Supporting Information Reynolds et al (2015) SI Species ecology and study sites Study sites. The Scopoli’s shearwater (Sh), the Cory’s shearwater (Cs) and Cape Verde shearwater (CVs) are three closely related species belonging to the Cory’s shearwater complex (Sangster et al. 2012; see also Genovart et al. 2013 for a discussion of its taxonomic status). They are pelagic seabirds, which breed in the Mediterranean, North Atlantic Ocean, and Central Atlantic Ocean, respectively. All three species spend the nonbreeding season in the Central and Southern Atlantic Ocean (González-Sólis et al. 2007; Muller et al. 2014), with a few birds from Berlenga also overwintering in the north-west Atlantic Ocean (Catry et al. 2011, Dias et al. 2012). They generally feed on pelagic fish species, cephalopods and crustaceans (Paiva et al. 2010a; Xavier et al. 2011; Alonso et al. 2014). In the Mediterranean, the Sh also seems widely to exploit discards from fishing boats (Cecere et al. 2014a). The three species nest in the ground in burrows or in rock crevices. During incubation, the adults spend several days incubating the egg until their partner, which is foraging at sea, comes back for the changeover. Foraging trips last on average 7.53 ± 0.7 days in Sh (Cecere et al. 2013), 9.20 ± 6.80 days in Cs (Paiva et al. 2010b) and 9.90 ± 2.13 days in CVs (V.H. Paiva unpublished data). A few days after hatching, adults leave the chick alone and return for a daily feed during the night (Rubolini et al. 2014). In most studied colonies parents perform the dual foraging strategy alternating short trips, which last about 1-4 days and are mostly for chick provisioning, with longer trips for self-provisioning (Paiva et al. 2010d; Cecere et al. 2014b). Fieldwork on Sh was carried out during both the incubation and chick-rearing periods (Table S1) at three Mediterranean colonies: one on Linosa island, one on the islet of Capraia in the Tremiti Archipelago, and one on La Maddalena Archipelago (Fig. S1). Linosa (35°52’N; 12°52’E), located in the Tunisian Plateau/Gulf of Sidra region between Sicily, Tunisia and Libya, hosts the second largest colony of Sh with an estimated 10,000 breeding pairs (Baccetti et al. 2009). The Tremiti Archipelago (42°08’N; 15°31’E) hosts approximately 400 pairs (Baccetti et al. 2009), and it represents the largest breeding colony of the species in the Adriatic Sea. La Maddalena Archipelago (41°13’N; 9°24’E), located in the Tyrrhenian Sea between 1 Sardinia and Corsica, hosts 400-1,000 pairs (Baccetti et al. 2009); fieldwork was carried out on the islets of Spargiotto (120-180 pairs) and Barettini (50-100 pairs). Birds from the three colonies inhabit different seascapes: compared to the relatively shallow and flat Adriatic sea, both the Tyrrhenian Sea and the Tunisian Plateau present much lower primary production (Bosc et al. 2004), deeper waters and higher mean sea surface temperature (Coll et al. 2010). Cs birds were tracked during the chick-rearing period (Table S1) at three north Atlantic islands: Corvo, Berlenga and Selvagem Grande (Fig. S1). Corvo (39°40’N; 31°06’W), located at the oriental group of the Azores Archipelago, hosts roughly 30,000 individuals (Ramírez et al. 2008). Berlenga (39°24’N; 9°30’W), the largest island of the Berlengas Archipelago, holds 300 breeding pairs (~1,100 breeding pairs for the whole archipelago; Lecoq et al. 2011). Selvagem Grande (30°08’N; 15°51’W), the largest island of the Selvagens Archipelago, hosts the largest population of Cs in the Atlantic, with ~ 30,000 breeding pairs (Granadeiro et al. 2006). At Corvo island, the birds breed within an oceanic system, i.e. oceanic islands with a short continental shelf. On Berlengas, birds breed within a neritic system, i.e. an island within a long continental shelf of about 200 m depth. Selvagem Grande, surrounded by an oceanic environment, is situated within 375 km of a large neritic system, the African continental shelf (Fig. S1). Surroundings of the former oceanic colonies are usually less productive than the nearby area of the neritic colony, in which the shallow waters and the strong upwelling phenomenon fuels productivity to the system and naturally enhances prey availability for seabirds (Paiva et al. 2010b). Cs from the three former colonies typically alternate between short foraging trips exploiting its colony surroundings (Paiva et al. 2010c) and long excursions to the north of Azores (Corvo population; Ceia et al. 2014a), seamounts offshore mainland Portugal (Berlenga population; Paiva et al. 2013; Ceia et al. 2014b) and the north African shelf (Selvagem Grande population; Paiva et al. 2010d) Fieldwork on CVs was carried out during both