Discovering multi-scale metagenomic signatures through hierarchical organization of species

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# Discovering multi-scale metagenomic signatures through hierarchical organization of species
## PhD defense
### Antoine BICHAT
### LaMME – Enterome
### December 9, 2020

---

<table style="border:0px">
<tr>
<td>
 <center>
 <img src="img/pp_ambroise.jpeg"/ width="150"> 
 C. Ambroise
 </center>
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<td>
</td>
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 <center>
 <img src="img/pp_mariadassou.jpeg"/ width="150"> 
 M. Mariadassou
 </center>
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 <center>
 <img src="img/pp_plassais.jpeg"/ width="150"> 
 J. Plassais
 </center>
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 <center>
 <img src="img/pp_strozzi.jpeg"/ width="150"> 
 F. Strozzi
 </center>
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# Context

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name: microbiota
# Microbiota

_Ecological community of microorganisms that reside in an environmental niche._

---
template: microbiota
count: false

.footnote[📄 Ley Peterson, et al. [LPG06]; Flint Scott, et al. [Fli+12]; Canani Di Costanzo, et al. [Can+11]]

.pull-left[

#### For human gut

* `$10^{14}$` bacterial cells in one gut...

* ... weighting `$2~kg$`.

* More than `$1500$` different species.

* More than 10 millions unique genes.

* Helpful for nutrient absorption  and anti inflammatory properties.

]

---
template: microbiota
count: false

.footnote[📄 Ley Peterson, et al. [LPG06]; Flint Scott, et al. [Fli+12]; Canani Di Costanzo, et al. [Can+11] – 🖼  [lelivrescolaire.fr](https://www.lelivrescolaire.fr/books/6067633)]

.pull-left[

#### For human gut

* `$10^{14}$` bacterial cells in one gut...

* ... weighting `$2~kg$`.

* More than `$1500$` different species.

* More than 10 millions unique genes.

* Helpful for nutrient absorption  and anti inflammatory properties.

]

.pull-right[
<center>
 <img src="img/human_biots.png"/ width="350">
</center>
]

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# Microbiota everywhere

.footnote[🖼 [MicrobiomeSupport](https://www.microbiomesupport.eu/infographics/)]

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# Sequencing

.footnote[📄 Cryan O'Riordan, et al. [Cry+19]]

---
# Abundance table

* Matrix with `$m$` taxa and `$p$` samples.

* Count or compositional data, with inflation in zero.

* Correlation between abundances.

.footnote[📄 Brito Yilmaz, et al. [Bri+16]]

