Lévy flights are scale-free (fractal) search patterns found in a wide range of animals. They can be an advantageous strategy promoting high encounter rates with rare cues that may indicate prey items, mating partners or navigational landmarks. The robustness of this behavioural strategy to ubiquitous threats to animal performance, such as pathogens, remains poorly understood. Using honeybees radar-tracked during their orientation flights in a novel landscape, we assess for the first time how two emerging infectious diseases (Nosema sp. and the Varroa-associated Deformed wing virus (DWV)) affect bees’ behavioural performance and search strategy. Nosema infection, unlike DWV, affected the spatial scale of orientation flights, causing significantly shorter and more compact flights. However, in stark contrast to disease-dependent temporal fractals, we find the same prevalence of optimal Lévy flight characteristics (μ ≈ 2) in both healthy and infected bees. We discuss the ecological and evolutionary implications of these surprising insights, arguing that Lévy search patterns are an emergent property of fundamental characteristics of neuronal and sensory components of the decision-making process, making them robust against diverse physiological effects of pathogen infection and possibly other stressors.
Most animals benefit from behavioural decision-making based on information about their current environment1. Any movement pattern that promotes the efficient acquisition of informative cues can thus be assumed advantageous2. This is particularly true for central place foragers exploring novel or transient unpredictable environments, where efficient sampling of informative cues is crucial for their ability to return to the nest, den or colony. In such cases, movement patterns resembling Lévy flights can be advantageous because these patterns of movement curtail needless resampling of terrain when searching blindly with limited or no information about the landscape3,4,5,6. Lévy flights alternate clusters of many short steps (bouts of unidirectional flight) with longer steps between them, creating fractal movement patterns that have no characteristic scale. The hallmark of a Lévy flight is a step-length distribution with a heavy power-law tail: P(l) ~ l−μ. Accordingly, Lévy flights seem to govern probabilistic search movements in a wide and diverse range of terrestrial and aquatic organisms including basking sharks, bony fish, turtles, jellyfish, honeybees, fruit flies, the wandering albatross, E. coli, human T cells, human hunter-gatherers, and have even been observed in trace fossils – the oldest records of animal movement patterns7,8,9,10,11,12,13,14.
While much attention has been paid to how Lévy flight-based searches are affected by environmental context, prey density or distribution e.g.7,10,15,16,17,18,19, there is very limited information on how internal physiological factors may affect an animal’s search strategy20. This is surprising since analysis of fractal characteristics of the temporal structure of behavioural sequences (e.g. time allocation to foraging, resting, grooming), which are also associated with optimized interactions with the environment, reveal that both environmental and internal physiological variables strongly affect behavioural optimization. Fractal complexity in behavioural sequence structure was found to increase with both complexity21 and novelty of the environment22. While an increased motivation to forage may lead to more complex sequential patterns23, most forms of physiological stress (social disharmony, pregnancy, intoxication, pathogen load) entailed an overall reduction of behavioural complexity24,25,26, resulting in more stereotypical and suboptimal behavioural sequences. For example, in Spanish ibex, the sequential time allocation pattern between feeding and vigilance was significantly less complex in both pregnant and parasite-infected females24. Health status was also a major factor affecting time spent moving and foraging in Japanese macaques21,24. However, the effects of physiological stress, such as that induced by pathogen infection, on the spatial search patterns in animals (e.g. foraging, mate-search) has been highlighted as a major open question in the understanding of how universal laws of optimal searches arise and shape animal behaviour20,27.
We address for the first time the effects of pathogen infection on optimized scale-free search behaviour, using honeybees (Apis mellifera) as a model organism. Honeybees are central-place foragers exploring vast areas of up to 300 km2 in search of floral resources28,29. Their navigation relies on learned and memorized landmarks; though there is a debate about exactly how bees utilize landmark information30,31,32,33,34. When they first leave the hive, honeybee workers have to efficiently acquire a sufficient set of informative landmarks to allow them to navigate back to the hive. They do so by performing successive and spatially increasing orientation flights around the colony35,36,37. Lacking any a priori information about the position of landmark cues, their orientation flights represent probabilistic searches and as such can be expected to have Lévy flight characteristics. Indeed, orientation flights in both honeybees and bumblebees have been found to follow a Lévy distributed optimal search strategy37,38.
