Loose coupling and human intervention promote collective foraging success
We first determined group search performance by assessing the average search time, consumption time, and total targets found in each movement condition with and without intervention.
Results showed that search performance as measured by mean trial time was better with loose coupling and human intervention, as seen in the lowest average trial times in Fig. 3. Movement type had a reliable effect on performance without human intervention, F(1,59) = 27.65, p < 0.001, ηp2 = 0.319, and with human intervention, F(1,59) = 20.85, p < 0.001, ηp2 = 0.261. The specific direction of effect was supported by post-hoc Tukey HSD comparison tests showing that loose coupling was significantly better than other movement types both with and without human intervention (each p < 0.001). By necessity, the same pattern of results was found when performance was measured by number of targets found per session: On average, more targets were found with human intervention (M = 16.94) than without (M = 5.89), and more targets were found with loose coupling (M = 16.26), compared with other movement types (M = 9.8). Human intervention did not interact with movement type, F(1,59) = 2.55, p = 0.116, ηp2 = 0.141, which indicates that human intervention resulted in more targets found on average per session for all movement conditions (M = 11.04), see Fig. 4 below.
Mean trial time per session as a function of movement type without human intervention (left) and with human intervention (right). Mean trial times are divided into their composite search times (red) and consumption times (teal).
Mean targets found per session as a function of movement type without human intervention (left) and with human intervention (right).
Next we broke the performance measure of mean trial time into its two component parts of search time (i.e. the time from start of a trial to when any of the agents detecting the target) and consumption time (the time from the first agent landing on the target to its complete consumption, which went faster as additional agents landed to share in consumption). Mirroring mean trial times, search times were fastest in the loose coupling condition regardless of human intervention: without, F(1,59) = 48.17, p < 0.001, ηp2 = 0.449, and with intervention, F(1,59) = 41.24, p < 0.001, ηp2 = 0.411, refer back to Fig. 3. Tukey HSD for both loose coupling conditions were significantly faster than all other respective movement conditions, p < 0.001. By contrast, consumption times were fastest in the flocking condition: without, F(1,59) = 542.2, p < 0.001, ηp2 = 0.902, and with intervention, F(1,59) = 56.79, p < 0.001, ηp2 = 0.49. All Tukey HSD flocking condition comparisons were significant, p < 0.001. Flocking produced faster consumption times because agents were usually clumped together when the target was found, so they all landed on the target to consume it together. This effect of flocking was predicted to occur, and we also predicted that the distancing condition would produce the fastest search times by means of a divide and conquer strategy. Results were not consistent with this latter prediction because adding flocking to distancing actually improved search times. We return to this unexpected result later when we present analyses of the rate at which agents collectively covered the search area.
Analyses of search times and consumption times as a function of human intervention found that, again mirroring mean trial times, human intervention improved search times substantially across all four movement conditions, albeit less reliably for loose coupling because of an apparent ceiling effect (loose coupling without human intervention already produced fast search times): F(1,59) = 22.24, p < 0.001, ηp2 = 0.086. By contrast, human intervention improved consumption times in most conditions, F(1,59) = 80.00, p < 0.001, ηp2 = 0.253, but surprisingly, humans caused slower consumption rates in the flocking condition, comparison Tukey HSD p < 0.001. The apparent detriment of human intervention on flocking consumption times can be explained by humans finding targets on their own, without the benefit of other agents nearby to join in consumption. This explanation is further addressed in the next section.
Loose coupling diversifies groupings of search agents
Collective foraging performance was best with loose coupling, which was predicted based on the hypothesis that loose coupling balances the benefit of flocking versus distancing. This balance should result in more flexibility in agent groups as they merge and split over time—the agents only partially affect each other’s movements, thereby allowing interactions between search agents to vary as they come in and out of view of each other. To quantify flexibility in grouping, we examined the distribution of numbers of agents in view for each given tick, trial, and agent. If groupings do not change much within each trial, then there should be little variation in the numbers of agents in view, and the distribution should have a sharp peak. By contrast, if groupings vary during a trial, then the numbers of agents in view should vary, and hence their distribution should be more spread out.
