unmarked (version 1.4.3)

makePiFuns: Create functions to compute multinomial cell probabilities

Description

These are factory functions that generate piFuns with the required defaults, which are enclosed within the environment of the piFun. See the main entry for piFuns.

Usage

makeRemPiFun(times)
makeCrPiFun(nOcc)
makeCrPiFunMb(nOcc)
makeCrPiFunMh(nOcc)

Value

A piFun with the appropriate defaults.

Arguments

times

a vector of times for each interval, length(times) is the number of survey occasions; can be all 1's if times are the same.

nOcc

the number of survey occasions

Details

makeRemPiFun produces a piFun for a removal model with the required number of occasions and potentially varying time intervals. The input to the piFun must be probabilities per unit time. This is a generalisation of the piFun in the Examples section of piFuns.

makeCrPiFun produces a piFun for a standard capture-recapture model, M0, Mt or Mx. Probabilities of detection may vary across occasions. See Kery & Royle (2016) section 7.8.1.

makeCrPiFunMb produces a piFun for a capture-recapture model with a behavioral response after the first capture, Mb. Probabilities of detection are constant across occasions. The first column is the probability of detection for animals not caught before, column #2 is for animals after the first capture. The remaining columns are ignored. See Kery & Royle (2016) section 7.8.2.

makeCrPiFunMh produces a piFun for a capture-recapture model with individual heterogeneity in detection probability, Mh, using a logit-normal distribution. Probabilities of detection are constant across occasions. The first column is the mean of the logit-normal on the probability scale. Cell p[1, 2] is a value in [0, 1] which controls the spread of the distribution. The remaining cells are ignored. See Kery & Royle (2016) section 7.8.3.

References

Kery, M., Royle, J. A. (2016) Applied Hierarchical Modeling in Ecology Vol 1.

Examples

# Generate piFuns and check their behaviour:

# makeRemPiFun
# ============
( pRem <- matrix(0.4, nrow=5, ncol=3) )
myPi <- makeRemPiFun(times=c(2,3,5))
myPi(pRem)
ls(environment(myPi))  # See what's in the environment
environment(myPi)$times

( pRem <- matrix(runif(15), 5, 3) )
myPi(pRem)

myPi <- makeRemPiFun(c(5,3,2))
environment(myPi)$times
myPi(pRem)

# More than 3 occasions
myPi <- makeRemPiFun(c(1,2,3,5))
try(myPi(pRem))  # Error
( pRem <- matrix(runif(20), 5, 4) )
myPi(pRem)
# Probability of escaping detection
1 - rowSums(myPi(pRem))

# makeCrPiFun
# ===========
p <- matrix(0.4, 2, 3)
myPi <- makeCrPiFun(3)
myPi(p)
myPi  # Look at the function
ls(environment(myPi))
environment(myPi)$histories

p <- matrix(runif(6, 0.1, 0.9), 2, 3)  # different p's everywhere
myPi(p)

p <- matrix(runif(4*5, 0.1, 0.9), 4, 5)  # > 3 occasions
try(myPi(p))  # Error
myPi <- makeCrPiFun(5)
( tmp <- myPi(p) )
1 - rowSums(tmp) # Probability of non-capture

# makeCrPiFunMb
# ==============
( pMb <- cbind(rep(0.7, 5), 0.3, NA) )
myPi <- makeCrPiFunMb(3)
myPi(pMb)

( pMb <- matrix(runif(15), 5, 3) )  # col #3 will be ignored
myPi(pMb)

# with > 3 occasions
( pMb <- matrix(runif(15), 3, 5) )
try(myPi(pMb))
myPi <- makeCrPiFunMb(5)
myPi(pMb)

# makeCrPiFunMh
# =============
pMh <- cbind(rep(0.4, 5), NA, NA)
pMh[1, 2] <- 0.3
pMh
myPi <- makeCrPiFunMh(3)
myPi(pMh)
pMh <- cbind(runif(5), NA, NA)
pMh[1, 2] <- 0.3
pMh
myPi(pMh)

# with > 3 occasions
pMh <- cbind(runif(5), NA, NA, NA, NA)
pMh[1, 2] <- 0.3
pMh
try(myPi(pMh))
myPi <- makeCrPiFunMh(5)
1 - rowSums(myPi(pMh))  # Probability of non-detection