abundance {caribou}

Post-calving method for caribou abundance estimation

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

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 p_i. 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"):

p_i = r \mbox{ if } X_i \geq 1

- independence model (model="I"):

p_i = 1-(r^{X_i})

- threshold model (model="T"):

p_i = \left\{ \begin{array}{ll} 1 & \mbox{if } X_i \geq \mbox{\code{B}} \\ r & \mbox{if } 1 \leq X_i < \mbox{\code{B}} \end{array} \right.

where p_i is the probability that a group with collared animals is detected, X_i 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 p_i 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)

Louis-Paul Rivest [e-mail] and
Helene Crepeau [e-mail] and
Serge Couturier [e-mail] and
Sophie Baillargeon [e-mail]

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.

See Also

petersen

Examples

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)