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BayesianDEB

BayesianDEB provides a Bayesian framework for Dynamic Energy Budget (DEB) modelling in R, using Stan as the computational backend via cmdstanr.

The package implements the standard DEB model (Kooijman, 2010) as a Bayesian state-space model. Parameters are estimated via Hamiltonian Monte Carlo (NUTS; Hoffman & Gelman, 2014), with full posterior uncertainty propagation to derived biological quantities such as ultimate length, von Bertalanffy growth rate, EC50, and NEC.

Overview

Four model types cover the most common DEB applications:

Type	States	Stan model	Use case
`"individual"`	E, V	`bdeb_individual_growth`	Single organism growth
`"growth_repro"`	E, V, R	`bdeb_growth_repro`	Growth + reproduction
`"hierarchical"`	E, V + RE	`bdeb_hierarchical_growth`	Multi-individual, partial pooling
`"debtox"`	E, V, R, D	`bdeb_debtox`	Ecotoxicology (TKTD)

Each model is bundled as a pre-written Stan program; the R layer handles data preparation, prior specification, fitting, diagnostics, and visualisation.

Note on model maturity. The "individual" and "growth_repro" models have the most complete downstream tooling (L_hat trajectories, posterior predictive checks, log_lik for LOO-CV). The "hierarchical" and "debtox" models use reduce_sum for within-chain parallelism, which means PPC and L_hat are not stored in Stan; trajectory plots are instead produced via R-side forward simulation from the posterior. All four model types support full diagnostics, summary, derived quantities, and trace/posterior/pairs plots.

Feature status

Feature	Status	Notes
Individual growth model	stable	2-state DEB, full PPC
Growth + reproduction model	stable	3-state DEB, NegBin/Poisson offspring
Hierarchical growth model	stable	Non-centred param., `reduce_sum` threading
DEBtox (TKTD) model	beta	Group-level (1 ODE/conc.); hierarchical DEBtox planned
Observation models (normal, lognormal, student-t)	stable	Switchable per model via `obs_*()`
Arrhenius temperature correction	stable	Global correction on rate parameters
Prior specification	stable	6 families, weakly informative defaults
Species-specific priors (`prior_species()`)	stable	Built-in for E. fetida, E. andrei, F. candida, D. magna, L. rubellus
Derived quantities (L_m, L_inf, k_M, g, r_B)	stable	Kooijman (2010) formulas, dimensional tests
EC50 / NEC extraction	stable	Analytical, full posterior
Within-chain parallelism (`reduce_sum`)	stable	Hierarchical + DEBtox models
Trajectory plots for hierarchical/debtox	stable	R-side LSODA simulation from posterior
PPC for hierarchical/debtox	not available	Use trajectory plots and `bdeb_diagnose()`
Survival endpoint	planned	Not in current API; will be added in future version
Per-observation temperature (time-varying T)	planned	Currently global only
Multiple stress modes (maintenance, growth cost)	planned	Assimilation stress implemented
Prior-posterior comparison plot	stable	`plot(fit, type = "prior_posterior")`
Prior predictive checks	stable	`bdeb_prior_predictive()` with plot method
Standalone simulators	stable	`deb_simulate()`, `debtox_simulate()`
Maturity dynamics (wider)	planned	Currently post-puberty only
Hierarchical DEBtox (individual-level TKTD)	planned	Currently group-level only
Weight endpoint	planned	Requires shape coefficient in model
Shape coefficient (\(\delta_M\)) estimation	planned	Currently user-supplied conversion
Real-data benchmark dataset	planned	Simulated data validated against AmP

Current limitations

"individual" and "growth_repro" support exactly one individual; multi-individual data require "hierarchical".
"debtox" fits one ODE per concentration group, not per individual. Multi-individual data within a group are aggregated to means (with warning). Hierarchical individual-level DEBtox is planned.
"hierarchical" models random effects on p_Am only; other parameters are shared across individuals.
Survival endpoint is not implemented (not in API).
Temperature correction is global (single T for the entire experiment); time-varying temperature is planned.
Food level (f_food) is constant; time-varying food is not supported.
All lengths are structural (\(L = V^{1/3}\)); the shape coefficient \(\delta_M\) is not estimated (user must convert physical lengths).
R-side simulators (deb_simulate, trajectory plots, prior predictive) use the LSODA solver from deSolve, matching Stan’s BDF solver.

Installation

BayesianDEB requires cmdstanr and a working CmdStan installation.

# 1. Install cmdstanr from r-universe
install.packages("cmdstanr",
  repos = c("https://stan-dev.r-universe.dev", getOption("repos")))

# 2. Install CmdStan (one-time)
cmdstanr::install_cmdstan()

# 3. Install BayesianDEB
# install.packages("BayesianDEB")
# or from source:
# remotes::install_github("sciom/BayesianDEB")

Quick start

library(BayesianDEB)

# Bundled example data: 21 Eisenia fetida individuals, 12 weeks
data(eisenia_growth)

# 1. Prepare data (single individual)
dat <- bdeb_data(growth = eisenia_growth[eisenia_growth$id == 1, ])

# 2. Specify model with custom priors
mod <- bdeb_model(dat, type = "individual",
  priors = list(
    p_Am  = prior_lognormal(mu = 1.5, sigma = 0.5),
    kappa = prior_beta(a = 3, b = 2)
  ))

# 3. Fit
fit <- bdeb_fit(mod, chains = 4, iter_sampling = 1000)

# 4. Inspect
bdeb_diagnose(fit)
plot(fit, type = "trajectory")

# 5. Posterior predictive check
ppc <- bdeb_ppc(fit)
plot(ppc)

# 6. Derived quantities
bdeb_derived(fit, quantities = c("L_inf", "growth_rate"))

Citation

If you use BayesianDEB in your work, please cite:

Hackenberger, B.K., Djerdj, T. and Hackenberger, D.K. (2026). BayesianDEB: Bayesian Dynamic Energy Budget Modelling. R package version 0.1.3. https://github.com/sciom/BayesianDEB

Key references

Kooijman, S.A.L.M. (2010). Dynamic Energy Budget Theory for Metabolic Organisation. 3rd ed. Cambridge University Press. doi:10.1017/CBO9780511805400
Jager, T., Heugens, E.H.W. and Kooijman, S.A.L.M. (2006). Making sense of ecotoxicological test results: towards application of process-based models. Ecotoxicology, 15(3), 305–314. doi:10.1007/s10646-006-0060-x
Carpenter, B. et al. (2017). Stan: A probabilistic programming language. Journal of Statistical Software, 76(1). doi:10.18637/jss.v076.i01

License

MIT

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.