# Calculate the survey effort necessary to detect species presence, given the species expected catch rate.

Source:`R/detectionCalculate.R`

`detectionCalculate.Rd`

This function calculates the number of survey effort units to necessary detect species presence using median estimated parameter values from jointModel(). Detecting species presence is defined as producing at least one true positive eDNA detection or catching at least one individual. See more examples in the Package Vignette.

## Arguments

- modelfit
An object of class

`stanfit`

.- mu
A numeric vector of species densities/capture rates. If multiple traditional gear types are represented in the model, mu is the catch rate of gear type 1.

- cov.val
A numeric vector indicating the values of site-level covariates to use for prediction. Default is NULL.

- probability
A numeric value indicating the probability of detecting presence. The default is 0.9.

- qPCR.N
An integer indicating the number of qPCR replicates per eDNA sample. The default is 3.

## Value

A summary table of survey efforts necessary to detect species presence, given mu, for each survey type.

## Note

Before fitting the model, this function checks to ensure that the function is possible given the inputs. These checks include:

Input model fit is an object of class 'stanfit'.

Input mu is a numeric vector.

Input probability is a univariate numeric value.

If model fit contains alpha, cov.val must be provided.

Input cov.val is numeric.

Input cov.val is the same length as the number of estimated covariates.

Input model fit has converged (i.e. no divergent transitions after warm-up).

If any of these checks fail, the function returns an error message.