incubation and chick-rearing periods at Raso islet (16°36’N; 24°35’W), the southernmost islet between São Vicente and São Nicolau islands. This place holds nearly 10,000 breeding pairs of CVs (Biosfera I unpublished data), which should be the largest population of this near threatened species from the Cape Verde Archipelago. The colony surroundings are generally low in productivity, but the species exploits frequently the turbulent and productive waters on the “channels” 2 between Cape Verde islands and perform longer trips to exploit the upwelling area at the shelf break off the western African coast (V. H. Paiva unpublished data). Alonso, H., Granadeiro, J.P., Waap, S., Xavier, J., Symondson, W.O.C., Ramos, J.A., Catry, P. (2014) An holistic ecological analysis of the diet of Cory’s shearwaters using prey morphological characters and DNA barcoding. Molecular Ecology 23:3719-3733. doi: 10.1111/mec.12785. Baccetti N, Capizzi D, Corbi F, Massa B, Nissardi S, Spano G, Sposimo P (2009) Breeding shearwaters on Italian islands: population size, island selection and co-existence with their main alien predator, the black rat. Riv. Ital. Orn. 78: 83-100. Bosc, E., Bricaud, A., Antoine, D. (2004) Seasonal and interannual variability in algal biomass and primary production in the Mediterranean Sea, as derived from 4 years of SeaWiFS observations. Glob. Biogeochem. Cycles. 18: GB1005. Catry P, Dias MP, Phillips RA, Granadeiro JP (2011) Different Means to the Same End: Long-Distance Migrant Seabirds from Two Colonies Differ in Behaviour, Despite Common Wintering Grounds. PLoS ONE 6(10): e26079. Cecere, J.G., Catoni, C., Maggini, I., Imperio, S.; Gaibani, G. (2013) Movement patterns and habitat use during incubation and chick-rearing of Cory’s shearwaters (Calonectris diomedea diomedea) (Aves: Vertebrata) from Central Mediterranean: influence of seascape and breeding stage. It. J. Zool. 80, 82-89. Cecere JG, Catoni C, Gaibani G, Geraldes P, Celada C, Imperio S. (2014a) Anthropogenic and environmental variables affecting foraging locations of Scopoli’s shearwater in the Mediterranean sea. Ibis. Cecere, J.G., Gaibani, G. , Imperio, S. 2014b: Effects of environmental variability and offspring growth on the movement ecology of breeding Scopoli’s shearwater Calonectris diomedea. Curr. Zool. 60: 622-630. Ceia, F.R., Paiva, V.H., Ceia, R.S., Hervías, S., Garthe, S., Marques, J.C., Ramos, J.A. (2014a) Spatial foraging segregation by close neighbours of a highly mobile seabird species. Oecologia. DOI: 10.1007/s00442-014-3109-1 3 Ceia, F.R., Paiva, V.H., Garthe, S., Marques, J.C., Ramos, J.A. (2014b) Can variations in the spatial distribution at sea and isotopic niche width be associated with consistency in the isotopic niche of a pelagic seabird species? Marine Biology. DOI: 10.1007/s00227-014-2468-9 Coll, M., Piroddi, C., Steenbeek, J., Kaschner, K., Ben Rais Lasram, F. et al. (2010) The Biodiversity of the Mediterranean Sea: Estimates, Patterns, and Threats. PLoS ONE 5(8): e11842. Dias, M. P., Granadeiro, J.P., Catry, P. (2012) Working the day or the night shift? Foraging schedules of Cory’s shearwaters vary according to marine habitat. Mar. Ecol. Prog. Ser. 467: 245-252. Genovart, M., Thibault, J.-C., Igual, J.M., Bauzà-Ribot, M.M., Rabouam, C. & Bretagnolle, V. (2013) Population Structure and Dispersal Patterns within and between Atlantic and Mediterranean Populations of a Large-Range Pelagic Seabird. PLoS ONE 8, e70711. González-Solís, J., Croxall, J.P., Oro, D., Ruiz, X. (2007) Trans-equatorial migration and mixing in the wintering areas of a pelagic seabird. Frontiers in Ecology and the Environment 5: 297-301. Granadeiro J. P., Dias M. P., Rebelo R., Santos C. D, Catry P. (2006) Numbers and population trends of Cory’s Shearwater Calonectris diomedea at Selvagem Grande, Northeast Atlantic. Waterbirds 29(1):5660. Muller MS, Massa B, Phillips RA, Dell’Omo G. (2014) Individual consistency and sex differences in migration strategies of Scopoli shearwaters despite year differences. Current Zoology 60: 631-641. Paiva, V.H., Xavier, J., Geraldes, P., Ramirez, I., Meirinho, A., Ramos, J.A. & Garthe, S. (2010a). Foraging ecology of Cory’s shearwaters in different ecological environments of the North Atlantic. Marine Ecology Progress Series 410: 257-268. DOI:10.3354/meps08617 Paiva VH, Geraldes P, Ramírez I, Meirinho A, Garthe S, Ramos JA (2010b). Foraging plasticity in a pelagic seabird species along a marine productivity gradient. Marine Ecology Progress Series, 398, 259-274. Paiva, V.H., Geraldes, P., Ramirez, I., Ramos, J.A., Garthe, S. (2010c). How Area Restricted search of a pelagic seabird changes while performing a dual foraging strategy. Oikos 119: 1423-1434. DOI: 10.1111/j.1600‐0706.2010.18294. Paiva, V.H., Geraldes, P., Ramirez, I., Meirinho, A., Ramos, J.A., Garthe, S. (2010d). Oceanographic characteristics of areas used by Cory’s shearwaters during short and long foraging trips in the North Atlantic. Marine Biology 157: 1385-1399. 