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ORDINATION METHODS TO BUILD MICROBIOTA
SIMILARITY MATRICES FOR COMPLEX TRAITS
PREDICTION
Alejandro Saborío-Montero
Oscar González-Recio
EAAP 2018
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There are evidences of:
• Microbiome influencing complex traits in ruminants
• Partial control of host genotype over microbiome composition
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• These evidences pose the hypothesis of microbiome as asource of information to predict complex traits
• Complex traits as feed efficiency and methane emissionscould be included into genetic evaluations taking intoaccount a microbiome effect to select highly profitable andsustainable animals
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• Single given OTU vs whole microbiota in statistical analysis.
• Microbiota relationship matrices (MRM) consider microbiotaas a whole; However there are differences in the methods ofordination of matrices leading to differences in MRM outputs.
• The comparison of MRM has not been evaluated previously inan animal breeding context.
• We propose to compare the MRM obtained from differentordination methods to disentangle which are the mostappropriate to be included in statistical models analyzinggenotype and microbiome to predict feed efficiency.
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• Develop and test some statistical approaches to evaluate feed efficiency indairy cows including host genotype and microbiome simultaneously.
• Compare ordination methods to build MRM using simulation
• Estimate the proportion of phenotypic variance for feed efficiency explainedby microbiome variance (microbiability), considering the interactionbetween microbiota and host genotype
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• Simulated data
• 1000 Holstein cows and 92 OTUs
• Microbiota effect (co(variances) matrix from real data)
• Genetic effect (assigning effects to simulated QTL)
• Phenotype
• Real data
• 70 Holstein cows
• Microbiota
• V3-V4 hypervariable regions 16S rRNA (92 OTU)
• Genotype
• 54609 SNPs
• Phenotype
• Parity, DMI, milk yield, fat, protein body weight, feed efficiency.
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Genomic + Microbiota
𝐲 = 1′𝛍 + 𝐙𝐮 +𝐖𝐦+ 𝐞
Residual
Microbiota effect
Incidence matrix (microbiota)
Additive genetic effect
Incidence matrix (genotype)
Population mean
An nx1 vector of ones
Feed efficiency
• u ~N (0, GRM𝜎𝑢2),
• m ~N (0, MRM𝜎𝑚2 ) y
• e ~N (0,𝜎𝑒2)
ConclusionsResultsMat. y MethodsObjectivesJustificationBackground
Bayesian resolution approach
BGLR package in R environment
Effects were included as RKHS
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Genomic + Microbiota + Genomic*Microbiota
Residual
genetic-microbiota interaction
Incidence matrix (interaction)
Microbiota effect
Incidence matrix (microbiota)
Additive genetic effect
Incidence matrix (genotype)
Population mean
An nx1 vector of ones
Feed efficiency
𝐲 = 1′𝛍 + 𝐙𝐮 +𝐖𝐦+𝐓𝐮𝑥𝐦+ 𝐞 • u ~N (0, GRM𝜎𝑢2),
• m ~N (0, MRM𝜎𝑚2 )
• u x m ~N (0, GRM#MRM𝜎𝑢xm2 )
• e ~N (0,𝜎𝑒2)
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Reference MRM
x11 x12 x13 . . . xij
x21 x22 x23 . . . xij
x31 x32 x33 . . . xij
. . . . . . xij
. . . . . . xij
. . . . . . xij
xij xij xij xij xij xij xij
OTU
Sam
ple
Each element (xij) from the X matrix is the log-transformed andstandardized count for relative abundance for sample i in OTU j
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Ordination methods used• Metric Multidimensional Scaling (MDS/PCoA)
• Detrended Correspondence Analysis (DCA)
• Non-Metric Multidimensional Scaling (NMDS)
• Redundancy Analysis (RDA)
• Constrained Correspondence Analysis (CCA)
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Relative abundance of OTUs
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Association between diagonal elements
vs
A
B
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vs
A
B
ConclusionsResultsMat. y MethodsObjectivesJustificationBackground
Association between diagonal elements
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Association between non-diagonal elements
A
B
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A
B
ConclusionsResultsMat. y MethodsObjectivesJustificationBackground
Association between non-diagonal elements
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Variance components 𝐲 = 1′𝛍 + 𝐙𝐮 +𝐖𝐦+ 𝐞
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Heritability and Microbiability
𝐲 = 1′𝛍 + 𝐙𝐮 +𝐖𝐦+ 𝐞
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Accuracy (GEBV vs TBV)
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Accuracy (GEBV vs TBV)
ConclusionsResultsMat. y MethodsObjectivesJustificationBackground
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Accuracy (EMV vs TMV)
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Accuracy (EMV vs TMV)
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Variance components
𝐲 = 1′𝛍 + 𝐙𝐮 +𝐖𝐦+𝐓𝐮𝑥𝐦+ 𝐞
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Heritability and Microbiability𝐲 = 1′𝛍 + 𝐙𝐮 +𝐖𝐦+𝐓𝐮𝑥𝐦+ 𝐞
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Real Data
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𝐲 = 1′𝛍 + 𝐙𝐮 +𝐖𝐦+ 𝐞
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𝐲 = 1′𝛍 + 𝐙𝐮 +𝐖𝐦+𝐓𝐮𝑥𝐦+ 𝐞
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Statistical model comparison
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• The obtained MRM using MDS, RDA and CCA were as suitable as, or even betterthan the benchmark matrix in terms of the estimation of variance components,heritability and microbiability using simulation analysis.
• The genomic breeding values were accurately predicted when a microbiome effectwas accounted for; the benchmark matrix and the canonical ordination methods ofCCA and RDA showed higher accuracies than MDS, DCA and NMDS.
• It is possible to include a whole microbiota effect in the statistical analysis of feedefficiency.
• From the deviance information criteria, there is not enough evidence to reject anyof the models that include microbiota information.
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Thanks
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Simulation of microbiota
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Simulation of microbiota effect
• 50 out of the 92 OTUs were randomly selected. An effect (𝜷𝒋) was
sampled from a normal distribution (N ~ (0, 1)) and assigned toeach of the 50 selected OTUs.
• The microbiota effect (m) for each animal was simulated as follow:
𝒎𝒊 =𝒋𝜷𝒋 × 𝑶𝑻𝑼𝒊𝒋
• Where 𝜷𝒋 i s the effect of 𝑂𝑇𝑈𝑗 and 𝑂𝑇𝑈𝑖𝑗 is the relative
abundance of OTU j in animal i. The resulting {mi} was scaled tohave a variance of 𝜎𝑚
2
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Simulation of genotype effect
• A dataframe with 1000 genotyped Holstein cows with allelic variants for 9244 SNPs was used
• The additive genetic effects were determined by 1000 QTL which were simulated from a normal distribution (~N (0, 1))
• The true breeding values (u) were calculated by adding all QTL effects which were subsequently scaled to a realized variance of 𝜎𝑢
2
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Simulation of phenotype
• Phenotypes were simulated assigning a residual variance toobtain a heritability of 0,3 and a microbiability of 0,5
• Simulated for an independent effect model and for aninteraction effect model as follow:
𝒚𝒊 = 𝝁 + 𝒖𝒊 +𝒎𝒊 + 𝒆𝒊
𝒚𝒊 = 𝝁 + 𝒖𝒊 +𝒎𝒊 + 𝒖𝒊 ×𝒎𝒊 + 𝒆𝒊
• Where µ is the population mean, ui is the genomic effect, mi
is the microbiota effect, 𝒖𝒊 × mi is the genomic-microbiotainteraction effect and ei is the residual.
ConclusionsResultsMat. y MethodsObjectivesJustificationBackground