Wildlife Sightability Modeling

Description

Uses logistic regression to model the probability of detection as a function of covariates. This model is then used with observational survey data to estimate population size, while accounting for uncertain detection. See Steinhorst and Samuel (1989).

Author(s)

John Fieberg

Maintainer: John Fieberg <jfieberg@umn.edu>, Carl James Schwarz <cschwarz.stat.sfu.ca@gmail.com>

References

Fieberg, J. 2012. Estimating Population Abundance Using Sightability Models: R SightabilityModel Package. Journal of Statistical Software, 51(9), 1-20. URL https://doi.org/10.18637/jss.v051.i09

Steinhorst, Kirk R. and Samuel, Michael D. 1989. Sightability Adjustment Methods for Aerial Surveys of Wildlife Populations. Biometrics 45:415–425.

R function that gives the same functionality as the MoosePop program.

Description

A stratified random sample of blocks in a survey area is conducted. In each block, groups of moose are observed (usually through an aerial survey). For each group of moose, the number of moose is recorded along with attributes such as sex or age. MoosePopR() assumes that sightability is 100%. Use the SightabilityPopR() function to adjust for sightability < 100%.

Usage

MoosePopR(
  survey.data,
  survey.block.area,
  stratum.data,
  density = NULL,
  abundance = NULL,
  numerator = NULL,
  denominator = NULL,
  block.id.var = "Block.ID",
  block.area.var = "Block.Area",
  stratum.var = "Stratum",
  stratum.blocks.var = "Stratum.Blocks",
  stratum.area.var = "Stratum.Area",
  conf.level = 0.9,
  survey.lonely.psu = "fail"
)

Arguments

Value

A data frame containing for each stratum and for all strata (identified as stratum id .OVERALL), the density, or abundance or ratio estimate along with its estimated standard error and large-sample normal-based confidence interval.

Author(s)

Schwarz, C. J. cschwarz.stat.sfu.ca@gmail.com.

References

To Be Added.

Examples

 
##---- See the vignettes for examples on how to run this analysis.

Classical and Domain Stratification using MoosePopR()

Description

This function allows for classical or domain stratification when using MoosePopR(). Caution **SE are NOT adjusted for measurements on multiple domains on the same sampling unit. Bootstrapping may be required**. Consult the vignette for more details.

MoosePopR_DomStrat() assumes that sightability is 100%. Use the SightabilityPopR_DomStrat() function to adjust for sightability < 100%.

Usage

MoosePopR_DomStrat(
  stratum.data,
  selected.unit.data,
  waypoint.data,
  density = NULL,
  abundance = NULL,
  numerator = NULL,
  denominator = NULL,
  stratum.var = "Stratum",
  domain.var = "Domain",
  stratum.total.blocks.var = "Total.Blocks",
  stratum.total.area.var = "Total.Area",
  block.id.var = "Block.ID",
  block.area.var = "Block.Area",
  conf.level = 0.9,
  survey.lonely.psu = "fail"
)

Arguments

Value

A data frame containing for each stratum and for all combinations of strata and domains (identified as stratum id .OVERALL), the density, or abundance or ratio estimate along with its estimated standard error and large-sample normal-based confidence interval.

Author(s)

Schwarz, C. J. cschwarz.stat.sfu.ca@gmail.com.

References

To Be Added.

Examples

 
##---- See the vignettes for examples on how to run this analysis.

Generate a bootstrap replicate of data for call to MoosePopR_DomStrat()

Description

This function takes the data from a classical/domain stratification and generates a bootstrap replicate suitable for analysis using MoosePopR_DomStrat(). A sightability model is allowed which "adjusts" the input data for sightability. This can also be used for SightabilityPopR() models by forcing block areas to 1 and the total block area in stratum to the number of blocks to mimic a mean-per-unit estimator. See the vignette for examples of usage.

