From d55eef50e86b5b3d0ff9c42d6a4787bf3a9fdfe1 Mon Sep 17 00:00:00 2001
From: Sophia120199 <105356774+Sophia120199@users.noreply.github.com>
Date: Thu, 29 Jun 2023 14:02:58 +0200
Subject: [PATCH 01/36] Create tutorial.md
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+---
+layout: tutorial_hands_on
+title: Calculating α and β diversity with Krakentools
+zenodo_link: xxx
+questions:
+- How many different species are present in my sample? How do I additionally take their relative abundance into account?
+- How similar or how dissimilar are my samples?
+- What are the different metrics used to calculate the diversity of my samples?
+objectives:
+- Explain what diversity is
+- Explain different metrics to calculate α and β diversity
+- Apply Krakentools to calculate α and β diversity and understand the output
+level: Introductory
+key_points:
+- There are 2 different types of diversity metrics (α and β diversity)
+- Krakentools can be used in Galaxy for calculating the diversity
+time_estimation: 20M
+contributions:
+ authorship:
+ - sophia120199
+ - bebatut
+tags:
+- metagenomics
+- diversity
+---
+
+# Introduction
+
+A **diversity index** is a quantitative measure that is used to assess the level of diversity or variety within a particular system, such as a biological community, a population, or a workplace. It provides a way to capture and quantify the distribution of different types or categories within a system.
+
+In various fields, diversity indexes are employed to understand and compare the composition and richness of various elements. Apart from ecology, fields such as social and cultural science are interested in the diversity within a population or workplace. In these cases, the indexes may consider factors like age, gender, ethnicity, or other relevant characteristics to assess the diversity and inclusiveness of a group or organization.
+
+To study microbiome data, indirect methods like **metagenomics** can be used. Metagenomic samples contain DNA from different organisms at a specific site, where the sample was collected. Metagenomic data can be used to find out which organisms coexist in that niche and which genes are present in the different organisms.
+
+Once we know which species are present in a metagenomic sample ([Tutorial on Taxonomic Profiling and Visualization of Metagenomic Data](https://training.galaxyproject.org/training-material/topics/metagenomics/tutorials/taxonomic-profiling/tutorial.html])), we can do diversity analyses.
+
+Related to ecology, the term **diversity** describes the number of different species present in one particular area and their relative abundance. More specifically, several different metrics of diversity can be calculated. The most common ones are α, β and γ diversity:
+
+- **α diversity** describes the diversity within a community
+
+ It considers the number of different species in an environment (also referred to as species **richness**). Additionally, it can take the abundance of each species into account to measure how evenly individuals are distributed across the sample (also referred to as species **evenness**).
+
+ xxx
+ ![richness and evenness](../images/richness_evenness.png "richness and evenness")
+
+- **β diversity** measures the distance between two or more separate entities
+
+ It therefore describes the difference between two communities or ecosystems.
+
+- **γ diversity** is a measure of the overall diversity for the different ecosystems within a region.
+
+ xxx
+ ![α, β and γ diversity](../images/diversity_differences.png "α, β and γ diversity")
+
+In this analysis we will use Galaxy for calculating the Shannon's alpha diversity index and the Bray-Curtis dissimilarity index for β diversity.
+
+# Background on data
+
+The dataset we will use for this tutorial comes from an oasis in the Mexican desert called Cuatro Ciénegas ({% cite Okie.2020 %}). The researchers were interested in genomic traits that affect the rates and costs of biochemical information processing within cells. They performed a whole-ecosystem experiment, thus fertilizing the pond to achieve nutrient enriched conditions.
+
+Here we will use 2 datasets:
+- `JP4D`: a microbiome sample collected from the Lagunita Fertilized Pond
+- `JC1A`: a **control** samples from a control mesocosm.
+
+The datasets differ in size, but according to the authors this doesn't matter for their analysis of genomic traits. Also, they underline that differences between the two samples reflect trait-mediated ecological dynamics instead of microevolutionary changes as the duration of the experiment was only 32 days. This means that depending on available nutrients, specific lineages within the pond grow more successfully than others because of their genomic traits.
+
+The datafiles are named according to the first four characters of the filenames.
+
+Originally, it was a collection of paired-end data with R1 being the forward reads and R2 being the reverse reads. The samples have than been analysed as explained in the [Taxonomic profiling tutorial]({% link topics/sequence-analysis/tutorials/taxonomic-profiling/tutorial.md %}).