We used Shannon entropy to quantify the degree to which the frequency distributions in groupings were more peaked (low entropy) versus more spread out (high entropy). Entropy has been used previously for capturing the fission–fusion dynamics for various groups animal species32. Hereafter, we refer to it as Grouping entropy which was calculated as,(-sum [p({mathrm{x}}_{i})mathrm{ log}(p({mathrm{x}}_{i}))]) where xi is the number of agents viewed by (i)-th agent over time, and p is the probability associated with the proportion of time that xi agents were in view.
To focus on grouping entropy from the perspective of autonomous agents, we removed the human player from entropy calculations, and to make analyses comparable, we removed a simulated agent at random in sessions without intervention so that entropy was computed over zero to eight possible agents in view in both conditions. The first 14 ticks at the start of each new trial (when each new target was generated) was removed to avoid initial transients due to agents starting together from the previous target location. Entropy was computed over the subsequent ticks for each trial, up to the tick when the next target was detected by one of the agents. We also computed grouping entropy with respect to the human agent, and again we removed one autonomous agent at random so that entropy was computed over zero to eight possible agents in view.
Figures 5 and 6 show the proportion of agents in view aggregated over trials and individuals for each movement condition with respect to autonomous agents in the simulation (Fig. 7) and with respect to human agents in the experiment (Fig. 8). These histograms show that the rules governing agent movements and interactions had large effects on agent groupings. The random and distancing conditions were similar in that agents traveled solo much of the time, with another agent in view sometimes, and two or three more on occasion. Adding the flocking rule to each of these two conditions resulted in opposite effects on grouping entropy than the other movement conditions. Flocking agents constantly maintained each other within their respective fields of view, best shown in Fig. 5b. Flocking plus correlated noise (the random condition) resulted in all agents converging and moving together such that variability caused by noise was not enough to disperse the single grouping of autonomous agents once it was formed. By contrast, adding the distancing term to flocking (along with the correlated noise) was sufficient to counteract flocking and disperse agents such that their flight configurations varied over time. This variation resulted in more varied group sizes and hence more variability and greater entropy in the numbers of agents in view.
Normalized histogram of the number of agents in view during the search time period respective to one autonomous agent without intervention.
Normalized histogram of the number of agents in view during the search time period respective to only human agents.
Entropy values for simulated agents as a function of movement type (Random, Flocking, Distancing, and Loose coupling) in the experiment (with human) versus the simulation (without human).
Entropy values by movement condition (Random, Flocking, Distancing, and Loose coupling) for human players (Human) versus simulated agents (autonomous) in the experiment.
We tested the effects of movement type and human intervention on grouping entropy using two different statistical analyses. First, we tested entropy values for individual simulated agents with and without human intervention, as a function of movement type, as shown in Fig. 7. Entropy values were minimal in the flocking condition because agents were always in a unified group, so we removed this condition from statistical analyses. Second, we ran the same analyses after removing trials in the human intervention condition when the human player was first to find the target, so that entropy values were not directly affected by human intervention. The second analysis allowed us to ascribe differences to the effect of human intervention on the movements of autonomous agents.
We conducted a mixed-effects ANOVA with movement condition as a within-subjects factor, human intervention as a between-subjects factor, and entropy as the dependent variable. First there was a significant main effect of human intervention whereby human players caused autonomous agents to exhibit less entropy in their distributions over agents in view, F(1,59) = 21.43, p < 0.001, ηp2 = 0.058; and a marginally significant main effect of movement type, F(2,59) = 2.41, p = 0.091, ηp2 = 0.014. The interaction was non-significant, F(2,59) = 0.49, p = 0.613, ηp2 = 0.003. Individual post-hoc tests confirmed that grouping entropy was highest with loose coupling compared with the distancing and random conditions, p < 0.001. Human intervention appeared to decrease grouping entropy for autonomous agents by giving them less time to group by means of converging on targets. This decrease in grouping entropy was evident even in the random condition when humans had no direct effect on agent movements—instead, humans had indirect effects because they helped find and consume targets more quickly, thereby decreasing the time available for agents to converge on targets, leaving them less grouped and more disbursed in general.
