38. This subsurface warming is qualitatively similar to that ofprevious experiments with North Atlantic MWF, especially inthe tropical region and Southern Hemisphere [e.g., (30, 48)];it seems also to be consistent with benthic d18O inferredtemperature changes in the tropical Atlantic (49), westernsubtropical North Atlantic (4), and Nordic Sea (50), as wellas Mg/Ca-based benthic temperatures from the easternsubtropical North Atlantic (51).

39. S. Rahmstorf et al., Geophys. Res. Lett. 32, L23605 (2005).40. The MWF varies slowly during this period at a rate of

~0.1 sverdrup/ky in DGL-B, comparable to that used inprevious standard hysteresis tests (18, 39).

41. About a third of the model BA warming appears to beassociated with a nonlinear convective response in theNordic Sea. As seen in experiment DGL-B, under agradual forcing, the AMOC and Greenland temperature,after a long period of gradual change, increase abruptlyat the end stage (14.6 ka) in 100 years (6 sverdrupand 6°C), nearly identical to the last 100 years of warmingin experiment DGL-A (Fig. 1, D and E, and fig. S4). Thisabrupt warming is induced by regional convectiveinstability in the Nordic Sea (18) on a background deep-ocean warming (52) and is enhanced by the northwardheat transport associated with the enhanced AMOC.

42. With a slower reduction in MWF, the AMOC resumptionand attendant BA warming in CCSM3 usually occur fasterthan the rate at which the MWF is reduced, partly due to

the convective instability process in the Nordic Sea (41).In a deglaciation sensitivity experiment similar to DGL-B,but with a faster termination time of 2000 years, theBA warming takes only 500 years, substantially fasterthan the MWF itself (not shown).

43. Except for an earlier generation of CGCM with fluxadjustments (53, 54), all published results from CGCMs aresimilar to those of CCSM3 in showing that the AMOCrecovers its strength after the termination of the freshwaterpulse. Because these CGCM hosing experiments areusually short (

tional quality and number of trials were limited.We show through detailed biological experimentand development of a model of the locomotionthat subsurface sandfish motion is not driven bylimbs but by an undulatory gait without use oflimbs. Thrust and drag result from frictional grainflow, which leads to features of the swimmingthat are intermediate to movement in fluids and

on solid surfaces, and surprisingly are indepen-dent of f.

To perform controlled studies of the burial andswimming of the sandfish (11 animals; mass =16.2 T 4 g, body length L = 8.3 T 3.3 cm, de-fined as the length from snout tip to the base ofthe tail), we used a fluidized bed (fig. S1) (19)to prepare a 10-cm-deep container of 0.27 T

0.04 mm glass beads into naturally occurringloosely packed and closely packed volumefractions f = 0.58 and f = 0.62, respectively.The sandfish took 672 T 239 ms to complete itsentire burial process, independent of volumefraction (Student’s t test, P > 0.05) (movieS1). Once below the surface, the dorsal x-rayvideo imaging (movies S2 and S3) revealed thatthe animal no longer used limbs for propulsion.Instead, the animal placed its limbs against itssides and executed an undulatory motion (Fig.1, E and F) with large-amplitude axial oscilla-tion, using its body to propel itself at speeds ofup to ~10 cm/s. We observed similar limblessundulatorymotion in beads withmean diametersranging from 0.1 mm to 3 mm. To quantify thelack of limb use, we measured the distancebetween pairs of limbs (fore and hind) (Fig. 1G).As the animal ran across the surface, this inter-limb distance oscillated around 2.75 T 0.59 cm,indicating the sprawl of the limbs during thediagonal gait (1, 9). As it began to bury, the inter-limb distance decreased significantly (Student’st test, P < 0.01) until it became a constant (1.72 T0.53 cm) close to body width (1.23 T 0.51 cm)because limbs were placed close to the side of thebody. Like in (18), side-view x-ray imaging of thesandfish subsurface showed that the animalundulates in a plane at ~ 22.2 T 3.7° with respectto the horizontal and buries consistently to adepth of 2.1 T 0.5 cm (surface to top of mid-pointof the back), independent of volume fraction(Student’s t test, P > 0.05).

We characterized the undulatory kinematicsby digitizing the midline from the dorsal x-rayimages (Figs. 1F and 2A). The undulatorymotion fit well (r2 > 0.85, P < 0.01) the formof a posteriorly traveling single-period sinusoidalwave (Fig. 2A) such that y = Asin 2p(x + vwt)/l,with y the displacement away from themidline ofa straight animal, A the amplitude, l the wave-length, f the wave frequency, and vw = f l¸ thewave speed. From the fit, we deduced theseparameters as well as the forward swimmingspeed of the center of mass vx (which was notequal to the wave speed; see discussion below).During a swim, there was no change in either A(P = 0.12) or l (P = 0.66), and neither A nor lvaried significantly for the different f (P > 0.05comparing each treatment by using a repeatedmeasures one-way analysis of variance) (Fig. 2B).The large-amplitude undulations over the entirebody are unlike the kinematics of other undula-tory swimming organisms on the sandfish-sizedscale [such as eels (20)], which tend to increase inamplitude posteriorly. The undulations do resem-ble those of eel movement on land (20) as well assmall (

ume fraction (Student’s t test, P > 0.05). Wefound, however, that vx is not simply the productof f and l, but instead the slope is reduced by aconstant factor h so that vx = h f (Fig. 2C) with h =0.54 T 0.12 and h = 0.49 T 0.09 for loosely andclosely packed material, respectively. Becausevw= lf, this implies that the average forward speedis a fraction of the wave speed. Thus, the animal isnot moving in a tube because successive undu-lations do not trace a continuous path; this can beseen in Fig. 1F. Instead, tracer particles placed in thebulk reveal that there is backward displacement ofmaterial as the animal moves forward. Slippingwhile progressing is common to undulatory swim-mers in deformablemedia across length scales (forexample, eels and spermatozoa in fluids) (1) and ischaracterized by the wave efficiency (h) (21), de-fined as the ratio between the forward speed of theanimal (vx) and the velocity of the wave travelingdown its body (vw): h = vx/vw. Because l for thesandfish is independent of f in our experiments, his the slope of the vx/l versus f curve and is shownin Fig. 2C. Typical wave efficiencies of organismsin moving in fluids at low Re (such as nematodes)are 0.25 (23), nearly a factor of two smaller thanthe sandfish, whereas organisms undulating (creep-ing) along the solid surface of an agar-air inter-face can have h close to unity [h ~ 0.8 − 0.9 (21)]because deformations in the surface allow move-ment that is effectively in a tube. h for the sand-fish in granular media is intermediate to that forfluids and solids and is independent of f, eventhough materials with different f have penetra-tion resistances that can vary by a factor of 2 (15).