Usage

MoosePopR_DomStrat_bootrep(
  stratum.data,
  selected.unit.data,
  waypoint.data,
  density = NULL,
  abundance = NULL,
  numerator = NULL,
  denominator = NULL,
  sight.model = NULL,
  sight.beta = NULL,
  sight.beta.cov = NULL,
  stratum.var = "Stratum",
  domain.var = "Domain",
  stratum.total.blocks.var = "Total.Blocks",
  stratum.total.area.var = "Total.Area",
  block.id.var = "Block.ID",
  block.area.var = "Block.Area",
  conf.level = 0.9,
  survey.lonely.psu = "fail",
  check.args = TRUE
)

Arguments

Value

A list containing the input data (input.data), the bootstrap replicate (boot.data), and a data frame (boot.res) with the estimated density, or abundance or ratio along with its estimated standard error and large-sample normal-based confidence interval. The density/abundance/ratio over all strata is also given on the last line of the data.frame.

Author(s)

Schwarz, C. J. cschwarz.stat.sfu.ca@gmail.com.

References

To Be Added.

Examples

 
##---- See the vignettes for examples on how to use this function

Sightability estimate with variance components estimator from Steinhorst and Samuel (1989) and Samuel et al. (1992).

Description

Estimates population size, with variance estimated using Steinhorst and Samuel (1989) and Samuel et al.'s (1992) estimator. Usually, this function will be called by Sight.Est

Usage

SS.est(
  total,
  srates,
  nh,
  Nh,
  stratum,
  subunit,
  covars,
  beta,
  varbeta,
  smat = NULL
)

Arguments

Value

Author(s)

John Fieberg

References

Steinhorst, R. K., and M.D. Samuel. 1989. Sightability adjustment methods for aerial surveys of wildlife populations. Biometrics 45:415-425.

Wong, C. 1996. Population size estimation using the modified Horvitz-Thompson estimator with estimated sighting probabilities. Dissertation, Colorado State University, Fort Collins, USA.

See Also

Sight.Est, Wong.est

Sightability estimate or ratio with variance components estimator from Steinhorst and Samuel (1989) and Samuel et al. (1992). This is merely a stub and has not been implemented.

Description

Estimates ratio, with variance estimated using Steinhorst and Samuel (1989) and Samuel et al.'s (1992) estimator. Usually, this function will be called by Sight.Est.Ratio()

Usage

SS.est.Ratio(
  numerator,
  denominator,
  srates,
  nh,
  Nh,
  stratum,
  subunit,
  covars,
  beta,
  varbeta,
  smat = NULL
)

Arguments

Value

Author(s)

Carl James Schwarz, cschwarz.stat.sfu.ca@gmail.com

References

Steinhorst, R. K., and M.D. Samuel. 1989. Sightability adjustment methods for aerial surveys of wildlife populations. Biometrics 45:415-425.

Wong, C. 1996. Population size estimation using the modified Horvitz-Thompson estimator with estimated sighting probabilities. Dissertation, Colorado State University, Fort Collins, USA.

See Also

Sight.Est, Wong.est

Sightability Model Estimator

Description

Estimates population abundance by 1) fitting a sightability (logistic regression) model to "test trial" data; 2) applying the fitted model to independent (operational) survey data to correct for detection rates < 1.

Usage

Sight.Est(
  form,
  sdat = NULL,
  odat,
  sampinfo,
  method = "Wong",
  logCI = TRUE,
  alpha = 0.05,
  Vm.boot = FALSE,
  nboot = 1000,
  bet = NULL,
  varbet = NULL
)

Arguments

Details

Variance estimation methods: method = Wong implements the variance estimator from Wong (1996) and is the recommended approach. Method = SS implements the variance estimator of Steinhorst and Samuel (1989), with a modification detailed in the Appendix of Samuel et al. (1992).

Estimates of the variance may be biased low when the number of test trials used to estimate model parameters is small (see Wong 1996, Fieberg and Giudice 2008). A bootstrap can be used to aid the estimation process by specifying Vm.boot = TRUE [note: this method is experimental, and can be time intensive].

