# IQWST foxes and rabbits model

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## WHAT IS IT?

This model explores the stability of predator-prey ecosystems.

Foxes and rabbits wander randomly around the landscape. Each step costs both animals energy and they must consume a food source (rabbits must eat grass and foxes must eat rabbits) to replenish their energy - when they run out of energy they die. To allow the population to continue, each fox or rabbit must have enough energy to have a litter of offspring and the offspring and parent split the energy amongst themselves. Grass grows at a fixed rate, and when it is eaten, a fixed amount of grass energy is deducted from the patch (square) where the grass was eaten.

Different starting conditions for number of each species, amount of grass, maximum age of each species, number of offspring in a litter will lead to stable or unstable systems, depending on these values.

## SETTING UP

- Adjust the slider parameters (see below), or use the default settings.
- Press the SETUP button.
- Press the GO button to begin the simulation.
- View the POPULATIONS plot to watch the populations fluctuate over time
- View the rabbits/foxes monitors to view current population sizes.

Initial Settings:

PERCENT-GRASS: The percentage of patches in the world & view that produce grass

INITIAL-NUMBER-RABBITS: The initial size of rabbit population

INITIAL-NUMBER-FOXES: The initial size of snake population

Notes:

- one unit of energy is deducted for every step a fox or rabbit. In a step, each of these animals moves a different fraction of a patch (square).

## THINGS TO NOTICE

Watch as the fox and rabbit populations fluctuate. Notice that increases and decreases in the sizes of each population are related. In what way are they related?

Why do you suppose that some variations of the model might be stable while others are not?

When the model is run with rabbit and grass, but no foxes, the rabbit population only fluctuates a little bit, and does not show the large increases and decreases it did when foxes were included. What causes this behavior?

## THINGS TO TRY

Try adjusting the parameters under various settings. How sensitive is the stability of the model to the particular parameters?

## RELATED MODELS

Look at Wolf-Sheep and Rabbit Grass Weeds for other models of interacting populations with different rules.

NetLogo Wolf Sheep Predation model. http://ccl.northwestern.edu/netlogo/models/WolfSheepPredation. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

