This model simulates the entirety of an idealized salmon smolt migration. In the Spring of each year, salmon egss hatch in the streams and hatcheries of tributaries of rivers leading to the ocean. These very large populations of salmon grow into a juvenile stage in which they are known as smolts, but any further development will need to occur in the oceans themselves. Thus, nearly simultaneously they begin a migration to the ocean.
Mortality is very high -- even independent of human involvement -- but the migration occurs relatively rapidly. This model simulates the movement of the smolts through zone 1 from the streams and hatcheries where they were spawned, which is represented by zone 0. However, mortality is not incorporated into this model.
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view/download model file: Zone0toZone7(NoMortality).nlogo
The Setup command initializes the system and the plots by creating "Initial-Population" numbers of smolts in zone 0. In this simulation, the initial population consists of thousands of smolts, whereas actual populations often involve millions of them. The Go command starts the random migration out of zone 0, and each smolt randomly moves about zone 0 until it encounters the channel exiting the zone. Once in the channel, it is highly unlikely that the smolt will backtrack into zone0 itself. The degree to which each smolt in zone 0 is controled by the flow of the zone toward the channel can be adjusted using the "Relative-flow-in-lake" slider.
Adjust the Initial-Population, ticks-per-unit-time, and Relative-Flow-In-Lake sliders to desired settings. Press Setup and then Go (press Step for one tick of the model at a time). Press setup and then go. To "smooth out" the measurements of Emigration and the percentage migration rate, the number of ticks per unit time can be varied up to 20 ticks per unit time. There is also a flow in each of the lakes (i.e., the large "boxes" ) toward the channels leading away from the lakes, and the "Relative-Flow-In-Lake" slider adjusts this from no influence at 0 to flow-controlled at 1.
The smolts swim "randomly" as a group regardless of the relative-flow settings. In fact, if the Relative-Flow-In-Lake setting is close to 0, then the probability of a smolt being in "zone j" is approximately Poisson distributed. Thus, at high values of j, the population curves will more and more resemble bell curves -- i.e., normal distributions -- as we see the Central Limit theorem in action here!!
However, as the Relative-Flow-In-Lake parameter is increased, the accuracy of this model decreases as m is not nearly as close to being constant during the migration.
Try varying the Initial-Population. Also, try changing the relative rate of flow of the smolts (relative to the flow of the lake, that is). Changing this slider during the migration also may lead to some interesting results, especially if the initial population is quite large.
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 [ InitPop MaxDist Current-Time Previous-Time AllTime N0P N1P zonewidth m0 Departures-per-tick
Z0P Z1P Z2P Z3P Z4P Z5P Z6P Z7P
]
patches-own [ iswater? inlake? pzone flow-heading flow-strength ] ; flow-strength is 0 to 1, percentage of main-channel flow speed
turtles-own [ zone ]
to setup
clear-all
set Previous-Time 0
set Current-Time 0
set zonewidth 24
setup-patches
CreateSmolts
set Z0P 1
set Z1P 0
set Z2P 0
set Z3P 0
set Z4P 0
set Z5P 0
set Z6P 0
set Z7P 0
set InitPop Initial-Population
set-current-plot "N0(t)"
set-plot-y-range 0 Initial-Population
set-current-plot-pen "N0(t)"
plotxy 0 Initial-Population
set-current-plot "N1(t)"
set-plot-y-range 0 Initial-Population
set-current-plot-pen "N1(t)"
plotxy 0 0
set-current-plot "N2(t)"
set-plot-y-range 0 Initial-Population
set-current-plot-pen "N2(t)"
plotxy 0 0
set-current-plot "N3(t)"
set-plot-y-range 0 Initial-Population
set-current-plot-pen "N3(t)"
plotxy 0 0
set-current-plot "N4(t)"
set-plot-y-range 0 Initial-Population
set-current-plot-pen "N4(t)"
plotxy 0 0
set-current-plot "N5(t)"
set-plot-y-range 0 Initial-Population
set-current-plot-pen "N5(t)"
plotxy 0 0
set-current-plot "N6(t)"
set-plot-y-range 0 Initial-Population
set-current-plot-pen "N6(t)"
plotxy 0 0
set-current-plot "N7(t)"