Confidence interval construction: often the sampling distribution of tau^ is skewed right. If logCI = TRUE, the confidence interval for tau^ will be constructed under an assumption that (tau^ - T) has a lognormal distribution, where T is the total number of animals seen. In this case, the upper and lower limits are constructed as follows [see Wong(1996, p. 64-67)]:

LCL = T + [(tau^-T)/C]*sqrt(1+cv^2), UCL = T+[(tau^-T)*C]*sqrt(1+cv^2), where cv^2 = var(tau^)/(tau^-T)^2 and C = exp[z[alpha/2]*sqrt(ln(1+cv^2))].

Value

An object of class sightest, a list that includes the following elements:

The list also includes the original test trial and operational survey data, sampling information, and information needed to construct a confidence interval for the population estimate.

Author(s)

John Fieberg, Wildlife Biometrician, Minnesota Department of Natural Resources

References

Fieberg, J. 2012. Estimating Population Abundance Using Sightability Models: R SightabilityModel Package. Journal of Statistical Software, 51(9), 1-20. URL https://doi.org/10.18637/jss.v051.i09.

Fieberg, John and Giudice, John. 2008 Variance of Stratified Survey Estimators With Probability of Detection Adjustments. Journal of Wildlife Management 72:837-844.

Samuel, Michael D. and Steinhorst, R. Kirk and Garton, Edward O. and Unsworth, James W. 1992. Estimation of Wildlife Population Ratios Incorporating Survey Design and Visibility Bias. Journal of Wildlife Management 56:718-725.

Steinhorst, R. K., and M.D. Samuel. 1989. Sightability adjustment methods for aerial surveys of wildlife populations. Biometrics 45:415-425.

Wong, C. 1996. Population size estimation using the modified Horvitz-Thompson estimator with estimated sighting probabilities. Dissertation, Colorado State University, Fort Collins, USA.

Examples

# Load data frames
  data(obs.m) # observational survey data frame
  data(exp.m) # experimental survey data frame
  data(sampinfo.m) # information on sampling rates (contained in a data frame)
 
# Estimate population size in 2007 only
  sampinfo <- sampinfo.m[sampinfo.m$year == 2007,]
  Sight.Est(observed ~ voc, odat = obs.m[obs.m$year == 2007,],
    sdat = exp.m, sampinfo, method = "Wong", 
    logCI = TRUE, alpha = 0.05, Vm.boot = FALSE) 


# BELOW CODE IS SOMEWHAT TIME INTENSIVE (fits models using 2 variance estimators to 3 years of data)
# Estimate population size for 2004-2007
# Compare Wong's and Steinhorst and Samuel variance estimators
  tau.Wong <- tau.SS <- matrix(NA,4,3)
  count <- 1
  for(i in 2004:2007){
    sampinfo <- sampinfo.m[sampinfo.m$year == i,]

# Wong's variance estimator 
    temp <- Sight.Est(observed ~ voc, odat = obs.m[obs.m$year == i,],
       sdat = exp.m, sampinfo, method = "Wong", 
       logCI = TRUE, alpha = 0.05, Vm.boot = FALSE) 
    tau.Wong[count, ] <- unlist(summary(temp)) 
 
# Steinhorst and Samuel (with Samuel et al. 1992 modification) 
    temp <- Sight.Est(observed ~ voc, odat = obs.m[obs.m$year == i,],  
       sdat = exp.m, sampinfo, method = "SS")
    tau.SS[count, ] <- unlist(summary(temp)) 
    count<-count+1
  }  
  rownames(tau.Wong) <- rownames(tau.SS) <- 2004:2007
  colnames(tau.Wong) <- colnames(tau.SS) <- c("tau.hat","LCL","UCL")
  (tau.Wong <- apply(tau.Wong, 1:2, 
      FUN=function(x){as.numeric(gsub(",", "", x, fixed = TRUE))}))
  (tau.SS <-   (tau.Wong <- apply(tau.Wong, 1:2, 
     FUN = function(x){as.numeric(gsub(",", "", x, fixed = TRUE))})))

## Not run: 
  require(gplots)
  par(mfrow = c(1,1))
    plotCI(2004:2007-.1, tau.Wong[,1], ui = tau.Wong[,3], 
        li = tau.Wong[,2], type = "l", xlab = "", 
        ylab = "Population estimate", xaxt = "n",
        xlim=c(2003.8, 2007.2))
    plotCI(2004:2007+.1, tau.SS[,1], ui = tau.SS[,3], li = tau.SS[,2], 
         type = "b", lty = 2, add = TRUE)
    axis(side = 1, at = 2004:2007, labels = 2004:2007)  
  
## End(Not run)

Sightability Model Estimator - Ratio of variables

Description

Estimates population ratios by 1) fitting a sightability (logistic regression) model to "test trial" data; 2) applying the fitted model to independent (operational) survey data to correct for detection rates < 1.

