# abundance: Post-calving method for caribou abundance estimation In caribou: Estimation of caribou abundance based on large scale aggregations monitored by radio telemetry

## Description

The function `abundance` applies the methodology found in Rivest et al. (1998) for estimating caribou abundance using postcalving aggregations detected by radio telemetry.

## Usage

 ```1 2 3 4``` ```abundance(mat, n, model = c("H", "I", "T"), B, maxT.hat) ## S3 method for class 'abundance' print(x,...) ```

## Arguments

 `mat` A matrix containing in the first column the number of radio-collared animals in the detected (photographed) groups and in the second column the corresponding size of the detected groups. `n` A numeric: the total number of active collars during the census. `model` A character string indicating the model to determine the probability that a group with collared animals is detected pi. It can be either "H" = homogeneity model, "I" = independence model or "T" = threshold model (see Details). The default is "H". `B` A numeric: a bound for the threshold model. `maxT.hat` A numeric: an upper bound used in the numerical computation of `T.hat`, the estimator for the total number of animals in a herd (used by the `optimize` function). Useful when a warning is generated about `T.hat` being equal to `maxT.hat`. The default is `n*max(mat[,2])`. `x` An object, produced by the `abundance` function, to print. `...` Further arguments to be passed to methods (see `print.default`).

## Details

DETECTION MODELS

- homogeneity model (`model="H"`):

pi = r if xi>=1

- independence model (`model="I"`):

pi = 1-(r^xi)

- threshold model (`model="T"`):

pi = 1 if xi>=B, r if 1<=xi<B

where pi is the probability that a group with collared animals is detected, xi is the number of radio-collared in the detected (photographed) groups and r is a parameter related to the probability of detection. For the threshold model, `B` is a bound given as a function's argument.

## Value

 `mp ` The number of detected groups having radio-collared animals. `xt ` The total number of radio-collared animals found in the detected groups. `gnt ` The total number of animals counted in the detected groups. `rr ` The estimated parameter related to the probability of detection. `se_rr ` The estimated standard error of `rr`. `mat_pi ` A matrix containing a sorted copy of the input matrix `mat` in the first two columns, the detection probabilities pi in the third column and the probabilities that the group has at least one collared animal pi.i in the last column. `T.hat ` The estimator for the total number of animals in a herd. `se_T.hat ` The estimated standard error of `T.hat`. `loglikelihood ` The maximum value of the loglikelihood function for the detected model. `randomness_test ` A vector with the statistic and the p-value of a score test for the randomness assumption available only for the homogeneity, independence and threshold model with B=2 or 3. `call ` The function call (object of class "call").

## Author(s)

Helene Crepeau [email protected] and
Louis-Paul Rivest [email protected] and
Serge Couturier [email protected] and
Sophie Baillargeon [email protected]

## References

Rivest, L.-P., Couturier, S. and Crepeau, H. (1998). Statistical Methods for estimating caribou abundance using postcalving aggregations detected by radio telemetry. Biometrics, 54(3), 865-876.

`petersen`
 ```1 2 3 4 5 6 7``` ```data(GRH93) abundance(GRH93, n=92) # default model="H" abundance(GRH93, n=92, model="H") abundance(GRH93, n=92, model="I") abundance(GRH93, n=92, model="T", B=2) abundance(GRH93, n=92, model="T", B=4) abundance(GRH93, n=92, model="T", B=6) ```