Single-season occupancy estimation

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Description

Functions to estimate occupancy from detection/non-detection data for a single season. occSS is the general-purpose function, and occSStime provides plots of detection probability against time. occSS0 and occSScovSite are faster functions for simpler models with summarized data. See occSSrn for the Royle-Nichols model for abundance-induced heterogeneity in detection probability.

Usage

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occSS(DH, model=NULL, data = NULL, ci=0.95, link=c("logit", "probit"), verify=TRUE)

occSStime(DH, model=p~1, data=NULL, ci=0.95, plot=TRUE, link=c("logit", "probit"),
  verify=TRUE)

occSS0(y, n, ci=0.95, link=c("logit", "probit"))

occSScovSite(y, n, model=NULL, data = NULL, ci=0.95, link=c("logit", "probit"))

Arguments

DH

a 1/0/NA matrix (or data frame) of detection histories, sites x occasions.

model

a list of formulae symbolically defining a linear predictor for each parameter in terms of covariates. If NULL, an intercept-only model is used, ie, psi(.) p(.).

ci

the confidence interval to use.

data

a data frame containing the variables in the model. For occSStime, a data frame with a row for each survey occasion; otherwise, a row for each site. Each site covariate has one column. Each survey covariate has one column for each occasion, and the column name must end with the occasion number (without leading zeros); eg, Cov1, Cov2, ..., Cov15. All covariates should be included in data, otherwise they will be sought in enclosing environments, which may not produce what you want – and they won't be standardised.

link

the link function to use, either logit or probit; see Links.

verify

if TRUE, the data provided will be checked.

plot

if TRUE (default), draws a plot of probability of detection vs time.

y

a vector with the number of detections at each site.

n

a scalar or vector with the number of visits (survey occasions) at each site.

Details

occSS allows for psi or p to be modelled as a logistic function of site covariates or survey covariates, as specified by model. It includes a built in .time covariate which can be used for modelling p with time as a fixed effect, and .Time for a linear or quadratic trend. A built-in .b covariate corresponds to a behavioural effect, where detection depends on whether the species was detected on the previous occasion or not.

occSStime allows for time-varying covariates that are the same across all sites, eg, moon-phase. A categorical time variable .time and a time trend .Time are built-in. A plot of detection probability vs time is produced if plot=TRUE.

occSS0 implements a simple model with one parameter for probability of occupancy and one for probability of detection, ie. a psi(.) p(.) model.

occSScovSite allows for site covariates but not for occasion or survey covariates.

Numeric covariates in data are standardised to facilitate convergence. This applies to binary covariates coded as 1/0; if this is not what you want, code these as TRUE/FALSE or as factors.

For speed, use the simplest function which will cope with your model. For example, you can run psi(.) p(.) models in occSScovSite or occSS, but occSS0 is much faster.

Value

Returns an object of class wiqid, which is a list with the following elements:

call

The call used to produce the results

beta

Values of the coefficients of the terms in the linear predictors, with standard errors and confidence intervals.

beta.vcv

The variance-covariance matrix for the beta estimates.

real

Estimates of occupancy and probability of detection on the real scale, with confidence intervals.

logLik

a vector with elements for log(likelihood), number of parameters, and effective sample size. If parameters and their SEs cannot be estimated, the first element should be NA.

There are print, logLik, and nobs methods for class wiqid.

Benchmarks

Output has been checked against output from PRESENCE (Hines 2006) v.5.5 for the salamanders and weta data sets. Real values are mostly the same to 4 decimal places, though there is occasionally a discrepancy of 0.0001. AICs are the same.

Author(s)

Mike Meredith

References

MacKenzie, D I; J D Nichols; G B Lachman; S Droege; J A Royle; C A Langtimm. 2002. Estimating site occupancy rates when detection probabilities are less than one. Ecology 83:2248-2255.

MacKenzie, D I; J D Nichols; A J Royle; K H Pollock; L L Bailey; J E Hines 2006. Occupancy estimation and modeling : inferring patterns and dynamics of species occurrence. Elsevier Publishing.

Hines, J. E. (2006). PRESENCE - Software to estimate patch occupancy and related parameters. SGS-PWRC. http://www.mbr-pwrc.usgs.gov/software/presence.html.

See Also

See the examples for the weta data set. See occ2sps for single-season two-species models and occMS for multi-season models.

Examples

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# The blue ridge salamanders data from MacKenzie et al (2006) p99:
data(salamanders)
occSS(salamanders)
occSStime(salamanders, p ~ .time)  # time as a fixed effect
occSStime(salamanders, p ~ .Time + I(.Time^2))  # a quadratic time effect
occSS(salamanders, p ~ .b)

# or use the fast functions with y, n format:
y <- rowSums(salamanders)
n <- rowSums(!is.na(salamanders))
occSS0(y, n)
occSScovSite(y, n)

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