demographicRates: Sample expected survival and recruitment rates

In LandSciTech/caribouMetrics: Models and Metrics of Boreal Caribou Demography and Habitat Selection

Sample expected survival and recruitment rates

Description

Apply sampled coefficients to disturbance covariates to calculate expected recruitment and survival.demographicRates is a wrapper around sampleRates to sample both survival and recruitment rates based on the result of demographicCoefficients() and using recommended defaults.

Usage

demographicRates(
  covTable,
  popGrowthPars,
  ignorePrecision = FALSE,
  returnSample = FALSE,
  useQuantiles = TRUE,
  predInterval = list(PI_R = c(0.025, 0.975), PI_S = c(0.025, 0.975)),
  transformFns = list(S_transform = function(y) {
     (y * 46 - 0.5)/45
 }, R_transform
    = function(y) {
     y
 })
)

sampleRates(
  covTable,
  coefSamples,
  coefValues,
  modelVersion,
  resVar,
  ignorePrecision,
  returnSample,
  quantilesToUse = NULL,
  predInterval = c(0.025, 0.975),
  transformFn = function(y) {
     y
 }
)

Arguments

covTable	data.frame. A table of covariate values to be used. Column names must match the coefficient names in popGrowthTableJohnsonECCC. Each row is a different scenario.
popGrowthPars	list. Coefficient values and (optionally) quantiles returned by demographicCoefficients.
ignorePrecision	logical. Should the precision of the model be used if it is available? When precision is used variation among populations around the National mean responses is considered in addition to the uncertainty about the coefficient estimates.
returnSample	logical. If TRUE the returned data.frame has replicates * scenarios rows. If FALSE the returned data.frame has one row per scenario and additional columns summarizing the variation among replicates. See Value for details.
useQuantiles	logical or numeric. If it is a numeric vector it must be length 2 and give the low and high limits of the quantiles to use. Only relevant when ignorePrecision = FALSE. If useQuantiles != FALSE, each replicate population is assigned to a quantile of the distribution of variation around the expected values, and remains in that quantile as covariates change. If useQuantiles != FALSE and popGrowthPars contains quantiles, those quantiles will be used. If useQuantiles = TRUE and popGrowthPars does not contain quantiles, replicate populations will be assigned to quantiles in the default range of 0.025 and 0.975. If useQuantiles = FALSE, sampling is done independently for each combination of scenario and replicate, so the value for a particular replicate population in one scenario is unrelated to the values for that replicate in other scenarios. Useful for projecting impacts of changing disturbance on the trajectories of replicate populations.
predInterval	numeric vector with length 2. The default 95% interval is (c(0.025,0.975)). Only relevant when returnSample = TRUE and quantilesToUse = NULL.
transformFns	list of functions used to transform demographic rates. The default is list(S_transform = function(y){(y*46-0.5)/45},R_transform = function(y){y}). The back transformation is applied to survival rates as in Johnson et al. 2020.
coefSamples	matrix. Bootstrapped coefficients with one row per replicate and one column per coefficient
coefValues	data.table. One row table with expected values for each coefficient
modelVersion	character. Which model version to use. Currently the only option is "Johnson" for the model used in Johnson et. al. (2020), but additional options may be added in the future.
resVar	character. Response variable, typically "femaleSurvival" or "recruitment"
quantilesToUse	numeric vector of length coefSamples. See useQuantiles.
transformFn	function used to transform demographic rates.

Details

First the mean recruitment (\mu^R_t) and survival (\mu^S_t) are calculated from the sampled coefficients and provided disturbance covariates according to the beta regression models estimated by Johnson et al. (2020):

log(\mu^R_t)=\dot{\beta^R_0}+\dot{\beta^R_a}A_t+\dot{\beta}^R_fF_t

log(\mu^S_t)=\dot{\beta^S_0}+\dot{\beta^S_a}A_t

Then each replicate population is assigned to a quantile (if useQuantiles = TRUE) of the Beta distributed expected recruitment \bar{R}_t and survival \bar{S}_t where \phi^R and \phi^S are the precisions of the Beta distributed errors:

\bar{R}_t \sim \text{Beta}(\mu^R_t,\phi^R)

\bar{S}_t \sim (46\times \text{Beta}(\mu^S_t,\phi^S)-0.5)/45)

Using quantiles means that the population will stay in these quantiles as disturbance changes over time, so there is persistent variation in recruitment and survival among example populations. A transformation function is also applied to survival to avoid survival probabilities of 1.

Value

A data.frame of predictions. The data.frame includes all columns in covTable with additional columns depending on returnSample.

If returnSample = FALSE the number of rows is the same as the number of rows in covTable, additional columns are:

• "S_bar" and "R_bar": The mean estimated values of survival and recruitment (calves per cow)

• "S_stdErr" and "R_stdErr": Standard error of the estimated values

• "S_PIlow"/"S_PIhigh" and "R_PIlow"/"R_PIhigh": If not using quantiles, 95\ minimum values are returned.

If returnSample = TRUE the number of rows is nrow(covTable) * replicates additional columns are:

• "scnID": A unique identifier for scenarios provided in covTable

• "replicate": A replicate identifier, unique within each scenario

• "S_bar" and "R_bar": The expected values of survival and recruitment (calves per cow)

For sampleRates a similar data frame for one response variable

See Also

Caribou demography functions: caribouBayesianIPM(), caribouPopGrowth(), compositionBiasCorrection(), demographicCoefficients(), demographicProjectionApp(), getOutputTables(), getPriors(), getScenarioDefaults(), getSimsNational(), plotRes(), popGrowthTableJohnsonECCC, runScnSet(), simulateObservations()

Examples

# get coefficient samples
coefs <- demographicCoefficients(10)

# table of different scenarios to test
covTableSim <- expand.grid(Anthro = seq(0, 90, by = 20),
                           fire_excl_anthro = seq(0, 70, by = 20))
covTableSim$Total_dist = covTableSim$Anthro + covTableSim$fire_excl_anthro

demographicRates(covTableSim, coefs)

cfs <- getCoefs(popGrowthTableJohnsonECCC, "recruitment", "Johnson", "M3")

cfSamps <- sampleCoefs(cfs[[1]], 10)

# disturbance scenarios
distScen <- data.frame(Total_dist = 1:10/10)

# return summary across replicates
sampleRates(distScen, cfSamps$coefSamples, cfSamps$coefValues,
            "Johnson", "recruitment", ignorePrecision = TRUE, 
            returnSample = FALSE)

# return one row per replicate * scenario
sampleRates(distScen, cfSamps$coefSamples, cfSamps$coefValues,
            "Johnson", "recruitment", ignorePrecision = TRUE, 
            returnSample = TRUE)

# return one row per replicate * scenario with replicates assigned to a quantile
sampleRates(distScen, cfSamps$coefSamples, cfSamps$coefValues,
            "Johnson", "recruitment", ignorePrecision = TRUE, 
            returnSample = TRUE, 
            quantilesToUse = quantile(x = c(0, 1),
                                      probs = seq(0.025, 0.975, length.out = 10)))

LandSciTech/caribouMetrics documentation built on Feb. 3, 2024, 9:41 p.m.