Usage

Sight.Est.Ratio(
  form,
  sdat = NULL,
  odat,
  sampinfo,
  method = "Wong",
  logCI = TRUE,
  alpha = 0.05,
  Vm.boot = FALSE,
  nboot = 1000,
  bet = NULL,
  varbet = NULL
)

Arguments

Details

Variance estimation methods: method = Wong implements the variance estimator from Wong (1996) and is the recommended approach. Method = SS implements the variance estimator of Steinhorst and Samuel (1989), with a modification detailed in the Appendix of Samuel et al. (1992).

Estimates of the variance may be biased low when the number of test trials used to estimate model parameters is small (see Wong 1996, Fieberg and Giudice 2008). A bootstrap can be used to aid the estimation process by specifying Vm.boot = TRUE [note: this method is experimental, and can be time intensive].

Confidence interval construction: often the sampling distribution of tau^ is skewed right. If logCI = TRUE, the confidence interval for tau^ will be constructed under an assumption that (tau^ - T) has a lognormal distribution, where T is the total number of animals seen. In this case, the upper and lower limits are constructed as follows [see Wong(1996, p. 64-67)]:

LCL = T + [(tau^-T)/C]*sqrt(1+cv^2), UCL = T+[(tau^-T)*C]*sqrt(1+cv^2), where cv^2 = var(tau^)/(tau^-T)^2 and C = exp[z[alpha/2]*sqrt(ln(1+cv^2))].

Value

An object of class sightest_ratio, a list that includes the following elements:

The list also includes the estimates for the numerator and denominator total, the original test trial and operational survey data, sampling information, and information needed to construct a confidence interval for the population estimate.

Author(s)

Carl James Schwarz, StatMathComp Consulting by Schwarz, cschwarz.stat.sfu.ca@gmail.com

References

Fieberg, J. 2012. Estimating Population Abundance Using Sightability Models: R SightabilityModel Package. Journal of Statistical Software, 51(9), 1-20. URL https://doi.org/10.18637/jss.v051.i09.

Fieberg, John and Giudice, John. 2008 Variance of Stratified Survey Estimators With Probability of Detection Adjustments. Journal of Wildlife Management 72:837-844.

Samuel, Michael D. and Steinhorst, R. Kirk and Garton, Edward O. and Unsworth, James W. 1992. Estimation of Wildlife Population Ratios Incorporating Survey Design and Visibility Bias. Journal of Wildlife Management 56:718-725.

Steinhorst, R. K., and M.D. Samuel. 1989. Sightability adjustment methods for aerial surveys of wildlife populations. Biometrics 45:415-425.

Wong, C. 1996. Population size estimation using the modified Horvitz-Thompson estimator with estimated sighting probabilities. Dissertation, Colorado State University, Fort Collins, USA.

Examples

# Load data frames
  data(obs.m) # observational survey data frame
  data(exp.m) # experimental survey data frame
  data(sampinfo.m) # information on sampling rates (contained in a data frame)
 
# Estimate ratio of bulls to cows in 2007 only
  sampinfo <- sampinfo.m[sampinfo.m$year == 2007,]

  obs.m$numerator   <- obs.m$bulls
  obs.m$denominator <- obs.m$cows
  
  Sight.Est.Ratio(observed ~ voc, odat = obs.m[obs.m$year == 2007,],
    sdat = exp.m, sampinfo, method = "Wong", 
    logCI = TRUE, alpha = 0.05, Vm.boot = FALSE) 

R function that interfaces with the SightabilityModel package and gives similar functionality as the AerialSurvey program

Description

A stratified random sample of blocks in a survey area is conducted. In each block, groups of moose are observed (usually through an aerial survey). For each group of moose, the number of moose is recorded along with attributes such as sex or age.

