Software for Babine Lake Smolt Mark-Recapture Analysis

Author

Peter D.M. Macdonald, D.Phil.
 
Department of Mathematics and Statistics
McMaster University
1280 Main Street West
Hamilton, Ontario L8S 4K1
 
Voice: +1 (905) 525-9140 x 23423
Fax: +1 (905) 522-0935
Internet: pdmmac@mcmaster.ca
 
5235 Trinity Church Road
RR2
Binbrook, Ontario L0R 1C0
 
Voice: +1 (905) 679-9956

Version and Date

Version 1.6: 1999-01-22.

Computer Requirements

Windows 95, Windows 98 or Macintosh.

Installation

Macintosh

Make a folder for your smolt work and copy the application smolt_analysis into that folder. If your monitor is set for "millions of colours" or "thousands of colours", it may be necessary to increase the "Preferred" memory setting for the application.

Windows

Make a folder for your smolt work and copy the application Smolt_Analysis.exe and the DLLs TB510.DLL, XNMBA420.DLL and XNMTE420.DLL into that folder. If you prefer, the DLLs can be put into the folder C:\WINDOWS\SYSTEM\ instead of the working folder.

Summary

The program interprets Babine smolt mark-recapture data in terms of two different models. It computes daily estimates of the run size with confidence bounds, and estimates the early run, late run and seasonal total with standard errors. The date when the late run starts may be estimated. The results are tabulated and graphed.

Models Fitted

Constant Sampling Fraction (CSF)

This is the original DFO analysis, but the numbers will differ from the original analyses because the DFO software rounded all numbers to integers. This analysis was discussed in Macdonald & Smith (1980). It is valid if the same fraction of the run is sampled every day.

Parsimonious Model (PAR)

Macdonald & Smith (1980) introduced a parametric model which assumed that the behaviour of marked smolts was independent of the day of release. This was later extended in unpublished work to allow for different behaviour from "early run" and "late run" smolts. Early run smolts come from the North Arm and Nilkitkwa Lake and late run smolts come from the main lake basin and for the most part originate in the artificial spawning channels there. Confidence intervals for the daily run sizes based on the Poisson distribution were also tried and gave better results than previous methods when the number of recaptures is small.

Negative Binomial Estimates

Recent unpublished work by the author uses the negative binomial distribution as a generalisation of the Poisson distribution, to get more satisfactory bounds on the daily run sizes when the number of recaptures is small and the number of marks in the run is subject to error. This work is described in the seminar notes "Mark-recapture estimation with small numbers of recaptures and an uncertain number of marks."

The Data

The program accepts the following data for each day:

  • The number of smolts caught and inspected for marks;
  • The number of marked smolts released that day;
  • The number from that release group recaptured the same day, after 1 day, etc., up to r days after release, where r+1 is the number of days in the tag code cycle. It is assumed that very few marked fish will re-migrate more than r days after their release; those that do will be incorrectly classified if they are recaptured.

Typically, the fish will be caught and selected for marking on one day and released the next day, during the day. Some will be caught in the sampling the following night, hence the "same-day" recaptures.

The "first day of sampling" should be the first day that marked smolts are released.

Data can be entered through the program and saved to a file, or can be entered into a file with any text editor. It is convenient to enter data through the program.

Data File Format

Data files prepared with a text editor must have the following format. Numbers can be separated by blanks or commas. See the 1994 and 1984 data files for examples.

File Names

For the year 1984, e.g., suggested names are bs_1984.dat for data and bs_1984.out for the output file recording the session.

Running the Software

Launch the Smolt_Analysis application by double-clicking on its icon. To quit the application, answer "n" at the prompt "Run an analysis (y/n) ?". On Macintosh, you can enter command-. at any time to quit..

When the program launches, you can follow the prompts to open a data file or enter new data from the keyboard.

Steps in the Analysis

  1. Load data from a file, or enter data from the keyboard and save it to a file.
  2. Name an output file for the session output.
  3. The program fits the CSF run estimates and plots them.
  4. Inspect the plot of the CSF run estimates and try to estimate the "Transition Date" visually. The "Transition Date" is the first day of release for which released smolts show late-run behaviour. If they were captured the day before, what we are calling the "Transition Date" will actually be the day after the late run started. Pressing the space bar will bring up a prompt to save the graph, then return you to the session window. The suggested file name is bsXXcsf.bmp (Windows) or bsXXcsf.pic (Macintosh), where XX is the year.
  5. Enter upper and lower bounds for the Transition Date.The program will fit CSF and PAR models over this range of dates and pick the date for which PAR fits best. To force a pre-determined Transition Date, make the upper and lower bounds the same. The Transition Date can be set to be the first day of the run, in which case only the late run parameters will be fitted: the early run probabilities will be set equal to each other but will not be used in any calculations.
  6. For each date tried, and for both models, the program will compute the "run probabilities;" these are the probabilities that a marked fish will leave the lake after 0,1,...,r days, respectively. The PAR estimates are given with standard errors. Estimates will be computed for the size of the early run, late run and total run. The PAR estimates are given with standard errors.
  7. If the range of possible Transition Dates covers more than one day, a graph is plotted showing chi-square goodness-of-fit values versus day, to indicate how well-defined the optimum (smallest chi-square) is. Pressing the space bar will bring up a prompt to save the graph, then return you to the session window. The suggested file name is bsXXchi.bmp (Windows) or bsXXchi.pic (Macintosh), where XX is the year. You can accept this Transition Date or you can specify another range of dates and try the search again.
  8. When you accept a Transition Date, the parameter estimates are displayed graphically as "intensity of leaving;" this plot accentuates the differences between the early and late run behaviour and can help to determine if the chosen Transition Date is reasonable. Pressing the space bar will bring up a prompt to save the graph, then return you to the session window. The suggested file name is bsXXprb.bmp (Windows) or bsXXprb.pic (Macintosh), where XX is the year.
  9. For the best-fitting transition date, the daily run estimates are computed with 95% confidence bounds, using the negative binomial calculations and the fitted PAR model, and displayed on a graph together with the CFS estimates. Pressing the space bar will bring up a prompt to save the graph, then return you to the session window. The suggested file name is bsXXrun.bmp (Windows) or bsXXrun.pic (Macintosh), where XX is the year.

Examples

See an analysis of the 1994 Babine smolt run data, with the Transition Date fitted by the software. The input data file is bs_1994.dat.

See also an analysis of the 1984 Babine smolt run data, as a single run. This is done by choosing a Transition Date before the start of sampling. The input data file is bs_1984.dat.

Reference

Macdonald, P.D.M. & Smith, H.D. (1980), Biometrics 36, 401-417.

1999-01-23