globals [ syncindex sumsin sumcos ] turtles-own [ adjacents ; number cells in radius that are red period ; each agent's free-running period, set under setup phase ; phase within each firefly's free-running period (0-360) isee nadir ; tick count at which last nadir occurred for each agent counter ; the realised period of each agent as influenced by others interval ; for reporting to plot advance or delay synch for the individuals: +ve if period> 144 (phase delaying), -ve if < 144 (phase advancing) newnadir ; tick count for reporting the slope oldnadir; tick count for reporting the slope slope syncindex-reporter ] to setup clear-all If hundred_randoms? [ create-turtles 100 [ setxy random-xcor random-ycor] set number 100 ask turtles [set phase random 360 set period 24 set shape "dot" set size 2 recolor] ] If hundred_in_grid? [ create-turtles 100 set number 100 ask turtles [let row (floor (who / 10)) let col (who mod 10) setxy (-27 + col * 6) (-27 + row * 6) set phase random 360 set period 24; set period random-normal 24.5 .5; (tasmaniensis mean and SD is 24.5 .5) set shape "dot" set size 2 recolor] ] If layout4_on_a_square?; because there are 4 agents, this command specifies distribution on vertices of a square [ create-turtles 4 set number 4 layout-circle sort turtles 7; places all turtles around a circle with radius 7 ask turtle 0 [set phase 0] ask turtle 1 [set phase 90] ask turtle 2 [set phase 180] ask turtle 3 [set phase 270] ask turtles [ set period 24 ;set period 24.5 ;set period random-normal 24.5 .5; (tasmaniensis mean and SD) set shape "dot" set size 2 recolor ] ] If layout_number_in_circle [ create-turtles number layout-circle sort turtles 7; places all turtles around a circle with radius 7 ask turtles [ set phase random 360 set period 24 set shape "dot" set size 2 recolor ] ] If specify_number_of_randoms [ create-turtles number [ setxy random-xcor random-ycor] ask turtles [ set period 24 ;set period random-normal 24.5 .5; (tasmaniensis mean and SD) set phase random 360 set size 2 set shape "dot" recolor ] ] reset-ticks end to go ask turtles [ look If isee = 1 [decide] increment-phase report-nadir if ticks mod 144 = 0 [osziphase] recolor ] if ticks mod 144 = 0 ;Once a day calculates synchronisation index derived from Goel und Ermentrout Physica D 2002 "Synchrony, stability, and firing patterns“ [ set syncindex sqrt ( ( sumsin / number ) ^ 2 + ( sumcos / number ) ^ 2 ) set sumcos 0 set sumsin 0 ] if stop_at_x_ticks [if ticks = StopTicks - 1 [print ""] ; this is only used when printing a nadir list if ticks >= StopTicks [stop] ]; stops the run after a set number of ticks if stop_at_set_SI [if syncindex >= SIsetting [ stop ]]; stops the run when all agents are synchronised tick end to recolor ; turtle procedure colours the turtles according to their phase set color (( cos (phase) ) * 5) + 85 end to increment-phase ; turtle procedure to increment phase 10 minutes (2.5 degrees) at a time so that there is normally 144 increments per day. The precise increment is adjusted for FRP set phase (phase + 2.5 * 24 / period) if phase >= 360 [ set phase (phase - 360)] if phase < 0 [set phase (phase + 360)] end to look ; turtle procedure asking how many agents within a set radius are at or near their peak (phase >356 degrees) set adjacents max [phase] of other turtles in-radius visual-radius; finds the max phase value of the set of turtles within the specified radius Ifelse adjacents > 357 [set isee 1] [set isee 0] ;ifelse ticks mod 144 = 36 [set isee 1] [set isee 0]; to provide single forcing pulse every 24 h, annul the 2 foregoing statements and replace with this ;ifelse remainder ticks 144 < 72 [ set isee 1] [set isee 0]; to register daylight for 12 of every 24 h, annul the 3 