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Phytoplankton morphology controls on marine snowsinking velocity

Emmanuel C. Laurenceau-Cornec, Thomas W. Trull, Diana M. Davies,Christina L. Rocha, Stephane Blain

To cite this version:Emmanuel C. Laurenceau-Cornec, Thomas W. Trull, Diana M. Davies, Christina L. Rocha, StephaneBlain. Phytoplankton morphology controls on marine snow sinking velocity. Marine Ecology ProgressSeries, Inter Research, 2015, 520, pp.35-56. �10.3354/meps11116�. �hal-02558206�

MARINE ECOLOGY PROGRESS SERIESMar Ecol Prog Ser

Vol. 520: 35–56, 2015doi: 10.3354/meps11116

Published February 3

INTRODUCTION

In the ocean, the rain of large biogenic particles isa major pathway for the export of carbon from thesurface to the interior (Suess 1980, Fowler & Knauer1986, Asper et al. 1992). This mechanism contributessignificantly to the drawdown of atmospheric carbon

dioxide, and has become known as the ‘oceanic bio-logical carbon pump’ (Volk & Hoffert 1985). Substan-tial production of particulate organic matter (POM) inthe euphotic zone is essential but not sufficient toobtain high carbon export (Buesseler 1998). Thespeed at which particles settle is also a critical para -meter since it determines the duration of their expo-

© Inter-Research 2015 · www.int-res.com*Corresponding author: emmanuel.laurenceau@utas.edu.au

Phytoplankton morphology controls on marinesnow sinking velocity

Emmanuel C. Laurenceau-Cornec1,2,3,*, Thomas W. Trull2,3, Diana M. Davies2, Christina L. De La Rocha4, Stéphane Blain5,6

1Institute for Marine and Antarctic Studies, University of Tasmania, Private Bag 129, Hobart, Tasmania 7001, Australia 2Antarctic Climate and Ecosystems Cooperative Research Centre, University of Tasmania, Private Bag 80, Hobart,

Tasmania 7001, Australia3Commonwealth Scientific and Industrial Research Organisation, Marine and Atmospheric Research, Castray Esplanade,

Hobart, Tasmania 7000, Australia4CNRS, UMR 6539, Institut Universitaire Européen de la Mer, Université de Bretagne Occidentale, Technopôle Brest-Iroise,

Rue Dumont d’Urville, Plouzané 29280, France5CNRS and 6UPMC Université Paris 06, UMR 7621, LOMIC, Observatoire Océanologique, Banyuls-sur-Mer 66650, France

ABSTRACT: During the second KErguelen Ocean and Plateau compared Study (KEOPS2) inOctober−November 2011, marine snow was formed in roller tanks by physical aggregation ofphytoplankton assemblages sampled at 6 stations over and downstream of the Kerguelen Plateau.Sinking velocities, morphology, bulk composition (transparent exopolymer particles, biogenic sil-ica, particulate organic carbon), and phytoplankton contents were measured individually on 66aggregates to identify controls on sinking velocities. Equivalent spherical diameters (ESD) rangedfrom 1 to 12 mm, and the particle aspect ratios, Corey shape factors, and fractal dimensions (DF1 =1.5, DF2 = 1.8) were close to those of smaller natural aggregates (0.2 to 1.5 mm) collected in poly-acrylamide gel-filled sediment traps (DF1 = 1.2, DF2 = 1.9). Sinking velocities ranged between 13and 260 m d−1, and were correlated with aggregate size only when considering individually theexperiments conducted at each station, suggesting that a site-dependent control prevailed overthe general influence of size. Variation in dominant diatom morphologies among the sites (classi-fied as small spine-forming or chain without spines) appeared to be a determinant parameterinfluencing the sinking velocity (SV [m d−1] = 168 − 1.48 × (% small spine-forming cells), r2 = 0.98),possibly via a control on species-specific coagulation efficiency affecting particle structure andexcess density. Our results emphasize the importance of ecological considerations over that ofsimple compositional perspectives in the control of particle formation, and in accurate parameter-izations of marine snow sinking velocities that are essential to predictions of biological carbonsequestration.

KEY WORDS: Sinking velocity · Marine snow · Aggregation · Phytoplankton · Porosity

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Mar Ecol Prog Ser 520: 35–56, 2015

sure to extensive physical and biological transforma-tions (Karl et al. 1988, Boyd et al. 1999) responsiblefor the observed attenuation of the particle flux withdepth (Martin et al. 1987, Silver & Gowing 1991).

In the Southern Ocean, a region known to play aleading role in global climate and carbon systems(Sigman & Boyle 2000), primary productivity is lowdue to phytoplankton growth restriction by a combi-nation of iron and light limitation (Martin 1990, deBaar et al. 1995). These waters are described as‘high nutrient, low chlorophyll’ (HNLC), and containa large amount of unused surface macro nutrientscapable of fuelling the production of high quantitiesof organic carbon and potentially its se questration.Against this background, like oases in deserts, someareas in the Southern Ocean are fertilized by a natural supply of iron and display remarkable sea-sonal biomass increases (Sullivan et al. 1993), offer-ing a great opportunity to investigate the controlson carbon export efficiencies in the context of ironfertilization.

This study focuses on the bloom that occurs eachyear between October and February over and down-stream of the Kerguelen Plateau in the Indian sectorof the Southern Ocean (Blain et al. 2007). In Janu-ary−February 2005, the first KErguelen Ocean andPlateau compared Study (KEOPS1) demonstratedthat the downward flux of carbon was elevated by afactor of 2 to 3 in comparison to the surroundingHNLC waters (Savoye et al. 2008). Particle size spec-tra from an in situ camera demonstrated that moreand larger particles were present beneath the bloom(to 400 m depth) than in surrounding HNLC waters,although a comparison to size spectra of particles col-lected in gel-filled sediment traps showed slowersinking velocities (Jouandet et al. 2011), suggestingthat sinking velocity was not a simple monotonicfunction of particle size.

According to theory and empirical studies, size isknown to exert a major control on particle sinkingvelocity (Dietrich 1982, Gibbs 1985), but discrepan-cies in the size−sinking velocity relationship areoften reported, and other parameters (e.g. particlecomposition or structure) can prevail over size in thecontrol of the sinking velocity, as previously noted(Diercks & Asper 1997, Engel & Schartau 1999,Iversen & Ploug 2010). While extensive study ofthese parameters has verified their importance, ithas also turned out to be difficult to define a limitednumber of parameters suitable to predict carbonexport accurately — something that would be ofconsiderable use in computationally expensive mod-els of ocean biogeochemical cycling. Among these

parameters, the shape (McNown & Malaika 1950,Alldredge & Got schalk 1988), porosity or compact-ness (Kajihara 1971, Iversen & Ploug 2010), perme-ability (Matsumoto & Suganuma 1977), fractal struc-ture (Johnson et al. 1996, Engel et al. 2009), contentof high density minerals (Armstrong et al. 2001,Klaas & Archer 2002, Passow & De La Rocha 2006)or low density particulate polysaccharides (Engel &Schartau 1999, Azetsu-Scott & Passow 2004), phyto-plankton species (Passow 1991, Padisák et al. 2003)and their physiological state (Bienfang et al. 1982,Waite et al. 1992, Muggli et al. 1996) or individualorganism size (Boyd & Newton 1995, Waite et al.1997a) have been proposed as potential controls ofparticle sinking velocity. Due to this high complexityand the absence of clear controlling factors providedby empirical research, most biogeochemical modelshave no other alternative than simple sinking velocityparameterization (e.g. constant or size-dependent).Several modelling studies have focused on the sen-sitivity to sinking velocity para meterization, testify-ing to the awareness that im provements are neededand that more complexity needs to be added to themodels (Gehlen et al. 2006, Kriest & Oschlies 2008,2013, Losch et al. 2014). Here, we investigate acomprehensive set of morphological and composi-tional parameters in a single study to identify poten-tial influences on particle sinking velo city and to de -velop a possible explanation for the in consistenciesoften observed between sinking velo city and parti-cle size, offering a potential alternative for biogeo-chemical model parameterization.