4 Paiva, V.H., Geraldes, P., Marques, V., Rodríguez, R., Garthe, S., Ramos, J.A. (2013). Effects of environmental variability on different trophic levels of the North Atlantic food web. Marine Ecology Progress Series 477: 15-28. Ramírez, I., Geraldes, P., Meirinho, A., Amorim, P., Paiva, V.H. (eds.) (2008) Important Areas for Seabirds in Portugal. Project LIFE04NAT/PT/000213 - Sociedade Portuguesa Para o Estudo das Aves. Lisboa. http://lifeibasmarinhas.spea.pt/pt/y-book/ibasmarinhas/ Rubolini D, Maggini I, Ambrosini R, Imperio S, Paiva VH, Gaibani G, Saino N, Cecere JG. (2014) The Effect of Moonlight on Scopoli’s Shearwater Calonectris diomedea Colony Attendance Patterns and Nocturnal Foraging: A Test of the Foraging Efficiency Hypothesis. DOI: 10.1111/eth.12338. Sangster, G., Collinson, M., Crochet, P.A., Knox, A.G., Parkin, D.T., Votier, S.C. (2012) Taxonomic recommendation for British birds: eighth report. Ibis 154, 874-883. Xavier, J.C., Magalhães, M.C., Mendonça, A.S., Antunes, M., Carvalho, N., Machete, M., Santos, R.S., Paiva, V.H., Hamer, K.C. (2011) Changes in diet of Cory’s Shearwaters Calonectris diomedea breeding in the Azores . Marine Ornithology 39: 129-134. 5 Table S1. Sample sizes used to characterize the foraging behaviour of three species of Calonectris sp. shearwaters, breeding on 7 different colonies and foraging over the Mediterranean Sea and North and Central Atlantic Ocean. SPECIES Scopoli's shearwaters (Sh) Cory's shearwaters (Cs) Cape Verde shearwaters (CVs) COLONY PERIOD N° TRACKED BIRDS YEAR Linosa chick-rearing 55 2008-2012 Linosa incubation 14 2008 Tremiti incubation 26 2009-2010 La Maddalena chick-rearing 32 2013 Corvo chick-rearing 20 2007 Berlenga chick-rearing 29 2010 Selvagem Grande chick-rearing 16 2007 Raso incubation 11 2013 Raso chick-rearing 7 2013 6 Figure S1. Illustrative trips from Cory’s shearwaters (Cs) tracked on (1) Corvo, (2) Berlenga and (6) Selvagem Grande islands; Scopoli’s shearwaters (Sh) tracked on (3) La Maddalena, (4) Tremiti and (5) Linosa islands and Cape Verde shearwaters (CVs) tracked on (7) Raso islet. Different colours represent different individuals (Bird_ID) and the black star their breeding colonies location. 7 SI Level-crossing statistics of concentration fluctuations in odour plumes dispersing in turbulent flows. Here, using standard methods (Risken 1996), it is shown that the distribution of durations, , during which concentrations remain continually above some threshold, detectable to the birds, exhibits power-law scaling, p 3 / 2 with an exponential truncation that is dependent upon the local atmospheric conditions and is expected to increase with increasing atmospheric stability, i.e., with decreasing atmospheric turbulence (Fig. S2). The odour concentrations in turbulent flows are best represented by a clipped-normal distribution (Lewellen & Sykes 1986). However, an exponential distribution is only slightly conservative and has the advantage of simplicity (Sawford 1987) which facilitates mathematically analysis (Sawford, 1987) It is for this reason that the analysis presented here is based on the exponential probability distribution of concentrations, c , pc c exp c / C / C (1) where C is the mean concentration over time. When spatial variations of C are sufficiently small, the exponential distribution (1) is a stationary solution of the Fokker-Planck equation, p C p C 2 2 p t T c T c 2 (2) where T is the autocorrelation timescale, i.e., the durations over which concentrations remain significantly correlated (Thomson, 1987). A general, time-dependent, solution to (2) corresponding to the initial condition pc c c c0 is 2 C 2 t d pc c exp c / C exp t / 4T sin c c sin c0 c exp T 0 8 (3) where λs are eigenvalues of Eqn. (2). The distribution (3) vanishes at c c , where c is the threshold concentration above which birds may detect the odour. This constraint amounts to the imposition of an absorbing boundary. Once a concentration, c , falls below c it is ‘absorbed’ and does not rise above c at some * later time. This facilitates the determination of the distribution, p , of durations , during which concentrations * remain continually above the threshold concentration. This is because p is just the flux of concentrations into the absorbing boundary, p * C 2 p T c c c 2 C 2 C2 exp c / 2C exp / 4T sin c0 c exp T T 0 d 1 T 1 / 2 3 / 2 exp c / 2C exp / 4T c0 