Nothing
UniFrac Calculations
In ecodive: Parallel and Memory-Efficient Ecological Diversity Metrics
Introduction
The different UniFrac algorithms are listed below, along with examples for calculating them.
Input Data
library(ecodive)
counts <- matrix(
data = c(0, 0, 9, 3, 3, 1, 4, 2, 8, 0),
ncol = 2,
dimnames = list(paste0('Species_', 1:5), c('Sample_A', 'Sample_B')) )
tree <- read_tree(
underscores = TRUE,
newick = "
(((Species_1:0.8,Species_2:0.5):0.4,Species_3:0.9):0.2,(Species_4:0.7,Species_5:0.3):0.6);" )
L <- tree$edge.length
A <- c(9,0,0,0,9,6,3,3)
B <- c(7,5,1,4,2,8,8,0)
# local({ # man/figures/unifrac-tree.png
#
# par(xpd = NA)
# ape::plot.phylo(
# x = tree,
# direction = 'downwards',
# srt = 90,
# adj = 0.5,
# no.margin = TRUE,
# underscore = TRUE,
# x.lim = c(0.5, 5.5) )
#
# ape::edgelabels(tree$edge.length, bg = 'white', frame = 'none', adj = -0.4)
# })
#
# local({ # man/figures/unifrac-weights.png
#
# tree$edge.length <- c(1, 1, 1, 1, 2, 1, 2, 2)
#
# par(xpd = NA)
# ape::plot.phylo(
# x = tree,
# direction = 'downwards',
# srt = 90,
# adj = 0.5,
# no.margin = TRUE,
# underscore = TRUE,
# x.lim = c(.8, 6) )
#
# ape::edgelabels(1:8, frame = 'circle')
#
# ape::edgelabels(paste('A =', A), bg = 'white', frame = 'none', adj = c(-0.4, -1.2))
# ape::edgelabels(paste('B =', B), bg = 'white', frame = 'none', adj = c(-0.4, 0.0))
# ape::edgelabels(paste('L =', L), bg = 'white', frame = 'none', adj = c(-0.3, 1.2))
# })
- A numeric matrix with two samples and five species.
- A phylogenetic tree for those five species.
Sample_A Sample_B Species_1 `r counts[1,1]` `r counts[1,2]` Species_2 `r counts[2,1]` `r counts[2,2]` Species_3 `r counts[3,1]` `r counts[3,2]` Species_4 `r counts[4,1]` `r counts[4,2]` Species_5 `r counts[5,1]` `r counts[5,2]`
knitr::include_graphics('../man/figures/unifrac-tree.png')
Definitions
The branch indices (green circles) are used for ordering the $L$, $A$, and $B$ arrays. Values for $L$ are drawn from the input phylogenetic tree. Values for $A$ and $B$ are the total number of species observations descending from that branch; $A$ for Sample_A, and $B$ for Sample_B.
knitr::include_graphics('../man/figures/unifrac-weights.png')
$n = 8$ Number of branches $A = \{`r A`\}$ Branch **weights** for Sample_A. $B = \{`r B`\}$ Branch **weights** for Sample_B. $A_T = 15$ Total observations for Sample_A. $B_T = 15$ Total observations for Sample_B. $L = \{`r L`\}$ The branch **lengths**.
Unweighted
- Lozupone et al, 2005: Unweighted UniFrac
- R Package ecodive:
unweighted_unifrac()
- R Package abdiv:
unweighted_unifrac()
- R Package phyloseq:
UniFrac(weighted=FALSE)
- qiime2
qiime diversity beta-phylogenetic --p-metric unweighted_unifrac
- mothur:
unifrac.unweighted()
First, transform A and B into presence (1) and absence (0) indicators.
