Initial draft update alpha diversity chapter

inst/assets/bibliography.bib

@@ -1,3 +1,15 @@
+@article{bastiaanssen2023bugs1,
+  title={Bugs as features (part 1): concepts and foundations for the compositional data analysis of the microbiome--gut--brain axis},
+  author={Bastiaanssen, Thomaz FS and Quinn, Thomas P and Loughman, Amy},
+  journal={Nature Mental Health},
+  volume={1},
+  number={12},
+  pages={930--938},
+  doi = {10.1038/s44220-023-00148-3},
+
+  year={2023},
+  publisher={Nature Publishing Group US New York}
+}
 
 @Article{Xu2023,
   author =	 {Shuangbin Xu and Li Zhan and Wenli Tang and Qianwen Wang and Zehan Dai and Lang Zhou and Tingze Feng and Meijun Chen and Tianzhi Wu and Erqiang Hu and Guangchuang Yu},

inst/pages/alpha_diversity.qmd

@@ -5,82 +5,43 @@ library(rebook)
 chapterPreamble()
 ```
 
-Community diversity is a central concept in microbiome research. Several
-diversity indices are available in the ecological literature.
-
-The main categories of diversity indices include species richness,
-evenness, and diversity: each of these emphasizes different aspects of
-the community heterogeneity [@Whittaker1960], [@Willis2019]. The _Hill
-coefficient_ combines many standard indices into a single equation
-that provides observed richness, inverse Simpson, Shannon diversity,
-and generalized diversity as special cases, with varying levels of
-emphasis on species abundance values. Thus, the term _alpha diversity_
-is often used to collectively refer to all these variants.
-
-**Diversity** summarizes the distribution of
-  species abundances in a given sample into a single number that
-  depends on both species richness and evenness (see below). Diversity
-  indices measure the overall community heterogeneity that considers
-  both of these aspects simultaneously. A number of ecological
-  diversity measures are available. In general, diversity increases
-  together with increasing richness and evenness. **Phylogenetic
-  diversity** (PD), [@Faith1992], is a variant that incorporates
-  information from phylogenetic relationships between species, unlike
-  most other commonly used diversity indices. The `addAlpha()`
-  function uses a faster reimplementation of the widely used function
-  in _`picante`_ [@R_picante, @Kembel2010]. The method uses the
-  default rowTree from the `TreeSummarizedExperiment` object (`tse`).
-
-**Richness** refers to the total number of species in a community
-  (sample). The simplest richness index is the number of species
-  observed in a sample (observed richness). Assuming limited sampling
-  from the community, however, this may underestimate the true species
-  richness. Several estimators have been developed to address this,
-  including for instance ACE [@Chao1992] and Chao1 [@Chao1984]
-  indices. Richness estimates do not aim to characterize variations in
-  species abundances.
-
-Nonparametric richness estimators such as Chao1 and ACE, however, must not be 
-used with amplicon sequence variant (ASV) data. Algorithms that generate ASVs, 
-like DADA2 and Deblur, typically remove singletons, which are essential for 
-these richness calculations. This removal leads to meaningless results. 
-Although ASVs offer higher resolution than operational taxonomic units (OTUs) 
-and are increasingly used, the removal of singletons invalidates the application 
-of Chao1 and ACE. Therefore, alternative alpha diversity metrics that do not 
-depend on singletons or doubletons should be considered, or OTUs could be 
-used specifically for alpha diversity analysis to retain low-abundance taxa.
-Additionally, the inability of denoising algorithms to distinguish true 
-singleton sequences from artifacts further complicates the issue, making 
-traditional richness estimators unsuitable for ASV datasets, which are often 
-standardized for sequencing depth.[@Deng2024]
-
-**Evenness** focuses on the distribution of species abundances, and it
-  can thus complement the number of species. Pielou's evenness is a
-  commonly used index, obtained by normalizing Shannon diversity by
-  (the natural logarithm of) observed richness.
-
-These main classes of alpha diversity are sometimes complemented with
-indices of dominance or rarity:
-
-**Dominance** indices are in general negatively correlated with alpha
-  diversity. A high dominance is obtained when one or a few species have
-  a high share of the total species abundance in the community. Note
-  that dominance indices are generally inversely correlated with other
-  alpha diversity indices.
-
-**Rarity** indices characterize the concentration of species at low
-  abundance.  Prevalence and detection thresholds determine rare
-  species whose total concentration will determine the value of a
-  rarity index.
+Alpha diversity, diversity within a sample, is a central concept in microbiome 
+research. In ecological literature, several distinct but related alpha diversity
+indices, often referring to richness, evenness and diversity, are commonly used 
+[@Whittaker1960], [@Willis2019]. The term _alpha diversity_ is often used to 
+collectively refer to all these indices.
+
+
+The majority of alpha diversity indices are closely related, though this is not 
+evident from their names. It is helpful to understand an alpha diversity metric 
+through two factors. First, alpha diversity measures can be defined as special 
+cases of a unifying equation where the _Hill coefficient_ determines whether the
+equation captures richness, inverse Simpson, Shannon diversity or generalized 
+diversity. Secondly, alpha diversity indices vary in whether they are weighed by
+phylogeny [@Faith1992]. The figure below further illustrates this classification 
+using several popular alpha diversity metrics, adapted with permission [@bastiaanssen2023bugs1]. 
+
+![Alpha Diversity metrics are numerically related and can be classified along two axes. Here, we show Hill coefficient on the x-axis and whether the index considers phylogeny on the y-axis](alpha_diversity_files/figure-html/alpha_div_fig.png) 
+
+
+
+::: {.callout-note}
+## Note: Richness estimators and denoising
+
+Several estimators have been developed to address the confounding effect of 
+limited sampling size on observed richness, most notably ACE [@Chao1992] and 
+Chao1 [@Chao1984]. Notably, these approaches may yield misleading results for 
+modern 16S data, which commonly features denoising and removal of singletons 
+[@Deng2024]. 
+:::
 
 ## Alpha diversity estimation in practice
 
 ### Calculate diversity measures {#sec-estimate-diversity}
 
-Alpha diversity can be estimated with `addAlpha()` wrapper function that interact
-with other packages implementing the calculation, such as `vegan`
-[@R_vegan].
 
+Alpha diversity can be estimated with the `addAlpha()` function, which interacts
+with other packages implementing the calculation, such as `vegan` [@R_vegan].  
 These functions calculate the given indices, and add them to the
 `colData` slot of the `SummarizedExperiment` object with the given
 `name`.
@@ -148,15 +109,16 @@ pairwise.wilcox.test(
 ### Faith phylogenetic diversity {#sec-faith-diversity}
 
 The Faith index is returned by the function `addAlpha()`. It utilizes the widely
-used function in _`picante`_ [@R_picante, @Kembel2010].
+used function in _`picante`_ [@R_picante, @Kembel2010]. The method uses the 
+default rowTree from the `TreeSummarizedExperiment` object (`tse`).
 
 ```{r phylo-div-1}
 tse <- addAlpha(tse, assay.type = "counts", index = "faith")
 tse$faith |> head()
 ```
 
 ::: {.callout-note}
-## Note
+## Note: Requires phylogenetic tree
 
 Because `tse` is a `TreeSummarizedExperiment` object, its phylogenetic tree is
 used by default. However, the optional argument `tree` must be provided if