+
+In a nutshell, taxonomic labels have been assigned to the metagenomics data using [Kraken2](toolshed.g2.bx.psu.edu/repos/iuc/kraken2/kraken2/2.1.1+galaxy1) to find out which species are present in the samples. Finally, species abundance was estimated using [Bracken](toolshed.g2.bx.psu.edu/repos/iuc/bracken/est_abundance/2.7+galaxy1). For this tutorial, we will use the output file of Bracken.
+
+Here, to get an overview, you can find a Krona chart visualizing the different species present in the two samples.
+
+
+
+The dataset we will work with in this tutorial is the output file of Bracken, which estimates species abundance.
+
+![Output file of Bracken](../images/bracken_output.png "Output file of Bracken")
+
+xxx output file description
+
+# Prepare Galaxy and data
+
+Any analysis should get its own Galaxy history. So let's start by creating a new one:
+
+> Data upload
+>
+> 1. Create a new history for this analysis
+>
+> {% snippet faqs/galaxy/histories_create_new.md %}
+>
+> 2. Rename the history
+>
+> {% snippet faqs/galaxy/histories_rename.md %}
+>
+{: .hands_on}
+
+We need now to import the data
+
+> Import datasets
+>
+> 1. Import the following samples via link from [Zenodo]({{ page.zenodo_link }}) or Galaxy shared data libraries:
+>
+> ```text
+> {{ page.zenodo_link }}/files/xxx
+> {{ page.zenodo_link }}/files/xxx
+
+> ```
+>
+> {% snippet faqs/galaxy/datasets_import_via_link.md %}
+> {% snippet faqs/galaxy/datasets_import_from_data_library.md %}
+>
+> 2. 3. Create a paired collection.
+>
+> {% snippet faqs/galaxy/collections_build_list_paired.md %}
+>
+{: .hands_on}
+
+# Calculating α diversity
+
+**α diversity** describes the diversity within a community. There are several different indexes used to calculate α diversity because different indexes capture different aspects of diversity and have varying sensitivities to different factors. These indexes have been developed to address specific research questions, account for different ecological or population characteristics, or highlight certain aspects of diversity.
+
+There are various measures of alpha diversity accessible:
+- **richness** indexes that estimate the quantity of distinct species within a sample
+- **evenness** indexes that evaluate the relative abundances of species rather than their total count
+- **diversity** indexes that incorporate both the relative abundances and total count of distinct species
+
+In the table below you can find a list of commonly used indexes to calculate α diversity and their description.
+
+![α diversity](../images/alphadiversity_metrics.png "α diversity")
+
+| Indices for α diversity | Description | Class |
+| ----------------------- | --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | --------- |
+| Shannons | Calculates the uncertainty in predicting the species identity of an individual that is selected from a community. | Diversity |
+| Berger-Parker | Expresses the proportional importance of the most abundant type. Highly biased by sample size and richness. | Diversity |
+| Simpsons | Calculates the probability that two individuals selected from a community will be of the same species. Obtains small values in datasets of high diversity and large values in datasets of low diversity. | Diversity |
+| Inverse Simpons | Transformation of Simpsons index that increases with increasing diversity. | Diversity |
+| Fishers | Describes the relationship between the number of species and the number of individuals in those species. Parametric index of diversity that assumes that the abundance of species follows a log series distribution. | Diversity |
+| Pielou’s evenness | Quantifies how close the community’s diversity is to the maximum possible diversity. This index is calculated by taking the Shannon Diversity Index (which measures the overall diversity of the community) and dividing it by the maximum possible diversity given the observed species richness. | Evenness |
+| Margalef’s richness | Indicates the estimated species richness, accounting for the community size. This metric takes into account that a larger community size can support a greater number of species. | Richness |
+| Chao1 | Estimates the true species richness or diversity of a community, particularly when there might be rare or unobserved species. Chao1 estimates the number of unobserved species based on the number of singletons and doubletons. It assumes that there are additional rare species that are likely to exist but have not been observed. The estimation considers the number of unobserved singletons and doubletons and incorporates them into the observed species richness to provide an estimate of the true species richness. | Richness |
+| ACE | ACE (Abundance-based Coverage Estimator) takes into account the abundance distribution of observed species and incorporates the presence of rare or unobserved species. ACE estimates the number of unobserved species based on the abundance distribution and incorporates it into the observed species richness. It takes into account the relative rarity of observed species and uses this information to estimate the true species richness. | Richness | |
+
+> Mathematical expressions for calculating α diversity
+
+
+| Index | Mathematical Expression | Description |
