receiver_line_det_sim: Simulate detection of acoustic-tagged fish crossing a...

In jsta/glatos: A package for the Great Lakes Acoustic Telemetry Observation System

Simulate detection of acoustic-tagged fish crossing a receiver line

Description

Estimate, by simulation, the probability of detecting an acoustic-tagged fish on a receiver line, given constant fish velocity (ground speed), receiver spacing, number of receivers, and detection range curve.

Usage

receiver_line_det_sim(vel = 1, delayRng = c(120, 360), burstDur = 5,
  recSpc = 1000, maxDist = 2000, rngFun, outerLim = c(0, 0),
  nsim = 1000, showPlot = FALSE)

Arguments

vel	A numeric scalar with fish velocity in meters per second.
delayRng	A 2-element numeric vector with minimum and maximum delay (time in seconds from end of one coded burst to beginning of next)
burstDur	A numeric scalar with duration (in seconds) of each coded burst (i.e., pulse train).
recSpc	A numeric vector with distances (in meters) between receivers. The length of vector is N-1, where N is number of receivers. One receiver is simulated when recSpc = NA (default).
maxDist	A numeric scalar with maximum distance between tagged fish and any receiver during simulation (i.e., sets spatial boundaries)
rngFun	A function that defines detection range curve; must accept a numeric vector of distances and return a numeric vector of detection probabilities at each distance.
outerLim	A two-element numeric vector with space (in meters) in which simulated fish are allowed to pass to left (first element) and right (second element) of the receiver line.
nsim	Integer scalar with the number of crossings (fish) to simulate
showPlot	A logical scalar. Should a plot be drawn showing receivers and fish paths?

Details

Virtual tagged fish (N=nsim) are "swum" through a virtual receiver line. The first element of recSpc determines spacing between first two receivers in the line, and each subsequent element of recSpc determine spacing of subsequent receivers along the line, such that the number of receivers is equal to length(recSpc) + 1. Each fish moves at constant velocity (vel) along a line perpendicular to the receiver line. The location of each fish path along the receiver line is random (drawn from uniform distribution), and fish can pass outside the receiver line (to the left of the first receiver or right of last receiver) if outerLim[1] or outerLim[2] are greater than 0 meters. Each fish starts and ends about maxDist meters from the receiver line.

A simulated tag signal is transmitted every delayRng[1] to delayRng[2] seconds. At time of each transmission, the distance is calculated between the tag and each receiver, and rngFun is used to calculate the probability (p) that the signal was detected on each receiver. Detection or non-detection on each receiver is determined by a draw from a Bernoulli distribution with probability p.

Value

A data frame with one column:

detProb

The proportion of simulated fish that were detected more than once on any single receiver.

Author(s)

C. Holbrook [e-mail]

References

For application example, see:

Hayden, T.A., Holbrook, C.M., Binder, T.R., Dettmers, J.M., Cooke, S.J., Vandergoot, C.S. and Krueger, C.C., 2016. Probability of acoustic transmitter detections by receiver lines in Lake Huron: results of multi-year field tests and simulations. Animal Biotelemetry, 4(1), p.19.
https://animalbiotelemetry.biomedcentral.com/articles/10.1186/s40317-016-0112-9

Examples

#EXAMPLE 1 - simulate detection on line of ten receivers
  
 #Define detection range function (to pass as rngFun) 
 # that returns detection probability for given distance
  # assume logistic form of detection range curve where 
  #   dm = distance in meters
  #   b = intercept and slope
 pdrf <- function(dm, b=c(5.5, -1/120)){
    p <- 1/(1+exp(-(b[1]+b[2]*dm)))
    return(p)
 }

 #preview detection range curve
 plot(pdrf(0:2000),type="l",ylab="Probability of detecting each coded burst", 
xlab="Distance between receiver and transmitter")

 #Simulate detection using pdrf; default values otherwise
 dp <- receiver_line_det_sim(rngFun=pdrf)
 dp

 #Again with only 10 virtual fish and optional plot to see simulated data
 dp <- receiver_line_det_sim(rngFun=pdrf, nsim=10, showPlot=T) #w/ optional plot
 dp

 #Again but six receivers and allow fish to pass to left and right of line
 dp <- receiver_line_det_sim(rngFun=pdrf, recSpc=rep(1000,5),
	outerLim=c(1000, 1000), nsim=10, showPlot=T)
 dp

 #Again but four receivers with irregular spacing
 dp <- receiver_line_det_sim(rngFun=pdrf, recSpc=c(2000,4000,2000),
 	outerLim=c(1000, 1000), nsim=10, showPlot=T)
 dp


#EXAMPLE 2 - summarize detection probability vs. receiver spacing
 
 #two receivers only, spaced 'spc' m apart
 #define scenarios where two receiver are spaced 
 spc <- seq(100,5000, 100) #two receivers spaced 100, 200, ... 5000 m
 #loop through scenarios, estimate detection probability for each
 for(i in 1:length(spc)){
   if(i==1) dp <- numeric(length(spc)) #pre-allocate
   dp[i] <- receiver_line_det_sim(recSpc=spc[i], rngFun=pdrf)
 }
 cbind(spc,dp) #view results  
 #plot results
 plot(spc, dp, type="o",ylim=c(0,1), 
   xlab="distance between receivers in meters",
  ylab="proportion of virtual fish detected") 
 # e.g., >95% virtual fish detected up to 1400 m spacing in this example


#EXAMPLE 3 - summarize detection probability vs. fish swim speed
 
 #define scenarios of fish movement rate
 swim <- seq(0.1, 5.0, 0.1) #constant velocity
 for(i in 1:length(swim)){
   if(i==1) dp <- numeric(length(swim)) #pre-allocate
   dp[i] <- receiver_line_det_sim(vel=swim[i], rngFun=pdrf)
 }
 cbind(swim,dp) #view results
 #plot results
 plot(swim, dp, type="o", ylim=c(0,1), xlab="fish movement rate, m/s",
  ylab="proportion of virtual fish detected")
 # e.g., >95% virtual fish detected up to 1.7 m/s rate in this example
 # e.g., declines linearly above 1.7 m/s


#EXAMPLE 4 - empirical detection range curve instead of logistic
 
 #create data frame with observed det. efficiency (p) at each distance (x)
 edr <- data.frame(
   x=c(0,363,444,530,636,714,794,889,920), #tag-receiver distance
   p=c(1,1,0.96,0.71,0.67,0.75,0.88,0.21,0)) # detection prob

 #now create a function to return the detection probability
 # based on distance and linear interpolation within edr
 # i.e., estimate p at given x by "connecting the dots" 
 edrf <- function(dm, my.edr=edr) {
   p <- approx(x=my.edr$x,y=my.edr$p,xout=dm, rule=2)$y
   return(p)
 }

 #preview empirical detection range curve
 plot(edrf(0:2000),type="l",
   ylab="probability of detecting each coded burst", 
  xlab="distance between receiver and transmitter, meters")

 #use empirical curve (edrf) in simulation
 dp <- receiver_line_det_sim(rngFun=edrf, nsim=10, showPlot=T) #w/ optional plot
 dp

jsta/glatos documentation built on July 11, 2022, 7:01 a.m.