Prediction of h for undulatory movement influids and solids has been accomplished by use ofmodels of interaction of the organism and theenvironment: In low Re Newtonian fluids, forcesare purely viscous (Stoke’s law) such that force isproportional to instantaneous velocity (22, 23),and in undulatory crawling on solids force isdetermined with static/dynamic friction coeffi-cients (22). Although the equivalent force lawsare not available in granular media, features of thesandfishmotion allow us to hypothesize about themedium in which it swims: (i) It is well knownthat for slow enough disturbances, the drag ingranular systems is dominated by friction be-tween flowing grains, and thus this makes dragindependent of velocity (14, 24–26). (ii) At theobserved body speeds and accelerations duringundulatory motion, inertial forces due to accel-erating material are small as compared with fric-tional drag forces (ma/F ≈ 0.2, where F ≈ 2 N isestimated for a small cylinder dragged in sandand ma ≈ 0.4 N is found from the product of theacceleration of the sandfish body and a mass ofsand surrounding it), and thus inertia can be ne-glected. (iii) Because grain interactions are dissi-pative, disturbances typically dampen in shorttimes, and thus changes in the static configurationdominate the drag force.

Therefore, we hypothesize that the animalswims in a so-called “frictional fluid” (27), suchthat flowing grain-grain and grain-animal friction

determine the thrust and drag forces. Such africtional fluid superficially resembles low Reswimming in that there is no inertia, but themechanism for drag is frictional, rather thanviscous. Movement in a frictional fluid differsfrom noninertial crawling on a surface in whichanisotropic friction [originating from, for exam-ple, deforming the surface and pushing off asdoes nematode on agar (21) or using overlappingbelly scales or changes in weight distribution asdoes a snake (28)] generates net propulsive forcewithout net flow of material.

To test this hypothesis, we developed amodelinspired by similar local force, noninertial models[typically called Resistive Force Theory (RFT)(23)] such that the body of the organism ispartitioned into elements, each of which generatesthrust and experiences drag whenmoving througha media and whose forces are not influenced byforce fields from other segments. If FN and FL arethe normal and lateral forces (perpendicular andparallel to the element respectively) acting on thesides of the sandfish body, net forward force on theelement can be written as Fx = FN sinq − FL cosq,where q is the angle between the forward directionof the animal and the orientation of an elementof the organism (Fig. 3A). The forces for eachelement are integrated over the length of the body(snout to tail tip) and for a full period of atraveling wave to obtain average swimmingspeed. Unlike in fluids, we have no validatedtheory to calculate the force on an intruder as afunction of its angle relative to displacement or

for varying f. Therefore, we used a combinationof measurements (19) of the granular thrust anddrag forces on a stainless steel cylindrical rod[with grain-surface friction coefficient similar tothe sandfish (16)], insights from Fig. 3B, and anempirical fitting function that incorporates dragon the sidewalls and end-faces of the cylinder(equation S8) so as to approximate FN and FL forelements of the sandfish body as:

FN = 2lr(CS sinb0 + CF siny)FL = 2lrCF cosy (1)

where tanb0 = cotg0 sin y, y is the angle of thesegment with respect to its local velocity vector, land r are the length and radius of the segment (as-sumed cylindrical), and the constantsCS,CF, and g0characterize the material response to drag. Plots ofFN andFL as a function ofy are shown in Fig. 3, Cand D. Equation 1 represents the data well (R2 =0.97) (solid lines shown in Fig. 3, C andD), and thefit coefficients are given in table S1.

FL is well approximated by the cosine func-tion, similar to viscous fluids or frictional ma-terial, indicating that its source is the resolvedcomponent of friction between the grains and thebody. The form of FN is not well approximatedby the corresponding sine component (Fig. 3C,dashed gray lines) but rather increases morerapidly for y < 30° and increases more slowly fory > 30°. We hypothesize that above this angle[close to the angle at which internal slip planesor shear bands form and move (14)], the force

Fig. 2. Kinematics ofthe undulatory sandfishmotion. (A) Travelingwave moving down thebody of the sandfishopposite to the directionof the sandfish forwardmotion (sampled every0.04 s). For each time in-stant, the instantaneouslateral displacement of atracked section of thesandfish is representedin color. The black curvesrepresent the trackedmidline (for example,Figure 1E, snout tip totail tip) of the sandfish.(B) The amplitude A andwavelength l of the si-nusoidal fit to the trackedmidline of the sandfish(inset), for loosely andclosely packed media.(C) Red circles (closely packed, n = 24 trials), and blue triangles (loosely packed, n = 22 trials) showdependence of swimming velocity on wave frequency. The slope of green line is the approximate waveefficiency h ≈ 0.5 of animal (Fig. 4A) and the dashed black line represents h = 1. The horizontal andvertical blue and red bars (mean T 2 SD) represent the range of frequencies and forward velocities(normalized by l) accessed in loosely packed (2.10 T 0.75Hz, 0.98 T 0.27 per second) and closely packed(2.63 T 1.13 Hz, 1.28 T 0.37 per second), respectively. The average frequency and average speed aregreater in closely packed than in loosely packed material (Student’s t test, P < 0.01). n = 46 trialswere recorded.