Theory

We refer the reader to the classic textbook on fluiddynamics from Batchelor (1967) for further details onthe theory of particle sinking velocity.

For a sphere settling in a fluid, the immersedweight (Wi) is the difference between the force ofgravity acting downward and the buoyancy forceacting upward, and is given by (e.g. Komar &Reimers 1978):

(1)

where D is the diameter of the sphere, ρs and ρf arethe sphere and fluid densities, respectively, and g(9.81 m s−2) is the acceleration due to gravity. TheReynolds number (Re; Reynolds 1883) is the para -meter that determines a flow field for boundaries of agiven form and is given by:

6( )i

3s f= π ρ − ρW D g

36

Laurenceau-Cornec et al.: Phytoplankton controls on sinking velocity

(2)

where Us is the sphere sinking velocity and ν is thekinematic viscosity of the fluid.

Particles termed ‘marine snow’ are large aggre-gates (>0.5 mm) formed by physical aggregation ofphytoplankton and miscellaneous debris: mostlyfecal pellets, inorganic particles and zooplanktonfeeding structures (Alldredge & Silver 1988, All-dredge & Gotschalk 1990). Because of their large sizeand potentially high sinking velocity (Alldredge &Silver 1988), the settling of marine snow aggregatesin the water column occurs at Re > 0.5 (Alldredge &Gotschalk 1988). In these conditions the drag forceFD is proportional to the square of the velocity:

(3)

where Uagg is the sinking velocity of the aggregate,CD is the drag coefficient (an empirical proportional-ity coefficient between FD and U2

agg) and A is theprojected area of the aggregate in the direction ofmotion. At terminal velocity, the drag force is balan -ced by the immersed weight giving a force balanceequation which, after algebraic manipulations, leadsto a general expression for the sinking velocity:

(4)

where Δρ is the aggregate excess density calculatedas the difference between aggregate density andseawater density (ρsw). In this equation, applicable toall Reynolds numbers, the drag coefficient is a com-plex function of both aggregate shape and Reynoldsnumber. For simplicity, we refer to Eq. (4) as the ‘gen-eral sinking velocity model’ in the rest of the text.

Considering a small perfect sphere settling througha quiescent fluid and assuming that the inertial forcesare negligible compared to viscous forces, G. G. Stokessolved in December 1850 the low Reynolds numberlimit of the Navier-Stokes equations (Stokes 1851),and obtained a simplified expression of the drag force:

FD = 3πμDUs (5)

where μ is the dynamic viscosity of the fluid. Again,at terminal velocity, the immersed weight equals thedrag force yielding the Stokes expression:

(6)

In this expression, the properties of the sphereinfluencing its settling velocity are only the densityand the diameter. Because of the assumptions made

by Stokes, Eqs. (5) & (6) are only valid at smallReynolds number, empirically found to apply to Re< 0.5 (Graf & Acaroglu 1966, White 1974, Komar &Reimers 1978).

By comparing the general model (Eq. 4) to its par-ticular case represented by the Stokes’ expression(Eq. 6), one can notice that the settling velocity has aweaker dependence on size in the general modelsince the diameter is raised to the power of 0.5, ratherthan 2 as in the Stokes’ law.

In Fig. 1 we plot various empirical and theoreticaldata of sinking velocity versus size for marine snow,from the present study and others using differentmethods and approaches. Since these studies werecarried out over a range of different water tempera-tures and salinities, we investigated whether temper-ature and salinity variations could contribute signifi-cantly to sinking velocity variations through theirinfluence on seawater dynamic viscosity (μ) and den-sity (ρsw). Stokes’ law predicts that, at a fixed aggre-gate porosity and solid content density (e.g. 99%porosity and ρsol = 1170 kg m−3, corresponding to30% transparent exopolymeric particles [TEP], 20%biogenic silica [BSi], and 50% particulate organicmatter [POM] in solid content), a temperature in -crease from 2 to 20°C or a salinity decrease from 34 to2 would lead respectively to a 40 and 20% increasein the sinking velocity. It is very likely that the differ-ences between the studies did not exceed these verylarge range of temperature and salinity variations,and given that Fig. 1 is a log−log plot, the effect oftemperature and salinity changes on the sinkingvelocity can reasonably be neglected here.

Overall, the data suggest a relatively weak depend-ence of sinking velocity on particle size both whenconsidering the whole dataset or each study sepa-rately. The general model gives to size a weaker con-trol on sinking velocity and a stronger dependence ondrag and excess density influenced by particle struc-ture and composition; our calculations show that thegeneral model provides a better representation of theobservations for large particles than the usual Stokes’law (Fig. 1). In combination with porosity increasingwith size according to a fractal scaling known toapply to marine snow, and using the formula pro-posed by Logan & Wilkinson (1990; see ‘Materialsand methods: Measurement of aggregate morpho -logy and structure’), the general model shows poorsize−sinking velocity correlation for the large particlesize range (Fig. 1, line 2). Based on this, it appearsthat particle structure, morphology and compositioncould prevail over size in the control of sinking velo -city via a control on particle drag and excess density.

Re s= U Dν

2D D

f agg2

=ρ

F C AU

43

( )agg

D sw

12

= Δρρ

⎡⎣⎢

⎤⎦⎥

Ug DC

Ug D

ss f= −1

18

2( )ρ ρμ

37

Mar Ecol Prog Ser 520: 35–56, 201538

10−210−1

100

101

102

103

104

10−1 100 101 102

ESD (mm)

SV

(m d

−1 )

1

4

5

2

3

This study

Jouandet et al. (2011)

McDonnell & Buesseler (2010)

Azetsu-Scott & Johnson (1992)

Azetsu-Scott & Johnson (1992)

Carder et al. (1982)

Shanks & Trent (1980)

Kajihara (1971)

Alldredge & Gotschalk (1988)

Diercks & Asper (1997)

Gibbs (1985)

Laurenceau-Cornec et al. (unpubl.)

Nowald et al. (2009)

Syvitski et al. (1995)

Iversen & Ploug (2010)

Iversen & Ploug (2010)

Particle type – Method used Location SourceMarine snow from natural phyto. assemblages – Roller tank, settling column

Diatom culture agg. – Roller tank, video recording

Natural agg. – Gel trap and in situ imaging

Kerguelen region (Southern Ocean)

n/a

Kerguelen region (Southern Ocean)

West Antarctic peninsulaNatural agg. – Gel trap and in situ imaging

Carbonate-ballast culture agg. – Roller tank, vertical flow, video recording

Opal-ballast culture agg. – Roller tank, vertical flow, video recording

n/a

n/a

Natural marine snow – In situ settling chamber, Cherokee ROV Cape Blanc (Mauritania)

Natural marine snow – In situ (MASCOT) Central Black Sea

River flocs – In situ Floc Camery Assembly Halifax river estuary (Nova Scotia)

Natural agg. – In lab., linear density gradient column Bedford basin (Nova Scotia)

Diatom culture agg. – In lab., linear density gradient column n/a

Natural marine snow – SCUBA diving Santa Barbara Channel (S. California)

Estuarine flocs – Settling tank Chesapeake bay (Maryland)

Natural agg. – In situ holographic measurements Western North Atlantic

Natural marine snow – Settling chamber Monterey bay (Calif.) and NE Atlantic

Recoagulated marine snow – KUROSHIO II submarine Off Muroran (Japan)