The SightabilityPopR() function adjusts for sightability < 100%.

Usage

SightabilityPopR(
  survey.data,
  survey.block.area,
  stratum.data,
  density = NULL,
  abundance = NULL,
  numerator = NULL,
  denominator = NULL,
  sight.formula = observed ~ 1,
  sight.beta = 10,
  sight.beta.cov = matrix(0, nrow = 1, ncol = 1),
  sight.logCI = TRUE,
  sight.var.method = c("Wong", "SS")[1],
  block.id.var = "Block.ID",
  block.area.var = "Block.Area",
  stratum.var = "Stratum",
  stratum.blocks.var = "Stratum.Blocks",
  stratum.area.var = "Stratum.Area",
  conf.level = 0.9
)

Arguments

Value

A data frame containing for each stratum and for all strata (identified as stratum id .OVERALL), the density, or abundance or ratio estimate along with its estimated standard error and large-sample normal-based confidence interval. Additional information on the components of variance is also reported.

Author(s)

Schwarz, C. J. cschwarz.stat.sfu.ca@gmail.com.

References

To Be Added.

Examples

 
##---- See the vignettes for examples on how to run this analysis.

Classical and Domain Stratification using SightabilityPopR()

Description

This function allows for classical or domain stratification when using SightabilityPopR(). Caution **SE are NOT adjusted for measurements on multiple domains on the same sampling unit. Bootstrapping may be required**. Consult the vignette for more details.

SightabilityPopR_DomStrat() adjusts for sightability < 100%.

Usage

SightabilityPopR_DomStrat(
  stratum.data,
  selected.unit.data,
  waypoint.data,
  density = NULL,
  abundance = NULL,
  numerator = NULL,
  denominator = NULL,
  sight.formula = ~1,
  sight.beta = 10,
  sight.beta.cov = matrix(0, nrow = 1, ncol = 1),
  sight.logCI = TRUE,
  sight.var.method = c("Wong", "SS")[1],
  stratum.var = "Stratum",
  domain.var = "Domain",
  stratum.total.blocks.var = "Total.Blocks",
  stratum.total.area.var = "Total.Area",
  block.id.var = "Block.ID",
  block.area.var = "Block.Area",
  conf.level = 0.9
)

Arguments

Value

A data frame containing for each stratum and for all combinations of strata and domains (identified as stratum id .OVERALL), the density, or abundance or ratio estimate along with its estimated standard error and large-sample normal-based confidence interval.

Author(s)

Schwarz, C. J. cschwarz.stat.sfu.ca@gmail.com.

References

To Be Added.

Examples

 
##---- See the vignettes for examples on how to run this analysis.

Sightability estimate with variance components estimator from Wong (1996)

Description

Estimates population size, with variance estimated using Wong's (1996) estimator. This function will usually be called by Sight.Est function (but see details).

Usage

Wong.est(
  total,
  srates,
  nh,
  Nh,
  stratum,
  subunit,
  covars,
  beta,
  varbeta,
  smat = NULL
)

Arguments

Details

This function is called by Sight.Est, but may also be called directly by the user (e.g., in cases where the original sightability [test trial] data are not available, but the parameters and var/cov matrix from the logistic regression model is available in the literature).

Value

Author(s)

John Fieberg

References

Rice CG, Jenkins KJ, Chang WY (2009). Sightability Model for Mountain Goats." The Journal of Wildlife Management, 73(3), 468- 478.

Steinhorst, R. K., and M.D. Samuel. (1989). Sightability adjustment methods for aerial surveys of wildlife populations. Biometrics 45:415-425.

Wong, C. (1996). Population size estimation using the modified Horvitz-Thompson estimator with estimated sighting probabilities. Dissertation, Colorado State University, Fort Collins, USA.

See Also

Sight.Est, SS.est

Sightability estimate of ratio with variance components estimator from Wong (1996)

Description

Estimates population ratio, with variance estimated using Wong's (1996) estimator. This function will usually be called by Sight.Est,Ratio() function (but see details).