4

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increases slowly because of the formation of asolid region of grains that moves along with therod (14, 26). Preliminary numerical simulationindicates that the size of the solid region growsslowly with y for y > 20°. The fitting function(Eq. 1) incorporates these effects in FN and FLthrough terms proportional to the angular com-ponent of CS (which is determined primarily bygrain-object frictional forces) and an extra termin FN that increases rapidly and then saturatesfor y > 20°. In this term, the coefficientCS is setby grain-grain frictional force and g0, which isrelated to the internal slip angle. CF ≈ CS/2, in-dicating that grain-grain friction is larger thangrain-surface friction.

To determine the wave efficiency (and thusswimming speed for a given frequency), webalanced thrust and drag over a cycle (net force,Fx = 0 in equation S7, assuming constant cycleaverage speed vx). Because vx and vw appear onlyas a ratio (from the kinematics in equation S2) inthe argument of the integral in Equation S7, anddo not appear in the FN and FL terms (fig. S2B),the force balance predicts h. Numerical integrationof the model over a measured organism sinus-oid from Fig. 2 with constant cylindrical cross-section predicts 0.4 ≤ h ≤ 0.65 independent of f(Fig. 4A), which is in accord with experimentalobservation; the bounds on h are set by assum-ing the head drag is zero or that of a flat platebecause measurements for the drag force on anobject with the exact morphology of the shovel-

shaped head are unavailable. The model predictsa maximum in forward progress per cycle whenA/l ≈ 0.2, and we find that the measured kin-ematics fall close to this speed (Fig. 4B). Themaximum is due to a competition between in-creased h (less slipping) from increased A anddecreased l because for an inextensible ani-mal l decreases as A increases. An analytic low-amplitude approximation (equations S9 to S14)demonstrates the relevant scaling of h.

It is remarkable that h does not change sig-nificantly for different f, especially because dragforces between closely and loosely packed ma-terial differ by ≈ 80%. The model indicates that his essentially constant because FN and FL scaleby the same ratio of 2.1 between closely andloosely packed material (Fig. 3, C and D, insets),and it is this ratio that determines h (equation S14).The model implies that h is greater than in low-Refluids because of the greater thrust to drag forceratio in the frictional granular media.

The agreement between experiment andmodel indicates that the assumptions of velocityindependence, local interaction, and the use ofthe average FN and FL for all phases of themotion are good approximations at these slowswimming speeds. Although the assumption thatall body and head segments encounter materialwith the same f is probably not true (because thebody encounters grains disturbed by the head andother body segments), because FN and FL scalein the same ratio in all f and this ratio determines

h, wave efficiency should be independent ofposition along the body. The model assumptionsbreak down in the approximation that the in-stantaneous force (Fig. 3B) can be replaced bythe average force. This is a good approximationexcept forFN in closely packedmaterial (Fig. 3B,red curves); enhancement of FN because of peakstress significantly greater than the mean could ex-plain why, contrary to expectation, the range of f(and vx) that the animal accessed was greater inclosely packedmaterial and themaximal swimmingspeed the animal was able to access was ≈50%larger in closely packed material (Fig. 2C).

In conclusion, we used high-speed x-rayimaging to show that the sandfish lizard pro-pels itself within granular media using a large-amplitude traveling-wave oscillation of its bodywithout using its limbs and that the wave effi-ciency of this motion is independent of the vol-ume fraction of the medium. Using a model thatbalances thrust and drag with measured granulardrag laws, we can predict the wave efficiency andoptimal kinematics. We demonstrated that theanimal swims in a medium with properties inter-mediate to those of low Re viscous fluids andfrictional solid surfaces and that are unique todense granular beds, namely velocity-independentforces and enhanced normal-drag forces. Ourresults demonstrate that burrowing and swimmingin complex media can have similar complexity to

Fig. 4. Comparison of experimental results andmodel predictions; blue denotes loosely packedand red denotes closely packedmaterial. (A) Animalwave efficiencies from experiment are representedby solid bars (loosely packed average h = 0.54 T0.12; closely packed average h = 0.49 T 0.09).Shaded bars correspond to model predictionsassuming head drag of a flat disk (FH) and no headdrag (NH). (B) Predicted swimming speed (in body-length per cycle) versus amplitude normalized bywavelength. The dashed lines are model predictionswith no-head (short-dashes) and flat-head (long-dashes) for loosely packed and closely packed ma-terial. Squares denote themeasured average animalswimming speed for loosely packed and closelypacked material. The range of frequency and speedaccessed is given by the extent of the solid lines. n =46 trials were recorded.

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Fig. 3. Drag measurements to model undulatory locomotion: (A) Diagram of forces FN (perpen-dicular) and FL (parallel) on a given element of a sinusoidal traveling wave. (B) Representative totaldrag force profiles (including sidewalls and end-faces) versus time for a stainless-steel cylinder(diameter = 1.58 cm and length = 4.00 cm) oriented at an angle y = 60° to the direction of itsforward velocity (10 cm/s). The solid lines correspond to FN and the dashed to FL. The red and bluecolors correspond to closely and loosely packed media, respectively. The label A representsdisplacement associated with the average amplitude of oscillation of the sandfish. (C) Average FNand (D) FL on the cylinder (removing force contribution from the end-faces); red circles and bluetriangles correspond to closely and loosely packed preparations, respectively. In (C) and (D), theaverage forces corresponding to the force profiles in (B) are indicated with the respective rect-angles. Both insets show the loosely packed force data scaled by 2.1. Averages of FN and FL arecalculated over the shaded region in (B). Solid lines are model fits described by Eq. 1. For com-parison, dashed gray lines correspond to FN and FL calculated for a fluid (water) by choosing avelocity that fits FL versus y.

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GoldmanHighlightThis should be $C_F$

movement in air or water, and that organisms canexploit the solid and fluidlike properties of thesemedia to move effectively within them.