foregoing statements and replace with this end to decide; turtle procedure deciding direction and degree of phase shift (hrs converted to degrees) if "isee" criteria met: sinusoidal curve fit in R set phase (phase + ( ( (-17.597 - 29.233 * SIN (phase + horizontal-shifter) + 21.397 * COS (phase + horizontal-shifter) - 7.254 * SIN ((phase + horizontal-shifter) * 2) + 8.711 * COS ((phase + horizontal-shifter) * 2)) + vertical-shifter) * modifier)); tasmaniensis' PRC ;set phase (phase + (((-0.000020166873981 * (phase + horizontal-shifter) ^ 3 + 0.013002660989270 * (phase + horizontal-shifter) ^ 2 - 3.026077821383480 * (phase + horizontal-shifter) + 232.501180575072000) + vertical-shifter) * modifier)); flava's PRC end to report-nadir if phase > 178.75 and phase < 181.25 ; the nadir is at phase 180 degrees. Use this window to accommodate the 2.5 degree increment [ set nadir ( ticks ) if ticks - counter < 20 [ set interval (nadir) set counter (counter - 144) ]; this eliminates the rare cases where an agent registers nadir then registers again because the decide process has shifted its phase back into the detector window set interval (ticks - counter) ; the interval is the duration of one cycle, it is 144 if cycle is 24 h; it is unaffected by phase-shifts If interval < 0 [ set interval (interval + 144)] ; corrects to stop interval going below zero If interval > 120 [ set interval (interval - 144)] ; corrects ongoing phase-delay to keep plot "period of 4 agents" within a single day on y-axis set counter (counter + 144) ;calculate slope set newnadir (ticks) set slope ((newnadir - oldnadir) / 144 * 24) set oldnadir (newnadir) ] end to osziphase set sumsin sumsin + (sin( phase )) set sumcos sumcos + (cos( phase )) end @#$#@#$#@ GRAPHICS-WINDOW 305 10 708 434 30 30 6.443 1 10 1 1 1 0 1 1 1 -30 30 -30 30 1 1 1 ticks 30.0 SLIDER 50 240 255 273 number number 0 200 100 1 1 NIL HORIZONTAL BUTTON 50 480 138 513 setup setup NIL 1 T OBSERVER NIL NIL NIL NIL 1 BUTTON 160 480 245 513 go go T 1 T OBSERVER NIL NIL NIL NIL 0 PLOT 725 255 1002 430 peaking agents NIL NIL 0.0 10.0 0.0 10.0 true false "set-plot-y-range 0 number" "" PENS "pen-1" 0.00694444444 0 -2674135 true "" "plot count turtles with [color > 89 ]" SLIDER 45 925 445 958 visual-radius visual-radius 0 20 18 1 1 NIL HORIZONTAL SLIDER 45 885 445 918 modifier modifier 0 1 0.15 .01 1 NIL HORIZONTAL PLOT 300 665 1000 870 glowworm 1 NIL NIL 0.0 25.0 0.0 2.5 true false "" "" PENS "default" 1.0 1 -16777216 true "" "plot [isee] of turtle 1" "pen-1" 1.0 0 -5298144 true "" "plot [ ( cos phase ) + 1 ] of turtle 1\nif ticks > 1000\n[ \nset-plot-x-range (ticks - 1000) ticks \n]" PLOT 300 455 1000 650 glowworm 0 NIL NIL 0.0 25.0 0.0 2.5 true false "" "" PENS "default" 1.0 1 -16777216 true "" "plot [isee] of turtle 0" "pen-2" 1.0 0 -2674135 true "" "plot [ ( cos phase ) + 1 ] of turtle 0\nif ticks > 1000\n[ \nset-plot-x-range (ticks - 1000) ticks \n]" PLOT 10 665 285 870 time of day of nadir of turtles 0 – 3 NIL NIL 0.0 10.0 -20.0 144.0 true false "" "" PENS "default" 1.0 2 -12440034 true "" "if ticks mod 144 = 0 [ plot [ interval ] of turtle 0]" "pen-1" 1.0 2 -11221820 true "" "if ticks mod 144 = 0 [ plot [ interval ] of turtle 1]" "pen-2" 1.0 2 -5825686 true "" "if ticks mod 144 = 0 [ plot [ interval ] of turtle 2]" "pen-3" 1.0 2 -955883 true "" "if ticks mod 144 = 0 [ plot [ interval ] of turtle 3]" PLOT 720 10 1000 230 Synchronization Index NIL NIL 0.0 10.0 0.0 1.0 true false "" "" PENS "default" 1.0 0 -16777216 true "" "if ticks mod 144 = 0 [ plot syncindex ]" MONITOR 890 145 980 190 SyncIndex precision syncindex 3 17 1 11 MONITOR 100 545 190 590 NIL ticks 17 1 11 SWITCH 50 20 255 53 layout4_on_a_square? layout4_on_a_square? 