Homing studies have provided tantalizing evidence that the remarkable ability of shearwaters (Procellariiformes) to pinpoint their breeding colony after crossing vast expanses of featureless open ocean can be attributed to their assembling cognitive maps of wind-borne odours but crucially, it has not been tested whether olfactory cues are actually used as a system for navigation. Obtaining statistically important samples of wild birds for use in experimental approaches is, however, impossible because of invasive sensory manipulation. Using an innovative non-invasive approach, we provide strong evidence that shearwaters rely on olfactory cues for oceanic navigation. We tested for compliance with olfactory-cued navigation in the flight patterns of 210 shearwaters of three species (Cory's shearwaters, Calonectris borealis, North Atlantic Ocean, Scopoli's shearwaters, C. diomedea Mediterranean Sea, and Cape Verde shearwaters, C. edwardsii, Central Atlantic Ocean) tagged with high-resolution GPS loggers during both incubation and chick rearing. We found that most (69%) birds displayed exponentially truncated scale-free (Lévy-flight like) displacements, which we show are consistent with olfactory-cued navigation in the presence of atmospheric turbulence. Our analysis provides the strongest evidence yet for cognitive odour map navigation in wild birds. Thus, we may reconcile two highly disputed questions in movement ecology, by mechanistically connecting Lévy displacements and olfactory navigation. Our approach can be applied to any species which can be tracked at sufficient spatial resolution, using a GPS logger.
After foraging in the open ocean, Procellariiformes (albatrosses, petrels and shearwaters) are able to pinpoint their breeding colonies, often located on small remote islands in apparently featureless seascapes. It has been hypothesized that this remarkable ability to navigate over vast distances can be attributed to the birds being able to learn an olfactory map or landscape on the basis of local wind-borne odours rather than their relying on geomagnetic cues [1–4]. Dimethyl sulfide and other biogenic odours whose concentration varies predictably in space may contribute to form an olfactory landscape used in navigation . In long-lived birds like Procellariiformes, these odours may be learnt (dimethyl sulfide originates in high quantity from phytoplankton and is persistent in marine seascapes) but airborne odour concentrations are highly intermittent due to the presence of atmospheric turbulence, and, as a result, olfactory cues for navigation will not always be present .
Recently, the odour-map hypothesis gained considerable credence from a study of the homing flights of displaced Cory's shearwaters that had been subject to sensory manipulation . Gagliardo et al.  reported that Cory's shearwaters deprived of their sense of smell showed dramatically impaired homing ability, whereas magnetically disturbed shearwaters showed unaltered navigational performance similar to that of unmanipulated control birds. Eight birds were yielded anosmic by washing their olfactory mucosa with a zinc sulfate solution . However, this experiment , as well as the few attempts to demonstrate olfactory maps in wild birds [9–11], only suggests that olfaction plays a role in homing, without demonstrating the use of olfactory navigation. It also leaves open the question of whether olfactory cues are of crucial importance to pelagic seabirds in oceanic navigation when, for example, heading to favoured and profitable foraging areas  as shown in figure 1. Nonetheless, it is known that at small spatial scales (tens to hundreds of square kilometres), procellariiform seabirds use odours and also visual cues to pinpoint and capture prey directly .
Neuroanatomical comparisons  suggest that olfactory navigation is common in vertebrates, and genetic studies show that the olfactory gene repertoire is well developed in birds . However, it is impossible to obtain a satisfactory sample size using intrusive experimental approaches on pelagic birds, such as shearwaters and albatrosses, especially when there are concerns for their conservation. This fact casts away the possibilities to use classical experimental/control groups of treatments  and one has to rely on spontaneous birds displacements.