.pull-left[
<div class="tabwid"><table style='border-collapse:collapse;'><thead><tr style="overflow-wrap:break-word;"><td style="width:144px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:left;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:3px;padding-top:3px;padding-left:3px;padding-right:3px;background-color:transparent;"></td><td style="width:54px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:right;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:3px;padding-top:3px;padding-left:3px;padding-right:3px;background-color:transparent;">S1</td><td style="width:54px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:right;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:3px;padding-top:3px;padding-left:3px;padding-right:3px;background-color:transparent;">S2</td><td style="width:54px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:right;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:3px;padding-top:3px;padding-left:3px;padding-right:3px;background-color:transparent;">S3</td><td style="width:54px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:right;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:3px;padding-top:3px;padding-left:3px;padding-right:3px;background-color:transparent;">S4</td><td style="width:54px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:right;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:3px;padding-top:3px;padding-left:3px;padding-right:3px;background-color:transparent;">S5</td><td style="width:54px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:right;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:3px;padding-top:3px;padding-left:3px;padding-right:3px;background-color:transparent;">S6</td></tr></thead><tbody><tr style="overflow-wrap:break-word;"><td style="width:144px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(190, 190, 190, 1.00);border-top: 1.00px solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:left;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:3px;padding-top:3px;padding-left:3px;padding-right:3px;background-color:transparent;">Akkermansia muciniphila</td><td style="width:54px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(190, 190, 190, 1.00);border-top: 1.00px solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:right;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:3px;padding-top:3px;padding-left:3px;padding-right:3px;background-color:transparent;">0</td><td style="width:54px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(190, 190, 190, 1.00);border-top: 1.00px solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:right;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:3px;padding-top:3px;padding-left:3px;padding-right:3px;background-color:transparent;">934850</td><td style="width:54px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(190, 190, 190, 1.00);border-top: 1.00px solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:right;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:3px;padding-top:3px;padding-left:3px;padding-right:3px;background-color:transparent;">247037</td><td style="width:54px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(190, 190, 190, 1.00);border-top: 1.00px solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:right;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:3px;padding-top:3px;padding-left:3px;padding-right:3px;background-color:transparent;">0</td><td style="width:54px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(190, 190, 190, 1.00);border-top: 1.00px solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:right;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:3px;padding-top:3px;padding-left:3px;padding-right:3px;background-color:transparent;">181167</td><td style="width:54px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(190, 190, 190, 1.00);border-top: 1.00px solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:right;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:3px;padding-top:3px;padding-left:3px;padding-right:3px;background-color:transparent;">0</td></tr><tr style="overflow-wrap:break-word;"><td style="width:144px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(190, 190, 190, 1.00);border-top: 1.00px solid rgba(190, 190, 190, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:left;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:3px;padding-top:3px;padding-left:3px;padding-right:3px;background-color:transparent;">Bacteroides dorei</td><td style="width:54px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(190, 190, 190, 1.00);border-top: 1.00px solid rgba(190, 190, 190, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:right;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:3px;padding-top:3px;padding-left:3px;padding-right:3px;background-color:transparent;">89893</td><td style="width:54px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(190, 190, 190, 1.00);border-top: 1.00px solid rgba(190, 190, 190, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:right;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:3px;padding-top:3px;padding-left:3px;padding-right:3px;background-color:transparent;">2567192</td><td style="width:54px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(190, 190, 190, 1.00);border-top: 1.00px solid rgba(190, 190, 190, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:right;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:3px;padding-top:3px;padding-left:3px;padding-right:3px;background-color:transparent;">648639</td><td style="width:54px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(190, 190, 190, 1.00);border-top: 1.00px solid rgba(190, 190, 190, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:right;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:3px;padding-top:3px;padding-left:3px;padding-right:3px;background-color:transparent;">0</td><td style="width:54px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(190, 190, 190, 1.00);border-top: 1.00px solid rgba(190, 190, 190, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:right;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:3px;padding-top:3px;padding-left:3px;padding-right:3px;background-color:transparent;">0</td><td style="width:54px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(190, 190, 190, 1.00);border-top: 1.00px solid rgba(190, 190, 190, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:right;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:3px;padding-top:3px;padding-left:3px;padding-right:3px;background-color:transparent;">8498</td></tr><tr style="overflow-wrap:break-word;"><td style="width:144px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(190, 190, 190, 1.00);border-top: 1.00px solid rgba(190, 190, 190, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:left;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:3px;padding-top:3px;padding-left:3px;padding-right:3px;background-color:transparent;">Bifidobacterium longum</td><td style="width:54px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(190, 190, 190, 1.00);border-top: 1.00px solid rgba(190, 190, 190, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:right;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:3px;padding-top:3px;padding-left:3px;padding-right:3px;background-color:transparent;">376119</td><td style="width:54px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(190, 190, 190, 1.00);border-top: 1.00px solid rgba(190, 190, 190, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:right;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:3px;padding-top:3px;padding-left:3px;padding-right:3px;background-color:transparent;">0</td><td style="width:54px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(190, 190, 190, 1.00);border-top: 1.00px solid rgba(190, 190, 190, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:right;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:3px;padding-top:3px;padding-left:3px;padding-right:3px;background-color:transparent;">30671</td><td style="width:54px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(190, 190, 190, 1.00);border-top: 1.00px solid rgba(190, 190, 190, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:right;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:3px;padding-top:3px;padding-left:3px;padding-right:3px;background-color:transparent;">0</td><td style="width:54px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(190, 190, 190, 1.00);border-top: 1.00px solid rgba(190, 190, 190, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:right;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:3px;padding-top:3px;padding-left:3px;padding-right:3px;background-color:transparent;">1292193</td><td style="width:54px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(190, 190, 190, 1.00);border-top: 1.00px solid rgba(190, 190, 190, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:right;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:3px;padding-top:3px;padding-left:3px;padding-right:3px;background-color:transparent;">1830318</td></tr><tr style="overflow-wrap:break-word;"><td style="width:144px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(190, 190, 190, 1.00);border-top: 1.00px solid rgba(190, 190, 190, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:left;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:3px;padding-top:3px;padding-left:3px;padding-right:3px;background-color:transparent;">Enterobacter cloacae</td><td style="width:54px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(190, 190, 190, 1.00);border-top: 1.00px solid rgba(190, 190, 190, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:right;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:3px;padding-top:3px;padding-left:3px;padding-right:3px;background-color:transparent;">756064</td><td style="width:54px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(190, 190, 190, 1.00);border-top: 1.00px solid rgba(190, 190, 190, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:right;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:3px;padding-top:3px;padding-left:3px;padding-right:3px;background-color:transparent;">12234</td><td style="width:54px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(190, 190, 190, 1.00);border-top: 1.00px solid rgba(190, 190, 190, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:right;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:3px;padding-top:3px;padding-left:3px;padding-right:3px;background-color:transparent;">142652</td><td style="width:54px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(190, 190, 190, 1.00);border-top: 1.00px solid rgba(190, 190, 190, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:right;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:3px;padding-top:3px;padding-left:3px;padding-right:3px;background-color:transparent;">2186</td><td style="width:54px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(190, 190, 190, 1.00);border-top: 1.00px solid rgba(190, 190, 190, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:right;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:3px;padding-top:3px;padding-left:3px;padding-right:3px;background-color:transparent;">238175</td><td style="width:54px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(190, 190, 190, 1.00);border-top: 1.00px solid rgba(190, 190, 190, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:right;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:3px;padding-top:3px;padding-left:3px;padding-right:3px;background-color:transparent;">535786</td></tr><tr style="overflow-wrap:break-word;"><td style="width:144px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(190, 190, 190, 1.00);border-top: 1.00px solid rgba(190, 190, 190, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:left;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:3px;padding-top:3px;padding-left:3px;padding-right:3px;background-color:transparent;">Escherichia coli</td><td style="width:54px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(190, 190, 190, 1.00);border-top: 1.00px solid rgba(190, 190, 190, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:right;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:3px;padding-top:3px;padding-left:3px;padding-right:3px;background-color:transparent;">256424</td><td style="width:54px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(190, 190, 190, 1.00);border-top: 1.00px solid rgba(190, 190, 190, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:right;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:3px;padding-top:3px;padding-left:3px;padding-right:3px;background-color:transparent;">5551041</td><td style="width:54px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(190, 190, 190, 1.00);border-top: 1.00px solid rgba(190, 190, 190, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:right;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:3px;padding-top:3px;padding-left:3px;padding-right:3px;background-color:transparent;">9905179</td><td style="width:54px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(190, 190, 190, 1.00);border-top: 1.00px solid rgba(190, 190, 190, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:right;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:3px;padding-top:3px;padding-left:3px;padding-right:3px;background-color:transparent;">76052</td><td style="width:54px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(190, 190, 190, 1.00);border-top: 1.00px solid rgba(190, 190, 190, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:right;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:3px;padding-top:3px;padding-left:3px;padding-right:3px;background-color:transparent;">70234</td><td style="width:54px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(190, 190, 190, 1.00);border-top: 1.00px solid rgba(190, 190, 190, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:right;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:3px;padding-top:3px;padding-left:3px;padding-right:3px;background-color:transparent;">79805</td></tr><tr style="overflow-wrap:break-word;"><td style="width:144px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(190, 190, 190, 1.00);border-top: 1.00px solid rgba(190, 190, 190, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:left;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:3px;padding-top:3px;padding-left:3px;padding-right:3px;background-color:transparent;">Klebsiella pneumoniae</td><td style="width:54px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(190, 190, 190, 1.00);border-top: 1.00px solid rgba(190, 190, 190, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:right;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:3px;padding-top:3px;padding-left:3px;padding-right:3px;background-color:transparent;">1057187</td><td style="width:54px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(190, 190, 190, 1.00);border-top: 1.00px solid rgba(190, 190, 190, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:right;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:3px;padding-top:3px;padding-left:3px;padding-right:3px;background-color:transparent;">0</td><td style="width:54px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(190, 190, 190, 1.00);border-top: 1.00px solid rgba(190, 190, 190, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:right;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:3px;padding-top:3px;padding-left:3px;padding-right:3px;background-color:transparent;">515407</td><td style="width:54px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(190, 190, 190, 1.00);border-top: 1.00px solid rgba(190, 190, 190, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:right;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:3px;padding-top:3px;padding-left:3px;padding-right:3px;background-color:transparent;">0</td><td style="width:54px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(190, 190, 190, 1.00);border-top: 1.00px solid rgba(190, 190, 190, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:right;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:3px;padding-top:3px;padding-left:3px;padding-right:3px;background-color:transparent;">887678</td><td style="width:54px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(190, 190, 190, 1.00);border-top: 1.00px solid rgba(190, 190, 190, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:right;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:3px;padding-top:3px;padding-left:3px;padding-right:3px;background-color:transparent;">1620535</td></tr><tr style="overflow-wrap:break-word;"><td style="width:144px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(190, 190, 190, 1.00);border-top: 1.00px solid rgba(190, 190, 190, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:left;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:3px;padding-top:3px;padding-left:3px;padding-right:3px;background-color:transparent;">Megamonas hypermegale</td><td style="width:54px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(190, 190, 190, 1.00);border-top: 1.00px solid rgba(190, 190, 190, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:right;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:3px;padding-top:3px;padding-left:3px;padding-right:3px;background-color:transparent;">0</td><td style="width:54px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(190, 190, 190, 1.00);border-top: 1.00px solid rgba(190, 190, 190, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:right;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:3px;padding-top:3px;padding-left:3px;padding-right:3px;background-color:transparent;">0</td><td style="width:54px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(190, 190, 190, 1.00);border-top: 1.00px solid rgba(190, 190, 190, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:right;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:3px;padding-top:3px;padding-left:3px;padding-right:3px;background-color:transparent;">0</td><td style="width:54px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(190, 190, 190, 1.00);border-top: 1.00px solid rgba(190, 190, 190, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:right;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:3px;padding-top:3px;padding-left:3px;padding-right:3px;background-color:transparent;">0</td><td style="width:54px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(190, 190, 190, 1.00);border-top: 1.00px solid rgba(190, 190, 190, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:right;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:3px;padding-top:3px;padding-left:3px;padding-right:3px;background-color:transparent;">0</td><td style="width:54px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(190, 190, 190, 1.00);border-top: 1.00px solid rgba(190, 190, 190, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:right;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:3px;padding-top:3px;padding-left:3px;padding-right:3px;background-color:transparent;">27317</td></tr><tr style="overflow-wrap:break-word;"><td style="width:144px;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 1.00px solid rgba(190, 190, 190, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:left;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:3px;padding-top:3px;padding-left:3px;padding-right:3px;background-color:transparent;">Streptococcus anginosus</td><td style="width:54px;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 1.00px solid rgba(190, 190, 190, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:right;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:3px;padding-top:3px;padding-left:3px;padding-right:3px;background-color:transparent;">0</td><td style="width:54px;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 1.00px solid rgba(190, 190, 190, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:right;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:3px;padding-top:3px;padding-left:3px;padding-right:3px;background-color:transparent;">0</td><td style="width:54px;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 1.00px solid rgba(190, 190, 190, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:right;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:3px;padding-top:3px;padding-left:3px;padding-right:3px;background-color:transparent;">0</td><td style="width:54px;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 1.00px solid rgba(190, 190, 190, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:right;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:3px;padding-top:3px;padding-left:3px;padding-right:3px;background-color:transparent;">985</td><td style="width:54px;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 1.00px solid rgba(190, 190, 190, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:right;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:3px;padding-top:3px;padding-left:3px;padding-right:3px;background-color:transparent;">0</td><td style="width:54px;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 1.00px solid rgba(190, 190, 190, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:right;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:3px;padding-top:3px;padding-left:3px;padding-right:3px;background-color:transparent;">19134</td></tr></tbody></table></div>
]

