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12 May 2021 Predictability of Functional Diversity Depends on the Number of Traits
Zhang Zihao, Hou Jihua, He Nianpeng
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Analysis of functional diversity, based on plant traits and community structure, provides a promising approach for exploration of the adaptive strategies of plants and the relationship between plant traits and ecosystem functioning. However, it is unclear how the number of plant traits included influences functional diversity, and whether or not there are quantitatively dependent traits. This information is fundamental to the correct use of functional diversity metrics. Here, we measured 34 traits of 366 plant species in nine forests from the tropical to boreal zones in China. These traits were used to calculate seven functional diversity metrics: functional richness (functional attribute diversity (FAD), modified FAD (MFAD), convex hull hypervolume (FRic)), functional evenness (FEve), and functional divergence (functional divergence (FDiv), functional dispersion (FDis), quadratic entropy (RaoQ)). Functional richness metrics increased with an increase in trait number, whereas the relationships between the trait divergence indexes (FDiv and FDis) and trait number were inconsistent. Four of the seven functional diversity indexes (FAD, MFAD, FRic, and RaoQ) were comparable with those in previous studies, showing predictable trends with a change in trait number. We verified our hypothesis that the number of traits strongly influences functional diversity. The relationships between these predictable functional diversity metrics and the number of traits facilitated the development of a standard protocol to enhance comparability across different studies. These findings can support integration of functional diversity index data from different studies at the site to the regional scale, and they focus attention on the influence of quantitative selection of traits on functional diversity analysis.

1 Introduction

Functional traits are core plant properties, and are closely related to the colonization, survival, growth, and mortality of plants (Cornelissen et al., 2003). In particular, these traits allow plants to optimize productivity (Craven et al., 2018; Xu et al., 2018b; Kordbacheh et al., 2019; Mahaut et al., 2020). Recently, scientists have demonstrated that community traits on per land area using community-weighted means (He et al., 2019a), scaled up from the organ or species level, could be used to interpret certain ecosystem processes and functions at larger spatial scales (He et al., 2019a). To date, trait-based approaches have been used to explore various ecological issues from the species or community level to the ecosystem level (Faucon et al., 2017; Greenwood et al., 2017; Ma et al., 2018).

There are trade-offs or synergies that exist among traits (Cornelissen et al., 2003; de Deyn et al., 2008; Reich, 2014; Li et al., 2015; He et al., 2019b), and studing multiple traits has hence become important. The classic leaf economic spectrum demonstrates the trade-off strategy of plant resources (Wright et al., 2004). The adaptation of a single trait to an environmental change may not be important as the adaptive evolution of the specific trait may lag behind environmental change, and the adaptation rather manifested as a coordinated adaptation of multiple traits. Plants adapt to the environment by adjusting multiple traits, with the complex relationships between these traits crucial for maintaining the ecosystem structure and function (Fontana et al., 2016). Furthermore, there is consensus that species diversity influences ecosystem functioning, as well as the diversity of functional traits within communities (Leps et al., 2006). The combination of functional diversity, community structure, and plant traits could help us explore how multiple traits determine ecosystem processes and functioning (Fontana et al., 2016).

Various indices have been proposed to measure plant functional diversity (Pérez-Harguindeguy et al., 2013). In general, functional diversity can be subdivided into functional richness, evenness, and divergence (Table 1). Functional richness indices can quantify the size of the niche space utilized by these measured traits per volume of multidimensional space. Functional evenness can describe the distribution of the trait space occupied by species traits. It refers to whether the distance between the traits of any two nearest species is equal in the trait space. The functional divergence describes the formation of species clusters in the character space, where higher dispersion indicates that the species clusters are distributed at the edge of the character space (Mason and Mouillot, 2005; Laliberte and Legendre, 2010; Schleuter et al., 2010) (The detailed formula is provided in the supplementary file). Through the research of functional diversity, certain diversity indexes have been developed, including functional attribute diversity (FAD) (Walker et al., 2005), convex hull hypervolume (FRic) (Laliberte and Legendre, 2010), functional evenness (FEve) (Laliberte and Legendre, 2010), functional divergence (FDiv) (Mason and Mouillot, 2005; Laliberte and Legendre, 2010; Schleuter et al., 2010), and quadratic entropy (RaoQ) (Botta-Dukát, 2005).