## Comments and Questions

globals [ time foxes-color rabbits-color grass-color dirt-color invasive-color rabbits-stride ;; how much a rabbi moves in each simulation step invaders-stride ;; how much an invader moves in each simulation step foxes-stride ;; how much a fox moves in each simulation step fox-size rabbit-reproduce-age invader-reproduce-age fox-reproduce-age rabbits-energy-gain-from-food foxes-energy-gain-from-rabbits foxes-energy-gain-from-invaders max-plant-energy max-rabbits-age ;; grass-delay min-reproduce-energy-rabbits ;; energy required for reproduction min-reproduce-energy-invaders ;; energy required for reproduction min-reproduce-energy-foxes ;; energy required for reproduction invaded? max-foxes-age max-invaders-age max-rabbits-offspring max-foxes-offspring max-invaders-offspring ] breed [ rabbits rabbit] breed [ invaders invader] breed [ foxes fox] turtles-own [ energy current-age max-age female?] patches-own [ fertile? plant-energy ] to setup ;; (for this model to work with NetLogo's new plotting features, ;; __clear-all-and-reset-ticks should be replaced with clear-all at ;; the beginning of your setup procedure and reset-ticks at the end ;; of the procedure.) clear-all set time 0 set invaded? false set max-plant-energy 100 set rabbits-stride 0.3 set invaders-stride 0.3 set foxes-stride 0.4 ;; a larger foxes-stride than rabbits-stride leads to scenarios where less foxes ;; can keep a larger number of rabbitss in balance. set rabbit-reproduce-age 20 set invader-reproduce-age 20 set fox-reproduce-age 40 set max-foxes-age 100 set max-invaders-age 100 set max-rabbits-age 100 set rabbits-energy-gain-from-food 4 set foxes-energy-gain-from-rabbits 25 set foxes-energy-gain-from-invaders 25 set min-reproduce-energy-rabbits 10 set min-reproduce-energy-invaders 10 set min-reproduce-energy-foxes 10 set max-rabbits-offspring 3 set max-invaders-offspring 3 set max-foxes-offspring 2 set fox-size 1 set foxes-color (red - 1) set rabbits-color (gray - 1) set invasive-color (blue - 3) set grass-color (green) set dirt-color (white) set-default-shape rabbits "rabbit" set-default-shape foxes "fox" set-default-shape invaders "mouse" add-starting-grass add-rabbits add-foxes do-plots reset-ticks end to go if time >= 2500 [stop] ask rabbits [ rabbits-live reproduce-rabbits] ask foxes [ foxes-live reproduce-foxes] ask patches [grow-grass] ;;only the fertile patches can grow grass do-plots ;; plot populations set time time + 1 end to add-starting-grass ask patches [ ifelse random 100 < percent-grass ;;student sets the maximum number of fertile patches [ set fertile? true set plant-energy (max-plant-energy - random max-plant-energy) ] [ set fertile? false set plant-energy 0 ] color-grass ] end to add-rabbits create-rabbits initial-number-rabbits ;; create the rabbits, then initialize their variables [ set color rabbits-color set energy 20 + random 20 - random 20;;randomize starting energies set current-age 0 + random max-rabbits-age ;;don't start out with everyone at the same age set max-age max-rabbits-age setxy random world-width random world-height ;;ifelse (random 2 = 0) [set female? true] [set female? false] ] end to add-foxes create-foxes initial-number-foxes ;; create the rabbits, then initialize their variables [ set color foxes-color set energy 40 + random 40 - random 40 ;;randomize starting energies set current-age 0 + random max-foxes-age ;;don't start out with everyone at the same age set max-age max-foxes-age set size fox-size setxy random world-width random world-height ;; ifelse (random 2 = 0) [set female? true] [set female? false] ] end to rabbits-live move-rabbits set energy energy - 1 ;; rabbitss lose energy as they move set current-age current-age + 1 rabbits-eat-grass death end to foxes-live move-foxes set energy energy - 1 ;; foxes lose energy as they move set current-age current-age + 1 eat-prey death end to move-rabbits ;; turtle procedure rt random 50 - random 50 fd rabbits-stride end to move-invaders ;; turtle procedure rt random 40 - random 40 fd invaders-stride end to move-foxes ;; turtle procedure rt random 50 - random 50 fd foxes-stride end to rabbits-eat-grass ;; rabbits procedure ;; if there is enough grass to eat at this patch, the rabbits eat it ;; and then gain energy from it. if plant-energy > rabbits-energy-gain-from-food [ ;; plants lose ten times as much energy as the rabbits gains (trophic level assumption) set plant-energy (plant-energy - (rabbits-energy-gain-from-food * 10)) set energy energy + rabbits-energy-gain-from-food ;; rabbits gain energy by eating ] ;; if plant-energy is negative, make it positive if plant-energy <= rabbits-energy-gain-from-food [set plant-energy 0] end to eat-prey ;; foxes procedure if (any? rabbits-here and not any? invaders-here) [ask one-of rabbits-here [die] set energy (energy + foxes-energy-gain-from-rabbits) ] if (any? invaders-here and not any? rabbits-here) [ask one-of invaders-here [die] set energy (energy + foxes-energy-gain-from-invaders) ] if (any? invaders-here and any? rabbits-here) [ifelse random 2 = 0 ;; 50/50 chance to eat an invader or a rabbit if both are on this patch [ask one-of invaders-here [die] set energy (energy + foxes-energy-gain-from-invaders)] [ask one-of rabbits-here [die] set energy (energy + foxes-energy-gain-from-rabbits)] ] end to reproduce-rabbits ;; rabbits procedure let number-offspring (random (max-rabbits-offspring + 1)) ;; set number of potential offpsring from 1 to (max-rabbits-offspring) if (energy > ((number-offspring + 1) * min-reproduce-energy-rabbits) and current-age > rabbit-reproduce-age) [ if random 2 = 1 ;;only half of the fertile rabbitss reproduce (gender) [ set energy (energy - (number-offspring * min-reproduce-energy-invaders)) ;;loose energy when reproducing --- given to children hatch number-offspring [ set size 1 set color rabbits-color set energy min-reproduce-energy-rabbits ;; split remaining half of energy amongst litter set current-age 0 ;; ifelse (random 2 = 0) [set female? true] [set female? false] rt random 360 fd rabbits-stride ] ;; hatch an offspring set it heading off in a a random direction and move it forward a step ] ] end to reproduce-invaders ;; rabbits procedure let number-offspring (random (max-invaders-offspring + 1)) ;; set number of potential offpsring from 1 to (max-invaders-offspring) if (energy > ((number-offspring + 1) * min-reproduce-energy-invaders) and current-age > invader-reproduce-age) [ if random 2 = 1 ;;only half of the fertile invaders reproduce (gender) [ set energy (energy - ( number-offspring * min-reproduce-energy-invaders)) ;;loose energy when reproducing --- given to children hatch number-offspring [ set size 1 set color invasive-color set energy min-reproduce-energy-invaders ;; split remaining half of energy amongst litter set current-age 0 ;; ifelse (random 2 = 0) [set female? true] [set female? false] rt random 360 fd invaders-stride ] ;; hatch an offspring set it heading off in a a random direction and move it forward a step ] ] end to reproduce-foxes ;; rabbits procedure let number-offspring (random (max-foxes-offspring + 1)) ;; set number of potential offpsring from 1 to (max-invaders-offspring) if (energy > ((number-offspring + 1) * min-reproduce-energy-foxes) and current-age > fox-reproduce-age) [ if random 2 = 1 ;;only half of the fertile rabbitss reproduce (gender) [ set energy (energy - (number-offspring * min-reproduce-energy-foxes)) ;;loose energy when reproducing --- given to children hatch number-offspring [ ;;set breed eggs set current-age 0 set size fox-size set color foxes-color set energy min-reproduce-energy-foxes ;; split remaining half of energy amongst litter set current-age 0 ;; ifelse (random 2 = 0) [set female? true] [set female? false] rt random 360 fd foxes-stride ] ;; hatch an offspring set it heading off in a a random direction and move it forward a step ] ] end to death ;; turtle procedure ;; die when energy dips below zero (starvation), or get too old if (current-age > max-age) or (energy < 0) [ die ] end to grow-grass ;; patch procedure ;; fertile patches gain 1 energy unit per turn, up to a maximum max-plant-energy threshold if fertile? [set plant-energy (plant-energy + 1) if plant-energy > max-plant-energy [set plant-energy max-plant-energy]] if not fertile? [set plant-energy 0] if plant-energy < 0 [set plant-energy 0] color-grass end to color-grass ifelse fertile? [ ifelse plant-energy > 0 ;; scale color of patch from whitish green for low energy (less foliage) to green - high energy (lots of foliage) [set pcolor (scale-color green plant-energy (max-plant-energy * 2) 0)] [set pcolor dirt-color] ] [set pcolor dirt-color] end to do-plots set-current-plot "populations" set-current-plot-pen "rabbits" plot count rabbits ;; set-current-plot-pen "invaders" ;; plot count invaders set-current-plot-pen "foxes" plot count foxes set-current-plot-pen "grass" plot (sum [plant-energy] of patches / max-plant-energy) end

There is only one version of this model, created about 6 years ago by Michael Novak.

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