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Distance function with segmented attenuation

dist_fun2.Rd

Distance function with segmented attenuation crossing a number of boundaries of strata with different attenuation characteristics following results in Yip et al. (2017).

Usage

dist_fun2(d, tau, dist_fun, breaks = numeric(0), ...)

Arguments

d

distance from observer.

tau

a parameter passed to the the distance function. Length of tau must equal length(b) + 1 referring to distance function parameters in the different strata (a stratum is defined by an interval surrounded by 1 or 2 boundaries).

dist_fun

distance function taking two arguments: distance, and tau, see examples.

breaks

distance breakpoints, must be length(tau) - 1 in length. These breakpoints represent the boundaries between the intervals characterized by homogeneous attenuation characteristics.

...

other arguments passed to dist_fun

Value

Probability of detection given the distance, stratum specific parameters and the arrangement of breakpoints.

References

Yip, D. A., Bayne, E. M., Solymos, P., Campbell, J., and Proppe, J. D., 2017. Sound attenuation in forested and roadside environments: implications for avian point count surveys. Condor, 119: 73--84. <doi:10.1650/CONDOR-16-93.1>

Author

Peter Solymos

Examples

tau <- c(1, 2, 3, 2, 1)
d <- seq(0, 4, 0.01)
dist_fun <- function(d, tau) exp(-(d/tau)^2) # half normal
#dist_fun <- function(d, tau) exp(-d/tau) # exponential
#dist_fun <- function(d, tau) 1-exp(-(d/tau)^-2) # hazard rate

b <- c(0.5, 1, 1.5, 2) #  boundaries

op <- par(mfrow=c(2, 1))
plot(d, dist_fun2(d, tau[1], dist_fun), type="n",
  ylab="P(detection)", xlab="Distance", axes=FALSE,
  main="Sound travels from left to right")
axis(1)
axis(2)
for (i in seq_len(length(b)+1)) {
  x1 <- c(0, b, 4)[i]
  x2 <- c(0, b, 4)[i+1]
  polygon(c(0, b, 4)[c(i, i, i+1, i+1)], c(0, 1, 1, 0),
    border=NA,
    col=c("darkolivegreen1", "burlywood1", "lightgrey",
    "burlywood1", "darkolivegreen1")[i])
}
lines(d, dist_fun2(d, tau[1], dist_fun))
lines(d, dist_fun2(d, tau[2], dist_fun))
lines(d, dist_fun2(d, tau[3], dist_fun))
lines(d, dist_fun2(d, tau, dist_fun, b), col=2, lwd=3)

plot(rev(d), dist_fun2(d, tau[1], dist_fun), type="n",
  ylab="P(detection)", xlab="Distance", axes=FALSE,
  main="Sound travels from right to left")
axis(1)
axis(2)
for (i in seq_len(length(b)+1)) {
  x1 <- c(0, b, 4)[i]
  x2 <- c(0, b, 4)[i+1]
  polygon(c(0, b, 4)[c(i, i, i+1, i+1)], c(0, 1, 1, 0),
    border=NA,
    col=c("darkolivegreen1", "burlywood1", "lightgrey",
    "burlywood1", "darkolivegreen1")[i])
}
lines(rev(d), dist_fun2(d, tau[1], dist_fun))
lines(rev(d), dist_fun2(d, tau[2], dist_fun))
lines(rev(d), dist_fun2(d, tau[3], dist_fun))
lines(rev(d), dist_fun2(d, tau, dist_fun, rev(4-b)), col=2, lwd=3)

par(op)