Functional diversity can be used to accurately assess and predict ecosystem functioning, because multiple traits collectively accomplish this (Kearney and Porter, 2006). Similarly, functional evenness and functional divergence are used to elucidate the variation in functional and adaptive mechanisms (Komac et al., 2015). Functional diversity has received extensive attention recently; and research on the relationships between functional diversity and ecosystem function has rapidly increased (Ross et al., 2017). However, dispute remains over how to scientifically calculate and use these metrics. In practice, researchers tend to select certain traits based on their own objectives or the availability of data, leading to inconsistent results across studies that make comparisons among studies difficult (Petchey and Gaston, 2002; Wright et al., 2006; Pasari et al., 2013). Knowledge about how to use a wide variety of plant traits is crucial because different traits will generate different results (Petchey and Gaston, 2006). Therefore, development of a uniform protocol is needed that could be used consistently, or that could enhance comparability across different studies. To accomplish this, it is necessary to identify how the number of selected traits influences functional diversity indexes from the site to the regional scale, and whether these influences are consistent across the different functional diversity metrics.

To explore these issues, we measured 34 traits of 366 plant species from nine forest communities along the North-South Transect of Eastern China (NSTEC), extending from the tropical to the boreal zones. Morphological, chlorophyll, stomatal, and anatomical leaf traits were measured, in addition to multiple element content, and other traits (Fig. 1). The main objectives of this study were to: 1) demonstrate the predictability of the functional diversity metrics by altering the numbers of selected traits, and 2) develop a uniform protocol for metrics that predict functional diversity consistently from the site to the regional scale for use in future studies.

The conceptual framework of functional diversity holds promise as a way to explore relationships in natural communities. Specifically, these functional diversity are predictable (invariably, regularly, or irregularly) under different scenarios of trait number, diversity in importance of different traits, and differences in species diversity. Development of a functional diversity protocol is needed to promote the applicability of these metrics.

2 Materials and methods

2.1 Study sites

Nine typical forest communities were selected for field sampling along the NSTEC (Fig. 2), which is the 15th standard transect of the International Geosphere-Biosphere Program (Zhang and Yang, 1995; Wang et al., 2016). To minimize the effects of human disturbance, we set up these sampling plots in national nature reserves. From south to north, the forests sampled were: tropical, south-subtropical evergreen broad-leaved, subtropical evergreen broad-leaved, and north-subtropical evergreen deciduous broad-leaved mixed forests. The study area covered almost all the main types of forest vegetation in the Northern Hemisphere (He et al., 2018). Across the study sites, the annual average temperature and precipitation ranged from –4.4 to 20.9 °C and 481.6 to 2449.0 mm, respectively, with the precipitation mainly concentrating in summer, from June to August (Xu et al., 2018a).

Fig. 1

The opportunities and challenges associated with functional diversity


Fig. 2

The spatial distribution of nine forest communities from the boreal to the tropical zone in China Note: A total of 34 functional traits and 366 species were sampled across the nine forest sites (orange circles).


2.2 Field sampling and measurement of traits

Field sampling was carried out from the end of July to the beginning of August 2013. We set up four representative plots of 30 m × 40 m in each forest type to collect mature leaves of common tree species within and around the plots. The specific sampling method involved selection of healthy, disease-free, mature trees of different species. Thereafter, four branches at different levels and orientations, specifically from four different directions in the upper, southeast, and northwest of the canopy, were collected from each tree using high-pruning shears or artificial tree-climbing methods. A mixture of leaf samples was obtained from the cut branches, placed in plastic bags, and transported to a laboratory for processing. One tree in each plot represented one replicate; consequently, four trees were considered as replicates per site (Li et al., 2018).

