Using Physical and Computer Simulations of Collective Behaviour as an Introduction to Modelling Concepts for Applied Biologists

Abstract

Models are an important tool in science: not only do they act as a convenient device for describing a system or problem, but they also act as a conceptual tool for framing and exploring hypotheses. Models, and in particular computer simulations, are also an important education tool for training scientists, but it is difficult to teach students the value and use of models as a conceptual tool in their own right. Within the applied and whole-organism biological sciences, students often enter their courses with little trust of their mathematical abilities, and teaching them that scientific models are tools that they can engage with themselves is arguably a difficult task (especially given limitations in curriculum time and prior background knowledge). Here, I describe a half-day practical session designed to introduce modelling concepts to undergraduates on an applied biology course. This practical follows a progression from observation of a natural phenomenon (flocking behaviour in animals), to hypothesis formation, and then simulation of these hypotheses using a mixture of physical activity and individual computer work using agent-based models. Discussion focuses on why physical activity may be important for the students to be able to properly understand and appreciate the computer simulations.

Keywords:

• flocking
• complexity
• group behaviour
• simulations
• teaching/learning strategies

Introduction

Practicing scientists clearly understand the importance of scientific models and model creation as a conceptual tool within science (van Driel & Verloop, 2002; Van Der Valk et al., 2007). There is an appreciation that scientific models not only act as a ‘toy’ system to describe complicated ideas, but also allow the exploration and refinement of these ideas in a way that would perhaps not be possible just by empirical observation. Model creation is a fundamental part of the scientific process and students need to be grounded in the process of creating, formulating and testing models of their own (Schwarz & White, 2005). They need to understand the underlying processes and assumptions behind creating models (‘metamodelling’ by the definition of Schwarz & White, 2005) in order to be able to engage with the value of models. However, teaching students about the purpose and function of models is no easy task, if the aim is to empower them to use and create exploratory models of their own. Most of the models that students experience are only used as ‘toy’ representations of real phenomena — for example, Akpan (2001) catalogues the many representative models used in biological education — and in many cases it is unclear whether the students are gaining any appreciation of the use of scientific modelling when they are using these representative models.

The various disciplines such as ecology, zoology, botany, conservation and experimental psychology that could be classified as ‘whole organism biology’ moved on from being just ‘natural history’ subjects to full-blown hypothesis-driven science when evolution was first formally acknowledged as a fundamental process behind observed phenomena (Darwin, 1859). Conceptually, these subjects rely on a rich range of hypotheses explored as mathematical models and simulations, and many of the most exciting advances in our knowledge in these fields has come from hand-in-hand development of theoretical models with empirical work (see any modern textbook, e.g. Fox et al., 2001; Begon et al., 2006; May & McLean, 2007; Danchin et al., 2008). This means that students being trained as the next generation of whole-organism biologists need a thorough grounding in the use of conceptual scientific models as a tool for framing and exploring both hypotheses and data. Educators teaching whole-organism biology therefore need suitable tools for transferring this understanding to their students. However, in published studies of how science education works, a majority of the studies published focus on the ‘hard’ or lab-based sciences like physics and chemistry, and the field and life sciences that deal with whole organisms are deeply under-represented (Bowen Roth, 2007). Although using models as a conceptual tool may not be an immediate, day-to-day concern for many practicing whole-organism biologists, they are nonetheless a vital part of the scientific toolbox (as argued above), and a grounding in modelling techniques in addition to statistical techniques is arguably essential to prepare whole-organism biology students for their intended future careers (e.g. Burger & Leopold, 2001).

Here, I describe a practical session that has been designed to introduce modelling concepts and computer simulation to students taking an applied biology degree programme, specialising in animal behaviour. The aim here is to introduce modelling as a legitimate tool that is used by biologists to explore animal behaviour. Through a series of connected short activities using a number of different teaching modes, this practical introduces the process of model formulation based on the students initially observing and trying to explain natural behaviour, and introduces the concept of experimental simulations using both computers and physical activity. As well as giving the class insights into how modelling is carried out, all the way from hypothesis formulation to result analysis, this practical ultimately aims to persuade the students that modelling is a tool that they should trust rather than ignore.

