trps (version 0.1.0)

two_source_model_arc: Bayesian model - Two Source Trophic Position with ${\alpha }_r$ and carbon mixing model

Description

Estimate trophic position using a two source model with ${\alpha }_r$ derived from Post 2002 and Heuvel et al. (2024) tools:::Rd_expr_doi("doi:10.1139/cjfas-2024-0028") using a Bayesian framework.

Usage

two_source_model_arc(bp = FALSE, lambda = NULL)

Value

returns model structure for two source model to be used in a brms() call.

Arguments

bp

logical value that controls whether informed priors are supplied to the model for both ${\delta }^{15}$N and ${\delta }^{15}$C baselines. Default is FALSE meaning the model will use uninformed priors, however, the supplied data.frame needs values for both ${\delta }^{15}$N and ${\delta }^{15}$C baseline (c1, c2, n1, and n2).

lambda

numerical value, 1 or 2, that controls whether one or two lambdas are used. See details for equations and when to use 1 or 2. Defaults to 1.

Details

We will use the following equations derived from Post 2002 and Heuvel et al. (2024) tools:::Rd_expr_doi("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. $${\delta }^{13}C=c_1\times {\alpha }_c+c_2\times (1-{\alpha }_c)$$

4. $${\delta }^{15}N=\mathrm{\Delta }N\times (tp-{\lambda }_1)+n_1\times {\alpha }_c+n_2\times (1-{\alpha }_c)$$

5. $${\delta }^{15}N=\mathrm{\Delta }N\times (tp-({\lambda }_1\times {\alpha }_c+{\lambda }_2\times (1-{\alpha }_c)))+n_1\times {\alpha }_c+n_2\times (1-{\alpha }_c)$$

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) tools:::Rd_expr_doi("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 ${\alpha }_c$ 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, $\mathrm{\Delta }$N 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).

The data supplied to brms() when using baselines at the same trophic level (lambda argument set to 1) needs to have the following variables, d15n, n1, n2, l1 (${\lambda }_1$) which is usually 2. If using baselines at different trophic levels (lambda argument set to 2) the data frame needs to have l1 and l2 with a numerical value for each trophic level (e.g., 2 and 2.5; ${\lambda }_1$ and ${\lambda }_2$).

See Also

brms::brms()

Examples

two_source_model_arc()