@article{lozupone2008metaunifrac,
	author = {Lozupone, Catherine A. and Hamady, Micah and Cantarel, Brandi L. and Coutinho, Pedro M. and Henrissat, Bernard and Gordon, Jeffrey I. and Knight, Rob},
	title = {The convergence of carbohydrate active gene repertoires in human gut microbes},
	volume = {105},
	number = {39},
	pages = {15076--15081},
	year = {2008},
	doi = {10.1073/pnas.0807339105},
	publisher = {National Academy of Sciences},
	abstract = {The extreme variation in gene content among phylogenetically related microorganisms suggests that gene acquisition, expansion, and loss are important evolutionary forces for adaptation to new environments. Accordingly, phylogenetically disparate organisms that share a habitat may converge in gene content as they adapt to confront shared challenges. This response should be especially pronounced for functional genes that are important for survival in a particular habitat. We illustrate this principle by showing that the repertoires of two different types of carbohydrate-active enzymes, glycoside hydrolases and glycosyltransferases, have converged in bacteria and archaea that live in the human gut and that this convergence is largely due to horizontal gene transfer rather than gene family expansion. We also identify gut microbes that may have more similar dietary niches in the human gut than would be expected based on phylogeny. The techniques used to obtain these results should be broadly applicable to understanding the functional genes and evolutionary processes important for adaptation in many environments and useful for interpreting the large number of reference microbial genome sequences being generated for the International Human Microbiome Project.},
	issn = {0027-8424},
	URL = {https://www.pnas.org/content/105/39/15076},
	eprint = {https://www.pnas.org/content/105/39/15076.full.pdf},
	journal = {Proceedings of the National Academy of Sciences}
}

@article{faith1992conservation,
  title = {Conservation evaluation and phylogenetic diversity},
  author = {Faith, Daniel P},
  journal = {Biological conservation},
  volume = {61},
  number = {1},
  pages = {1--10},
  year = {1992},
  publisher = {Elsevier},
  doi = {10.1016/0006-3207(92)91201-3}
}

@article{pielou1966measurement,
  title = {The measurement of diversity in different types of biological collections},
  author = {Pielou, Evelyn C},
  journal = {Journal of theoretical biology},
  volume = {13},
  pages = {131--144},
  year = {1966},
  publisher = {Elsevier},
  doi = {10.1016/0022-5193(66)90013-0}
}

% TODO: Selected during a preliminary assay of the literature - must be confirmed/augmented
@article{shannon1948communication,
  title = {A mathematical theory of communication},
  author = {Shannon, Claude E},
  journal = {The Bell System Technical Journal},
  volume = {27},
  issue = {3},
  pages = {379--423, 623--656},
  year = {1948},
  publisher = {Nokia Bell Labs},
  doi = {10.1002/j.1538-7305.1948.tb01338.x}
}

% TODO: Selected during a preliminary assay of the literature - must be confirmed/augmented
@article{jaccard1908nouvelles,
  title = {Nouvelles recherches sur la distribution floral},
  author = {Jaccard, P},
  journal = {Bull. Soc. Vard. Sci. Nat},
  volume = {44},
  pages = {223--270},
  year = {1908}
}

% TODO: Selected during a preliminary assay of the literature - must be confirmed/augmented
@article{sorensen1948method,
  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},
  author = {S{\o}rensen, Thorvald},
  journal = {Biol. Skr.},
  volume = {5},
  pages = {1--34},
  year = {1948}
}

@article{mcdonald2018unifrac,
  title = {Striped UniFrac: enabling microbiome analysis at unprecedented scale},
  author = {McDonald, Daniel and Vázquez-Baeza, Yoshiki and Koslicki, David and McClelland, Jason and Reeve, Nicolai and Xu, Zhenjiang and Gonzalez, Antonio and Knight, Rob},
  journal = {Nature Methods},
  volume = {15},
  issue = {11},
  pages = {847--848},
  issn = {1548-7105},
  year = {2018},
  doi = {10.1038/s41592-018-0187-8}
}

