[MUSIC] Hi, guys. Welcome to the 21st lecture of the course, Biological Diversity, Theories, Measures and Data sample techniques. Today, we will talk about functional diversity. Functional diversity is very useful if the comparison between two or more communities this samples contain hypothetically the same number of individuals per species, and the same quantity of species. In this case, there would be no difference at all, and it will lead to a conclusion that the community are identical. This would be the case despite the possibility that the species are in the same number, but different among the samples. In order to differentiate and analyze biodiversity in this case or sometimes to simply use different indicators than traditional indices of alpha and beta diversity, there are alternative measures of biological diversity. Some of them continue to assess biodiversity quantitatively, for instance, functional taxonomic and phylogenetic diversity. Other that have been recently proposed are intended to monitor the species' diversity in terms of quality. The diversity of characters, trait diversity, can be used as a proxy of full functional diversity, and it is defined as the degree of variability of the functional characteristics for non specific traits, for instance, of coexisting species. Functional diversity is usually zero when only one taxon is in the sample. So, what are these different ways to assess functional diversity? One of these is the convex hull volume. This index estimates the volume occupied by traits of a coexisting species. The species that fall in the volume does not increase it, and therefore this index is influenced by the species are placed in this margin. That have very dissimilar traits. And those which form the vertices of the parameter in the case of only two species or volume more than two species. There are also indices on dendrograms. A dendrogram is constructed using a distance metrics of the trades for each sample, and the total length of the branches is summarized and compared between the samples. If the samples contain a similar number of species, the indices become available. There is no mathematical equation for this calculation. But dendrograms anyway are very intricate system to understand the differences the function of diversity and the diversity of species. Function of this person is an index that measured the average distance from the centroid of the community in the space of trades. They are weighted in comparison with relative abundance. You will see here, the formula, where A is the abundance of each species, and z is the weighted average distance of each species from the mean centroid. Weighted, that is calculated in the following way. In this formula, loss one, c is the weighted average of trace vector, ai is the abundance of each species i, and t is the value of the k characters. Functional diversity is the degree of distance among the most abundant axis centroid in the space of trades standardized to the average distance of not weighted centroid of the species that is prostrate on the perimeter of the convex rule. This index is higher when the species have extreme values in the traits. At least three taxa are required for the calculation of this measure. First, the centroid of the community is calculated by using only the vtax on the perimeter of the convex u. The centroid, g, is thus the vector g, that is g1, g2, g3, et al of the mean of each character key, you will see it in this formula where ti is the value of the k character, so the species or traits of the species. i and v is the number of species on the perimeter. If the number of traits is greater than the number of taxa+1 So t is greater than s plus one, then all taxa are vertices of the perimeter and this is possible to use, in this case, we can use s instead of v. This index has a maximum value of 1 if all taxa are presented at equal distance from the centroid. And represent the weighted distance based on the abundance with respect to which the most common species tend to position itself at the periphery of the community in the space of trades. If communities have fewer than two taxa, this index is not recommended. Another way to measure functional diversity is the functional evenness. Functional evenness is an index that combines the units of the species distributed in the trade space with the evenness of the species' relative abundance. This index is equal to one while all species have identical and equal length of the branches and tends to 0 with the increase of homogeneity. The minimum request for this index is that at least three taxa are included. You can see from the formula how to calculate it where the terms EW is the total length of the branch from species I to species J and S is the total number of species and p the relative abundance. Min distance is an index that is calculated on the coexisting tax sum and measure the average difference among the tax as a simply estimator of trace volume. The average distance may decrease when the intermediate tax are a for instance, in case of immigration to the community. And increase when they emigrate or become extinct. You can see in this formula where s is the richness. And dij is the distance between the species i and the species j. An entity way to understand the differences in functional diversity is the minimum spanning tree. That is the length of the minimum not recursive tree that connects all species in the trait space. In other words, is the shorter continue segment of connection between points without passing two times from the same point. It is a simple and very similar meter to venograms, but it has the advantage of not requiring the grouping of points and their calculation of the distances. The quadratic entropy is at any index that sums the distance between pairs of species in the trade space. Weighted by the relative abundance. A kind of distance weighted average of the abundances. It increases at the removal of taxa, and decreases when you want. You will see the formula in the picture when all taxa are completely different from each other dij is equal to 1 and fdq, so the quadratic entropy becomes nothing more than the index of Simpson Diversity. So, it can be easily converted into this index. Functional diversity are based also on variance. So, we can find a way to calculate the functional diversity based on variance that is simply the weighted sum of the abundances of the square of the values of trades observed. And therefore, is an analog of the weighted variance. The partitioning of the components of trait diversity is a method used to calculate both the variance of characteristics between and within taxa, and it's important to add data on intraspecific variability of traits. The traits variance among taxa is just calculated according to this formula where Ti is the mean value of the character for the species i, and p the relative abundance. The mean t is calculated as in this formula. The variants of the characters within taxa or the trace within taxa is calculated according to this formula as the sum of the variants among and within taxa can be used to measure traits diversity. One of the most complex aspects in the function of diversity measurements is the identification of taxa traits. One approach is to analyze the measured challenges or limitation to the species' performances, and then identify the ideal characters or traits simply and phenotypically measurable. For plants for example, the main challenges include dispersion, the rooting ability, and the persistence. And it is therefore possible to identify as the main trace the mass of seeds, the type of leaves and the height. However, when the inconsistent function are considered, it is fundamental to individuate a subset of species traits. An alternative method is to identify the characteristics associated with the life history or the acquisition of resources, for instance motility, anatomical structure for foraging, and resource utilization methods. So as the generality among all the we can differently say that fdq or the quadratic entropy is the most simple, quick and use it in addition to the advantage of incorporating the abundance data and to be similar to data Simpson. However, it is better to don't consider a single indicator as a true representative of the functional diversity of the community, but to calculate at least three of them to get the more complete picture. So guys, thanks for your attention and see you next time.