Fig. 1. Sinking velocity (SV) of large marine aggregates (agg.) versus their equivalent spherical diameter (ESD) for this studyand others. Theoretical lines and empirical relationships using different approaches are also represented. 1: Stokes’ law (Eq. 6)(solid line) and general sinking velocity model (Eq. 4) (dashed line) applying to distinct ranges of Reynolds number for solidbody particles with constant excess density (Δρ = 0.0014 g cm−3); large black square: specific conditions of the models, fixingthe initial drag characteristics of the particle (ESD0 = 1 mm and SV0 = 100 m d−1). 2: Same models with excess density scaledon a typical fractal geometry for marine snow (DF3 = 1.39, a = 0.03; Logan & Wilkinson 1990) (see Fig. 3 and ‘Results: Sinkingvelocity’ for details). 3: Guidi et al. (2008). 4−5: SV calculated using the coagulation model from Stemmann et al. (2004) withdifferent parameter values (4: excess density Δρ = 0.08, fractal number DF3 = 2.33; 5: Δρ = 0.01, DF3 = 1.79), Phyto.: phytoplankton;

Calif.: California; n/a: not applicable

Laurenceau-Cornec et al.: Phytoplankton controls on sinking velocity

Aggregate morphological and structural propertieslikely to control excess density and drag are numer-ous, and the combined effects of these 2 parametersmake their relative influence on the measuredsinking velocity hard to distinguish. The drag experi-enced by a particle might be the result of several pa-rameters, including shape, permeability, and surfaceroughness, while excess density depends on aggre-gate composition and compactness (i.e. poro sity). Theinfluence of macroscopic shape, permeability, andsurface roughness on the sinking velocity have beeninvestigated in the theoretical, experimental, and en-gineering fields, on natural and artificial particles,but these parameters have generally been describedas poor contributors to the sinking velocity (Williams1966, Achenbach 1974, Matsu moto & Suganuma1977, Baba & Komar 1981, Alldredge & Gotschalk1988, Li & Logan 2001, Li & Yuan 2002).

The excess density of a marine snow aggregatedepends on the density and volume fraction of itssolid components (mostly phytoplankton cells in thecase of diatom marine snow) and how tightly they areassembled, giving more or less inner space filled byseawater, defined as the porosity (e.g. De La Rocha &Passow 2007). To our knowledge the species-specificeffect of phytoplankton on the alteration of the size−sinking velocity relationship of marine snow aggre-gates has not been studied to date. We tested herethe possible combined effects of varying phytoplank-ton assemblages on aggregate sinking velocity viaballast effect (Engel et al. 2009) and control on aggre-gate structure, assuming species-specific aggregatecompactness, based on aggregation experiments ofphytoplankton cultures (Iversen & Ploug 2010).

Experimental setup

We focused on marine snow aggregates, a majorcomponent of the vertical flux of organic carbon(Fowler & Knauer 1986). They represented the mainnumerical fraction of the flux during KEOPS1 (Ebers-bach & Trull 2008) and KEOPS2 (Laurenceau et al.2014), and could represent an efficient way to exportcarbon over the Kerguelen Plateau if they sink rapidlyenough to reach the deep ocean before being con-sumed or remineralized. Because it is difficult torecord in situ the sinking velocity of natural marinesnow (Alldredge & Silver 1988), we took an experi-mental approach. Marine snow aggregates wereformed in rotating cylindrical tanks following themethod developed by Shanks & Edmonson (1989).In contrast to the majority of roller tank experiments

using phytoplankton cultures, we incubated variousnatural mixtures of phytoplankton sampled carefullyfrom Niskin bottles to produce aggregates as close aspossible to those forming in the water column at dif-ferent sites. This ‘roller tank’ technique allows theparticles to sink continuously as they would in the water column, and thus to aggregate mainly by differ-ential settling (after a short period of shear during theinitiation of solid-body rotation), in which fast-sinkingparticles scavenge suspended and slower-sinkingparticles. Thus, the technique minimizes the influ-ences of the 2 other main mechanisms forming marinesnow in natural environments: (1) shear, which canalso cause disaggregation, and (2) brownian motion,which dominates the collision rate for small (<1 µm)particles (McCave 1984, Burd & Jackson 2009).

Once macroscopic aggregates had formed, theywere photographed and their sinking velocitiesmeasured. Bulk chemical compositions were deter-mined and the abundances of organisms within theaggregates were examined using light microscopy.To test our hypothesis, all aggregate propertiesneeded to be explored as potential controls of thesinking velocity. Data were thus evaluated in termsof morphological, chemical and biological relativeinfluences on the sinking velocity.

To evaluate the oceanic applicability of the resultsdetermined in the roller tank experiments, we com-pared our aggregates with natural aggregates col-lected at the same time using polyacrylamide gel-filled sediment traps which allow the sampling ofintact particles as they exist in the water column(Jannasch et al. 1980, Ebersbach & Trull 2008, Lau-renceau et al. 2014).

MATERIALS AND METHODS

Study site and sampling

This work was conducted during the second KErguelen Ocean and Plateau compared Study(KEOPS2) onboard the RV ‘Marion Dufresne’ from8 October to 30 November 2011, over and downstreamof the Kerguelen Plateau. One of the major purposeswas to characterize the downward particle flux by theuse of sediment traps and identify the physical and biological controls on the efficiency of carbon export.

In the present work, duplicate sampling was con-ducted at 6 stations (Fig. 2) at surface (20 and 30 m)and deeper layers (65, 80 and 150 m) of high and mod-erate biomass according to CTD calibrated fluores-cence profiles. Stations (Stns) E-3, E-4W (west), E-4E

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Mar Ecol Prog Ser 520: 35–56, 2015

(east), and E-5 formed a time series within a moderatebiomass, eddy-like, bathymetrically-trapped recir cu -lation feature in deep waters east of the Kerguelen Islands. Stns F-L and A3-2 were respectively in a re-gion of elevated biomass near the Polar front and atthe Kerguelen on-plateau bloom reference station ofKEOPS1 (A3). Seawater was sampled using 12 l Niskinbottles mounted on a CTD rosette frame. At each sta-tion the whole content of 2 Niskin bottles was trans-ferred into a clean 30 l carboy to avoid any undersam-pling of particulate organic matter from the Niskins.Sampling was repeated at 2 different depths at eachsite (2 carboys per station). The carboys were stored indarkness for 1 d to initiate phytoplankton senescence.

Roller tank experiments

Carboy contents were poured into 10 l transparentcylindrical tanks cleaned previously with 2‰ alkalinedetergent (Decon) and washed 3 times with extrasampled seawater. At each station, 4 cylindrical tanks(2 duplicates by depth, except at E-4E where deeperlayers were not sampled) were placed on a rollingtable at a constant speed of 0.66 rpm and kept in dark-ness during the entire duration of the incubation. Allexperiments were conducted at a temperature of~10°C. To obtain sufficient millimeter sized aggre-gates to perform the chemical measurements on indi-vidual aggregates, incubations lasted from 1 to 4 d.

Measurements were conducted on 3 aggregates pertank (12 aggregates per experiment). When possible,aggregate selection was made in order to capturelarge variations of size, shape (e.g. spherical to elon-gated), and compactness (e.g. compact to loose). Ineach experiment, 6 aggregates were used for chemicalmeasurements and 6 preserved in Lugol’s solution forpost-cruise microscopic observations in the laboratory.

Measurement of aggregate morphology and structure

At the end of the incubation, the tanks were re -moved from the rolling table and carefully rotated90° to allow the aggregates to settle to the bottom.The maximum length of the 3 aggregates selectedper tank was measured optically. Each aggregatewas photographed through the bottom of the tankwith a high-resolution Canon Powershot G12 camera(1 pixel ≈ 20 µm). The images were thresholded tocreate binary images and processed using the USNational Institutes of Health free software, Image J(Abràmoff et al. 2004). The minimum length wastaken to be the minimum axis of the ellipse fitted tothe shape by the software. The aspect ratio (AR) wascalculated from the ratio between smallest andlargest axes of the fitted ellipse. The commonly usedCorey shape factor (CSF) (Corey 1949, McNown &Malaika 1950) re presenting particle flatness (low val-

40

Fig. 2. Sampling stations over the Ker-guelen Plateau on a MODIS satelliteimage of sur face chl a concentration on11 November 2011. Location of eachstation and sampling date (dd/mm/yyyy):E-3: 71.97°E, 48.704°S (4/11/2011);F-L: 74.668°E, 48.523°S (6/11/2011);E-4W: 71.43°E, 48.766°S (11/11/2011);E-4E: 72.567°E, 48.717°S (13/11/2011);A3-2: 72.055°E, 50.624°S (16/11/2011);

E-5: 71.9°E, 48.412 (19/11/2011)

Laurenceau-Cornec et al.: Phytoplankton controls on sinking velocity

ues of CSF corresponding to flat particles) was alsoused as a shape descriptor. The equivalent sphericaldiameter (ESD) and volume of aggregates were cal-culated from the projected area, assuming a sphere.

