-
+
- The MetabarSchool Package
- What do the reading numbers per PCR mean? -
- Rarefaction vs. relative frequencies +
- Rarefaction vs. relative frequencies
- alpha diversity metrics
- beta diversity metrics
- multidimentionnal analysis
- comparison between datasets
As :
$$
-H(X) = \log|A| \;\Rightarrow\; ^1D = e^{H(X)}
+H(A) = \log|A| \;\Rightarrow\; ^1D = e^{H(A)}
$$
-where $^1D$ is the theoretical number of species in a evenly distributed community that would have the same Shanon's entropy than ours.
+where $^1D$ is the theoretical number of species in a evenly distributed community that would have the same Shannon's entropy than ours.
Summary
The MetabarSchool Package
Instaling the package
You need the devtools package
+ +install.packages("devtools",dependencies = TRUE)
+
+Then you can install MetabarSchool
+ +devtools::install_git("https://git.metabarcoding.org/MetabarcodingSchool/biodiversity-metrics.git")
+
+You will also need the vegan package
+ +install.packages("vegan",dependencies = TRUE)
+
The dataset
The mock community
The experiment
-
-
192 PCR of the mock community using SPER02 trnL-P6-Loop primers
+192 PCR of the mock community using SPER02 trnL-P6-Loop primers
+ +6 dilutions of the mock community: 1/1, 1/2, 1/4, 1/8, 1/16, 1/32
32 repeats per dilution
+
Loading data
data("positive.count")
+library(MetabarSchool)
+
+data("positive.count")
data("positive.samples")
data("positive.motus")
@@ -880,7 +905,9 @@ sample.TM_POS_d16_2_a_A1
Loading data
data("positive.count")
+library(MetabarSchool)
+
+data("positive.count")
data("positive.samples")
data("positive.motus")
@@ -992,7 +1019,9 @@ sample.TM_POS_d16_1_b_A2
Loading data
data("positive.count")
+library(MetabarSchool)
+
+data("positive.count")
data("positive.samples")
data("positive.motus")
@@ -1212,11 +1241,11 @@ positive.motus = positive.motus[are.not.singleton,]
positive.count is now a \(192 \; PCRs \; \times \; 5579 \; MOTUs\) matrixNot all the PCR have the number of reads
Not all the PCR have the same number of reads
Despite all standardization efforts
-
Is it related to the amount of DNA in the extract ?
Rarefying read count (2)
Rarefying read count (3)
## are.still.present ## FALSE TRUE -## 1942 3637+## 1886 3693
Rarefying read count (4)
par(bg=NA) boxplot(colSums(positive.count) ~ are.still.present, log="y")-
The MOTUs removed by rarefaction were at most occurring 21 times
+The MOTUs removed by rarefaction were at most occurring 13 times
The MOTUs kept by rarefaction were at least occurring 2 times
@@ -1306,7 +1335,7 @@ positive.motus.rare = positive.motus[are.still.present,]
Whittaker (2010)
-
-
\(\alpha-diversity\) : Mean diversity per site (\(species/site\))
-\(\gamma-diversity\) : Regional biodiversity (\(species/region\))
-\(\beta-diversity\) : \(\beta = \frac{\gamma}{\alpha}\) (\(site\))
+\(\alpha\text{-diversity}\) : Mean diversity per site (\(species/site\))
+\(\gamma\text{-diversity}\) : Regional biodiversity (\(species/region\))
+\(\beta\text{-diversity}\) : \(\beta = \frac{\gamma}{\alpha}\) (\(sites/region\))
\(\alpha\)-diversity
Gini-Simpson's index
Gini-Simpson’s index
-
+The Simpson's index is the probability of having the same species twice when you randomly select two specimens.
The Simpson’s index is the probability of having the same species twice when you randomly select two specimens.
\[ @@ -1597,7 +1626,7 @@ Environment.2
\(\lambda\) decrease when complexity of your ecosystem increase.
-Gini-Simpson's index defined as \(1-\lambda\) increase with diversity
+Gini-Simpson’s index defined as \(1-\lambda\) increase with diversity
Shanon entropy
Shannon entropy
-
-
+
+
-
-Shanon entropy is based on information theory.
+Shannon entropy is based on information theory:
-Let \(X\) be a uniformly distributed random variable with values in \(A\)
+\[ -H(X) = \log|A| +\(H^{\prime }=-\sum _{i=1}^{S}p_{i}\log p_{i}\) + +
if \(A\) is a community where every species are equally represented then \[ +H(A) = \log|A| \]
-
-
-
\[
-H^{\prime }=-\sum _{i=1}^{S}p_{i}\log p_{i}
-\]
@@ -1701,7 +1726,7 @@ H^{\prime }=-\sum _{i=1}^{S}p_{i}\log p_{i}
Hill's number
Hill’s number
As : \[
-H(X) = \log|A| \;\Rightarrow\; ^1D = e^{H(X)}
+H(A) = \log|A| \;\Rightarrow\; ^1D = e^{H(A)}
\]
-
+where \(^1D\) is the theoretical number of species in a evenly distributed community that would have the same Shanon's entropy than ours.
where \(^1D\) is the theoretical number of species in a evenly distributed community that would have the same Shannon’s entropy than ours.
