vitalBayes

Bayesian Vital Rates for Elasmobranchs

vitalBayes provides a coherent Bayesian framework for estimating vital rates in elasmobranchs—from birth and maturity through growth to natural mortality and survival. The package implements hierarchical models using Stan software via the CmdStan R package. For fast and reliable inference, the user will precompile several Stan models upon instillation.

Installation

# Install dependencies
install.packages(c("cmdstanr", "data.table", "ggplot2", "loo", "pracma"))

# Install cmdstan (if not already installed)
cmdstanr::install_cmdstan()

# Install vitalBayes from GitHub
pak::pak("Brian-J-Moe/vitalBayes")

# compile Stan models
vitalBayes::precompile_models()

The Workflow

vitalBayes implements an integrated four-stage workflow where posterior distributions flow forward through life stages:

Birth  ──▶  Maturity  ──▶  Growth  ──▶  Mortality/Survival
(L₀)       (L₅₀, t₅₀)      (L∞, k)         (M, S(t))

library(vitalBayes)
library(data.table)

data(growth_data)

# Stage 1: Birth size ─────────────────────────────────────────
birth_fit <- fit_bayesian_birth(
  embryo_lts        = growth_data[embryo == TRUE, fl],
  free_swimming_lts = growth_data[embryo == FALSE, fl]
)

# Stage 2: Maturity ───────────────────────────────────────────
mat_data <- growth_data[embryo == FALSE & !is.na(mat)]

L50_fit <- fit_bayesian_maturity(
  maturity = "mat", lt = "fl", sex = "sex",
  data = mat_data, use_pooling = TRUE
)

t50_fit <- fit_bayesian_maturity(
  maturity = "mat", age = "age", sex = "sex",
  data = mat_data[!is.na(age)], use_pooling = TRUE
)

# Stage 3: Growth ─────────────────────────────────────────────
growth_fit <- fit_bayesian_growth(
  lt = "fl", age = "age", sex = "sex",
  data = growth_data[embryo == FALSE & !is.na(age)],
  model   = "vb",
  k_based = FALSE,      # Maturity-based parameterization
  birth_stanfit         = birth_fit,
  length.mature_stanfit = L50_fit,
  age.mature_stanfit    = t50_fit,
  use_pooling = TRUE
)

# Stage 4: Mortality & Survival ───────────────────────────────
mort <- get_stochastic_mortality(
  method       = "CW",
  Linf = c(100, 8), L0 = c(30, 3), Lmat = c(70, 5), tmat = c(12, 2),
  growth_model = "vb",
  iter = 2000, scaled = TRUE, p = 0.001
)

surv <- simulate_survivorship(mc_object = mort, n = 50000, n_iter = 2000)
surv$Aggregate$Age_of_Death
surv$Aggregate$Survival_to_tmat

Key Methodological Features

Maturity-Based Growth Parameterization

The growth coefficient k is derived from observable maturity milestones (L₅₀, t₅₀) rather than estimated directly. This breaks the notorious L∞–k correlation and anchors the growth curve to data within the observed range. Supports von Bertalanffy, Gompertz, and Logistic models.

Partial Pooling for Imbalanced Data

Hierarchical models borrow strength across sexes when sample sizes are unequal—common in elasmobranch research. The sparse sex gets regularized estimates without assuming identical parameters. Selective pooling prevents “double-pooling” when maturity priors are themselves pooled.

Unified Mortality Framework

Natural mortality uses a consistent formulation across growth models: M(t) = M∞ / G(t), where M∞ is computed from biological milestones and G(t) uses the native growth trajectory. This ensures comparable survival predictions regardless of which growth model best fits your data.

Probit Link for Thresholds

Birth size and maturity ogives use probit rather than logit links, providing direct interpretation as cumulative normal distributions of developmental thresholds.

CV-Based Priors

Prior uncertainty is specified via coefficient of variation—intuitive, scale-invariant, and easily communicated (e.g., “20% uncertainty on L∞”).

Supported Models

Component	Options
Growth	von Bertalanffy, Gompertz, Logistic
Mortality	Chen-Watanabe (with optional two-phase senescence), Peterson-Wroblewski, Lorenzen
Pooling	None, partial (hierarchical), or selective

Example Datasets

Dataset	Sex Ratio	Use Case
growth_data	189F, 176M	Main workflow examples
imbalanced_data	150F, 34M	Partial pooling demonstrations
limited_data	24F, 18M	Prior sensitivity analysis

Vignettes

Topic	Vignette
Birth size	vignette("fit_bayesian_birth")
Maturity ogives	vignette("fit_bayesian_maturity")
Growth models	vignette("fit_bayesian_growth")
Partial pooling	vignette("partial_pooling")
Mortality estimation	vignette("mortality_estimation")
Mortality framework	vignette("chen_watanabe_reparameterization")
Survival simulation	vignette("survivorship_simulation")
Diagnostics	vignette("model_diagnostics")

Citation

@manual{vitalBayes,
  title = {{vitalBayes}: Bayesian Vital Rate Estimation for Elasmobranchs},
  author = {Brian J. Moe},
  year = {2025},
  note = {R package version 0.7.0},
  url = {https://github.com/Brian-J-Moe/vitalBayes}
}

License

MIT