Details of Practical

Background

The practical described here was developed specifically for teaching modelling concepts to second-year undergraduates enrolled in a Bachelor of Science degree in ‘Animal Behaviour and Welfare’ at the University of Bristol. The details described here are informed by iterative changes to the protocol used over six consecutive years (2006–2011), to teach a medium-sized group (between 12 and 20 students) of students on a degree programme where the students are normally taught a range of pure and applied topics relating to the biology and behaviour of animals.

This practical explores the flocking behaviour of large groups of animals, which was chosen because:

• the students are likely to have seen the phenomenon beforehand, either in wildlife documentaries or through eye-witness experience;

• there are lots of explanations about why it occurs, but the students are unlikely to have encountered them in much depth at this stage of their educational career, meaning that they should be open to considering multiple hypotheses for the phenomenon;

• the behaviour of flocks can be easily modelled with multi-agent models, and no prior knowledge is required to understand how the agents are behaving within the modelling environment;

• the emergent collective group behaviours thrown up by these multi-agent models are something that it isn’t possible to predict from verbal arguments, reinforcing the usefulness of models to the students;

• it is possible to reinforce the concepts used in the multi-agent models using physical activities prior to starting the computing component of the practical, enhancing the students’ understanding of how multi-agent models work; and,

• it is easily possible to make the simulations graphically appealing, with a simple user interface.

Aims of Practical

This quick introduction to behavioural modelling is intended to take place in a single period of teaching (or two sessions, if the initial seminar session is given earlier), which could take place in a morning or afternoon. The aim here is to introduce the topic for discussion, and then quickly direct the students’ thinking about modelling the process through the four stages of the Kolb model of learning (Kolb, 1981; Svinicki & Dixon, 1987), by immersing them in the problem and the simulation techniques that could be used to address it. In activities 1 and 2, evidence is presented that leads to reflective observation. Activity 3 encourages the students to step back from their observations, and derive some abstract concepts about the phenomenon they are studying. Activities 4 and 5 then give the students the opportunity to actively experiment and then consolidate their findings, through a mixture of physical activity and computer simulation.

Practical Activities

Activity 1. Seminar session (60 minutes)

This is scheduled time that is used to talk about using scientific models to model animal behaviour. The first part of the seminar is devoted to thinking about what models can be used for, and how and why scientists use them. Discussion time can be given to the relationship between modelling and the formulation and testing of scientific hypotheses (which the students have had some experience of, through introductory statistics courses). Care should be taken here to emphasise that modelling isn’t just hard mathematics, following on from the negative effect this could have on the students’ uptake of the information. The fact that verbal arguments, graphs and pictures can all be types of model in addition to computer simulations and explicitly mathematical formulations should be emphasised. The second part of the seminar can focus on questions directly relevant to the students’ curriculum (in the case of the cohort of students this practical was developed for, we consider how ‘motivation’ behaviour is modelled). This seminar does not need to be tied directly with the following practical work — it can easily be taught a week or so before.

Activity 2. Introduction of example system, with small group discussion of function (15 minutes)

As a class, the students are shown videos of large flocks of birds or shoaling fish, which are easily available from the web: the students that this practical is designed for are shown footage of European starling (Sturnus vulgaris) flocks, which during the winter can aggregate in flocks of tens of thousands of individuals prior to roosting at the end of the day (Carere et al., 2008). The film is shown with appropriate commentary on the animals’ natural history, but with no explanation about either the purpose of the collective behaviour, or the mechanisms involved in producing it.

After viewing the film, the students are split into pairs or threes, and given five minutes to talk about the purpose of the behaviour, and how large collective behaviours might be coordinated.

The class is then reassembled, and these purposes are discussed and recorded. Many suggestions are possible, but in order for Activity 3 to make sense to the students, some of this discussion should have focussed on how being in a flock could dilute the risk of predation, as well as the fact that being in a flock must provide some sort of fitness advantage to an individual (at least, compared to not being in a flock when everybody else is). See Krause & Ruxton (2002) for more discussion of the biological advantages of being in groups, and Bajec & Heppner (2009) for discussion of how a multi-disciplinary approach can be used for studying flock behaviour.