\begin{align*}
A &= \{`r A`\} \\
A' &= \{`r as.numeric(A > 0)`\}
\end{align*}
\begin{align*}
B &= \{`r B`\} \\
B' &= \{`r as.numeric(B > 0)`\}
\end{align*}
Then apply the formula:
\begin{align}
U &= \displaystyle \frac{\sum_{i = 1}^{n} L_i(|A'i - B'_i|)}{\sum{i = 1}^{n} L_i(max(A'_i,B'_i))} \ \
U &= \displaystyle \frac{L_1(|A'_1-B'_1|) + L_2(|A'_2-B'_2|) + \cdots + L_n(|A'_n-B'_n|)}{L_1(max(A'_1,B'_1)) + L_2(max(A'_2,B'_2)) + \cdots + L_n(max(A'_n,B'_n))} \ \
U &= \displaystyle \frac{0.2(|1-1|) + 0.4(|0-1|) + \cdots + 0.3(|1-0|)}{0.2(max(1,1)) + 0.4(max(0,1)) + \cdots + 0.3(max(1,0))} \ \
U &= \displaystyle \frac{0.2(0) + 0.4(1) + 0.8(1) + 0.5(1) + 0.9(0) + 0.6(0) + 0.7(0) + 0.3(1)}{0.2(1) + 0.4(1) + 0.8(1) + 0.5(1) + 0.9(1) + 0.6(1) + 0.7(1) + 0.3(1)} \ \
U &= \displaystyle \frac{0.4 + 0.8 + 0.5 + 0.3}{0.2 + 0.4 + 0.8 + 0.5 + 0.9 + 0.6 + 0.7 + 0.3} \ \
U &= \displaystyle \frac{2}{4.4} \ \
U &= 0.4545455
\end{align}
Weighted
- Lozupone et al, 2007: Raw Weighted UniFrac
- R Package ecodive:
weighted_unifrac()
- R Package abdiv:
weighted_unifrac()
- R Package phyloseq:
UniFrac(weighted=TRUE, normalized=FALSE)
- qiime2
qiime diversity beta-phylogenetic --p-metric weighted_unifrac
\begin{align}
W &= \sum_{i = 1}^{n} L_i|\frac{A_i}{A_T} - \frac{B_i}{B_T}| \ \
W &= L_1|\frac{A_1}{A_T} - \frac{B_1}{B_T}| + L_2|\frac{A_2}{A_T} - \frac{B_2}{B_T}| + \cdots + L_n|\frac{A_n}{A_T} - \frac{B_n}{B_T}| \ \
W &= 0.2|\frac{9}{15} - \frac{7}{15}| + 0.4|\frac{0}{15} - \frac{5}{15}| + \cdots + 0.3|\frac{3}{15} - \frac{0}{15}| \ \
W &= 0.02\overline{6} + 0.1\overline{3} + 0.05\overline{3} + 0.1\overline{3} + 0.42 + 0.08 + 0.2\overline{3} + 0.06 \ \
W &= 1.14
\end{align}
Normalized
- Lozupone et al, 2007: Normalized Weighted UniFrac
- R Package ecodive:
weighted_normalized_unifrac()
- R Package abdiv:
weighted_normalized_unifrac()
- R Package phyloseq:
UniFrac(weighted=TRUE, normalized=TRUE)
- qiime2
qiime diversity beta-phylogenetic --p-metric weighted_normalized_unifrac
- mothur:
unifrac.weighted()
\begin{align*}
N &= \displaystyle \frac
{\sum_{i = 1}^{n} L_i|\frac{A_i}{A_T} - \frac{B_i}{B_T}|}
{\sum_{i = 1}^{n} L_i(\frac{A_i}{A_T} + \frac{B_i}{B_T})}
\ \
N &= \displaystyle \frac
{L_1|\frac{A_1}{A_T} - \frac{B_1}{B_T}| + L_2|\frac{A_2}{A_T} - \frac{B_2}{B_T}| + \cdots + L_n|\frac{A_n}{A_T} - \frac{B_n}{B_T}|}
{L_1(\frac{A_1}{A_T} + \frac{B_1}{B_T}) + L_2(\frac{A_2}{A_T} + \frac{B_2}{B_T}) + \cdots + L_n(\frac{A_n}{A_T} + \frac{B_n}{B_T})}
\ \
N &= \displaystyle \frac
{0.2|\frac{9}{15} - \frac{7}{15}| + 0.4|\frac{0}{15} - \frac{5}{15}| + \cdots + 0.3|\frac{3}{15} - \frac{0}{15}|}