Usage

Wong.est.Ratio(
  numerator,
  denominator,
  srates,
  nh,
  Nh,
  stratum,
  subunit,
  covars,
  beta,
  varbeta,
  smat = NULL
)

Arguments

Details

This function is called by Sight.Est.Ratio, but may also be called directly by the user (e.g., in cases where the original sightability [test trial] data are not available, but the parameters and var/cov matrix from the logistic regression model is available in the literature).

Value

Author(s)

Carl James Schwarz cschwarz.stat.sfu.ca@gmail.com

References

Rice CG, Jenkins KJ, Chang WY (2009). Sightability Model for Mountain Goats." The Journal of Wildlife Management, 73(3), 468- 478.

Steinhorst, R. K., and M.D. Samuel. (1989). Sightability adjustment methods for aerial surveys of wildlife populations. Biometrics 45:415-425.

Wong, C. (1996). Population size estimation using the modified Horvitz-Thompson estimator with estimated sighting probabilities. Dissertation, Colorado State University, Fort Collins, USA.

See Also

Sight.Est.Ratio, SS.est.Ratio

Check the sightability model arguments for consistency

Description

Check the sightability model arguments for consistency

Usage

check.sightability.model.args(data, sight.model, sight.beta, sight.beta.cov)

Arguments

Value

Error condition or invisible

Author(s)

Schwarz, C. J. cschwarz.stat.sfu.ca@gmail.com.

Examples

sightability.table <- data.frame(VegCoverClass=1:5)
sight.beta <- c(4.2138, -1.5847)
sight.beta.cov <- matrix(c(0.7821634, -0.2820000,-0.2820000,  0.1114892), nrow=2)
check.sightability.model.args( sightability.table, 
                               ~VegCoverClass, 
                               sight.beta, 
                               sight.beta.cov)
## Not run: 
check.sightability.model.args( sightability.table, 
                              ~VegCoverClass2, 
                              sight.beta,
                              sight.beta.cov)
check.sightability.model.args( sightability.table, 
                               ~VegCoverClass,
                                sight.beta[1],
                               sight.beta.cov)

## End(Not run)

Compute the sightability correction factor given a sightability and covariates

Description

Compute the sightability correction factor given a sightability and covariates

Usage

compute.SCF(
  data,
  sight.model,
  sight.beta,
  sight.beta.cov,
  check.args = FALSE,
  adjust = TRUE
)

Arguments

Value

Vector of sightability factors (SCF)

Author(s)

Schwarz, C. J. cschwarz.stat.sfu.ca@gmail.com.

See Also

compute.detect.prob

Examples

sightability.table <- data.frame(VegCoverClass=1:5)
sight.beta <- c(4.2138, -1.5847)
sight.beta.cov <- matrix(c(0.7821634, -0.2820000,-0.2820000,  0.1114892), nrow=2)
sightability.table$detect.prob <- compute.detect.prob( sightability.table, 
                                                       ~VegCoverClass, 
                                                       sight.beta, 
                                                       sight.beta.cov)
sightability.table$SCF         <- compute.SCF        ( sightability.table, 
                                                       ~VegCoverClass, 
                                                       sight.beta, 
                                                       sight.beta.cov)
sightability.table
#"Note that the SCF != 1/detect.prob because of correction terms for covariance of beta.terms"

Compute the detection probability given a sightability model

Description

Compute the detection probability given a sightability model

Usage

compute.detect.prob(
  data,
  sight.model,
  sight.beta,
  sight.beta.cov,
  check.args = FALSE
)

Arguments

Value

Vector of detection probabilities

Author(s)

Schwarz, C. J. cschwarz.stat.sfu.ca@gmail.com.