In our second analysis, we compared the same grouping entropy measure as before but for human players against grouping entropy for individual simulated agents in the experiment with human intervention (Fig. 8). We ran another ANOVA like the previous analysis, but with intervention type replaced by agent type (human or autonomous) as a between-subjects factor, again excluding the flocking condition from movement type. We found that grouping entropy was greater for humans compared with autonomous agents, F(1,59) = 213.85, p < 0.001, ηp2 = 0.379, and grouping entropy was again influenced by the movement condition, F(2,59) = 8.11, p < 0.001, ηp2 = 0.044, with post-hoc tests showing that entropy was greatest with loose coupling, p < 0.001. There was also an interaction such that grouping entropy for human players was more like autonomous agents when the latter were loosely coupled compared with other movement types, F(2,59) = 16.9, p < 0.001, ηp2 = 0.088. Moreover, human movements exhibited the most grouping entropy when coordinating with loosely coupled agents based on our post-hoc comparisons, p < 0.001.
In summary, grouping entropy was higher, and performance was better, with loose coupling overall, and with human intervention overall (human intervention lowered entropy for simulated agents, but only as a byproduct of shortening time for them to converge on targets). We infer from the main pattern of results that collective foraging in our simulation benefits from loose coupling between autonomous agents as well as between agents and humans.
Human intervention benefits search performance for non-random agents
Entropy analyses in the previous section showed that human intervention decreased the grouping entropy of autonomous agents, even though performance was generally better with human intervention and with increased grouping entropy. Therefore, it is unclear whether human intervention improved the way that autonomous agents searched, or if humans are simply better searchers and therefore find and consume more targets than autonomous agents.
To test the search performance of autonomous agents themselves, we measured how fast they covered the game space when searching for each next target, and we compared their rates of search area coverage with and without human intervention as a function of movement type. Specifically, area search rate was computed as the number of unique pixels searched on each trial, divided by the time spent searching prior to finding the target, and converted into a percentage of total pixels (200 × 200 = 40,000 pixels).
To test more specifically how human intervention affected autonomous agents, we measured area search rate at both the individual and collective levels for autonomous search agents. For the individual level, search rate was computed per agent and then averaged to gauge how fast each agent covered space separately, whereas for the collective level, search rate was computed for all agents simultaneously to gauge how fast the group covered space collectively. Figure 9 shows area search rates for autonomous agents with and without human intervention (the human is always removed from rate calculations, and as before, trials were excluded when search was terminated by the human player finding the target first), for individual search as well as collective search. We used ANOVA models as in the previous results for grouping entropy, but with area search rate as the dependent measure instead, and flocking was included this time.
Area search rate for autonomous agents, averaged for each session, and plotted as a function of movement type and human intervention for agents individually (left) and collectively (right).
We found that human intervention improved both individual search rates and collective search rates, F(3,59) = 43.09, p < 0.001, ηp2 = 0.044, but had no effect on random movement conditions because humans had no direct effect on random agent search movements, all post-hoc tests p > 0.95. The benefit of intervention was greater for collective versus individual area search rates, F(3,59) = 17.28, p < 0.001, ηp2 = 0.018, indicating that human intervention reduced overlap in autonomous agent search areas, as well as reduced the degree to which individual agents returned to areas they already covered. Conducting a post-hoc Tukey HSD analysis found that individual area search rates were not reliably different between the flocking and loose coupling conditions, all p > 0.7, but collective search rates were greater with loose coupling compared with flocking, all p < 0.001. These results indicate that loose coupling preserved the individual diffusiveness of flocking agents, whose individual grouping entropy was relatively high. By contrast, the addition of distancing helped to reduce agent overlap—collective grouping entropy was highest for loose coupling—and thereby improve collective search performance.
Human search benefits from coordinating with loosely coupled agents
The previous section focused on the beneficial effect of human intervention on the individual and collective search performance of autonomous agents as a function of different movement rules. We can also test whether different movement rules have different effects on human search performance. In theory, human players could search on their own, unresponsive to the movements of other agents. However, to the extent that players try to guide or otherwise coordinate with autonomous agents, the efficacy of human search movements may be affected by the way agents move and coordinate. Results presented earlier showed that human intervention affected autonomous agents via their grouping entropy, and agents affected human players in kind. Given that human players showed the greatest grouping entropy when agents themselves showed the greatest grouping entropy in the loose coupling condition, we can hypothesize that human search performance may benefit from coordination with loosely coupled agents.
