Diagnostics for Soil-Plant-Microbial Redox Recovery

Provides diagnostic functions for integrating longitudinal soil, plant and microbial observations during redox disturbance and recovery. Functions calculate stoichiometric potential oxygen demand, accessible electron capacity from explicitly supplied inventories and kinetic parameters, recovery signatures, fixed-reference domain scores, and exploratory multiblock scores with observation-coverage diagnostics. Memory is represented as a holobiont state accumulating from mineralogical, plant-acclimation and microbial-community legacies. An illustrative simulator produces closed Fe and Mn inventories alongside synthetic observations; its carbon, nitrogen, sulfur and oxygen budgets are not closed and its parameters are not calibrated to field rates. Simulation benchmarks assess agreement with a prescribed synthetic target and do not constitute empirical validation or parameter identification. Accuracy assessment is cluster-aware: intervals come from resampling whole trajectories, agreement is reported as Lin's concordance coefficient alongside correlation, and mean squared error is partitioned into bias, variance mismatch and lack of correlation. The measured quantities follow Sander, Hofstetter and Gorski (2015) for mediated electrochemical determination of electron-accepting and electron-donating capacity, Kluepfel, Piepenbrock, Kappler and Sander (2014) for regeneration of electron-accepting capacity across repeated anoxic periods, Thompson, Chadwick, Rancourt and Chorover (2006) for the increase in iron-oxide crystallinity under redox oscillation, and Keiluweit, Wanzek, Kleber, Nico and Fendorf (2017) for anaerobic microsites in otherwise aerobic soil. Agreement statistics follow Lin (1989) and Kobayashi and Salam (2000) .

HRRI

Diagnostics for soil–plant–microbial redox recovery across hydroclimatic disturbance events.

HRRI provides transparent, assumption-explicit diagnostics for longitudinal soil, plant and microbial observations spanning redox disturbance and recovery. It computes stoichiometric oxygen demand, event-window accessible electron capacity, six recovery signatures, fixed-reference domain scores, and exploratory multiblock composites — each with coverage diagnostics and documented limits on what may be inferred.

Installation

# CRAN release
install.packages("HRRI")

# install.packages("remotes")
remotes::install_github("mghotbi/HRRI", build_vignettes = TRUE)

Quick start

library(HRRI)

## 1 — Generate illustrative trajectories (flood–drain, one cycle)
sim <- simulate_redox_holobiont(
  n_plot = 2, n_depth = 2, n_plant = 3, n_time = 30,
  scenario = "flood_drain", n_cycles = 1, seed = 42
)

## 2 — Score the three observed domains
res <- rri_pipeline(
  plant = sim$ROS_flux,
  soil  = sim$Eh_stability,
  micro = log1p(sim$micro_gene_abundance),
  id    = sim$id,
  direction_anchor_phys  = "FvFm",   # anchor otherwise-arbitrary PCA signs
  direction_anchor_soil  = "Eh",
  direction_anchor_micro = "mtrA"
)

## 3 — Extract recovery signatures (one row per trajectory)
scored <- attach_hrri_ids(res$row_scores, sim$id)
agg    <- aggregate(RRI ~ plot + depth + time, data = scored, FUN = mean)

rri_recovery_metrics(
  agg, time_col = "time", group_cols = c("plot", "depth"),
  perturb_start = 8, perturb_end = 18
)

The four hidden-state controls

Property	Symbol	Interpretation
Capacity	Q	Electron-accepting and electron-donating inventory available within the system (mmol e⁻ kg⁻¹)
Connectivity	α	Fraction of capacity functionally connected to active electron-transfer pathways
Kinetics	k	Characteristic rate of electron exchange under physicochemical and biological constraints (h⁻¹)
Memory	M	Legacy of prior disturbances retained through persistent biogeochemical, microbial and physiological states that influence future system responses

Accessible capacity over an event window of duration τ:

$$C_{\mathrm{acc}}(\tau) ;=; \sum_i Q_i , \alpha_i \left(1 - e^{-k_i \tau}\right)$$

Function reference

Simulation

simulate_redox_holobiont() — mass-conserved Fe/Mn trajectories with plant and microbial observation models
rri_simulation_demo() — reproducible end-to-end demonstration

Capacity and stoichiometry

rri_accessible_capacity() — event-window C_acc for declared reservoirs
rri_o2_demand() — complete-oxidation O₂ demand from reduced-pool inventories
rri_capacity_index() — oxidative-oriented soil feature composite

