bSims (version 0.3-2)

dist_fun2: Distance function with segmented attenuation

Description

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), ...)

Value

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

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

Author

Peter Solymos

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>

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)