We characterized the fractal structure of our aggre-gates by determining their 1-, 2- and 3-dimensionalfractal numbers DF1, DF2 and DF3, respectively. Thenumber of individual particles (N) composing a frac-tal aggregate increases non-linearly with its size andcan be described by the power relationship (Logan &Wilkinson 1990):

N ~ l DFn (7)

where DFn is the fractal dimension determined for theobject in n dimensions, and l is the maximum lengthof the aggregate. Since phytoplankton aggregatesand their constitutive particles have finite sizes, theyare not strictly self-similar at all scales and their frac-tal dimensions are approximations to real fractaldimensions obtained only for infinite size objects.The fractal dimension describes intuitively howmuch the individual particles fill the available spacewhen they aggregate (e.g. Logan & Wilkinson 1990,Kilps et al. 1994, Jackson 1998, Burd & Jackson 2009)and is an indicator of particle compactness.

The maxima of DF1 = 1, DF2 = 2 and DF3 = 3 arereached for Euclidean objects. For instance, DF3 = 3describes a solid compact sphere having no porositywhere all individual particles filled the total volumeavailable when they assembled. Unlike Euclideanobjects, aggregates formed in marine systems, suchas marine snow, have lower fractal dimension thantheir maximum values (Logan & Wilkinson 1990). Itim plies that the number of particles filling the spaceduring aggregation increases at a lower rate thanaggregate maximum length does. It results in theimportant property that marine snow has a porosityincreasing with size (Logan & Wilkinson 1990), con-sequently reducing its excess density.

Following Kilps et al. (1994), the 1- and 2-dimen-sional fractal numbers (DF1 and DF2), were calculatedfrom the slopes of log−log relationships of perimeterand area respectively, against the Feret’s diameterrepresenting the largest dimension (e.g. Engel et al.2009). The 3-dimensional fractal number (DF3) can becalculated from the slope of a log−log relationshipbetween solid content (1 – Porosity) and the largestdiameter l, according to the formula proposed byLogan & Wilkinson (1990):

(1 – P ) = a × l DF3 –3 (8)

where a is an empirical constant. Due to large uncer-tainties on solid content estimates, especially for TEP

(see ‘Chemical measurements’ below), DF3 values forthe experimental aggregates could not be reliablyobtained, and only DF1 and DF2 results, based onimage analysis, are presented. To avoid any bias dueto small scale heterogeneity between images, noconversion from pixels to size unit was made for DF1

and DF2 determination.

Sinking velocity measurements

A non-destructive method was required to meas-ure the sinking velocity and still be able to conductother analyses on single aggregates. A method basedon video recording the rotating tanks (Ploug et al.2010) was not applicable onboard because of the shipmotion altering the trajectories of particles. Instead,all the settling rates were measured directly insidethe tanks using a 13.5 mm diameter and 23 cm longpipette acting as a static column. Right after the mor-phological measurements, the pipette was insertedand filled with water sampled at the surface of thetank. An aggregate was then selected at the bottomand gently sucked up into the pipette to the height ofthe water in the tank. The aggregate then sank freelyin the column for several centimeters, and the aver-age sinking velocity was measured over a distance of7 cm at its apparent terminal velocity. Workingdirectly inside the tanks avoided any transfer of theaggregates likely to alter their structure. Only 1measurement was done on each aggregate due totheir extremely fragile nature and the high probabil-ity of breaking, matter loss or structural alterationoccuring during repeated manipulations, whichwould have flawed the study.

The length and diameter of the pipette limited theinfluence of turbulence induced by ship motion,which otherwise could be responsible for a bias insinking velocity measurements. Nevertheless, ourcolumn dimensions presented possible issues worthyof evaluation. Specifically, the method would be in error if (1) wall effects affected aggregate sinking ve-locity without a clear correlation with size, thus re-cluding a reliable correction, or (2) aggregates did notreach their terminal velocity during settling. We de-termined the wall factor (f; Chhabra 1995), defined asthe ratio between the assumed terminal velocity of aparticle in our pipette to that in a 50 cm high and20 cm wide cylinder considered as an unboundedmedium. Following the protocol of Ploug et al. (2010),we made agar spheres of 0.4 to 1 cm, used as modelparticles and covering most of the size range of ourroller tank aggregates. The deviation to the Stokes’

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Mar Ecol Prog Ser 520: 35–56, 2015

law expectations for our pipette and large cylinderwas assessed by the use of 1 mm polystyrene beads(Duke Scientific, 4400A, 1004 ± 20 µm, ρ = 1.05 g cm−3)sinking in filtered seawater (temperature T = 21°C;salinity S = 34.57; dynamic viscosity µ = 105 × 10−5 kgm−1 s−1; ρsw = 1.0243 g cm−3). Over more than 70 meas-urements, polystyrene beads sank at very similar ve-locities in the large cylinder and pipette (mean ± SD:941 ± 37 and 911 ± 51 m d−1, respectively) suggestingthat the pipette induced a negligible wall effect andpermitted the particles to sink close to their terminalvelocity. At this water temperature and salinity, theo-retical expectations from Stokes’ law for the minimumand maximum bead sizes possibly encountered in ourbatch (984 and 1024 µm) led to sinking velocities of862 and 933 m d−1, respectively, very close to our ex-perimental values. For larger particles, modeled byagar spheres, the pipette induced a wall effect wellcorrelated with size: f = −0.084 × ESD (mm) + 1.1 (n =28, r2 = 0.98, p < 0.005). A correction based on this cor-relation was applied on our aggregate sinking veloci-ties. In addition, as a precaution, all sinking velocitymeasurements of aggregates >8 mm ESD (where thelargest correction applies) were excluded from thestudy. The correction augmented the measuredvalues by 50 ± 30% on average. It corresponded to anincrease of 30 ± 29 m d−1 and represented a limited al-teration of the raw data, which extended over 2 ordersof magnitude.

Chemical measurements

Each individual aggregate was collected in 10 ml oftank water and directly processed or stored <1 d at2°C in 15 ml Falcon tubes. These 10 ml were homoge-nized and then divided into thirds for particulate or-ganic carbon (POC), BSi and TEP measurements.Since each aggregate was sampled along with 10 mlof tank water, these 3 components were also measuredin the tank water, and that amount was subtracted toyield the amount contained only within the aggregate.

BSi was measured following the alkaline extractionand colorimetric analysis procedure of Ragueneau etal. (2005). Subsamples were filtered onto 25 mmpolycarbonate 0.4 µm pore filters, dried at 60°C inEppendorf vials, sealed and stored at room tempera-ture until analysis.

TEP were measured using a spectrophotometricmethod in accordance with Passow & Alldredge(1995). Subsamples were filtered onto 25 mm poly-carbonate 0.4 µm pore filters and stained with 500 µlof a 0.02% aquaeous solution of Alcian blue in 0.06%

acetic acid. The filters were stored in Eppendorf vialsand immediately frozen at −20°C. Prior to analysis,all samples were soaked onboard for 2 h in 6 ml of80% H2SO4 to redissolve the stain. The absorbanceof the solution was measured at 787 nm with a spec-trophotometer to quantify the TEP. The calibrationcurve relating the absorbance to the amount of TEPwas established in the laboratory after the voyagewith the remaining Alcian blue stock, using a proto-col modified from Passow & Alldredge (1995).

