Introduction

Colony success in social insects often depends on the colony's ability to mobilize workers and allocate them to where work is needed [1]-[4]. Accordingly, insects have evolved different ways to communicate in these situations, such as when nestmates must be recruited to valuable resources [1], [2]. One of the most remarkable means of recruitment is the honeybee waggle dance. Foragers perform this dance-like behavior inside the nest after finding a profitable food source or on a swarm during nest-hunting to advertise suitable nest-sites [3], [5]-[8]. Other foragers following a waggle dance learn the location and are subsequently able to fly to the area of the food source [8]–[12], where they use additional visual and olfactory information to localize the food [6], [8], [13], [14].

Only recently have attempts been made to quantify empirically the colony level benefits of this spatial information [15]–[19]. Surprisingly, these studies found that colonies would often not benefit from spatial communication [16]–[19]. For example, Donaldson-Matasci and Dornhaus [17] tested the effect of spatial communication in five different habitats, but found a positive effect of communication only in one. Dornhaus & Chittka [18] found benefits only in a tropical habitat, but not in temperate European habitats. These findings suggest that the benefits of spatial information strongly depend on the spatiotemporal distribution of food sources, a conclusion that is in agreement with theoretical studies [20]–[22]. Recruitment by waggle dances is costly in terms of time and energy [21], [23], [24] and it is thus conceivable that these costs outweigh the benefits under certain conditions, for example when food sources are easy to find by independent search (scouting).

However, the apparent absence of benefits resulting from spatial information use in many habitats could also be the result of confounding effects caused by the experimental designs used to quantify these benefits. In previous studies, researchers took advantage of the fact that honeybees are unable to perform oriented dances on a horizontal comb with no or only diffuse light [16]–[19]. It is thus possible to create colonies with oriented (with spatial information; SI) or disoriented (no direction information; NI) dances and compare the foraging success of colonies in these two conditions. Importantly, in these studies, colonies were kept in one condition for relatively short time periods (2 or 3 days in [16]–[18]; a variable number of days with a mean of ∼12 days in [19]) and repeatedly switched between the two experimental conditions (SI vs. NI), presumably to use paired statistical tests.

If a bee that was recruited on the last day of the SI treatment returns to that food source on the following day, the food she collects on that day will be added to the NI treatment, even though her success was a consequence of acquiring spatial information during the SI treatment. Thus, the continued availability of food sources combined with “site fidelity” (persistency) leads to confounded results and makes the interpretation of such data challenging. This seems particularly important since flower patches can remain in bloom for weeks or even months [25], and honeybees often return to the same foraging sites for days and up to 3 weeks [6], [8], [26]–[34].

Here we explored, using an agent-based simulation model, whether there is a benefit to the use of spatial information over longer periods of time than previously explored. We hypothesized that forager persistency causes long-term benefits of successful recruitment events, and therefore the benefits of spatial information might have been underestimated in experimental designs such as those used in empirical studies. Furthermore, we hypothesized that the degree to which results are confounded depends on various factors, including the duration of the experimental period, the longevity of food patches, the density of food sources, and the size of the colony.

Model Description

The present model is a spatially explicit agent-based simulation model (ABM) of two types of agents in a foraging context, scouts and recruits. We used NetLogo 4.1.3 to implement the model (Text S1), and we follow the “Overview, Design Concepts, and Details” (ODD) protocol in our description of it below [35], [36].

Entities, state variables and scale

Our agents were located on a two-dimensional square grid with 201×201 patches. The agents' nest was located on the center patch. Every other patch on the grid could either be void or contain suitable forage for our agents. Food patches were of variable quality (Table 1) and lasted for a limited number of days.