References and Notes1. R. M. Alexander, Principles of Animal Locomotion

(Princeton Univ. Press, Princeton, NJ, 2003).2. M. H. Dickinson et al., Science 288, 100 (2000).3. S. Vogel, Life in Moving Fluids (Princeton Univ. Press,

Princeton, NJ, 1994).4. E. R. Trueman, J. Exp. Biol. 53, 701 (1970).5. C. R. Darwin, The Formation of Vegetable Mould, Through

the Action of Worms: With Observations on Their Habits(John Murray, London, 1881).

6. K. Dorgan, P. Jumars, B. Johnson, B. Boudreau, E. Landis,Nature 433, 475 (2005).

7. G. Lauder, E. Drucker, Physiology (Bethesda) 17, 235(2002).

8. F. Meysman, J. Middelburg, C. Heip, Trends Ecol. Evol.21, 688 (2006).

9. E. Arnold, J. Zool. 235, 351 (1995).10. C. White, Aust. J. Zool. 49, 663 (2001).

11. E. Ezcurra, Global Deserts Outlook (United NationsEnvironmental Programme, Nairobi, Kenya, 2006).

12. H. M. Jaeger, S. R. Nagel, R. P. Behringer, Phys. Today49, 32 (1996).

13. W. W. Dickinson, J. D. Ward, J. Sediment. Res. Sect. A 64,226 (1994).

14. R. Nedderman, Statics and Kinematics of GranularMaterials (Cambridge Univ. Press, New York, 1992).

15. C. Li, P. B. Umbanhowar, H. Komsuoglu, D. E. Koditschek,D. I. Goldman, Proc. Natl. Acad. Sci. U.S.A. 106, 3029(2009).

16. W. Baumgartner et al., J. Bionic Eng. 4, 1 (2007).17. C. Gans, Integr. Comp. Biol. 15, 455 (1975).18. W. Baumgartner et al., PLoS One 3, (e3309), 1 (2008).19. Materials and methods are available as supporting

material on Science Online.20. A. A. Biewener, G. B. Gillis, J. Exp. Biol. 202, 3387 (1999).21. J. Gray, H. Lissman, J. Exp. Biol. 41, 135 (1964).22. J. Korta, D. Clark, C. Gabel, L. Mahadevan, A. Samuel,

J. Exp. Biol. 210, 2383 (2007).23. J. Gray, G. J. Hancock, J. Exp. Biol. 32, 802 (1955).24. I. Albert et al., Phys. Rev. E Stat. Nonlin. Soft Matter

Phys. 64, 61303 (2001).

25. R. Albert, M. Pfeifer, A. Barabási, P. Schiffer, Phys. Rev.Lett. 82, 205 (1999).

26. K. Wieghardt, Annu. Rev. Fluid Mech. 7, 89 (1975).27. A. N. Schofield, C. P. Wroth, Critical State Soil Mechanics

(McGraw-Hill, London, 1968).28. B. R. Moon, C. Gans, J. Exp. Biol. 201, 2669 (1998).29. This work was supported by NSF Physics of Living Systems

grant PHY-0749991 and the Burroughs Wellcome Fund. Wethank R. Full and T. Papenfuss for helpful discussion. Wethank S. Steinmetz and N. Gravish for experimentalassistance and P. Umbanhowar for discussion of the dragmodel and careful reading of the manuscript.

Supporting Online Materialwww.sciencemag.org/cgi/content/full/325/5938/314/DC1Materials and MethodsFigs. S1 to S3Table S1ReferencesMovies S1 to S3

18 February 2009; accepted 5 June 200910.1126/science.1172490

Targeted Retrieval and Analysis ofFive Neandertal mtDNA GenomesAdrian W. Briggs,1* Jeffrey M. Good,1 Richard E. Green,1 Johannes Krause,1 Tomislav Maricic,1Udo Stenzel,1 Carles Lalueza-Fox,2 Pavao Rudan,3 Dejana Brajković,4 Željko Kućan,3Ivan Gušić,3 Ralf Schmitz,5,6 Vladimir B. Doronichev,7 Liubov V. Golovanova,7Marco de la Rasilla,8 Javier Fortea,8 Antonio Rosas,9 Svante Pääbo1

Analysis of Neandertal DNA holds great potential for investigating the population history of thisgroup of hominins, but progress has been limited due to the rarity of samples and damaged stateof the DNA. We present a method of targeted ancient DNA sequence retrieval that greatly reducessample destruction and sequencing demands and use this method to reconstruct the completemitochondrial DNA (mtDNA) genomes of five Neandertals from across their geographic range.We find that mtDNA genetic diversity in Neandertals that lived 38,000 to 70,000 years ago wasapproximately one-third of that in contemporary modern humans. Together with analyses ofmtDNA protein evolution, these data suggest that the long-term effective population size ofNeandertals was smaller than that of modern humans and extant great apes.

Currently, DNA sequences determined frommultiple Neandertals are restricted to shortfragments [120 to 360 base pairs (bp)] ofthe hypervariable regions (HVRs) ofmitochondrialDNA (mtDNA) (1, 2). These data have demon-strated that Neandertal mtDNA is distinct fromthat of modern humans (3). However, collectingsequence data from the rest of the mtDNA ge-

nome has proven difficult due to numerous tech-nological difficulties (4). Recently, the completemtDNA genome sequence of a ~38,000-year-oldNeandertal individual from Vindija Cave, Croatia,was determined by high-throughput shotgun se-quencing from total DNA extract (5). A similarapproach has been used to recover completemtDNA sequences from permafrost-preservedmammoths and a human (6, 7). However, theamount of shotgun sequencing needed to retrievecomplete mtDNA sequences is prohibitive formost ancient bone specimens due to the highfraction of environmental DNA that they contain.For example, only 0.001% of DNA sequencesdetermined from typical well-preservedNeandertalspecimens are derived from mtDNA (table S1).Thus, a simple shotgun approach would requirehundreds or thousands of high-throughput pyro-sequencing runs to recover a single Neandertalmitochondrial genome (table S1). Direct poly-merase chain reaction (PCR) is also poorly suitedfor retrieving complete Neandertal mtDNA ge-nomes, because DNA extracted from the fossils

is so fragmented that hundreds of overlappingamplicons would be necessary, either requiringhighly multiplexed primer mixes that presentsevere difficulties for avoiding modern humancontamination, or many parallel amplification re-actions that consume large amounts of preciousancient DNA extracts (8).