c exp T2 c c0 2 4C 4C (4) An analogous result can be found for the distribution of durations during which concentrations remain continually above some threshold concentration. It is noteworthy that the long-time, 3 / 2 , asymptotic behaviour is a manifestation of the Sparre Andersen Theorem (Sparre Andersen 1953, 1954) and so generic rather than model specific.The model is displayed in Fig. S2. We compute the time when odour concentration is continuously above the detection threshold c . According to our theory 1 𝑇(𝑐𝜏 − 𝑐0 )2⁄ 4𝐶 2 = 1 / 4T and 2 = . Furthermore, our analytic result is consistent with the observations of Yee et al., (1994a, b) who made highspeed recordings of odour concentrations within the atmospheric boundary-layer and found 3 / 2 scaling behavior over about 3 orders of magnitude. Yee et al. (1994a,b) reported on concentration fluctuations and scales in a dispersing plume in the atmospheric surface layer. They found clear evidence for power-law scaling on time intervals, τ , from 0.1 s up to and including the longest recorded intervals which lasted several 100 s., i.e. comparable to the duration of the observations (600 sec).These experiments do not preclude the possibility 9 that the 3 / 2 scaling extends too much longer time intervals that were not captured by the measurements. Power-law scaling at much longer time intervals is expected to be more in evidence above the ground where the spatial-temporal scales of turbulence are larger. We do not imagine that shearwaters respond to the fastest turbulent fluctuations in odour concentration but instead expect them to react to the more prolonged fluctuations. When the odours are present above the threshold of detection then the odour map is present and the birds ‘know’ to keeping flying forward. But when the odour concentration fall 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. A flight-segment length distribution with an exponentially-truncated -3/2 power-law tail is therefore predicted to be hallmark of olfactory-cued navigation. Our predictions apply equally well to pure odours and blends having several components because the ratio among constituents of a blend is largely preserved as the mixture is carried by a turbulent airstream (Duplat et al. 2010). The ratio of constituent components of an odour blend will change only gradually over time with the rate limiting process being driven by differences in the molecular diffusivities of the components. Duplat, J., Innocenti C., Villermaux E. (2010) A nonsequential turbulent mixing process, Physics of Fluids 22 article 035104. Lewellen W.S. & Sykes A.I. (1986) Analysis of concentration fluctuations from Lidar observations of atmospheric plumes. J Climate Appl Meteorol 25, 1145-1150. Risken H. (1996) The Fokker-Planck Equation: Methods of Solutions and Applications (Springer Series in Synergetics) ISBN-13 978-3540615309 Springer. Sawford B.L. (1987) Conditional concentration statistics for surface plumes in the atmospheric boundary-layer, Boundary-Layer Meteorology 38, 209-223. Sparre Andersen E. (1953) On the fluctuations of sums of random variables, Mathematica Scandinavica 1, 263285. Sparre Andersen E. (1954) On the fluctuations of sums of random variables II, Mathematica Scandinavica 2, 195-223. 10 Thomson D.J. (1987) Criteria for the selection of stochastic models of particle trajectories in turbulent flows, Journal of Fluid Mechanics 180, 529-556 Yee E., Chan R., Kosteniuk P.R., Chandler G.M., Biltoft C.A., Bowers J.F. (1994a) Experimental measurements of concentration fluctuations and scales in a dispersing plume in the atmospheric surface layer obtained using a very fast response concentration detector, J. Applied Meteorology 33, 996-1016,. Yee E., Chan R., Kosteniuk P.R., Chandler G.M., Biltoft C.A. & Bowers J.F. (1994b) Measurements of levelcrossing statistics of concentration fluctuations in plumes dispersing in the atmospheric surface layer’, Boundary-Layer Meteorology 73, 53-90 11 Figure S2. Graphic representation of the model of time series of odour concentration. The blue line represents the fluctuation in the odour concentration in the environment. The dotted line represents the critical concentration detectable to birds and the green line represents the mean concentration over time. We aimed to find the distribution of times, , when odour concentration is above the detection threshold. 