! ! !

! ! DEPARTMENT OF COMPUTER SCIENCE

An improved agent-based Model of the speed accuracy Trade-offs in house-hunting ants

Alisdair Venn

____________________________________________ A dissertation submitted to the University of Bristol in accordance with the requirements of the degree of Master of Science in the Faculty of Engineering

__________________________________________________________________________________ January 2015 | CSMSC-15

Declaration This dissertation is submitted to the University of Bristol in accordance with the requirements of the degree of Master of Science in the Faculty of Engineering. It has not been submitted for any other degree or diploma of any examining body. Except where specifically acknowledged, it is all the work of the Author. Alisdair Venn, January 30, 2015

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Executive Summary This project is concerned with the decentralised decision making process used by ants when choosing a new nest site. Although several computational models have been proposed to describe this process, the details are still not well understood. This project begins by providing an in-depth analysis of a stateof-the-art model, called AH-HA, which reveals several biologically implausible behaviours. The project goes on to reimplement the AH-HA model in order to overcome some of its previous limitations. Our contributions are specifically: • Package the original AH-HA model to include the required libraries and data files not available in the repository where AH-HA is located. • Port AH-HA to the latest version of the key library (Repast Symphony) to make use of extended batch running features, data collection and graphical features. • Verify the previously published AH-HA results. • Perform in depth, critical analysis of the processes leading to the results published in [Marshall et al., 2006]. • Redesign AH-HA operation to use biologically possible mechanisms. • Analyse the new model to assess the a↵ect of the modifications.

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Acknowledgements I would like to thank Dr. Oliver Ray for his patience, persistence and continued support in preparing this Thesis. I would also like to thank Martin Garrad and Gleb Kolpakov for their insight, advice and feedback. I owe the aforementioned an inordinate debt of thanks, that I am sure I could never fully repay. I look forward to following their progress and discoveries over the coming years. I must, lastly, thank Hazel Price for her unwavering support and understanding.

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together, the ants can conquer the elephants [D et al., 2005]

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Contents 1 Introduction

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2 Biological Background 2.1 Introduction . . . . . . . . . . . . 2.2 Emigration . . . . . . . . . . . . 2.2.1 Individual Actions . . . . 2.2.2 Group Actions . . . . . . 2.2.3 Reverse Tandem Running

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3 Computational Background 13 3.1 Ant House-Hunting Algorithm as published . . . . . . . . . . . . 13 3.1.1 Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3.1.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 4 Analysis of AH-HA 4.1 Population Dynamics . . . . . . . . . 4.2 Problems with Assessment Cost . . . 4.3 Problems with Recruitment Strategy 4.4 Implementation . . . . . . . . . . . . 4.4.1 Repeating Results . . . . . . 4.4.2 Supplied Code Analysis . . . 4.5 Ported Code . . . . . . . . . . . . . . 4.6 Conclusions . . . . . . . . . . . . . .

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5 Improving the AH-HA model 5.1 A new model of Ant House Hunting 5.1.1 States . . . . . . . . . . . . . 5.1.2 Architecture . . . . . . . . . 5.2 Reconsidering the model . . . . . . . 5.2.1 Starting scouting . . . . . . . 5.2.2 Quorum sensing . . . . . . . 5.2.3 Concept of physical space . . 5.2.4 Decision to recruit . . . . . . 5.2.5 Recruitment strategy . . . . .

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6 Evaluation 33 6.1 Speed Accuracy tradeo↵ . . . . . . . . . . . . . . . . . . . . . . . 33 6.2 Nest quorum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 7 Conclusions

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1

Introduction

Relative speed and accuracy are indubitably desirable aspects in any decision making process. However in most systems improvement in either of these aspects must come at the detriment of the other i.e. a decision could be made more quickly by considering fewer options but then is less likely to be optimal, in the same way that an optimal decision can only be made after thorough and, hence lengthly, evaluation of the available options. One such system that has been shown to come to collective decisions in a de-centralised manner is ant colonies. Similarly to many social animals, ants arrive at decisions through consensus rather than central control. With individuals modifying various aspects of their behaviour in proportion to both the urgency with which a decision is required and the quality of the options the individual is aware of. Colony-wide decisions can then be reached with relative and proportional speed and accuracy, without the requirement of any individual making direct comparisons between all, or indeed any, of the available options. Not only are the processes with which these system operate worthy of study to further our understanding of the ants and the natural world, but collective and de-centralised decision making have become important research areas informing the design and function of autonomous and distributed systems. The day-to-day activities of an ant colony doubtless involve many actions that require decision making and consensus in order to be e↵ective and efficient. Of these the process of emigration from one nest to another lends itself particularly well to empirical observation and study. The task can be o↵set by providing a single, adequate nest option, it can be simulated by introducing preferable nest options and/or destruction of the original nest and the end of the process can be defined in scientifically robust way, such as the evacuation of the original nest. As such it has been the subject of many studies and from the results of these studies a number of models of the process have been proposed [Marshall et al., 2006,Pratt et al., 2005,Sampson, 2013,Garrad, 2014]. This paper will make its focus an agent based model of the emigration process, the Ant House-Hunting Algorithm (AH-HA) [Marshall et al., 2006]. By modelling the behaviour of the individual ants and their interactions with other colony members the algorithm was able to demonstrate a trade o↵ between speed and accuracy reminiscent of that in real world emigrations. The AH-HA model is built in an early version of the Repast agent based modelling software RepastJ 3 [North et al., 2006]. Of particular interest is the way ants are able to tune their decision making process in response to threats in the environment. It is believed the ants do this by varying a parameter known as the quorum threshold (the number of ants that must be present in a nest option before the decision is made to move the colony to that nest). The lower the quorum threshold the faster decisions are reached. Our first contribution comprises an in depth analysis of the AH-HA model in order to establish its biological plausibility and the success with which it models a true emigration process. This analysis lead to the discovery of several behaviours that are clearly inconsistent with biological evidence (such as the 6