We have developed a method—primer ex-tension capture (PEC)—that directly isolates spe-cific DNA sequences from complex libraries ofhighly degraded DNA (Fig. 1). PEC uses 5′-biotinylated oligonucleotide primers and a DNApolymerase to capture specific target sequencesfrom an adaptor-ligated DNA library. It combinesthe high specificity of PCR primers with the nu-merous advantages of a library sequencing approach,including immortalization through reamplifica-tion from adaptor priming sites (9) (fig. S1), con-tamination control with project-specific barcodes(5, 10), access to very short fragments predom-inant in ancient extracts (11), and quantification ofthe number of unique ancient DNA molecules,which is necessary to identify nucleotide misin-corporations (10–12).

We used PEC to recover the entire NeandertalmtDNA genome [supporting online material(SOM)] of five individuals from four sites acrossthe geographic range of Neandertals (Fig. 2 andtable S2). One individual (Vindija 33.25) fromVindija Cave, Croatia, is undated but was foundin an older stratigraphic layer than the previouslysequenced bone (5) (Vindija 33.16), which wasdated to ~38,000 years before present (yr B.P.) (3).Two individuals (Feldhofer 1 and 2, the former be-ing theNeandertal type specimen) come fromKleineFeldhofer Grotte, Neander Valley, Germany, and aredated to~40,000yrB.P. (13).One individual (Sidron1253) comes from El Sidron Cave, Spain, and isdated to ~39,000yrB.P. (14), and one (Mezmaiskaya1) comes fromMezmaiskaya Cave, Russia, and isdated to 60,000 to 70,000 yr B.P. (15).

We generated between 170,330 and 521,680sequence reads per individual on the 454 FLXplatform and processed them with a mapping

1Max-Planck Institute for Evolutionary Anthropology, D-04103Leipzig, Germany. 2Institute of Evolutionary Biology, ConsejoSuperior de Investigaciones Científicas, Universitat PompeuFabra, 08003Barcelona, Spain. 3Croatian Academy of Sciencesand Arts, Zrinski trg 11, HR-10000 Zagreb, Croatia. 4CroatianAcademy of Sciences and Arts, Institute for Quaternary Pale-ontology and Geology, Ante Kovačića 5, HR-10000 Zagreb,Croatia. 5Landschaftsverband Rheinland Landesmuseum,D-53115 Bonn, Germany. 6Department of Early Prehistory andQuaternary Ecology, University of Tübingen, Germany. 7Labora-tory of Prehistory, St. Petersburg, Russia. 8Área de PrehistoriaDepartamento de Historia Universidad de Oviedo, Oviedo,Spain. 9Departamento de Paleobiología, Museo Nacional deCiencias Naturales, Consejo Superior de InvestigacionesCientíficas, Madrid, Spain.

*To whom correspondence should be addressed. E-mail:briggs@eva.mpg.de

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www.sciencemag.org/cgi/content/full/325/5938/314/DC1

Supporting Online Material for

Undulatory Swimming in Sand: Subsurface Locomotion of the Sandfish Lizard

Ryan D. Maladen, Yang Ding, Chen Li, Daniel I. Goldman*

*To whom correspondence should be addressed. E-mail: daniel.goldman@physics.gatech.edu

Published 17 July 2009, Science 325, 314 (2009)

DOI: 10.1126/science.1172490

This PDF file includes:

Materials and Methods

Figs. S1 to S3

Table S1

References Other Supporting Online Material for this manuscript includes the following: (available at www.sciencemag.org/cgi/content/full/325/5938/314/DC1)

Movies S1 to S3

Corrections: Equations S4, S7, and S12 were missing square root symbols; this was an error introduced in proofs and they have been restored. Equation S11 is now correctly labeled as Equation S11. The section “Analytic Solution of Small Amplitude Resistive Force Model” has been more accurately retitled “Approximate Analytic Solution of the Resistive Force Model.”

Undulatory swimming in sand: subsurface locomotionof the sandfish lizard - Supplement

Ryan D. Maladen1, Yang Ding2, Chen Li2 and Daniel I. Goldman,2,1∗

1Interdisciplinary Bioengineering Program2School of Physics, Georgia Institute of Technology,

Atlanta, GA 30332, USA

∗E-mail: daniel.goldman@physics.gatech.edu

Materials and Methods

Sandfish X-ray ExperimentsSandfish lizards (Scincus scincus) were obtained from a commercial supplier (LLL Reptile, CA,USA), housed in a dedicated animal care facility, and kept in a 12 hour day/night light cycle.The average snout vent length (SVL), which we denote as body-length L in the manuscriptand which is ≈ 75% of the snout-tip to tail-tip length, was 8.3 ± 3.3 cm. The average masswas 16.2 ± 4 grams. High speed (250 fps) x-ray and visible light video of the sandfish weretaken as they moved on and within a 10 cm deep layer of granular material (0.27 ± 0.04 mmdiameter spherical glass beads, density ρ ≈ 2.4 g/cm3 ) held in a container (21.5 cm × 18cm). The granular material was prepared in two volume fractions (φ = 0.58 and φ = 0.62),loose and close packings for dry grains. The material state was set using an air fluidized bed,a counter flow of air to a collection of granular media. Below a critical flow rate (the onsetof fluidization), grains are stationary; above it, the material is fluidized and grains flow. Togenerate loosely packed states (φ = 0.58) the flow is increased to above the fluidization onsetand then slowly decreased to zero. To generate closely packed states the air flow is repeatedlypulsed. Increasing the number of pulses increases φ; typically we delivered over 200 pulses toachieve the closely packed state (φ = 0.62).

