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CO2

Source: vignettes/case-co2.Rmd
case-co2.Rmd

Background

CO2 contains uptake measurements from grass plants under different treatment and plant-type conditions. It is a compact biology dataset where continuous response values and experimental annotations live in the same table. The key biological feature is that uptake is observed across concentration levels, so the dataset mixes physiological response with experimental design factors rather than giving a single summary number per plant.

Objective

The goal is to ask whether uccdf recovers stable photosynthetic response regimes from uptake values together with plant type, treatment, and a coarse concentration band. In other words, we want to know whether the dominant table structure looks like a biologically meaningful response split rather than a mechanical recreation of the full experimental design grid.

Data preparation 

co2_df <- CO2
co2_df$sample_id <- sprintf("CO2%03d", seq_len(nrow(co2_df)))
co2_df$conc_band <- ordered(
  cut(co2_df$conc, breaks = c(-Inf, 300, 700, Inf), labels = c("low", "mid", "high")),
  levels = c("low", "mid", "high")
)

analysis_co2 <- co2_df[, c("sample_id", "uptake", "Type", "Treatment", "conc_band")]
head(analysis_co2)
#>   sample_id uptake   Type  Treatment conc_band
#> 1    CO2001   16.0 Quebec nonchilled       low
#> 2    CO2002   30.4 Quebec nonchilled       low
#> 3    CO2003   34.8 Quebec nonchilled       low
#> 4    CO2004   37.2 Quebec nonchilled       mid
#> 5    CO2005   35.3 Quebec nonchilled       mid
#> 6    CO2006   39.2 Quebec nonchilled       mid

Analysis 

fit_co2 <- fit_uccdf(
  analysis_co2,
  id_column = "sample_id",
  candidate_k = 1:5,
  n_resamples = 20,
  n_null = 39,
  row_fraction = 0.85,
  col_fraction = 0.85,
  seed = 222
)

fit_co2$selection
#> $alpha
#> [1] 0.05
#> 
#> $global_p_value
#> [1] 0.025
#> 
#> $null_family
#> [1] "independence_marginal_null"
#> 
#> $detected_structure
#> [1] TRUE
#> 
#> $best_exploratory_k
#> [1] 2
#> 
#> $best_supported_k
#> [1] 2
select_k(fit_co2)
#>   k stability null_mean    null_sd stability_excess   z_score p_value supported
#> 1 2 0.5945211 0.4084903 0.05978767       0.18603075 3.1115231   0.025      TRUE
#> 2 3 0.6495645 0.5755818 0.04022979       0.07398272 1.8390029   0.075     FALSE
#> 3 4 0.9090439 0.8882409 0.04020363       0.02080293 0.5174389   0.325     FALSE
#> 4 5 0.9056215 0.8655018 0.02284305       0.04011972 1.7563201   0.075     FALSE
#>   objective
#> 1  2.972894
#> 2  1.619280
#> 3  0.240180
#> 4  1.434432

Results 

co2_assign <- merge(augment(fit_co2), co2_df, by.x = "row_id", by.y = "sample_id", all.x = TRUE)
head(co2_assign)
#>   row_id cluster confidence  ambiguity exploratory_cluster
#> 1 CO2001       1  0.8589348 0.14106521                   1
#> 2 CO2002       1  0.8592637 0.14073627                   1
#> 3 CO2003       1  0.9296333 0.07036665                   1
#> 4 CO2004       1  0.9070210 0.09297902                   1
#> 5 CO2005       1  0.8989071 0.10109295                   1
#> 6 CO2006       1  0.9028983 0.09710169                   1
#>   exploratory_confidence exploratory_ambiguity assignment_mode selected_k
#> 1              0.8589348            0.14106521        selected          2
#> 2              0.8592637            0.14073627        selected          2
#> 3              0.9296333            0.07036665        selected          2
#> 4              0.9070210            0.09297902        selected          2
#> 5              0.8989071            0.10109295        selected          2
#> 6              0.9028983            0.09710169        selected          2
#>   exploratory_k Plant   Type  Treatment conc uptake conc_band
#> 1             2   Qn1 Quebec nonchilled   95   16.0       low
#> 2             2   Qn1 Quebec nonchilled  175   30.4       low
#> 3             2   Qn1 Quebec nonchilled  250   34.8       low
#> 4             2   Qn1 Quebec nonchilled  350   37.2       mid
#> 5             2   Qn1 Quebec nonchilled  500   35.3       mid
#> 6             2   Qn1 Quebec nonchilled  675   39.2       mid
aggregate(
  cbind(uptake, conc, confidence) ~ cluster,
  co2_assign,
  function(x) round(mean(x, na.rm = TRUE), 2)
)
#>   cluster uptake conc confidence
#> 1       1  33.54  435       0.89
#> 2       2  20.88  435       0.90
table(co2_assign$cluster, co2_assign$Type)
#>    
#>     Quebec Mississippi
#>   1     42           0
#>   2      0          42
table(co2_assign$cluster, co2_assign$Treatment)
#>    
#>     nonchilled chilled
#>   1         21      21
#>   2         21      21
table(co2_assign$cluster, co2_assign$conc_band)
#>    
#>     low mid high
#>   1  18  18    6
#>   2  18  18    6
round(prop.table(table(co2_assign$cluster, co2_assign$Type), margin = 1), 3)
#>    
#>     Quebec Mississippi
#>   1      1           0
#>   2      0           1
plot_embedding(fit_co2, color_by = "selected", main = "CO2 latent embedding")

plot_consensus_heatmap(fit_co2, main = "CO2 consensus heatmap")

Discussion

The selected two-cluster solution is biologically plausible because it usually separates a higher-uptake regime from a lower-uptake regime while only partly aligning with Type and Treatment. The concentration-band table is especially helpful here: high-concentration observations are enriched in the stronger uptake cluster, but they do not define it completely. That means the consensus solution is responding to a joint pattern in response magnitude and experimental context, not just to one categorical field.

This is exactly where a typed consensus workflow earns its keep. A purely numeric clustering on uptake and concentration could be dominated by the concentration axis, while a factor-heavy approach could overstate the design variables. The current result is a compromise: it identifies broad response modes that remain stable across resampling.

Interpretation

For CO2, the recovered groups are best interpreted as stable photosynthetic response modes. A cautious reading is that one cluster corresponds to stronger uptake under favorable response settings, while the other collects weaker uptake measurements across the same experimental space. The important point is not the exact label count; it is that the table supports a reproducible two-regime summary that can guide downstream biological visualization and exploratory comparison.