# detect: Probability of circular patch detection In emon: Tools for Environmental and Ecological Survey Design

## Description

The function can calculate the probability of detection of a circular patch of specified radius for a specified density of points; the density needed to achieve a specified probability of detection; or the radius of the patch that will be detected with specified probability and sampling density.This is done for random, square lattice, and triangular lattice spatial sampling designs.

## Usage

 `1` ```detect(method, statistic, area=NA, radius=NA, pdetect=NA, ssize=NA) ```

## Arguments

 `method` Defines the spatial sampling design to be used. The values can be `"R"` (random), `"S"` (square lattice) or `"T"` (triangular lattice). See Barry and Nicholson (1993) for details and formulae for the probabilities of detection for the square lattice and triangular lattice designs. For the random design, `prob(detect)=1 - (1 - a/A)^N`, where `a` is the patch area and `A` is the survey area. This gives similar answers to the formula in Barry and Nicholson, but is exact for fixed sample size. `statistic` Describes what aspect of design you want calculated. The choices are `"P"` (probability detection); `"N"` (sample size) or `"R"` (patch radius). `area` The survey area (same units as distance and radius). `radius` Patch radius. Not needed if `statistic="R"`. `pdetect` Probability detection. Not needed if `statistic="P"`. `ssize` Sample size. Not needed if `statistic="N"`.

## Details

The basic idea is that you wish to conduct a survey in an area `area` to detect some object (patch) of interest. This could be a cockle patch, an area of reef or an archaeological deposit. This function asssumes that the object is circular with radius `radius`. You have three choices of sampling deign to use: spatial, square lattice and triangular lattice. In terms of patch detection, for a given sample size, the triangular design gives the highest probability - because its points are equi-distant apart.

The simplest application of this function is to assess the patch detection probability for a particular design. This is obtained using the `statistic="P"` option. However, the problem can be turned around and this function used to calculate the sample size needed to obatain a specific patch detection probability (`statistic="N"`) or the radius of the patch that would be detected with some desired probability (`statistic="R"). Th`is last scenario might be useful if there was some particular size of patch that you wanted to be sure (say, 90 percent) of detecting.

## Value

 `prob` Probability of patch detection `ssize` Sample size `rad` Patch radius `sep` Separation distance (for square and triangular lattice designs)

## Author(s)

Jon Barry: [email protected]

## References

Barry J and Nicholson M D (1993) Measuring the probabilities of patch detection for four spatial sampling schemes. Journal of Applied Statistics, 20, 353-362.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21``` ```detect(method='R', statistic='P', area=100, radius=2, ssize=15)\$prob detect(method='R', statistic='N', area=100, radius=2, pdetect=0.95)\$ssize detect(method='R', statistic='R', area=100, pdetect=0.95, ssize=15)\$rad detect(method='S', statistic='P', area=100, radius=1.4, ssize=15) detect(method='S', statistic='N', area=100, radius=1.4, pdetect=0.6) # Plot patch detection as a function of radius square = rep(0,200); rand = square; triang = rand radius = seq(0.01, 2, 0.01) for (j in 1:200) { rand[j] = detect(method='R', statistic='P', area=100, radius=radius[j], ssize=15)\$p square[j] = detect(method='S', statistic='P', area=100, radius=radius[j], ssize=15)\$p triang[j] = detect(method='T', statistic='P', area=100, radius=radius[j], ssize=15)\$p } plot(radius, rand, ylim=c(0,1), xlab='Patch radius', ylab='Probability detection', type='l') lines(radius, square, col=2, lty=2) lines(radius, triang, col=3, lty=3) legend('topleft', legend=c('Random', 'Square', 'Triangular'), col=c(1,2,3), lty=c(1,2,3)) ```

emon documentation built on May 30, 2017, 1:42 a.m.