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Table 1. Overview of the model parameters and the values used in our simulations.

https://doi.org/10.1371/journal.pone.0104660.t001

The population of agents (N_default  =  300) consisted of two groups, the scouts (N_default  =  30) and the recruits (N_default  =  270). We used a default colony size of 300 agents, but we also tested other colony sizes to explore if results are sensitive to colony size. Colony size had no effect on the benefits of communication in a previous model [22] and was chosen to be similar to colony size in [38]. Honeybee scouts usually represent 5–25% of all foragers [3]. They search for food source locations without following waggle dances and have a high probability to abandon even rewarding food sources and search for new ones [39]. Scouts could assume any of six states: idle in the colony, scouting for food sources, feeding at a food source, returning to the colony, recruiting of idle foragers to the newly discovered food source, returning to the nest without having discovered food. Recruits decoded waggle dances to find a food patch, but they could also scout (Table 1) if they were unable to find a dancing bee [40]. Recruits could adopt any of 8 states: idle in the nest, idly waiting to be recruited, flying to food source, feeding on food source, returning to colony after feeding, recruiting new idle foragers, scouting for forage, returning to the colony without having discovered food.

Simulations were run in discrete time steps (t). We choose the model parameters (Table 1) such that one time step in a simulation corresponded to approximately 10 s real time, so that each simulated day was t_day  =  8640 time steps long, with days starting at 6:00 in the morning. The simulated world allowed foraging when the following condition was true: . Conditions were therefore suitable between 6:23 and 17:37 real time. There was no change of foraging time with the progression of a simulation run (no seasonal change), and all days were assumed to have weather suitable for the agents to forage all day long. Often plants offer nectar during the better part of the day, but in varying amounts and qualities [41]. With our parameters (Table 1), the width of a patch corresponded to ca. 100 m, e.g. a group of trees or a flower field, and the world expanded 10 km from the nest patch. No foraging occured on the central patch. This means that our agents could not exploit food sources that were closer than 50 m to the nest. The agents could occupy any specific location on the two-dimensional plane (i.e. they were not restricted to move on a lattice) at every point in time.

Results

Experiments 1: switch durations, density and foraging success

When there is no switching between SI and NI, spatial information transfer improves colony foraging success at all food source densities. The benefits increase when food resources are at lower densities (Figure 1; +2.5% at high density and +21.6% at low density). For all densities, the lack of spatial information leads to smaller variance in the colony energy intake compared to the situation where spatial information is always available (Figure 1).

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Figure 1. A comparison of foraging success measured as daily gain in honey under high, medium and low food densities, either with spatial information transfer (SI) or without spatial information transfer (NI).

Model runs lasted 48 days after an initial period of 3 days SI (the 3 day acclimatization period is not shown). The first row shows the pure SI (solid black line) and NI (dotted black line) cases. These baselines are also shown for the model runs where switching between SI and NI occurred (rows 2–4, black solid and dotted lines). Rows 2–4 show the cases for SI (white background)/NI (grey background) cycles that last 2 days, 3 days or 12 days respectively. All the simulations shown here started with the SI treatment on day 4. The last row shows the aggregated simulation results (means ± s.e.) for the three food densities and SI/NI cycles (solid circles: SI, open circles: NI) including the second set of simulations that started with the NI treatment on day 4.

https://doi.org/10.1371/journal.pone.0104660.g001

In contrast, when switching colonies back and forth between SI and NI states every 2 or 3 days, the benefit of the information transfer remain undetected in all situations except when food density is low (Figure 1). But even in this situation, the detected relative benefits of SI are substantially lower than in untreated colonies with SI (+4.4% and +5.4% vs. + 21.6%). Of the 3 experimental designs, the results most similar to the untreated condition come from colonies subjected to 12-day experimental periods. Here, colonies benefit almost as much when having SI (+6.6% compared to NI over all densities), as in untreated colonies (+8.8%). The explanation for the lower relative benefits in switch experiments can be seen in Figure 1: switching between experimental states causes considerable carry-over effects, so that the collected energy on the first day of a new cycle is strongly dominated by the previous cycle.

