# freq: capture frequecies In FREQ: FREQ: Estimate population size from capture frequencies

## Description

Real capture frequencies will be fitted to a geometric, a truncated geometic, a Poisson, and a negative binomial distribution. These distributions provide the basis for estimating population sizes, their standard error, and symmetric as well as asymmetric confidence intervalls. Moreover, expected values for these four distributions will be calculated allowing comparisons betweens real and expected capture frequecies.

## Usage

 `1` ```freq(fi) ```

## Arguments

 `fi` a vector of capture frequencies with length of all (successive) sampling periods; start the vector using c()

## Value

 `All meassured and expected values: ` All measured an expected values of actual and possible distributions `All estimated values: ` All estimted values including number of individuals captured, distribution parameters, population size and respective standard error, symmetric and asymmetric 95 percent confidence interval

## Warning

unused argument –> fi must be a vector starting c(a,b,c,..)

## Author(s)

Annegret Grimm & Klaus Henle annegret.grimm@ufz.de

## References

Grimm, A. (submitted to PLOS One) Reliability of different mark-recapture methods for population size estimation tested with field data from populations of known size.

Henle, K. (1990) Population ecology and life history of the arboreal gecko Gehyra variegata in arid Australia. Herpetological Monographs, 4, 30-60.

Seber, GAF. (1982) The estimation of animal abundance and related parameters. Second edition. Griffin, London.

## Examples

 ```1 2 3 4 5 6``` ```# In your field population, 53 individuals were captured once, 19 were captured twice, # 4 were captured three times, 1 was captured four times # and no individual was captured five or six times. # As there were six capture occasions, the fifth and sixth capture occasion is set to 0. # call your capture frequencies as follows: freq(c(53,19,4,1,0,0)) ```

### Example output

```All meassured and expected values:
original data Geometric Distribution Truncated Geometric Distribution
1            53             55.2075472                      54.87685904
2            19             15.6247775                      15.37846357
3             4              4.4221068                       4.30959690
4             1              1.2515397                       1.20770358
5             0              0.3542093                       0.33844185
6             0              0.1002479                       0.09484354
Poisson Distribution Negative Binomial Distribution
1          53.21190442                   53.051026876
2          18.58550001                   18.796079471
3           4.32761321                    4.322183883
4           0.75575998                    0.725159065
5           0.10558673                    0.094612167
6           0.01229288                    0.009991121

All estimated values:
Geometric Distribution
number of individuals captured                     77
parameter q or lambda                           0.283
population size N                              272.07
standard error                                  41.79
lower symmetric 95%-CI                         190.17
upper symmetric 95%-CI                         353.97
lower asymmetric 95%-CI                        205.79
upper asymmetric 95%-CI                        372.45
Truncated Geometric Distribution
number of individuals captured                               77
parameter q or lambda                                    0.2802
population size N                                        274.77
standard error                                            42.57
lower symmetric 95%-CI                                   191.32
upper symmetric 95%-CI                                   358.21
lower asymmetric 95%-CI                                  207.31
upper asymmetric 95%-CI                                  377.15
Poisson Distribution
number of individuals captured                   77
parameter q or lambda                        0.6985
population size N                            153.18
standard error                                 8.58
lower symmetric 95%-CI                       136.36
upper symmetric 95%-CI                       169.99
lower asymmetric 95%-CI                      138.13
upper asymmetric 95%-CI                      171.93
Negative Binomial Distribution
number of individuals captured                             77
parameter q or lambda                                   0.714
population size N                                      149.87
standard error                                           8.44
lower symmetric 95%-CI                                 133.32
upper symmetric 95%-CI                                 166.41
lower asymmetric 95%-CI                                135.11
upper asymmetric 95%-CI                                168.37

If you want to continue with further data, recall freq(c(...)).

FREQ 2013
written by Annegret Grimm :-)
```

FREQ documentation built on May 1, 2019, 8:06 p.m.