+| ------------------- | ----------------------------------------------------------------------------------------------- | ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |
+| Simpson | D = ∑i=1S (ni/N)2 | ni is the number of individuals in species i, N = total number of individuals of all species, and ni/N = pi (proportion of individuals of species i), and S = species richness. |
+| Shannon | H' = -∑i=1S pi \* ln(pi) | pi = proportion of individuals of species i, and ln is the natural logarithm, and S = species richness. |
+| Berger-Parker | D = nmax/N | nmax is the abundance of the most dominant species, and N is the total number of individuals (sum of all abundances). |
+| Fisher's alpha | S\=a\*ln(1+n/a) | S is number of taxa, n is number of individuals and a is the Fisher's alpha. |
+| Pilou's Evenness | J = H'/ln(S) | H' is Shannon Weiner diversity and S is the total number of species in a sample, across all samples in dataset. |
+| Margalef's richness | D = (S - 1) / Log (n) | S is the total number of species, and n is the total number of individuals in the sample |
+| Chao1 | Schao1 = Sobs + (n1(n1 - 1))/(2(n2 + 1)) | Sobs is the observed species richness, n1 represents the number of species represented by a single individual (singletons), and n2 represents the number of species represented by two individuals (doubletons). |
+
+{: .details}
+
+Krakentools introduction + metrics available there
+
+> Calculate α diversity with Krakentools
+>
+> 1. {% tool [Krakentools: Calculate alpha diversity]([toolshed.g2.bx.psu.edu/view/iuc/krakentools_alpha_diversity/9d0330e23bfd)) %} with the following parameters:
+> - *"Abundance file"*: `Dataset Collection`: uploaded Bracken output file
+>
+> - *"Specify alpha diversity type"*: `Shannon's alpha diversity`
+>
+>
+{: .hands_on}
+
+
+
+>
+>
+> 1. Calculate the 5 different alpha indexes available in Krakentools and compare the results. What do these numbers tell you?
+> 2. Are the results consistent among the different indexes?
+>
+> >
+> >
+> > 1.
+
+| | JC1A | JP4D | Explanation |
+|-----------|-----------|-----------|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
+| Shannon | 5.3441 | 6.4429 | When the Shannon index is given as a value of 5, it indicates a relatively high level of diversity within the community. The index ranges from 0 to a maximum value that depends on the number of species and their relative abundances. The higher the Shannon index value, the greater the diversity within the community. |
+| Berger-Parker | 0.2299 | 0.0581 | When the Berger-Parker index is given as a value of 0.23, it suggests that a single species dominates the community, as it represents 23% of the total individuals in the community. This indicates a relatively low level of species evenness, meaning that the abundance of individuals is heavily skewed towards one dominant species. In contrast to the Shannon index, which considers both species richness and evenness, the Berger-Parker index emphasizes the dominance of a particular species. A value of 0.23 indicates that the community is heavily influenced by one species, while the other species in the community are less abundant. In the case of JP4D, the dominant species accounts for only 5% of the total individuals, which implies a more balanced distribution of individuals among different species compared to a higher Berger-Parker index value. |
+| Simpson | 0.9401 | 0.9926 | When the Simpson's index is given as a value of 0.94, it indicates a high level of species diversity and evenness within the community. The index ranges from 0 to 1, with 1 representing maximum diversity. Therefore, a Simpson's index of 0.94 suggests that the community is highly diverse, with a relatively even distribution of individuals among different species. In other words, the value of 0.94 indicates that if you were to randomly select two individuals from the community, there is a 94% probability that they would belong to different species. This implies a rich and balanced community where multiple species coexist in relatively equal abundance. |
+| Inverse Simpson | 16.6941 | 136.0287 | When the Inverse Simpson's index is given as a value of 16.69, it suggests a relatively low level of species diversity within the community. The index ranges from 1 to the total number of species in the community, with higher values indicating higher diversity. Therefore, a value of 16.69 indicates a lower diversity compared to a higher index value. An Inverse Simpson's index of 136 suggests a relatively high level of species diversity within the community. The index ranges from 1 to the total number of species in the community, with higher values indicating greater diversity. Therefore, a value of 136 indicates a higher diversity compared to a lower index value. The Inverse Simpson's index is the reciprocal of the Simpson's index, which quantifies species diversity and evenness within a community. A higher Inverse Simpson's index value signifies a community with a greater number of species and a more even distribution of individuals among those species. |
+| Fisher | 3240.0957 | 9163.5027 | > >
+> > 2. The results are consistent as all indexes show JP4D to be the more diverse sample compared to JC1A.
