1. Functional and Phylogenetic diversity estimated by genomics as a way to assess structure of the communities
Saverio Vicario
Institute of Biomedical Technology – National Council of Research, Bari, Italy (CNR-ITB)

2. Outline Biodiversity as a variable of state of the ecosystem
Defining the type of diversity used and the necessity of a clear statistical framework
PhyloH a program for performing Phylogenetic diversity
A limited use case

3. Biodiversity as a variable of state of the ecosystem
Ecosystem services are the output of communities
The capacity of system to maintain their output confronting external perturbation is the robustness (i.e. resilience)
The capacity of system to respond to prolonged external change is the evolvability
Both feature are relevant to maintain ecosystem and their outputs

4. System structure influences Robustness and Evolvability
functional redundancy R R
LEVIN and LUBCHENCO E E

5. Functional redundancy
Community with species or taxon that that perform same function using very different method (possessing very different Bauplan or genetic architecture). It is expected that in changed condition functional redundant member will react differently
Night predator of flying insect

6. Potential Relationship PD vs Traits
Srivastava DS, Cadotte MW, Macdonald AAM, et al. Phylogenetic diversity and the functioning of ecosystems. Ecology letters. 2012;15(7):637–48.

7. When Phylogenetic structure matter
An index of how much organisms are different is the phylogenetic structure. Depending from the kind of data used to reconstruct (single gene, multiple genes, time calibrated or not) and the evolutionary history of the organism the approach could be more or less efficient in prediction To measure functional redundancy would be enough a sample from the communities, its subdivision

8. Limit of Shannon applied to biodiversity
Field 1
Field 2

9. Limit of Shannon applied to biodiversity
Field 1
=3/9
H=1.1 nats
D=3.0 equally abundant species
Field 2
=3/9
H=1.1, D=3.0
Same Average Shannon Surprise!
But Adding a species of the dragon fly increase much more biodiversity of the observations than adding another butterfly species

10. Phylogenetic entropy of Allen/Chao
Observing sample at different level of taxonomic resolution
T1 -> I got 9 insects (q5=1)
H1=0 D1=1
T2 -> I got 6 Lepidoptera and 3 Odonata (q4=p2+p3)
H2=0.636 D2=1.889
T3-> I got 3 for each of the 3 species
H3=1.10 D3=3.0 T1 T2 T3

11. Partitioning Diversity
A large body of literature, a large diversity of opinions
I do not agree
I do agree

12. a, b, g Diversities I do agree that:
a entropy if q=1 is equal to Shannon entropy, while b entropy is mutual information or the Kullback-Leiber divergence between S and E vectors
To pass from entropy to diversity is sufficient to exponentialize for q=1
This framework put the partitioning well within the frame of Information Theory.
Beta diversity is measured in equivalent number of sample.
In case of N perfectly different samples but with unequal counts this measure do not reach N but exp(H(E)).
In case of perfectly identical sample but unequal count this measure is perfectly 1
S=Species
E=Environment
L. splendens
Grassland
O. horribilis
Forest …

13. Experimental design and entropy partitioning
HalphaR=H(S|R)= Biological Noise
HbetaR|E= H(S|E)-H(S|R,E)= Experimental Noise +
HalphaE=H(S|E)=Noise R
HbetaE=H(S)-H(S|E)=Signal S E
HalphaE
HbetaE
HalphaR + +
=H(S)
HbetaR|E
HalphaR+HbetaR|E+HbetaA=H(S)
HalphaE HbetaA =H(S)

14. Problems of methods They do use rarefaction to assess significance.
Not surprisingly the effect observed is small and not significant

15. Significance levels evaluation
Permutations of the annotations (replicates and environment) of the read allow to estimates expected Dbeta if no differentiation across environments exist given the observed level of variation and sampling effort
S=Species
R=Replicates
E=Environment
L. splendens
RG1 G
RG2
RG3
O. horribilis
RL1 L …

16. Power of permutation procedure
Simulated data set of 500 taxa over a phylogeny. 12 related taxa differ in their relative frequency across two environment of 0.01, while the rest of taxa have same relative frequency.

17. PhyloH features in measuring Phylogenetic diversity
differently from entropart (R) :
Being Beta entropy is a summation of difference
Each difference refer to a branch in the phylogeny. So is possible to plot the contribution of each branch on the tree plot and spot relevant patterns
Work also on non time scaled (non ultrametric)

19. Caso d’uso Impianto di depurazione nell’acquedotto milanese
In collaborazione con Maurizio Casiraghi, Antonella Bruno, Anna ZooPlantLab
Un impianto monitorato in tre zone (entrata,dopo filtri al carbone, dopo clorazione) per 14 mesi
Dati ora disponibili solo su Parcubacteria/Nanobacteria.

20. Diversità di ogni comparto

21. Differenze tra comparti

22. Differenze nel tempo

23. Contributo dei cladi alla differenza fra comparti