fact that passive ants are transported to a new nest before the quorum threshold is met). The second contribution therefore is to reimplement the AH-HA model to overcome some of the limitations of the earlier implementation.. Our contributions are specifically: 1. Package original AH-HA to allow execution and analysis. Section 4 The AH-HA library is supplied in the supplementary materials accompanying [Marshall et al., 2006]; however an executable is not provided and it depends on a number of external libraries contemporary to its development in 2006. An AH-HA executable is provided in the supplementary materials to this thesis, along with source code of the libraries that it requires (that are redistributed in accordance with the terms of their BSD licences). The code is provided along with the publishing in order to allow others to reproduce and validate their findings; however it took significant amounts of reverse engineering and trial and error to find the libraries required, and so their being documented and included in the supplementary materials represents the removal of a significant hurdle faced by future investigators. 2. Verify the results published in [Marshall et al., 2006]. Section 4.4.1 In order to substantiate our analysis we must first verify the published results from the model. By establishing these results as valid from the evidence available to the author we also validate the further analysis into the processes that lead to these results and the conclusions we are able to draw from this. 3. Port AH-HA to latest Repast Simphony version to make use of extended batch running features, data collection and graphical features. Section 4.5 The original AH-HA implementation, written in RepastJ 3, requires data abstraction and graphing be implemented in the code and batch parameters read from a formatted text file. The latest version allows for data collection, batch running and graphing to be specified in the GUI, removing the need for future investigators to become accustomed with the code in order to run and analyse the model. These are made available as source and executable along with dependencies in the supplementary materials. 4. Perform in depth, critical analysis of the processes leading to the results published in [Marshall et al., 2006]. 4.6 From the extended data gathering capabilities we show that the Ah-HA model is based on a number of mechanisms inconsistent with those understood to be in the true process. These inconsistencies lead to the discovery that emigrations under parameters that should be impossible are possible, which calls into question the results arising from the model. 5. Redesign AH-HA operation to use biologically possible mechanisms. 5 Following the discoveries from the analysis of the model a number of areas for development are highlighted. These changes are implemented in a new

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model, taking the opportunity to restructure the code and restate the model. 6. Analyse the new model assess the a↵ect of the modifications. 6 To validate the modifications to the model the analysis applied to the original model is repeated with the new model. In doing so we are able to make direct comparisons between the models and draw robust conclusions about the emigration process.

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2 2.1

Biological Background Introduction

Ants are defined taxonomically as the species of insects that make up the family Formicidae, in the order including other social insects such as bees and wasps, Hymenoptera. The term social insects describes the cooperative nature of the individuals within the colony to meet colony-wide ends. Labour tasks such as brood care, foraging for food etc. are undertaken cooperatively and in a coordinated manner. Labour is divided amongst the colony members dependent on the necessity of the task from the point of view of the colony rather than the individual. A species that has lent itself particularly well to scientific analysis is Temnothorax albipennis in the subfamily Myrmicinae. These diminutive species, native throughout Northern Europe, form colonies numbering from a tens to a few hundred individuals and make their nests in small rock crevices, typically occupying an area of few square centimetres. Their preference for small nests of simple construction have made their culturing in laboratory conditions relatively straightforward and the ants will readily nest between two microscope slides with a spacer of a few millimetres depth that also provides a perimeter. Given the space-constrained and fragile nature of their chosen nest sites in the wild, Temnothorax albipennis will periodically emigrate from one site to another. Typical impetuses for emigrations include destruction of the original nest and the colony requiring more space to house its number. Therefore inducing emigrations from these ants for the purpose of observation should not be considered unduly stressful to the ants such as to make them behave unnaturally.

2.2

Emigration

Emigration is a particularly perilous process for the ants. During the course of an emigration, by definition, every individual (including the ”vital organ” queen) must leave the safe confines of the nest and traverse some distance fully exposed to the danger of the outside world to the new nest site. Therefore organisation, accuracy and colony cohesion are of particular importance. During the emigration process individual ants are observed to perform various (apparently) distinct roles [Pratt et al., 2002]. At the highest level ants can be described as passive or active. Passive ants appear to not be actively engaged in the emigration process and continue with tasks in the confines of the nest. The active ants, who usually comprise between roughly a quarter to half of the colony, perform the scouting for new nests, their assessment and then recruitment roles. It is the behaviour of these active ants that drives the emigration process: 2.2.1

Individual Actions

Scouting In order for an emigration to take place a suitable new nest site must be found. Active ants leave the current nest and search the environment

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for potential nest sites. In their study of T.albipennis Stroeymeyt et al. describe the search strategy as ”random exploration” but without any mathematical analysis [Stroeymeyt et al., 2011], however a detailed study into the search strategy of another ant species, Melophorus bagoti, Reynolds et al. showed the path taken by scouts more closely resembled that of a L´evy flight (an angle and distance biased random walk) than a purely random walk [Reynolds et al., 2014]. Assessing On discovering a potential nest site an ant active in the emigration process will enter and change their behaviour in order to make an assessment of the potential nest site’s suitability. From experimentation and direct observation a number of the features considered during nest assessment have been identified from both the assessors behaviour and decision making tendencies: 1. Perimeter Assessing ants spend much of their time following the periphery of the nest, [Franks et al., 2003] showed T.albipennis have a preference for nests with narrow entrance-ways, although this can vary among species. 2. Area Assessors will interrupt their wall following action to make apparently random explorations into the centre of the nest. [Mugford et al., 2001] showed that this behaviour is consistent with a Bu↵on’s needle-type area estimation process. 3. Light [Cammaerts and Cammaerts, 2014] showed that ants are most sensitive to visible light at shorter wavelengths with their acuity diminishing the wavelengths lengthen towards red and infra-red. Ants show preference for nests o↵ering complete darkness but their insensitivity to red light allows experimenters to provide glass nests with a red filter, providing the ants with what they perceive as a darkness while facilitating observation. Recruiting Having concluded the assessment of a suitable nest the assessor will then turn to the task of recruiting other colony members to their preferred nest. Recruiters introduce others to their preferred new nest in one of two ways dependent on the number of other colony members who share their preference relative to the urgency with which the emigration is required: 1. Tandem Running In the early stages of emigration ants will find other colony members to lead to the potential new nest site. The process of leading other ants to the new nest is relatively slow and may be interrupted by the leader losing the follower or visa versa, however it allows the follower to learn the route to the new nest. Assuming the follower makes an assessment of the new nest that is in agreement with the ant that led her there the follower will then be able to recruit further ants to the new nest site, in what [Franks et al., 2009] describe as a positive-feedback information cascade. 2. Social Carrying Once there is sufficient adoption of the new nest site, i.e. it has exceed the quorum threshold, the ants switch their recruitment 10

method to carrying other colony members to the new nest site. Social carrying has the advantage of being three times faster than tandem running, however the carried ants do not learn the path to the new nest and therefore are unable to become recruiters to it [Pratt et al., 2002]. 2.2.2

