# eDNAjoint

# Chapter 1 Introduction

This vignette provides examples and use cases of functions in the *eDNAjoint* package, as well as more details about the model that can be fit with *eDNAjoint*.

The primary purpose of the joint model is to use observations from both environmental DNA (eDNA) surveys and traditional surveys (i.e., seine sampling, trap sampling, etc.) to jointly estimate parameters like expected catch rate, \(\mu\), at a site and false positive probability of eDNA detection, \(p_{10}\). The model is intended for use with paired, replicated eDNA qPCR and traditional observations at multiple sites across the landscape. Below is a summary table of all parameters estimated by the model.

symbol | name | description |
---|---|---|

\(\mu_{i,k}\) | mu | Vector of expected catch rate at site, i. If multiple traditional gear types are used, mu is an array of expected catch rate at site, i, with gear type, k. |

\(p_{10}\) | p10 | Probability of false positive eDNA detection |

\(q_k\) | q | Vector of catchability coefficients for traditional gear type, k. |

\(\beta\) | beta | Parameter that scales the sensitivity of eDNA relative to traditional sampling. If site-level covariates are used, \(β\) is a vector of length, i, and a function of \(α_n\). If site-level covariates are not used, \(β\) is a scalar. |

\(\alpha_n\) | alpha | Vector of regression coefficients for site-level covariates that scale the sensitivity of eDNA sampling relative to traditional sampling. Note \(α_1\) refers to the regression intercept. |

\(\phi\) | phi | Overdispersion parameter in negative binomial distribution, if used. |

The main functionality in *eDNAjoint* is the use of `jointModel()`

that will fit the model to data. Further functions like `jointSummarize()`

and `detectionCalculate()`

can be used to help with model fit interpretation.

Below are detailed descriptions of two use cases of *eDNAjoint*. The first demonstrates the use of the joint model in a scenario where site-level covariates scale the sensitivity of eDNA sampling relative to traditional surveys. The second demonstrates the use of the joint model in a scenario where multiple traditional gear types are used.