The x-ray system (Radiological Imaging Systems, OEC 9000) energy was varied in therange of 85 − 100 kV at 20 mA. After the x-ray beam was turned on, a gate to a holding penwas rapidly raised to release the animal onto the surface of the granular media. A thin above-ground plexiglas barrier (visible in Movies S1 and S2) forced the animal into the dive at the

1

same location in the bed. The animal consistently took a few steps and then dove into thematerial. The sandfish appears dark in the above ground x-ray images since the radiation musttravel through the sand and the animal, while below ground it appears lighter since sand hasbeen displaced horizontally by the body of the organism. Experiments were conducted between30 and 35 ◦C.

The x-ray (Movies S2 and S3) and visible light (Movie S1) videos were synchronized todetermine when the sandfish was moving subsurface. The temporal frequency and forward ve-locity of the animal were measured from this section of video. Displacement was calibratedusing a grid. X-ray visible natural body markers (the snout and lungs) as well as the silhouetteof the animal were used to estimate the mid-line of the animal and track it using MATLAB. Thedigitized undulation profiles of the animal were fit with the equation of a sinusoidal travelingwave to obtain the spatial and temporal characteristics of the animal. We collected representa-tive runs with opaque markers bonded to the body midline and limbs of the sandfish to verifythe lack of limb use subsurface (Movie S3). The total mass of the markers was 0.04 g, muchless than the 16 g animals, The inter-limb distance measure allowed us to determine the natureof limb use subsurface and contrast it with the diagonal gait used in surface locomotion. Thevisible light video was used to determine the sandfish burial time.

Our model (explained later) suggests (Fig. S3) that the variability in the animal (the spreadin velocity for a given frequency) is a result of the sensitivity of the swimming speed to smallchanges (within experimental variation during a swim) in both the amplitude and the wave-length.

Resistive Force Theory for Granular MediaWe developed our Resistive Force Theory for sandfish locomotion in granular media based onwork by Gray & Hancock (S1) for non-inertial low Re swimmers. The animal is modeled as aflexible cylinder with a sinusoidal traveling wave progressing from head to tail (Fig. 3A) suchthat:

y = A sin2π

λ(x + vwt), (S1)

where y is the displacement away from the midline of a straight animal, A the amplitude, λ thewavelength, f the wave frequency, and vw = fλ the wave speed. For a given forward velocityvx, other quantities characterizing the motion can be calculated:

vy =dy

dt=

2Aπvwλ

cos2π

λ(x + vwt)

tan θ =dy

dx=

2Aπ

λcos

2π

λ(x + vwt)

ψ = arctan(vyvx

)− θ,

(S2)

2

where θ is the angle of the axis of an infinitesimal cylindrical element with respect to the forwarddirection and ψ the angle between the axis of the element and its instantaneous velocity.

We assume that the forces FN and FL (see Fig. 3A for the force diagram, and text and RodDrag Empirical Fitting Function section for discussion of the force model) on an infinitesimalelement of the animal are proportional to the area of the longitudinal cross section δA = 2rδsand are functions of ψ. The resultant force on the element in the forward direction (+x-axis) is:

δFx = (PN sin θ − PL cos θ)2rδs, (S3)where PN and PL are the forces per cross section area normal and parallel to the axis of theelement. Then the total force on the body Fbx in the direction of motion can be expressed as

Fbx =

∫ λ0

(PN sin θ − PL cos θ)√

1 + tan2 θ2rdx. (S4)

Although the angle of each element changes in time, since the integral is over one full wave-length the integral in Equation S4 is time invariant.

Equation S4 accounts for forces acting on the body but not the head. To account for thehead we use two limits, a flat head that produces maximum drag and no head which producesno drag. For the flat head model (FH), we assume that the drag on the head Fh is the sameas the drag on the flat end face of a rod in our experiment. This drag is decomposed into twoorthogonal components F TN and F

TL and its form is approximated by Equation S8, setting the

length l = 0 and r as the average radius of the sandfish. The net force in the forward (+x)direction on the head is:

Fhx(t) = FTN sin θ − F TL cos θ. (S5)

The drag force on the head is set to zero for the no head model (NH).The time average of the force on the head (F̄hx) is equal to the spatial average:

F̄hx =1

T

∫ T0

Fhxdt =1

λ

∫ λ0

(F TN sin θ − F TL cos θ)dx. (S6)

Combining the head drag with the body force we obtain the total time averaged force on thesandfish:

F̄x =

∫ λ0

[(PN(ψ) sin θ − PL(ψ) cos θ)√

1 + tan2 θ2r

+ (F TN sin θ − F TL cos θ)/λ]dx.(S7)

At constant average velocity, F̄x is zero. The forward velocity vx can then be found numericallyif vw, A, λ, PN(ψ) and PL(ψ) are known. Since the wave and body velocities in EquationS7 only appear as ratios (see Equation S2) and do not appear in expressions for PN or PL, aproportional relation between vx and vw is expected. We can thus solve for the wave efficiencyη = vx/vw. Figure S3 shows that η increases rapidly with increasing A/λ for A/λ / 0.3 andincreases slowly for A/λ ' 0.3.

3

Drag Experiments in Granular MediaTo obtain expressions for the forces on the sandfish, we moved a stainless steel cylindricalcylinder representing a sandfish body element through granular media at constant velocity (10cm/s) and measured the resulting normal and lateral forces for angles ψ between the elementand its displacement direction ranging from 0◦ to 90◦ (Fig. 3 C and D, and Fig. S2 C). We useda fluidized bed (filled to a depth of 12 cm) to set the initial volume fraction (φ) of the media.We chose stainless steel because a previous study (S2) as well as our measurements have shownthat sandfish skin and stainless steel have about the same friction coefficient with sand (∼ 0.2).The diameter of the cylinder (2r = 1.58 cm) is similar to that of the sandfish body (1.75 cm). Toavoid effects on the drag due to the finite size of the container, the cylinder is small comparedto the size of the fluidized bed but large compared to the size of the grains. The cylinder isattached to a robotic arm (CRS Robotics) via a thin but stiff supporting rod which moves thestructure at constant depth and velocity while a 6 d.o.f. force sensor (ATI industrial) mountedbetween the robotic arm and the supporting rod measures the net force generated during thedrag motion (accurate to 0.06 N). The force on the supporting pole is also measured separatelyand subtracted to obtain the force on just the cylinder.