@article{sfiligoi2022unifrac,
    title = {Optimizing UniFrac with OpenACC yields >1000x speed increase},
    author = {Sfiligoi, Igor and Armstrong, George and Gonzalez, Antonio and McDonald, Daniel and Knight, Rob},
    journal = {mSystems},
    year = {in press}
}

@article{armstrong2021faithspd,
    author = {Armstrong, George and Cantrell, Kalen and Huang, Shi and McDonald, Daniel and Haiminen, Niina and Carrieri, Anna Paola and Zhu, Qiyun and Gonzalez, Antonio and McGrath, Imran and Beck, Kristen L. and Hakim, Daniel and Havulinna, Aki S. and Méric, Guillaume and Niiranen, Teemu and Lahti, Leo and Salomaa, Veikko and Jain, Mohit and Inouye, Michael and Swafford, Austin D. and Kim, Ho-Cheol and Parida, Laxmi and Vázquez-Baeza, Yoshiki and Knight, Rob}, 
    title = {Efficient computation of Faith's phylogenetic diversity with applications in characterizing microbiomes},
    volume = {31}, 
    number = {11}, 
    pages = {2131-2137}, 
    year = {2021}, 
    doi = {10.1101/gr.275777.121}, 
    abstract ={The number of publicly available microbiome samples is continually growing. As data set size increases, bottlenecks arise in standard analytical pipelines. Faith's phylogenetic diversity (Faith's PD) is a highly utilized phylogenetic alpha diversity metric that has thus far failed to effectively scale to trees with millions of vertices. Stacked Faith's phylogenetic diversity (SFPhD) enables calculation of this widely adopted diversity metric at a much larger scale by implementing a computationally efficient algorithm. The algorithm reduces the amount of computational resources required, resulting in more accessible software with a reduced carbon footprint, as compared to previous approaches. The new algorithm produces identical results to the previous method. We further demonstrate that the phylogenetic aspect of Faith's PD provides increased power in detecting diversity differences between younger and older populations in the FINRISK study's metagenomic data.}, 
    URL = {http://genome.cshlp.org/content/31/11/2131.abstract}, 
    eprint = {http://genome.cshlp.org/content/31/11/2131.full.pdf+html}, 
    journal = {Genome Research} 
}

@article {lozupone2005unifrac,
	author = {Lozupone, Catherine and Knight, Rob},
	title = {UniFrac: a New Phylogenetic Method for Comparing Microbial Communities},
	volume = {71},
	number = {12},
	pages = {8228--8235},
	year = {2005},
	doi = {10.1128/AEM.71.12.8228-8235.2005},
	publisher = {American Society for Microbiology Journals},
	abstract = {We introduce here a new method for computing differences between microbial communities based on phylogenetic information. This method, UniFrac, measures the phylogenetic distance between sets of taxa in a phylogenetic tree as the fraction of the branch length of the tree that leads to descendants from either one environment or the other, but not both. UniFrac can be used to determine whether communities are significantly different, to compare many communities simultaneously using clustering and ordination techniques, and to measure the relative contributions of different factors, such as chemistry and geography, to similarities between samples. We demonstrate the utility of UniFrac by applying it to published 16S rRNA gene libraries from cultured isolates and environmental clones of bacteria in marine sediment, water, and ice. Our results reveal that (i) cultured isolates from ice, water, and sediment resemble each other and environmental clone sequences from sea ice, but not environmental clone sequences from sediment and water; (ii) the geographical location does not correlate strongly with bacterial community differences in ice and sediment from the Arctic and Antarctic; and (iii) bacterial communities differ between terrestrially impacted seawater (whether polar or temperate) and warm oligotrophic seawater, whereas those in individual seawater samples are not more similar to each other than to those in sediment or ice samples. These results illustrate that UniFrac provides a new way of characterizing microbial communities, using the wealth of environmental rRNA sequences, and allows quantitative insight into the factors that underlie the distribution of lineages among environments.},
	issn = {0099-2240},
	URL = {https://aem.asm.org/content/71/12/8228},
	eprint = {https://aem.asm.org/content/71/12/8228.full.pdf},
	journal = {Applied and Environmental Microbiology}
}