1 1 -1000 SWITCH 50 105 255 138 hundred_randoms? hundred_randoms? 1 1 -1000 SWITCH 50 63 255 96 hundred_in_grid? hundred_in_grid? 0 1 -1000 SWITCH 50 195 256 228 specify_number_of_randoms specify_number_of_randoms 1 1 -1000 SWITCH 50 150 255 183 layout_number_in_circle layout_number_in_circle 1 1 -1000 SLIDER 475 885 950 918 horizontal-shifter horizontal-shifter -180 180 0 1 1 degrees HORIZONTAL SLIDER 475 925 950 958 vertical-shifter vertical-shifter -180 180 0 1 1 degrees shift HORIZONTAL SWITCH 85 285 220 318 stop_at_x_ticks stop_at_x_ticks 0 1 -1000 SLIDER 52 326 256 359 StopTicks StopTicks 1000 20000 7200 1 1 NIL HORIZONTAL SLIDER 51 413 252 446 SIsetting SIsetting 0 1 0.99 .01 1 NIL HORIZONTAL SWITCH 73 368 243 401 stop_at_set_SI stop_at_set_SI 1 1 -1000 MONITOR 100 605 190 650 sync slope (h) [ slope ] of turtle 1 2 1 11 @#$#@#$#@ ## WHAT IS IT? This model simulates the interactions of a population of glowworms in a cave where there is no light other than that from other glowworms. The interactions between them cause them to either advance or delay the phase of their daily bioluminescence cycle until they synchronize. The phase-change is based on a phase-response curve derived from laboratory experiments in which individuals were exposed to a 3-h pulse of light under free-running conditions. Another species of glowworm does not have any known cave populations, instead, they are found in moist, dark forest where they are exposed to the light:dark cycles. ## HOW IT WORKS Once the procedure starts, each glowworm looks around and if a glowworm within its visible field is at or near its peak (358-360 degrees) then isee returns a value of 1. If isee is 1 then a decision is made about whether to advance, delay or stay the same. The degree of phase adjustment is decided by the equation that takes into account the amplitude-modifier value, the vertical-shifter value and the phase-shift value. The PRC equation for Arachnocampa tasmaniensis is derived from a sine fit to the data; the equation for Arachnocampa flava is derived from a 3rd order polynomial fit to the data. ## HOW TO USE IT GO: starts and stops the simulation. SETUP: resets the simulation according to the parameters set by the switches and sliders. RADIUS: sets the visual radius of individuals. MODIFIER: sets the degree of attenuation or amplification of the standard PRC that the glowworms’ apply to their own phase. If the value is low the degree of phase-advance or delay is low and vice versa. A setting of 0.05 is a recommended starting point. Values exceeding … result in faster sync but do so erratically. The next 4 switches allow you to set up different numbers of individual glowworms and arranged in different ways. LAYOUT_4_on_A_SQUARE?: sets up 4 larvae arranged in a square formation. The code sets the phases of the 4 individuals to 90, 180, 270, 360. HUNDRED_IN_A_GRID?: sets up one hundred individuals across the world in a grid pattern. The default code sets their starting phase randomly between 0 and 360 degrees (where 0 degrees is the peak (or acrophase) of each glowworm’s daily bioluminescence cycle. The default setting gives each glowworm a period of 24 h but this can be changed in code (a line of code that gives each larva a randomly chosen period within a specified range is grayed out or by default inactivated). HUNDRED_RANDOMS?: sets up 100 larvae distributed randomly across the world. Each is allocated a random starting phase between 0 and 360. LAYOUT_NUMBER_IN_CIRCLE: sets up a number specified in the number slider that sits below these switches. SPECIFY_NUMBER_OF_RANDOMS: this slider sets up the number specified in the number slider distributed randomly across the world. Each is allocated a random starting phase