**2. A brief history of studies on biodiversity and ecosystem functioning — BEF**

Knowledge about biodiversity has passed through various stages in recent years, resulting from an accelerated scientific production. This scientific output, in turn, is a result of concerns arising from anthropogenic disturbances, which occur on spatial scales ranging from local to global [1].

To illustrate the changes observed in the study of biodiversity, Kevin Gaston in 1996 published a book entitled "Biodiversity: a biology of numbers and difference" [2]. In the first chapter of this book, Gaston emphasizes the relative infancy of the biodiversity issue, stating that a science can be seen by passing through three stages, as it matures [3]. The first stage of biodiversity

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studies is called the stage "What?", in which scientists seek only to know what are the species that occur in a particular location. In the second stage, the stage called "How?", is characterized by the attempts to search for patterns of biodiversity, and the third stage (the stage "Why?"), seeks to explain the factors that lead to the patterns observed before. Also according to [1], when the book was written, biodiversity studies remained "emphatically in the second stage of development, with more discussions on the measures and standards, than with issues related to the mechanisms."

**3. Biodiversity in studies of BEF**

would be an increase in functional diversity [20].

usual when using functional diversity in BEF studies.

that directly affect in how ecosystem operates [22].

Biodiversity may be estimated through several different metrics, and the most traditional approach is to access it via taxonomic diversity [10]. Later in the studies of BEF, functional diversity started to be used as an additional metric [11, 12] and, more recently, phylogenetic

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Taxonomic diversity, in turn, may be translated by species abundance, richness and compo‐ sition [16, 17] parameters that are easily accessed and that may give basic information to the generation of diversity indices (such as Simpson or Shannon). These diversity indices are useful to synthesize and compare the biodiversity in different environments or sites [18, 19]. However, the indiscriminate use of diversity indices, and as a goal in itself, rather than using them as a useful metric of diversity, prompted several authors to avoid its use in favor of species richness as a metric. Species may be identified from morphological or genetic traits and, when using taxonomic diversity as a metrics, it is assumed that the differences among species are determined by these aspects. Nevertheless, some authors suggest that taxonomic diversity may not be the most adequate metric [12] to evaluate the effect of organisms on ecosystem functioning. To better evaluate such effects, it would be necessary to use the functional diversity, even though it is expected that, with an increase in species richness, there

Functional diversity may be understood as the group of characteristics, of species or organisms, responsible by altering one or more aspects of ecosystem functioning [21]. Such characteristics may be related to the abilities that organisms have to engage or to alter ecosystem processes such as seed dispersal [22], pest biological control [23], pollination [24], nutrient cycling [25], decomposition [26], productivity [27, 28], amongst others. However, when inferring functional diversity from species richness, it is assumed that the relationship between species number

Therefore, the use of species richness as an estimate of functional diversity has been criticized, and the estimate of functional diversity has been achieved by species classification by their trophic level, guild, as well as physiological and phenotypic characteristics. Functional diversity is usually used to estimate the biodiversity of plant communities, classifying plant species according to their physiognomy, phenology or photosynthetic pathways. Animals are frequently grouped in guilds based on their consumption, but commonly with a low level of resolution, due to the weak knowledge of their biology. Such characteristics are frequently considered to determine functional diversity because they supposedly relate to aspects of the niches occupied and, consequently, they may express the effects of the organisms in ecosystem processes [21, 29]. From the analysis of these characteristics it is possible to determine and to include species in functional groups, which assemble organisms that fulfill similar functions and, consequently, have similar effects on the ecosystem [30, 22]. This approach is the most

Functional diversity is considered an estimate that may express more powerfully the effects of biodiversity on ecosystem functioning, because it refers to those biodiversity components

diversity has been included as a proposal of metric to biodiversity [13-15].

and niche occupation is linear, which usually does not occur in nature [7].

In just over a decade after the publication of Gaston, several mechanisms that determine and influence biodiversity were discussed [1], and today the statement made by the author would certainly be very wrong. Many studies have been carried out in different spatial and temporal scales [1], using several different biological systems and in different regions of the world. Much remains to be done, but it is not risky to affirm that little knowledge is still to be generated regarding the mechanisms responsible for determining biodiversity, especially with respect to the definition of biodiversity as the number of species in a given area.

Around the same time of the publication of the book by Gaston, there was a shift in the view of scientists on biodiversity: the thought that biodiversity was an expression of abiotic environmental conditions gave way to the recognition that the properties of the environment were also affected by the biota [4]. This recognition spurred the search for the elucidation of the effect of the loss of biodiversity on ecosystem functioning, generating more than 50 different hypotheses to explain how this relationship would be [5]. Ecosystem functioning can be understood as a set of biogeochemical processes and ecosystem functions [6], responsible for the flow of matter and energy, and it is directly related to the dynamics of resources and the stability of the ecosystem [7].

The hypotheses that explain the effect of biodiversity on ecosystem functioning may be classified into three major classes [8]. Within the first class fall the cases which species are assumed as redundant, and the loss of some species may be compensated by the presence of others, which perform the same function. Thus, to some extent, there would be no reduction of ecosystem functioning due to the lost of species and, on the other hand, there was no increase in the ecosystem functioning when species are added. In the second category of hypotheses are the cases when species are singular or unique, such as, for example, key species. According to this hypothesis, species lack redundancy and the loss or addition of some species would cause drastic changes to ecosystem functioning. Finally, there are hypotheses in which the ecosystem functioning effects of the loss or gain of species does not depend neither on the number nor the identity of the species present, but on the conditions under which this loss occurs, so that the effects of species on the functioning become idiosyncratic.

These model-hypotheses formed the necessary structure to the experimental tests of the relationship between biodiversity and ecosystem functioning [5]. The initial tests involved theoretical approaches, as well as the use of simplified micro and mesocosm laboratory experiments. Posterior studies incorporated actual environmental variation through observa‐ tional and manipulative experiments, allowing higher applicability in public policy manage‐ ment and biodiversity conservation [9].