2.2.1 Selection of metrics for plant traits

We measured 34 plant traits of 366 species in the nine forest communities, using a consistent method for recording specific traits across all forest types (cold-temperate to tropical) (He et al., 2020; Table S1 and Fig. S2).

2.2.2 Measurement of leaf morphological traits

Six to ten healthy, intact leaves were flattened out and scanned using a Cano Scan LiDE 110 (Japan), before determining their area using ImageJ software (Nanes, 2015). The leaves were dried to a constant weight in an oven and were weighed to calculate the specific leaf area based on the leaf area and dry weight (Wang et al., 2016).

2.2.3 Measurement of C and N content

An elemental analyzer method (vario MAX CN Elemental Analyzer, Elementar, Germany) was used to determine foliar N content. The leaves were first cleaned to remove soil and other impurities and then dried. The N content in 0.3–0.5 mg of the dried samples was determined (Zhao et al., 2014).

2.2.4 Measurement of chlorophyll traits

Fresh leaf samples (0.1 g) were cut into pieces and, together, with 10 mL of 95% ethanol, were homogenized in a mortar. An additional 5 mL of 95% ethanol was added to the homogenate, which was then filtered, and the filtrate diluted to 50 mL with ethanol. The chlorophyll-ethanol solution was injected into a cuvette with a light path of 1 cm. Pure ethanol was injected into another cuvette of the same specification to serve as a control. The chlorophyll content was calculated according to Lambert Beer's law (Li et al., 2018).

Table 1

The protocol of the functional diversity index


2.2.5 Measurement of stomatal traits

From the samples, five to ten leaves were cut into 1 cm × 0.5 cm sections along the main vein and fixed in FAA solution (75% alcohol: formalin: glacial acetic acid: glycerol = 90: 5: 5: 5) (Field sampling was completed). These sections were dried, pasted to the sample stage, and observed using a scanning electron microscope (Hitachi s-3400 II, Hitachi, Japan). Three small blocks were randomly selected from the sample stage for observation. Two photographs were taken in each of the blocks, resulting in six replicate images for each species. The number of stomata in each image was counted and the area of each image was determined to calculate stomatal density. Five pores in each image were randomly selected to determine the average stomatal pore width, and length, and stomatal area (Liu et al., 2018).

2.2.6 Measurement of anatomical traits

Samples were removed from the FAA fixative and permanent cross-section slides were made using paraffin sectioning, with a total of three replicate sections per species. Anatomical data was acquired using scanning electron microscopy (Liu et al., 2019).

2.3 Selection of metrics for functional diversity

Functional diversity is used to reflect the overall difference or diversity of traits in plant communities. At the beginning of the formation of the functional diversity, the functional diversity index should generally meet the following criteria: 1) multiple traits must be processed simultaneously, 2) species traits and species richness influence the functional diversity of the community, and 3) increasing or decreasing the number of new species or traits affects functional diversity (Villéger et al., 2008). These criteria reinforce the fact that functional diversity requires consideration of both the number of species and traits. Although many types of functional diversity exist, we selected three kinds of diversity corresponding to the three components of functional diversity: functional richness, functional evenness, and functional divergence (Table 1).

Functional richness is mainly used to quantify how much niche space is occupied by all species in the community (Laliberte and Legendre, 2010). Low trait richness indicates that the available niche in the community is occupied, meaning that some of the resources in the community are not utilized, resulting in lower productivity. In this study, we used the following functional richness indexes: functional attribute diversity (FAD), modified functional attribute diversity (MFAD) (Schmera et al., 2009), and convex hull hypervolume (FRic) (Villéger et al., 2008).

The evenness of traits (FEve) is the distribution law of the mean value of species traits in the trait space. This index quantifies the degree of trait uniformity. Low trait evenness indicates that some resources are over-utilized, whereas other resources are rarely utilized or have not yet been utilized.

Trait dispersion can be used to describe the degree of convergence of traits in the functional space. High functional dispersion indicates that the species group is distributed at the edge of the trait space. This metrics can be used to indicate the degree to which community resources differ as well as the degree of competition. We selected the following three trait dispersion indexes for used in our study: functional divergence (FDiv), functional dispersion (FDis), and Rao's Quadratic entropy (RaoQ).

