The study of animal foraging behaviour is of practical ecological importance 1 , and exemplifies the wider scientific problem of optimizing search strategies 2 .Lévy flights are random walks whose step lengths come from probability distributions with heavy power-law tails 3, 4 , such that clusters of short steps are connected by rare long steps. flight durations (time intervals between landing on the ocean) were then calculated as consecutive hours for which a bird remained dry, to a resolution of 1 h. It was assumed that birds landed on the water solely to feed, and that flight durations were thus indicative of distances between prey.Time series for 19 separate foraging trips 7 were pooled to give a total of 363 3 flights. The resulting log-log histogram of flight durations gave a straight line with a slope of approximately 2, and is reproduced in Supplementary Fig. 1 from the original raw data. The crux of the conclusion that the albatrosses were performing Lévy flights was that the slope of 2 implied the probability density function (pdf) of flight durations t (in hours), was 7, 10for t ≥ 1 h (leaving out the normalization constant). This is consistent with the Lévy flight definition that the tail of the pdf is of the power-law form t −µ , where 1 < µ ≤ 3 (though technically this is a Lévy walk 4,7,22 We first analyze a newer, larger, and higher resolution data set of albatross flight durations to test for Lévy flights. In 2004, 20 wandering albatrosses on BirdIsland were each fitted with a salt-water logger and a GPS device. The GPS data were too infrequent (at most one location h −1 ) to give distances between landings, but were needed to estimate each bird's departure time from Bird Island, in order to calculate the duration of the initial flight before first landing on the water (we calculated return flights similarly). The resulting data set of flight records was 4 pooled, as in ref. 7, yielding a total of 1416 flights to a resolution of 10 s (Fig. 1).The flights ≥ 1 h are clearly inconsistent with coming from the power law t −2 ascertained 7 for the 1992 data. Furthermore, data from a power law of any exponent (not just 2) would yield a straight line 23 , and this is clearly not the case.In fact, the flight durations t (in h) are consistent with coming from the shifted gamma distribution given by the pdfwhere y = t − 1/120 accounts for the assumed 30 s period before the bird searches for new food sources (see Methods), s = 0.31 is the shape parameter, r = 0.41 h −1 is the rate parameter, and Γ(·) is the gamma function. Equation (2) is valid for flights >30 s; for shorter flights we have f (t) = 0. The exponential term of (2) dominates for large t, implying Poisson behaviour, such that for long enough flights the birds essentially encounter prey randomly with a constant low probability.A Brownian random walker's displacement increases as t H where H = 1/2.If H > 1/2, we have "superdiffusion" as originally inferred in Fig. 2a The gamma distribution (2) has µ = 1 − s = 0.69. This is such a slow powerlaw ...

The study of long-distance migration provides insights into the habits and performance of organisms at the limit of their physical abilities. The Arctic tern Sterna paradisaea is the epitome of such behavior; despite its small size (<125 g), banding recoveries and at-sea surveys suggest that its annual migration from boreal and high Arctic breeding grounds to the Southern Ocean may be the longest seasonal movement of any animal. Our tracking of 11 Arctic terns fitted with miniature (1.4-g) geolocators revealed that these birds do indeed travel huge distances (more than 80,000 km annually for some individuals). As well as confirming the location of the main wintering region, we also identified a previously unknown oceanic stopover area in the North Atlantic used by birds from at least two breeding populations (from Greenland and Iceland). Although birds from the same colony took one of two alternative southbound migration routes following the African or South American coast, all returned on a broadly similar, sigmoidal trajectory, crossing from east to west in the Atlantic in the region of the equatorial Intertropical Convergence Zone. Arctic terns clearly target regions of high marine productivity both as stopover and wintering areas, and exploit prevailing global wind systems to reduce flight costs on long-distance commutes.

37We present the first objective quantitative assessment of the threats to all 359 species of seabirds, 38 identify the main challenges facing them, and outline priority actions for their conservation. We applied 39 the standardised Threats Classification Scheme developed for the IUCN Red List to objectively assess 40 threats to each species and analysed the data according to global IUCN threat status, taxonomic group, 41and primary foraging habitat (coastal or pelagic). The top three threats to seabirds in terms of number 42 of species affected and average impact are: invasive alien species, affecting 165 species across all the 43 most threatened groups; bycatch in fisheries, affecting fewer species (100) but with the greatest 44 average impact; and climate change/severe weather, affecting 96 species. In addition to impacting 86% 45 of globally threatened species, these three top threats also affect 81% of the species currently classified 46as Near Threatened or as Least Concern but declining. Reversing these three threats would benefit two-47 thirds of all species and c. 380 million individual seabirds (c. 45% of the total global seabird population). 48Most seabirds (c. 70%), especially globally threatened species, face multiple threats. For albatrosses, 49 petrels and penguins in particular (the three most threatened groups of seabirds), it is essential to 50 tackle both terrestrial and marine threats to reverse declines. As the negative effects of climate change 51 are harder to mitigate, it is vital to compensate by addressing other major threats that often affect the 52 same species, such as invasive alien species and bycatch, for which proven solutions exist. 53 54