Group Actions

As a decentralised decision making process the nest selection task does not fall to a single ant. It is sum of the actions of many active ants that result in the colony emigrating and these individuals base their behaviour on cues from their environment and immediate colony members. The problem is e↵ectively solved in parallel with the ”positive-feedback information cascade” described in 2.2.1 moving the colony towards suitable nest choice from the available options. The Decision to Recruit As we have seen in 2.2.1 there are a number of reasons that may lead to a colony’s emigration and likewise a number of criteria with which ants assess potential nest sites. Having made an assessment a potential nest site the assessor must decide whether to recruit to the nest or continue their search. [Robinson et al., 2009] showed mathematically by making the decision to recruit to the a nest probabilistically in proportion to the sites perceived quality leads to accurate decisions. Whereas [Pratt et al., 2002] suggests that delaying recruitment in inverse proportion to the new nest’s perceived quality will also result in a similar decision. The Method of Recruitment The two methods of recruitment discussed in 2.2.1 further allow the colony to tune their decision making in favour of preferable options. Early in an emigration recruitment is done via tandem running. By allowing their recruits to learn the path to a new nest they in turn are able to become recruiters. However the task of tandem running is comparatively slow and once a consensus has been reached on a new nest the recruiters can proceed to social carrying to speed the emigration towards conclusion. The consensus of ants that have adopted a new nest site is described as it quorum and is known to the ants through assessment of the number of ants in their preferred new nest. Once the quorum at their chosen nest exceeds a threshold they switch from tandem running to social carrying [Pratt et al., 2002]. Carrying their nest-mates is approximately three times faster than tandem running, but as the recruits do not learn the location of the site they are carried to relative to the nest they are moving from they are at the mercy of the decision made by their recruiter. During the social carrying phase brood items (i.e. unhatched eggs) are moved between the nests. By varying the quorum threshold the colony is e↵ectively able to vary the number of positive resulting assessments required before committing to new nest relative to the urgency of the emigration - trading speed for accuracy. [Franks et al., 2013] showed this feature of emigration also allows the colony to trade speed for colony cohesion in disaster situations as very low thresholds allow recruiters to quickly evacuate a nest rendered useless to any nest site they have discovered. 11

Figure 1: State transition diagram for the models tested in [Planqu´e et al., 2007]. Where µ is the rate at which active ants at the old nest become scouts, k is the rate at which scouts independently become recruiters and the rate at which passive ants are carried to the new nest. Taken from [Planqu´e et al., 2007]. 2.2.3

Reverse Tandem Running

In an action that may at first sight appear to be working in opposition to the emigration process ants are observed to perform tandem runs in the reverse direction i.e from their preferred nest to the original nest site during the carrying phase. [Mallon et al., 2001] notes that these reverse tandem runs (RTRs) are often more numerous than forward tandem runs (FTRs) over an emigration. The precise role of RTRs are yet to be fully understood however a number of hypotheses based on both mathematical modelling and direct experimentation have been put forward. [Planqu´e et al., 2007] takes a top-down view of the emigration process to devise two mathematical models of the number of ants in each state during the emigration process (see Figure 1). By solving their system across a range of parameters they found the optimal strategy almost always involves RTRs and agree with the experimental evidence in [Mallon et al., 2001]. By providing a mechanism with which ants that are currently not recruiting (either scouting or having been carried to the new nest) might be induced to start recruiting the colony is able to reach swifter decisions. [Franks et al., 2009] present results from direct experimentation to test the hypotheses that RTRs compensate for unsuccessful FTRs and that RTRs compensate for a lack of candidates for FTRs. They found interrupting FTRs had no e↵ect on the number of RTRs, but that when scouts are widely dispersed in the environment and are therefore not readily accessible to recruit the frequency of RTRs increase. They go on to speculate that RTRs are performed when further recruitment e↵ort is required but an ideal candidate (another active scout) is unavailable. Both set of results lend weight to the hypothesis that there is a conflation between the decision and implementation processes as a result of the de-centralized nature of the system. By including actions that serve to backup their decision the colony ensures that, when required, swift decisions result in swift implementation.

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3 3.1

Computational Background Ant House-Hunting Algorithm as published

The Ant House-Hunting Algorithm (AH-HA) described in [Marshall et al., 2006] takes an agent-based view of the emigration process in order to explore the role of the accuracy of and the cost associated with nest assessment by the individual active ants and the properties and dynamics that emerge from it. The AH-HA model is described by equation 1 and state transition diagram in Figure 2. ⇢ oi if qi  Qmax Qmax , di = (1) 1 otherwise The AH-HA model works on the basis of their being two nests equidistant from the original nest with an exact value describing the quality of each Qi . The model begins with all the ants in a uninhabitable nest. Scouts then emerge from the nest with probability s and then have an equal chance of discovering either prospective nest. On encountering a nest the assessors will take a time steps to make an assessment. Upon completing their assessment the assessing ant draw a value of perceived nest quality o from a normal distribution with mean Qi and standard deviation ⌃. Providing a noisy nest quality value the model simulates the (assumed) imperfect nature of ant senses and assessment process. The ant will then begin recruiting to the nest with probability d at each time step, the value of d is inversely proportional to the perceived nest quality o (see equation 1). Additionally at each time step if the decision is not taken to begin recruiting the ant may discover the alternative nest option with fixed probability p and make an assessment in the same way as before. The ant will then begin recruiting to the preferred nest with probability dpref erred nest . The recruiter then decides on their recruitment method by comparing the quorum at the nest they are recruiting to q to the quorum threshold T . Until the threshold is met recruitment is performed via tandem runs and social carrying thereafter. Social carrying takes c time-steps and tandem running takes 3c; incorporating the empirical observations in [Pratt et al., 2002] previously described. Having completed a recruitment the ant returns to the state of waiting to recruit with probability d or assessing another nest with probability p. The recruiters start their recruitment by looking for other active ants who have yet to make a nest assessment and so have no allegiance to either. If no ants without allegiance are remain in the model then the recruiter seeks out ants who might be willing to shift their allegiance. If there are no willing scouts the recruiter returns to the original nest and transports the passive members and brood items. Once the original nest has been emptied and no scouts willing to shift allegiance are available the recruiter returns to its preferred nest and becomes passive, with the probability s of becoming active again and making an assessment of the alternative site.