+ |
+
+> {: .solution}
+>
+{: .question}
+
+
+>
+
+>Apart from Krakentools, there are two more tools available in Galaxy that can be used to calculate diversity indexes, QIIME2 and Vegan.
+
+
+> QIIME 2 (Quantitative Insights Into Microbial Ecology 2) is a powerful open-source bioinformatics software package that provides a comprehensive suite of tools and methods for processing, analyzing, and visualizing microbiome data. It offers a modular approach to microbiome analysis, allowing researchers to build flexible analysis pipelines tailored to their specific research goals. The software supports a wide range of data types, including 16S rRNA gene sequencing, metagenomics, metatranscriptomics, and others.
+>
+>Some of the key features and functionalities of QIIME 2 include:
+>1. Data Import and Preprocessing: QIIME 2 supports the import of raw sequencing data and performs quality control and data preprocessing steps, such as demultiplexing, quality filtering, and primer removal.
+>2. Taxonomic Assignments: The software enables taxonomic classification of microbial sequences using various algorithms and reference databases.
+>3. Diversity Analysis: QIIME 2 allows users to explore and quantify microbial diversity within and between samples. It provides metrics for alpha diversity (within-sample diversity) and beta diversity (between-sample diversity).
+>4. Community Analysis: Users can investigate the composition and structure of microbial communities, including taxonomic summaries, abundance profiles, and statistical comparisons between groups.
+>5. Phylogenetic Analysis: QIIME 2 supports the construction of phylogenetic trees to infer evolutionary relationships among microbial taxa and perform phylogenetic diversity analysis.
+>6. Statistical Analysis: The software offers a wide range of statistical methods for differential abundance analysis, correlation analysis, multivariate analysis, and other types of statistical tests.
+>7. Visualization: QIIME 2 provides interactive and customizable visualizations to aid in the exploration and interpretation of microbiome data, including heatmaps, bar plots, PCoA plots, and taxonomic trees.
+
+>The vegan package is a community ecology package in the R programming language. It provides a wide range of tools and methods for analyzing and interpreting ecological data, particularly in the context of community ecology. The package is designed to handle multivariate data and offers various statistical techniques for studying species composition, diversity, and community dynamics.
+
+>The vegan package encompasses several functionalities, including:
+
+>1. Diversity Analysis: vegan offers numerous diversity indices, such as species richness, Shannon diversity index, Simpson index, and many others. These indices allow researchers to quantify the diversity of species within a community and compare diversity between different samples or groups.
+>2. Community Similarity: The package provides tools for measuring community similarity or dissimilarity, including popular metrics such as Bray-Curtis dissimilarity and Jaccard index. These metrics allow researchers to assess the degree of similarity between communities and perform clustering or ordination analyses.
+>3. Ordination Techniques: vegan includes several ordination methods, such as Principal Component Analysis (PCA), Correspondence Analysis (CA), Non-Metric Multidimensional Scaling (NMDS), and Canonical Correspondence Analysis (CCA). These techniques aid in visualizing and exploring patterns in multivariate ecological data.
+>4. Community Classification: The package offers tools for performing community classification and assessing the significance of group differences. It includes methods such as Permutational Multivariate Analysis of Variance (PERMANOVA) and Analysis of Similarities (ANOSIM).
+>5. Ecological Network Analysis: vegan provides functions for analyzing ecological networks, including network visualization, calculation of network metrics (e.g., connectance, centrality), and testing network structure.
+>6. Ecological Indices: The package includes various ecological indices, such as niche overlap indices, indicator species analysis, and null model analysis for testing community patterns against null hypotheses.
+>7. Plotting and Visualization: vegan offers flexible plotting functions to visualize ecological data, including bar plots, scatter plots, biplots, and ordination plots.
+
+{: .comment}
+
+# Calculating β diversity
+
+**β diversity** measures the distance between two or more separate entities. It therefore describes the difference between two communities or ecosystems.