The possibility to reliably record optimized search behaviour using harmonic radar16,38 in combination with the current call for a better understanding of the individual and colony-level effects of the numerous native and exotic emerging pathogens threatening an economically valuable livestock animal and pollinator39,40 makes honeybees an ideal model system to study the optimization of movement patterns in the context of pathology. Here we focus on two types of emergent honeybee disease with fundamentally different modes of action: Nosema ceranae, a gut parasite acquired only by adult bees and mainly interfering with the digestive system and energetics41,42 (henceforth, Nosema), and a virus-complex (Deformed wing virus (DWV) and a variant of DWV termed DWV genotype B or Varroa destructor virus (VDV), henceforth DWV), which is transmitted by the parasitic mite Varroa destructor to pre-adult bees during their development and can be found in all host body parts, including the brain43,44.
Here we ask if infection levels of these two fundamentally different pathogen types affect 1) behavioural performance i.e. flight characteristics and spatial exploration of the landscape, and 2) spatial exploration patterns in orientating bees, i.e. consistency with an optimized Lévy-flight searching pattern. Nosema is expected to have an adverse effect on flight performance due to its interference with bees’ metabolism42,45. Viruses, on the other hand, are not known to affect flight energetics but were found to alter a bee’s in-hive behaviour46. However, based on previous work on temporal fractals21,24,25, we hypothesize that high pathogen levels, particularly of viruses detected in the neural system, result in deficient search patterns of reduced fractal complexity, i.e. in a suppression of optimal Lévy flight characteristics. Our study provides the first insights into the effects of these physiological stressors on the robustness of navigational optimization strategies in animals.
Material and Methods
We tracked landscape-naïve honeybees on their first orientation flight after being released from a flight cage into an unknown landscape (Fig. 1) using a stationary, horizontally scanning radar45,47. A colony (host colony, HC) was placed in an insect-proof flight cage (3 m × 3 m × 1.8 m) located next to a grass field margin within flat and harvested farmland at Rothamsted Farm, UK, providing a suitable arena for radar tracking of bees over several hundred metres.
The hive consisted of two stacked brood boxes separated by a mesh, with the lower one containing the colony and opening into the flight cage via a Perspex tunnel, allowing the bees to forage on a sucrose-gravity feeder and a pollen feeder. The top brood box could not be entered by the bees and contained unpopulated honeycomb onto which individual foragers were placed prior to tracking. This ensured the test bees naturally embarked on foraging when leaving the hive via a similar Perspex tunnel (dummy exit) yet leading to the outside of the cage so that they could explore the novel landscape outside of the cage (Fig. 1).
All experimental bees were obtained from naturally Varroa-infected donor colonies (DCs) from Rothamsted Research stock. Varroa mite-fall over 10 days, a standard beekeeping practice to assess a colony’s Varroa infestation, served as a proxy indicator for putatively high and low virus-infection probability and virus load of the donor colonies48. Mature brood frames were taken from the DCs and were transferred into an incubator (34.5 °C) until the bees emerged. Two to three days after emergence the worker bees were marked individually with numbered queen marking tags (Opalithplättchen, Bienen-Voigt and Warnholz GmbH and Co. KG, Germany) and were randomly separated into two identical holding cages.
These groups of bees were subsequently bulk-fed either with a freshly prepared Nosema-inoculum (500 μl of 40% sucrose (w/w) containing 250,000 spores per bee) (NOS) or with 500 μl of 40% sucrose, free of Nosema spores but otherwise identical to the Nosema-inoculum (C)45 in order to ensure that Nosema infection was present in at least half of the bees. Six hours after inoculation, all bees were introduced to the HC, where they developed under identical natural conditions into foragers. Tracking bees from the same cohort allowed us to control for behavioural effects of age.
