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 Super Dual Auroral Radar Network (SuperDARN) has been operating as an international co-operative organization for over 10 years. The network has now grown so that the fields of view of its 18 radars cover the majority of the northern and southern hemisphere polar ionospheres. SuperDARN has been successful in addressing a wide range of scientific questions concerning processes in the magnetosphere, ionosphere,

We present a new quantitative technique that determines the times and durations of substorm expansion and recovery phases and possible growth phases based on percentiles of the rate of change of auroral electrojet indices. By being able to prescribe different percentile values, we can determine the onset and duration of substorm phases for smaller or larger variations of the auroral index or indeed any auroral zone ground‐based magnetometer data. We apply this technique to the SuperMAG AL (SML) index and compare our expansion phase onset times with previous lists of substorm onsets. We find that more than 50% of events in previous lists occur within 20 min of our identified onsets. We also present a comparison of superposed epoch analyses of SML based on our onsets identified by our technique and existing onset lists and find that the general characteristics of the substorm bay are comparable. By prescribing user‐defined thresholds, this automated, quantitative technique represents an improvement over any visual identification of substorm onsets or indeed any fixed threshold method.

Recent observations of ionospheric flows by ground‐based radars, in particular by the European Incoherent Scatter (EISCAT) facility using the “Polar” experiment, together with previous analyses of the response of geomagnetic disturbance to variations of the interplanetary magnetic field (IMF), suggest that convection in the high‐latitude ionosphere should be considered to be the sum of two intrinsically time‐dependent patterns, one driven by solar wind‐magnetosphere coupling at the dayside magnetopause, the other by the release of energy in the geomagnetic tail (mainly by dayside and nightside reconnection, respectively). The flows driven by dayside coupling are largest on the dayside, where they usually dominate, are associated with an expanding polar cap area, and are excited and decay on ∼10‐min time scales following southward and northward turnings of the IMF, respectively. The latter finding indicates that the production of new open flux at the dayside magnetopause excites magnetospheric and ionospheric flow only for a short interval, ∼10 min, such that the flow driven by this source subsequently decays on this time scale unless maintained by the production of more open flux tubes. Correspondingly, the flows excited by the release of energy in the tail, mainly during substorms, are largest on the nightside, are associated with a contracting polar cap boundary, and are excited on ∼1‐hour time scales following a southward turn of the IMF. In general, the total ionospheric flow will be the sum of the flows produced by these two sources, such that due to their different response times to changes in the IMF, considerable variations in the flow pattern can occur for a given direction and strength of the IMF. Consequently, the ionospheric electric field cannot generally be regarded as arising from a simple mapping of the solar wind electric field along open flux tubes.