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Figure 2: (a) State transition diagram for ant scouts in the AH-HA model. (b) Recruitment strategy for ant scouts recruiting to a site in the AH-HA model. Taken from [Pratt et al., 2002]. 14

3.1.1

Variables

The results in [Marshall et al., 2006] are considering performance over a range of three parameters: 1. Preference switch probability p This parameter defines the likelihood of an ant who has discovered a potential nest assessing another site while it is attempting to recruit to the site it has discovered or an ant that has finished a recruitment act and is about to make another recruitment assesses an alternative option (if available). 2. Assessment Delay a This parameter defines the length of time an active ants spends in a nest that it has either discovered, been recruited to or just finished a successful recruitment to spends making an assessment before either recruiting to the nest or scouting for another. 3. Assessment noise This parameter defines the received assessment nest quality standard deviation (with mean of the true nest quality). 3.1.2

Results

[Marshall et al., 2006] hypothesised that the time spent assessing potential nests and the varying perception of a nest quality in the individual assessors due to assessment noise play an important role in the true emigration process and are a necessary feature of systems attempting to simulate it. By performing sweeps across a range of assessment noise, assessment cost and nest preference switching probability parameters they show that without assessment noise and cost optimal decisions can be made at minimal cost by allowing the ants to more readily switch their nest preference, eliminating the role of the quorum threshold in the process. But as the noise and cost parameters, that are reasonably assumed in the true process [Mugford et al., 2001], are increased, the model shows the speed-accuracy trade o↵.

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4 4.1

Analysis of AH-HA Population Dynamics

As an initial sanity check the population dynamics in the AH-HA model were checked to ensure the model was running correctly and outputting sensible. It was this initial assessment that indicated that passive ants could be recruited by tandem running. As many of the number that make up the passive contingent of a colony are brood item, i.e eggs and immobile ants, this represents a significant indication that the mechanisms within the AH-HA model not only diverge from those widely considered to be part of the true process but are not biologically possible.

4.2

Problems with Assessment Cost

The title of [Marshall et al., 2006] is ”Noise, cost and speed-accuracy tradeo↵s: decision-making in a decentralized system”, by cost they refer to the time delay incurred as an active ant makes their assessment of a potential nest option and their results range across values of 0-10 on this parameter. As the theory of quorum based decision making suggests, ants assessing a nest consider the number of other ants in the nest as the basis for their decision of whether to recruit using tandem runs or social carrying; and before a quorum is reached the only ants in a nest option should be those who are assessing it having arrived there following discovering the nest, being recruited to the nest, switching to the nest or reassessing following recruiting to the nest. It therefore follows that an assessment cost (a) of 0 is impossibly low value for an emigration to take place, as no active ant would ever spend time in a nest and a quorum would never be reached. Once a is increased past a value at which a quorum could be reached and assuming there are more passive ants than active we would expect nests to achieve quorum faster. While total delay incurred by all the assessors at a nest during an emigration remains less than the time taken to carry all the passive ants to the nest site we would expect to see swifter emigrations. The reverse however is reported in the AH-HA paper, where they find that emigration time increases with a, and that emigrations with a = 0 are not only possible but fastest. This shows us that the quorum used in the AH-HA model is not the number of ants that are actually in the nest but something else. From the analysis that follows in Section 4.4.2 we will show the quorum at a nest in the AH-HA model is only ever contributed to by of ants that are recruiting to a nest, considering switching to recruit to another nest and passive ants. Passive ants aside all the quorum contributors in the AH-HA model are explicitly outside the nest that they are contributing to the quorum in.

4.3

Problems with Recruitment Strategy

Figure 2, part b shows the recruitment strategy of ants in the AH-HA model. We firstly note the glaring omission of the mention of quorum in this diagram, there

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is no confusion in the literature [Franks et al., 2009] that before the quorum is reached recruitment occurs among the active ants, with passive ants only ever being recruited once a quorum is met i.e by social carrying. With AH-HA allowing the prequorate recruitment of passive ants we note a major departure from the true process and are lead to the conclusion that at least a proportion of the relationship between emigration time and quorum threshold (see Figure 3) is artificially created by the quorum threshold simply limiting the rate at which passive ants are recruited to the nest (i.e. prequorate slow tandem running must proceed for longer to reach higher quorums at which point postquorate fast social carrying starts) rather than exclusively taking the active ants longer to reach a quorum (decision) amongst themselves. The recruitment strategy contains another point of note in that recruiters will attempt to recruit an active ant from the home nest that is yet to start scouting before any others. The only way that a recruiter could be aware of an active ant in the home nest would be if she first travelled there which is not noted in observed emigrations and would seem to be a gross inefficiency in the process if it were part of the true strategy.

4.4

Implementation

The AH-HA model was supplied in the supplementary materials accompanying the publishing. An executable was not provided rather relatively pure Java classes that require a number of libraries contemporary to its publishing in 2006. The most critical to the program’s execution is the RepastJ agent modelling library. RepastJ is published under a BSD license and the required version (Repast 3.0) is supplied in the supplementary materials. Also required in order to run the Repast GUI and plotting functions are the CERN Colt, Ptolemy Ptplot and Teatrove Trove libraries that are similarly distributable and supplied. Those wishing to build the Trove library should note it specifically requires the Java JDK version 1.3.

