detect.prop: Probability of detecting a feature that covers a proportion...
In emon: Tools for Environmental and Ecological Survey Design

Description Usage Arguments Details Value Author(s) Examples

The function can calculate the probability of a feature that occupies a proportion theta of the sampling area and where the sampling point density of the survey is specified; the sampling point density needed to achieve a specified probability of detection, where theta is also specified ; or the value of theta that will be detected with specified probability and sampling density.Unless the feature is made of a large number of random segments (see below for how to deal with this situation), these methods apply only when the pattern of points in the sampling deisgn is random.

1	detect.prop(statistic, theta=NA, pdetect=NA, ssize=NA)

`statistic`	Describes what aspect of design you want calculated. The choices are `"P"` (probability detection); `"N"` (sample size) or `"F"` (feature proportion).
`theta`	Feature proportion. Not needed if `statistic="F"`.
`pdetect`	Probability detection. Not needed if `statistic="P"`.
`ssize`	Sample size. Not needed if `statistic="N"`.

The probability of detection is p = 1 - (1 - theta)^{N}. Formulae for theta and N are readily obtained from this formula. If the spatial pattern of the feature consists of lots of small, random uniformly distributed fragments, then we can redefine theta = Na/A where a is the area of the sampling unit and A is the sampling area.In this situation, the probability of patch detection applies no matter what the spatial pattern of points in the sampling design. Unlike detect, detect.prop works for vectors - so long as the input vectors are of the same length.

`prob`	Probability of detection
`ssize`	Sample size
`prop`	Feature proportion

Jon Barry: Jon.Barry@cefas.co.uk

1
2
3

detect.prop(statistic='P', theta=0.02, ssize=80)
detect.prop(statistic='N', theta=0.02, pdetect=0.9)
detect.prop(statistic='F', pdetect=0.9, ssize=80)