---
title: "Dominant Community State Types: From Normalization to a Gut Demonstration"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Dominant Community State Types: From Normalization to a Gut Demonstration}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{css, echo=FALSE}
table td, table th { white-space: nowrap; }
```

```{r setup, include=FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment  = "#>",
  fig.width = 7,
  fig.height = 5
)
library(linf)
```

The `linf` package implements L-infinity normalization and Dominant Community
State Types (dCSTs) for compositional data. This vignette demonstrates the
complete workflow in two parts: first a quick-start with toy data to introduce
the core functions, then a real-data analysis of gut microbiome samples from
the American Gut Project showing how to inspect dominant and subdominant
community structure.

## Part 1: Quick Start with Toy Data

### L-infinity normalization

L-infinity normalization scales each row of a count matrix by its maximum
value, projecting samples onto the L-infinity unit ball. Every normalized row
has a maximum of exactly 1.

```{r toy-normalize}
set.seed(1)
S.counts <- matrix(
  rpois(30, lambda = 5),
  nrow = 10, ncol = 3,
  dimnames = list(paste0("s", 1:10), c("Taxon_A", "Taxon_B", "Taxon_C"))
)

Z <- normalize.linf(S.counts)
apply(Z, 1, max)   # all 1
```

### Dominance sample sets

Each sample is assigned to its dominant feature: the column achieving the
within-sample maximum. Samples with the same dominant feature form a
depth-1 *dominance sample set*.

```{r toy-dominant.features}
dominant.features <- linf.dominant.features(Z)
table(dominant.features$label)
```

### Truncated dCSTs

`linf.csts()` groups samples by dominant feature and collapses small groups
(below threshold `n0`) into a `RARE_DOMINANT` bucket. This produces
*Dominant Community State Types* (dCSTs).

```{r toy-csts}
A <- matrix(c(5, 1, 0), nrow = 6, ncol = 3, byrow = TRUE)
B <- matrix(c(1, 5, 0), nrow = 2, ncol = 3, byrow = TRUE)
C <- matrix(c(1, 0, 5), nrow = 2, ncol = 3, byrow = TRUE)
S <- rbind(A, B, C)
S <- sweep(S, 1, rowSums(S), "/")
colnames(S) <- c("Dom1", "Dom2", "Dom3")

res <- linf.csts(S, n0 = 5)
table(res$lineage.label, useNA = "ifany")
```

Only Dom1 (6 samples) meets the `n0 = 5` threshold. Dom2 and Dom3 are
collapsed into `RARE_DOMINANT`.


## Part 2: Gut Microbiome dCST Demonstration

### Background

Single-species dominance is common in some microbial ecosystems and less
common in others. dCSTs provide a deterministic way to summarize the dominant
feature and then refine large groups by subdominant features. The gut example
below demonstrates those mechanics without treating the selected package
subset as an epidemiologic sample.

### The data

The `agp_gut` dataset bundled with this package contains `r nrow(agp_gut$counts)`
gut microbiome samples from the American Gut Project (PRJEB11419), a citizen-science
16S rRNA V4 survey. The dataset is a dCST-stratified demonstration subset
that includes all samples in four selected uncommon dCSTs and fills
the remaining slots with a seed-42 simple random sample from the eligible
background. Phenotypes are joined only after selection and do not influence
membership. Because inclusion probabilities differ by dCST, it is not a
probability sample of the underlying cohort; phenotype frequencies, effect
sizes, and hypothesis tests must not be interpreted as population results.

```{r load-data}
data(agp_gut)
str(agp_gut, max.level = 1)

dim(agp_gut$counts)   # samples x taxa
```

Metadata includes self-reported health conditions parsed from the AGP
questionnaire:

```{r meta-summary}
disease_cols <- c("IBS", "IBD", "Obesity", "Cardiovascular_disease",
                  "Autoimmune", "Acid_reflux")
sapply(disease_cols, function(col) sum(agp_gut$meta[[col]], na.rm = TRUE))
```

### Step 1: Quality filtering

`filter.asv()` removes low-depth samples and rare taxa in one call. We
require at least 1,000 reads per sample and taxa present in at least 5% of
samples.

