run_eDITH_optim_joint {eDITH}

Optimize eDITH based on joint eDNA and direct sampling data

Description

Function that performs search of optimal parameters of an eDITH model fitted on both eDNA and direct sampling data.

Usage

run_eDITH_optim_joint(data, river, covariates = NULL, Z.normalize = TRUE,
           use.AEM = FALSE, n.AEM = NULL, par.AEM = NULL,
           no.det = FALSE, ll.type = "norm", source.area = "AG",
           likelihood = NULL, sampler = NULL, n.attempts = 100,
           n.restarts = round(n.attempts/10), par.optim = NULL,
           tau.prior = list(spec="lnorm",a=0,b=Inf, meanlog=log(5), 
		                    sd=sqrt(log(5)-log(4))),
           log_p0.prior = list(spec="unif",min=-20, max=0),
           beta.prior = list(spec="norm",sd=1),
           sigma.prior = list(spec="unif",min=0,
                              max=1*max(c(1e-6, data$values[data$type=="e"]), 
							  na.rm = TRUE)),
           omega.prior = list(spec="unif",min=1,
                              max=10*max(c(0.11, data$values[data$type=="e"]), 
							  na.rm = TRUE)),
           Cstar.prior = list(spec="unif",min=0,
                              max=1*max(c(1e-6, data$values[data$type=="e"]), 
							  na.rm = TRUE)),
           omega_d.prior = list(spec="unif",min=1,
                                max=10*max(c(0.11, data$values[data$type=="d"]), 
								na.rm = TRUE)),
           alpha.prior = list(spec="unif", min=0, max=1e6),
           verbose = FALSE)

Arguments

data

eDNA and direct observation data. Data frame containing columns ID (index of the AG node/reach where the sample was taken), values (value of the eDNA or direct measurement) and type (equal to "e" for eDNA data and to "d" for direct observation data). eDNA values are expressed as concentration or number of reads; direct observations are expressed as numbers of individuals.

river

A river object generated via aggregate_river.

covariates

Data frame containing covariate values for all river reaches. If NULL (default option), production rates are estimated via AEMs.

Z.normalize

Logical. Should covariates be Z-normalized?

use.AEM

Logical. Should eigenvectors based on AEMs be used as covariates? If covariates = NULL, it is set to TRUE. If TRUE and covariates are provided, AEM eigenvectors are appended to the covariates data frame.

n.AEM

Number of AEM eigenvectors (sorted by the decreasing respective eigenvalue) to be used as covariates. If par.AEM$moranI = TRUE, this parameter is not used. Instead, the eigenvectors with significantly positive spatial autocorrelation are used as AEM covariates.

par.AEM

List of additional parameters that are passed to river_to_AEM for calculation of AEMs. In particular, par.AEM$moranI = TRUE imposes the use of AEM covariates with significantly positive spatial autocorrelation based on Moran's I statistic.

no.det

Logical. Should a probability of non-detection be included in the model?

ll.type

Character. String defining the error distribution used in the log-likelihood formulation. Allowed values are norm (for normal distribution), lnorm (for lognormal distribution), nbinom (for negative binomial distribution) and geom (for geometric distribution). The two latter choices are suited when eDNA data are expressed as read numbers, while norm and lnorm are better suited to eDNA concentrations.

source.area

Defines the extent of the source area of a node. Possible values are "AG" (if the source area is the reach surface, i.e. length*width), "SC" (if the source area is the subcatchment area), or, alternatively, a vector with length river$AG$nodes.

likelihood

Likelihood function. If not specified, it is generated based on arguments no.det and ll.type.

sampler

Function generating sets of initial parameter values for the optimization algorithm. If NULL, initial parameter values are drawn from the default prior distributions of run_eDITH_BT. See details.

n.attempts

Number of times the optimizing function optim is executed. Every time a "restart" happens (see n.restarts), sampler is used to draw an initial parameter set. If a "restart" does not happen, the optimal parameter set from the previous attempt is used as initial parameter set.

n.restarts

Number of times a random parameter set is drawn as initial condition for optim.

par.optim

List of parameters to be passed to optim. By default, the likelihood is maximized (i.e., control$fnscale = -1), and the maximum number of iterations is set to 1e6. The default optimization method is "Nelder-Mead" (same default as in optim).

tau.prior, log_p0.prior, beta.prior, sigma.prior, omega.prior, Cstar.prior

Prior distribution for the relevant parameters of the eDITH model.

omega_d.prior

Prior distribution for the overdispersion parameter for direct sampling density observations.

alpha.prior

Prior distribution for the inverse DNA shedding rate (i.e., the organismal density that sheds a unit eDNA value per unit time).

verbose

Logical. Should console output be displayed?

Details

This function attempts to maximize the log-posterior (sum of log-likelihood and log-prior) via the non-linear optimization function optim.

If specified by the user, sampler must be a function that produces as output a "named num" vector of parameters. Parameter names must be same as in the likelihood. See example.

By default, AEMs are computed without attributing weights to the edges of the river network. Use e.g. par.AEM = list(weight = "gravity") to attribute weights.

Value

A list with objects:

p

Vector of best-fit eDNA production rates corresponding to the optimum parameter estimates param. It has length equal to river$AG$nNodes.

C

Vector of best-fit eDNA values (in the same unit as data$values, i.e. concentrations or read numbers) corresponding to the optimum parameter estimates param. It has length equal to river$AG$nNodes.

probDet

Vector of best-fit detection probabilities corresponding to the optimum parameter estimate param_map. It has length equal to river$AG$nNodes. If a custom likelihood is provided, this is a vector of null length (in which case the user should calculate the probability of detection independently, based on the chosen likelihood).

param

Vector of named parameters corresponding to the best-fit estimate.

covariates

Data frame containing input covariate values (possibly Z-normalized).

source.area

Vector of source area values.

out_optim

List as provided by optim. Only the result of the call to optim (out of n.attempts) yielding the highest likelihood is exported.

attempts.stats

List containing relevant output for the different optimization attempts. It contains lp (vector of maximized log-posterior values for each single attempt), counts (total function evaluations), conv (convergence flags as produced by optim), and tau (best-fit decay time values in h).

Moreover, arguments ll.type (possibly changed to "custom" if a custom likelihood is specified), no.det and data are added to the list.

Examples

data(wigger)
data(dataCD)

## fit eDNA concentration and direct observation data - use AEMs as covariates
set.seed(9)
out <- run_eDITH_optim_joint(dataCD, wigger, n.AEM = 10, 
	n.attempts = 1) # reduced n.AEM, n.attempts for illustrative purposes
	# it is recommended to attempt optimization several times to ensure convergence 

library(rivnet)
# best-fit map of eDNA production rates
plot(wigger, out$p)

# best-fit map of detection probability
plot(wigger, out$probDet)

# compare best-fit vs observed values
data.e <- which(dataCD$type=="e")
data.d <- which(dataCD$type=="d")

plot(out$C[dataCD$ID[data.e]], dataCD$values[data.e],
	xlab="Modelled (MAP) eDNA concentrations", ylab="Observed eDNA concentrations")
abline(a=0, b=1) 

plot(out$p[dataCD$ID[data.d]], dataCD$values[data.d],
	xlab="Modelled (MAP) eDNA production rate", ylab="Observed density data")