+
+There are **multiple indexes** used to calculate β diversity because different indexes emphasize different aspects of compositional dissimilarity between communities or sites.
+
+These indexes have been developed to address specific research questions, accommodate different data types, or provide insights into different dimensions of β diversity. In the table below you can find a list of commonly used indexes to calculate β diversity and their description.
+
+
+
+| Indices for β diversity | Description |
+|---------------------------------|--------------------------------------------------------------------------------------|
+| Jaccard Index | Measures the proportion of shared species between two samples |
+| Sørensen Index | Similar to Jaccard Index, but accounts for species abundance |
+| Bray-Curtis Dissimilarity | Measures the dissimilarity of species abundances between two samples |
+| Kulczynski Dissimilarity | Measures the dissimilarity in the proportional abundances of shared species |
+|UniFrac|Incorporates information on phylogenetic distances between observed species in the computation. Can be calculated either weighted (accounts for abundances) or unweighted (accounts only for richness).|
+
+> More details on calculating β diversity
+
+| Index | Mathematical Expression | Description |
+| ------------------------- | ---------------------------------------------------------------------------- | --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |
+| Jaccard Index | J(X, Y) = \vert X ∩ Y \vert / \vert X ∪ Y\vert | X ∩ Y represents the intersection of sets X and Y (elements common to both sets), and X ∪ Y represents the union of sets X and Y (all unique elements from both sets combined). |
+| Sørensen Index | DSC = 2 \vert X ∩ Y \vert / \vert X \vert + \vert Y \vert | X ∩ Y represents the intersection of sets X and Y (elements common to both sets), and \vert X \vert and \vert Y \vert are the cardinalities of the two sets (i.e. the number of elements in each set) |
+| Bray-Curtis Dissimilarity | BCij = 1 - (2Cij / (Si + Sj)) | Cij represents the sum of the absolute differences in abundances between corresponding species in samples i and j, Si represents the total abundance or sum of species abundances in sample i, and Sj represents the total abundance or sum of species abundances in sample j. |
+| Kulczynski Dissimilarity | D = 1 - (SAB / (SA + SB - 2SAB)) | SAB the number of shared OTUs between communities A and B, SA the number of OTUs in community A, and SB the number of OTUs in community B |
+
+
+xxx
+![UniFrac](../images/unifrac.png "UniFrac")
+
+
+{: .details}
+
+## Hands on: Calculate β diversity with Krakentools
+
+> Calculate α and β diversity with Krakentools
+>
+>
+> {% tool [Krakentools: Calculate beta diversity (Bray-Curtis dissimilarity)]([https://toolshed.g2.bx.psu.edu/view/iuc/krakentools_beta_diversity/b33f117e9b67]) %} with the following parameters:
+> - *"Taxonomy file"*: `Dataset Collection`: uploaded Bracken output file
+>
+> - *"Specify type of input file"*: `Bracken species abundance file`
+{: .hands_on}
+
+>
+>
+> 1. What is the Bray-Curtis dissimilarity calculated for the two samples?
+> 2. What does this number tell you?
+>
+> >
+> >
+> > 1. xxx
+> > 2. The Bray-Curtis dissimilarity measures the dissimiliraty of two samples. Consequently, an output of 0 represents two samples that are exactly the same, while an output of 1 means they are maximally divergent. In our case, xxx
+> {: .solution}
+>
+{: .question}
+
+# Conclusion
+
+In this tutorial, we look how to calculate α and β diversity from microbiome data. We apply **Krakentools** to calculate the α and β diversity of two microbiome sample datasets.