.pull-right[
<center>
 <img src="img/correlation.png"/ width="500">
</center>
]

---
# Phylogeny

.footnote[📄 Brito Yilmaz, et al. [Bri+16]]

* Tree with `$m$` leaves which describes the evolutionary history of the taxa.

* Associated with a patristic distance matrix `$\left(d_{i,j}\right)_{i,j}$`.

---

# Differential abundance studies

Used to find **associations** between microbiota and

<table style="border:0px">
<tr>
<td>
<ul>
<li>diet [Dav+14],</li>
<li>birth mode [Bok+16],</li>
<li>age [Yat+12],</li>
</ul>
</td>
<td>
</td>
<td>
<ul>
<li>pet owning [Kat+20],</li>
<li>tobacco [Ops+16],</li>
<li>antibiotics [Pal+18],</li>
</ul>
</td>
<td>
</td>
<td>
<ul>
<li>Crohn's disease [Mor+12],</li>
<li>cirrhosis [Qin+14]</li>
<li>schizophrenia [Zhe+19]...</li>
</ul>
</td>
</table>

---
# Classical approach

Vector `$\pv \in \mathopen[0,1\mathclose]^m$` of `$p$`-values, computed on each taxa independently.

Wilcoxon and Kruskal-Wallis non-parametric tests can be used.

A taxon `$i$` is detected differentially abundant if `$\pv_i < \alpha$`.

Each taxon fall into one class of the confusion matrix:

<div class="tabwid"><table style='border-collapse:collapse;'><tbody><tr style="overflow-wrap:break-word;"><td colspan="2" rowspan="2" style="width:54px;background-clip: padding-box;background-color:rgba(255, 255, 255, 1.00);vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:right;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:2px;padding-top:2px;padding-left:5px;padding-right:5px;background-color:transparent;"></td><td colspan="2" style="width:54px;background-clip: padding-box;background-color:rgba(255, 255, 255, 1.00);vertical-align: middle;border-bottom: 1.00px solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:center;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:2px;padding-top:2px;padding-left:5px;padding-right:5px;background-color:transparent;">True condition</td></tr><tr style="overflow-wrap:break-word;"><td style="width:54px;background-clip: padding-box;background-color:rgba(255, 255, 255, 1.00);vertical-align: middle;border-bottom: 1.00px solid rgba(0, 0, 0, 1.00);border-top: 1.00px solid rgba(0, 0, 0, 1.00);border-left: 1.00px solid rgba(0, 0, 0, 1.00);border-right: 1.00px solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:center;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:2px;padding-top:2px;padding-left:5px;padding-right:5px;background-color:transparent;">Positive</td><td style="width:54px;background-clip: padding-box;background-color:rgba(255, 255, 255, 1.00);vertical-align: middle;border-bottom: 1.00px solid rgba(0, 0, 0, 1.00);border-top: 1.00px solid rgba(0, 0, 0, 1.00);border-left: 1.00px solid rgba(0, 0, 0, 1.00);border-right: 1.00px solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:center;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:2px;padding-top:2px;padding-left:5px;padding-right:5px;background-color:transparent;">Negative</td></tr><tr style="overflow-wrap:break-word;"><td rowspan="2" style="width:54px;background-clip: padding-box;background-color:rgba(255, 255, 255, 1.00);vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 1.00px solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:right;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:2px;padding-top:2px;padding-left:5px;padding-right:5px;background-color:transparent;">Detection</td><td style="width:54px;background-clip: padding-box;background-color:rgba(255, 255, 255, 1.00);vertical-align: middle;border-bottom: 1.00px solid rgba(0, 0, 0, 1.00);border-top: 1.00px solid rgba(0, 0, 0, 1.00);border-left: 1.00px solid rgba(0, 0, 0, 1.00);border-right: 1.00px solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:center;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:2px;padding-top:2px;padding-left:5px;padding-right:5px;background-color:transparent;">Positive</td><td style="width:54px;background-clip: padding-box;background-color:rgba(160, 207, 99, 1.00);vertical-align: middle;border-bottom: 1.00px solid rgba(0, 0, 0, 1.00);border-top: 1.00px solid rgba(0, 0, 0, 1.00);border-left: 1.00px solid rgba(0, 0, 0, 1.00);border-right: 1.00px solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:center;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:2px;padding-top:2px;padding-left:5px;padding-right:5px;background-color:transparent;">TP</td><td style="width:54px;background-clip: padding-box;background-color:rgba(235, 82, 78, 1.00);vertical-align: middle;border-bottom: 1.00px solid rgba(0, 0, 0, 1.00);border-top: 1.00px solid rgba(0, 0, 0, 1.00);border-left: 1.00px solid rgba(0, 0, 0, 1.00);border-right: 1.00px solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:center;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:2px;padding-top:2px;padding-left:5px;padding-right:5px;background-color:transparent;">FP</td></tr><tr style="overflow-wrap:break-word;"><td style="width:54px;background-clip: padding-box;background-color:rgba(255, 255, 255, 1.00);vertical-align: middle;border-bottom: 1.00px solid rgba(0, 0, 0, 1.00);border-top: 1.00px solid rgba(0, 0, 0, 1.00);border-left: 1.00px solid rgba(0, 0, 0, 1.00);border-right: 1.00px solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:center;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:2px;padding-top:2px;padding-left:5px;padding-right:5px;background-color:transparent;">Negative</td><td style="width:54px;background-clip: padding-box;background-color:rgba(235, 82, 78, 1.00);vertical-align: middle;border-bottom: 1.00px solid rgba(0, 0, 0, 1.00);border-top: 1.00px solid rgba(0, 0, 0, 1.00);border-left: 1.00px solid rgba(0, 0, 0, 1.00);border-right: 1.00px solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:center;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:2px;padding-top:2px;padding-left:5px;padding-right:5px;background-color:transparent;">FN</td><td style="width:54px;background-clip: padding-box;background-color:rgba(160, 207, 99, 1.00);vertical-align: middle;border-bottom: 1.00px solid rgba(0, 0, 0, 1.00);border-top: 1.00px solid rgba(0, 0, 0, 1.00);border-left: 1.00px solid rgba(0, 0, 0, 1.00);border-right: 1.00px solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:center;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:2px;padding-top:2px;padding-left:5px;padding-right:5px;background-color:transparent;">TN</td></tr></tbody></table></div>

