data_btspas_diag1 {Petersen}

Estimating abundance of outgoing smolt - BTSPAS - diagonal case

Description

This is the first diagonal case dataset from BTSPAS.

Usage

data(data_btspas_diag1)

Format

data_btspas_diag1

A data frame with many rows and 3 columns

cap_hist.

Capture history of the form ‘jweek..jweek’ for fish that are recaptured in the same julian week; '0..jweek' for unmarked fish newly captured in that julian week ; 'jweek..0' for fish released in the julian week but never recaptured.

freq.

Number of fish with this history.

logflow

log(flow) for this julian week

Details

Consider an experiment to estimate the number of outgoing smolts on a small river. The run of smolts extends over several weeks. As smolts migrate, they are captured and marked with individually numbered tags and released at the first capture location using, for example, a fishwheel. The migration continues, and a second fishwheel takes a second sample several kilometers down stream. At the second fishwheel, the captures consist of a mixture of marked (from the first fishwheel) and unmarked fish.

The efficiency of the fishwheels varies over time in response to stream flow, run size passing the wheel and other uncontrollable events. So it is unlikely that the capture probabilities are equal over time at either location, i.e. are heterogeneous over time.

We suppose that we can temporally stratify the data into, for example, weeks, where the capture-probabilities are (mostly) homogeneous at each wheel in each week. Furthermore, suppose that fish captured and marked in each week tend to migrate together so that they are captured in a single subsequent stratum. For example, suppose that in each julian week j, n1_j fish are marked and released above the rotary screw trap. Of these, m2_j are recaptured. All recaptures take place in the week of release, i.e. the matrix of releases and recoveries is diagonal. The n1_j and m2_j establish the capture efficiency of the second trap in julian week j.

At the same time, u2_j unmarked fish are captured at the screw trap.

Capture-efficiency may be related to flow, so the log(flow) is also recorded.