TEP determination is semi-quantitative, as thechemical composition varies and is mostly unknown(Passow 2012). The accuracy of measured TEP con-tent depends on the ability of the batch of xanthangum (XG) to behave like TEP during the calibration,and on variations in Alcian blue staining propertiesbetween measurements done onboard and cali -bration done in the laboratory. The use of differentbatches of XG or Alcian blue leads therefore to a highvariability and renders difficult quantitative compar-isons between distinct works. Alcian blue is a hydro -philic cationic dye that complexes with anionic carboxyl or halfester-sulfate groups of acidic poly -saccharides, and the selectivity of the stain dependson the pH and salt content of the dye solution (Passow& Alldredge 1995). These properties are of course al-tered during the staining process, further influencingthe possibility of variable or non-specific staining. Inaddition, the ratio of non-TEP material potentiallystainable by Alcian blue to strict TEP may be higherin small or low TEP content samples.

POC content was determined by CHN elementalanalysis using a Thermo Finnigan EA1112 FlashElemen tal Analyser and acetanilide standards. Eachsubsample was filtered through a Sartorius T29313 mm quartz filter (polycarbonate filter holder) with anominal pore size of 0.8 µm (precombusted at 450°Cfor 4 h in clean foil to remove carbon contamination).The filters were blown dry using filtered air and thentransferred to a clean, gravity circulation oven anddried at 50°C for more than 48 h. On completion of thesample set, the dry filters were loaded into silver 5 ×9 mm capsules (Sercon SC0037), acidified with 40 µl of2 N HCl, dried for at least 48 h at 60°C, en capsulatedand then stored over silica gel. Aggregate content inPOM was estimated from POC values assuming aPOM:POC mass ratio of 1.87 (Anderson 1995).

Particulate inorganic carbon (PIC), a potentially im-portant ballast mineral, was not measured becauseanalyses of particles collected by large volume fil -tration revealed PIC to be very low, at levels thatwould have been below detection in the individualaggregates.

42

Laurenceau-Cornec et al.: Phytoplankton controls on sinking velocity

Microscope observations

Each aggregate reserved for microscopic observa-tion was collected in Eppendorf vials in 1.5 ml of tankwater and preserved with 1 drop of Lugol’s solution.In the laboratory, the samples were re suspended in3 ml of artificial seawater and transfered to a mi-croscopy chamber for observation with a Zeiss AxioObserver A1 high-magnification inverted micro -scope. An average of 60 pictures per sample wastaken at several magnifications (×160, 320 and 640) tocover the entire observable field. Pictures were usedto identify numbers, sizes and genera (or specieswhen possible) of phytoplankton and other organisms.An average cell diameter (or maximum length fornon-circular species), excluding the length of setae(spines) when present, was calculated by sizing a fewto >10 specimens of the organism, depending on itsabundance in the aggregate. In order to investigatethe potential influence of various phytoplanktonmorpho logical types on the sinking velocity, propor-tions of chain diatoms without setae (e.g. Fragilari -opsis spp. and Eucampia antarctica) and small setae-forming diatoms (e.g. Chaetoceros spp.) werecalculated. For simplicity, we refer to chain diatomswithout setae as ‘type 1’ and to small setae-formingdiatoms as ‘type 2’ in the rest of the text.

Multivariate analyses

Multiple regression analyses were conducted toquantify the relative contribution of size, as opposedto the other factors measured, in the prediction ofsinking velocity variations. All analyses were per-formed using the statistical computing language andenvironment R. Since chemical composition andphytoplankton type contents were analysed on 2 dif-ferent sets of aggregates, 2 distinct multiple regres-sions were carried out. The first model, fitted to thechemical composition data (fit 1), regressed sinkingvelocity against projected area, volume, ESD, Coreyshape factor (CSF), aspect ratio (AR), and averagemass fractions of BSi, POM and TEP in aggregatesolid contents; the second model, fitted to the phyto-plankton data (fit 2), regressed sinking velocityagainst projected area, volume, ESD, CSF, AR, andaverage type 1 and type 2 phytoplankton cell frac-tions in aggregates.

Linear regressions were applied, and the relativecontribution of the parameters to the correlation wasassessed by estimating the variation on the corre -lation coefficient (r2) induced by removals of terms

from the fit. To limit biases due to collinearity, para -meters indicating the same aggregate property (size,shape, chemical or phytoplankton composition),were grouped and removed together. To identifyaggregate properties playing the most importantcontrols on the sinking velocity, ANOVAs were per-formed; the 2 models containing all terms (fits 1 and2) were compared to the reduced models by areduced sums of square F-test; with p < 0.05 used asindicator of a significant change.

RESULTS

All morphological properties and compositions ofthe aggregates are reported in Table 1. Comparisonsof sinking velocity and several aggregate propertiesfrom morphology (AR and CSF) to composition (BSi,TEP, POM and plankton content) were conducted toassess the possible effect of sampling depth onaggregate properties. No significant statistical differ-ence was found between aggregates made fromwater sampled in surface layers and deeper layers(1 > p > 0.45) for a selected sample of the measuredproperties (sinking velocity, shape, chemical compo-sition, phytoplankton content), and thus no distinc-tion is made between these 2 aggregate groups in therest of the study.

Sinking velocity

Sinking velocity data, corrected for wall effects,ranged from 13 to 260 m d−1 (1 aggregate sank at569 m d–1 but this extreme value was excluded, alongwith all sinking velocity measurements for aggre-gates >8 mm ESD, as explained in ‘Materials andmethods: Sinking velocity measurements’). In Fig. 3,data from each site are compared to expectationsfrom the Stokes’ law and general sinking velocitymodels for porous fractal particles. For these expec-tations, theoretical excess densities were calculatedassuming 3 major solid components in fixed volumefractions (TEP:0.3, BSi:0.2, POM:0.5). These propor-tions are based on measured values of BSi and POCpresenting the best scaling with size (see Fig. 6) andusing a TEP:POC mass ratio of 0.7 (Alldredge et al.1998, Martin et al. 2011). The theoretical porosity wasscaled with size according to a fractal relationship(Eq. 8).

TEP, BSi, POM and seawater densities were fixedat 800, 2000, 1060 and 1026 g cm−3 respectively, ac -cording to documented values (Klaas & Archer 2002,

43

Mar Ecol Prog Ser 520: 35–56, 201544

Agg. Stn Depth Tank Incub. lmax lmin ESD SV BSi POC TEP Mean % chain % small (m) # (d) (mm) (mm) (mm) (m d−1) (µmol) (µmol) (µg XG cell diatom setae-