Under `$\mathbb{H}_0$`, `$\pv_i \sim \mathcal{U}(\mathopen[0,1\mathclose])$`.

---
# Multiple testing problem

.footnote[🖼 [XKCD](https://xkcd.com/882)]

---
# TPR and FDR

True Positive Rate:

`$$\text{TPR} = \frac{\text{TP}}{\text{TP} + \text{FN}}.$$`

False Discovery Rate:

`$$\text{FDP} = \frac{\text{FP}}{\text{TP} + \text{FP}}\text{, FDR}=\EE{\text{FDP}}.$$`

---
# Multiple testing problem correction

.footnote[📄 Benjamini and Hochberg [BH95]]

Correction with Benjamini-Hochberg procedure to respect an _a priori_ FDR : `$\qv^{\text{bh}}$`.

But it assumes independence between taxa and it is not respected.

---
count: false
# Multiple testing problem correction

.footnote[📄 Benjamini and Hochberg [BH95]; Benjamini and Yekutieli [BY01]]

Correction with Benjamini-Hochberg procedure to respect an _a priori_ FDR : `$\qv^{\text{bh}}$`.

But it assumes independence between taxa and it is not respected.

One can use Benjamini-Yekutieli correction which does not make any assumption about dependence between taxa but

* it's too conservative,
 
 * we want to correct explicitly for correlation between taxa.

---
class: inverse, center, middle

# Incorporation of hierarchical information

---

# Goal

* Correct explicitly for correlation between taxa.

* Increase power.

* Keep FDR under a desired level.

---
name: rationale
# Rationale

.footnote[📄 Philippot Andersson, et al. [Phi+10]]

---
count: false
# Rationale

.footnote[📄 Philippot Andersson, et al. [Phi+10]]

<center>
 <img src="img/coherence_1.png"/ width="480">
</center>
.center[These species are associated with animals.]

---
count: false
# Rationale

.footnote[📄 Philippot Andersson, et al. [Phi+10]]

<center>
 <img src="img/coherence_2.png"/ width="480">
</center>
.center[These species are associated with soil.]

---
template: rationale
count: false

Already used in

* Hierarchical FDR [Yek08; SH14],

* **TreeFDR [XCC17]**.

---
# z-scores smoothing with TreeFDR

`$\zs = \Phi^{-1}\left(\pv\right)$` is the vector of observed _z_-scores and `$\mu$` the vector of “true” _z_-scores.

Assume a hierarchical model: `$\left. \zs \mid \mu \right. \sim \mathcal{N}_m\left(\mu,\sigma^2 \mathbf{I}_m\right)$` and `$\mu \sim \mathcal{N}_m\left(\gamma \mathbf{1}_m,\tau^2C_{\rho}\right)$` with `$C_{\rho} = \left(\exp\left(-2\rho d_{i,j}\right)\right)_{i,j}$`.

---
# z-scores smoothing with TreeFDR

Then `$\zs \sim \mathcal{N}_m \left(\gamma \mathbf{1}_m,\tau^2 C_{\rho} + \sigma^2 \mathbf{I}_m\right)$` by Bayes formula and the maximum a posteriori gives 
 
`$$\mu^* = \left(\mathbf{I}_m + k^2 C_{\rho}^{-1}\right)\left(k^2 C_{\rho}^{-1} \gamma \mathbf{1}_m + \zs \right),$$`

with `$k = \frac{\sigma}{\tau}$` and `$\rho_0$` hyperparameters to optimize.

At the end, a multiple testing correction by resampling is done on smoothed values.

---
# Which tree?

* Phylogeny? Taxonomy?

😀 Proxy for correlations at high-level niches.

☹️ Not so much for low-level niches?

☹️ Not available every time.

.footnote[📄 Bichat Plassais, et al. [Bic+20]]

* Correlation tree?

😀 Actual correlation between taxa.
  
😀 Always available.
  
☹️ Risk of overfitting.

---
# Billera-Holmes-Vogtmann distance

.footnote[📄 Billera Holmes, et al. [BHV01]]

.pull-left[
 <center><img src="img/dBHV_4.png" height=300/></center>
]

.pull-right[

* Each tree is mapped into a space composed by merged orthants.

* An orthant corresponds to a topology.

* The BHV distance is the length of the unique shortest path between the trees on treespace.

* It can be computed with a `$O\left(m^4\right)$` algorithm.
]

---
# Quantifying distance between trees

* Trees of primary interest:

* correlation tree on original data,
 
 * phylogeny.
 
--

* What is the confidence region for the correlation tree?

* correlation trees on boostrapped data (resampling on samples).

* Are trees significantly closer than two random trees?

* trees created by random shuffling of correlation tree tip labels,
 
 * trees created by random shuffling of phylogeny tip labels.

We compute all pairwise distances between these trees.

---
# Comparisons between trees

Neither phylogeny nor taxonomy is in the confident region of the correlation tree.

.footnote[📄 [Bic+20; Rav+11; Zel+14; Cha+15]]

---
count: false
# Comparisons between trees

Neither phylogeny nor taxonomy is in the confident region of the correlation tree.

.footnote[📄 [Bic+20; Rav+11; Zel+14; Cha+15]]

---
# Impact of the tree with Zeller dataset

.footnote[📄 Bichat Plassais, et al. [Bic+20]; Zeller Tap, et al. [Zel+14]]

All hierarchies give highly similar results.