Scoring

rri_pipeline() — convenience wrapper over available observed domains
rri_pipeline_st() — full-control multiblock interface
rri_reference_scores() — fixed-reference, externally anchored scoring
attach_hrri_ids() — join design identifiers with explicit alignment checks

Recovery and diagnostics

rri_recovery_metrics() — lag, overshoot, hysteresis, depth, incomplete return, displaced plateau
rri_memory_index(), rri_kinetics_score(), rri_connectivity_score(), rri_compensation_index()
rri_property_scores() — property summary with provenance
rri_sensitivity() — sensitivity to domain aggregation weights

Visualisation

plot_rri_timeseries(), plot_rri_state_space(), plot_RRI_ternary(), plot_rri_recovery_map(), plot_rri_properties(), plot_rri_validation()

Scope and limits

HRRI is deliberately conservative about inference. Please note:

Latent axis directions are not biologically identifiable without justified anchors — supply direction_anchor_* arguments.
A score decline does not identify pathway truncation; a displaced plateau does not establish alternative electron routing.
Gene abundance indicates potential, not process rate.
Simulator benchmarks measure agreement with a prescribed synthetic target. They are internal consistency checks, not empirical validation.
pnorm scaling is a monotone transform, not a calibrated probability.

Each function's help page states what its output does and does not support.

Vignette

vignette(package = "HRRI")     
browseVignettes("HRRI")

vignette("HRRI_workflow", package = "HRRI")
vignette("HRRI_gallery", package = "HRRI")

Walks through simulation, accessible-capacity estimation, domain scoring, recovery signatures, and the mineralogical-ratchet disturbance-history experiment.

Citation

citation("HRRI")

Companion manuscripts

HRRI is the software component of three manuscripts, none yet published; two are under review. They are listed because the package implements what they describe. Please cite the published version once available.

Software and framework — the paper this package accompanies Ghotbi, M., Ghotbi, M., Komluski, J., & Holtgrewe-Stukenbrock, E. H. HRRI: a framework for diagnosing redox recovery in soil–plant–microbiome systems. In preparation. → implemented by rri_pipeline_st(), rri_property_scores(), rri_recovery_metrics(), rri_accuracy().

Theory — where the four hidden states come from Ghotbi, M., Kolody, B. C., Ghotbi, M., & Holtgrewe-Stukenbrock, E. A Theory of Hydroclimatic Redox Resilience. Submitted to Communications Earth & Environment. → the capacity–connectivity–kinetics–memory decomposition and the accessible-capacity expression, implemented by rri_accessible_capacity().

Mechanistic review — the biology the simulator encodes Ghotbi, M., Ghotbi, M., Mühling, K. H., & Stukenbrock, E. H. Rhizosphere redox recovery after hydrological disturbances: mechanisms across the soil–plant–microbiome continuum. Submitted to Soil Biology & Biochemistry. → the plant, microbial and mineralogical legacy terms in simulate_redox_holobiont().

None is required to use the package, and none is cited in DESCRIPTION: CRAN asks that the Description field carry only references a reader can retrieve, so it lists the published methods sources instead.

Published methods this package builds on

Every DOI below was resolved against Crossref before being listed.

Measuring the four quantities

Reference	What HRRI takes from it
Sander, Hofstetter & Gorski (2015) Environ. Sci. Technol. 49:5862 doi:10.1021/acs.est.5b00006	Mediated electrochemical measurement of EAC and EDC in electron equivalents — the capacity Q the index scores, rather than an elemental concentration
Dorau et al. (2022) Eur. J. Soil Sci. 73:e13165 doi:10.1111/ejss.13165	Connected air-filled porosity, not total air content, governs the shift toward oxidising conditions — the measurement behind α
Peiffer et al. (2021) Nat. Geosci. 14:264–272 doi:10.1038/s41561-021-00742-z	Framework coupling redox-active compound pools to hydrological forcing — why inventory and event timescale must be carried separately

Why bulk state variables are not enough

Reference	What HRRI takes from it
Rooney et al. (2024) Commun. Earth Environ. 5 doi:10.1038/s43247-024-01927-1	Redox processes decouple from soil saturation — moisture recovery does not imply redox recovery
Keiluweit et al. (2017) Nat. Commun. 8:1771 doi:10.1038/s41467-017-01406-6	Anaerobic microsites persist in aerobic soil — why connectivity is separated from capacity rather than folded into it
Angle et al. (2017) Nat. Commun. 8:1567 doi:10.1038/s41467-017-01753-4	Methanogenesis in oxygenated soils — reducing metabolism where a bulk measurement would not predict it