{0.2(\frac{9}{15} + \frac{7}{15}) + 0.4(\frac{0}{15} + \frac{5}{15}) + \cdots + 0.3(\frac{3}{15} + \frac{0}{15})}
\ \
N &= \displaystyle \frac
{0.02\overline{6} + 0.1\overline{3} + 0.05\overline{3} + 0.1\overline{3} + 0.42 + 0.08 + 0.2\overline{3} + 0.06}
{0.21\overline{3} + 0.1\overline{3} + 0.05\overline{3} + 0.1\overline{3} + 0.66 + 0.56 + 0.51\overline{3} + 0.06}
\ \
N &= \displaystyle \frac{1.14}{2.326667} \ \
N &= 0.4899713
\end{align*}
Generalized
- Chen et al. 2012: Generalized UniFrac
- R Package ecodive:
generalized_unifrac(alpha = 0.5)
- R Package abdiv:
generalized_unifrac(alpha = 0.5)
- R Package GUniFrac:
GUniFrac(alpha = 0.5)
- qiime2
qiime diversity beta-phylogenetic --p-metric generalized_unifrac -a 0.5
\begin{align*}
G &= \displaystyle \frac
{\sum_{i = 1}^{n} L_i(\frac{A_i}{A_T} + \frac{B_i}{B_T})^{\alpha}
|\displaystyle \frac
{\frac{A_i}{A_T} - \frac{B_i}{B_T}}
{\frac{A_i}{A_T} + \frac{B_i}{B_T}} |}
{\sum_{i = 1}^{n} L_i(\frac{A_i}{A_T} + \frac{B_i}{B_T})^{\alpha}} \ \
G &= \displaystyle \frac
{
L_1(\frac{A_1}{A_T} + \frac{B_1}{B_T})^{0.5}
|\displaystyle \frac
{\frac{A_1}{A_T} - \frac{B_1}{B_T}}
{\frac{A_1}{A_T} + \frac{B_1}{B_T}}| +
\cdots +
L_n(\frac{A_n}{A_T} + \frac{B_n}{B_T})^{0.5}
|\displaystyle \frac
{\frac{A_n}{A_T} - \frac{B_n}{B_T}}
{\frac{A_n}{A_T} + \frac{B_n}{B_T}}|
}{
L_1(\frac{A_1}{A_T} + \frac{B_1}{B_T})^{0.5} +
\cdots +
L_n(\frac{A_n}{A_T} + \frac{B_n}{B_T})^{0.5}
}
\ \
G &= \displaystyle \frac
{
0.2(\frac{9}{15} + \frac{7}{15})^{0.5}
|\displaystyle \frac
{\frac{9}{15} - \frac{7}{15}}
{\frac{9}{15} + \frac{7}{15}}| +
\cdots +
0.3(\frac{3}{15} + \frac{0}{15})^{0.5}
|\displaystyle \frac
{\frac{3}{15} - \frac{0}{15}}
{\frac{3}{15} + \frac{0}{15}}|
}{
0.2(\frac{9}{15} + \frac{7}{15})^{0.5} +
\cdots +
0.3(\frac{3}{15} + \frac{0}{15})^{0.5}
}
\ \
G &\approx \displaystyle \frac
{0.03 + 0.23 + 0.21 + 0.26 + 0.49 + 0.08 + 0.27 + 0.13}
{0.21 + 0.23 + 0.21 + 0.26 + 0.77 + 0.58 + 0.60 + 0.13}
\ \
G &= \displaystyle \frac{1.701419}{2.986235} \ \
G &= 0.569754
\end{align*}
Variance Adjusted
- Chang et al, 2011: Variance Adjusted Weighted (VAW) UniFrac
- R Package ecodive:
variance_adjusted_unifrac()
- R Package abdiv:
variance_adjusted_unifrac()
- qiime2
qiime diversity beta-phylogenetic --p-metric weighted_normalized_unifrac --p-variance-adjusted
\begin{align*}
V &= \displaystyle \frac
{\sum_{i = 1}^{n} L_i\displaystyle \frac
{|\frac{A_i}{A_T} - \frac{B_i}{B_T}|}
{\sqrt{(A_i + B_i)(A_T + B_T - A_i - B_i)}} }
{\sum_{i = 1}^{n} L_i\displaystyle \frac
{\frac{A_i}{A_T} + \frac{B_i}{B_T}}
{\sqrt{(A_i + B_i)(A_T + B_T - A_i - B_i)}} } \ \
V &= \displaystyle \frac
{
L_1\displaystyle \frac
{|\frac{A_1}{A_T} - \frac{B_1}{B_T}|}