set-plot-y-range 0 Initial-Population
set-current-plot-pen "N7(t)"
plotxy 0 0
end
to CreateSmolts
set-default-shape turtles "fish"
create-turtles Initial-Population
[
set color green
move-to one-of patches with [ pzone = 0 ]
set heading random 360
set zone 0
]
end
to setup-patches
;set source info and zone transition points
ask patches
[
ifelse ( pxcor > min-pxcor and pycor > -4 and pycor < 4 )
[ set pcolor blue
set iswater? true
set inlake? false
set pzone -1
set flow-heading 90
set flow-strength 1
]
[ set pzone -1
set iswater? false
set inlake? false
]
]
make-compartment min-pxcor ( min-pxcor + zonewidth ) 0
make-compartment ( min-pxcor + zonewidth ) ( min-pxcor + 2 * zonewidth ) 1
make-compartment ( min-pxcor + 2 * zonewidth ) ( min-pxcor + 3 * zonewidth ) 2
make-compartment ( min-pxcor + 3 * zonewidth ) ( min-pxcor + 4 * zonewidth ) 3
make-compartment ( min-pxcor + 4 * zonewidth ) ( min-pxcor + 5 * zonewidth ) 4
make-compartment ( min-pxcor + 5 * zonewidth ) ( min-pxcor + 6 * zonewidth ) 5
make-compartment ( min-pxcor + 6 * zonewidth ) ( min-pxcor + 7 * zonewidth ) 6
make-compartment ( min-pxcor + 7 * zonewidth ) ( min-pxcor + 8 * zonewidth ) 7
end
to make-compartment [ L R zn ]
let U max-pycor
let B min-pycor
set MaxDist sqrt ( ( R - 4 - L ) ^ 2 + U ^ 2 )
ask patches [
if ( pxcor > min-pxcor and pxcor > L and pxcor < ( R - 4 ) and pycor < U and pycor > B )
[ set pcolor blue
set iswater? true
set inlake? true
set pzone zn
set flow-heading towardsxy ( R - 4 ) 0
set flow-strength 1 - sqrt ( ( pxcor - R ) ^ 2 + pycor ^ 2) / MaxDist ]
if ( pxcor <= R and pxcor >= ( R - 4 ) and pxcor <= max-pxcor and pycor > -4 and pycor < 4 )
[ set pcolor blue
set iswater? true
set inlake? false
set pzone -1
set flow-heading 90
set flow-strength 1 ]
]
end
to go
if( not any? turtles ) [ stop ]
ask turtles [
if ( random-float 1 < 1 / ticks-per-unit-time )
[ smoltMove
smoltLearn
]
]
smoltCount
end
to smoltMove
rt random 90
lt random 90
let p [ flow-strength ] of patch-here
if( [ pzone ] of patch-here >= 0 ) [ set p p * Relative-Flow-In-Lake ]
ifelse ( heading < 270 )
[ set heading ( ( 1 - p ) * heading + p * ( [ flow-heading ] of patch-here ) ) ]
[ set heading ( ( 1 - p ) * heading + p * ( [ flow-heading ] of patch-here + 360 ) ) ]
if not ( member? patch-ahead 1 neighbors with [ iswater? ] )
[ set heading towards one-of neighbors with [ iswater? ] ]
fd 1
set zone [pzone] of patch-here
if ( xcor >= max-pxcor )
[ die ]
end
to smoltCount
tick
set Current-time precision ( ticks / ticks-per-unit-time ) 4
set N0P ( count turtles with [ zone = 0 ] )
set Z0P precision ( ( count turtles with [ zone = 0 ] ) / InitPop ) 4
set Z1P precision ( ( count turtles with [ zone = 1 ] ) / InitPop ) 4
set Z2P precision ( ( count turtles with [ zone = 2 ] ) / InitPop ) 4
set Z3P precision ( ( count turtles with [ zone = 3 ] ) / InitPop ) 4
set Z4P precision ( ( count turtles with [ zone = 4 ] ) / InitPop ) 4
set Z5P precision ( ( count turtles with [ zone = 5 ] ) / InitPop ) 4
set Z6P precision ( ( count turtles with [ zone = 6 ] ) / InitPop ) 4
set Z7P precision ( ( count turtles with [ zone = 7 ] ) / InitPop ) 4
if( Current-Time < Previous-Time )
[ clear-all-plots
reset-ticks
set Current-Time 0
]
if( 2 * N0P > InitPop and Current-Time > 0 )
[ set m0 precision ( ln( InitPop / N0P ) / Current-Time ) 4 ]
set-current-plot "N0(t)"
set-current-plot-pen "N0(t)"
plotxy Current-Time count turtles with[ zone = 0 ]
set-current-plot "N1(t)"
set-current-plot-pen "N1(t)"
plotxy Current-Time count turtles with [ zone = 1 ]
set-current-plot "N2(t)"
set-current-plot-pen "N2(t)"
plotxy Current-Time count turtles with [ zone = 2 ]
set-current-plot "N3(t)"
set-current-plot-pen "N3(t)"
plotxy Current-Time count turtles with [ zone = 3 ]
set-current-plot "N4(t)"
set-current-plot-pen "N4(t)"
plotxy Current-Time count turtles with [ zone = 4 ]
set-current-plot "N5(t)"
set-current-plot-pen "N5(t)"
plotxy Current-Time count turtles with [ zone = 5 ]
set-current-plot "N6(t)"
set-current-plot-pen "N6(t)"
plotxy Current-Time count turtles with [ zone = 6 ]
set-current-plot "N7(t)"
set-current-plot-pen "N7(t)"
plotxy Current-Time count turtles with [ zone = 7 ]
set Previous-Time Current-Time
end
to smoltLearn
; Zone number, simple flow concept means no going to earlier zone
end