2.4 Statistical analysis

The seven functional diversity metrics mentioned above (specific index in Table 1) were calculated using R language and FDiversiry software (Casanoves et al., 2011). Based on the well-matched trait and species data collected, we developed a calculation scheme to explore our objectives. The importance of different traits was attenuated by random selection and repeated simulation. At the same time, the multi-site simulated sampling ensured consistency of species diversity. In this way, we could focus more on the effect of trait number on functional diversity. In practice, the procedure was as follows: 1) according to the calculated metric of functional diversity, corresponding data were consistently compiled; 2) different sampling scenarios were simulated and specific trait indicators were extracted from the data table; 3) R language was used to randomly select trait indicators according to a specific number, and these metrics were calculated; and 4) the selected number of plant traits was increased one at a time from 3 to 34, with these traits being randomly selected 100 times, and the average was calculated as the result of each cycle.

Fig. 3

Relationship between functional diversity metrics and trait number


3 Results and discussion

Altering the number of traits had different effects on the metrics of functional diversity. The specific indexes FAD, MFAD, FRic, and RaoQ were predictable using the equations indicated in Fig. 3 and Table 1. Theoretically, the niche space of functional richness quantification depends on the traits of species (Fig. 3). The more functional traits included, the larger the niche space that can be quantified (Mason et al., 2005). Therefore, the trait richness metrics could be measured and used to predict the total resource or niche space of different communities (de la Riva et al., 2018; Solefack et al., 2018)(Figs. S1S4). Using a different number of traits to calculate functional diversity should yield different results.

Four of the seven functional diversity metrics included in this study were predictable, namely functional attribute diversity (FAD), modified FAD (MFAD), convex hull hypervolume (FRic), and Rao's quadratic entropy (RaoQ). When the number of traits increased from 3 to 34, 100 random combinations were calculated on average (The supplementary files provide these equations for the different regions).

The three metrics of trait richness and RaoQ increased with the number of selected traits. Specifically, FRic showed a linear increasing trend, and FAD and MFAD were well fitted as power functions (Table 1 and Fig. 3). Furthermore, RaoQ was linearly correlated with the number of selected traits, similar to FRic. A plausible explanation for these results is that the calculated equation (Eqs.116) contained information on both functional richness and trait dispersion; however functional richness was dominant. Furthermore, the general equations used to determine FAD, MFAD, FRic, and RaoQ were similar across the forest communities sampled (from the tropical to the boreal zone); however, some data sets differed among these functional richness metrics (Tables S2S5).

Some of the functional diversity metrics could not be predicted, including FEve, FDiv, and FDis. The R2 of FEve fitting curve is not predictable and ranged from 0.033 to 0.808. The metrics FDiv and FDis were similar, with R2 values ranging from 0.3792 to 0.9546. Laliberté and Legendre (2010) improved FDiv to achieve FDis. The similarity of the FDis and FDiv results in this study may be due to the fact that the distribution of the center of gravity was offset through calculating the mean value of FDis and FDiv multiple times, therefore making the difference between them smaller. Altering the number of traits resulted in irregularly or even consistent change in these metrics, making it difficult to identify any clear trends (Figs. S5S7). The indexes FEve, FDiv, and FDis have been commonly used as indicators for quantifying the range of traits and the degree of distribution rules (Kraft and Ackerly, 2010). Our results indicated that the three functional diversity range and distribution metrics were more variable than the functional richness metrics. Consequently, we suggest that the three range and distribution indexes should be used cautiously, especially avoiding reliance on experience or extrapolation of the unknown from the known, because the number of traits had an unpredictable effect on them. Therefore, our findings show that the selection of traits or number of traits is very important when using these metrics.