equi- diameter without forming valent) (µm) setae diatom

1 E-3 30 1 3 12 9 9.2 569 3.6 10.6 488 – – –2 | | 1 | 3 2 2.7 143 0.1 2.7 210 – – –3 | | 1 | 4 2 2.6 149 0.1 0.9 199 – – –4 | | 1 | 3 2 1.9 98 0.2 0.6 232 – – –5 | | 1 | 5 1 2.2 114 0.1 1.0 199 – – –6 | | 2 3.3 4 2 3.5 161 – – – 52 43 127 | | 2 | 6 3 4.3 220 – – – 54 65 58 | | 2 | 3 2 2.1 105 – – – 54 69 39 | 150 3 3.3 6 4 4.4 258 0.4 1.1 283 – – –10 | | 3 | 10 3 4.6 168 0.9 4.5 150 – – –11 | | 4 3.5 20 5 2.2 113 – – – 58 65 412 | | 4 | 10 1 4.6 109 – – – 69 55 013 F-L 20 1 1 7 4 5.2 135 0.6 1.6 272 – – –14 | | 1 | 6 3 4.1 89 0.4 3.9 272 – – –15 | | 1 | 10 6 5.6 127 1.9 4.7 439 – – –16 | | 2 1 10 7 7.0 158 – – – 41 30 417 | | 2 | 4 1 1.6 58 – – – 48 23 1218 | | 2 | 8 4 4.9 145 – – – 29 25 1319 | 65 3 1 7 5 5.7 254 1.4 4.4 286 – – –20 | | 3 | 5 3 3.7 96 0.2 1.1 209 – – –21 | | 3 | 3 1 1.3 87 0.1 0.4 242 – – –22 | | 4 1 12 6 7.4 203 – – – 32 13 3223 | | 4 | 7 4 4.8 167 – – – 35 7 4024 | | 4 | 4 2 2.1 79 – – – 41 5 3625 E-4W 30 1 1.2 15 7 8.7 46 0.7 0.3 377 – – –26 | | 1 | 15 12 10.3 66 1.0 0.8 377 – – –27 | | 1 | 15 12 12.3 172 1.0 1.7 333 – – –28 | | 2 1.3 10 7 7.0 17 – – – 34 14 5629 | | 2 | 10 5 5.6 23 – – – 37 11 5630 | | 2 | 8 6 5.6 23 – – – 36 18 3731 | 80 3 1.3 8 4 4.6 23 0.5 0.5 109 – – –32 | | 3 | 10 7 6.9 30 0.4 13.0 298 – – –33 | | 3 | 10 7 7.1 13 1.0 1.8 287 – – –34 | | 4 1.4 10 6 6.6 17 – – – 25 2 6835 | | 4 | 13 8 9.1 60 – – – 38 10 4436 | | 4 | 10 8 7.3 24 – – – 29 15 4737 E-4E 30 1 1.1 11 6 7.8 240 1.1 2.0 166 – – –38 | | 1 | 12 6 7.4 217 1.2 2.1 300 – – –39 | | 1 | 5 3 4.1 145 0.5 2.4 133 – – –40 | | 2 1.2 6 4 4.6 184 – – – 44 26 5641 | | 2 | 7 5 5.5 173 – – – 58 40 1742 | | 2 | 7 5 5.2 198 – – – 56 33 3043 A3-2 30 1 1.2 7 5 5.7 74 0.5 2.1 60 – – –44 | | 1 | 7 5 4.8 64 0.4 2.6 160 – – –45 | | 1 | 8 3 4.2 20 0.2 1.2 160 – – –46 | | 2 1.3 7 5 5.3 60 – – – 22 4 7747 | | 2 | 6 4 4.0 46 – – – 22 8 4848 | | 2 | 7 4 4.6 60 – – – 17 0 6749 | 80 3 1.3 7 6 5.4 73 0.6 2.8 156 – – –50 | | 3 | 7 3 3.6 49 0.6 1.8 289 – – –51 | | 3 | 7 6 5.7 52 0.3 1.2 78 – – –52 | | 4 1.4 8 7 6.7 59 – – – 14 2 8153 | | 4 | 7 5 4.6 52 – – – 26 11 5354 | | 4 | 7 6 5.8 37 – – – 17 2 85

Table 1. Composition and morphological parameters of aggregates (Agg.) made in roller tank experiments conducted at 6 stations (Stn; seeFig. 2 for locations and sampling dates). Incub.: days of incubation in each tank; l: length (max/min) of Agg.; ESD: equivalent sphericaldiameter; SV: sinking velocity; BSi: biogenic silica; POC: particulate organic carbon; TEP: transparent exopolymeric particles; XG: xanthan

gum (table continued on next page)

Laurenceau-Cornec et al.: Phytoplankton controls on sinking velocity

Azetsu-Scott & Passow 2004). All calculations as -sumed a dynamic viscosity of 0.00135 kg m−1 s−1 cho-sen according to the conditions existing in the tanks(T = ~10°C and S = 34).

Using the drag coefficient calculated at an ob -served data point from its sinking velocity and size(called here ‘specific conditions’), the apparentReynolds number for this particle was determinedby solving numerically the empirical relationshipfrom White (1974), valid for a large range of Re(0.5 < Re < 2 × 105):

(9)

The general model curves for other particle sizeswere then calculated from this chosen observedvalue and the linear proportionality between Re andsize, i.e. as embedded in the definition of theReynolds number (Eq. 2).

The variation in the relationship between sinkingvelocity and size was explored for different fractaldimension DF3, empirical constant a (Eq. 8), andspecific conditions determining distinct initial dragcoefficients. Fig. 3A shows that the steepest slopeis obtained for the solid spheres (DF3 = 3) of theStokes’ law model assuming a constant particleexcess density. The different general sinking veloc-ity models display decreasing slopes for DF3 valuesfrom 1.8 to 1.2, leading to a possible decrease of thesinking velocity with increasing size for low fractalnumbers. This result suggests that for high fractaldimensions (compact aggregates), the size exertsa stronger control on the sinking velocity than for

lower fractal dimensions (loose aggregates), andhighlights the possible dominance of structure oversize. For distinct specific conditions (distinct initialdrag coefficients; 1 and 2 on Fig. 3A), the solutionsconverge when size increases, consistent with adecreasing in fluence of the drag coefficient in com-parison to size.

Fig. 3B illustrates the sensitivity of the modelcurves to the empirical constant a, for 2 distinct frac-tal dimensions. The large variations of the curveslopes for a varying over several orders of magnitude(0.001 to 100), and particularly for small values of a,suggests that an accurate characterization of aggre-gate structure requires the fractal dimension to beused in combination with the constant a.

Fig. 3C shows tight correlations between sinkingvelocity and ESD when considering each site sepa-rately, suggesting the existence of site-specificparameters which alter the size−sinking velocityrelationship. The general sinking velocity modelsare compared to data from each experiment withspecific conditions of sinking velocity and ESD ofeach model corresponding to an average of all dataof the experiment considered, assumed to reflect itsdrag characteristics. The best model fits to the data,agreeing with realistic values expected for marinesnow, were obtained by decreasing DF3 from 1.8 inexperiments with the highest sinking velocities, to1.2 in experiments with the lowest sinking veloci-ties. Data slopes were reproduced by the modelcurves with variable accuracy, suggesting that frac-tal structure may have varied from one experimentto another.

24Re

61 Re

0.4D 0.5= ++

+C

45

Agg. Stn Depth Tank Incub. lmax lmin ESD SV BSi POC TEP Mean % chain % small (m) # (d) (mm) (mm) (mm) (m d−1) (µmol) (µmol) (µg XG cell diatom setae-

equi- diameter without forming valent) (µm) setae diatom

55 E-5 30 1 2.7 8 6 5.7 80 0.7 4.0 335 – – –56 | | 1 | 7 6 5.7 67 0.6 2.5 290 – – –57 | | 1 | 5 3 3.6 46 0.2 4.2 68 – – –58 | | 2 2.7 9 6 6.4 62 – – – 58 23 2159 | | 2 | 8 6 5.5 40 – – – 76 9 2360 | | 2 | 8 5 5.1 43 – – – 59 25 2761 | 80 3 2.7 8 6 6.6 91 1.3 2.7 405 – – –62 | | 3 | 5 3 3.7 72 0.3 3.1 138 – – –63 | | 3 | 6 4 3.1 50 0.3 2.5 138 – – –64 | | 4 2.8 5 3 3.8 75 – – – 92 40 1465 | | 4 | 5 3 3.7 74 – – – 89 52 766 | | 4 | 7 3 4.6 60 – – – 80 25 25

Table 1 (continued)

Mar Ecol Prog Ser 520: 35–56, 2015

Morphology and fractal numbers DF1 and DF2

Aggregates formed in roller tanks had similarshapes to aggregates collected in polyacrylamidegel-filled sediment traps at similar times and loca-tions (Fig. 4). Maximum lengths ranged from 3 to20 mm, and projected areas from 1.3 to 118 mm2,leading to ESD of 1.3 to 12.3 mm (Table 1) and vol-umes of 1.1 to 965 µl. Their aspect ratios extendedfrom 1.03 to 4.15, except one very long ‘comet-shaped’ aggregate with an extreme value of 13. TheCorey shape factors ranged from 0.26 to 0.95. Over-all, aggregates produced in roller tank experimentswere bigger than natural aggregates (ESD: ~0.1 to1.4 mm). This is the result of our choice to maintainincubations over a duration long enough to providesufficient material for the chemical measurements.

