Estimate probability of collision for telemetry transmitters

Estimate (by simulation) probability of collision for co-located telemetry transmitters with pulse-period-modulation type encoding

Usage

calc_collision_prob(
  delayRng = c(60, 180),
  burstDur = 5,
  maxTags = 50,
  nTrans = 10000
)

Arguments

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).

maxTags

A numeric scalar with maximum number of co-located transmitters (within detection range at same time).

nTrans

A numeric scalar with the number of transmissions to simulate for each co-located transmitter.

Value

A data frame containing summary statistics:

nTags

Number of tags within detection range at one time

min

Minimum detection probability among simulated tags

q1

First quartile of detection probabilities among simulated tags

median

Median detection probability among simulated tags

q3

Third quartile of detection probabilities among simulated tags

max

Maximum detection probability among simulated tags

mean

Mean detection probability among simulated tags

expDetsPerHr

Expected number of detections per hour assuming perfect detection probability, given the number of tags within detection range

totDetsPerHr

Observed number of detections per hour for a given number of tags

effDelay

Eeffective delay of the transmitter after incorporating collisions

detsPerTagPerHr

Mean number of detections per hour per tag

Details

Calculates the detection probability associated with collision, given delay range (delayRng), burst duration (burstDur), maximum number of co-located tags (maxTags), and number of simulated transmission per tag (nTrans). The simulation estimates detection probability due only to collisions (i.e., when no other variables influence detection probability) and assuming that all tags are co-located at a receiver for the duration of the simulation.

References

For application example, see:

Binder, T.R., Holbrook, C.M., Hayden, T.A. and Krueger, C.C., 2016. Spatial and temporal variation in positioning probability of acoustic telemetry arrays: fine-scale variability and complex interactions. Animal Biotelemetry, 4(1):1.
http://animalbiotelemetry.biomedcentral.com/articles/10.1186/s40317-016-0097-4

Author

C. Holbrook (cholbrook@glfc.org) and T. Binder

Examples

# parameters analagous to Vemco tag, global coding, 45 s nominal delay
foo <- calc_collision_prob(
  delayRng = c(45, 90), burstDur = 5.12, maxTags = 50,
  nTrans = 10000
)

# plot probabilities of detection
plot(med ~ nTags,
  data = foo, type = "p", pch = 20, ylim = c(0, 1),
  xlab = "# of transmitters within range", ylab = "Probability of detection"
)


# plot probability of collision by subtracting detection probability from 1
plot((1 - med) ~ nTags,
  data = foo, type = "p", pch = 20, ylim = c(0, 1),
  xlab = "# of transmitters within range", ylab = "Probability of collision"
)