Determination of functional diversity provides a promising approach for explaining variation in community or ecosystem function, including productivity, nutrient acquisition, flexibility, and resilience (Cornwell et al., 2006; Sonkoly et al., 2019), and can also reflect the adaptation of the community to anthropic disturbances (Biswas et al., 2019). Consequently, the metrics of functional diversity have been widely used across multiple fields of ecology (Petchey et al., 2004). However, our results showed that only one component of functional diversity (mainly functional richness) was predictable, indicating the necessity to further consider the theoretical basis for applying functional diversity. In practice, scientists generally cannot evaluate the repeatability or comparability of different studies, due to differences in the number of selected traits. Theoretically, it is speculated that the basis of calculated functional diversity is similar to species diversity (Petchey and Gaston, 2002), and the theoretical basis of the latter is the theory of niche complementarity. The differentiation of different species is actually the differentiation of traits. The basis of functional diversity is a variety of plant traits and their adaptation and response to environmental changes. Plant traits more directly reflect the resource acquisition of species and the complementation of a niche (Mason et al., 2005; Poos et al., 2009). Therefore, using functional diversity to directly measure all aspects of the spatial distribution of traits in a niche could be used to test these theoretical mechanisms. However, the methods used to calculate functional diversity cannot be overlooked, because of the difference in the relative importance of specific traits. For example, Fig. 3 shows that, as used in this study, the three metrics of trait richness (FAD, MFAD, and FRic) and RaoQ were predictable and similar in different regions. Consequently, these functions should be used as a protocol for guiding future studies or should be incorporated into different studies.

The number of traits is a non-negligible factor for the study functional diversity; however, there is no implementation standard that can be referenced at present. Consequently, small numbers of traits (three or four) have been used to calculate functional diversity in previous studies (Mensah et al., 2016; Staples et al., 2019). Researchers should design experimental protocols for their own experimental purposes more rigorously and scientifically. Some researchers may consider functional redundancy and abandon the use of larger number of functional traits in their analyses (Correia et al., 2018; Lozanovska et al., 2018; Kearsley et al., 2019). Thus, it is important to determine which functional traits perform the more important roles in the community, along with identifying the importance of the traits (Garcia et al., 2015). In natural communities, functional redundancy must exist, and could facilitate the stability and anti-interference ability of the community (Pillar et al., 2013). In this study, the predictive equations of the three trait richness metrics (FAD, MFAD, and FRic) and RaoQ increased non-linearly with the number of traits. This may be related to functional redundancy between traits, and requires further study. Furthermore, researchers are encouraged to select more traits to explore ecosystem processes and functions, to reduce potential errors, and facilitate comparisons across studies in the future.

Using a database of consistently measured traits of plant species found in a range of forest types, we explored the predictability of functional diversity with respect to trait richness, trait evenness, and trait divergence. Our results demonstrated that only the three trait richness metrics and RaoQ were predictable, in relation to the influence of the number of traits on functional diversity. The relationship between each of the three functional richness metrics and number of traits, as well as the relationship between entropy and trait number, are expected to provide standard protocols to enable incorporation of different studies from the site to the regional scale in future. However, at present, uniform standards on what number of traits influences other functional diversity indexes do not exist, nor is there information about how this is achieved. More research is required to improve both the theory of, and methodology used to calculate functional diversity, even though the conceptual framework of functional diversity is promising.


The data of this research have been shared from Functional Trait database of terrestrial ecosystems in China (China_Traits). For further data sharing contact HE Nianpeng (



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Appendix I

Fig. S1

The relationship between convex hull hypervolume (FRic) and the selected number of traits in different typical forests Note: HZ, HuZhong; LS, LiangShui; CB, ChangBai; DL, DongLing; TY, TaiYue; SN, ShenNong; JL, JiuLian; DH, DingHu; JF, JianFengLing.


Fig. S2

The relationship between quadratic entropy (RaoQ) and the number of traits in different typical forests Note: HZ, HuZhong; LS, LiangShui; CB, ChangBai; DL, DongLing; TY, TaiYue; SN, ShenNong; JL, JiuLian; DH, DingHu; JF, JianFengLing.


