estStrength {MigConnectivity}R Documentation

Estimate MC, migratory connectivity strength

Description

Resampling of uncertainty for MC (migratory connectivity strength) from estimates of psi (transition probabilities) and/or relative abundance. Psi estimates can come from an estMigConnectivity object, an RMark psi matrix, MCMC samples, or other samples expressed in array form. Abundance estimates for each origin site can be either just point estimates (no uncertainty propagated) or MCMC samples. Other inputs include distances between origin sites, distances between target sites, and sample size used to estimate psi.

Usage

estStrength(
  originDist,
  targetDist,
  originRelAbund,
  psi,
  sampleSize = NULL,
  originSites = NULL,
  targetSites = NULL,
  originNames = NULL,
  targetNames = NULL,
  nSamples = 1000,
  row0 = 0,
  verbose = 0,
  alpha = 0.05,
  approxSigTest = FALSE,
  sigConst = 0,
  maintainLegacyOutput = FALSE,
  returnAllInput = TRUE
)

Arguments

originDist

Distances between the B origin sites. Symmetric B by B matrix

targetDist

Distances between the W target sites. Symmetric W by W matrix

originRelAbund

Relative abundance estimates at B origin sites. Either a numeric vector of length B that sums to 1, or an mcmc object (such as is produced by modelCountDataJAGS) or matrix with at least nSamples rows. If there are more than B columns, the relevant columns should be labeled "relN[1]" through "relN[B]"

psi

Transition probabilities between B origin and W target sites. Either a matrix with B rows and W columns where rows sum to 1, an array with dimensions x, B, and W (with x samples of the transition probability matrix from another model), an 'estPsi' object (result of calling estTransition), or a MARK object with estimates of transition probabilities

sampleSize

Total sample size of animals that psi will be estimated from. Should be the number of animals released in one of the origin sites and observed in one of the target sites (or vice-versa). Optional, but recommended, unless psi is an estPsi object (in which case this function can pull it from there)

originSites

If psi is a MARK object, this must be a numeric vector indicating which sites are origin

targetSites

If psi is a MARK object, this must be a numeric vector indicating which sites are target

originNames

Optional. Vector of names for the origin sites. Mostly for internal use

targetNames

Optional. Vector of names for the target sites. Mostly for internal use

nSamples

Number of times to resample psi and/or originRelAbund. The purpose is to estimate sampling uncertainty; higher values here will do so with more precision

row0

If originRelAbund is an mcmc object or array, this can be set to 0 (default) or any greater integer to specify where to stop ignoring samples ("burn-in")

verbose

0 (default) to 2. 0 prints no output during run. 1 prints a progress update and summary every 100 samples. 2 prints a progress update and summary every sample

alpha

Level for confidence/credible intervals provided. Default (0.05) gives 95 percent CI

approxSigTest

Should function compute approximate one-sided significance tests (p-values) for MC from the resampling? Default is FALSE

sigConst

Value to compare MC to in significance test. Default is 0

maintainLegacyOutput

version 0.4.0 of MigConnectivity updated the structure of the estimates. If you have legacy code that refers to elements within an estMigConnectivity object (results of estMC), you can set this to TRUE to also keep the old structure. Defaults to FALSE

returnAllInput

if TRUE (the default) the output includes all of the inputs. If FALSE, only the inputs currently used by another MigConnectivity function are included in the output.

Value

estStrength returns a list with the elements:

MC

List containing estimates of migratory connectivity strength:

  • sample nSamples sampled values for MC. Provided to allow the user to compute own summary statistics.

  • mean Mean of MC$sample. Main estimate of MC, incorporating parametric uncertainty.

  • se Standard error of MC, estimated from SD of MC$sample.

  • simpleCI Default1 - alpha confidence interval for MC, estimated as alpha/2 and 1 - alpha/2 quantiles of MC$sample.

