Some unknown number of salmon smolts (juvenile salmon) are swimming around in a lake. They will with uniform probability wander into a pen adjoining the lake. The gate can be closed, trapping the smolts and allowing them to be marked. The marks are with PIT tags, so that the number of marked smolts in the pen can be counted in real time. We assume that the total number in the pen can also be counted in real time, so that the applet has a continuously updated Lincoln-Peterson estimate and a refined Lincoln-Peterson estimate.
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Hit Go to get started. While Go is active, the gate can be opened and closed, and the smolts can be marked and counted. Hit Reset to randomly generate a new population of unmarked smolts. Placing the cursor on a curve will reveal a population estimate for a given time. When the gate is closed, the estimates remain constant. How many smolts are in the lake? !!
First notice how the marked smolts must have time to leave the pen and become uniformly mixed in the lake population. An important observation may be how much variation there is in the population estimates. Also, notice how the variation narrows as more and more smolts are marked (hitting marked while the gate is closed will mark all the unmarked smolts in the pen).
This model created by Dr. Jeff Knisley as part of the Symbiosis project module on migratory models in differential calculus. It is one of the simulations located at http://math.etsu.edu/symbiosis/migrations.
globals [ ActualSize Inited TotalFishInPen MarkedFishInPen TotalMarked XX ]
breed [ fishes fish ]
fishes-own [ IsMarked ]
to startup
set Inited false ;
Go
end
to Reset
set Inited false ;
end
to Go
if ( not Inited )
[ ca
ask patches [
ifelse ( pxcor > -11 )
[ set pcolor blue ]
[ if ( pycor > -6 and pycor < 6 )
[ set pcolor blue ]
]
]
if Pop_Size = "Small" [ set ActualSize 120 ]
if Pop_Size = "Medium" [ set ActualSize 420 ]
if Pop_Size = "Large" [ set ActualSize 920 ]
if Pop_Size = "Random" [ set ActualSize 100 + random 900 ];
if Pop_Size = "Keyed"
[ set ActualSize read-from-string user-input "Enter A 5 digit number: "
ifelse(ActualSize > 9999 )
[ set ActualSize ActualSize * 3 mod 995 ]
[ user-message "A Five digit number is required."
stop
]
]
create-fishes ActualSize [
set shape "fish"
set IsMarked false
set color green
rt random 90
lt random 90
setxy ( ( random 30 ) - 10 ) random-ycor
]
set Inited true;
set TotalMarked 0;
set XX 0;
]
ask patches with [ ( ( pxcor = -11 ) and ( pycor < 6 ) and ( pycor > -6 ) ) ]
[
ifelse ( pycor > -6 + OpenGate )
[ set pcolor grey ]
[ set pcolor blue ]
]
move
end
to move
tick
ask fishes [
ifelse ( can-move? 1 and ( ( [ pcolor ] of patch-ahead 1 ) = blue ))
[ fd 1 ]
[ set heading ( heading + 90 * ( random 2 - 1 ) ) ]
rt random 30
lt random 30
]
set MarkedFishInPen count fishes with [ xcor < -11 and IsMarked ]
set TotalFishInPen count fishes with [ xcor < -11 ]
if ( MarkedFishInPen > 0 )
[ update-plot ]
end
to update-plot
set XX ( XX + 1 )
if ( XX > 99 )
[ set XX 0
clear-plot
]
set-current-plot "Fish Population Estimates"
set-current-plot-pen "Lincoln-Petersen"
plotxy XX ( TotalFishInPen * TotalMarked / MarkedFishInPen )
set-current-plot-pen "Chapman's Modification"
plotxy XX ( ( TotalFishInPen + 1 ) * ( TotalMarked + 1 ) / ( MarkedFishInPen + 1 ) - 1 )
end
to mark
ifelse ( OpenGate = 0 ) ; gate is closed
[
let MarkCount 0
ask fishes with [ xcor < -11 and ( not IsMarked )]
[
if ( MarkCount <= ( NumberToMark - 1 ) )
[
set IsMarked true;
set color red ;
set MarkCount ( MarkCount + 1 )
]
]
set TotalMarked count fishes with [ IsMarked ] ;
output-print " "
output-print " "
]
[ output-print "Gate must be"
output-print "closed" ]
end
to unmark
ask fishes [
set IsMarked false
set color green
]
set TotalMarked 0;
end