Marked foragers at least 14 days old and previously observed foraging at the feeder were collected from the hive entrance using a queen marking cage and transferred into the top brood box. Upon leaving the hive through the dummy exit they were briefly contained in the tunnel with shutters and equipped with a transponder before being released and allowed to exit the colony into the landscape. Only one bee was released and tracked at any time. Returning bees were caught when landing at the dummy entrance or on the external surface of the cage netting. These bees were subsequently frozen at −80 °C until pathogen screening. Released bees returning no radar signal for 45 min were declared lost. All experiments were conducted in favourable weather conditions (ambient temperature > 15 °C, no rain, no or light wind) from June to September 2012 and 2013.
The radar obtained positional fixes (range (m) and bearing (rad)) every 3 s (20 rpm rotational scan)45 (see Supplementary Information, Fig. S2) from which we reconstructed the bees’ flight trajectories and inferred flight speed, total stop time, total track length, and maximal displacement distance (furthest location of the bee from the colony) as measures of flight performance. Based on the smallest polygonal hull completely enclosing the flight track we compared the spatial characteristics of the orientation flights using area and perimeter of the hull and isoperimetry; i.e. circularity of the track hull (Eq. S1 in Supplementary Information).
It is not possible to precisely control the ontogeny of infection of DWV or Nosema in individual bees, where infection success and recurring horizontal transmission may lead to high variation in actual pathogen loads. To account for this, all tracked bees were analysed post-hoc for their disease load at the time of their orientation flight, and these pathogen loads were used for all statistical analyses. Post-hoc virus screening of tracked bees was done individually via qRT-PCR (primers: DWV: DWV-F2, DWV-R2a; VDV: VDV-F2, VDV-R2a49) based on cDNA (reverse-transcribed RNA) obtained from the bees’ head, using RP49 as housekeeping gene. A negative control containing RNA-free HPLC-water, and a virus-positive abdominal cDNA sample were included as controls in each reaction run. We used an upper Ct – value of 35 cycles to minimize the risk of false positives50,51. Using a DWV standard curve for qPCR efficiency, we inferred virus loads per head of a bee. Nosema spore loads were assessed microscopically from dissected mid-guts using a haemocytometer following standard protocol52,53. Based on these diagnostics, the tracked bees were assigned to the following groups: Nosema-free (representing a Nosema control group), low Nosema infection (<1000 spores/μl) and high infection (>1000 spores/μl), as well as presence (Ct-value < 35) and absence (Ct-value > 35) of DWV (Table 1). These form the basis of robust comparative statistics of our highly variable behavioural and pathological data-set to unravel the pathogen effects on flight performance (Tables 1 and 2, Supplementary Fig. S3).
We employed the same five pathogen groups of bees (3 Nosema groups and 2 DWV groups) for a robust and reliable comparison of Lévy flight characteristics. We focussed on both pooled flight data per pathogen-group as well as individual flight trajectories in these groups to compare Lévy exponents and the Akaike weights for power-laws in the context of pathogen load. (Tables 2 and 3 and Figs 2, 3 and S4). In both approaches we tested for the presence of optimal Lévy flight patterns following the approach of Reynolds et al.18. The analysis is based on flight path-derived sequences of straight-line movements between points (turning points) of significant directional change. These turning points are defined by a directional change between the flight direction immediately before and after the putative turning point of more than 90°. Statistical properties of these path representations do not change significantly when the critical angle of 90° is changed by ±30°. Following well-established practice54, flight-length distributions were then fitted to power-law distributions (indicative of Lévy flights) and to exponential distributions (a null distribution) using maximum likelihood methods55. These model distributions are prescribed by
where and are normalization factors which ensure that the frequency distributions sum correctly to unity when integrated over all flight-lengths between the lower and upper cut-offs, μ is the power-law exponent (also called the Lévy exponent) and λ is the decay rate of the exponential. The lower cut-off was taken to be 10 m (which is comparable to the shortest step that can be resolved by the radar), and the upper cut-off was taken to be length of the longest flight segment in the dataset under analysis. The best-fitting model distribution was identified using the Akaike information criterion, the weight of which ranges from 0 (no support for the model) to 1 (full support for the model).