Here, using an innovative non-invasive approach, we provide evidence that shearwaters rely on olfactory cues for oceanic navigation. It is based upon a mathematically rigorous and general description of olfactory-cued navigation in the presence of atmospheric turbulence. This theory accounts for how odours disperse in the atmosphere and for how birds can use these odours to orient their flights. The approach used to model the process of olfactory navigation is displayed in figure 2. When the odours are continually present above the threshold of detection, then the ‘odour map’ is present and the birds will maintain nearly unidirectional flight. But when the odour concentration falls below this level, the birds are without their map and so effectively lost. They may change course either because they become disoriented or because they are attempting to re-establish contact with the odour map. The lengths of the unidirectional flights are predicted to be distributed according to exponentially truncated power-laws that are characterized by a universal exponent whose value, 3/2, is independent of ecological context (electronic supplementary material, Level-crossing statistics of concentration fluctuations in odour plumes dispersing in turbulent flows). The 3/2 scaling is not model-specific as all physically realistic models of odour dispersal in turbulent flows will produce it by virtue of the Sparre Andersen theorem [17,18]. We assessed whether the flight-segment lengths empirically determined in tracking experiments displayed the expected distribution. This was done using standard techniques in the literature on Lévy flights . The presence of these distributions indicates that the flight patterns are consistent with a reliance on olfactory maps for oceanic navigation. This provides a new diagnostic test for olfactory-cued navigation; a test which can be made without interfering with the animal's sensory mechanisms.
2. Material and methods
(a) Bird species and colonies
The location of the studied colonies is reported in figure 1 and electronic supplementary material, figure S1. The ecology of the study species is described in detail in electronic supplementary material, Species ecology and study sites. Our samples are reported in electronic supplementary material, table S1.
(b) GPS-logger deployment
Birds were tracked using five models of GPS loggers: one by Earth & Ocean Technologies (Kiel, Germany) (mini-GPS, 19.4 g, battery 500 mA), two different models by Technosmart (Guidonia, Italy) (GiPSy-2, 11.9 g, battery 500 mA, and GiPSy-2, 9.8 g, battery 250 mA), and two different models by Perthold Engineering LLC (CatTraq GT-120, 16 g, battery 500 mA, and CatTraq GT-120, 11 g, battery 250 mA). All GPS loggers were configured to record the position of the bird every 10 min which was empirically selected as a good compromise between battery consumption and resolution. Shorter times would make impossible to record the longer trips to which we are especially interested. Devices were attached to the back feathers using three to four strips of Tesa® marine cloth tape (Tesa SE, Hamburg, Germany). During incubation, birds were captured, ringed and equipped with GPS loggers during the day. Afterwards, burrows were checked every day to record departure of the tagged bird, and, subsequently, the return of the equipped individuals. Loggers were removed immediately after a bird returned from a foraging trip. During chick rearing, birds were handled during the night after chick feeding. As adults normally spent little time in their burrow, it was not always possible to re-capture the equipped bird after the first foraging trip, and hence more than one trip might have been recorded for a given bird. Nevertheless, only the first trip of each bird was included in the analyses. Electronic supplementary material, table S1, reports metadata used in this study.
As recommended by several authors [20,21], the weight of GPS loggers was kept below 3% of the birds' body mass (range = 1.9–2.9%; median = 2.6%). External devices of this size are considered not to have any detectable influence on the foraging behaviour of Scopoli's shearwater [22,23], though they may possibly reduce nestling feeding rate and hamper nestling growth . Deployment of data-loggers took less than 10 min and birds were returned to their nest immediately afterwards. Handling and GPS deployment during incubation did not affect hatching success at the Linosa colony in 2008  nor the fledging success at Berlenga colony during 2006 .
(c) Model flight-segment-length frequency distributions
Birds belonging to seven colonies of three species were tagged with high-resolution GPS loggers during both incubation and chick rearing (electronic supplementary material, Species ecology and study sites). To test for the hallmark of olfactory navigation, we used robust and accurate statistical methods [19,26,27]. Displacement length frequency distributions were fitted to exponentially truncated power-laws (the theoretical expectation for olfactory-cued navigation), power-laws (indicative of random Lévy flight searching and the absence of knowledge about prey locations [28,29], bi-exponentials (indicative of two-mode searching, occasionally seen in seabirds ; tri-modal searching has never been observed in seabirds) and exponentials (a null model of the flight pattern data).
These model distributions are prescribed by 2.1a 2.1band 2.1cwhere N1, N2, N3 and N4 are normalization factors which ensure that the frequency distributions sum correctly to unity when integrated over all lengths between the lower and upper cut-offs; μ is the power-law (known as the Lévy exponent in the literature on Lévy flight foraging); λ1 and λ2 are related to atmospheric conditions (see equation S4 in electronic supplementary material, Level-crossing statistics of concentration fluctuations in odour plumes dispersing in turbulent flows); and and are the characteristic flight lengths in the intensive and extensive phases of a bi-modal search, respectively. A simple exponential is obtained from equation (2.1c) by setting A = 1.
