globals [ total-return-time ;; used for calc of average return time no-foragers-returned ;; used for calc of average return time length-arm ;; the absolute length of the arms of the t-maze as calculated during setup width-arm ;; the absolute width of the arms of the t-maze as calculated during setup half-width-main ;; half the absolute width of the main branch of the t-maze as calculated during setup length-food ;; the absolute length of food patches of the t-maze as calculated during setup half-length-main ;; half the absolute length of the main branch of the t-maze as calculated during setup length-nest ;; the absoulte length of the nest as calculated during setup ] patches-own [ chemical ;; amount of chemicals on patch patch-type ;; 0 = nothing, 1 = nest, 2 = maze, 3 = food-left, 4 = food-right, 5 = left-arm, 6 = right-arm nest-scent ;; scent stronger close to nest source-left-scent ;; scent stronger to left food source, not used at the moment source-right-scent ;; scent stronger to right food source, not used at the moment ] breed [ idle-ants idle-ant ] breed [ foraging-ants foraging-ant ] breed [ disappointed-ants disappointed-ant ] breed [ feeding-ants feeding-ant ] breed [ returning-ants returning-ant ] breed [ unloading-ants unloading-ant ] turtles-own [ visited-source return-time moved-this-tick ] feeding-ants-own [ load-timer ] disappointed-ants-own [ disappointed-timer ] unloading-ants-own [ unload-timer ] to setup clear-all set-default-shape turtles "bug" setup-scale ;; setup the global scale setup-patches ;; setup t-maze, nest and food sources, including scents setup-ants ;; put population of ants in nest as idle-ants do-plotting end to setup-scale ask patches [ set length-arm 16 * scale * rel-arm-length set width-arm 5 * scale set half-width-main 3 * scale set length-food 4 * scale set half-length-main 12 * scale * rel-main-length set length-nest 4 * scale ] end to setup-patches ask patches [ if pxcor > (length-arm + half-width-main) * (-1) and pxcor <= half-width-main * (-1) and pycor < (half-length-main + width-arm) and pycor > half-length-main [ set patch-type 5 ; left arm set pcolor white ] if pxcor > half-width-main * (-1) and pxcor <= 0 and pycor < (half-length-main + width-arm) and pycor > half-length-main [ set patch-type 2 ; left arm to middle set pcolor white ] if pxcor >= 0 and pxcor < half-width-main and pycor < (half-length-main + width-arm) and pycor > half-length-main [ set patch-type 2 ; right arm to middle set pcolor white ] if pxcor >= half-width-main and pxcor < (half-width-main + length-arm) and pycor < (half-length-main + width-arm) and pycor > half-length-main [ set patch-type 6 ; right arm set pcolor white ] if pxcor > half-width-main * (-1) and pxcor < half-width-main and pycor <= half-length-main and pycor >= half-length-main * (-1) [ set patch-type 2 ; main arm set pcolor white ] if pxcor > (length-arm + half-width-main + length-food) * (-1) and pxcor <= (length-arm + half-width-main) * (-1) and pycor < (half-length-main + width-arm) and pycor > half-length-main [ set patch-type 3 ; left food source set pcolor red ] if pxcor >= (length-arm + half-width-main) and pxcor < (length-arm + half-width-main + length-food) and pycor < (half-length-main + width-arm) and pycor > half-length-main [ set patch-type 4 ; right food source set pcolor red ] if pxcor > half-width-main * (-1) and pxcor < half-width-main and pycor <= half-length-main * (-1) and pycor > (half-length-main + length-nest) * (-1) [ set patch-type 1 ; nest set pcolor blue ] let nest-y-center (half-length-main * (-1) - (0.5 * length-nest)) set nest-scent 100 - distancexy 0 nest-y-center set source-left-scent 3200 - distancexy -25 20 set source-right-scent 3200 - distancexy 25 20 ] end to setup-ants create-idle-ants pop-size ask idle-ants [ setxy 0 (half-length-main + length-nest / 2) * (-1) set color black ] end to go ask turtles [ set moved-this-tick false ] ask idle-ants [ let exitprob (random 1000 / 1000) if exitprob < exit-probability [ set breed