@article {lozupone2007unifrac,
	author = {Lozupone, Catherine A. and Hamady, Micah and Kelley, Scott T. and Knight, Rob},
	title = {Quantitative and Qualitative β Diversity Measures Lead to Different Insights into Factors That Structure Microbial Communities},
	volume = {73},
	number = {5},
	pages = {1576--1585},
	year = {2007},
	doi = {10.1128/AEM.01996-06},
	publisher = {American Society for Microbiology Journals},
	abstract = {The assessment of microbial diversity and distribution is a major concern in environmental microbiology. There are two general approaches for measuring community diversity: quantitative measures, which use the abundance of each taxon, and qualitative measures, which use only the presence/absence of data. Quantitative measures are ideally suited to revealing community differences that are due to changes in relative taxon abundance (e.g., when a particular set of taxa flourish because a limiting nutrient source becomes abundant). Qualitative measures are most informative when communities differ primarily by what can live in them (e.g., at high temperatures), in part because abundance information can obscure significant patterns of variation in which taxa are present. We illustrate these principles using two 16S rRNA-based surveys of microbial populations and two phylogenetic measures of community β diversity: unweighted UniFrac, a qualitative measure, and weighted UniFrac, a new quantitative measure, which we have added to the UniFrac website (http://bmf.colorado.edu/unifrac). These studies considered the relative influences of mineral chemistry, temperature, and geography on microbial community composition in acidic thermal springs in Yellowstone National Park and the influences of obesity and kinship on microbial community composition in the mouse gut. We show that applying qualitative and quantitative measures to the same data set can lead to dramatically different conclusions about the main factors that structure microbial diversity and can provide insight into the nature of community differences. We also demonstrate that both weighted and unweighted UniFrac measurements are robust to the methods used to build the underlying phylogeny.},
	issn = {0099-2240},
	URL = {https://aem.asm.org/content/73/5/1576},
	eprint = {https://aem.asm.org/content/73/5/1576.full.pdf},
	journal = {Applied and Environmental Microbiology}
}

@article {hamady2010unifrac,
  author = {Hamady, Micah and Lozupone, Catherine and Knight, Rob},
  title = {Fast UniFrac: facilitating high-throughput phylogenetic analyses of microbial communities including analysis of pyrosequencing and PhyloChip data},
  journal = {The ISME Journal},
  pages = {17--27},
  volume = {4},
  issue = {1},
  abstract = {Next-generation sequencing techniques, and PhyloChip, have made simultaneous phylogenetic analyses of hundreds of microbial communities possible. Insight into community structure has been limited by the inability to integrate and visualize such vast datasets. Fast UniFrac overcomes these issues, allowing integration of larger numbers of sequences and samples into a single analysis. Its new array-based implementation offers orders of magnitude improvements over the original version. New 3D visualization of principal coordinates analysis results, with the option to view multiple coordinate axes simultaneously, provides a powerful way to quickly identify patterns that relate vast numbers of microbial communities. We show the potential of Fast UniFrac using examples from three data types: Sanger-sequencing studies of diverse free-living and animal-associated bacterial assemblages and from the gut of obese humans as they diet, pyrosequencing data integrated from studies of the human hand and gut, and PhyloChip data from a study of citrus pathogens. We show that a Fast UniFrac analysis using a reference tree recaptures patterns that could not be detected without considering phylogenetic relationships and that Fast UniFrac, coupled with BLAST-based sequence assignment, can be used to quickly analyze pyrosequencing runs containing hundreds of thousands of sequences, showing patterns relating human and gut samples. Finally, we show that the application of Fast UniFrac to PhyloChip data could identify well-defined subcategories associated with infection. Together, these case studies point the way toward a broad range of applications and show some of the new features of Fast UniFrac.},
  issn = {1751-7370},
  doi = {10.1038/ismej.2009.97},
  year = {2010}
}