Until recently, the identification of turns (and so bouts of unidirectional flight) within two-dimensional flight patterns relied on ad hoc parameter choices for critical turning angles . We overcome this limitation by projecting the flight patterns onto the x- and y-axes to create two one-dimensional movement patterns for each individual. Turns in these projected movement patterns can be identified in an unambiguous way as occurring where the direction of travel along the x- and y-axes changes . It can be shown that the projection preserves any power-law scaling characteristics in the original data . We checked for consistent scaling in the x- and y-directions and consequently we merged the two datasets. Model distribution functions were truncated below 1 km and above the length of the longest recorded displacement. Analysis outcomes did not change in a meaningful way when a shorter lower truncation scale was used. The lower truncation excludes from the analysis more convoluted parts of the flight patterns that are presumably associated with feeding or resting rather than with navigation.
Here, we analysed the flight patterns of 210 shearwaters belonging to three species (figure 1; electronic supplementary material, Species ecology and study sites).
We found clear and persistent evidence of exponentially truncated power-laws that are consistent with the theoretical expectations for olfactory-cued navigation. This was evident in 69% of the birds analysed (electronic supplementary material, table S2). Relative maximum-likelihood estimates for model fits to the displacement-length distributions for all three species and seascapes strongly support exponentially truncated power-law distributions, typically over 2 or more orders of magnitude, with characteristic power-law exponents close to the theoretical expectation of 3/2 (figures 3 and 4).
This is evident in birds which may rely more (Maddalena, Tremiti, Mediterranean Sea) or rely less (Corvo, Cape Verde, North Atlantic Ocean) on previous coastal landscape knowledge (figure 1). At the individual level, we computed the best-fitting distribution and estimates of μ, λ1 and λ2 (electronic supplementary material, table S2). More specifically, our estimates of μ (figure 5) are biased high with respect to the reference value (Student's t = 5.37, p < 0.0001), but this difference vanishes (Student's t = 0.31, p = 0.75) after taking into account the effect of the number of displacements (reported in electronic supplementary material, table S2) used to compute μ.
Our indicator of olfactory-cued navigation was evident in nearly all of the flights lasting 4 or more days but was only present in about 50% of the shorter flights lasting less than 2 days. The other flights were better represented as bi-exponentials. This is not at variance with the predominance of olfactory hallmarks at the population level as long records are required to reliably distinguish between exponentially truncated power-laws and bi-exponentials. Indeed, we found that the proportion of synthetic olfactory-cued flights (produced in numerical simulations) that were misidentified by our statistical diagnostics decreases as the flight length increases. This decrease mirrors that seen in our empirical data (electronic supplementary material, figure S3). This artefact was not present at the population level when data for many synthetic flights was pooled for data analysis purposes (electronic supplementary material, Synthetic flights).
In contrast with the maximum-likelihood estimates for the power-law exponent which, in accordance with theoretical expectation, show only modest variation, there is about a 10-fold variation in individual estimates for the exponential decay rates, λ1 and λ2 (figure 5). This variation is not surprising and is indicative of a wide variety of weather conditions.
We claim that shearwaters use olfactory maps for navigation and hence during both the forward and return branches of their foraging trips. We therefore expect to find the hallmark statistical signatures of olfactory-cued navigation in both of these branches. This expectation is supported by our data. This is illustrated in figure 6, which shows that the first and second halves of the flight patterns of the shearwaters breeding at Maddalena share common statistical properties that are consistent with olfactory-cued navigation.
Antecedents of our findings on shearwaters can be found in previous studies [26,30,31]. Reynolds et al.  reported that male Agrotis segetum moths flying in the presence of dispersing sex pheromone have scale-free dynamics, and Focardi & Cecere  reported that 36 out of a set of 77 foraging flight patterns made by Scopoli's shearwaters from two Mediterranean colonies had scale-free characteristics with power-law exponents around 1.6. Humphries et al.  reported on strong evidence for 20 out of 27 wandering albatross Diomedea exulans foraging patterns having truncated scale-free characteristics and these were attributed to the execution of advantageous random searching strategies; patterns of movement that are expected in probabilistic foragers with little or no knowledge of their environment. This interpretation is based upon model expectations for random searching but these authors did not consider olfactory models and so we do not know which interpretation is more appropriate for D. exulans. We showed that the hallmark of olfactory-cued navigation is a universal exponentially truncated power-law. We therefore suggest that these birds together with shearwaters rely on cognitive olfactory maps rather than on Lévy flight random searching to find preferred foraging locations and breeding colonies. Taken together the theoretical deduction and the analysis of the empirical data are seemingly compelling because as noted by Stumpf & Porter [32, p. 666] ‘a statistically sound power-law is no evidence of universality without a concrete underlying theory’.
