two_source_priors_params_arc {trps}R Documentation

Adjust Bayesian priors - Two Source Trophic Position with \alpha_r and carbon mixing model

Description

Adjust priors for trophic position using a two source model with \alpha_r derived from Post 2002 and Heuvel et al. (2024) doi:10.1139/cjfas-2024-0028

Usage

two_source_priors_params_arc(
  a = NULL,
  b = NULL,
  n1 = NULL,
  n1_sigma = NULL,
  n2 = NULL,
  n2_sigma = NULL,
  c1 = NULL,
  c1_sigma = NULL,
  c2 = NULL,
  c2_sigma = NULL,
  dn = NULL,
  dn_sigma = NULL,
  tp_lb = NULL,
  tp_ub = NULL,
  sigma_lb = NULL,
  sigma_ub = NULL,
  bp = FALSE
)

Arguments

a

(\alpha) exponent of the random variable for beta distribution. Defaults to 1. See beta distribution for more information.

b

(\beta) shape parameter for beta distribution. Defaults to 1. See beta distribution for more information.

n1

mean (\mu) prior for first \delta^{15}N baseline. Defaults to 8.0.

n1_sigma

variance (\sigma)for first \delta^{15}N baseline. Defaults to 1.

n2

mean (\mu) prior for second \delta^{15}N baseline. Defaults to 9.5.

n2_sigma

variance (\sigma) for second \delta^{15}N baseline. Defaults to 1.

c1

mean (\mu) prior for first \delta^{13}C baseline. Defaults to -21.

c1_sigma

variance (\sigma)for first \delta^{13}C baseline. Defaults to 1.

c2

mean (\mu) prior for second \delta^{13}C baseline. Defaults to -26.

c2_sigma

variance (\sigma) for second \delta^{13}C baseline. Defaults to 1.

dn

mean (\mu) prior value for \DeltaN. Defaults to 3.4.

dn_sigma

variance (\sigma) for \delta^{15}N. Defaults to 0.25.

tp_lb

lower bound for priors for trophic position. Defaults to 2.

tp_ub

upper bound for priors for trophic position. Defaults to 10.

sigma_lb

lower bound for priors for \sigma. Defaults to 0.

sigma_ub

upper bound for priors for \sigma. Defaults to 10.

bp

logical value that controls whether informed baseline priors are supplied to the model for \delta^{15}N baselines. Default is FALSE meaning the model will use uninformed priors, however, the supplied data.frame needs values for both \delta^{15}N baseline (n1 and n2)

Details

We will use the following equations derived from Post 2002 and Heuvel et al. (2024) doi:10.1139/cjfas-2024-0028:

  1. \alpha = (\delta^{13} C_c - \delta ^{13}C_2) / (\delta ^{13}C_1 - \delta ^{13}C_2)

  2. \alpha = \alpha_r \times (\alpha_{max} - \alpha_{min}) + \alpha_{min}

  3. \delta^{13}C = c_1 \times \alpha_r + c_2 \times (1 - \alpha_r)

  4. \delta^{15}N = \Delta N \times (tp - \lambda_1) + n_1 \times \alpha_r + n_2 \times (1 - \alpha_r)

  5. \delta^{15}N = \Delta N \times (tp - (\lambda_1 \times \alpha_r + \lambda_2 \times (1 - \alpha_r))) + n_1 \times \alpha_r + n_2 \times (1 - \alpha_r)

For equation 1)

This equation is a carbon source mixing model with \delta^{13}C_c is the isotopic value for consumer, \delta^{13}C_1 is the mean isotopic value for baseline 1 and \delta^{13}C_2 is the mean isotopic value for baseline 2.

For equation 2)

\alpha is being corrected using equations in Heuvel et al. (2024) doi:10.1139/cjfas-2024-0028. with \alpha_r being the corrected value (bound by 0 and 1), \alpha_{min} is the minimum \alpha value calculated using add_alpha() and \alpha_{max} being the maximum \alpha value calculated using add_alpha().

For equation 3)

This equation is a carbon source mixing model with \delta^{13}C being estimated using c_1, c_2 and \alpha_r calculated in equation 1.

For equation 4) and 5)

\delta^{15}N are values from the consumer, n_1 is \delta^{15}N values of baseline 1, n_2 is \delta^{15}N values of baseline 2, \DeltaN is the trophic discrimination factor for N (i.e., mean of 3.4), tp is trophic position, and \lambda_1 and/or \lambda_2 are the trophic levels of baselines which are often a primary consumer (e.g., 2 or 2.5).

This function allows the user to adjust the priors for the following variables in the equation above:

Value

stanvars object to be used with brms() call.

See Also

two_source_priors_arc(), two_source_model_arc(), and brms::brms()

Examples

two_source_priors_params_ar()

[Package trps version 0.1.0 Index]