In discussion of how collective behaviours are coordinated, the students frequently start off by talking about one or two individuals acting as leaders. This is a good point at which to discuss whether it is possible for leaders to coordinate the movements of thousands of individuals at once, given that the flock is a dense noisy place, and movements are perhaps too coordinated for any one individual to be able to make decisions. Discussion should then turn to how collective behaviours can emerge from the actions of autonomous individuals responding to their immediate environment — it can be helpful here to add in some biological examples, such as the different forms of shoaling behaviour seen in fish, or trail-forming and nest-building behaviour in ants: Camazine et al. (2001) and Couzin & Krause (2003) give many good examples. Also, see Smith & Duncan (2011) for a different approach to using the simulation of collective behaviour to teach modelling.

Activity 3. Movement rule generation by small groups, leading to class discussion (10–15 minutes)

Having discussed the possible functions of behaviour, and having been introduced to the concept of emergent properties through the actions of autonomous agents, the class should again be split, and asked to discuss what sort of rules each individual should show. After five minutes, the class then comes back together, and directed discussion should take place — the following ideas about movement rules should emerge (and, from experience, did emerge without prompting from the students’ own input from the group discussion):

• Avoiding predators. The best place to be if you are trying to avoid predators is behind other individuals, and so a behavioural component where individuals move towards the centre of the group is useful. This follows on from biological arguments about the ‘selfish herd’ (Hamilton, 1971; Rands et al., 2004).

• Avoiding hitting other members of the flock. This can in turn lead to discussion about having a minimum distance of safety around each individual, and some sort of evasive behaviour kicking in if neighbours get too close.

• Staying with your co-flockers. There must be some functional disadvantage to not being in a flock, or else the birds wouldn’t be flocking. Since the flock is moving at speed through space, then tending to move in the same direction as everyone else means that an individual will tend to stay with the flock.

These concepts are analogous to the three basic movement and turning rules proposed by Reynolds (1987) in his influential ‘Boids’ model, although it should be emphasised that these are only one possible set of rules. For other possible rule-sets, see for example Couzin et al. (2002), Rands et al. (2004), Morrell & James (2008), Conradt et al. (2009), Sumpter (2010), and see Rands (2010) for general criticism of the assumptions that go into these models. Discussion should focus on the fact that flocking animals can’t be static, and that their behaviour has to account for how the physical momentum of both the focal animal’s own movements and those of its flockmates when they are moving.

Activity 4. Physical simulation of rules (20–30 minutes)

Having developed the set of rules given above, the students are now encouraged to try using them. To make sure they fully understand how each individual is following its own set of behavioural rules, the students initially act as the individuals within a ‘simulation’. A suggested protocol for this physical activity is given in Appendix 1. Here, the students are taken to a suitably large empty space (such as an exam room or large, flat field — although mobility is not an issue with the practical, care should be taken to ensure that no tripping hazards exist), and are then taught to move as rule-following agents, using a set of rules similar to those described in the ‘Boids’ model. This model relies on the agents only being able to turn through a limited angle during their orientation behaviour. This limit in turning angles is physically simulated by giving the students masks that limit their field of vision.

Although it is unlikely that the students will be following the rule-set with any degree of precision, they will get a feel for how collective group behaviour can emerge from the individual actions of a group of interacting agents, and it is likely that some sort of ‘flocking’ behaviour will be seen. After the practical component has finished, some open-ended class discussion should be given to how we could quantify and describe the behaviour seen.

Activity 5. Computer simulations of group behaviour (40–60 minutes)

Having derived the behavioural rules that individuals should show in activity 3, and then emphasised the role that individuals play within collective behaviours, the students now bring together this information by running individual simulations of their own in the computing laboratory, conducting a guided exploration of the effects that the model’s parameters have on the behaviour of the system. Several packages are available (many for free) that allow one to perform multi-agent simulations. I used an implementation of the Flocking model that comes in the ‘models library’ packaged with NetLogo (Wilensky, 1999), available to download for free at http://ccl.northwestern.edu/netlogo/. NetLogo is recommended here as it presents a good graphical interface, is straightforward to learn, and can be used to generate java applets embedded within simple HTML webpages which can be run on any machine using a suitable browser. Furthermore, NetLogo has a good track record of professional use (e.g. Rands et al., 2004; 2006; Smith & Conrey, 2007; Wilensky & Rand, 2007; Weisberg & Reisman, 2008; Rands, 2012).