12 SI Synthetic flights Synthetic flight lengths were drawn at random from an exponentially-truncated power-law distribution, the hallmark distribution of an olfactory-cued navigation: p l N1l exp 1l exp 2 / l where pl is the probability of a move of length l, 3 / 2 is the power-law (Lévy) exponent,1 and2 describe the truncation and N1 is a normalization factor. To evaluate the statistical power of our method (which is expected to increase with trip length, because of a larger sample of displacements) we computed the probability of detecting the true model (ETPL) in synthetic flights as a function of trip length and overlap them to the results obtained with a sample of 210 shearwaters, in Fig. S3. It appears evident that the sample size plays a sharp role in determining the possibility of correctly detecting an ETPL model in data. Accordingly, almost 80% of birds with a trip length of 1,000 km appear to perform ETPL. Note that the statistical power function derived by the synthetic trajectories overlaps to what it is observed for actual birds, in the studied range of trip length. This suggest that most of actual birds whose movement pattern was biexponential or power law, were misidentified due to a small number of recorded displacements, also reported in Table S2. For experimental data (Table S2) we tested whether it exists an interaction between colony and trip length which might have an effect in detecting ETPL, but this hypothesis was less supported (AIC=228.9) than the only effect of trip length (AIC=226.4). The effect of trip length on the probability of performing ETPL movements is highly significant (2 = 33.43, P<0.0001), while the effect of colony is not (2 = 5.37, P=0.50). 13 Figure S3. Synthetic flights: red dotted line represents the proportion of synthetic odour-cued flights that are misidentified as being bi-modal flights by the maximum likelihood method, because the Akaike weights for an odour-cued flight are <0.5. Actual data: the blue continuous line represents the probability of performing an ETPL movement pattern as a function of trip length. Light blue band represents 95% confidence interval. 14 SI Individual flight characteristics The main statistical features of our samples are reported in Table S2. It shows that 70% of birds show an ETPL movement model, 20% exhibit a PL model and 9.5% a biexponential pattern. No bird exhibits an exponential movement pattern. For the ETPL model we report also the results of a goodness of fit test which is not significant (at P=0.05 level) for 75 birds and is weakly significant (0.05<P≤0.01) for 72 birds, overall indicating a quite good fit of the ETPL model. In Fig. S4 we report some examples of model fitting at the individual level, selecting at random one animal per colony. It appears clear that the fitting is quite good with a nice overlap between theoretical predictions and actual data. 15 Table S2. For each bird (ring) we report the year of study, the breeding colony, the period (CHI=chick rearing, INC=incubation), the best-fit model (ETPL = exponentially truncated power law, PL=power law, BIEXP=biexponential and EXP=exponential), the ETPL Akaike weight (AW), duration of the trip (Dur), total flight length, number of displacements (Displ) and the probability of the Kolmogorv-Smirnoff goodness-of-fit test (KS). is reported with 95% confidence interval. Obs Year Colony Ring Period Dur Length Displ Model AW (hours) (km) 2 1 KS 1 2010 Berlenga 22372 CHI 44 3058 298 ETPL 2 2010 Berlenga 22388 CHI 23 1261.2 303 ETPL 0.87 1.36[1.25,1.47] 0.06 0.02 0.02 3 2010 Berlenga 22525 CHI 23 996.3 235 ETPL 0.7 2.15[2.02,2.28] 0.021 2.45 0.03 4 2010 Berlenga 39109 CHI 21 2219.6 316 ETPL 5 2010 Berlenga 39114 CHI 41 1571.8 326 ETPL 0.98 1.99[1.88,2.10] 6 2010 Berlenga 44531 CHI 21 2963.5 456 ETPL 1 1.36[1.27,1.45] 7 2010 Berlenga 44824 CHI 21 3463.2 240 ETPL 1 1.52[1.39,1.65] 0.0019 0.24 0.03 8 2010 Berlenga 54006 CHI 208 1411.1 195 ETPL 1 1.56[1.42,1.70] 0.0005 0.16 0.05 9 2010 Berlenga 59360 CHI 65 761 76 ETPL 0.67 1.58[1.35,1.81] 0 10 2010 Berlenga 59755 CHI 16 58.2 16 ETPL 0.87 1.00[0.50,1.50] 0 0.04 0.12 11 2010 Berlenga 61358 CHI 71 1053.1 117 ETPL 1 1.40[1.22,1.58] 0.0054 12 2010 Berlenga 64211 CHI 307 3814.5 428 ETPL 1 2.00[1.90,2.10] 0 1.76 0.03 13 2010 Berlenga 64222 CHI 25 320.1 36 ETPL 0.39 1.48[1.15,1.81] 0 0.44 0.08 14 2010 Berlenga 64228 CHI 21 116.4 29 BIEXP 0.42 15 2010 Berlenga 64331 CHI 16 88 20 PL 0.73 1.45[1.00,1.90] 0 0 16 2010 Berlenga 64338 CHI 165 2942.1 149 PL 1 1.44[1.28,1.60] 0 0 17 2010 Berlenga 64391 CHI 41 601.1 74 ETPL 0.89 1.69[1.46,1.92] 0 1.05 0.08 18 2010 Berlenga 64393 CHI 40 373.9 90 ETPL 0.72 2.11[1.90,2.32] 0 1.72 0.06 19 2010 Berlenga 64397 CHI 21 88.7 27 PL 0.77 1.63[1.25,2.01] 0 0 20 2010 Berlenga 67769 CHI 41 451.5 51 PL 0.97 1.59[1.31,1.87] 0 0 21 2010 Berlenga 73254 CHI 45 427.3 71 ETPL 0.74 1.67[1.43,1.91] 0 0.64 0.05 22 2010 Berlenga 73290 CHI 69 828.7 111 ETPL 23 2010 Berlenga 76503 CHI 21 85 23 ETPL 0.75 1.57[1.15,1.99] 