Both flight parameters and individual Lévy exponents (Table 3) for each of the pathogen groups were compared using a linear mixed model (LMM) with restricted maximum likelihood (REML) and a fully crossed fixed model (Nosema infection level (no/low/high) × virus-infection (presence/absence)), with tracking day as a random factor. Pathogen interactions were tested excluding individuals free of Nosema (n = 16). In the absence of significant interactions, the interaction-term was dropped from the LMM for statistical comparison of the pathogen effects on the flight parameters and Lévy exponents (Table 2).
All statistical analyses were performed using the statistical software GenStat V17.1. (VSN International, 2011).
In total, 78 bees were successfully tracked on their first orientation flights and successfully pathogen-screened. The average Nosema infection level was 4.79 × 103 spores/μl bee gut extract (range: 0–2.36 × 104) (equivalent to an extrapolated mean of 2.4 × 106 spores per bee) and they were naturally infected with an average of 1.42 × 1010 copies of DWV per bee head (range: 0–1.99 × 1011) (Supplementary Fig. S2). 45% and 26% of all bees were single-infected with DWV or Nosema, respectively, with the rest of the bees showing co-infection (Table 1).
We found that the spatial scale of the orientation flight was significantly reduced in bees with Nosema infection in comparison to bees free of spores (Table 2; Fig. 2, Supplementary Fig. S3) with infection intensity playing a secondary role in shaping behavioural performance. While orientation flights of bees with low and high Nosema loads covered on average an area of 34,353 m2 and 20,390 m2, respectively, the orientation flights were over three times larger for bees with no Nosema infection (127,123 m2). Similarly, we found a significant Nosema-associated reduction in overall track length and track perimeter, both of which dropped by half with Nosema infection, but differed only marginally between high and low infection levels (Table 2, Supplementary Fig. S3); the maximum displacement distance only reached an average of 148 m in highly infected bees compared to 317 m for bees with no Nosema infection.
While total flight time was significantly longer in Nosema-clean bees, we also find a surprising and significant increase in total stop time in Nosema-clean bees, which is typically associated with Nosema infection. We attribute this to the overall longer activity time of these Nosema-clean bees, allowing or indeed requiring longer rest times (Table 2). Testing the track area the bees covered during the bees’ actual flight time (excluding stop time), we find that Nosema infected bees explore >65% less area per time unit flown than Nosema-free bees.
In contrast, none of the measured parameters varied significantly with the presence or absence of DWV nor was there any significant interaction between the two pathogen types for any parameter (Table 2). In response, we removed the non-significant interaction-term from the statistical comparison of pathogen effects. In no case did this approach affect the results of our initial analysis. Though not significant, there is an interesting tendency for larger orientation flights in DWV-infected bees that warrants further investigation (Table 2, Fig. 2).
In line with previous work45, the mean flight speed was affected by neither Nosema nor Deformed wing virus. Likewise, the circularity (isoperimetry) of orientation flights was not significantly affected by either pathogen (Table 2).
Analysing the individual bee movement patterns in relation to their disease load, we found no significant difference in the prevalence of Lévy flight characteristics (AIC >0.5) between bees infected with either Nosema or DWV as compared to bees without these pathogens (among Nosema categories: χ2 = 0.06, d.f. = 2, p = 0.97; between DWV categories: χ2 = 0.22, d.f. = 1, p = 0.64) (Fig. 3, Table 3). Overall 54% of the bee tracks indicated Lévy exponents of μ ≈ 2 (Tables 2 and 3), which were supported by Akaike weights > 0.5.