  • bcCI Bias-corrected 1 - alpha confidence interval for MC. May be preferable to MC$simpleCI when MC$mean is the best estimate of MC. MC$simpleCI is preferred when MC$median is a better estimator. When MC$mean==MC$median, these should be identical. Estimated as the pnorm(2 * z0 + qnorm(alpha / 2)) and pnorm(2 * z0 + qnorm(1 - alpha / 2)) quantiles of MC$sample, where z0 is the proportion of MC$sample < MC$mean.

  • hpdCI 1 - alpha credible interval for MC, estimated using the highest posterior density (HPD) method.

  • median Median of MC, alternate point estimate also including parametric uncertainty.

  • point Simple point estimate of MC, using the point estimates of psi and originRelAbund (usually the mean values), not accounting for sampling error.

  • simpleP Approximate p-value for MC, estimated as the proportion of bootstrap iterations where MC < sigConst (or MC > sigConst if pointMC < sigConst). Note that if the proportion is 0, a default value of 0.5 / nSamples is provided, but this is best interpreted as p < 1 / nSamples. NULL when approxSigTest==FALSE.

  • bcP Approximate bias-corrected p-value for MC, estimated as pnorm(qnorm(simpleP) - 2 * z0), where z0 is the proportion of sampleMC < meanMC. May be a better approximation of the p-value than simpleP, but many of the same limitations apply. NULL when approxSigTest==FALSE.

input

List containing the inputs to estStrength.

See Also

calcMC, estTransition, estMC, estMantel, plot.estMigConnectivity

Examples


  set.seed(101)
  # Uncertainty in detection (RMark estimates) with equal abundances
  # Number of resampling iterations for generating confidence intervals
  nSamplesCMR <- 100
  nSimulationsCMR <- 10
  originPos13 <- matrix(c(rep(seq(-99, -81, 2), each = 10),
                          rep(seq(49, 31, -2), 10)), 100, 2)
  targetPos13 <- matrix(c(rep(seq(-79, -61, 2), each = 10),
                          rep(seq(9, -9, -2), 10)), 100, 2)
  originPosCMR <- rowsum(originPos13, c(rep(1:2, 5, each = 5),
                                        rep(3:4, 5, each = 5))) / 25
  originPosCMR
  targetPosCMR <- rowsum(targetPos13, c(rep(1:2, 5, each = 5),
                                        rep(3:4, 5, each = 5))) / 25
  targetPosCMR

  originDist <- distFromPos(originPosCMR, 'ellipsoid')
  targetDist <- distFromPos(targetPosCMR, 'ellipsoid')
  originRelAbundTrue <- rep(0.25, 4)
  # the second intermediate psi scenario, the "low" level
  psiTrue <- samplePsis[["Low"]]
  trueMC <- calcMC(originDist, targetDist, originRelAbundTrue, psiTrue)
  trueMC

  # Storage matrix for samples
  cmrMCSample <- matrix(NA, nSamplesCMR, nSimulationsCMR)
  summaryCMR <- data.frame(Simulation = 1:nSimulationsCMR, True=trueMC,
                           mean=NA, se=NA, lcl=NA, ucl=NA)
  # Get 'RMark' psi estimates and estimate MC from each
  for (r in 1:nSimulationsCMR) {
    cat("Simulation",r,"of",nSimulationsCMR,"\n")
    # Note: getCMRexample() requires a valid internet connection and that GitHub
    # is accessible
    fm <- getCMRexample(r)
    results <- estStrength(originRelAbund = originRelAbundTrue, psi = fm,
                     originDist = originDist, targetDist = targetDist,
                     originSites = 5:8, targetSites = c(3,2,1,4),
                     nSamples = nSamplesCMR, verbose = 0,
                     sampleSize = length(grep('[2-5]', fm$data$data$ch)))
    cmrMCSample[ , r] <- results$MC$sample
    summaryCMR$mean[r] <- results$MC$mean
    summaryCMR$se[r] <- results$MC$se
    # Calculate confidence intervals using quantiles of sampled MC
    summaryCMR[r, c('lcl', 'ucl')] <- results$MC$simpleCI
  }

  summaryCMR <- transform(summaryCMR, coverage = (True>=lcl & True<=ucl))
  summaryCMR
  summary(summaryCMR)
  biasCMR <- mean(summaryCMR$mean) - trueMC
  biasCMR
  mseCMR <- mean((summaryCMR$mean - trueMC)^2)
  mseCMR
  rmseCMR <- sqrt(mseCMR)
  rmseCMR