```{r filter}
filt <- filter.asv(agp_gut$counts, min.lib = 1000, prev.prop = 0.05,
                   min.count = 2)
dim(filt$counts)
dim(filt$rel)
```

### Step 2: L-infinity normalization

```{r normalize}
M <- normalize.linf(filt$counts)

# Verify: every row max is 1
stopifnot(all(abs(apply(M, 1, max) - 1) < 1e-10))
```

### Step 3: Depth-1 dCSTs

```{r dcst-depth1}
csts <- linf.csts(M, n0 = 30)

# dCST size distribution
sort(table(csts$lineage.label), decreasing = TRUE)
```

The landscape is dominated by *Bacteroides* and *Escherichia-Shigella*, with
*Prevotella*, *Faecalibacterium*, and several smaller dCSTs forming the tail.
The `RARE_DOMINANT` bucket collects samples dominated by taxa too infrequent
to form their own dCST at this threshold.

Note on *Escherichia-Shigella*: this genus is known to be inflated in 16S V4
data due to primer cross-reactivity. Its high prevalence should be interpreted
with caution.

### Step 4: Depth-2 refinement

`refine.linf.csts()` subdivides large dCSTs by their *subdominant* species.
For instance, a Bacteroides-dominated sample might be further classified by
whether its second-most-abundant taxon is *Faecalibacterium* or
*Lachnospiraceae*. This captures co-dominance patterns that are especially
important in the diverse gut environment.

```{r dcst-depth2}
csts2 <- refine.linf.csts(M, csts, n0 = 30)

# Show depth-2 dCSTs with >= 20 samples
tab2 <- sort(table(csts2$lineage.label), decreasing = TRUE)
tab2[tab2 >= 20]
```

### Dominance strength

A useful diagnostic: the relative abundance of the dominant species in each
sample. In the gut, most samples have modest dominance (< 50%), consistent
with the diverse nature of the ecosystem.

```{r dominance-dist, fig.cap = "Distribution of dominance strength across gut samples. Most samples show moderate dominance, with a tail of strongly dominated communities."}
rel <- filt$rel
dom_strength <- apply(rel, 1, max)
hist(dom_strength, breaks = 50, col = "#2ecc71", border = "white",
     main = "Dominance Strength in Gut Microbiome",
     xlab = "Relative abundance of dominant species",
     ylab = "Number of samples")
abline(v = 0.5, col = "red", lty = 2, lwd = 2)
legend("topright", "50% dominance", col = "red", lty = 2, lwd = 2, bty = "n")
```


### dCST size distribution

```{r dcst-barplot, fig.cap = "dCST size distribution at depth 1. Bacteroides and Escherichia-Shigella dominate; rare dCSTs in the tail are collapsed into RARE_DOMINANT."}
tab1 <- sort(table(csts$lineage.label), decreasing = TRUE)
par(mar = c(10, 4, 3, 1))
bp <- barplot(tab1,
        col = ifelse(names(tab1) == "RARE_DOMINANT", "#e74c3c", "#3498db"),
        las = 2, cex.names = 0.7,
        ylab = "Number of samples",
        main = "Gut dCST Size Distribution (depth 1)")
text(bp, tab1 + 5, labels = tab1, cex = 0.7, pos = 3)
```


### Phenotype metadata

The bundle retains selected self-reported phenotype fields so that users can
inspect the object structure and practice data alignment. The following table
is purely descriptive; dCST-stratified selection precludes population
prevalence estimation or treating association calculations as cohort results.

```{r phenotype-summary}
meta <- agp_gut$meta[match(rownames(M), agp_gut$meta$Run), ]
stopifnot(all(meta$Run == rownames(M)))

conditions <- c("IBS", "IBD", "Obesity", "Cardiovascular_disease",
                "Autoimmune", "Acid_reflux", "Lung_disease")
phenotype_summary <- data.frame(
  Condition = conditions,
  Recorded_cases = vapply(
    conditions,
    function(x) sum(meta[[x]] == 1, na.rm = TRUE),
    integer(1)
  ),
  Non_missing = vapply(
    conditions,
    function(x) sum(!is.na(meta[[x]])),
    integer(1)
  )
)
knitr::kable(
  phenotype_summary,
  caption = "Recorded phenotypes in the selected demonstration subset"
)
```


## Limitations

This analysis has several important caveats:

- **Self-reported metadata.** AGP health conditions are self-reported by
  citizen-science participants, with unknown accuracy.
- **16S resolution.** The Escherichia-Shigella inflated abundance is a known
  V4 artifact. Shotgun metagenomics would resolve this.
- **dCST-stratified demonstration subset.** Four uncommon dCSTs are included
  exhaustively and the eligible background is sampled with seed 42.
  Phenotypes do not affect membership, but differing inclusion probabilities
  mean the object must not be used for population prevalence estimates,
  effect-size estimation, or association testing.

The repository also contains the source for a separate 5,000-sample companion
analysis. It is not installed as a package vignette.

## Summary

The dCST framework provides a clustering-free approach to
community typing that is deterministic, hierarchical, and biologically
interpretable. The combination of depth-1 dCSTs (dominant species) and depth-2
refinement (co-dominance patterns) captures structure at multiple resolutions
without requiring any parameter tuning beyond the minimum support threshold
`n0`.