In addition, and in contrast to our hypothesis, we find no evidence for reduced fractal complexity i.e. lower Lévy exponents, as a function of pathogen infection. Comparing all Lévy exponents of individual tracks (Fig. 3), which were supported by individual AIC’s of >0.5, we find that Nosema-free bees exhibit a mean Lévy exponent of μ = 2.17, whereas bees with low or high Nosema spore load showed mean Lévy exponents of μ = 2.27 and μ = 2.24 (standard error of difference (s.e.d.) = 0.16), respectively. There was no significant difference in the Lévy exponents with respect to Nosema infection (p = 0.86, Table 2). Similarly, μ was 2.28 and 2.17 (s.e.d. = 0.14) for bees without and with Deformed wing virus, respectively, and did not differ significantly (p = 0.62, Table 2).
Based on data pooled across all bees in a specific pathogen group the Akaike weights for power-laws (mean μPOOLED ≈ 2.1) were 1.00, thus giving full support for Lévy-flights in each of the pathogen groups as is clearly illustrated in Figs 3 and S4. Our data indicate that the two focal pathogens do not lead to a significant reduction in fractal complexity in the spatio-temporal domain, contrasting with the pathogen-sensitive temporal fractals (Figs 3 and S4, Table 2).
Though warranting caution in the interpretation, there is an interesting tendency for the Lévy exponent to slightly increase with Nosema load, i.e., for searching to become sub-optimal and closer to being scale-finite rather than scale-free (as μ > 3 corresponds to Brownian (scale-finite) flight patterns). However, since Nosema infection may reduce the size of the search flights, longer flight segments may be curtailed in these cases. Such truncations (under-representation) of longer flight segments will tend to increase the maximum likelihood estimates for μ, effectively over-estimating the exponent without biological causation. The reverse may apply for DWV infection where the presence of DWV, loosely associated with spatially more expansive tracks, seems to lead to a Lévy exponent closer to 2 (μ = 2.17), very similar to the exponents found for Nosema-free bees. It remains to be investigated if these (non-significant) variations in Lévy exponents indeed foreshadow subtle, yet genuine effects of pathogen infections on orientation flight characteristics and are thus biologically relevant.
Overall, our data indicate that Lévy flights are not only a common feature of honeybee orientation flights, being the most parsimonious flight-pattern model in 54% of the colony workforce of foragers, but also that they are robust against otherwise marring effects of pathogen infection
Fractal patterns are a widespread and robust feature in animal behaviour27,56,57,58 and have been implicated in facilitating an animal’s ability to efficiently respond to environmental change5,56,59,60. However, while the underlying principles of time allocation to given behaviours have been intensely studied in the context of the internal state of an animal, investigations in the spatial domain are thus far restricted to environmental characteristics, a fact that has been highlighted as a substantial shortcoming to our understanding of the occurrence, origin and general characteristics of scale-free patterns in animal behaviour20,27.
Using honeybee orientation flights as a model to investigate if and how pathogens may affect spatial search patterns, we show for the first time that, while the size and duration of the orientation flight was clearly associated with Nosema load, the underlying search algorithm was not. During their orientation flights, honeybees and bumblebees “collect” salient visual cues such as prominent landmarks (trees, houses, etc.) and linear landscape features (roads, hedges, etc.)34 in spatially increasing search flights36 that aid their successful navigation between the colony and foraging grounds35. Efficient acquisition of such information is thus a pre-requisite for successful foraging, and any impairment of this ability can be assumed to negatively affect individual and colony performance. In line with previous studies on search flights of honeybees16,17,18,38 and orienting bumblebees37, we find that our orientation flight data not only followed the expected optimal Lévy distribution, a hallmark of highly efficient environmental exploration, but that these search patterns were robust against both Nosema and virus infection, with disease load having no significant effect on either the Lévy prevalence or the numerical value of the Lévy exponent.