.pull-left[
<center>
 <img src="img/zeller_detected.png" height=350/>
</center>
]

.pull-right[
* 119 genera

* 199 patients 
  * 66 healthy
  * 42 adenoma
  * 91 colorectal cancer
]

---
class: inverse, center, middle

# zazou

### Z-scores AZ Ornstein-Uhlenbeck

---
# Ornstein-Uhlenbeck process

An Ornstein-Uhlenbeck (OU) process with an optimal value of `$\ou{\optim}$` and a strength of selection `$\ou{\alpha} > 0$` is a Gaussian process that satisfies the SDE

`$$\dx{W_t} = -\ou{\alpha} (W_t - \ou{\optim}) \dx{t} + \ou{\sigma}\dx{B_t}.$$`

.pull-left[
<center>
 <img src="img/ou_param.gif"/ width="350">
</center>
]

.pull-right[

`$W_t$` is Gaussian with bounded variance and

`$$W_t \xrightarrow[t\rightarrow\infty]{} \normal{\ou{\optim}}{\frac{\ou{\sigma}^2}{2\ou{\alpha}}}.$$`
]

---
# OU process on a tree with shifts `$\shifts$`

.footnote[📄 Bastide Mariadassou, et al. [BMR17]]

* On a branch, the process behaves like on `$\RR_+$`.

* At each node, the process splits into two independent processes with the same initial value.

* The optimal value can shift at a node.

---
# Incidence matrix and vector of shifts

.pull-left[
<center>
 <img src="img/tree_ou_left.png"/ width="400">
</center>
]

`$T = (\indic_{\{i \in \desc(j)\}})_{ij} \in\{0,1\}^{m \times n}$` is the incidence matrix of the tree:

$$
`\begin{bmatrix}
1 & \color{#4aac8b}{0} & \color{#cc5561}{1} & \color{#bf6e3f}{1} & \color{#c55d93}{1} & \color{#6da148}{0} & \color{#9d63cb}{0} & \color{#c3a030}{0} & \color{#7088c8}{0} \\
1 & \color{#4aac8b}{0} & \color{#cc5561}{1} & \color{#bf6e3f}{1} & \color{#c55d93}{0} & \color{#6da148}{1} & \color{#9d63cb}{0} & \color{#c3a030}{0} & \color{#7088c8}{0} \\
1 & \color{#4aac8b}{0} & \color{#cc5561}{1} & \color{#bf6e3f}{0} & \color{#c55d93}{0} & \color{#6da148}{0} & \color{#9d63cb}{1} & \color{#c3a030}{0} & \color{#7088c8}{0} \\
1 & \color{#4aac8b}{1} & \color{#cc5561}{0} & \color{#bf6e3f}{0} & \color{#c55d93}{0} & \color{#6da148}{0} & \color{#9d63cb}{0} & \color{#c3a030}{1} & \color{#7088c8}{0} \\
1 & \color{#4aac8b}{1} & \color{#cc5561}{0} & \color{#bf6e3f}{0} & \color{#c55d93}{0} & \color{#6da148}{0} & \color{#9d63cb}{0} & \color{#c3a030}{0} & \color{#7088c8}{1} \\
\end{bmatrix}`
$$

and `$\shifts$` the vector of shifts:

`$$\begin{bmatrix} 0 & \color{#4aac8b}{0} & \color{#cc5561}{0} & \color{#bf6e3f}{4} & \color{#c55d93}{0} & \color{#6da148}{0} & \color{#9d63cb}{0} & \color{#c3a030}{0} & \color{#7088c8}{0} \end{bmatrix}^T.$$`
--

The product `$T\delta$` is the vector of optimal values on leaves.

---
# Random variables on leaves

The random variables on leaves are jointly Gaussian `$\mathcal{N}_m\left(T\shifts, \Sigma \right)$` with

`$$\Sigma_{i, j} = \frac{\ou{\sigma}^2}{2\ou{\alpha}}\left(1 - e^{-2\ou{\alpha} t_{i,j} }\right) \times e^{-\ou{\alpha} d_{i,j}}.$$`

---
# First assumption

`$\mathfrak{z}$` is the realization of an OU on a tree with shifts `$\delta$`.

Then,

$$
\zs \sim \mathcal{N}_m\left(\mu,\Sigma\right)
$$

with `$\mu = T\delta$` and `$\Sigma$` depends on `$\alpha_{\text{ou}}$` and `$\sigma_{\text{ou}}$` by

`$$\Sigma_{i,j} = \frac{\ou{\sigma}^2}{2\ou{\alpha}}\left(e^{-\ou{\alpha} d_{i,j}} - e^{-2\ou{\alpha} h}\right)$$`

for a tree with total height `$h$`.

---
name: secondassumption
# Second assumption

.footnote[📄 McLachlan and Peel [MP04]]

For a taxa `$i$`,

* if `$\mathcal{H}_i \in \mathbb{H}_0$`, `$\mathfrak{p}_i \sim \mathcal{U}(\mathopen[0,1\mathclose])$` so `$\mathfrak{z}_i \sim \mathcal{N}(0,1)$`,

* if `$\mathcal{H}_i \notin \mathbb{H}_0$`, `$\mathfrak{p}_i \preccurlyeq \mathcal{U}(\mathopen[0,1\mathclose])$` so `$\mathfrak{z}_i \sim \mathcal{N}(\mu_i,1)$` with `$\mu_i \lt 0$`.

---
template: secondassumption
count: false

---
template: secondassumption
count: false

Then,

`$$\mathfrak{z} \sim \mathcal{N}_m\left(\mu \in \RR_-^m, \Sigma\right).$$`

One will find **differentially abundant** taxa by finding the **non-zero elements** of `$\mu$`.

This impose `$\Sigma_{i,i} = 1$` so `$\ou{\sigma}=\frac{2\ou{\alpha}}{1 - e^{-2\ou{\alpha}h}}$`.

---
# Estimation of `$\mu$`

With `$\Sigma$` known, a naive ML estimator gives

`$$\hat{\mu} = \argmin_{\mu\in\RR_-^m} \|\mathfrak{z} - \mu\|_{\Sigma^{-1}, 2}^2.$$`

To take the tree into account, `$\hat{\mu} = T\hat{\shifts}$` with

`$$\hat{\shifts} = \argmin_{\shifts\in \RR^{n} / T\shifts \in\RR_-^m} \left\|\mathfrak{z} - T\shifts\right\|_{\Sigma^{-1},2}^2.$$`

To add hierarchically coherent sparsity in our estimate

`$$\hat{\shifts} = \argmin_{\shifts\in \RR^{n} / T\shifts \in\RR_-^m} \left\|\mathfrak{z} - T\shifts\right\|_{\Sigma^{-1},2}^2 + \lambda \|\shifts\|_1.$$`

---
# Estimation of `$\mu$` (bis)

By Cholesky decomposition, `$\Sigma^{-1} = R^TR$`

`\begin{align*}
\left\|\mathfrak{z} - T\shifts\right\|_{\Sigma^{-1},2}^2 & = \left(\mathfrak{z} - T\shifts\right)^T\Sigma^{-1}\left(\mathfrak{z} - T\shifts\right)  \\
& = \left(\mathfrak{z} - T\shifts\right)^TR^TR\left(\mathfrak{z} - T\shifts\right)   \\
& = \left(R\mathfrak{z} - RT\shifts\right)^T\left(R\mathfrak{z} - RT\shifts\right) \\
& = \left(y - X\shifts\right)^T\left(y - X\shifts\right) = \left\|y - X\shifts\right\|_2^2
\end{align*}`

with `$y = R\mathfrak{z}$` and `$X = RT$`.