{\sqrt{(A_1 + B_1)(A_T + B_T - A_1 - B_1)}} +
\cdots +
L_n\displaystyle \frac
{|\frac{A_n}{A_T} - \frac{B_n}{B_T}|}
{\sqrt{(A_n + B_n)(A_T + B_T - A_n - B_n)}}
}{
L_1\displaystyle \frac
{\frac{A_1}{A_T} + \frac{B_1}{B_T}}
{\sqrt{(A_1 + B_1)(A_T + B_T - A_1 - B_1)}} +
\cdots +
L_n\displaystyle \frac
{\frac{A_n}{A_T} + \frac{B_n}{B_T}}
{\sqrt{(A_n + B_n)(A_T + B_T - A_n - B_n)}}
}
\ \
V &= \displaystyle \frac
{
0.2\displaystyle \frac
{|\frac{9}{15} - \frac{7}{15}|}
{\sqrt{(9 + 7)(15 + 15 - 9 - 7)}} +
\cdots +
0.3\displaystyle \frac
{|\frac{3}{15} - \frac{0}{15}|}
{\sqrt{(3 + 0)(15 + 15 - 3 - 0)}}
}{
0.2\displaystyle \frac
{\frac{9}{15} + \frac{7}{15}}
{\sqrt{(9 + 7)(15 + 15 - 9 - 7)}} +
\cdots +
0.3\displaystyle \frac
{\frac{3}{15} + \frac{0}{15}}
{\sqrt{(3 + 0)(15 + 15 - 3 - 0)}}
}
\ \
V &\approx \displaystyle \frac
{0.002 + 0.012 + 0.010 + 0.013 + 0.029 + 0.005 + 0.016 + 0.007}
{0.014 + 0.012 + 0.010 + 0.013 + 0.046 + 0.037 + 0.036 + 0.007}
\ \
V &= \displaystyle \frac{4.09389}{4.174402} \ \
V &= 0.9807128
\end{align*}
Try the ecodive package in your browser
Any scripts or data that you put into this service are public.
ecodive documentation built on Aug. 23, 2025, 1:13 a.m.
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
Introduction
The different UniFrac algorithms are listed below, along with examples for calculating them.
Input Data
library(ecodive) counts <- matrix( data = c(0, 0, 9, 3, 3, 1, 4, 2, 8, 0), ncol = 2, dimnames = list(paste0('Species_', 1:5), c('Sample_A', 'Sample_B')) ) tree <- read_tree( underscores = TRUE, newick = " (((Species_1:0.8,Species_2:0.5):0.4,Species_3:0.9):0.2,(Species_4:0.7,Species_5:0.3):0.6);" ) L <- tree$edge.length A <- c(9,0,0,0,9,6,3,3) B <- c(7,5,1,4,2,8,8,0) # local({ # man/figures/unifrac-tree.png # # par(xpd = NA) # ape::plot.phylo( # x = tree, # direction = 'downwards', # srt = 90, # adj = 0.5, # no.margin = TRUE, # underscore = TRUE, # x.lim = c(0.5, 5.5) ) # # ape::edgelabels(tree$edge.length, bg = 'white', frame = 'none', adj = -0.4) # }) # # local({ # man/figures/unifrac-weights.png # # tree$edge.length <- c(1, 1, 1, 1, 2, 1, 2, 2) # # par(xpd = NA) # ape::plot.phylo( # x = tree, # direction = 'downwards', # srt = 90, # adj = 0.5, # no.margin = TRUE, # underscore = TRUE, # x.lim = c(.8, 6) ) # # ape::edgelabels(1:8, frame = 'circle') # # ape::edgelabels(paste('A =', A), bg = 'white', frame = 'none', adj = c(-0.4, -1.2)) # ape::edgelabels(paste('B =', B), bg = 'white', frame = 'none', adj = c(-0.4, 0.0)) # ape::edgelabels(paste('L =', L), bg = 'white', frame = 'none', adj = c(-0.3, 1.2)) # })
- A numeric matrix with two samples and five species.