In contrast, for the flight performance we find that even bees with moderate Nosema infection levels, likely to be commonly found in naturally infected bees61, exhibit significant impairments. Infected bees covered on average only a third of the area during their orientation flights and flew a shorter distance from the hive (a reduction of over 41% in maximum displacement distance) in comparison to bees which had no Nosema infection. This is in line with previous studies showing that Nosema sp., an obligatory gut pathogen infecting intestinal cells, interferes with honeybee energetics42,62 and affects flight performance45,63,64. For infections with DWV, we see putatively infection-induced changes in some track parameters, albeit non-significant; as DWV may alter in-hive behaviour of honeybees46, such changes in flight performance warrant further investigation. Other flight parameters such as a bee’s mean flight speed (∅total = 3.42 ms−1 ± 0.58 ms−1) closely matches previously reported estimates of honeybee flight speed (3.6 ms−1, range: 0.6 ms−1–6.2 ms−1 36; 3.19 ms−1, range: 2.86 ms−1–3.53 ms−1 45) and did not vary significantly with pathogen load.
It remains to be studied if and how the Nosema-induced spatial reduction of a honeybee’s orientation flights translate into deficits in foraging performance, or even prevents bees becoming successful foragers reliably able to navigate through the wider landscape. The reduced access to landscape features is unlikely to be compensated by an efficient search strategy, suggesting that these effects may play an important yet cryptic and thus far unreported role in poor colony fitness observed in various regions of the world40,65.
While the effects on bee flight performance are in line with previous reports, the robustness of the fractal characteristics of the orientation flight (optimal Lévy flight, μ ≈ 2) is not. Our findings are in contrast to temporal fractal patterns governing the time-allocation to behavioural routines, which was shown to be highly sensitive to diseases and parasites, among other stressors, leading to more stereotypical and less optimal behaviours in infected as compared to healthy individuals21,24,25,26.
This pronounced contrast in robustness of temporal versus spatial scale-free patterns raises interesting questions about the origin of fractal features in animal behaviour27,57. The fact that pathogens, though clearly affecting the bees’ flight behaviour, do not interfere with the search patterns suggests that Lévy flights are not a sophisticated cognitive skill, which can be assumed to be costly to acquire and to maintain; and would be potentially prone to interference from stressors. Rather, such fundamental characteristics in animal movement may result from innate neuronal stochasticity and accumulated sensory imprecision of the decision making process27,66,67, similar to the universal activity patterns found in cue-deprived insects58.
Our data support the idea that Lévy flight characteristics may not be the product of direct selection but that, conversely, selection favours individuals not losing their innate ability to optimally Lévy-fly27,57. In fact, MacIntosh27 highlighted ‘error tolerance’, i.e. the ability to maintain Lévy-like movement patterns under adverse conditions such as pathogen infection, as a potentially strong selective force that may explain the widespread occurrence of Lévy flights27. We provide an interesting new insight into the evolutionary foundations of optimal movement patterns in animals, which we hope will inspire further research in this little explored field.
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Dedicated to HW. We thank Rothamsted Farm staff, S. Kennedy J. Swain and D. Andrew for experimental support, D.P. McMahon and A. Miersch for assistance with the pathogen screening and M. Roper for constructive comments on the manuscript. This study was funded jointly by a grant from BBSRC, Defra, NERC, the Scottish Government and the Wellcome Trust, under the Insect Pollinators Initiative (grant numbers BB/I00097/1 and BB/I000100/1). Additional support came from the Deutsche Forschungsgemeinschaft (DFG, grant number WO 1745/2-1) to S.W. Rothamsted Research is a national institute of bioscience strategically funded by the UK Biotechnology and Biological Sciences Research Council (BBSRC).
The authors declare no competing financial interests.
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Wolf, S., Nicholls, E., Reynolds, A. et al. Optimal search patterns in honeybee orientation flights are robust against emerging infectious diseases. Sci Rep 6, 32612 (2016). https://doi.org/10.1038/srep32612
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