## Examples

```
# \donttest{
# Ex. 1: Calculating necessary effort for detection with site-level
# covariates
# Load data
data(gobyData)
# Fit a model including 'Filter_time' and 'Salinity' site-level covariates
fit.cov <- jointModel(data = gobyData, cov = c('Filter_time','Salinity'),
family = "poisson", p10priors = c(1,20), q = FALSE,
multicore = FALSE)
#>
#> SAMPLING FOR MODEL 'joint_binary_cov_pois' NOW (CHAIN 1).
#> Chain 1:
#> Chain 1: Gradient evaluation took 8.3e-05 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.83 seconds.
#> Chain 1: Adjust your expectations accordingly!
#> Chain 1:
#> Chain 1:
#> Chain 1: Iteration: 1 / 3000 [ 0%] (Warmup)
#> Chain 1: Iteration: 500 / 3000 [ 16%] (Warmup)
#> Chain 1: Iteration: 501 / 3000 [ 16%] (Sampling)
#> Chain 1: Iteration: 1000 / 3000 [ 33%] (Sampling)
#> Chain 1: Iteration: 1500 / 3000 [ 50%] (Sampling)
#> Chain 1: Iteration: 2000 / 3000 [ 66%] (Sampling)
#> Chain 1: Iteration: 2500 / 3000 [ 83%] (Sampling)
#> Chain 1: Iteration: 3000 / 3000 [100%] (Sampling)
#> Chain 1:
#> Chain 1: Elapsed Time: 0.684 seconds (Warm-up)
#> Chain 1: 1.743 seconds (Sampling)
#> Chain 1: 2.427 seconds (Total)
#> Chain 1:
#>
#> SAMPLING FOR MODEL 'joint_binary_cov_pois' NOW (CHAIN 2).
#> Chain 2:
#> Chain 2: Gradient evaluation took 5e-05 seconds
#> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.5 seconds.
#> Chain 2: Adjust your expectations accordingly!
#> Chain 2:
#> Chain 2:
#> Chain 2: Iteration: 1 / 3000 [ 0%] (Warmup)
#> Chain 2: Iteration: 500 / 3000 [ 16%] (Warmup)
#> Chain 2: Iteration: 501 / 3000 [ 16%] (Sampling)
#> Chain 2: Iteration: 1000 / 3000 [ 33%] (Sampling)
#> Chain 2: Iteration: 1500 / 3000 [ 50%] (Sampling)
#> Chain 2: Iteration: 2000 / 3000 [ 66%] (Sampling)
#> Chain 2: Iteration: 2500 / 3000 [ 83%] (Sampling)
#> Chain 2: Iteration: 3000 / 3000 [100%] (Sampling)
#> Chain 2:
#> Chain 2: Elapsed Time: 0.866 seconds (Warm-up)
#> Chain 2: 1.743 seconds (Sampling)
#> Chain 2: 2.609 seconds (Total)
#> Chain 2:
#>
#> SAMPLING FOR MODEL 'joint_binary_cov_pois' NOW (CHAIN 3).
#> Chain 3:
#> Chain 3: Gradient evaluation took 4.6e-05 seconds
#> Chain 3: 1000 transitions using 10 leapfrog steps per transition would take 0.46 seconds.
#> Chain 3: Adjust your expectations accordingly!
#> Chain 3:
#> Chain 3:
#> Chain 3: Iteration: 1 / 3000 [ 0%] (Warmup)
#> Chain 3: Iteration: 500 / 3000 [ 16%] (Warmup)
#> Chain 3: Iteration: 501 / 3000 [ 16%] (Sampling)
#> Chain 3: Iteration: 1000 / 3000 [ 33%] (Sampling)
#> Chain 3: Iteration: 1500 / 3000 [ 50%] (Sampling)
#> Chain 3: Iteration: 2000 / 3000 [ 66%] (Sampling)
#> Chain 3: Iteration: 2500 / 3000 [ 83%] (Sampling)
#> Chain 3: Iteration: 3000 / 3000 [100%] (Sampling)
#> Chain 3:
#> Chain 3: Elapsed Time: 0.906 seconds (Warm-up)
#> Chain 3: 1.759 seconds (Sampling)
#> Chain 3: 2.665 seconds (Total)
#> Chain 3:
#>
#> SAMPLING FOR MODEL 'joint_binary_cov_pois' NOW (CHAIN 4).
#> Chain 4:
#> Chain 4: Gradient evaluation took 5.1e-05 seconds
#> Chain 4: 1000 transitions using 10 leapfrog steps per transition would take 0.51 seconds.
#> Chain 4: Adjust your expectations accordingly!
#> Chain 4:
#> Chain 4:
#> Chain 4: Iteration: 1 / 3000 [ 0%] (Warmup)
#> Chain 4: Iteration: 500 / 3000 [ 16%] (Warmup)
#> Chain 4: Iteration: 501 / 3000 [ 16%] (Sampling)
#> Chain 4: Iteration: 1000 / 3000 [ 33%] (Sampling)
#> Chain 4: Iteration: 1500 / 3000 [ 50%] (Sampling)
#> Chain 4: Iteration: 2000 / 3000 [ 66%] (Sampling)
#> Chain 4: Iteration: 2500 / 3000 [ 83%] (Sampling)
#> Chain 4: Iteration: 3000 / 3000 [100%] (Sampling)
#> Chain 4:
#> Chain 4: Elapsed Time: 0.65 seconds (Warm-up)
#> Chain 4: 1.729 seconds (Sampling)
#> Chain 4: 2.379 seconds (Total)
#> Chain 4:
#> Refer to the eDNAjoint guide for visualization tips: https://ednajoint.netlify.app/tips#visualization-tips
# Calculate at the mean covariate values
# (covariates are standardized, so mean = 0)
detectionCalculate(fit.cov$model, mu = seq(from = 0.1, to = 1, by = 0.1),
cov.val = c(0,0), qPCR.N = 3)
#> mu n_traditional n_eDNA
#> [1,] 0.1 24 14
#> [2,] 0.2 12 7
#> [3,] 0.3 8 5
#> [4,] 0.4 6 4
#> [5,] 0.5 5 4
#> [6,] 0.6 4 3
#> [7,] 0.7 4 3
#> [8,] 0.8 3 3
#> [9,] 0.9 3 2
#> [10,] 1.0 3 2
# Calculate mu_critical at salinity 0.5 z-scores greater than the mean
detectionCalculate(fit.cov$model, mu = seq(from = 0.1, to = 1, by = 0.1),