Fractal numbers DF1 and DF2 of aggregates pro-duced in roller tanks were 1.49 ± 0.16 and 1.82 ± 0.18respectively (Fig. 5), and also close to those of naturalaggregates calculated with the same method (DF1 =1.25 ± 0.006 and DF2 = 1.86 ± 0.015), suggesting simi-lar fractal structure.

Solid components (BSi, POC, TEP)

The amount of BSi in aggregates increased withsize with values ranging from 0.09 to 3.6 µmol (Fig. 6).Values of POC and TEP in aggregates ranged from0.28 to 13 µmol and 60.5 to 488 µg XG equivalent, respectively. POC content in aggregates from the

46

C

DF3 = 1.8

DF3 = 1.4

DF3 = 1.2

E-3F−LE-4WE-4EA3−2E-5

A

1

2

DF3 = 1.2

DF3 = 1.4

DF3 = 1.8

101

102

103

Stoke

s (D

F3 =

3)

101

102

103

a = 0.001

a = 0.01

a = 100

DF3 = 1.2

DF3 = 1.8

B

a = 0.001

a = 0.01

a = 100

100 10110

1

102

103

ESD (mm)

SV

(m d

–1)

Fig. 3. Sinking velocities (SV) of aggregates versus theirequivalent spherical diameter (ESD) recorded at 6 stations,and theoretical expectations. (A) Stokes’ law assuming asolid body with constant excess density (thick line: Δρ =0.0014 g cm−3, DF3 = 3) and general sinking velocity models(thin and dashed lines) for porous fractal particles withporosity scaled on size for fractal numbers of 1.2, 1.4 and 1.8and 2 different specific conditions; 1: ESD0 = 1.5 mm, SV0 =100 m d−1; 2: ESD0 = 2 mm, SV0 = 50 m d−1. (B) Sensitivity ofthe general sinking velocity model to different values ofcoefficient a varying over 5 orders of magnitude from 0.001to 100, for 2 fractal dimensions (dashed lines: DF3 = 1.8; solidlines: DF3 = 1.2) and one set of specific conditions: ESD0 = 1.5mm, SV0 = 100 m d−1. (C) Data for each station (symbols)compared to general sinking velocity models (solid lines)with coefficient a fixed at 0.01 and different DF3 values (E-3,F-L, E-4E: DF3 = 1.8; A3-2, E-5: DF3 = 1.4; E-4W: DF3 = 1.2).Filled circles: specific conditions for each model; dashedlines: best fits to data (1 outlier excluded from A3-2 fit). E-3:y = 71x0.63 (n = 11, r2 = 0.49, p < 0.05); F-L: y = 53x0.61 (n = 13,r2 = 0.67, p < 0.005); E-4W: y = 53x−0.52 (n = 8, r2 = 0.1,p = 0.46); E-4E: y = 66x0.62 (n = 6, r2 = 0.8, p < 0.05); A3-2:y = 36x0.26 (n = 11, r2 = 0.5, p = 0.5); E-5: y = 45x0.2 (n = 12,

r2 = 0.4, p = 0.55)

Laurenceau-Cornec et al.: Phytoplankton controls on sinking velocity

Stn E-4W experiment presented a highvariability compared to all other exper-iments. TEP content did not scale withaggregate volume, possibly suggestingthat only one-third of the volume ofan aggregate (subsampling in 3.3 ml;see ‘Materials and methods: Chemicalmeasurements’) represented a toosmall amount of matter to be de tect -able by the method used, especiallyfor the smallest aggregates. This studyaim ed to obtain a complete set ofchemical analyses conducted on singleaggregates, which unfortuna tely con-strained the analyses to single meas-urements on amounts well un der theusual limits. Replicate measurementsand on larger particles would haveprobably increased the accuracy ofTEP measurements, but limited the applicability of our results to naturalconditions where smaller particlesdominate.

47

0

1

2

3

4

5

AR

10–1 100 1010

0.5

1

ESD (mm)

CS

F

A

B

Roller tanksGel traps

Fig. 4. Shape descriptors versus equivalent spherical diameter (ESD) for rollertank aggregates (one very long ‘comet-shaped’ aggregate excluded) and natural aggregates collected in polyacrylamide gel sediment traps deployedduring KEOPS2. (A) Aspect ratio (AR) and (B) Corey shape factor (CSF) are

in the same range of values for the 2 categories of aggregates

102

102 103 101 102

103

104

Per

imet

er (p

ixel

s)

103

104

105

101

102

103

101

102

103

Are

a (p

ixel

s2 )

Per

imet

er (p

ixel

s)A

rea

(pix

els2 )

A

B

y = 0.309x1.495

DF1 = 1.49 ± 0.16(n = 64, r2 = 0.86, p < 0.0001)

Feret’s diameter (pixels)

C

D

y = 1.313x1.248

DF1 = 1.25 ± 0.006(n = 7749, r2 = 0.94, p < 0.0001)

y = 1.4842x1.863

DF2 = 1.86 ± 0.015(n = 7749, r2 = 0.87, p < 0.0001)

y = 0.95x1.824

DF2 = 1.82 ± 0.18(n = 64, r2 = 0.88, p < 0.0001)

Fig. 5. Fractal numbers of (A,B) roller tank aggregates (one very long ‘comet-shaped’ aggregate excluded) and (C,D) naturalaggregates collected in polyacrylamide gel sediment traps deployed during KEOPS2 at the same sites. 1- and 2-dimensionalfractal numbers (DF1 and DF2): calculated from the slope of the relationships between perimeter (A,C) and area (B,D) versustheir Feret’s diameter. On each panel: best fit lines, fractal numbers (±95% CI) and regression statistics. An area cut-off at20 pixels2 was applied on gel trap data (visible in panel D) to exclude from the regression potential ‘fake particles’ deriving

from small gel imperfections

Mar Ecol Prog Ser 520: 35–56, 2015

High-resolution pictures and phytoplankton content

Aggregates from different sites displayed diverseaspects, colors and apparent compositions as shownin high-resolution pictures (Fig. 7). Similar observa-tions were done on natural particles collected inpolyacrylamide gel traps at the same sites. Aspectsranged from compact yellow aggregates (e.g.Fig. 7A,B & G) to very fluffy, green and fragile aggre-gates (e.g. Fig. 7C,E & H). Microscopic observationsrevealed distinct phytoplankton species assemblagescomposing the roller tank aggregates (Fig. 7J−L).The proportion and average sizes of phytoplanktoncells for the main species or genera identified in theaggregates are reported in Table 2. The largest aver-age proportions of the total organisms counted in all

aggregates in descending order were Chaetocerossubgenus Hyalochaete spp. (mean ± SD: 27 ± 24%);Fragilariopsis spp. (19 ± 20%) including the specieskerguelensis and rhombica; small centrics repre-sented mainly by Thalassiosira spp. (13 ± 15%);Pseudo-nitzschia spp. (11 ± 7%); and Eucampia ant -arctica (7 ± 8%). The average cell diameter meas-ured over each species ranged from 13.6 ± 1.94 to91.8 ± 23.3 µm. Phytoplankton classified as type 1(see ‘Materials and methods: Microscopic observa-tions’) ranged from 0.24 (Stn A3-2) to 70% (Stn E-3)of total organisms counted in aggregates. Type 2 represented 0 (Stn E-3) to 84.8% (Stn A3-2).

Sinking velocity controls

Results of the multiple regression analyses (Table 3)suggest that chemical composition and phytoplank-ton cell length and type predict the largest part ofsinking velocity variations, overcoming the effect ofaggregate size or shape. A decrease in the correla-tion coefficient (r2) of 0.26 and 0.32 was induced bythe removal of chemical composition and phyto-plankton type terms, respectively. ANOVA F-testsrevealed that models reduced from chemical compo-sition and phytoplankton types were significantlydifferent from the initial models (p < 0.05). Con-versely, the removal of aggregate size terms from fits1 and 2 led to decreases in r2 of 0.17 and 0.12 respec-tively. The removal of aggregate shape terms fromfits 1 and 2 induced decreases of r2 of 0.09 and 0.03respectively. None of the models reduced from sizeor shape terms were significantly different from thecomplete models.

