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.