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Figure 3: AH-HA Speed accuracy tradeo↵ for start scouting probability s set at 0.26 Mean values displayed from 140,000 runs ranging over the parameters published in [Marshall et al., 2006]. Number of active ants = 52, colony size = 208. 4.4.1

Repeating Results

Using the parameters used in their investigation the model predicts the speed accuracy trade-o↵ as described (Figure 3). However the a↵ect of quorum on emigration time is not as pronounced as one might expect and the disaster situation, represented by very low quorums, does not achieve any benefit below 10 ants and little below 20. [Pratt et al., 2002] report quorums of 10 20 in benign conditions and so it is surprising not to see sensitivity in the model to parameters in this range. Figure 4 a and d shows that without assessment noise and cost as the nest preference switching probability increases beyond 0.06 perfect decisions can be achieved at a quorum threshold of 1 with no adverse e↵ect on emigration speed. Increasing assessment noise d f then dampens the e↵ect of increasing the nest switching probability and increases the role of quorum threshold in the decision time achieved. By then also increasing the assessment cost we see in d that increasing the nest switching parameter forces increasingly longer emigrations. These findings are in agreement with those published in [Marshall et al., 2006] and show that in their experimental set-up assessment noise and cost are necessary features of the system in order to show a trade-o↵ between speed and accuracy.

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a)

d)

b)

e)

c)

f)

Figure 4: Paper Results from Original AH-HA. ”Results of systematically varying preference switching probability, assessment cost and assessment noise in the AH-HA model. Plots demonstrate the e↵ect of varying these three parameters on the speed-accuracy trade-o↵, by showing statistics for speed dependent on quorum threshold, and accuracy dependent on quorum threshold: (a) mean accuracy for minimum quorum threshold (T=1); (b) slope of line of best fit for accuracy; (c) rank correlation coefficient (rs) of accuracy with quorum threshold; (d) mean speed for minimum quorum threshold (T=1); (e) slope of line of best fit for speed; (f) rank correlation coefficient (rs) of speed with quorum threshold.” Thanks to James Marshall for providing the Java class ”Analysis” missing from the supplementary materials but mentioned in the included readme, future investigators will be pleased to read that it is included in the supplementary materials.

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4.4.2

Supplied Code Analysis

Quorum The suspicions raised from our early analysis turn out to be correctly placed. The AH-HA model’s measure of active ant quorum is not the number of ants in a nest rather the number of ants who have accepted the nest as their preference. The quorum in/decrementing functions are only called when: 1. an active ant discovers, assesses, accepts a new nest and begins recruiting (Ant.java:472/3). 2. an active at is recruited to, assesses, accepts a new nest and begins recruiting (Ant.java:111/112) 3. an active ant recruiting to another nest discovers (during her search for a recruit), assesses and accepts a new nest and begins recruiting (Ant.java:509) 4. an active ant recruiting to another nest discovers (following a successful recruitment to her prior preference), assesses, accepts a new nest and begins recruiting (Ant.java:509) 5. A passive ant is transported to a new site (Ant.java:545) With this being the case the quorum value at a site is not going to be particularly changeable as ants are more likely to upgrade than downgrade their nest choice i.e. active quorum at a better nest site is only likely to increase and visa versa for second best nest options. There is no notion of current location in AH-HA, only ant active ants current and preferred nests are known to the program. Recruitment Rooted in a similar cause to the quorum accounting, the active ant recruitment strategy in AH-HA is relatively deterministic and reliant on information that would not be available to ants in the true process. Active ants are only recruited when they are yet to find a nest option. If no active ants meet this criteria a passive ant is recruited without consideration of quorum. This means that once all the active ants have found any of the nest options the way the active quorum at any site can further increase is via discovery rather than recruitment only. Furthermore the decision on whether to recruit via tandem running or social carrying is taken on the basis of the (incorrect) quorum measured at the moment of recruiting another ant to the site. This information would not be available to the recruiter as they have, by definition, left the nest some time previously. By providing global information to the agents in the system, the benefits of taking an agent based approach to modelling the process is almost completely eroded. As the behaviour of the agents is not based on local information. Results With the model untouched from its published state we are able to arrive at the same conclusions as published in [Marshall et al., 2006]. There is, however, a discrepancy between the parameters stated in the paper and the parameters set in the model. The start scouting probability s di↵ers by an order of 20

magnitude in the paper (0.026) and the code (0.26). s defines the rate at which ants leave the home nest in search of alternatives, and thusly limits the rate at which the nest alternatives are found before scouts assess and begins recruiting to the nest. Setting this parameter low increases the likelihood of scouts being recruited to nest option by ants that left the home nest before them, before they have a chance to independently discover a nest for themselves. Figure 5 shows the speed accuracy tradeo↵ in the model when s is set at 0.026. We noted from Figure 3 that with s set at 0.26 the speed accuracy tradeo↵ is shown by the model. However when the s is set to 0.026 we see the tradeo↵ is destroyed and in fact the model shows a quorum threshold of 25 30 is optimal. We can conclude therefore that the its was the author’s intention to run the model with s set to 0.26 rather than 0.026 as stated in the text.

Figure 5: AH-HA Speed accuracy tradeo↵ for start scouting probability s set at 0.026 Mean values displayed from 140,000 runs ranging over the parameters published in [Marshall et al., 2006]. Number of active ants = 52, colony size = 208. As we know that only active ants that have yet to accept any nest option are available to be active recruits, by decreasing the rate at which active ants discover their first nest (as a result of their starting scouting with probability s) more active ants are available for recruitment. It is this active ant recruitment that hinders the progress of emigrations at low quorums as more active ants are transported by social carrying after which they consider the nest they have been placed in as the home nest and only recruit if they find a better nest option. By requiring larger quorums the time it takes nests to achieve their quorum takes longer and therefore increasing the quorum means more active ants will both participate in the quorum and actively recruit. We then see the tipping point of this gain at quorum thresholds between 25 and 30 as this equates to 21

half the active population of ants. The delay afterwhich simply caused by it requiring longer for the number of ants required for the quorum to discover or be recruited to the nest.