Finally, we fall back to a constrained lasso problem:

`$$\hat{\shifts} = \argmin_{\shifts\in \RR^{n} / T\shifts \in\RR_-^m} \left\|y - X\shifts\right\|_2^2 + \lambda \|\shifts\|_1.$$`

---
# Numerical resolution

.footnote[📄 Fu [98]]

The previous problem could be numerically solved by the shooting algorithm, **iterating unidirectional updates** form the associated problem:

`\begin{equation}
\left\{
  \begin{aligned}
    \argmin_{\param \in \RR} h(\param) & = \frac{1}{2} \|y - z - x\param\|^2_2 + \lambda |\param| \\
    & \text{s.t. } u + v\param \leq 0.
  \end{aligned}
\right.
\end{equation}`

But `$\Sigma$` and `$\lambda$` are not yet known.

---
# Estimation of `$\Sigma$` and choice of `$\lambda$`

`$\widehat{\Sigma} = \left(\frac{e^{-\ou{\hat{\alpha}} d_{ij}} - e^{-2\ou{\hat{\alpha}} h }}{1 - e^{-2\ou{\hat{\alpha}} h }}\right)_{i,j}$` is determined by `$\ou{\hat{\alpha}}$`.

The optimal `$\left(\ou{\alpha}, \lambda\right)$`, is chosen on a bidimensional grid as the `$\argmin$` of the BIC

`\begin{equation}
\left\|\zs - T\shifts_{\ou{\alpha}, \lambda}\right\|_{\Sigma(\ou{\alpha})^{-1},2}^2 + \log|\Sigma(\ou{\alpha})| + \|\shifts_{\ou{\alpha}, \lambda}\|_0 \log m.
\end{equation}`

---
# Effect of hierarchical smoothing

---
# Find non zero values

Estimation from lasso provides biased estimators without confidence intervals.

We need confidence intervals on `$\hat{\shifts}$` and `$\hat{\mu}$`.

Use of a debiasing procedure

* **score system (ss) [ZZ14],**

* column-wise inverse (ci) [JM13; JM14].

---
# Scaled lasso

The debiasing procedure requires a **initial joint estimator** of `$\shifts^{\text{(init)}}$` and its associated standard error `$\sigma$`.

This can be done with a scaled lasso

`$$\left(\hat{\shifts}^{\text{(init)}}, \hat{\sigma}\right) = \argmin_{\shifts, \sigma} \frac{\|y - X\shifts\|_2^2}{2\sigma n} + \frac{\sigma}{2} + \lambda \|\shifts\|_1.$$`

.footnote[📄 Sun and Zhang [SZ12]]

---
# Score system

The **score system** `$S \in \RR^{n\times p}$` associated with `$X$` and `$y$` where `$s_j$` is the residual of the (classical) lasso regression of `$y$` against `$X_{-j}$`:

`$$s_j = y - \shifts^{-j}_{\text{lasso}} X_{-j}.$$`

`$S$` is as **weak orthogonalisation** of `$X$`.

---
# Debiasing procedure

From the initial estimator `$\hat{\shifts}_j^{\text{(init)}}$` of the scaled lasso, one can do a **one-step correction**

`$$\hat{\shifts}_j = \hat{\shifts}_j^{\text{(init)}} + \frac{\langle s_j,y-X\hat{\shifts}^{(\text{init})}\rangle}{\langle s_j,x_j\rangle}.$$`

Asymptotically, `$\hat{\shifts} \sim \mathcal{N}_n\left(\shifts, V\right)$` with

`$$v_{i,j} = \hat{\sigma} \frac{\langle s_i,s_j \rangle}{\langle s_i,x_i \rangle\langle s_j,x_j \rangle}.$$`
--

Then the **bilateral confidence interval** for a shift `$\hat{\shifts}_j$` is

`$$\left[ \hat{\shifts}_j \pm \phi^{-1}\left(1-\frac{\alpha}{2}\right) \sqrt{v_{j,j}} \right].$$`

---
# Smoothed p-values

To have the **unilateral hierarchically smoothed p-values** `$\pv^\text{h}$`, we need to propagate the shifts with the incidence matrix `$T$`

`$$\pv^\text{h}_i = \Phi\left(\frac{t_{i.}^T\hat{\shifts}}{\left(t_{i.}^TVt_{i.}\right)^{1/2}}\right)$$`

with `$t_{i.}$` the `$i^{\text{th}}$` row of `$T$`.

---
# Multiple testing correction

.footnote[📄 Javanmard Javadi, et al. [JJ19]]

Let `$\ts_i = \frac{t_{i.}^T\hat{\shifts}}{\left(t_{i.}^TVt_{i.}\right)^{1/2}}$` be the `$t$`-scores, `$t_{\text{max}} = \sqrt{2 \log m - 2 \log \log m}$` and

`$$t^{\star} = \inf \bigg\{ 0 \leq t \leq t_{\max} : \underbrace{\frac{2m(1 - \Phi(t))}{R(t) \vee 1}}_{\widehat{\text{FDR}}(t)} \leq \alpha \bigg\}$$`

with `$R(t)= \sum_{i = 1}^m \indic_{\{\ts_i \leq -t\}}$`.

One reject if `$\ts_i \leq -t^{\star}$` and the associated **hierarchical q-values** are

`$$\qv^{\text{h}}_i = \frac{\pv^{\text{h}}_i \alpha}{\Phi(-t^{\star})}.$$`

---
# zazou overview

zazou is a recipe with four steps:

* a modeling of `$z$`-scores by an Ornstein-Uhlenbeck process on a tree with shifts,

* a constrained scaled lasso to estimate a sparse distribution of the shifts,

* a debiasing procedure for the scaled lasso,

* a debiased lasso designed multiple testing procedure.

---
class: center, middle, inverse

# Evaluation of zazou

---
# Simulations

.footnote[📄 Bichat Plassais, et al. [Bic+20]]

.pull-left[
<center>
 <img src="img/workflow_simu.png"/ width="430">
</center>
]

.pull-right[
The choice of differentially abundant taxa is done in a hierarchically consistent manner.

* `$m = 127$`, `$p=49$` split into two groups.

* Fold-changes of `$3$`, `$5$` and `$10$`.

* `$5$` estimated proportions of `$\pi_1$`.

* `$100$` replicates for each parameters.
]

---
# Results

`zazou` increases the TPR but does not always control the FDR.

---
# Results

`zazou` has better AUC and ROC curves.

---
# Association with age

.footnote[📄 Brito Yilmaz, et al. [Bri+16]]

`zazou` identifies phylogenetically coherent taxa.