cov.val = c(0,0.5), qPCR.N = 3)
#> mu n_traditional n_eDNA
#> [1,] 0.1 24 12
#> [2,] 0.2 12 6
#> [3,] 0.3 8 5
#> [4,] 0.4 6 4
#> [5,] 0.5 5 3
#> [6,] 0.6 4 3
#> [7,] 0.7 4 2
#> [8,] 0.8 3 2
#> [9,] 0.9 3 2
#> [10,] 1.0 3 2
# Ex. 2: Calculating necessary effort for detection with multiple traditional
# gear types
# Load data
data(greencrabData)
# Fit a model with no site-level covariates
fit.q <- jointModel(data = greencrabData, cov = NULL, family = "negbin",
p10priors = c(1,20), q = TRUE, multicore = FALSE)
#>
#> SAMPLING FOR MODEL 'joint_binary_catchability_negbin' NOW (CHAIN 1).
#> Chain 1:
#> Chain 1: Gradient evaluation took 0.000384 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 3.84 seconds.
#> Chain 1: Adjust your expectations accordingly!
#> Chain 1:
#> Chain 1:
#> Chain 1: Iteration: 1 / 3000 [ 0%] (Warmup)
#> Chain 1: Iteration: 500 / 3000 [ 16%] (Warmup)
#> Chain 1: Iteration: 501 / 3000 [ 16%] (Sampling)
#> Chain 1: Iteration: 1000 / 3000 [ 33%] (Sampling)
#> Chain 1: Iteration: 1500 / 3000 [ 50%] (Sampling)
#> Chain 1: Iteration: 2000 / 3000 [ 66%] (Sampling)
#> Chain 1: Iteration: 2500 / 3000 [ 83%] (Sampling)
#> Chain 1: Iteration: 3000 / 3000 [100%] (Sampling)
#> Chain 1:
#> Chain 1: Elapsed Time: 3.443 seconds (Warm-up)
#> Chain 1: 11.272 seconds (Sampling)
#> Chain 1: 14.715 seconds (Total)
#> Chain 1:
#>
#> SAMPLING FOR MODEL 'joint_binary_catchability_negbin' NOW (CHAIN 2).
#> Chain 2:
#> Chain 2: Gradient evaluation took 0.000285 seconds
#> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 2.85 seconds.
#> Chain 2: Adjust your expectations accordingly!
#> Chain 2:
#> Chain 2:
#> Chain 2: Iteration: 1 / 3000 [ 0%] (Warmup)
#> Chain 2: Iteration: 500 / 3000 [ 16%] (Warmup)
#> Chain 2: Iteration: 501 / 3000 [ 16%] (Sampling)
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#> Chain 2: Iteration: 2000 / 3000 [ 66%] (Sampling)
#> Chain 2: Iteration: 2500 / 3000 [ 83%] (Sampling)
#> Chain 2: Iteration: 3000 / 3000 [100%] (Sampling)
#> Chain 2:
#> Chain 2: Elapsed Time: 3.646 seconds (Warm-up)
#> Chain 2: 11.413 seconds (Sampling)
#> Chain 2: 15.059 seconds (Total)
#> Chain 2:
#>
#> SAMPLING FOR MODEL 'joint_binary_catchability_negbin' NOW (CHAIN 3).
#> Chain 3:
#> Chain 3: Gradient evaluation took 0.00029 seconds
#> Chain 3: 1000 transitions using 10 leapfrog steps per transition would take 2.9 seconds.
#> Chain 3: Adjust your expectations accordingly!
#> Chain 3:
#> Chain 3:
#> Chain 3: Iteration: 1 / 3000 [ 0%] (Warmup)
#> Chain 3: Iteration: 500 / 3000 [ 16%] (Warmup)
#> Chain 3: Iteration: 501 / 3000 [ 16%] (Sampling)
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#> Chain 3: Iteration: 3000 / 3000 [100%] (Sampling)
#> Chain 3:
#> Chain 3: Elapsed Time: 3.191 seconds (Warm-up)
#> Chain 3: 10.927 seconds (Sampling)
#> Chain 3: 14.118 seconds (Total)
#> Chain 3:
#>
#> SAMPLING FOR MODEL 'joint_binary_catchability_negbin' NOW (CHAIN 4).
#> Chain 4:
#> Chain 4: Gradient evaluation took 0.000277 seconds
#> Chain 4: 1000 transitions using 10 leapfrog steps per transition would take 2.77 seconds.
#> Chain 4: Adjust your expectations accordingly!
#> Chain 4:
#> Chain 4:
#> Chain 4: Iteration: 1 / 3000 [ 0%] (Warmup)
#> Chain 4: Iteration: 500 / 3000 [ 16%] (Warmup)
#> Chain 4: Iteration: 501 / 3000 [ 16%] (Sampling)
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#> Chain 4: Iteration: 2500 / 3000 [ 83%] (Sampling)
#> Chain 4: Iteration: 3000 / 3000 [100%] (Sampling)
#> Chain 4:
#> Chain 4: Elapsed Time: 3.436 seconds (Warm-up)
#> Chain 4: 10.242 seconds (Sampling)
#> Chain 4: 13.678 seconds (Total)
#> Chain 4:
#> Refer to the eDNAjoint guide for visualization tips: https://ednajoint.netlify.app/tips#visualization-tips
# Calculate
detectionCalculate(fit.q$model, mu = seq(from = 0.1, to = 1, by = 0.1),
cov.val = NULL, qPCR.N = 3)
#> mu n_traditional_1 n_traditional_2 n_eDNA
#> [1,] 0.1 25 31 28
#> [2,] 0.2 13 16 14
#> [3,] 0.3 9 11 10
#> [4,] 0.4 7 9 8
#> [5,] 0.5 6 8 6
#> [6,] 0.6 5 7 5
#> [7,] 0.7 5 6 5
#> [8,] 0.8 5 5 4
#> [9,] 0.9 4 5 4
#> [10,] 1.0 4 5 4
# Change probability of detecting presence to 0.95
detectionCalculate(fit.q$model, mu = 0.1, cov.val = NULL,
probability = 0.95, qPCR.N = 3)
#> mu n_traditional_1 n_traditional_2 n_eDNA
#> [1,] 0.1 32 40 36
# }
```