- A phylogenetic tree for those five species.
|
knitr::include_graphics('../man/figures/unifrac-tree.png') |
Definitions
The branch indices (green circles) are used for ordering the $L$, $A$, and $B$ arrays. Values for $L$ are drawn from the input phylogenetic tree. Values for $A$ and $B$ are the total number of species observations descending from that branch; $A$ for Sample_A, and $B$ for Sample_B.
knitr::include_graphics('../man/figures/unifrac-weights.png')
| $n = 8$ | Number of branches |
| $A = \{`r A`\}$ | Branch **weights** for Sample_A. |
| $B = \{`r B`\}$ | Branch **weights** for Sample_B. |
| $A_T = 15$ | Total observations for Sample_A. |
| $B_T = 15$ | Total observations for Sample_B. |
| $L = \{`r L`\}$ | The branch **lengths**. |
Unweighted
- Lozupone et al, 2005: Unweighted UniFrac
- R Package ecodive:
unweighted_unifrac() - R Package abdiv:
unweighted_unifrac() - R Package phyloseq:
UniFrac(weighted=FALSE) - qiime2
qiime diversity beta-phylogenetic --p-metric unweighted_unifrac - mothur:
unifrac.unweighted()
First, transform A and B into presence (1) and absence (0) indicators.
| \begin{align*} A &= \{`r A`\} \\ A' &= \{`r as.numeric(A > 0)`\} \end{align*} | \begin{align*} B &= \{`r B`\} \\ B' &= \{`r as.numeric(B > 0)`\} \end{align*} |
Then apply the formula:
\begin{align} U &= \displaystyle \frac{\sum_{i = 1}^{n} L_i(|A'i - B'_i|)}{\sum{i = 1}^{n} L_i(max(A'_i,B'_i))} \ \ U &= \displaystyle \frac{L_1(|A'_1-B'_1|) + L_2(|A'_2-B'_2|) + \cdots + L_n(|A'_n-B'_n|)}{L_1(max(A'_1,B'_1)) + L_2(max(A'_2,B'_2)) + \cdots + L_n(max(A'_n,B'_n))} \ \ U &= \displaystyle \frac{0.2(|1-1|) + 0.4(|0-1|) + \cdots + 0.3(|1-0|)}{0.2(max(1,1)) + 0.4(max(0,1)) + \cdots + 0.3(max(1,0))} \ \ U &= \displaystyle \frac{0.2(0) + 0.4(1) + 0.8(1) + 0.5(1) + 0.9(0) + 0.6(0) + 0.7(0) + 0.3(1)}{0.2(1) + 0.4(1) + 0.8(1) + 0.5(1) + 0.9(1) + 0.6(1) + 0.7(1) + 0.3(1)} \ \ U &= \displaystyle \frac{0.4 + 0.8 + 0.5 + 0.3}{0.2 + 0.4 + 0.8 + 0.5 + 0.9 + 0.6 + 0.7 + 0.3} \ \ U &= \displaystyle \frac{2}{4.4} \ \ U &= 0.4545455 \end{align}
Weighted
- Lozupone et al, 2007: Raw Weighted UniFrac
- R Package ecodive:
weighted_unifrac() - R Package abdiv:
weighted_unifrac() - R Package phyloseq:
UniFrac(weighted=TRUE, normalized=FALSE) - qiime2
qiime diversity beta-phylogenetic --p-metric weighted_unifrac
\begin{align} W &= \sum_{i = 1}^{n} L_i|\frac{A_i}{A_T} - \frac{B_i}{B_T}| \ \ W &= L_1|\frac{A_1}{A_T} - \frac{B_1}{B_T}| + L_2|\frac{A_2}{A_T} - \frac{B_2}{B_T}| + \cdots + L_n|\frac{A_n}{A_T} - \frac{B_n}{B_T}| \ \ W &= 0.2|\frac{9}{15} - \frac{7}{15}| + 0.4|\frac{0}{15} - \frac{5}{15}| + \cdots + 0.3|\frac{3}{15} - \frac{0}{15}| \ \ W &= 0.02\overline{6} + 0.1\overline{3} + 0.05\overline{3} + 0.1\overline{3} + 0.42 + 0.08 + 0.2\overline{3} + 0.06 \ \ W &= 1.14 \end{align}