between 0 and 360. A number of plots are used to display the progress to synchronization. SYNCHRONIZATION INDEX: This value is calculated day-by-day. When maximally unsynchronized the value is 0 and when synchronized the value is 1.. PEAKING AGENTS: This is an alternative way to track synchronization. It is a plot of the number of agents that are at their peak (i.e. a phase of 0 degrees) at each tick. GLOWWORM0 and GLOWWORM1: allows the viewer to see the effect of phase adjustments on these two representative glowworms’ phase. The daily cycle is shown in the form of a sine wave where the upswing crossing of the zero line represents when each glowworm is at its acrophase. The smaller black bars indicate when a glowworm has seen another glowworm within its visual radius at its peak. TIME OF DAY OF NADIR OF TURTLES 0 – 3: This plot displays the time of day in degrees at which these representative glowworms are at their nadir (180 degrees). The purpose is to show the day-to-day trend in the period, especially when synchronized. An upward slope tells the viewer that the glowworms have a period > 24 h and a downward line shows a period < 24h. It is for display only: sometimes it does not display correctly. STOP_AT_X_SI: when switch is on, a run will stop when the synchronization Index reaches a set value, displayed live alongside. STOP_AT_SET_TICKS: when switch is on, a run will stop at the set number of ticks, displayed live alongside. MODIFIER: this value determines how much change is made at each refrence to the phase-response curve. Higher values cause rapid but ragged synchronization. Low values slow down synchronization. VERTICAL_SHIFTER: shifts the phase-response curve along the y-axis HORIZONTAL_SHIFTER: shifts the phase-response curve along the x-axis VIDSUAL-RADIUS: determines the radius of vision of each agent. If too small, agents can't see others at all and the run is terminated. ## THINGS TO NOTICE First, clusters become synchronized and then the whole field locks into sync. ## THINGS TO TRY To follow the process outlined in the results section of the publication, set the radius to 18 and amplitude-modifier to 0.2, then turn on the switch "layout_4_in_a_square?". Make sure the other switches are in the off position. The code sets the phases of the 4 individuals to 90, 180, 270, 360. Turn off the "stop at x ticks" button and the "stop at set SI" button so that you can see the ongoing synchronization. Now hit the “go” button. Watching the color display, you will see the 4 glowworms gradually synchronize. The plots on the dashboard show this process: the SI will gradually climb to 1, the number of peaking agents will climb to the maximum of 4, the sine-wave displays will show two of the glowworms gradually coming into phase with each other. The “time of day of nadir” plot will show their relative advance and delay and their synchronisation. If you want you can change the code; for example, Figure 4 of the paper shows the process of sync when 3 agents are set on 0 and the phase of the 4th agent is varied. Change the “set phase” values of turtles 0, 1, 2 to, say, 0 degrees and and vary the phase of turtle 3 (note: radius has to be set to at least 10 to allow them to see each other) Try changing the amplitude-modifier value: low values slow up the process of synchronization but do it smoothly when you observe the sine-wave representation. High values speed it up but do it in a ragged manner with large advances and delays producing abnormally-distorted curves. Try setting up a non-24 h FRP. To do this first decide your start-up conditions.Go into teh code and inactivate the set period 24 command and instead acvate the set period random-normal 24.5 .5; (tasmaniensis mean