foraging-ants ] set moved-this-tick true ] ask feeding-ants with [ moved-this-tick = false ] [ set color yellow ifelse load-timer > 0 [ set load-timer (load-timer - 1) ][ set breed returning-ants ] set moved-this-tick true ] ask disappointed-ants with [ moved-this-tick = false ] [ set color blue move-foraging wiggle let patch-type-here [patch-type] of patch-here if patch-type-here = 1 [ set breed foraging-ants ] if ((patch-type-here = 3) and (ticks > delay-left-source)) or ((patch-type-here = 4) and (ticks > delay-right-source))[ load-forager who ] set moved-this-tick true ] ask foraging-ants with [ moved-this-tick = false ] [ set color black move-foraging wiggle let patch-type-here [patch-type] of patch-here if ((patch-type-here = 3) and (ticks > delay-left-source)) or ((patch-type-here = 4) and (ticks > delay-right-source))[ load-forager who ] set moved-this-tick true ] ask returning-ants with [ moved-this-tick = false ] [ set color yellow move-to-nest wiggle let patch-type-here [patch-type] of patch-here if patch-type-here = 1 [ set breed unloading-ants empty-forager who ] set moved-this-tick true ] ask unloading-ants with [ moved-this-tick = false ] [ set color red set unload-timer unload-timer - 1 if unload-timer < 1 [ set breed foraging-ants ] set moved-this-tick true ] ask patches [ set chemical chemical * (100 - evaporation-rate) / 100 ;; slowly evaporate chemical ] tick do-plotting end to move-foraging ifelse (breed = foraging-ants) and (chemical >= 0.05) [ uphill-chemical ][ right random 360 ] let move-yes 0 ask patch-ahead 1 [ if pcolor = white or pcolor = blue or pcolor = red [ set move-yes 1 ] ] forward move-yes end to load-forager [ forager ] ask turtle forager [ let crowding-levels 0 set visited-source patch-type if patch-type = 3 [ set crowding-levels crowding-levels-left ] if patch-type = 4 [ set crowding-levels crowding-levels-right ] let number-neighbours count feeding-ants with [load-timer > 0] in-radius 25 ifelse number-neighbours < crowding-levels [ set breed feeding-ants set load-timer 60 set visited-source patch-type set return-time 0 ][ set breed disappointed-ants set visited-source patch-type ] ] end to move-to-nest uphill-nest-scent let ahead-is-path false ask patch-ahead 1 [ if pcolor != black [ set ahead-is-path true ] ] ifelse (ahead-is-path = true) [ set chemical chemical + 60 forward 1 ][ rt 180 ] set return-time return-time + 1 end to empty-forager [ forager ] ask unloading-ant forager [ set total-return-time total-return-time + return-time set no-foragers-returned no-foragers-returned + 1 set unload-timer 60 ] end ;; sniff left and right, and go where the strongest smell is to uphill-chemical let scent-ahead chemical-scent-at-angle 0 let scent-right chemical-scent-at-angle 45 let scent-left chemical-scent-at-angle -45 if (scent-right > scent-ahead) or (scent-left > scent-ahead) [ ifelse scent-right > scent-left [ right 45 ] [ left 45 ] ] end to-report chemical-scent-at-angle [angle] let p patch-right-and-ahead angle 1 if p = nobody [ report 0 ] report [chemical] of p end ;; sniff left and right, and go where the strongest smell is to uphill-nest-scent let scent-ahead nest-scent-at-angle 0 let scent-right nest-scent-at-angle 45 let scent-left nest-scent-at-angle -45 if (scent-right > scent-ahead) or (scent-left > scent-ahead) [ ifelse scent-right > scent-left [ right 45 ] [ left 45 ] ] end ;; wiggle so ants don't get stuck to wiggle right random 40 left random 40 end to-report nest-scent-at-angle [angle] let result 0 ask patch-right-and-ahead angle 1 [ if (pcolor = red) or (pcolor = white) or (pcolor = blue)[ set result nest-scent ] ] report result end ;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;; Plotting procedures ;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;; to do-plotting set-current-plot "Ants at food source" let foragers-left count feeding-ants with [ load-timer > 0 and visited-source = 3 ] let foragers-right count feeding-ants with [ load-timer > 0 and visited-source = 4 ] set-current-plot-pen "ants-left" plotxy ticks foragers-left set-current-plot-pen "ants-right" plotxy ticks foragers-right set-current-plot-pen "ants-with-food" plotxy ticks count feeding-ants with [ load-timer > 0 ] set-current-plot "Return time" set-current-plot-pen "default" if no-foragers-returned > 0 [ plotxy ticks total-return-time / no-foragers-returned ;plotxy ticks no-foragers-returned ] set-current-plot "Pheromone strength" let sum-pheromone-left sum [ chemical ] of patches with [ patch-type = 5 ] set-current-plot-pen "left" plotxy ticks sum-pheromone-left let sum-pheromone-right sum [ chemical ] of patches with [ patch-type = 6 ] set-current-plot-pen "right" plotxy ticks sum-pheromone-right end @#$#@#$#@ GRAPHICS-WINDOW 914 19 1614 740 48 48 7.1134021 1 10 1 1 1 0 0 0 1 -48 48 -48 48 0 0 1 seconds BUTTON 470 19 534 52 Setup setup NIL 1 T OBSERVER NIL NIL NIL NIL BUTTON 472 74 535 107 Go go T 1 T OBSERVER NIL NIL NIL NIL SLIDER 63 57 235 90 evaporation-rate evaporation-rate 0 10 0.4 0.1 1 NIL HORIZONTAL PLOT 66 312 541 603 Ants at food source ticks no ants 0.0 10.0 0.0 10.0 true true PENS "ants-left" 1.0 0 -16777216 true "ants-right" 1.0 0 -13791810 true "ants-with-food" 1.0 0 -8630108 true SLIDER 63 16 235 49 pop-size pop-size 0 500 300 25 1 NIL HORIZONTAL PLOT 550 311 894 600 Return time NIL NIL 0.0 10.0 0.0 10.0 true false PENS "default" 1.0 0 -16777216 true SLIDER 268 16 440 49 scale scale 0.2 1.4 1 0.1 1 NIL HORIZONTAL SLIDER 268 56 440 89 rel-arm-length rel-arm-length 0 1.5 0.65 0.05 1 NIL HORIZONTAL SLIDER 65 96 237 129 exit-probability exit-probability 0 1 1 0.001 1 NIL HORIZONTAL SLIDER 64 214 236 247 delay-left-source delay-left-source 0 3000 3000 50 1 NIL HORIZONTAL SLIDER 63 254 235 287 delay-right-source delay-right-source 0 3000 0 50 1 NIL HORIZONTAL SLIDER 65 134 237 167 crowding-levels-left crowding-levels-left 0 216 25 1 1 NIL HORIZONTAL SLIDER 64 174 236 207 crowding-levels-right crowding-levels-right 0 216 8 1 1 NIL HORIZONTAL PLOT 67 610 488 838 Pheromone strength ticks sum of pheromones 0.0 10.0 0.0 10.0 true true PENS "left" 1.0 0 -955883 true "right" 1.0 0 -2064490 true BUTTON 472 111 554 144 Go once go NIL 1 T OBSERVER NIL NIL NIL NIL SLIDER 269 95 441 128 rel-main-length rel-main-length 0 1.4 1 .1 1 NIL HORIZONTAL @#$#@#$#@ WHAT IS IT? ----------- Many ants, bees and termites lay pheromone trails to recruit and direct nestmate foragers to food sources. This causes a strong positive feedback as more and more individuals are adding their own pheromones to the trails, as they start exploiting the resource. The feedback will enable a colony of insects to quickly respond to a novel food source, but it can also compormise the flexibility of foraging colony. Experiments have shown that for example ant colonies are sometimes unable to exploit multiple food sources or to quickly switch from a low quality food source to a new one that yields higher quality food. Because of the strong pheromone trails they are locked in a suboptimal state. This model demonstrates that in a stable environment crowding at a food source can can create a negative feedback that is able to break these asymmetries, and can lead to an "ideal free distribution" of foragers. In a changing environment the negative feedback created by crowding enables a colony to quickly re-allocate foragers to newly emerging foodsources. The model is part of Grüter et al. (in prep): Negative feedback enables fast and flexible collective decision-making in ants. PURPOSE ------- The purpose of the model was to explore the effects of different crowding levels on the allocation of foragers as described in experiments 1 and 2 of Grüter et al. (in prep). Additionally, we tested the role of pheromone decay rates on forager allocation in a changing environment. The model is not intended to be an exact and fully parameterized model of L. niger foraging. While the modelled situation is based on our experimental set-up, the aim was to build a more generic model that captures the key elements of ant foraging