From 4fa2ff70fa1164feb127f1d595f8d4062cfca37e Mon Sep 17 00:00:00 2001
From: Sophia120199 <105356774+Sophia120199@users.noreply.github.com>
Date: Thu, 29 Jun 2023 14:03:45 +0200
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From 31ded0e366859ce2e22df2383a7b906f6520f446 Mon Sep 17 00:00:00 2001
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Date: Thu, 29 Jun 2023 14:04:58 +0200
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From 9d4143aa041f072fc755dc820dcacc338b02000b Mon Sep 17 00:00:00 2001
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From 8036206af9c9caa27d9511ca9dad16cfde69137c Mon Sep 17 00:00:00 2001
From: Sophia120199 <105356774+Sophia120199@users.noreply.github.com>
Date: Thu, 29 Jun 2023 14:06:33 +0200
Subject: [PATCH 05/36] Update tutorial.bib
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@@ -1 +1,139 @@
+% This file was created with Citavi 6.14.4.0
+
+@article{Berger.1970,
+ abstract = {The diversity of a planktonic foraminiferal assemblage on the ocean floor depends on the state of preservation of that assemblage. As dissolution progresses, species diversity (number of species in the assemblage) decreases, but compound diversity (based on relative species abundance) first increases and then decreases; species dominance first decreases and then increases. The reason for these changes is that the species most susceptible to solution deliver moresediment to the ocean floor than do species with solution-resistant shells, possibly because the more soluble tests are produced in surface waters, where growth and production are greatest.},
+ author = {Berger, W. H. and Parker, F. L.},
+ year = {1970},
+ title = {Diversity of planktonic foraminifera in deep-sea sediments},
+ pages = {1345--1347},
+ volume = {168},
+ number = {3937},
+ issn = {0036-8075},
+ journal = {Science (New York, N.Y.)},
+ doi = {10.1126/science.168.3937.1345.}
+}
+
+
+@article{Bolyen.2019,
+ author = {Bolyen, Evan and Rideout, Jai Ram and Dillon, Matthew R. and Bokulich, Nicholas A. and Abnet, Christian C. and Al-Ghalith, Gabriel A. and Alexander, Harriet and Alm, Eric J. and Arumugam, Manimozhiyan and Asnicar, Francesco and Bai, Yang and Bisanz, Jordan E. and Bittinger, Kyle and Brejnrod, Asker and Brislawn, Colin J. and Brown, C. Titus and Callahan, Benjamin J. and Caraballo-Rodr{\'i}guez, Andr{\'e}s Mauricio and Chase, John and Cope, Emily K. and {Da Silva}, Ricardo and Diener, Christian and Dorrestein, Pieter C. and Douglas, Gavin M. and Durall, Daniel M. and Duvallet, Claire and Edwardson, Christian F. and Ernst, Madeleine and Estaki, Mehrbod and Fouquier, Jennifer and Gauglitz, Julia M. and Gibbons, Sean M. and Gibson, Deanna L. and Gonzalez, Antonio and Gorlick, Kestrel and Guo, Jiarong and Hillmann, Benjamin and Holmes, Susan and Holste, Hannes and Huttenhower, Curtis and Huttley, Gavin A. and Janssen, Stefan and Jarmusch, Alan K. and Jiang, Lingjing and Kaehler, Benjamin D. and Kang, Kyo Bin and Keefe, Christopher R. and Keim, Paul and Kelley, Scott T. and Knights, Dan and Koester, Irina and Kosciolek, Tomasz and Kreps, Jorden and Langille, Morgan G. I. and Lee, Joslynn and Ley, Ruth and Liu, Yong-Xin and Loftfield, Erikka and Lozupone, Catherine and Maher, Massoud and Marotz, Clarisse and Martin, Bryan D. and McDonald, Daniel and McIver, Lauren J. and Melnik, Alexey V. and Metcalf, Jessica L. and Morgan, Sydney C. and Morton, Jamie T. and Naimey, Ahmad Turan and Navas-Molina, Jose A. and Nothias, Louis Felix and Orchanian, Stephanie B. and Pearson, Talima and Peoples, Samuel L. and Petras, Daniel and Preuss, Mary Lai and Pruesse, Elmar and Rasmussen, Lasse Buur and Rivers, Adam and Robeson, Michael S. and Rosenthal, Patrick and Segata, Nicola and Shaffer, Michael and Shiffer, Arron and Sinha, Rashmi and Song, Se Jin and Spear, John R. and Swafford, Austin D. and Thompson, Luke R. and Torres, Pedro J. and Trinh, Pauline and Tripathi, Anupriya and Turnbaugh, Peter J. and Ul-Hasan, Sabah and {van der Hooft}, Justin J. J. and Vargas, Fernando and V{\'a}zquez-Baeza, Yoshiki and Vogtmann, Emily and von Hippel, Max and Walters, William and Wan, Yunhu and Wang, Mingxun and Warren, Jonathan and Weber, Kyle C. and Williamson, Charles H. D. and Willis, Amy D. and Xu, Zhenjiang Zech and Zaneveld, Jesse R. and Zhang, Yilong and Zhu, Qiyun and Knight, Rob and Caporaso, J. Gregory},