and SD is 24.5 .5). The agents now have different starting periods. Try turning on the "100 in a grid" button (making sure the other startup buttons are off). You can see clusters of glowworms coming into synchronization. Try creating conditions where glowworms are on the cusp of being able to synchronize and see if you can create runs where rolling patterns emerge. We recommend 100 in grid (make sure the other switches are in the off position), set radius to 8 (a low value slows down sync). Under these conditions, some runs show sweeping bands or swirling patterns among the glowworms due to the individuals having a restricted visual capability; thay can’t see very far so they are restricted to reacting to only the closest neighbours. This is similar to the sweeping bands of firefly flashes seen in some studies. You can change parameters such as the visual radius and the modifier value while the model is running. Start with a low visual radius, and increase it as the model runs and watch the process of synchronization. ## EXTENDING THE MODEL You can change the model so that the phase response curve referred to is not from A. tasmaniensis but from a related species, A. flava. It does not synchronize under laboratory conditions or in the field. When its PRC is put into the model, synchronization does not occur. To implement in code, inactivate tasmaniensis PRC equation and activate flava's equation. set phase (phase + ( ( (-17.597 - 29.233 * SIN (phase + horizontal-shifter) + 21.397 * COS (phase + horizontal-shifter) - 7.254 * SIN ((phase + horizontal-shifter) * 2) + 8.711 * COS ((phase + horizontal-shifter) * 2)) + vertical-shifter) * modifier)); tasmaniensis' PRC set phase (phase + (((-0.000020166873981 * (phase + horizontal-shifter) ^ 3 + 0.013002660989270 * (phase + horizontal-shifter) ^ 2 - 3.026077821383480 * (phase + horizontal-shifter) + 232.501180575072000) + vertical-shifter) * modifier)); flava's PRC You can turn off inter-agent interactions and expose agents to a single pulse of light every 24 h by activating the statement ;ifelse ticks mod 144 = 36 [set isee 1] [set isee 0]; to provide single forcing pulse every 24 h, annul the 2 foregoing statements and replace with this Alternatively expose to 12:12 LD conditions by activating the statement: ;ifelse remainder ticks 144 < 72 [ set isee 1] [set isee 0]; to register daylight for 12 of every 24 h, annul the 3 foregoing statements and replace with this ## NETLOGO FEATURES ## CREDITS AND REFERENCES Parts of the model were inspired by the Netlogo Fireflies model by Uri Wilensky (1997). Manfred Hartbauer provided the code for calculating the synchronization index. ## HOW TO CITE If you mention this model or the NetLogo software in a publication, we ask that you include the citations below. For the model itself: Merritt, DJ and Gilchrist, J (2018) NetLogo Glowworm Model. Please cite the NetLogo software as: Wilensky, U. (1999). NetLogo. http://ccl.northwestern.edu/netlogo/. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL. ## COPYRIGHT AND LICENSE ![CC BY-NC-SA 3.0](http://ccl.northwestern.edu/images/creativecommons/byncsa.png) This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License. To view a copy of this license, visit https://creativecommons.org/licenses/by-nc-sa/3.0/ or send a letter to Creative Commons, 559 Nathan Abbott Way, Stanford, California 94305, USA. Commercial licenses are also available. To inquire about commercial licenses, please contact Uri Wilensky at uri@northwestern.edu. @#$#@#$#@ default true 0 Polygon -7500403 true true 150 5 40 250 150 205 260 250 airplane true 0 Polygon -7500403 true true 150 0 135 15 120 60 120 105 15 165 15 195 120 180 135 240 105 270 120 285 150 270 180 285 210 