Previous studies show that drag in granular media is independent of speed (S3, S4) andincreases proportionally to depth (S3). To test if this effect persisted in the regime relevant tothe sandfish (0-40 cm/s), we dragged the cylinder perpendicular to velocity at 1, 5, 10, 20, and30 cm/s (which covers the sandfish’s range of speeds) at a fixed depth of 7.62 cm and foundthat over an order of magnitude change in speed, force only changed by 10% (Fig. S2 B);consequently we assumed force is independent of speed. We also dragged the cylinder orientedperpendicular to velocity at different depths (1.27, 2.54, 3.81, 5.08, 6.35, and 7.62 cm) at 10 cm/sand confirmed that as seen previously (S3) drag is proportional to depth (Fig. S2 A). Therefore,we measured drag force on the cylinder as a function of angle (for input into the Resistive ForceTheory model) by dragging the cylinder at a fixed depth (7.62 cm) and a constant speed of 10cm/s for different φ.

Before each trial, the initial state of the medium was set using a fluidized bed and the testrod rotated to the desired angle using the robotic arm. For each angle the rod was pushedinto the material to a depth of 7.62 cm and, after a 2 second pause, was dragged for 15.24 cmthrough the medium and then extracted. Both the force and position of the rod were recorded at140 Hz. The forces parallel (FL) and perpendicular (FN ) to the surface of the rod were resolvedby the force sensor and averaged over the steady state drag region (Fig. 3 B). Three trials wereconducted for each ψ and φ.

Rod Drag Empirical Fitting FunctionTo characterize the relation between the measured values of normal and lateral drag force onthe rod and its orientation ψ relative to the direction of motion we developed an empiricalfitting function inspired by soil mechanics (S5). Because there is a drag induced normal force

4

perpendicular to the front half of the surface of the rod, there are two contributions to theresistive force in the horizontal plane of the motion. The first is the in-plane component of thenormal force, characterized by CS , and from the velocity independence of force (Fig. S2 B)we expect to be constant. The second is the in-plane component of the frictional force actingeverywhere tangential to the surface of the rod characterized by CF . We expect the planarnormal force to be larger than the frictional force because the friction between the grains andthe rod is less than unity. The total force has contributions from the sidewall of the cylinderand the flat ends. For a cylinder with length l and radius r, the total forces F TN and F

TL can be

written as:F TN = 2lr(CS sin β0 + CF sin ψ) + πr

2CF sin(ψ)

F TL = 2lrCF cos ψ + πr2CS sin β

′0,

(S8)

where tan β0 = cot γ0 sin ψ and tan β′0 = cot γ0 sin(π/2 − ψ) and γ0 is a parameter related tothe internal slip angle in granular media (S5).

The total forces F TN and FTL are determined as the averages over the shaded region in Fig.

3B. The fits to the measurements of F TN and FTL determine the three parameters CS , CF and γ0.

These parameters are given in Table S1 and are used in Equation 1 to approximate the forces onthe body FN and FL as the forces on the sidewalls of the cylinder without contributions fromthe flat ends (subtracting terms proportional to the flat end area, πr2).

Approximate Analytic Solution of the Resistive Force ModelTo gain insight into how η depends on kinematic parameters and features of the force model,we develop an approximate analytic expression assuming small amplitude oscillations such thatθ is small, and small slip (high η) such that we approximate arctan(vy/vx) as vy/vx. UsingEquation S2, ψ can be approximated as

ψ = arctan(vyvx

)− θ

ψ ≈ vyvx− θ

ψ ≈ 1vx

2Aπvwλ

cos2π

λ(x + vwt)− 2Aπ

λcos

2π

λ(x + vwt),

(S9)

and since η = vx/vw,

ψ = (1

η− 1)2Aπ

λcos

2π

λ(x + vwt). (S10)

The equation above shows that ψ decreases as η increases and ψ oscillates along the body.For a sandfish swimming in a horizontal plane, the forces are only functions of ψ and the sumof thrust and drag forces on the body is found from Equation S4.

5

Assuming large η, we approximate PN and PL as the low ψ region of the curves in Fig. 3Cand D. Thus the force per unit area is approximated as,

PN = CNψ

PL = CL,(S11)

where CN and CL are constants characterizing the granular medium’s drag.Using these approximations, the integral becomes:

Fbx =

∫ λ0

(CNψ sin θ − CL cos θ)√

1 + tan2 θ2rdx

Fbx =

∫ λ0

{CN(1η− 1)2Aπ

λcos[

2π

λ(x + vwt)] sin θ − CL cos θ}

√1 + tan2 θ2rdx

Fbx ≈∫ λ

0

{CN(1η− 1)2Aπ

λcos[

2π

λ(x + vwt)]

2Aπ

λcos[

2π

λ(x + vwt)]− CL}2rdx

Fbx = [1

2CN(

1

η− 1)(2Aπ

λ)2 − CL]2rλ.

(S12)

Note that vwt does not appear in the final form because the integral over a wavelength isindependent of the initial phase. If we assume that for small θ the head drag is a constant Fhx,and we set the net force to zero:

Fxnet = [1

2CN(

1

η− 1)(2Aπ

λ)2 − CL]2rλ− Fhx = 0. (S13)

The wave efficiency η can be found analytically. With Fhx = 0 the form of the solution isstraightforward:

η =1

1 + 2CLCN

( λ2πA

)2. (S14)

Estimating CN/CL ≈ 4 and taking A/λ ≈ 0.2 from the measured kinematics, EquationS14 gives η = 0.76. If the coefficient for head drag is estimated as CN , then η = 0.65. Theoverestimate is likely due to the poor approximation of arctan(vy/vx) ≈ vy/vx, since for typicalswimming speeds when vy is maximal, vy/vx ≈ 2.5 and thus arctan(vy/vx) ≈ 1.2.