The computing component of the practical should involve some directed exploration of several of the model parameters to give the students a feel for how models are used to generate data, and then some more open-ended questions that allow the students to explore the model. Questions at the end could then link the computing activities back to the original questions about how and why we can model the behaviour of ‘real’ systems. See the ‘Resources’ section below for details of how to obtain a worked example of how NetLogo can be used within a practical (written specifically for a cohort of students studying animal behaviour), with example worksheets and detailed discussion points exploring parameter manipulation.

Discussion

Schwarz et al. (2009) describe four transitional ‘levels’ of understanding the process of modelling: 1) models are seen as unchangeable entities that are either good or bad replicas of a phenomenon; 2) recognition by the students that models can be revised, but from a passive perspective (the student does not give input into changing the model); 3) the students become actively engaged in improving the explanatory power of the model; and, 4) the students not only understand that models are tools that can be adjusted to explain phenomena, but are also a legitimate means of both asking questions that can’t be easily addressed by experimental observation, and of experimentally exploring the validity of hypotheses. This practical is designed to shift a student’s understanding of modelling towards the latter two of these conceptual stages, meaning that they should be more open to discussion of conceptual models during the remainder of their academic tutoring.

Although it develops a conceptual shift, the practical may not have a large effect upon the students’ overall attitude to modelling (as has been suggested through discussion with the cohorts of students taking this practical). This would be unsurprising, given that the practical only takes an afternoon of activity. Within an applied course, this would represent a trade- off between teaching transferable scientific skills and relevance to the students’ own ideal curriculum (Schank, 1993/94). The time available naturally limits the depth to which scientific modelling concepts can be reinforced in the students. If suitable time were available, a greater degree of consolidation would be possible: for example, Schwarz et al. (2009) describe a longer-term sequence of curriculum stages that could be used to explore the process of modelling. These essentially follow a classical hypothesis-driven model of scientific discovery, where a model is constructed to address a phenomenon, and then tested and refined in light of the evidence. Longer term courses that did this (e.g. Hogan & Thomas, 2001; Winterstein et al., 2001; Voinov, 2002) would be very suitable for an ideal academic world without time constraints and with complete willingness from the students, but the practical presented here represents a step towards giving the students the necessary scientific skills they need, within the trade-offs in both time and attention.

The practical presented here could be run without the practical component, leading straight from rule formation to computer modelling. However, I would argue that jumping straight from formulating abstract concepts about the rule-sets conducted by individuals to using computers to simulate those rules would be an easy way of losing the interest and good-will of the students, thus missing the aim of the practical. It is likely that scientific computer simulations, programming, and modelling are novel, abstract concepts to a majority of the applied biology students. Moving from one abstraction to another could well cause moderate anxiety akin to that caused by mathematics or statistics in non-mathematicians (Betz, 1978; Onwuegbuzie & Wilson, 2003; Tomasetto et al., 2009). The practical component in this practical was designed to give the students the opportunity to explore the effects of the abstract rule set that they derived from the perspective of one of the animals that would ultimately be simulated within the computer models. Physical activity and object manipulation (where the student themselves are the objects in this simulation) are an excellent means of reinforcing abstract and novel concepts (Krontiris-Litowitz, 2003), and I would argue that this physical activity is absolutely essential to ensuring that the students are able to approach the computer simulations with enough prior knowledge to intuitively grasp the mechanics of the computational models, and thus develop their own understanding of how models can be used as legitimate scientific tools in their own right.

Resources

Details of the NetLogo simulation (written for NetLogo 4.0.4) are available on request, or can be downloaded from the author’s website (http://seis.bristol.ac.uk/~frsar/).

Appendix 1. Possible protocol for the ‘physical’ simulation (Activity 4), where the class act as individual flocking agents.

Figure A1 sketches a simple mask that can easily be created in bulk — the folding and cutting can be done prior to the practical, and string can be given out for the students to attach themselves. Prior to the session, the positioning of the masks’ eyeholes should be approximately measured such that when an ‘average’ student is wearing the mask, their visual field has an obvious ‘inner’ and ‘outer’ field as defined by the thick and thin sections of the eyeholes: the outer edge of the thicker sections of each eye-hole should be a little bit wider than the average inter-ocular distance of the class (I would recommend around 63mm). It’s recommended that the class is given a few minutes to decorate the masks and try them out, to allow them to engage with the idea of ‘being a bird’!