0 0.62 0.11 24 2010 Berlenga 76516 CHI 47 571.8 126 ETPL 0.94 2.23[2.05,2.41] 0 2.89 0.04 25 2010 Berlenga 76519 CHI 120 1762.4 196 ETPL 26 2010 Berlenga 76603 CHI 44 403.9 76 BIEXP 0.45 27 2010 Berlenga 78615 CHI 20 107.5 26 ETPL 0.73 2.16[1.77,2.55] 0 2.29 0.09 28 2010 Berlenga 78646 CHI 184 1696.9 265 ETPL 1 1.58[1.46,1.70] 0.01 0.39 0.03 29 2010 Berlenga 8043 CHI 69 1815.3 272 ETPL 0.99 1.86[1.74,1.98] 0.001 1.75 0.05 30 2007 Corvo 44207 CHI 91 1376.3 130 ETPL 1 2.00[1.82,2.18] 0 1.33 0.05 31 2007 Corvo 44242 CHI 17 60.6 21 ETPL 0.63 2.99[2.55,3.43] 0 3.66 0.12 32 2007 Corvo 44350 CHI 41 522.7 89 ETPL 0.83 1.49[1.28,1.70] 0.0034 33 2007 Corvo 61794 CHI 255 3705.1 319 ETPL 1 1.82[1.71,1.93] 34 2007 Corvo 63373 CHI 37 ETPL 0.9 1.14[0.81,1.47] 20 227.6 16 1 1.64[1.52,1.76] 0.0009 0.47 0.03 1 1.55[1.44,1.66] 0.0074 0.01 0.03 0 0.73 0.02 0.022 0 0.02 0 0.05 0 0.04 0.92 1.63[1.44,1.82] 0.0082 0.84 0.04 1 1.42[1.28,1.56] 0.0057 0 0.06 0 0.05 0 1.04 0.05 0 0 0.08 35 2007 Corvo 63822 CHI 49 1122 43 ETPL 0.97 1.58[1.28,1.88] 0 0.77 0.05 36 2007 Corvo 63855 CHI 16 104.4 16 PL 0.83 1.10[0.60,1.60] 0 37 2007 Corvo 63870 CHI 19 270 79 ETPL 0.64 1.93[1.70,2.16] 38 2007 Corvo 63890 CHI 17 59.5 20 PL 0.63 2.02[1.57,2.47] 0 0 39 2007 Corvo 63892 CHI 17 102.1 20 PL 0.58 1.45[1.00,1.90] 0 0 40 2007 Corvo 66724 CHI 102 268.1 9 ETPL 0.61 1.45[0.78,2.12] 0 1.88 0.11 41 2007 Corvo 69033 CHI 17 225.4 28 ETPL 0.82 1.25[0.87,1.63] 0 0.08 0.09 42 2007 Corvo 73366 CHI 17 248.7 55 BIEXP 43 2007 Corvo 73367 CHI 16 87.1 26 PL 0.69 1.54[1.15,1.93] 0 0 44 2007 Corvo 73369 CHI 17 4001 13 PL 0.71 1.53[0.98,2.08] 0 0 45 2007 Corvo 73370 CHI 21 148.1 33 ETPL 46 2007 Corvo 73372 CHI 16 100.1 24 BIEXP 0.43 47 2007 Corvo 78306 CHI 17 73.9 16 ETPL 0.83 1.37[0.87,1.87] 0 48 2007 Corvo 78307 CHI 15 89.7 25 PL 0.84 1.24[0.84,1.64] 0 49 2007 Corvo 78310 CHI 16 4055.4 27 ETPL 0.82 1.68[1.30,2.06] 0 1.49 0.07 50 2008 Linosa T72729 CHI 47 247.2 47 ETPL 0.71 1.44[1.15,1.73] 0.001 51 2012 Linosa T73139 CHI 25 138.3 12 PL 0.77 1.16[0.58,1.74] 0 52 2008 Linosa T73735 CHI 69 559.8 67 ETPL 0.56 1.67[1.43,1.91] 0 1.24 0.10 53 2008 Linosa T73783 CHI 28 119.1 27 ETPL 0.65 1.57[1.19,1.95] 0 0.54 0.10 54 2012 Linosa T73800 CHI 89 645.7 112 ETPL 0.65 1.61[1.42,1.80] 0.014 0.69 0.05 55 2012 Linosa T74208 CHI 47 154.1 15 BIEXP 0.21 56 2012 Linosa T74401 CHI 125 968.6 97 ETPL 0.98 1.39[1.19,1.59] 57 2012 Linosa T74554 CHI 27 148.8 23 ETPL 0.75 1.55[1.13,1.97] 58 2012 Linosa T75203 CHI 26 135 14 BIEXP 0.39 59 2008 Linosa T75215 CHI 44 264.9 48 BIEXP 0.43 60 2008 Linosa T75237 CHI 51 317.1 49 ETPL 0.86 1.52[1.23,1.81] 61 2012 Linosa T75239 CHI 22 924.4 6 ETPL 0.71 1.49[1.31,1.67] 0.023 0.05 0.39 62 2008 Linosa T75239 INC 148 126.9 129 ETPL 0.89 1.00[0.18,1.82] 0 4.99 0.05 63 2012 Linosa T75280 CHI 25 277.7 0.62 1.38[1.05,1.71] 0 64 2008 Linosa T75298 CHI 255 1630.1 213 ETPL 0.98 1.87[1.73,2.01] 0.003 2.23 0.05 65 2008 Linosa T75409 CHI 213 1065.1 165 ETPL 0.99 2.39[2.23,2.55] 0 2.97 0.03 66 2012 Linosa T75478 CHI 27 148.7 21 PL 0.81 1.38[0.94,1.82] 0 0 67 2012 Linosa T75499 CHI 40 299.8 33 PL 0.79 1.18[0.83,1.53] 0 0 68 2012 Linosa T75500 CHI 22 168.8 15 PL 0.66 1.24[0.72,1.76] 0 0 69 2012 Linosa TB4602 CHI 24 228.2 24 ETPL 0.7 1.72[1.31,2.13] 0 2.34 0.07 70 2012 Linosa TB4667 CHI 51 306.8 43 PL 0.6 1.42[1.12,1.72] 0 71 2008 Linosa TE9522 INC 16 92.2 72 2012 Linosa TH1744 CHI 19 98.9 5 PL 0.5 1.00[0.11,1.89] 73 2008 Linosa TH1759 INC 132 865.7 140 ETPL 0.97 1.96[1.79,2.13] 0.002 1.59 0.05 74 2008 Linosa TH1863 INC 244 1394.9 255 ETPL 0.96 1.89[1.76,2.02] 0 0.62 0.02 17 36 PL 14 ETPL 0 0.058 2.02 0.06 0.4 0.8 1.52[1.17,1.87] 0.75 1.28[0.75,1.81] 0 0.18 0.08 0.007 2.1 0.10 0 0 0.08 0 0 0.05 0 0.45 0.09 0 0 0.06 0 0 0 0.95 0.12 0 0 75 2008 Linosa TH1871 INC 162 1350.1 141 ETPL 0.86 1.35[1.18,1.52] 76 2008 Linosa TH4333 INC 252 1637.4 325 ETPL 0.98 2.09[1.98,2.20] 0.006 1.91 0.03 77 2008 Linosa TH4335 CHI 363.3 57 ETPL 0.6 1.00[0.74,1.26] 0.043 0.75 0.10 78 2008 Linosa TH4336 CHI 189 1683.2 159 ETPL 0.97 1.32[1.16,1.48] 0.013 0.63 0.03 79 2012 Linosa TH4343 CHI 80 2008 Linosa TH4398 CHI 81 2012 Linosa TH5971 CHI 21 155.7 30 PL 82 2008 Linosa TH7178 INC 77 338.6 48 BIEXP 0.46 83 2008 Linosa TH7179 INC 102 585.7 91 PL 84 2008 Linosa TH7183 INC 267 1411.1 256 ETPL 85 2008 Linosa TH7185 INC 273 1675.4 276 BIEXP 0.84 86 2008 Linosa TH7203 CHI 18 57.6 10 PL 0.63 1.34[0.71,1.97] 87 2012 Linosa TH7234 CHI 117 751 84 ETPL 0.77 1.37[1.15,1.59] 88 2012 Linosa TH7487 CHI 14 88.6 15 PL 89 2012 Linosa TH7489 CHI 23 131.4 13 ETPL 90 2012 Linosa TH7491 CHI 27 182.9 18 BIEXP 0.46 91 2012 Linosa TH7492 CHI 25 146.4 16 PL 0.71 1.13[0.63,1.63] 0 92 2008 Linosa TH8040 INC 74 580.9 72 ETPL 0.71 