Fig. S3

The relationships between functional Attribute Diversity (FAD)and the number of traits in different typical forests Note: HZ, HuZhong; LS, LiangShui; CB, ChangBai; DL, DongLing; TY, TaiYue; SN, ShenNong; JL, JiuLian; DH, DingHu; JF, JianFengLing.


Fig. S4

The relationships between modified Functional Attribute Diversity (MFAD) and the number of traits in different typical forests Note: HZ, HuZhong; LS, LiangShui; CB, ChangBai; DL, DongLing; TY, TaiYue; SN, ShenNong; JL, JiuLian; DH, DingHu; JF, JianFengLing.


Fig. S5

The relationships between functional evenness (FEve) and the number of traits in different typical forests Note: HZ, HuZhong; LS, LiangShui; CB, ChangBai; DL, DongLing; TY, TaiYue; SN, ShenNong; JL, JiuLian; DH, DingHu; JF, JianFengLing.


Fig. S6

The relationship between functional divergence (FDiv) and the number of traits in different typical forests Note: HZ, HuZhong; LS, LiangShui; CB, ChangBai; DL, DongLing; TY, TaiYue; SN, ShenNong; JL, JiuLian; DH, DingHu; JF, JianFengLing.


Fig. S7

The relationship between functional dispersion (FDis) and the number of traits in different typical forests Note: HZ, HuZhong; LS, LiangShui; CB, ChangBai; DL, DongLing; TY, TaiYue; SN, ShenNong; JL, JiuLian; DH, DingHu; JF, JianFengLing.


Appendix II

Table S1

The list of these selected traits and their abbreviations


Table S2

The predictive equations of trait richness index (FRic) prediction equations at different sites (mean ±SE)


Table S3

The predictive equations of quadratic entropy (RaoQ) at different sites (mean ±SE)


Table S4

The predictive equations of functional attribute diversity (FAD) at different sites (mean ± SE).


Table S5

The predictive equations of modified functional attribute diversity (MFAD) at different sites (mean ±SE)


Appendix III

The formula of trait diversity index

1. FAD is commonly calculated as Eq. 1 and Eq. 2:


where T is the number of traits, and xti and xtj are the values of species i and species j for trait t, respectively. EDij is the Euclidean distance between species i and species j, and S is the number of species.

2. MFAD is a multidimensional trait richness index derived from the development of the FAD index, which considers the impact of species diversity (Eq. 3).


3. FRic is calculated by the area or volume of the smallest polygon generated within the multidimensional convex hull volume formed by multiple traits (Villeger et al. 2008). This is a complex calculation that can be done in both Qhull software ( and R languages ( php? option = com _ content & task = view & id=219 & Itemid=125).

4. The evenness of traits (FEve) is the distribution law of the mean value of species traits in the trait space (Eqs.46).


where S is the number of species, PEWb is the local weighted average uniformity, EWb is the weighted average uniformity, wi is the relative abundance of species i, and dij is the Euclidean distance between species i and species j.

5. FDiv was calculated as follows:


where S is the number of species, xik is the value of species i trait k, gk is the center of trait k, T is the number of traits, dGi is the average distance between species i and the center of gravity, and d is the dispersion degree with multiple degrees as the weight, wi is the relative

abundance of species i; fi01_332.gif is the mean of dGi .

6. FDis is a new index from FDiv's further improvement.


where aj is the relative abundance of species j and xij is the ith trait of species j. zj is the weighted distance from species j to center c. Where aj is the relative abundance of species j and xij is the ith trait of species j. zj is the weighted distance from species j to center c.

7. Rao defines a quadratic entropy equation that can be used to quantify the diversity and variability within a system.


where S is the number of species, xij is the t-characteristic of species i, pi is the relative abundance of species i, and dij is the distance of species i and j in the trait space.

Zhang Zihao, Hou Jihua, and He Nianpeng "Predictability of Functional Diversity Depends on the Number of Traits," Journal of Resources and Ecology 12(3), 332-345, (12 May 2021).
Received: 27 October 2020; Accepted: 4 January 2021; Published: 12 May 2021

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