4.5

Ported Code

Although still usable, the original AH-HA code base depends on a number of out-of-date libraries for which documentation is limited. In order to make the model more accessible for this and future investigations, it required porting to use modern libraries. The latest iterations of the Repast library provide a wealth of data gathering, visualisation, distributed batch running and parametrizing and batch running features that are limited or non-existent in the version used by the original code. Porting the original code to the latest version allows us to take advantage of these additional features and makes Repast (Repast Simphony 3.3) the only dependency required by the model for future investigators. Following the discussion and rather strange results of the previous sections a number of data gathering methods to allow further analysis of the membership of nests is required. Principally we need to investigate the method with which ants, passive and active, become contributors to quorums at nest options as everything points to this process being flawed. The AH-HA code is driven by a single class specifying the behaviour of all active ants. Passive ants exist only as number contributing to quorum at a nest. The active ants share an instance of a colony and each ant has a nest, that in turn has neighbours of the other nests in the simulation. The logic defining the majority of the emigration behaviour is included in the 164 lines of nested conditionals in the ant update function and as such requires particularly fine attention in order to modify the code to extract data beyond that originally intended by the software.

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a)

b) Figure 6: Nest membership and current action over sample emigration with s = 0.26. Horizontal line shows colony quorum threshold and the vertical line shows the tick on which the quorum was met at the nest. Worse quality = 20 and best nest quality = 50. 23

a)

b) Figure 7: Nest membership and current action over sample emigration with s = 0.026. Horizontal line shows colony quorum threshold and the vertical line shows the tick on which the quorum was met at the nest. Worse quality = 20 and best nest quality = 50. 24

Figures 6 and 7 show the output of these extended data gathering tools and confirm our earlier conclusions. Firstly, and the most readily apparent, these graphs shows the prequorate recruitment of passive ants. This behaviour is contrary the results from observation of emigrations and undermines the use of quorum as decision making tool. As the rate of recruitment of passive ants increases once the quorum has been met as the active ants switch from tandem running to carrying the quorum threshold in the AH-HA model only serves as a speed limit for the emigration. Figure 6 shows the membership of both nest options over a sample emigration using the parameters used to produce the results in [Marshall et al., 2006]. With an s value of 0.26 all the active ants start scouting and discover a nest in the first ten seconds of the emigration. From our analysis of the recruitment strategy we know that this prevents any further recruitment of active ants and in accordance we see that no active ants are either led or carried to either nest, they only switch. Figure 7 confirms the recruiting strategy as we see a small number active ants are led to both nests as the lower s value results in them leaving the home nest after other active ants have started recruiting to an alternative nest.

4.6

Conclusions

The analysis in this section in this section has shown severe shortcomings in the approach applied by the AH-HA model. The output of the original model provided results that prima facie indicated it modelled the true process. However as we know correlation is not causation and further analysis has shown that by using an incorrect measure of quorum and implementing a flawed recruitment strategy the model realizes a relatively deterministic selection process; with the stochastic elements providing enough noise and variation in the results not to call attention to this fact and not a collective decision making process as it intends. In summary we have noted the following shortcomings in the AH-HA model: • Recruitment strategy allows for the prequorate recruitment of active ants. • The only case in which an active ant contributes to the quorum at a nest that it is actually located inside is when it is reassessing it following a successful recruitment. The rest and majority of the active quorum is made up of ants in the arena recruiting or assessing other nests. • Recruiting ants make use of information that either they would not have access to in the true process or they are not subject to sufficient delay to account for them gaining this information. • Speed accuracy tradeo↵ reliant on unrealistically high rate of independent nest discovery. • Agent level decisions made on the basis of global level data.

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5

Improving the AH-HA model

With the extent of the problems in the AH-HA model being so great and no separation in the code of the di↵erent state behaviours, in the interest of ensuring accuracy, modifying the model to remove these issues is prohibitive. It is therefore necessary to redesign the model from the ground up, which has the added benefit of allowing the inclusion of more recent findings on ant emigrations. This section outlines the design and implementation of this system along with preliminary analysis.

5.1 5.1.1

A new model of Ant House Hunting States

Figure 8 shows the state transition diagram for the proposed system. For clarity in planning, explanation and implementation two addition states to those in the AH-HA model have been defined. The most drastic departure from the AH-HA nomenclature is the inclusion of a Canvasser class. These are ants in the arena that are waiting to recruit (see Equation 5). The other new state is PreActive, these are active ants either in the home nest follow initialisation or active ants that have been recruited to a alternative nest via social carrying that are waiting to start scouting for nest options (see Equation 2).

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Figure 8: Class diagram of Ant (and child) classes in the proposed model. Diagram details state actions and transitions on a single tick during the simulation. Gold indicates states when contributing to nest quorum. 5.1.2

Architecture

Figure 9 shows a class diagram for the ant class in the proposed model. To complement the state separation used to design the model in theory this separation has be incorporated into the architecture of the program. By implementing 27

polymorphism and inheritance we are able to keep the code for the various behaviours separate allowing us to modify the di↵erent state behaviours without fear of encountering unexpected side e↵ects. Ant class This is the super class that all other ant classes extend. Ants have a location in space and are a member of a colony. The runtime of Repast operates using the principle of a context objects in the context can be scheduled to update at an interval. In our case every object in the context updates every tick. At the beginning of each tick the environment identifies all the objects in the context and proceeds to iterate over them. It is this behaviour that necessitates the inclusion of the toRemove flag and endTickUpdate method. When the model requires an ant to change state a new ant of the relevant class is instantiated and added to the context with the toggleInContext method. The ant it replaces must remain in the context until the end of the tick as it is found in the Iterable of all context object Repast created at the start of the tick. By setting the toRemove and setting the ant’s current location as something other than the arena or any of the nests we ensure firstly the ant is unable to perform any actions and also no actions are performed upon it. At the end of the tick the endTickUpdate method is called by Repast and removes the ant from the context for the next tick. Passive and Recruitee class The passive and recruitee classes are empty classes that provide distinction within the program. Another way of approaching this problem would have been to include an enumerated type that defines the state as there is no di↵erence in behaviour. But defining them as separate classes gives little overhead compared with enumerated types and compliments the running of Repast that allows for straightforward querying objects in the context by their type. Active class The active class extends the ant class’ functionality with the currentNest and distanceTravelled properties. As assessments are made relative to and recruitments are made from an ants home nest active ants must have a concept of which nest is theirs. The distanceTravelled property is incremented in the method described previously every timestep and used to define when a scout arrives at a site, in the calculation of recruit probability (see Equation 3) and the delay incured during a recruitment act. PreActive class For the same reasons that led to the inclusion of the Passive and Recruitee classes and empty PreActive class is used to provide distinction. Scout class On instantiation scouts are assigned a nest to discover using a probability weighted by di↵erences in their respective distances. The distanceToTravel property is then set to this value. As timesteps elapse in the simulation the scout reduces the distance to travel by drawing distances using the method