1.60[1.36,1.84] 0 0.81 0.04 93 2008 Linosa TH8412 INC 46 129.8 32 PL 0.73 1.82[1.47,2.17] 0 0 94 2012 Linosa TH8414 CHI 18 142.5 24 PL 0.79 1.05[0.64,1.46] 0 0 95 2008 Linosa TH8438 INC 18 118.6 20 ETPL 0.76 1.33[0.88,1.78] 0 2.03 0.16 96 2008 Linosa TH8444 INC 254 1566.1 286 ETPL 0.94 1.57[1.45,1.69] 0.029 0.91 0.02 97 2008 Linosa TH8447 CHI 26 118.8 98 2008 Linosa TH8450 CHI 98 341 99 2012 Linosa TH8485 CHI 157 860.8 100 2012 Linosa TH8507 CHI 70 462.7 63 ETPL 0.85 1.51[1.26,1.76] 0 0.33 0.05 101 2008 Linosa TH8510 CHI 188 943.4 144 ETPL 0.93 1.99[1.82,2.16] 0 1.59 0.03 102 2008 Linosa TH8530 CHI 25 59.1 16 ETPL 0.64 1.75[1.25,2.25] 0 0.91 0.15 103 2008 Linosa TH8534 CHI 233 1392.4 219 ETPL 0.99 1.22[1.08,1.36] 0.03 0.01 0.04 104 2008 Linosa TH8535 CHI 188 981 171 ETPL 0.97 1.88[1.73,2.03] 0 1.81 0.03 105 2008 Linosa TH8544 CHI 73 470.7 70 ETPL 0.79 1.66[1.42,1.90] 0 1.26 0.05 106 2012 Linosa TJ8151 CHI 44 287.1 50 PL 107 2012 Linosa TJ8152 CHI 22 197.9 15 ETPL 0.55 1.16[0.64,1.68] 0 1.27 0.19 108 2012 Linosa TJ8154 CHI 22 133.2 13 ETPL 0.83 1.00[0.45,1.55] 0 1.17 0.16 109 2012 Linosa TJ8155 CHI 173 1205 110 2012 Linosa TJ8156 CHI 88 493.1 74 ETPL 0.77 1.84[1.61,2.07] 0 1.32 0.06 111 2012 Linosa TJ8157 CHI 91 546.3 60 ETPL 0.83 1.89[1.63,2.15] 0 1.81 0.09 112 2012 Linosa TJ8160 CHI 41 490.2 47 ETPL 0.91 1.13[0.84,1.42] 0 0.01 0.08 113 2012 Linosa TJ8165 CHI 260 1664.2 224 ETPL 0.99 1.74[1.61,1.87] 0.006 1.14 0.03 114 2012 Linosa TJ8168 CHI 82 ETPL 0.55 1.73[1.51,1.95] 0 1.53 0.04 70 91 902.4 192 1301.5 72 606.7 18 0.01 0 0.05 65 BIEXP 0.38 162 ETPL 1 1.72[1.56,1.88] 0.81 1.36[0.99,1.73] 0.004 0.89 0.03 0 0 0.87 1.45[1.24,1.66] 0 0 0.96 1.94[1.80,2.08] 0 1.38 0.03 0.8 1.00[0.48,1.52] 0.81 1.00[0.45,1.55] 26 PL 0.75 1.79[1.40,2.18] 73 ETPL 0.77 1.84[1.61,2.07] 0 0 0.014 0.43 0.07 0 0 0 0.96 0.15 0 0 0 0.023 2.52 0.06 151 BIEXP 0.31 0.9 1.59[1.31,1.87] 0 0 144 BIEXP 0.16 115 2012 Linosa TJ8170 CHI 79 882.1 123 ETPL 0.91 1.45[1.27,1.63] 0.012 0.57 0.04 116 2012 Linosa TJ8171 CHI 48 2416.3 311 ETPL 1 1.79[1.68,1.90] 0 1.54 0.05 117 2012 Linosa TJ8172 CHI 24 118.3 15 ETPL 0.79 1.36[0.84,1.88] 0 2.21 0.09 118 2012 Linosa TJ8173 CHI 42 604.7 66 ETPL 0.87 1.14[0.89,1.39] 0.01 0.01 0.04 119 2013 Maddalena TA6976 CHI 17 151.1 24 ETPL 0.75 1.28[0.87,1.69] 120 2013 Maddalena TA7167 CHI 19 298.2 18 BIEXP 0.14 121 2013 Maddalena TC4838 CHI 24 285.2 35 ETPL 122 2013 Maddalena TJ1376 CHI 23 167.2 22 PL 123 2013 Maddalena TJ8101 CHI 21 304.7 23 BIEXP 0.01 124 2013 Maddalena TJ8103 CHI 45 376 38 ETPL 0.72 1.81[1.49,2.13] 0 3.23 0.04 125 2013 Maddalena TJ8123 CHI 142 1712.6 255 ETPL 1 1.70[1.57,1.83] 0.014 1.22 0.03 126 2013 Maddalena TJ8124 CHI 24 96.6 22 PL 0.63 1.96[1.53,2.39] 0 0 127 2013 Maddalena TJ8126 CHI 20 207 27 PL 0.66 1.32[0.94,1.70] 0 0 128 2013 Maddalena TJ8135 CHI 24 77.3 19 ETPL 0.93 1.00[0.54,1.46] 0 0.64 0.12 129 2013 Maddalena TJ8137 CHI 91 799.7 96 ETPL 0.56 1.62[1.42,1.82] 0.0064 1.11 0.05 130 2013 Maddalena TJ8141 CHI 24 77.6 131 2013 Maddalena TJ8150 CHI 95 593.3 107 ETPL 0.67 1.97[1.78,2.16] 0 1.57 0.04 132 2013 Maddalena TK0413 CHI 19 91.6 32 ETPL 0.7 1.69[1.34,2.04] 0 0.09 0.09 133 2013 Maddalena TK0414 CHI 21 184.6 27 ETPL 0.63 1.07[0.69,1.45] 0.01 134 2013 Maddalena TK0415 CHI 20 154 21 PL 0.74 1.25[0.81,1.69] 0 135 2013 Maddalena TK0416 CHI 24 143.4 28 BIEXP 0.27 136 2013 Maddalena TK0418 CHI 35 237.3 49 ETPL 0.77 1.83[1.54,2.12] 0 0.93 0.06 137 2013 Maddalena TK0419 CHI 23 123.8 25 ETPL 0.69 2.00[1.60,2.40] 0 2.38 0.07 138 2013 Maddalena TK0420 CHI 52 181.8 29 ETPL 0.64 1.49[1.12,1.86] 0 1.26 0.10 139 2013 Maddalena TK0421 CHI 52 496.6 63 PL 0.66 1.55[1.30,1.80] 0 140 2013 Maddalena TK0422 CHI 141 2013 Maddalena TK0423 CHI 27 60.1 142 2013 Maddalena TK0424 CHI 21 143 2013 Maddalena TK0425 CHI 144 2013 Maddalena TK0426 166 1608.1 0.74 1.71[1.37,2.05] 0.7 1.56[1.13,1.99] 22 EXPL 0.63 1.33[0.90,1.76] 228 ETPL 1 2.07[1.94,2.20] 0 0.3 0.12 0 1.11 0.08 0 0.043 0 0 0 0.11 0 0 0 1.93 0.02 16 PL 0.84 1.11[0.61,1.61] 0 193.5 57 ETPL 0.67 2.58[2.32,2.84] 0 20 244.5 15 ETPL 0.75 1.01[0.49,1.53] 0 0.78 0.10 CHI 25 260.8 20 BIEXP 0.41 145 2013 Maddalena TK0430 CHI 46 396.7 58 ETPL 0.79 1.49[1.23,1.75] 0 0.57 0.08 146 2013 Maddalena TK0431 CHI 18 121.9 17 ETPL 0.58 1.77[1.28,2.26] 0 1.44 0.09 147 2013 Maddalena TK0432 CHI 82 196.4 63 ETPL 0.87 2.25[2.00,2.50] 0.0002 148 2013 Maddalena TK0433 CHI 43 484.5 54 BIEXP 0.37 149 2013 Maddalena TK0435 CHI 67 435.4 75 ETPL 150 2013 Maddalena TK0439 CHI 19 155.4 17 BIEXP 0.47 0.87 1.43[1.20,1.66] 0.017 0 2.7 0.06 0.6 0.05 0 0.05 151 2013 Raso CRlog100F CHI 14 3880.5 349 ETPL 1 1.79[1.68,1.90] 0 1.28 0.03 152 2013 Raso CRlog110F CHI 16 5674.2 532 ETPL 1 1.37[1.28,1.46] 0.009 1.44 0.02 