See Also

compute.SCF

Examples

sightability.table <- data.frame(VegCoverClass=1:5)
sight.beta <- c(4.2138, -1.5847)
sight.beta.cov <- matrix(c(0.7821634, -0.2820000,-0.2820000,  0.1114892), nrow=2)
sightability.table$detect.prob <- compute.detect.prob( sightability.table, 
                                                      ~VegCoverClass, 
                                                      sight.beta, 
                                                      sight.beta.cov)
sightability.table$SCF         <- compute.SCF        ( sightability.table,
                                                       ~VegCoverClass, 
                                                       sight.beta, 
                                                       sight.beta.cov)
sightability.table
#"Note that the SCF != 1/detect.prob because of correction terms for covariance of beta.terms"

Estimates var/cov matrix of inflation factors (1/prob detection) using a non-parametric bootstrap.

Description

Estimates var/cov matrix of inflation factors (1/prob detection) using a non-parametric bootstrap. Called by function Sight.Est if Vm.boot = TRUE.

Usage

covtheta(total, srates, stratum, subunit, covars, betas, varbetas, nboots)

Arguments

Value

Author(s)

John Fieberg

See Also

Sight.Est

Experimental (test trials) data set used to estimate detection probabilities for moose in MN

Description

Experimental (test trials) data set used to estimate detection probabilities for moose in MN

Format

A data frame with 124 observations on the following 4 variables.

year

year of the experimental survey (test trial)

observed

Boolean variable (=1 if moose was observed and 0 otherwise)

voc

measurement of visual obstruction

grpsize

group size (number of observed moose in each independently sighted group)

References

Giudice, J H. and Fieberg, J. and Lenarz, M. S. 2012. Spending Degrees of Freedom in a Poor Economy: A Case Study of Building a Sightability Model for Moose in Northeastern Minnesota. Journal of Wildlife Management 76(1):75-87.

Examples

data(exp.m)
exp.m[1:5,]

Mountain Goat Sightability Model Information

Description

Model averaged regression parameters and unconditional variance-covariance matrix for mountain goat sightability model (Rice et al. 2009)

Format

The format is: beta.g = list of regression parameters (intercept and parameters associated with GroupSize, Terrain, and X.VegCover) varbeta.g = variance-covariance matrix (associated with beta.g)

References

Rice C.G., Jenkins K.J., Chang W.Y. (2009). A Sightability Model for Mountain Goats. The Journal of Wildlife Management, 73(3), 468-478.

Examples

data(g.fit)

Mountain Goat Survey Data from Olympic National park

Description

Mountain Goat Survey Data from Olympic National park collected in 2004

Format

A data frame with 113 observations on the following 9 variables.

GroupSize

number of animals observed in each independently sighted group [cluster size]

Terrain

measure of terrain obstruction

pct.VegCover

measure of vegetative obstruction

stratum

stratum identifier

total

number of animals observed in each independently sighted group [same as GroupSize]

subunit

a numeric vector, Plot ID

Source

Patti Happe (Patti_Happe@nps.gov)

References

Jenkins, K. J., Happe, P.J., Beirne, K.F, Hoffman, R.A., Griffin, P.C., Baccus, W. T., and J. Fieberg. In press. Recent population trends in mountain goats in the Olympic mountains. Northwest Science.

Examples

data(gdat)

MN moose survey data

Description

Operational survey data for moose in MN (during years 2004-2007). Each record corresponds to an independently sighted group of moose, with variables that capture individual covariates (used in the detection model) as well as plot-level information (stratum identifier, sampling probability, etc).

Format

A data frame with 805 observations on the following 11 variables.

year

year of survey

stratum

stratum identifier

subunit

sample plot ID

total

number of moose observed

cows

number of cows observed

calves

number of calves observed

bulls

number of bulls observed

unclass

number of unclassified animals observed (could not identify sex/age class)

voc

measurement of visual obstruction

grpsize

group size (cluster size)

References

Giudice, J H. and Fieberg, J. and Lenarz, M. S. 2012. Spending Degrees of Freedom in a Poor Economy: A Case Study of Building a Sightability Model for Moose in Northeastern Minnesota. Journal of Wildlife Management 76(1):75-87.