Figure A1 Sketch of simple mask, which can be made with a sheet of standard printer-sized paper. Cut along the solid black lines, and remove the shaded sections. Fold along the dotted lines, so that the top region is at the front, and, using a hole punch to make holes through both layers of paper, tie sufficient string to go around the wearer’s head.

Once the students are satisfied with their masks, they should be led to a room or field of sufficient size for them to comfortably ‘flock’ without hazard (bearing in mind they are walking around with impaired vision — institutional health and safety requirements may need to be considered here). They should then be asked to assemble in front of the class leader, with enough space around them such that they can move freely.

A few minutes should now be spent making sure the class understand how to rotate, using the eyehole edges as a guide for rotation angles. First, get the class to do a ‘small turn to the left’. This is done by getting the students to identify an object or feature of their environment that is visible where the left eyehole changes from being thick to thin. Having fixed on this feature, they should then turn their entire body so that they are facing directly towards this feature. Get them to do this a few times. Then get them to do a similar ‘small turn to the right’ — after the same number of repetitions, they should be facing in the same direction as they were when instruction started. They should then go through a similar process for a ‘large turn to the left’ and ‘large turn to the right’, where this time they are fixing and then turning towards a landscape feature that falls at the outer edge of their eyeholes.

Once you are satisfied that the students understand the difference between the ‘small’ and ‘large’ turns, and can accurately perform them, distribute them randomly within the open space. Rather than simply asking them to distribute themselves randomly (which is likely to end up in a non-random, even distribution of students), it is easier them to walk round randomly for ten or twenty seconds, and then order them to stop. Then, ask them to close their eyes and spin slowly until they are again asked to stop: this should generate a sufficiently ‘random’ distribution for the purposes of the simulation. Explaining how and why you have done this is important here, as initial random distributions are also used within the computer simulations described in the next activity.

With randomly distributed students, you are now ready to begin a ‘simulation’:

1. Ask the students whether there is another student within an arms-length of them. If so, they should do a ‘small turn’ in the direction that makes them turn away from their neighbour (or nearest neighbour, if there are several neighbours — if they don’t know which is nearest, it’s okay if they just guess).

2. If they didn’t have another student within arm’s reach (and didn’t just rotate), they should instead do two rotations. Firstly, they should estimate which direction all the other students they can see are facing in (it helps if they point this out during the first few turns). Having done this, they need to work out whether they can rotate to match this direction within the space of a ‘large turn’: if they are able to, they should turn to face the average group heading; otherwise, they should turn as much towards this direction as a ‘large turn’ will take them.

3. The students that turned to align with their ‘flock’ (but not those that were turning to avoid neighbours) should now conduct another turn. They should identify the centre of the group of flock mates that they can see. They should then conduct a small turn towards that centre (so this time, the maximum turn possible is limited by the smaller thick region of the eyeholes).

4. Finally, to avoid collisions with fellow students, walls, etc., ask any students who now in danger of colliding to turn round such that they aren’t going to hit anything. At this point, you should also reassure any students that didn’t turn because they weren’t near anybody and couldn’t see any flockmates that they don’t need to have turned!

5. Having turned (if required), the whole class should take one step forwards (perhaps telling them to squawk and flap their arms at the same time!). From experience, some of the students are likely to take really large steps, which could lead to collisions — they should be encouraged early on to take normal walking steps.

6. Continue to repeat (1) — (4), getting faster. It is recommended that the instruction set is ran through in full for the first few repeats, and then the instruction set gets sparser and repeats get faster until the students are essentially only being told to ‘turn’ and ‘step’.

From experience, it doesn’t take long for the class to start flocking in a similar manner to the simulations used in activity 5, at which point the class should be stopped before they get bored, and their behaviour should be described to them, with reference to the ideas discussed in the earlier activities. Arguably, this flocking may in part come from confusion by some of the students on turning directions, but the important message for the students here is that a large collective behaviour is emerging from their actions as individuals.

Acknowledgments

SAR acknowledges the comments and feedback of the undergraduates who conducted and guided the development of this practical in 2006–2010, and would like to thank Heather Whitney and several anonymous reviewers for comments on the manuscript.