Fig 1.
Sketch of the movement decision-generating process.
The figure shows an individual who has not yet reached the foraging site, at some intermediate timestep during a simulation. Within a timestep, all individuals make a single movement decision, and the order in which they do this is randomised. If an individual chooses to conduct a social movement, it then moves according to one of the rules sketched in Fig 2.
Fig 2.
Sketches of the four social interaction rules.
Each simulation only considers a single rule, which all individuals follow when they choose to socially interact.
Table 1.
Changes in an individual’s variables over the course of a simulation.
Fig 3.
The effects of the outward probability adjustment parameter ωdifference on timing of measures of group behaviour.
This figure compares the three social interaction rules with simulations where all individuals behaved non-socially. Within each panel, ωdifference is systematically increased from 0.0001 (dark green) to 0.0020 (yellow), with the colour gradient representing equally-sized increments of 0.0001 between these values, and other parameters are set as described in the ’model exploration’ methods. Each panel plots the results of a social rule against the non-social values, and the non-social results are therefore identical in the panels for the three different social rules, and are replicated here to allow comparison between social and non-social behaviour. The black diagonal line on each panel represents the scenario where social and non-social individuals are behaving identically; if points fall below this line, the measured behaviour is happening faster with the social rule; if points fall above the line, the non-social rule causes the behaviour to happen faster. The panels show A)–C) the mean time until the end of a simulation, indicated by the last individual moving to the foraging site that is dfood units away from the refuge; D)–F) the mean time an individual spends travelling between the threshold distance close to the refuge and the foraging site; G)–I) the mean time that an individual first passes beyond the threshold distance away from the refuge; J)–L) the mean latency shown by other group members to pass the threshold distance once the first individual has left; M)–O) the mean time at which the first individual arrives at the foraging site beyond dfood; P)–R) the mean latency shown by other group members to arrive at the foraging site once the first individual has arrived. All datapoints show the mean value (± SD) for 10,000 independent group simulations.
Fig 4.
Quantifying variability within and between parameter sets.
F values describing the ratio of within- and between-parameter-set variance for the mean simulation value of the six behavioural measures that were recorded, when the parameter being systematically altered was: A) probability adjustment parameter, ωdifference; B) baseline time-dependent probability of moving outward, pbaseline; C) distance to the foraging site, dfood; or D) group size, n. The shape and colour of the points indicates the social interaction rule that was followed within a simulation set.
Fig 5.
Illustrative examples of mean rescaled individual behaviour.
Panels compare non-social individual behaviour and the three social behaviours. Individuals are labelled 1–10, where 1 is the individual with the baseline levels of all parameters, and incremental increases in the label represent the incremental increase by ωdifference as described in the methods. This means that when all individuals within a simulation are behaving independently (non-socially), individual 1 is the least likely to start moving towards the feeding site (the shyest), and individual 10 is the most likely (the boldest). Panels A-D show rescaled travel times, where 0 is the travel time of the individual who reaches the feeding site in the shortest time, and 1 is for the individual who takes the longest; E-H show rescaled leave times (at which an individual first crosses a threshold 10 units away from the start point), and I-L show rescaled arrival times at the feeding site. A, E and I show the behavioural metrics for individuals behaving non-socially (independently) within a simulation; B, F and J show the metrics for individuals using the central social rule; C, G and K show the metrics for individuals using the nearest neighbour rule; and D, H and L show the metrics for individuals using the majority rule. All boxplots show the median and interquartile values of the mean rescaled behavioural metric, and the tails show 1.5 × interquartile range, with points representing outliers. Data shown for dataset where ωdifference has been systematically altered in order to explore variation in response to this parameter (200 replicates each for ωdifference = (0.0001, 0.0002, … 0.0020), pooling all of these simulations together for each of the figures), with pbaseline = 0.001, dfood = 100 units and n = 10.
Table 2.
F values describing the contributions of both the model parameter being varied and the ‘boldness’ of the individual within a simulation, according to the behavioural metric measured and the parameter being varied.
Fig 6.
Mean rescaled differences in behavioural metrics between the non-social rule and each of the social interaction rules for each individual.
Positive values mean that individuals switch the observed behaviour to later in the hierarchical group order when behaving socially, and negative values mean they switch to earlier in the group order when behaving socially. This means a value of 1 represents the case where the individual is always first to finish/leave/arrive when behaving non-socially, and always the last to finish/leave arrive when behaving socially, a value of -1 represents the case where the individual is always last to finish/leave/arrive when non-social and always first to finish/leave/arrive when social, and a value of 0 represents the case where the individual does not change the ordering of its behaviour between social and non-social behaviours (e.g. the third individual to arrive when performing a non-social behaviour is also the third individual to arrive when performing a social behaviour). A, B and C show the difference in travel time; D, E and F show the difference in leave time; and G, H and I show the difference in arrival time. A, D and G give the values when comparing the central and non-social rules; B, E and H, the nearest neighbour and non-social rules; and C, F and I, the majority and non-social rules. See the legend of Fig 5 for a description of the boxplot ranges and the parameter set used for generating the figure.