In our model, the difference between recruits and scouts in individually collected energy per day is higher at low food densities but diminishes at higher densities. At low food densities () recruits have more than double the efficiency compared to scouts (236.1005 vs. 98.85329 ^J/_day per forager) when information transfer is allowed. The increased efficiency then diminishes at higher densities (, 243.8685 vs. 213.02885 ^J/_day per forager; , 250.1621 vs. 230.75986 ^J/_day per forager).

Experiments 2: switch durations, patch longevity and foraging success

Experiment 1 used the default patch longevity of 14 days. Experiment 2 explored the effect of environmental stability by testing additional patch longevities at a medium food density. Surprisingly, the results show that the benefits of SI increase in untreated colonies as patch longevity increases. If patches only last 1 day, spatial dance information is even detrimental (−15.8%). But as patches last longer, colonies gain more from having spatial dance information (+11% for 28 days). Experiments with 2-day and 3-day experimental cycles provide very different results for all patch longevities, except for when patches last only for 1 day (Figure 2). If patches persist longer (≥ 7 days), colonies perform more or less equally well during SI and NI periods. Again, the best results are obtained using 12-day experimental cycles. But even in this situation the relative benefit of SI is less than half the benefit in the untreated colonies in a very stable environment (+11% vs. + 4.9%).

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Figure 2. A comparison of foraging success measured as mean daily gain in honey (means ± s.e.) under varying patch longevities and with various intervals between experimental switches of spatial information transfer (SI) and no spatial information transfer (NI) treatments (no switches, 2-day cycles, 3-day cycles, 12-day cycles).

The benefit of SI varies with patch longevity, with increasing benefits from one day (a), 7 days (b), 14 days (c), to 28 days (d). SI is more beneficial, if patches are relatively stable over time. Switching between SI and NI treatment hides the benefit of SI to a large degree (solid circle: SI, open circles: NI).

https://doi.org/10.1371/journal.pone.0104660.g002

Recruitment success and, consequently, the energetic costs of recruitment are likely to be variable [22]. To test whether this affects our findings, we tested a situation with higher recruitment success (p_Dance  =  1) and no recruitment costs (c_Recruit  =  0) in a separate set of model runs. This could represent a situation in certain tropical habitats with many large and clustered food patches, where recruits locate advertised foraging sites quickly. The simulations show that SI is again beneficial and that the relative benefits of SI increase in a more stable environment (Figure 3; +5.8% when patches last for 7 days, +9.5% when patches last for 21 days), but the benefits of SI are again underestimated by a factor of 3.5 to 9.5 for 7 day patches and 21 day patches respectively when using 2-day experimental cycles.

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Figure 3. A comparison of foraging success measured as mean daily gain in honey (means ± s.e.) under the absence of costs to spatial information transfer (SI) and with SI, or no spatial information transfer (NI).

The switching between SI and NI treatments masks the benefit of SI even if there are no costs to SI (solid circle: SI, open circles: NI).

https://doi.org/10.1371/journal.pone.0104660.g003

The longevity of food patches also has an impact on the individual foragers. The longer patches last, the longer single agents can be persistent. The mean persistency of agents ranged from 1.008±0.004 day when patches lasted for a day to 2.842±0.0124 days when patches lasted for 28 days (Figure S3), but the maximum persistence was only limited by the patch longevities.

Discussion

Spatial location information of waggle dancing bees increased colony foraging success under almost all simulated circumstances. Spatial information did not improve colony success when patches lasted just 1 day, which is unrealistic for most natural habitats [25], [54]–[56]. The most surprising finding is that the relative benefits of spatial information increased as environmental stability increased (Figure 2). This contradicts the common assumption that dance information is most beneficial in an environment with ephemeral food sources [18], [19], [29], [57].