---
class: center, middle, inverse

# Conclusions

---
# Conclusions

* Phylogeny does not capture the true structure of the data.

* Previous methods (hFDR, TreeFDR) does not work in practice.

* zazou algorithm improves performances a bit ...

* ... but the choice of the rejection threshold could be improved.

* R packages `correlationtree` and `zazou` are available on [GitHub](https://github.com/abichat).

* Articles published in [Frontiers in Microbiology](https://doi.org/10.3389/fmicb.2020.00649) and submitted in [Statistics and Computing](https://www.springer.com/journal/11222).

---
# Outlooks

* More theoretical work on zazou is required.

* `zazou` could be speed up.

* Use hierarchical information during testing step, and not only correction step.

* Use the framework of prediction instead of association.

---
name: final
class: end-slide

# Thanks!

## <a href="https://abichat.github.io/thesis">Manuscript</a>
## <a href="https://abichat.github.io" target="_blank">abichat.github.io</a>
## <a href="https://www.linkedin.com/in/antoinebichat/" target="_blank">antoinebichat</a>
## <a href="https://twitter.com/_abichat" target="_blank">@_abichat</a>
## <a href="https://github.com/abichat" target="_blank">@abichat</a>

---
# R packages

[evabic](https://abichat.github.io/evabic) evaluates the performance of binary classifiers. It can compute compute 19 different measures with tidy outputs.

[yatah](https://abichat.github.io/yatah) provides functions to manage taxonomy when lineages are described like `k__Bacteria|p__Proteobacteria|c__Gammaproteobacteria`.

[correlationtree](https://github.com/abichat/correlationtree) computes correlation trees.

[zazou](https://github.com/abichat/zazou) implements the zazou procedure.

[hadamardown](https://github.com/abichat/hadamardown) contains the Université Paris-Saclay PhD manuscript template for `bookdown`.

---
# Hierarchical FDR

.footnote[ 📄 Yekutieli [Yek08]; Sankaran and Holmes [SH14] ]This procedure inscreases statistical power by lessening the number of test to do with a descending method:
* test the family `$\mathcal{T}_0$`,

* if node `$t$` is rejected, test `$\mathcal{T}_t = \left\{H_i \mid \text{Par}(i) = t\right\}$` with a BH procedure at level `$\alpha$`.

---
count: false
# Hierarchical FDR
.footnote[ 📄 Yekutieli [Yek08]; Sankaran and Holmes [SH14] ]This procedure inscreases statistical power by lessening the number of test to do with a descending method:
* test the family `$\mathcal{T}_0$`,

* if node `$t$` is rejected, test `$\mathcal{T}_t = \left\{H_i \mid \text{Par}(i) = t\right\}$` with a BH procedure at level `$\alpha$`.

* if node `$t$` is rejected, test `$\mathcal{T}_t = \left\{H_i \mid \text{Par}(i) = t\right\}$` with a BH procedure at level `$\alpha$`.

* if node `$t$` is rejected, test `$\mathcal{T}_t = \left\{H_i \mid \text{Par}(i) = t\right\}$` with a BH procedure at level `$\alpha$`.

The FDR is controlled at level `$\alpha' = 1.44 \times \alpha \times \frac{\#\text{discoveries } +\text{ } \#\text{families tested}}{\#\text{discoveries } +\text{ } 1}$`.

---
# Correlation tree

.pull-left[
Matrix of pairwise correlation `$C$`

]

.pull-right[
Hierarchical clustering on `$1 - C$`

<center>
 <img src="img/cortree.png" height="400">
</center>
]

---
# Convergence to the correlation tree

---
# With Robinson-Foulds distance

.footnote[📄 Robinson and Foulds [RF81]]

---
# Hierarchically consistent taxa

.pull-left[
> The choice of differentially abundant taxa is done in a hierarchically consistent manner.

A partitioning around medoids (PAM) algorithm on the patristic distances matrix `$\left(d_{i,j}\right)_{i,j}$` is use for this purpose.

1 to 5 clusters among 20 are selected to be differentially abundant.
]

.pull-right[
<center>
 <img src="img/clusters.png" height="500">
</center>
]