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previously described. On completing its traversal of the arena scouts arrive at a nest and become assessors. Assessor class Probably the simplest class that includes any logic. Assessors wait in the nest they are assessing for a length of time set as a parameter of the model. On completing their assessment the quorum at the nest is considered to inform the recruitment method to use. Canvasser class Each timestep canvassers attempt to recruit in accordance with Equations 3,4 and 5. If their preference is prequorate and the canvasser fails in their recruitment attempt as a result of Equation 8 they return to their preferred nest and become and assessor. If their preference is prequorate and they succeed in recruiting an active ant they become a recruiter. If the nest has reached its quorum and they fail to recruit an active ant they return to the home nest and recruit a PreActive ant if any are present and failing that a passive ant is recruited. Recruiter class Recruiters simply wait in the arena for the length of time it takes to travel the distance to their preferred nest. On arriving at their preferred nest they drop o↵ their recruitee that becomes an assessor if recruited by forward tandem running, PreActive if previously active ant recruited by social carrying or remains passive is passive previously. On dropping o↵ their recruitee recruiters make another assessment of the nest.

Figure 9: UML class diagram of Ant (and child) classes in the proposed model.

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5.2

Reconsidering the model

Having analysed and noted the weakness of the previous approach we have a number of features that we have deemed necessary in delivering a useful and accurate model. Here the new approach to these features are described and justified. 5.2.1

Starting scouting

We have shown in the AH-HA model how the value of the start scouting parameter could have a profound a↵ect on the model’s running. By setting this parameter high we find that all of the active ants independently discover the nest options in short succession of the emigration commencing. To overcome this problem and to avoid the use of magic numbers that have no basis in the science we propose a probabilistic mechanism that considers the number of active ants that have already left the home nest and suggest that the rate of leaving the nest is proportional to the number of active ants that are still in the nest. Such that: P (startScouting) = numberActiveInN est/numberActiveInColony 5.2.2

(2)

Quorum sensing

As we know the active ants gauge the level of consensus in the colony that they nest choice is indeed suitable by the number of ants that are in the nest, we therefore will take the number of ants in a nest as the measure of quorum. From [Franks et al., 2009] we know that having visited a nest ants will make a number of return visits proportional to the quality of the nest and make assessments. It is these return visits coupled with initial assessments and returning recruiters that make up the prequorate quorum at a nest. Our approach is then to have ants that have returned to the arena and been unsuccessful in recruiting another active and not recruited to another nest to return to their preference and reassess it. On completing a recruitment to their preference ants also will make another assessment of the nest. It is on leaving their preferred nest to seek for a recruit that ants receive the quorum measure dictating their decision to tandem run or social carry a recruit when they find one. 5.2.3

Concept of physical space

Incorporating and extending our method of quorum sensing, a notion of location in physical space is to be included in our model. That is to say ants at any one time can either be located in a nest or the arena. Recruitments occur in the arena, assessments occur in the nests. Coupled with this we introduce the notion that ants travel a certain distance in each timestep, the maximum distance an ant could travel per-timestep is defined and the di↵erence from this limit drawn from a normal distribution with mean 0 and standard deviation a parameter of the model. 30

5.2.4

Decision to recruit

There are two schools of thought on the mechanism with which ants decide to recruit to a nest and how long they take to do so. [Franks et al., 2009] suggest that ants delay their recruitment to a nest in inverse proportion to the quality of the site. With worse sites realising a greater delay before being recruited to; this give those considering recruiting to it longer to either discover another nest or be recruited to another nest. Another, more recent study [Robinson et al., 2011] that included investigators from the aforementioned, concluded that ants make the decision to recruit to a nest probabilistically, with the probability of recruiting to the nest proportional to the nest quality. Our approach to modelling this behaviour is therefore: P (travelledF arEnough) = distanceT ravelled/homeN estReturnDistance (3) P (nestSuf f icientQuality) = assessedQuality/maxN estQuality (4) where maxN estQuality is a parameter of the model. P (recruit) = P (travelledF arEnough)P (nestSuf f icientQuality)

(5)

Equation 3 gives us the property that the further an ant has travelled from a preference without successfully recruiting they more likely they are to recruit to the nest. Equation 4 weights the system in favour of nests of better quality. By combining these two probabilities we force ants looking for a recruit to search for longer the worse the quality of their discovered nest. Thus increasing the likelihood they will be recruited to a better nest if it exists or taking longer to return to they nest they have discovered and reassessing it and hence adding to the quorum there. 5.2.5

Recruitment strategy

The major issue of prequorate recruitment of passive ants is relatively straightforwardly implemented; it is the recruitment of Active ants that needs relatively careful thought. There is little evidence in the literature as to the specifics of the recruitment strategy among active ants. We know that active ants recruit among themselves before a quorum is met after which both active and passive ants are available for recruitment. The recruitment of ants to one nest interrupting the recruits assessment of another is not noted. From our analysis of the AH-HA models we acknowledge the pitfalls of supplying ants seeking a recruit with information that, in reality, they would not have access to and so the only robust method of approaching the problem with its current understand is to make it a stochastic one. As what we can be sure of is the more ants in a particular state there are in the arena the more likely they are to be recruited. We therefore propose the following approach to prequorate recruitment: P (recruitActiveF romColony) = arenaN umberActiveAnts/colonySize (6) 31

P (recruitClassF romActive) = arenaN umberClassAnts/numberOf ActiveAnts (7) P (recruitClass) = P (recruitActiveF romColony)P (recruitClassF romActive) (8) With such a method of recruitment can ensure proportional representation of the active classes in those recruited. This approach should still be viewed as an abstraction that warrants further investigation when empirical evidence is available. But it serves our purposes better than a deterministic approach as the true strategy will almost certainly be some function of this measure, as ants must be less likely to recruit an ant when they are less likely to come into contact with it. There is still a small issue of the recruitment strategy among ants that are both attempting to recruit to a site (be the sites the same or di↵erent). While a tandem leader is widely viewed to be the instigator to the recruitment act, it takes two to tandem and therefore requires the engagement of both parties. A basic approach would just be to rely on the way the program iterates over the ants in the simulation and allow the first ants that attempts a recruitment to be successful. However, by leaving this mechanism to the running environment rather than specifying it we leave open the potential for unexpected behaviour. The approach we have applied is to allow the canvasser that considers their nest to be better to become the recruiter, regardless of whether the nests are the same. Although this approach does not cover the first to ask first to get approach that relying on the program execution would provide, it does cover both the cases that canvassers to better nests make better cases for their nest when negotiating with another canvasser and that the canvassers make direct comparisons on their preferences perceived quality.