and recruitment to investigate how crowding affects worker allocation in a species with strong positive feedback via pheromone trails and negative feedback via crowding at food sources. ENTITIES, STATE VARIABLES AND SCALES ------------------------------------ For most simulations, we used 500 agents (see table S2 for parameters), which corresponds roughly to the number of ants that can be expected to forage during a typical experimental trial using colonies with several thousand ants (i.e., not all the ants in a colony forage). Agents could assume any one of 6 different states: idle inside the nest, searching for food, feeding at a food patch, at a food patch but unable to feed due to crowding (dissatisfied), laying a pheromone trail while returning to the nest (recruiter), unloading. The simulated agents occupied a specific location at every point in time and were located on a two-dimensional square grid with the shape of a T-maze connected to the nest. The default branch or stem width was 3 squares. The default lengths were 15 squares for the stem and 11 for each arm. The nest was located at the base of the T-maze (3 x 2 squares), with one food patch at the end of each branch (2 x 3 squares). Simulations were run in discrete time steps (t). One time step was made to correspond approximately to one second in the experiment in the following way. It took real ants approximately 40 seconds to walk from a food source to the nest. Hence, for the model we chose branch and stem lengths that required approximately 40 time steps with an agent walking-speed of 1 square per time step (agents did not always walk in a perfectly directly way from nest to feeder). Thus one time step in the model corresponds to one second. Total model running time was 5400 time steps, corresponding to approximately 90 minutes. Because of the stochastic nature of the model, 30 model runs were performed for each combination of parameter values. PROCESS OVERVIEW AND SCHEDULING ------------------------------- Agents that left the nest started to perform a random walk (searching) until a food patch or, at a later stage of the simulation, a pheromone trail was encountered. Agents finding a food patch spent 60 time steps taking on food at the patch if there was no crowding. Successful agents then walked directly to the nest and then took 60 time steps to unload. After unloading, agents could leave the nest and start searching again (random walk) or follow a trail. The quality of food patches was high in that all successful agents deposited a pheromone trail with amount C per patch when walking back to the nest. This is a simplification as in nature not all ants deposit trail pheromones and ants also deposit pheromone when walking from the nest to the food source [4]. However, for the purpose of our model this was irrelevant, because we simply wanted the agents to establish an attractive pheromone trail with a certain decay rate. If food patches were crowded, agents became dissatisfied. Dissatisfied agents performed a random walk without paying attention to the pheromone trail or laying a pheromone trail. During the simulation, the behavioural states and variables were updated for each agent at every time step. The different states were updated asynchronously in sequence (idle agents -> foraging agents -> feeding agents -> dissatisfied agents -> recruiting agents -> unloading agents). However, the model was robust to changes in the sequence. In model 1 (corresponding to experiment 1), two identical food sources were offered simultaneously. Fig. 2b shows that 1 feeding hole can accommodate a maximum of 8 foragers. Hence, we again used 4 different crowding levels, which corresponded to the crowding levels in the experiment: high (8 agents ? 1 feeding hole), medium (24 agents ? 3 feeding holes), low (72 agents ? 9 feeding holes) and very low (216 agents ? 