---
# Quantitative results about FDP

<div class="tabwid"><table style='border-collapse:collapse;'><thead><tr style="overflow-wrap:break-word;"><td style="width:108px;background-color:transparent;vertical-align: middle;border-bottom: 2.00px solid rgba(0, 0, 0, 1.00);border-top: 2.00px solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:center;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:2px;padding-top:2px;padding-left:5px;padding-right:5px;background-color:transparent;">(in %)</td><td colspan="3" style="width:108px;background-color:transparent;vertical-align: middle;border-bottom: 2.00px solid rgba(0, 0, 0, 1.00);border-top: 2.00px solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:center;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:2px;padding-top:2px;padding-left:5px;padding-right:5px;background-color:transparent;">FDR</td><td colspan="3" style="width:108px;background-color:transparent;vertical-align: middle;border-bottom: 2.00px solid rgba(0, 0, 0, 1.00);border-top: 2.00px solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:center;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:2px;padding-top:2px;padding-left:5px;padding-right:5px;background-color:transparent;">P(FDP > 5%)</td></tr><tr style="overflow-wrap:break-word;"><td style="width:108px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(190, 190, 190, 1.00);border-top: 1.00px solid rgba(255, 255, 255, 0.00);border-left: 1.00px solid rgba(255, 255, 255, 0.00);border-right: 1.00px solid rgba(255, 255, 255, 0.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:center;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:0;padding-top:0;padding-left:0;padding-right:0;background-color:transparent;">method</td><td style="width:108px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(190, 190, 190, 1.00);border-top: 1.00px solid rgba(255, 255, 255, 0.00);border-left: 1.00px solid rgba(255, 255, 255, 0.00);border-right: 1.00px solid rgba(255, 255, 255, 0.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:center;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:0;padding-top:0;padding-left:0;padding-right:0;background-color:transparent;">fc = 3</td><td style="width:108px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(190, 190, 190, 1.00);border-top: 1.00px solid rgba(255, 255, 255, 0.00);border-left: 1.00px solid rgba(255, 255, 255, 0.00);border-right: 1.00px solid rgba(255, 255, 255, 0.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:center;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:0;padding-top:0;padding-left:0;padding-right:0;background-color:transparent;">fc = 5</td><td style="width:108px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(190, 190, 190, 1.00);border-top: 1.00px solid rgba(255, 255, 255, 0.00);border-left: 1.00px solid rgba(255, 255, 255, 0.00);border-right: 1.00px solid rgba(255, 255, 255, 0.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:center;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:0;padding-top:0;padding-left:0;padding-right:0;background-color:transparent;">fc = 10</td><td style="width:108px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(190, 190, 190, 1.00);border-top: 1.00px solid rgba(255, 255, 255, 0.00);border-left: 1.00px solid rgba(255, 255, 255, 0.00);border-right: 1.00px solid rgba(255, 255, 255, 0.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:center;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:0;padding-top:0;padding-left:0;padding-right:0;background-color:transparent;">fc = 3</td><td style="width:108px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(190, 190, 190, 1.00);border-top: 1.00px solid rgba(255, 255, 255, 0.00);border-left: 1.00px solid rgba(255, 255, 255, 0.00);border-right: 1.00px solid rgba(255, 255, 255, 0.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:center;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:0;padding-top:0;padding-left:0;padding-right:0;background-color:transparent;">fc = 5</td><td style="width:108px;background-color:transparent;vertical-align: middle;border-bottom: 1.00px solid rgba(190, 190, 190, 1.00);border-top: 1.00px solid rgba(255, 255, 255, 0.00);border-left: 1.00px solid rgba(255, 255, 255, 0.00);border-right: 1.00px solid rgba(255, 255, 255, 0.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:center;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:0;padding-top:0;padding-left:0;padding-right:0;background-color:transparent;">fc = 10</td></tr></thead><tbody><tr style="overflow-wrap:break-word;"><td style="width:108px;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:center;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:2px;padding-top:2px;padding-left:5px;padding-right:5px;background-color:transparent;">bh</td><td style="width:108px;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 1.00px solid rgba(190, 190, 190, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:center;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:2px;padding-top:2px;padding-left:5px;padding-right:5px;background-color:transparent;">2.69</td><td style="width:108px;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:center;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:2px;padding-top:2px;padding-left:5px;padding-right:5px;background-color:transparent;">2.46</td><td style="width:108px;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:center;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:2px;padding-top:2px;padding-left:5px;padding-right:5px;background-color:transparent;">3.23</td><td style="width:108px;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 1.00px solid rgba(190, 190, 190, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:center;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:2px;padding-top:2px;padding-left:5px;padding-right:5px;background-color:transparent;">4.40</td><td style="width:108px;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:center;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:2px;padding-top:2px;padding-left:5px;padding-right:5px;background-color:transparent;">7.20</td><td style="width:108px;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:center;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:2px;padding-top:2px;padding-left:5px;padding-right:5px;background-color:transparent;">12.20</td></tr><tr style="overflow-wrap:break-word;"><td style="width:108px;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:center;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:2px;padding-top:2px;padding-left:5px;padding-right:5px;background-color:transparent;">by</td><td style="width:108px;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 1.00px solid rgba(190, 190, 190, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:center;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:2px;padding-top:2px;padding-left:5px;padding-right:5px;background-color:transparent;">0.40</td><td style="width:108px;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:center;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:2px;padding-top:2px;padding-left:5px;padding-right:5px;background-color:transparent;">0.36</td><td style="width:108px;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:center;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:2px;padding-top:2px;padding-left:5px;padding-right:5px;background-color:transparent;">0.85</td><td style="width:108px;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 1.00px solid rgba(190, 190, 190, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:center;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:2px;padding-top:2px;padding-left:5px;padding-right:5px;background-color:transparent;">0.40</td><td style="width:108px;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:center;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:2px;padding-top:2px;padding-left:5px;padding-right:5px;background-color:transparent;">0.60</td><td style="width:108px;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:center;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:2px;padding-top:2px;padding-left:5px;padding-right:5px;background-color:transparent;">2.20</td></tr><tr style="overflow-wrap:break-word;"><td style="width:108px;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:center;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:2px;padding-top:2px;padding-left:5px;padding-right:5px;background-color:transparent;">tf</td><td style="width:108px;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 1.00px solid rgba(190, 190, 190, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:center;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:2px;padding-top:2px;padding-left:5px;padding-right:5px;background-color:transparent;">4.75</td><td style="width:108px;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:center;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:2px;padding-top:2px;padding-left:5px;padding-right:5px;background-color:transparent;">5.96</td><td style="width:108px;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:center;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:2px;padding-top:2px;padding-left:5px;padding-right:5px;background-color:transparent;">4.90</td><td style="width:108px;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 1.00px solid rgba(190, 190, 190, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:center;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:2px;padding-top:2px;padding-left:5px;padding-right:5px;background-color:transparent;">8.72</td><td style="width:108px;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:center;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:2px;padding-top:2px;padding-left:5px;padding-right:5px;background-color:transparent;">14.58</td><td style="width:108px;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:center;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:2px;padding-top:2px;padding-left:5px;padding-right:5px;background-color:transparent;">18.06</td></tr><tr style="overflow-wrap:break-word;"><td style="width:108px;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:center;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:2px;padding-top:2px;padding-left:5px;padding-right:5px;background-color:transparent;">ss</td><td style="width:108px;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 1.00px solid rgba(190, 190, 190, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:center;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:2px;padding-top:2px;padding-left:5px;padding-right:5px;background-color:transparent;">8.17</td><td style="width:108px;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:center;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:2px;padding-top:2px;padding-left:5px;padding-right:5px;background-color:transparent;">5.26</td><td style="width:108px;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:center;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:2px;padding-top:2px;padding-left:5px;padding-right:5px;background-color:transparent;">3.99</td><td style="width:108px;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 1.00px solid rgba(190, 190, 190, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:center;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:2px;padding-top:2px;padding-left:5px;padding-right:5px;background-color:transparent;">12.40</td><td style="width:108px;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:center;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:2px;padding-top:2px;padding-left:5px;padding-right:5px;background-color:transparent;">8.40</td><td style="width:108px;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:center;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:2px;padding-top:2px;padding-left:5px;padding-right:5px;background-color:transparent;">8.80</td></tr><tr style="overflow-wrap:break-word;"><td style="width:108px;background-color:transparent;vertical-align: middle;border-bottom: 2.00px solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:center;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:2px;padding-top:2px;padding-left:5px;padding-right:5px;background-color:transparent;">ci</td><td style="width:108px;background-color:transparent;vertical-align: middle;border-bottom: 2.00px solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 1.00px solid rgba(190, 190, 190, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:center;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:2px;padding-top:2px;padding-left:5px;padding-right:5px;background-color:transparent;">9.41</td><td style="width:108px;background-color:transparent;vertical-align: middle;border-bottom: 2.00px solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:center;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:2px;padding-top:2px;padding-left:5px;padding-right:5px;background-color:transparent;">5.98</td><td style="width:108px;background-color:transparent;vertical-align: middle;border-bottom: 2.00px solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:center;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:2px;padding-top:2px;padding-left:5px;padding-right:5px;background-color:transparent;">5.63</td><td style="width:108px;background-color:transparent;vertical-align: middle;border-bottom: 2.00px solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 1.00px solid rgba(190, 190, 190, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:center;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:2px;padding-top:2px;padding-left:5px;padding-right:5px;background-color:transparent;">14.80</td><td style="width:108px;background-color:transparent;vertical-align: middle;border-bottom: 2.00px solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:center;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:2px;padding-top:2px;padding-left:5px;padding-right:5px;background-color:transparent;">12.60</td><td style="width:108px;background-color:transparent;vertical-align: middle;border-bottom: 2.00px solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;"><p style="margin:0;text-align:center;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:2px;padding-top:2px;padding-left:5px;padding-right:5px;background-color:transparent;">18.60</td></tr></tbody></table></div>

---
# Negative simulations

When differentially abundant taxa are chosen uniformly.

---

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