A closer examination of our model and the existing literature suggests that our results of long term benefits of the dance are plausible. Recruitment in honeybees is costly [21], [23], [24]: recruits need to wait for a dancing bee [21], and they usually require several field excursions before locating the advertised food source after following a dance [23], [58]–[60]. Thus, potential recruits incurred both energy and opportunity costs in our model. But after the advertised food source is located, the energetic returns are higher than for scouts. This result is consistent with empirical studies, which found that recruits tend to discover food sources of higher quality than scouts [23], [24], [60]. By dancing only for high quality food sources (see Figure S1 and [3], [8]) foraging bees effectively filter information, which allows recruits to exploit selectively the best food sources known to the colony [3], [61], [62]. After successful recruitment, costs of continuing to visit the food patch are low as bees quickly locate the previously visited patches using route-memory [63], [64], while benefits potentially remain high. The more stable the environment, the longer these benefits can accumulate. This is true even if there are short term fluctuations in a given patch's quality, such that it switches back and forth between profitable and non-profitable, because colonies with persistent individuals using private information can quickly decide which is the most profitable patch at a given time [65]. In contrast, if the environment completely changes (e.g., profitable patches become permanently unprofitable and vice versa), as in the case where patches only lasted for a day, recruits repeatedly have to pay the recruitment costs, while benefits remain short-lived.

One major difference between our model and previous models is our assumption that patches could last several days (and up to 4 weeks). Three lines of evidence suggest that this is a realistic assumption. First, it is known that flower patches in both tropical and temperate habitats often bloom for several days or even months [25], [54]–[56], [66]. Second, observations on naturally foraging honeybees show that foragers often return to the same patches for days and or even weeks [6], [8], [26], [28]–[30], [32]–[34]. Bees recruited by waggle dances are particularly likely to show site fidelity because food sources located by recruits are more profitable than those located by individually exploring bees [23], [24] and profitability positively affects site fidelity [33], [37]. In our model, foragers visited the same food patch for an average of 1 to 2.8 days, depending on the longevity of food patches (Figure S3). Third, honeybees readily learn the time of day when food sources are most rewarding and return to feeding sites on subsequent days at the appropriate time of day [27], [31], [67], [68]. This suggests that foragers are adapted to an environment where the spatiotemporal availability of the currently exploited food source is predictive for the next day. On the other hand, studies analyzing foraging locations by decoding waggle dances [3] show considerable daily changes in the locations that are advertised by dances. However, while such daily changes in dance maps inform us about the number of patches that receive increased exploitation (pp. 48 in [3]), they provide no information about how long individual foragers exploit patches. Clearly, the long-term foraging behavior of honeybee foragers in natural flower patches deserves further study.

Our findings help to explain the puzzling observation that experienced foragers following dances frequently ignore spatial waggle dance information [29], [69]–[74]. Our results show that foragers should continue to visit familiar food sources if these remain profitable in order to avoid recruitment costs and the lower benefits of individual exploration [23], [24], [60]. Decoding the spatial information of dances that advertise alternative food patches would become more beneficial if the currently visited patch deteriorates and using memory no longer provides rewards [29], [61], [75]. Accordingly, a recent simulation study found that individuals do best if they rely on learned behaviors most of the time and tailor social information-use to circumstances when the environment changes [76]. It is not yet entirely clear why experienced foragers follow dances at all if they subsequently ignore the spatial information. It is possible that these foragers follow dances mainly to acquire up-to-date information about the time period a particular flower species produces rewards, rather than its location, and is therefore worth inspecting by other foragers at other locations [6], [13], [60], [69], [77].