+ year = {2019},
+ title = {Reproducible, interactive, scalable and extensible microbiome data science using QIIME 2},
+ pages = {852--857},
+ volume = {37},
+ number = {8},
+ journal = {Nature biotechnology},
+ doi = {10.1038/s41587-019-0209-9}
+}
+
+
+@article{Bray.1957,
+ author = {Bray, J. Roger and Curtis, J. T.},
+ year = {1957},
+ title = {An Ordination of the Upland Forest Communities of Southern Wisconsin},
+ pages = {325--349},
+ volume = {27},
+ number = {4},
+ issn = {0012-9615},
+ journal = {Ecological Monographs},
+ doi = {10.2307/1942268}
+}
+
+
+@article{Chao.1992,
+ author = {Chao, Anne and Lee, Shen-Ming},
+ year = {1992},
+ title = {Estimating the Number of Classes via Sample Coverage},
+ pages = {210--217},
+ volume = {87},
+ number = {417},
+ issn = {0162-1459},
+ journal = {Journal of the American Statistical Association},
+ doi = {10.1080/01621459.1992.10475194}
+}
+
+
+@article{Fisher.1943,
+ author = {Fisher, R. A. and Corbet, A. Steven and Williams, C. B.},
+ year = {1943},
+ title = {The Relation Between the Number of Species and the Number of Individuals in a Random Sample of an Animal Population},
+ pages = {42},
+ volume = {12},
+ number = {1},
+ issn = {00218790},
+ journal = {The Journal of Animal Ecology},
+ doi = {10.2307/1411}
+}
+
+
+@article{Jaccard.1912,
+ author = {Jaccard, Paul},
+ year = {1912},
+ title = {THE DISTRIBUTION OF THE FLORA IN THE ALPINE ZONE.1},
+ pages = {37--50},
+ volume = {11},
+ number = {2},
+ issn = {0028-646X},
+ journal = {New Phytologist},
+ doi = {10.1111/j.1469-8137.1912.tb05611.x}
+}
+
+
+@article{Margalef.,
+ author = {Margalef, Ramon},
+ title = {Information Theory in Ecology},
+ pages = {36--71},
+ volume = {1958},
+ number = {3},
+ journal = {General Systems}
+}
+
+
+@article{Pielou.1966,
+ author = {Pielou, E. C.},
+ year = {1966},
+ title = {The measurement of diversity in different types of biological collections},
+ pages = {131--144},
+ volume = {13},
+ issn = {00225193},
+ journal = {Journal of Theoretical Biology},
+ doi = {10.1016/0022-5193(66)90013-0}
+}
+
+
+@article{Shannon.1948,
+ author = {Shannon, C. E.},
+ year = {1948},
+ title = {A Mathematical Theory of Communication},
+ pages = {379--423},
+ volume = {27},
+ number = {3},
+ issn = {00058580},
+ journal = {Bell System Technical Journal},
+ doi = {10.1002/j.1538-7305.1948.tb01338.x}
+}
+
+
+@article{SIMPSON.1949,
+ author = {SIMPSON, E. H.},
+ year = {1949},
+ title = {Measurement of Diversity},
+ pages = {688},
+ volume = {163},
+ number = {4148},
+ issn = {0028-0836},
+ journal = {Nature},
+ doi = {10.1038/163688a0}
+}
+
+
+@article{Srensen.1948,
+ author = {S{\o}rensen, T.},
+ year = {1948},
+ title = {A method of establishing groups of equal amplitude in plant sociology based on similarity of species and its application to analyses of the vegetation on Danish commons},
+ pages = {1--34},
+ number = {5},
+ journal = {Kongelige Danske Videnskabernes Selskab.}
+}
+
+
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From: Sophia120199 <105356774+Sophia120199@users.noreply.github.com>
Date: Thu, 29 Jun 2023 14:07:21 +0200
Subject: [PATCH 06/36] Add files via upload
---
.../alpha_diversity_richness_evenness.png | Bin 0 -> 36755 bytes
.../images/alphadiversity_metrics.png | Bin 0 -> 314303 bytes
.../diversity/images/bracken_output.png | Bin 0 -> 69955 bytes
.../diversity/images/diversity_differences.png | Bin 0 -> 334476 bytes
.../tutorials/diversity/images/unifrac.png | Bin 0 -> 479843 bytes
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