153 2013 Raso CRlog118F CHI 66 4728.1 436 ETPL 154 2013 Raso CRlog119F CHI 403 5231.4 470 ETPL 19 0.95 1.73[1.63,1.83] 0.0008 1.54 0.04 1 1.65[1.56,1.74] 0.003 1.24 0.02 155 2013 Raso CRlog34F CHI 15 5238.1 365 ETPL 1 1.60[1.50,1.70] 0.001 1.11 0.03 156 2013 Raso CRlog88F CHI 15 4766.4 296 ETPL 0.83 1.36[1.24,1.48] 0.004 0.54 0.03 157 2013 Raso CRlog92F CHI 22 4694.7 432 ETPL 158 2013 Raso INlog100F INC 159 2013 Raso 17 1 1.51[1.41,1.61] 0.0003 0.48 0.02 591 97 ETPL 0.91 2.01[1.81,2.21] 0 1.25 0.06 INlog104F INC 213 2806.2 192 ETPL 0.76 1.75[1.61,1.89] 0.001 2.19 0.03 160 2013 Raso INlog110F INC 258 3250.2 273 ETPL 1 1.86[1.74,1.98] 0.001 1.79 0.04 161 2013 Raso INlog118F INC 261 4705.5 274 ETPL 1 1.77[1.65,1.89] 0.0005 1.68 0.03 162 2013 Raso INlog119F INC 281 2760.3 300 ETPL 1 2.41[2.29,2.53] 0 3.51 0.04 163 2013 Raso INlog122F INC 197 1664.4 218 ETPL 1 2.17[2.03,2.31] 0 2.33 0.05 164 2013 Raso INlog123F INC 281 3233.1 329 ETPL 1 1.86[1.75,1.97] 0.001 1.46 0.03 165 2013 Raso INlog129F INC 238 2553.7 214 ETPL 0.85 2.15[2.01,2.29] 0 3.42 0.04 166 2013 Raso INlog131F INC 231 1923.7 304 ETPL 1 1.74[1.63,1.85] 0.016 167 2013 Raso INlog135F INC 0.54 1.51[0.99,2.03] 0 168 2013 Raso INlog79F INC 112 1103.1 74 ETPL 0.9 1.47[1.24,1.70] 0 0.71 0.05 169 2008 Selvagem 20101 CHI 91 1002.1 53 ETPL 0.84 1.45[1.18,1.72] 0 0.74 0.04 170 2008 Selvagem 33203 CHI 14 160.2 36 PL 0.8 1.38[1.05,1.71] 0 0 171 2008 Selvagem 37488 CHI 14 296.7 16 PL 0.67 1.22[0.72,1.72] 0 0 172 2008 Selvagem 40242 CHI 14 127.4 28 ETPL 0.73 1.82[1.44,2.20] 0 1.71 0.07 173 2008 Selvagem 43975 CHI 15 118.1 26 PL 0.57 1.65[1.26,2.04] 0 174 2008 Selvagem 43992 CHI 235 2739.8 290 ETPL 1 1.60[1.48,1.72] 0.005 0.53 0.03 175 2008 Selvagem 74835 CHI 184 2369.5 266 ETPL 1 1.43[1.31,1.55] 0.01 0.65 0.03 176 2008 Selvagem 76429 CHI 104 PL 1 1.71[1.51,1.91] 177 2008 Selvagem 76430 CHI 159 2042.3 154 ETPL 1 1.32[1.16,1.48] 0.01 0.48 0.04 178 2008 Selvagem 76434 CHI 188 1709.8 207 ETPL 0.97 2.00[1.86,2.14] 0.002 2.77 0.05 179 2008 Selvagem 76436 CHI 133 1235.6 136 ETPL 0.97 1.97[1.80,2.14] 0 1.67 0.04 180 2008 Selvagem 768379 CHI 15 117.2 31 PL 0.92 1.07[0.71,1.43] 0 0 181 2008 Selvagem 78380 CHI 14 78.1 17 PL 0.65 1.36[0.87,1.85] 0 0 182 2008 Selvagem 78383 CHI 20 271.6 33 BIEXP 0.16 183 2008 Selvagem 78384 CHI 10 262.5 13 ETPL 184 2008 Selvagem 78386 CHI 143 1646.8 165 ETPL 185 2009 Tremiti T97749 INC 119 706.3 148 PL 0.91 1.66[1.50,1.82] 186 2010 Tremiti T97769 INC 100 416 141 ETPL 0.56 2.25[2.08,2.42] 0.094 2.53 0.03 187 2010 Tremiti TB0524 INC 70 549.7 90 ETPL 0.81 1.92[1.71,2.13] 0 2.56 0.06 188 2009 Tremiti TC7503 INC 161 813.7 171 ETPL 0.55 1.30[1.15,1.45] 0.046 0.16 0.04 189 2009 Tremiti TC7505 INC 45 276 190 2009 Tremiti TC7506 INC 80 1009.7 191 2009 Tremiti TC7507 INC 124 192 2010 Tremiti TC7509 INC 193 2010 Tremiti TC7510 194 2009 Tremiti TC7511 17 97 197.7 1100 15 PL 0 0 0 0 1.52 0.15 1 1.78[1.62,1.94] 0.0006 0.95 0.06 0 0 0.97 1.17[0.89,1.45] 0 141 ETPL 0.73 1.61[1.44,1.78] 0 0.48 0.03 477.2 102 ETPL 0.92 1.72[1.52,1.92] 0 81 605 106 ETPL 0.73 1.36[1.17,1.55] 0.021 0.02 0.05 INC 69 301.3 65 ETPL 0.7 2.26[2.01,2.51] 0 2.75 0.05 INC 89 524 20 51 PL 0.77 1.13[0.58,1.68] 0 1.6 0.03 114 - 0.5 2.10[1.91,2.29] 0 1.1 0.06 0.006 1.69 195 2010 Tremiti TC7514 INC 196 2010 Tremiti TC7519 197 2010 Tremiti 63 304.2 55 ETPL 0.7 2.23[1.96,2.50] 0 3.34 0.06 INC 249 2212.3 345 ETPL 0.99 1.32[1.21,1.43] 0.028 0.54 0.03 TC7521 INC 137 1174.5 157 ETPL 0.99 1.48[1.32,1.64] 0.015 0.88 0.06 198 2010 Tremiti TC7522 INC 20 100.2 199 2010 Tremiti TC7524 INC 178 1428 232 ETPL 0.93 2.12[1.99,2.25] 0 2.74 0.03 200 2010 Tremiti TC7525 INC 99 944.1 103 ETPL 0.95 1.22[1.02,1.42] 0.017 0.09 0.04 201 2010 Tremiti TC7526 INC 194 1429.4 205 ETPL 1 1.47[1.33,1.61] 0.017 0.42 0.03 202 2010 Tremiti TC7527 INC 237 1763.3 313 ETPL 0.79 1.72[1.61,1.83] 203 2010 Tremiti TC7529 INC 82 510 121 ETPL 0.85 2.71[2.53,2.89] 0 3.77 0.04 204 2010 Tremiti TC7533 INC 39 222.5 52 ETPL 0.57 1.96[1.68,2.24] 0 1.65 0.06 205 2009 Tremiti TE1339 INC 18 111.9 19 ETPL 0.66 1.00[0.54,1.46] 0.031 0.01 0.11 206 2009 Tremiti TE1341 INC 174 957.8 221 ETPL 0.62 1.80[1.67,1.93] 0.062 2.46 0.04 207 2009 Tremiti TE1342 INC 68 490.6 63 ETPL 0.53 1.81[1.56,2.06] 0 1.61 0.07 208 2010 Tremiti TE1343 INC 224 2425.2 250 ETPL 1 1.48[1.35,1.61] 0.009 0.88 0.03 209 2009 Tremiti TE1345 INC 143 888.2 165 ETPL 0.87 1.82[1.66,1.98] 0.019 1.66 0.03 210 2009 Tremiti TE1347 INC 161 766.3 166 ETPL 0.85 2.42[2.26,2.58] 0 2.55 0.03 21 23 PL 0.8 1.43[1.01,1.85] 0 0.018 0 1.5 0.02 Figure S4. Rank frequency plots of theoretically predicted distribution of displacement derived by the ETPl model (black continous line) and actual data (red open circles). 22