Examples

data(obs.m) 
obs.m[1:5, ]

Print method for sightability estimators

Description

Prints fitted sightability model, sampling information, and sightability estimate (with confidence interval)

Usage

## S3 method for class 'sightest'
print(x, ...)

Arguments

Author(s)

John Fieberg and Carl James Schwarz

See Also

Sight.Est, Sight.Est.Ratio, summary.sightest, summary.sightest_ratio

Data set containing sampling information for observation survey of moose in MN

Description

Data set containing sampling information from a survey of moose in MN (during years 2004-2007)

Format

A data frame with 12 observations on the following 5 variables.

year

year of survey

stratum

stratum identifier

Nh

number of population units in stratum h

nh

number of sample units in stratum h

References

Giudice, J H. and Fieberg, J. and Lenarz, M. S. 2012. Spending Degrees of Freedom in a Poor Economy: A Case Study of Building a Sightability Model for Moose in Northeastern Minnesota. Journal of Wildlife Management 76(1):75-87.

Examples

data(sampinfo.m)
sampinfo.m

Summarize sightability estimator

Description

Calculates confidence interval (based on asymptotic [normal or log-normal assumption])

Usage

## S3 method for class 'sightest'
summary(object, ...)

Arguments

Value

Author(s)

John Fieberg and Carl James Schwarz

See Also

Sight.Est, Sight.Est.Ratio

Function to estimate the variance of the difference between two population estimates

Description

Function to estimate the variance of the difference between two population estimates formed using the same sightability model (to correct for detection).

Usage

vardiff(sight1, sight2)

Arguments

Details

Population estimates constructed using the same sightability model will NOT be independent (they will typically exhibit positive covariance). This function estimates the covariance due to using the same sightability model and subtracts it from the summed variance.

Value

Author(s)

John Fieberg

Examples

# Example using moose survey data 
  data(obs.m) # observational moose survey data
  data(exp.m) # experimental moose survey data
  data(sampinfo.m) # information on sampling rates
 
# Estimate population size in 2006 and 2007 
 sampinfo <- sampinfo.m[sampinfo.m$year == 2007, ]
 tau.2007 <- Sight.Est(observed ~ voc, odat = obs.m[obs.m$year == 2007, ], 
                         sdat = exp.m, sampinfo.m[sampinfo.m$year == 2007, ], 
                         method = "Wong", logCI = TRUE, alpha = 0.05, Vm.boot = FALSE) 
 tau.2006 <- Sight.Est(observed ~ voc, odat = obs.m[obs.m$year == 2006, ],
                         sdat = exp.m, sampinfo.m[sampinfo.m$year == 2006, ],
                         method = "Wong", logCI = TRUE, alpha = 0.05, Vm.boot = FALSE) 

# naive variance
  tau.2007$est[2]+tau.2006$est[2]

# variance after subtracting positvie covariance
  vardiff(tau.2007, tau.2006)

Calculates the variance of the log rate of change between 2 population estimates that rely on the same sightability model.

Description

Calculates the variance of the log rate of change between 2 population estimates that rely on the same sightability model.

Usage

varlog.lam(sight1, sight2)

Arguments

Details

This function uses the delta method to calculate an approximate variance for the log rate of change, log(tau^[t+1])-log(tau^[t]), while accounting for the positive covariance between the two estimates (as a result of using the same sightability model to correct for detection).

Value

Author(s)

John Fieberg

See Also

vardiff

Examples

# Example using moose survey data 
  data(obs.m) # observational moose survey data
  data(exp.m) # experimental moose survey data
  data(sampinfo.m) # information on sampling rates
 
# Estimate population size in 2006 and 2007 
  sampinfo <- sampinfo.m[sampinfo.m$year==2007, ]
  tau.2007 <- Sight.Est(observed ~ voc, odat = obs.m[obs.m$year==2007, ],
                          sdat = exp.m, sampinfo.m[sampinfo.m$year == 2007, ],
                          method = "Wong", logCI = TRUE, alpha = 0.05, Vm.boot = FALSE) 
  tau.2006 <- Sight.Est(observed ~ voc, odat = obs.m[obs.m$year==2006, ],
                          sdat = exp.m, sampinfo.m[sampinfo.m$year == 2006, ], 
                          method = "Wong", logCI = TRUE, alpha = 0.05, Vm.boot = FALSE)  

# Log rate of change 
  varlog.lam(tau.2006, tau.2007)