test lvip_glm

[rmcminds]

I've written a model that should be able to simultaneously control for and assess alpha diversity, overall beta diversity, and individual differential abundances and prevalences. I'd like to test it on a relatively simple experimental design.

[rmcminds]

The basic idea is that all these things can be modeled with a relatively simple zero-inflated generalized linear model.

• Alpha diversity is the tendency for a sample to have a greater number of taxa. When modeling prevalence with a logistic linear model, a main effect that applies to all taxa can capture this pattern. In other words, if treatment A causes all taxa to be more likely to be present, a given sample will have more taxa.

• Beta diversity is sometimes thought of as a somewhat abstract idea that the 'composition' of samples is different. In other words, if sample A has 3 taxa, and sample B has 3 taxa, their alpha diversity might be the same, but if the three taxa have different identities, there is higher beta diversity in the set that is created by the two samples. This pattern is the aggregate of the same pattern captured by 'differential abundance' analyses, which are simply linear models that allow individual taxa to differ between treatments (which a permanova/adonis would also capture), or allowing taxa to differ between samples as 'residual variance', which could be captured by permdisp if the residual variance differs among treatments. In addition, in a zero-inflated framework, taxon-specific effects can be modeled for both the zero inflation (presence/absence) and for differential abundance. These are distinct patterns that can be separated in a linear model that are often difficult to tell apart with 'multivariate analyses'. The aggregate 'beta diversity' tests analogous to permanova and permdisp can be replaced by determining the % variance explained for each factor.

• Differential abundance analysis and differences in prevalence can be determined by looking at the individual parameters in the above analysis.

• I've also included phylogenetic effects, which allows you to assess alpha diversity or differential prevalence/abundance within entire phylogenetic groups, without arbitrarily collapsing taxa. I've implemented an Ornstein Uhlenbeck effect to constrain the total possible variance, which is probably more realistic.

• I've also modified the 'zero-inflated' model to a 'low-value-inflated' model. This allows for contamination and/or relatively discrete differences in abundance between treatments.

[rmcminds]

Hopefully, the idea is that you just provide a (unrarefied) count matrix, a phylogenetic tree, and a model matrix, and my scripts can take that and analyze it. Some of the summarizations and hypothesis testing will need to be done 'by hand' after the model fits.