@article {lozupone2011unifrac,
  author = {Lozupone, Catherine and Lladser, Manuel E and Knights, Dan and Stombaugh, Jesse and Knight, Rob},
  title = {UniFrac: an effective distance metric for microbial community comparison},
  journal = {The ISME Journal},
  pages = {169--172},
  volume = {5},
  issue = {2},
  issn = {1751-7370},
  doi = {10.1038/ismej.2010.133},
  year = {2011}
}

@article {chen2012genUnifrac,
  author = {Chen, Jun and Bittinger, Kyle and Charlson, Emily S. and Hoffmann, Christian and Lewis, James and Wu, Gary D. and Collman, Ronald G. and Bushman, Frederic D. and Li, Hongzhe},
  title = {Associating microbiome composition with environmental covariates using generalized UniFrac distances},
  journal = {Bioinformatics},
  volume = {28},
  number = {16},
  pages = {2106--2113},
  year = {2012},
  month = {06},
  abstract = "{Motivation: The human microbiome plays an important role in human disease and health. Identification of factors that affect the microbiome composition can provide insights into disease mechanism as well as suggest ways to modulate the microbiome composition for therapeutical purposes. Distance-based statistical tests have been applied to test the association of microbiome composition with environmental or biological covariates. The unweighted and weighted UniFrac distances are the most widely used distance measures. However, these two measures assign too much weight either to rare lineages or to most abundant lineages, which can lead to loss of power when the important composition change occurs in moderately abundant lineages.Results: We develop generalized UniFrac distances that extend the weighted and unweighted UniFrac distances for detecting a much wider range of biologically relevant changes. We evaluate the use of generalized UniFrac distances in associating microbiome composition with environmental covariates using extensive Monte Carlo simulations. Our results show that tests using the unweighted and weighted UniFrac distances are less powerful in detecting abundance change in moderately abundant lineages. In contrast, the generalized UniFrac distance is most powerful in detecting such changes, yet it retains nearly all its power for detecting rare and highly abundant lineages. The generalized UniFrac distance also has an overall better power than the joint use of unweighted/weighted UniFrac distances. Application to two real microbiome datasets has demonstrated gains in power in testing the associations between human microbiome and diet intakes and habitual smoking.Availability:http://cran.r-project.org/web/packages/GUniFracContact:hongzhe@upenn.eduSupplementary information:Supplementary data are available at Bioinformatics online.}",
  issn = {1367-4803},
  doi = {10.1093/bioinformatics/bts342},
  url = {https://doi.org/10.1093/bioinformatics/bts342},
  eprint = {http://oup.prod.sis.lan/bioinformatics/article-pdf/28/16/2106/16905186/bts342.pdf}
}

@article{chang2011variance,
  author = {Chang, Qin and Luan, Yihui and Sun, Fengzhu},
  title = {Variance adjusted weighted UniFrac: a powerful beta diversity measure for comparing communities based on phylogeny},
  journal = {BMC Bioinformatics},
  year = {2011},
  month = {Apr},
  ay = {25},
  volume = {12},
  number = {1},
  pages = {118},
  abstract = {Beta diversity, which involves the assessment of differences between communities, is an important problem in ecological studies. Many statistical methods have been developed to quantify beta diversity, and among them, UniFrac and weighted-UniFrac (W-UniFrac) are widely used. The W-UniFrac is a weighted sum of branch lengths in a phylogenetic tree of the sequences from the communities. However, W-UniFrac does not consider the variation of the weights under random sampling resulting in less power detecting the differences between communities.},
  issn = {1471-2105},
  doi = {10.1186/1471-2105-12-118},
  url = {https://doi.org/10.1186/1471-2105-12-118}
}