Normalized
- Lozupone et al, 2007: Normalized Weighted UniFrac
- R Package ecodive:
weighted_normalized_unifrac() - R Package abdiv:
weighted_normalized_unifrac() - R Package phyloseq:
UniFrac(weighted=TRUE, normalized=TRUE) - qiime2
qiime diversity beta-phylogenetic --p-metric weighted_normalized_unifrac - mothur:
unifrac.weighted()
\begin{align*}
N &= \displaystyle \frac {\sum_{i = 1}^{n} L_i|\frac{A_i}{A_T} - \frac{B_i}{B_T}|} {\sum_{i = 1}^{n} L_i(\frac{A_i}{A_T} + \frac{B_i}{B_T})} \ \
N &= \displaystyle \frac {L_1|\frac{A_1}{A_T} - \frac{B_1}{B_T}| + L_2|\frac{A_2}{A_T} - \frac{B_2}{B_T}| + \cdots + L_n|\frac{A_n}{A_T} - \frac{B_n}{B_T}|} {L_1(\frac{A_1}{A_T} + \frac{B_1}{B_T}) + L_2(\frac{A_2}{A_T} + \frac{B_2}{B_T}) + \cdots + L_n(\frac{A_n}{A_T} + \frac{B_n}{B_T})} \ \
N &= \displaystyle \frac {0.2|\frac{9}{15} - \frac{7}{15}| + 0.4|\frac{0}{15} - \frac{5}{15}| + \cdots + 0.3|\frac{3}{15} - \frac{0}{15}|} {0.2(\frac{9}{15} + \frac{7}{15}) + 0.4(\frac{0}{15} + \frac{5}{15}) + \cdots + 0.3(\frac{3}{15} + \frac{0}{15})} \ \
N &= \displaystyle \frac {0.02\overline{6} + 0.1\overline{3} + 0.05\overline{3} + 0.1\overline{3} + 0.42 + 0.08 + 0.2\overline{3} + 0.06} {0.21\overline{3} + 0.1\overline{3} + 0.05\overline{3} + 0.1\overline{3} + 0.66 + 0.56 + 0.51\overline{3} + 0.06} \ \
N &= \displaystyle \frac{1.14}{2.326667} \ \ N &= 0.4899713 \end{align*}
Generalized
- Chen et al. 2012: Generalized UniFrac
- R Package ecodive:
generalized_unifrac(alpha = 0.5) - R Package abdiv:
generalized_unifrac(alpha = 0.5) - R Package GUniFrac:
GUniFrac(alpha = 0.5) - qiime2
qiime diversity beta-phylogenetic --p-metric generalized_unifrac -a 0.5
\begin{align*}
G &= \displaystyle \frac {\sum_{i = 1}^{n} L_i(\frac{A_i}{A_T} + \frac{B_i}{B_T})^{\alpha} |\displaystyle \frac {\frac{A_i}{A_T} - \frac{B_i}{B_T}} {\frac{A_i}{A_T} + \frac{B_i}{B_T}} |} {\sum_{i = 1}^{n} L_i(\frac{A_i}{A_T} + \frac{B_i}{B_T})^{\alpha}} \ \
G &= \displaystyle \frac
{
L_1(\frac{A_1}{A_T} + \frac{B_1}{B_T})^{0.5}
|\displaystyle \frac
{\frac{A_1}{A_T} - \frac{B_1}{B_T}}
{\frac{A_1}{A_T} + \frac{B_1}{B_T}}| +
\cdots +
L_n(\frac{A_n}{A_T} + \frac{B_n}{B_T})^{0.5}
|\displaystyle \frac
{\frac{A_n}{A_T} - \frac{B_n}{B_T}}
{\frac{A_n}{A_T} + \frac{B_n}{B_T}}|
}{
L_1(\frac{A_1}{A_T} + \frac{B_1}{B_T})^{0.5} +
\cdots +
L_n(\frac{A_n}{A_T} + \frac{B_n}{B_T})^{0.5}