We hypothesized that treating colonies by repeatedly switching between SI and NI states leads to confounded results and obscures the benefits of spatial information. Our simulations corroborate this hypothesis. When we used short treatment periods (2-day or 3-day cycles), as in previous empirical studies [16]–[18], we often found no improved collection performance during periods with spatial information (Figure 1 and 2), even in environments where colonies with continuous access to SI (no switch) outperformed those without SI. The best estimates of dance benefits were obtained with 12-day treatment periods (similar to [19]). However, even this experimental design lead to a considerable underestimation of the relative benefits of spatial information in some environmental situations (Figure 1 and 2). Our simulations suggest that the problems of repeatedly switching between SI and NI are caused by carry-over effects (Figure 1): the foraging success of colonies during the first days of a new treatment is affected by the foraging success during the last days of the previous treatment (Figure 1). It takes a few days before these carry-over effects are no longer apparent. Allowing for site-fidelity, foragers collecting at a good food source have a high probability to continue visiting this food sources irrespective of treatment changes. Hence, colonies newly switched to the NI state will initially perform well because foragers continue to visit the high quality food sources to which they were recruited by waggle dances during SI periods. If we prevented the agents from being true to a site, these carry-over effects disappeared (Figure S7).

An additional problem for the interpretation of data from switch-experiments is that the degree to which data is confounded depends on the spatiotemporal distribution of food sources (Figure 1). This makes it especially challenging to meaningfully compare the foraging success of colonies in switch-experiments in different environments or seasons. To solve the methodological problems, we propose the following changes to experimental designs: First, switch experiments should allow colonies to recover for several days between SI and NI periods. Second, SI and NI periods should not be shorter than the average patch-age to make sure the environment changes substantially. With such a design, differences in the gained weight (or energy) should be noticeable between treatments. Alternatively, if only a qualitative result needs to be obtained (whether SI or NI is better), researchers could look at the change in weight gain over time instead of the weight gain. In other words, instead of recording the weight of colonies and calculating the day to day weight gain or loss ((weight on day t + 1) – (weight on day t)), one would calculate the day to day change in the weight gain or loss ((weight change on day t + 1) – (weight change on day t)). This latter solution does not involve a different experimental protocol and should therefore be straightforward to implement, but because of carry-over effects it would still be impossible to gain quantitative data on the difference between pure SI and NI treatments.

So far, we have discussed our results in the context of honeybee recruitment by waggle dances. However, the main findings of the model – the beneficial effects of social information, particularly in more stable environments – are probably not restricted to honeybees alone. If acquiring social information is (i) more costly and (ii) subsequently associated with higher rewards than asocial information (e.g. individual exploration), then we would expect the relative payoff of social information to increase with increasing environmental stability. In support of the first assumption (i), Dechaume-Moncharmont and colleagues [21] show with a model that social information is often costlier than asocial information due to time costs (waiting for a demonstrator). The recent finding that social information is usually of high quality because demonstrators perform the most successful behavior they know of [62] supports the second assumption (ii). However, empirical research is needed to estimate costs and benefits of different types of information and test the role of environmental stability.

Communication about food source locations is common in the Apini and many Meliponini (as pheromone trails), but not in bumble bees. The specific circumstances that lowered the costs or increased the benefits to dancing in Apis bees so it could evolve in the first place are not known, and our model is not concerned with the initial evolution of the dance. Recent phylogenies suggest that dancing evolved only once (reviewed in [5]), suggesting some constraints to dance evolution even if simpler forms of recruitment seem to evolve readily [78]. Temperate bumble bees might be exposed to different resource distribution [78]. Additionally, even though the range of tested colony sizes did not affect our main result, a critical colony size for the dance to be beneficial is likely: if the waiting costs to recruits are too long, for example because only a small work force is collecting food, the benefit of finding high quality food might not outweigh these waiting costs [79]–[81].

In summary, our study and previous simulation studies suggest that dancing is most beneficial in environments where food sources vary greatly in quality [20], are hard to find [22], [38] and persist for several days or weeks. In such an environment, spatial information helps a colony to allocate its foragers to highly profitable, but hard-to-find food sources and exploit those for extended time periods. We argue that dancing is beneficial in almost every natural environment, but new empirical studies using different experimental designs are needed to test this prediction.

Supporting Information

Acknowledgments

We are grateful to Margaret Jane Couvillon, Elli Leadbeater and Francisca Segers, Matina Donaldson-Matasci and Anna Dornhaus for comments on earlier drafts.