Shearwaters may, however, use some form of random searching strategy at smaller scales to locate prey within their preferred feeding locations or they may exploit the presence of odour plumes emanating from the target . Our analysis thus provides novel insights into scale-free patterns and indicate that Lévy flight research still has much to learn from the touchstone flight patterns of the wandering albatross . They reconcile Lévy flight characteristics with the presence of directed flights (map-like behaviour) which are quite unlike the freely roaming patterns seen in probabilistic foragers. This study thereby introduces a novel conceptual connection between two highly disputed questions of movement ecology, namely Lévy displacements  and olfactory navigation  showing that the occurrence of the former can mechanistically be caused by the latter.
As previously noted, flight patterns may also be influenced by factors other than olfactory navigation, such as the presence of landmarks, fishing boats  and conspecifics or competitors leading to a movement pattern based on multi-modal cuing. However, the availability of such additional information is quite different among the studied populations. For instance, shearwaters nesting at Maddalena might navigate only using landmarks, as the northern Tyrrhenian Sea is full of islands, with a very high density of boats, a situation quite different from that experienced by the shearwaters nesting at Raso or Berlenga patrolling vast extensions of open ocean. Despite these important differences in seascape, we demonstrated that all these animals share the same basic pattern, strongly suggesting the presence of an underlying common mechanism of orientation which we have identified as olfactory-cued navigation. Our interpretation accounts naturally for the ability of seabirds to pinpoint their feeding colony and their preferring foraging locations after crossing vast expanses of featureless open ocean.
The ‘biologging revolution’, a discipline taking advantage of technological advancements and miniaturization  makes it possible, by the methods underlined here, to test the hypothesis of olfactory navigation in a large number of different organisms, living in most of Earth's ecosystems. Indeed, it would be interesting to test for scale-free characteristics in the movement patterns of other animals, such as turtles and seals that can detect airborne odours when they surface to breathe, and under natural conditions, this sensory ability might function in navigation [36–38] Furthermore, it is possible to speculate on the use of olfactory navigation for bird migration .
All the fieldwork was undertaken (capture, handling and ringing) under national and European laws, which regulates studies on wild bird species.
Data have been uploaded to The Seabird Tracking Database managed by BirdLife International (http://www.seabirdtracking.org/).
A.M.R. and S.F. wrote the paper with inputs from J.G.C., VP. and J.R. J.G.C., V.P. and J.R. collected the data. A.M.R. analysed the data with inputs from S.F.
We declare we have no competing interests.
This research is partially funded by the Biotechnology and Biological Sciences Research Council (UK). The work on Scopoli's shearwaters was part of the marine IBAs project carried out by LIPU and funded by the Italian Ministry of Environment (2008) and LIPU-UK (2009–2013). V.H.P. acknowledges the support provided by the Portuguese Foundation for Science and Technology (SFRH/BD/21557/2005, SFRH/BPD/63825/2009 and SFRH/BPD/85024/2012). The work on Cory's shearwaters was part of the marine IBAs (LIFE04 NAT/PT/000213) and FAME (2009–1/089) projects carried out by SPEA. The work on Cape Verde shearwaters was funded by the Critical Ecosystems partnership fund and coordinated by Biosfera I.
J.G.C. particularly thanks G. Gaibani, C. Celada and D. Lingard for promoting the conservation and scientific aspects of the telemetry activities. We acknowledge the logistic support of the Arcipelago della Maddalena National Park, the Madeira Natural Park, Secretaria Regional do Ambiente, Berlenga's Natural Reserve and Biosfera I. C. Catoni, I. Maggini, S. Imperio, G. Dell'Omo, M. Cianchetti, P. Brichetti, D. Pisu, B. Massa, P. Geraldes, I Ramírez, I. Fagundes, A. Werner, B. Fortes, T. Melo and J. Melo provided valuable help during fieldwork.
- Received February 27, 2015.
- Accepted May 28, 2015.
- © 2015 The Author(s) Published by the Royal Society. All rights reserved.