Impact of \(q\) on the log_q function
And its inverse function
Generalised Shanon entropy
Generalised Shannon entropy
\[ -^qH = - \sum_{i=1}^S pi \times ^q\log pi +^qH = - \sum_{i=1}^S p_i \; ^q\log p_i \]
H_q = function(x,q=1) {
sum(x * log_q(1/x,q),na.rm = TRUE)
}
-and generalized the previously presented Hill's number
+and generalized the previously presented Hill’s number
\[ ^qD=^qe^{^qH} @@ -1908,22 +1933,22 @@ qs = seq(from=0,to=3,by=0.1) environments.hq = apply(environments,MARGIN = 1,H_spectrum,q=qs) environments.dq = apply(environments,MARGIN = 1,D_spectrum,q=qs) -
Generalized entropy \(vs\) \(\alpha\)-diversity indices
\(^0H(X) = S - 1\) : the richness minus one.
-\(^1H(X) = H^{\prime}\) : the Shanon's entropy.
-\(^2H(X) = 1 - \lambda\) : Gini-Simpson's index.
+\(^1H(X) = H^{\prime}\) : the Shannon’s entropy.
+\(^2H(X) = 1 - \lambda\) : Gini-Simpson’s index.
When computing the exponential of entropy : Hill's number
+When computing the exponential of entropy : Hill’s number
\(^0D(X) = S\) : The richness.
\(^1D(X) = e^{H^{\prime}}\) : The number of species in an even community having the same \(H^{\prime}\).
-\(^2D(X) = 1 / \lambda\) : The number of species in an even community having the same Gini-Simpson's index.
+\(^2D(X) = 1 / \lambda\) : The number of species in an even community having the same Gini-Simpson’s index.
@@ -1941,7 +1966,7 @@ environments.dq = apply(environments,MARGIN = 1,D_spectrum,q=qs)
H.mock = H_spectrum(plants.16$dilution,qs) D.mock = D_spectrum(plants.16$dilution,qs)-
Biodiversity spectrum and metabarcoding (1)
Biodiversity spectrum and metabarcoding (2)
Biodiversity spectrum and metabarcoding (3)
Impact of data cleaning on \(\alpha\)-diversity (1)
Impact of data cleaning on \(\alpha\)-diversity (3)
\(\beta\)-diversity
For the fun… ;-)
For the fun… ;-)
You can generalize those distances as a norm of order \(k\)
@@ -2140,7 +2165,7 @@ d(x,z)\leq \max(d(x,y),d(y,z))The data set
s = tag_bad_pcr(guiana.samples$sample,guiana.count)-
guiana.count.clean = guiana.count[s$keep,] guiana.samples.clean = guiana.samples[s$keep,]@@ -2182,7 +2207,7 @@ guiana.samples.clean = guiana.samples[s$keep,]
s = tag_bad_pcr(guiana.samples.clean$sample,guiana.count.clean)-
guiana.count.clean = guiana.count.clean[s$keep,] guiana.samples.clean = guiana.samples.clean[s$keep,]@@ -2197,7 +2222,7 @@ guiana.samples.clean = guiana.samples.clean[s$keep,]
s = tag_bad_pcr(guiana.samples.clean$sample,guiana.count.clean)-
guiana.count.clean = guiana.count.clean[s$keep,] guiana.samples.clean = guiana.samples.clean[s$keep,]@@ -2264,7 +2289,7 @@ xy = xy[,1:2] xy.hellinger = decostand(xy,method = "hellinger")
-
+
\[ -BC_{jk}=\frac{\sum _{i=1}^{p}]N_{ij} - N_{ik}|}{\sum _{i=1}^{p}N_{ij}+\sum _{i=1}^{p}N_{ik}} +BC_{jk}=\frac{\sum _{i=1}^{p}|N_{ij} - N_{ik}|}{\sum _{i=1}^{p}N_{ij}+\sum _{i=1}^{p}N_{ik}} \]
\[ -BC_{jk}=\frac{\sum _{i=1}^{p}]N_{ij} - N_{ik}|}{1+1} +BC_{jk}=\frac{\sum _{i=1}^{p}|N_{ij} - N_{ik}|}{1+1} \]
\[ -BC_{jk}=\frac{1}{2}\sum _{i=1}^{p}]N_{ij} - N_{ik}| +BC_{jk}=\frac{1}{2}\sum _{i=1}^{p}|N_{ij} - N_{ik}| \]
Principale coordinate analysis (1)
Principale coordinate analysis (2)
Principale composante analysis
guiana.hellinger.pca = prcomp(guiana.hellinger.final,center = TRUE, scale. = FALSE)-
Comparing diversity of the environments