To test the effect of movement rules on human search performance, we computed area search rates for the human players individually. Not surprisingly, as shown in Fig. 10, humans overall covered the search space at a faster rate than the individual agents they foraged with, F(1,59) = 536.04, p < 0.001, ηp2 = 0.534. The exception to this overall effect was in the flocking condition where humans searched at about the same rate as agents they were coordinating with. Individual area search rates were relatively high for flocking agents because maintaining a single, steady bearing is a reasonably good strategy for covering a space with periodic boundary conditions.
Area search rate averaged for each session and plotted as a function of movement type and agent type for human players and individual agents with intervention.
We also found marginal differences in human area search rates depending on the movement rules governing autonomous agents, F(3,59) = 2.57, p = 0.055, ηp2 = 0.032. As predicted, a post-hoc analysis showed human search performance was better with loosely coupled agents compared with distancing (p < 0.001) and random (p < 0.01) movement conditions. Although no other comparisons were reliable, Fig. 10 shows that human search rates were also elevated when coordinating with flocking agents, which may be attributable to humans sometimes following the flock as they search at a faster rate than agents in the random and distancing conditions.
Taken together with results from the previous section, we can conclude that human players and loosely coupled agents benefitted from each other to improve search performance by virtue of flexibly coordinated movement patterns, as evidenced by higher area search rates along with higher values of grouping entropy.
Human players adapt their foraging strategies to agent behaviors
To this point, we have interpreted the result that human players improve collective foraging by means of memory and strategy, but the evidence has not been direct. It is difficult to infer specific strategies from game play data alone, but one apparent choice that players can make in collective foraging is the emphasis on finding versus consuming targets. Players may try to find targets with other agents following or not, or they may instead seek out other agents to collectively consume each target so the next one comes faster. Human players may improve collective foraging in part by adapting their emphasis on finding versus consuming targets based on the rules governing movements of autonomous agents.
To measure the emphasis on finding versus consuming targets, we analyzed the proportion of targets found versus consumed by human players as a function of movement type. As a baseline, if humans are no better than their autonomous counterparts, then they should find targets 10% of the time (0.1 proportion of times) and consume 10% of the target units (recall that each target consisted of 500 consumption units), given that the human player is one of ten foraging agents. The difference between finding and consuming proportions is a measure of the emphasis that human players placed on one versus the other component of collective foraging.
Figure 11 plots the two proportions for human players as a function of movement type. First one can see that both proportions were significantly above 0.1 in all movement conditions, all post-hoc tests p < 0.001. Greater-than-chance proportions are evidence that at least some benefit of human intervention for collective foraging comes from the superiority of human players, in that they both find and consume more targets than autonomous agents. Post-hoc analysis showed this benefit was reliably less in when agents were loosely coupled compared with other movement types, all p < 0.001, because loose coupling was the most effective movement rule.
Finding and consuming proportions for human players as a function of movement type. The red line indicates the expected proportion to be found and consumed if human performance was no better than that of simulated agents. Proportions above the expected baseline indicate the degree to which humans outperformed simulated agents.
Regarding adaptations in strategy, Fig. 11 indicates that the differential between proportions varied as a function of movement type, F(3,59) = 5.74, p < 0.001, ηp2 = 0.035. Specifically, players emphasized consuming targets over finding targets when coordinating with loosely coupled agents, t(59) = 4.96, p < 0.001, whereas players did the opposite when coordinating with flocking agents, t(59) = − 11.43, p < 0.001. This contrast is evidence that players adapted their strategy to the movement rules for agents—it was more beneficial for players to help with search when the collective area search rate was relatively low in the flocking condition, whereas it was more beneficial for players to help with consumption when collective area search rate was relatively high in the loose coupling condition.
Source: Ecology - nature.com