  # Simulation of BBS data to quantify uncertainty in relative abundance

  nSamplesAbund <- 700 #1700 are stored
  nSimulationsAbund <- 10
  #\dontrun{
  #  nSamplesAbund <- 1700
  #}
  # Storage matrix for samples
  abundMCSample <- matrix(NA, nSamplesAbund, nSimulationsAbund)
  summaryAbund <- data.frame(Simulation = 1:nSimulationsAbund, True = trueMC,
                             mean = NA, se = NA, lcl = NA, ucl = NA)
  for (r in 1:nSimulationsAbund) {
    cat("Simulation",r,"of",nSimulationsAbund,"\n")
    row0 <- nrow(abundExamples[[r]]) - nSamplesAbund
    results <- estStrength(originRelAbund = abundExamples[[r]], psi = psiTrue,
                     originDist = originDist, targetDist = targetDist,
                     row0 = row0, nSamples = nSamplesAbund, verbose = 1)
    abundMCSample[ , r] <- results$MC$sample
    summaryAbund$mean[r] <- results$MC$mean
    summaryAbund$se[r] <- results$MC$se
    # Calculate confidence intervals using quantiles of sampled MC
    summaryAbund[r, c('lcl', 'ucl')] <- results$MC$simpleCI
  }

  summaryAbund <- transform(summaryAbund, coverage = (True >= lcl & True <= ucl))
  summaryAbund
  summary(summaryAbund)
  biasAbund <- mean(summaryAbund$mean) - trueMC
  biasAbund
  mseAbund <- mean((summaryAbund$mean - trueMC)^2)
  mseAbund
  rmseAbund <- sqrt(mseAbund)
  rmseAbund

  # Ovenbird example with GL and GPS data
  data(OVENdata) # Ovenbird

  nSamplesGLGPS <- 100 # Number of bootstrap iterations, set low for example

  # Estimate transition probabilities
  Combined.psi<-estTransition(isGL=OVENdata$isGL, #Light-level geolocator (T/F)
                              isTelemetry = !OVENdata$isGL,
                  geoBias = OVENdata$geo.bias, # Light-level GL location bias
                  geoVCov = OVENdata$geo.vcov, # Location covariance matrix
                  targetSites = OVENdata$targetSites, # Nonbreeding/target sites
                  originSites = OVENdata$originSites, # Breeding/origin sites
                  originPoints = OVENdata$originPoints, # Capture Locations
                  targetPoints = OVENdata$targetPoints, #Device target locations
                  verbose = 3,   # output options
                  nSamples = nSamplesGLGPS, # This is set low for example
                  resampleProjection = sf::st_crs(OVENdata$targetPoints),
                  nSim = 1000)

  # Can estimate MC from previous psi estimate
  Combo.MC1 <- estStrength(targetDist = OVENdata$targetDist, # Distance matrix
                           originDist = OVENdata$originDist, # Distance matrix
                           targetSites = OVENdata$targetSites, # Target sites
                           originSites = OVENdata$originSites, # Breeding sites
                           psi = Combined.psi,
                           originRelAbund = OVENdata$originRelAbund,
                           nSamples = nSamplesGLGPS,
                           sampleSize = nrow(OVENdata$targetPoints))
  Combo.MC1

  # Doesn't have to be an estPsi object - can simply be array of psi samples
  Combo.MC2 <- estStrength(targetDist = OVENdata$targetDist,
                           originDist = OVENdata$originDist,
                           targetSites = OVENdata$targetSites,
                           originSites = OVENdata$originSites,
                           psi = Combined.psi$psi$sample, # Array of samples
                           originRelAbund = OVENdata$originRelAbund,
                           nSamples = nSamplesGLGPS,
                           sampleSize = nrow(OVENdata$targetPoints))
  Combo.MC2
[Package MigConnectivity version 0.4.7 Index]