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6 6.1

Evaluation Speed Accuracy tradeo↵

Figure 10: Speed accuracy tradeo↵ in proposed model. p equal to 0.008, colony of 200 ants 50 active ants. With the reimplemented model we see results much more akin to those we would expect following earlier discussion. The first major point of note on the output of the new model is the need to plot the time to completion on a separate axis. The time taken to emigrate in the new model is significantly longer the predictions of original AH-HA model. We can largely attribute this to the fact that active ants just spend less time contributing to the quorum as only a minor portion of their time is spent assessing nests relative to the time spent canvassing and recruiting. This will lead to a fluctuating active quorum at the nest options that will slowly build as ants are recruited to the site and they and their recruiter make assessments. This e↵ect is shown in Figure 13 where we see the passive quorum at nest sites only building after quorum is met and the active quorum fluctuating as assessors come and go from the nest.

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a)

b)

Figure 11: Results of Pairwise T-Tests for 1,000,000 runs ranging over the parameters used in [Marshall et al., 2006], with the exception of quorum threshold, the test value, for a time to evacuation of original nest and b quorum at best nest at completion. We also notice the model predicts far lower accuracy (i.e. the number of ants in the better nest) at low quorums than the original model; which again is to be expected. Extremely low quorum thresholds signify disaster conditions for the ant and compels assessors to accept any port in the storm. The astute reader will also notice the nest quorums do not sum to the total number of ants in the colony and that the sum quorum at the nest alternatives increases with quorum. This is due in part to lower quorums resulting in more active ants being carried to either nest option and so therefore are unable to recruit to it rather scout for preferred nests. Leaving those that have been carried via social carrying to the best nest scouting for the rest of the emigration. The other part of this number can then be attributed to the greater of passive ants that are being recruited by the larger cohort of recruiting ants and are yet to arrive at either nest at the moment the emigration ends (i.e. evacuation of the original nest). The tables of T-Tests in Figure 11 show the results of testing the null hypothesis their is no significant di↵erence in the speed or accuracy predicted by the model across the tested quorum thresholds. They show, statistically, that the model displays a speed accuracy trade-o↵ across all values that result in successful emigrations. We see zeros across the board for both tests due to the extremely large sample size. The pareto front of the speed accuracy tradeo↵ is plotted in Figure 12. Beyond quorums thresholds of 20 the simulated colony rarely evacuates the original nest in our model with colony size of 200 and 50 active ants. It might been seen as a criticism of the model that even at the maximal quorums that allow emigrations to actually take place a higher mean accuracy than 65% is not seen. Under low stress conditions we would expect to see the model approach unanimous decisions in the range preceding the point where the quorum are unattainably high. As there is a maximum of 50 active ants that are more likely than not to be out in the arena at the moment the emigration finishes and by definition at least one passive ant must be in the arena at the moment of completion as they were the last in the original nest, then the missing 35% of the colony (70 ants) from the best nest quorum is reasonably attributed to these ants.

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Figure 12: Mean emigration speed plotted against emigration accuracy (taken as the proportion of the colony in the best nest) resulting from the proposed model over 1,000,000 runs. Quorum threshold at point shown in red.

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a)

b) Figure 13: Contributors to the active quorum at preferred nest during sample emigration. Colony size of 200, 50 active ants, p 0.008 and quorum threshold 20. For best nest a and worse nest b. Horizontal lines show quorum threshold, vertical lines show the start of the last prequorate recruitment. 36

6.2

Nest quorum

The plot shown in Figure 13 is the equivalent to the nest membership plots show for the original AH-HA (Figure 7). Compared with the original models output we see a very di↵erent picture of how the nests achieve their quorum. Rather than the steady increase we saw earlier we note peaks and troughs in the nest quorums as ants either discover, switch to or reassess the nests. Slowly the better nest attracts more ants but we see that is not the job done; an element of chance is involved in sufficient ants returning to the nest at any one time in order to exceed the quorum threshold. This is clearly demonstrated when we consider the behaviour shown in the plot around the horizontal line that shows the tick that the last prequorate recruitment act started. Firstly we note that the nest had already exceeded the quorum threshold five times previously and recruiters had already started retrieving passive ants from the original nest. But due to the coming and going of the active ants from the nest the quorum was not maintained; The passive ants arriving at the nest can be seen as the beginning of the end in the decision making process. As the proportion of the quorum at a nest made up by passive ants increases, the need for passive ants to return lessens in order to maintain the quorum. It is only once the number of passive ants in the nest exceeds the quorum threshold that the decision is final and the colony accepts the decision.

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7

Conclusions

This project had a series of objectives: 1. Acquire and make executable the original AH-HA implementation to facilitate this and future studies. 2. Port and extend the original model to allow data gathering beyond the scope of the original implementation and the publishing it accompanies in order to gain further insight into the behaviours that lead to the conclusions resulting from it. 3. Provide in-depth critical analysis of the AH-HA model using the extended data gathering features. 4. Evaluate the analysis of the original model and provide grounded solutions to it’s shortcomings. 5. Implement a new model incorporating these suggestions. 6. Repeat the earlier analysis on the new model to show the benefit of the additions and modifications. Through this process we have seen that the original AH-HA model su↵ered from a number of shortcomings that invalidate the conclusions resulting from its output. By allowing biologically impossible actions and behaviour known specifically not to occur in the true system we are able to dismiss their findings. Having ascertained the cause of these shortcomings and investigated their e↵ects we have been able to propose alternative implementations of these behaviours and incorporated these into the a new model; which has then been tested using the same methods that lead to the earlier criticisms to establish their success.

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