27 feeding holes). For simplicity, crowding was modelled as an all-or-nothing state. For example, if 8 agents were already present at a food patch in the high crowding situation, other agents at the feeder location could no longer access the food and became dissatisfied. Apart from crowding, food patches were ad libitum as in the experiments. In model 2 (corresponding to experiment 2), one food source was introduced with a delay of 900 time steps (~ 15 minutes). This second food source permitted 3 times as many agents access to forage before the crowding threshold was reached (8 vs. 24 agents, 24 vs. 72 agents, 72 vs. 216 agents). If the number of agents on a food patch was higher than the crowding threshold for this patch, a newly arrived agent became dissatisfied and performed a random walk. DESIGN CONCEPTS --------------- The basic principle addressed by this model is symmetry breaking and how it is affected by negative feedback. To investigate this the This model allows variation in the strength of negative feedback at two food sources to be caused by manipulating the maximum number of agents that can feed at either source. The pheromone deposited on the trail system and the proportions of agents at the two food sources, as influenced by both negative and positive feedback, are emergent properties of the model. The concepts of adaptation, objectives and prediction are not important in this model. There is no learning in the model. Sensing is important in this model: agents leaving the nest were able to detect pheromone left on patches and oriented themselves according to the amount of pheromone. Agents that had fed successfully at either food source, and were walking back to the nest were assumed to know the direction of the nest (implemented by means of a nest odour). Furthermore, agents reaching the food patch were able to perceive whether the number of agents on a food patch equalled the crowding threshold for this patch (implemented by counting the number of feeding agents on the patch. In nature, ants simply would not be able to access the food source because of the presence of other ants). If so, the agent became dissatisfied and performed a random walk until it was able to feed at the current or at another food source. Hence, the agents interacted in two indirect ways. First, by responding to the pheromone deposited by other agents and, second, by responding to crowding caused by other agents on a food patch. Stochasticity is used to introduce variability in the number of agents leaving the nest at any time step (Table S2) and in their random walks. INITIALISATION -------------- At the beginning of each simulation trial, the nest, the T-maze and the food sources were initialised as described above. The amount of pheromone chemical was set Cpheromone = 0 for all patches, and the nest scent of patch X was set to Cnest = 100 - distance (Xnest, X), where Xnest is the patch at the centre of the nest. All agents were initiated at the nest centre and their state set to idle, with a probability Pleave (Table S2) to leave the nest. According to the purpose of the model, we tested different initial conditions for crowding levels at food sources, as well as the availability of food at the sources. INPUT DATA ---------- Apart from changing amounts of pheromone on the different patches of the trail system, the environment is assumed to be constant, so the model has no input data. Food is present as ad libitum throughout. Access to the food is limited but unchanging. SUBMODELS --------- The move-foraging submodel defined how agents behave after leaving the nest. If a food patch exceeded a threshold level of pheromone, dissatisfied agents leaving the patch followed pheromone trails by sampling 3 patches in walking direction (0°, 45° left and 45° right) and walking in the direction of the patch with most pheromone. We assumed the pheromone chemical to be volatile, and We used chose a decay evaporation rate that led to a decay of the pheromone trail below the perception threshold of the agents that was equivalent to approximately 45 minutes. This was based on the pheromone strengths we measured