Assumptions and Error AnalysisThere are several assumptions in our model of sandfish swimming, including those in the RFT,in the estimates of FN and FL from the rod drag experiments, in the empirical fitting function, inthe body shape, and in the form of the drag on the head. 1) The RFT assumes that the organismswims in a horizontal plane, while in reality it moves into the material in a plane inclined at

6

22◦ relative to the surface (S6). Since both drag and thrust are distributed over the body andare linear with depth (S4), we use the force on the central element as the average for the wholebody. From x-ray data, the sandfish’s head is ∼ 3 cm and its central element about ∼ 2 cmbelow the surface when the sandfish stops. Thus the force per area for the head is estimatedto be 1.5 times larger than on the middle of the body. We assume FN(ψ) and FL(ψ) are thesame as for horizontal drag. The projected force of gravity on the sandfish along the plane isneglected as it is small compared to the resistive force from the material (the ratio is estimatedto be under 2%). We scaled the measured wavelength by 1/ cos(22◦) = 1.08 to account forthe projected wavelength on the horizontal plane of the x-ray images. 2) The forces used inthe model are measured as the rod is dragged at constant velocity. In reality the velocity ofeach point on the body varies sinusoidally as the animal moves forward. 3) The diameter of thesandfish changes from head to tail, while a single diameter of 1.75 cm is used for the model.We approximated the sandfish as a single cylinder of fixed radius for simplicity of the modeland calculation (i.e. time invariance of Equation S4). Since in the animal the radius shrinksnear the head and tail, the surface of the body is not parallel to the spine of the sandfish. Ourmodel predicts that the change in the diameter near the head (which results in a smaller ψ thanin the uniform cylinder), causes decreased FN and increased FL. The taper of the tail resultsin larger ψ compared to the uniform cylinder which results in increased FN and decreased FL.We hypothesize that these effects result in a cancelation that makes the uniform cylinder a goodapproximation. 4) Since we did not have an estimate for the drag on the shovel shaped head ofthe sandfish, we computed η for two cases of head drag. We considered drag on the head zero(NH in Fig. 4A and S3) or that of a flat disk of radius comparable to the sandfish (FH). Thesepredictions in conjunction with the model for body drag bound the experimentally measured η.With the model assumptions in place, the major contribution to the uncertainty in η comes fromthe experimentally measured run to run variation in the spatial parameters A and λ.

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X-ray source

X-ray image

intensifier

Visible light high speed camera

Mechanical gate

Holding pen Fluidized bed with

granular substrate

High speed camera

Air flow direction

Figure S1: Experimental setup: a fluidized bed is placed between the source and image inten-sifier of a c-arm x-ray system. The initial state of the granular media (0.3 mm spherical glassbeads) used to fill the fluidized bed is set using air pulses. Once the material is prepared thesandfish is released from the holding pen using a mechanical gate. Simultaneous x-ray and vis-ible light video (250 fps) are recorded as the animal moves above and then below the surface.Drawings are not to scale.

8

0 4 8

4

8

12

Depth (cm)

Fo

rce

(N

)

0 16 32

Speed (cm/s)

A B

φ = 0.62

φ = 0.58

Angle ψ (degree)

C

0 30 60 90

FTN

FTL

Figure S2: Force on a stainless steel cylinder as it is dragged at different depths, velocities,and angles through granular media of low and high φ . In (A) and (B) the cylinder is orientedperpendicular to the direction of motion. Average force vs. (A) depth and (B) speed for closely(red) and loosely (blue) packed preparations. (C) Average total forces (including sidewalls andend-faces) F TN (closed symbols) and F

TL (open symbols) on the cylinder where the color of the

symbols denote closely (red) and loosely (blue) packed preparations. Solid and dashed linesare model fits described by Equation S8. All forces are calculated by averaging instantaneousforces over steady state motion (e.g., see gray region in Fig. 3B); there is a 94% probability thatthe mean forces fall within the error bars (which are comparable to the symbol size).

9

Wa

ve

Effi

cie

ncy

(η

)

sandfish range

0 0.3 0.6

0.3

0.6

0.9

A/λ

FH

NH

Figure S3: The wave efficiency predicted by the RFT model (numerical integration of the fullmodel, Equation S7) is plotted against the spatial characteristic (A/λ) of the sinusoid. The blueand red curves correspond to predictions for LP and CP respectively. The red and blue squareswith error bars show η measured from the kinematics of the sandfish in the x-ray experiments.Curves show model predictions using flat head (longer dash) and no head (shorter dash) limits.

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Packing φ CS (N/m2 × 10−4) CF (N/m2 × 10−4) γ0 (degree)LP 0.58 0.51 0.28 13.84CP 0.62 0.77 0.59 12.21

Table S1: The coefficients of the rod drag model: quantities related to the yield stress of thegranular media (CS), the flow resistance coefficient (CF ), and the internal slip angle of thegranular media under gravity (γ0).

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Supplementary References

S1. J. Gray, G. J. Hancock,Journal of Experimental Biology 32, 802 (1955).

S2. W. Baumgartner, et al., Journal of Bionic Engineering 4, 1 (2007).

S3. K. Wieghardt, Annual Review of Fluid Mechanics 7, 89 (1975).

S4. R. Albert, M. Pfeifer, A. Barabási, P. Schiffer, Physical Review Letters 82, 205 (1999).

S5. R. Nedderman, Statics and kinematics of granular materials (Cambridge University Press,1992).

S6. W. Baumgartner, et al., PLoS ONE 3, e3309:1 (2008).

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