}
\ \
G &= \displaystyle \frac
{
0.2(\frac{9}{15} + \frac{7}{15})^{0.5}
|\displaystyle \frac
{\frac{9}{15} - \frac{7}{15}}
{\frac{9}{15} + \frac{7}{15}}| +
\cdots +
0.3(\frac{3}{15} + \frac{0}{15})^{0.5}
|\displaystyle \frac
{\frac{3}{15} - \frac{0}{15}}
{\frac{3}{15} + \frac{0}{15}}|
}{
0.2(\frac{9}{15} + \frac{7}{15})^{0.5} +
\cdots +
0.3(\frac{3}{15} + \frac{0}{15})^{0.5}
}
\ \
G &\approx \displaystyle \frac {0.03 + 0.23 + 0.21 + 0.26 + 0.49 + 0.08 + 0.27 + 0.13} {0.21 + 0.23 + 0.21 + 0.26 + 0.77 + 0.58 + 0.60 + 0.13} \ \
G &= \displaystyle \frac{1.701419}{2.986235} \ \ G &= 0.569754
\end{align*}
Variance Adjusted
- Chang et al, 2011: Variance Adjusted Weighted (VAW) UniFrac
- R Package ecodive:
variance_adjusted_unifrac() - R Package abdiv:
variance_adjusted_unifrac() - qiime2
qiime diversity beta-phylogenetic --p-metric weighted_normalized_unifrac --p-variance-adjusted
\begin{align*}
V &= \displaystyle \frac {\sum_{i = 1}^{n} L_i\displaystyle \frac {|\frac{A_i}{A_T} - \frac{B_i}{B_T}|} {\sqrt{(A_i + B_i)(A_T + B_T - A_i - B_i)}} } {\sum_{i = 1}^{n} L_i\displaystyle \frac {\frac{A_i}{A_T} + \frac{B_i}{B_T}} {\sqrt{(A_i + B_i)(A_T + B_T - A_i - B_i)}} } \ \
V &= \displaystyle \frac
{
L_1\displaystyle \frac
{|\frac{A_1}{A_T} - \frac{B_1}{B_T}|}
{\sqrt{(A_1 + B_1)(A_T + B_T - A_1 - B_1)}} +
\cdots +
L_n\displaystyle \frac
{|\frac{A_n}{A_T} - \frac{B_n}{B_T}|}
{\sqrt{(A_n + B_n)(A_T + B_T - A_n - B_n)}}
}{
L_1\displaystyle \frac
{\frac{A_1}{A_T} + \frac{B_1}{B_T}}
{\sqrt{(A_1 + B_1)(A_T + B_T - A_1 - B_1)}} +
\cdots +
L_n\displaystyle \frac
{\frac{A_n}{A_T} + \frac{B_n}{B_T}}
{\sqrt{(A_n + B_n)(A_T + B_T - A_n - B_n)}}
}
\ \
V &= \displaystyle \frac
{
0.2\displaystyle \frac
{|\frac{9}{15} - \frac{7}{15}|}
{\sqrt{(9 + 7)(15 + 15 - 9 - 7)}} +
\cdots +
0.3\displaystyle \frac
{|\frac{3}{15} - \frac{0}{15}|}
{\sqrt{(3 + 0)(15 + 15 - 3 - 0)}}
}{
0.2\displaystyle \frac
{\frac{9}{15} + \frac{7}{15}}
{\sqrt{(9 + 7)(15 + 15 - 9 - 7)}} +
\cdots +
0.3\displaystyle \frac
{\frac{3}{15} + \frac{0}{15}}
{\sqrt{(3 + 0)(15 + 15 - 3 - 0)}}
}
\ \
V &\approx \displaystyle \frac {0.002 + 0.012 + 0.010 + 0.013 + 0.029 + 0.005 + 0.016 + 0.007} {0.014 + 0.012 + 0.010 + 0.013 + 0.046 + 0.037 + 0.036 + 0.007} \ \
V &= \displaystyle \frac{4.09389}{4.174402} \ \ V &= 0.9807128
\end{align*}
Try the ecodive package in your browser
Any scripts or data that you put into this service are public.
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
Embedding an R snippet on your website
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.