270 165 240 180 180 285 195 285 165 180 105 180 60 165 15 arrow true 0 Polygon -7500403 true true 150 0 0 150 105 150 105 293 195 293 195 150 300 150 box false 0 Polygon -7500403 true true 150 285 285 225 285 75 150 135 Polygon -7500403 true true 150 135 15 75 150 15 285 75 Polygon -7500403 true true 15 75 15 225 150 285 150 135 Line -16777216 false 150 285 150 135 Line -16777216 false 150 135 15 75 Line -16777216 false 150 135 285 75 bug true 0 Circle -7500403 true true 96 182 108 Circle -7500403 true true 110 127 80 Circle -7500403 true true 110 75 80 Line -7500403 true 150 100 80 30 Line -7500403 true 150 100 220 30 butterfly true 0 Polygon -7500403 true true 150 165 209 199 225 225 225 255 195 270 165 255 150 240 Polygon -7500403 true true 150 165 89 198 75 225 75 255 105 270 135 255 150 240 Polygon -7500403 true true 139 148 100 105 55 90 25 90 10 105 10 135 25 180 40 195 85 194 139 163 Polygon -7500403 true true 162 150 200 105 245 90 275 90 290 105 290 135 275 180 260 195 215 195 162 165 Polygon -16777216 true false 150 255 135 225 120 150 135 120 150 105 165 120 180 150 165 225 Circle -16777216 true false 135 90 30 Line -16777216 false 150 105 195 60 Line -16777216 false 150 105 105 60 car false 0 Polygon -7500403 true true 300 180 279 164 261 144 240 135 226 132 213 106 203 84 185 63 159 50 135 50 75 60 0 150 0 165 0 225 300 225 300 180 Circle -16777216 true false 180 180 90 Circle -16777216 true false 30 180 90 Polygon -16777216 true false 162 80 132 78 134 135 209 135 194 105 189 96 180 89 Circle -7500403 true true 47 195 58 Circle -7500403 true true 195 195 58 circle false 0 Circle -7500403 true true 0 0 300 circle 2 false 0 Circle -7500403 true true 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30 270 270 square 2 false 0 Rectangle -7500403 true true 30 30 270 270 Rectangle -16777216 true false 60 60 240 240 star false 0 Polygon -7500403 true true 151 1 185 108 298 108 207 175 242 282 151 216 59 282 94 175 3 108 116 108 target false 0 Circle -7500403 true true 0 0 300 Circle -16777216 true false 30 30 240 Circle -7500403 true true 60 60 180 Circle -16777216 true false 90 90 120 Circle -7500403 true true 120 120 60 tree false 0 Circle -7500403 true true 118 3 94 Rectangle -6459832 true false 120 195 180 300 Circle -7500403 true true 65 21 108 Circle -7500403 true true 116 41 127 Circle -7500403 true true 45 90 120 Circle -7500403 true true 104 74 152 triangle false 0 Polygon -7500403 true true 150 30 15 255 285 255 triangle 2 false 0 Polygon -7500403 true true 150 30 15 255 285 255 Polygon -16777216 true false 151 99 225 223 75 224 truck false 0 Rectangle -7500403 true true 4 45 195 187 Polygon -7500403 true true 296 193 296 150 259 134 244 104 208 104 207 194 Rectangle -1 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-7500403 true 150 285 150 15 Line -7500403 true 15 150 285 150 Circle -7500403 true true 120 120 60 Line -7500403 true 216 40 79 269 Line -7500403 true 40 84 269 221 Line -7500403 true 40 216 269 79 Line -7500403 true 84 40 221 269 x false 0 Polygon -7500403 true true 270 75 225 30 30 225 75 270 Polygon -7500403 true true 30 75 75 30 270 225 225 270 @#$#@#$#@ NetLogo 5.3.1 @#$#@#$#@ @#$#@#$#@ @#$#@#$#@ setup go syncindex setup go syncindex setup go syncindex setup go syncindex setup go syncindex setup go setup go setup go syncindex setup go [ slope ] of turtle 1 setup go [ slope ] of turtle 1 setup go [ slope ] of turtle 1 setup go syncindex setup go ticks setup go [ slope ] of turtle 1 setup go count turtles setup go SYNCINDEX setup go syncindex @#$#@#$#@ @#$#@#$#@ default 0.0 -0.2 0 0.0 1.0 0.0 1 1.0 0.0 0.2 0 0.0 1.0 link direction true 0 Line -7500403 true 150 150 90 180 Line -7500403 true 150 150 210 180 @#$#@#$#@ 1 @#$#@#$#@