during test runs and corresponds to experimentally measured values for L. niger [5]. The amount of pheromone was calculated for each square of the grid at each time step as Ci,t = Ci,(t – 1) × (100 - r)/100; where Ci is the chemical on patch i, r is the evaporation rate in % and t is the time point, leading to an exponential decay (see also table S2). If the current patch had no pheromone or below-threshold pheromone levels, then the agent moved in a random direction. The move-to-nest submodel defined the behaviour of agents after successful foraging. Full agents perceived the strength of the nest-odour (see section Initialisation) on patches and behaved as they did in the case of pheromone. In nature, ants find their nest relying on various methods such as land-mark learning and path-integration [6,7]. For the purpose of this model, the method of finding the way back to the nest was irrelevant. SENSITIVITY ANALYSIS -------------------- In order to test how strongly our results depended on the values of key parameters we systematically varied the number of agents, pheromone decay rates, side branch lengths, and the length of the stem. The model was robust over a wide range of these parameters. Some deviations (e.g. with larger T mazes) are given in the Results section of the main paper. REFERENCE LIST -------------- 1. Wilensky U. (1999). NetLogo. http://ccl.northwestern.edu/netlogo/. (Center for Connected Learning and Computer-Based Modeling: Northwestern University, Evanston, IL). 2. Grimm V., Berger U., Bastiansen F., Eliassen S., Ginot V., Giske J., Goss-Custard J., Grand T., Heinz S.K., Huse G. et al. (2006). A standard protocol for describing individual-based and agent-based models. Ecological Modelling 198: 115-126. 3. Grimm V., Berger U., DeAngelis D.L., Polhill J.G., Giske J., and Railsback S.F. (2010). The ODD protocol: A review and first update. Ecological Modelling 221: 2760-2768. 4. Beckers R., Deneubourg J.-L., and Goss S. (1992). Trail laying behaviour during food recruitment in the ant Lasius niger (L.). Insectes Sociaux 39: 59-72. 5. Beckers R., Deneubourg J.-L., and Goss S. (1993). Modulation of trail laying in the ant Lasius niger (Hymenoptera: Formicidae) and its role in the collective selection of a food source. Journal of Insect Behavior 6: 751-759. 6. Collett T.S., Graham P., and Durier V. (2003). Route learning by insects. Current Opinion in Neurobiology 13: 718-725. 7. Collett M. (2009). Spatial memories in insects. 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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 true false 195 60 195 105 Polygon -16777216 true false 238 112 252 141 219 141 218 112 Circle -16777216 true false 234 174 42 Rectangle -7500403 true true 181 185 214 194 Circle -16777216 true false 144 174 42 Circle -16777216 true false 24 174 42 Circle -7500403 false true 24 174 42 Circle -7500403 false true 144 174 42 Circle -7500403 false true 234 174 42 turtle true 0 Polygon -10899396 true false 215 204 240 233 246 254 228 266 215 252 193 210 Polygon -10899396 true false 195 90 225 75 245 75 260 89 269 108 261 124 240 105 225 105 210 105 Polygon -10899396 true false 105 90 75 75 55 75 40 89 31 108 39 124 60 105 75 105 90 105 Polygon -10899396 true false 132 85 134 64 107 51 108 17 150 2 192 18 192 52 169 65 172 87 Polygon -10899396 true false 85 204 60 233 54 254 72 266 85 252 107 210 Polygon -7500403 true true 119 75 179 75 209 101 224 135 220 225 175 261 128 261 81 224 74 135 88 99 wheel false 0 Circle -7500403 true true 3 3 294 Circle -16777216 true false 30 30 240 Line -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 4.1.2 @#$#@#$#@ @#$#@#$#@ @#$#@#$#@ setup go count turtles with [ forager-load-timer > 0 and forager-visited-source = 3 ] count turtles with [ forager-load-timer > 0 and forager-visited-source = 4 ] @#$#@#$#@ @#$#@#$#@ default 0.0 -0.2 0 1.0 0.0 0.0 1 1.0 0.0 0.2 0 1.0 0.0 link direction true 0 Line -7500403 true 150 150 90 180 Line -7500403 true 150 150 210 180 @#$#@#$#@ 0 @#$#@#$#@