Memory as a state, not a trend

Reference	What HRRI takes from it
Thompson et al. (2006) Geochim. Cosmochim. Acta 70:1710–1727 doi:10.1016/j.gca.2005.12.005	Iron-oxide crystallinity increases under redox oscillation — the mineralogical ratchet
Aeppli et al. (2019) Environ. Sci. Technol. 53:3568–3578 doi:10.1021/acs.est.8b07190	Reducibility falls as ferrihydrite transforms abiotically to goethite and magnetite — why the ratchet lowers the ceiling
Aeppli et al. (2019) Environ. Sci. Technol. 53:8736–8746 doi:10.1021/acs.est.9b01299	The same loss of reducibility under microbial reductive dissolution — the ratchet is not solely abiotic
Klüpfel et al. (2014) Nat. Geosci. 7:195–200 doi:10.1038/ngeo2084	Humic electron-accepting capacity is fully regenerable across repeated anoxic periods — a cycle, not a ratchet, so the two components cannot share one decay term
Meisner et al. (2021) ISME J. 15:1207–1221 doi:10.1038/s41396-020-00844-3	Microbial legacies differ by disturbance type — why soil, plant and microbial legacies are returned separately

Limits on what may be inferred

Reference	What HRRI takes from it
Louca et al. (2018) Nat. Ecol. Evol. 2:936–943 doi:10.1038/s41559-018-0519-1	Functional redundancy decouples taxonomy from function — gene abundance indicates potential, not process rate
Gloor et al. (2017) Front. Microbiol. 8:2224 doi:10.3389/fmicb.2017.02224	Microbiome data are compositional — why a log-ratio workflow must be declared rather than assumed

Statistics

Reference	What HRRI takes from it
Lin (1989) Biometrics 45:255–268 doi:10.2307/2532051	Concordance correlation coefficient — agreement, not merely association, reported by `rri_accuracy()`
Kobayashi & Salam (2000) Agron. J. 92:345–352 doi:10.2134/agronj2000.922345x	Exact partition of mean squared error into bias, variance mismatch and lack of correlation

Rate context for the O₂ demand calculation

Reference	What HRRI takes from it
Stumm & Lee (1961) Ind. Eng. Chem. 53:143–146 doi:10.1021/ie50614a030	Fe(II) oxygenation kinetics — stoichiometric demand is pH-independent, the rate is not
Millero, Sotolongo & Izaguirre (1987) Geochim. Cosmochim. Acta 51:793–801 doi:10.1016/0016-7037(87)90093-7	The ~100-fold rate increase per unit pH that separates a ceiling from a realised consumption

License

Publication figures (1.0.8)

p <- plot_rri_properties(props)  # separate descriptors; no centre average
p_recovery <- plot_rri_recovery_landscape(rec)  # retains unavailable metrics
p_map <- plot_rri_recovery_map(res, id, rec = rec,
  perturb_start = event_start, perturb_end = event_end)
# Use the independent experimental unit as cluster, e.g. plot, not each row.
p_agreement <- plot_rri_accuracy(acc)
ggplot2::ggsave("HRRI_profile.pdf", p, width = 7.2, height = 4.5,
                units = "in", device = "pdf")

All figures are computed from supplied objects. Do not paste manuscript values into plotting functions. Keep event definitions, component methods and unavailable measurements in figure captions. The default profile replaces the radar display; type = "radar" is still available explicitly. orient = "concern" and drop_empty = TRUE remain optional for recovery landscapes, but neither removes the need to explain cohort-relative scaling and missingness. Agreement limits for cluster means do not describe individual observations. Bootstrap intervals are conditional on supplied pairs, not a rerun of the complete fitted pipeline.

All six paper figures in R

Figure	Function
Framework	`plot_rri_framework()`
Identifiability and accounting	`plot_rri_identifiability()`
Forcing and responses	`plot_rri_timeseries()`
Score dynamics and availability	`plot_rri_recovery_diagnostics()`
Operational profile	`plot_rri_properties()`
Conditional agreement	`plot_rri_accuracy()`

See vignette("HRRI_paper_figures") for the complete map and captions. Both original vignettes remain available, with corrected terminology and sampling units; their existing references are retained.