to individual-based SFC data. Uncertainty however exists on which one would perform best with this type of data sets (Schleuter et al., 2010). We suggest to consider all these divergence measures in a detailed future assessment of their actual performance.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.