Two additional multiple regressions were per-formed to identify which of chemical composition orphytoplankton types presented the best correlationto sinking velocity. This was done by removingaggregate size and shape parameters at the sametime from the initial fits (Table 3 bottom row), leavingchemical composition and phytoplankton type asunique aggregate properties in fit 1 and fit 2, respec-tively. A better fit was obtained when sinking veloc-ity was regressed against phytoplankton types thanagainst chemical composition (n = 30; r2 = 0.36; p <0.05, and n = 31; r2 = 0.21; p < 0.5, respectively).

In addition, data of shape (Corey shape factor andaspect ratio) and solid content (BSi, TEP, POM) wereexplored separately by site (Fig. 8A−E). Results sug-gest that shape and chemical composition are notsite-dependent and exert no clear influence on thesinking velocity. According to our main hypothesis,

48

BS

i (µm

ol)

10–2

10–1

100

101

PO

C (µ

mol

)

100

100 101 102 103

101

Volume (µl)

TEP

(µg

XG

eq

.)

102

103

E-4W station

A

B

C

Fig. 6. Chemical component abundances in aggregates vs.volume. (A) Biogenic silica (BSi); (B) particulate organic car-bon (POC); (C) transparent exopolymer particles (TEP; µgxanthan gum equivalent). Best fit lines: BSi, y = 0.07x0.49; n =34; r2 = 0.65; p < 0.0001; POC, y = 0.58x0.35; n = 28; r2 = 0.44;p < 0.0005. (S): scattered Stn E-4W values excluded from the

fit. (s): all other data. Error bars: 10% uncertainty

Laurenceau-Cornec et al.: Phytoplankton controls on sinking velocity 49

Fig. 7. Pictures of (A−F) roller tank aggregates formed at each station and (G−I) natural marine snow collected in polyacryl-amide gel traps at the same locations (note the similarities in aspect, shape and compactness between natural particles andthose formed in roller tanks at the same sites). (J−L) Pictures showing distinct phytoplankton assemblages in roller tank aggre-gates from Stns E-3 (Fragilariopsis spp., Corethron pennatum and centric diatoms), A3-2 (Chaetoceros subgenus Hyalochaetespp., small centric diatoms and Pseudo-nitzschia spp.), and E-4W (Pseudo-nitzschia spp. and Chaetoceros subgenus

Hyalochaete spp.), respectively

Mar Ecol Prog Ser 520: 35–56, 201550

Ph

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116

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722

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919

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aeto

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s (H

yalo

chae

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spp

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270

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enn

atu

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191

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917

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550.

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304

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0.8

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221

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530.

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0.2

105

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8.8

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27D

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an

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147

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282

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415

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661.

1±

0.7

101

±28

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1.0

88±

10E

uca

mp

ia a

nta

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ca*

2.9

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755

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850

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957

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552

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046

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dia

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802.

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16M

emb

ran

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123

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590.

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174

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117

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660.

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189

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±0.

113

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210.

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186

±28

Nav

icu

lasp

p.

0.4

±0.

130

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228

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±0.

427

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zsch

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.0.

887

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120.

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207

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Pse

ud

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106

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294

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292

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izos

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437

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246

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01.

7±

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363

±64

Th

alas

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ema

nit

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es*

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1.0

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48.

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95.

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35±

141.

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0.3

20±

14.

5±

2.5

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37.

0±

5.3

20±

3T

hal

assi

oth

rix

anta

rcti

ca0.

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577

8±

366

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6±

0.2

825

±17

30.

0–

0.8

±0.

675

6±

233

Sm

all c

entr

ics*

*4.

1±

0.3

43±

1142

.1±

5.1

28±

411

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6.7

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12.

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1.4

25±

414

.3±

9.3

18±

13.

6±

1.6

32±

4L

arg

e ce

ntr

ics

2.0

±0.

112

6±

550.

3±

0.2

76±

290.

2±

0.2

123

0.1

±0.

296

±23

0.3

±0.

282

±47

0.4

±0.

688

±11

Cer

atiu

msp

.0.

138

80.

0–

0.0

–0.

0–

0.0

–0.

2±

0.6

161

Sili

cofl

agel

late

s2.

0±

0.2

21±

20.

6±

0.3

19±

20.

4±

0.3

20±

31.

4±

0.8

18±

10.

4±

0.2

18±

11.

9±

1.2

21±

3T

inti

nn

ids

0.8

±0.

194

±72

0.6

±0.

662

±10

0.1

±0.

115

6±

100

0.3

±0.

360

±4

0.0

–0.

0–

Tab

le 2

. P

hyt

opla

nk

ton

sp

ecie

s or

gen

era

pro

por

tion

s (%

mea

n ±

SD

) in

ag

gre

gat

es (

agg

.) a

nd

th

eir

cell

dia

met

er (

ø, m

ean

± S

D)

at 6

sta

tion

s. I

n b

old

: th

e 2

maj

or

spec

ies

or g

ener

a at

eac

h s

tati

on; t

he

**m

ost

and

*se

con

d m

ost

abu

nd

ant

spec

ies

or g

ener

a en

cou

nte

red

in

ag

gre

gat

es f

rom

at

leas

t 1

stat

ion

are

als

o in

dic

ated

Laurenceau-Cornec et al.: Phytoplankton controls on sinking velocity

dominant phytoplankton cell size and morphologicaltypes were further investigated as indirect controls ofthe sinking velocity (Fig. 8F−H). The clustering ofdata from each site suggested that dominant phyto-plankton type was a site-dependent factor possibly

influencing the sinking velocity. The cell length ap -peared to apply a moderate influence since aggre-gates where the largest cells were observed hadintermediate sinking velocity (Stn E5), and aggre-gates sinking faster and slower than 100 m d−1 con-

51

Terms removed from the fit Fit 1 Fit 2New r2 New F-test New r2 New F-test

p-value p-value p-value p-value

Size (projected area, volume, ESD) 0.25 (−0.17) 0.13 (+0.03) 0.17 0.38 (−0.12) 0.03 (−0.01) 0.22Shape (CSF, AR) 0.33 (−0.09) 0.1 0.25 0.47 (−0.03) 0.02 (−0.02) 0.51Chemical composition (BSi, POM, TEP) 0.16 (−0.26) 0.54 (+0.44) 0.03 – – –Phytoplankton (cell length, type 1, type 2) – – – 0.18 (−0.32) 0.4 (+0.36) 0.01Size + shape 0.21 (−0.21) 0.15 (+0.05) 0.27 0.36 (−0.14) 0.01 (−0.03) 0.5

Fit 1: SV = ƒ(projected area + volume + ESD + CSF + AR + BSi + POM + TEP); n = 30; r2 = 0.42; p = 0.1Fit 2: SV = ƒ(projected area + volume + ESD + CSF + AR + cell length + type 1 + type 2); n = 31; r2 = 0.5; p = 0.04

Table 3. Multiple regression analyses statistics: relative contribution of aggregate properties to sinking velocity (SV) varia-tions. Parameters investigated: aggregate size, shape, chemical composition (BSi, POM and TEP average mass fraction in solidcontent) and average phytoplankton type in aggregates. New r2 and p-values (variations in parentheses) after removal ofterms from the initial complete fits (1 and 2) are given. Initial and reduced models are compared by performing ANOVAF-tests. Significant modification of the initial model are in bold (p < 0.05) and show the importance of the terms removed insinking velocity variations. Type 1 and 2: average proportion (%) of (1) chain diatom cells without setae and (2) small setae-forming diatom cells in aggregates, respectively. ESD: equivalent spherical diameter; CSF: Corey shape factor; AR: aspect

ratio; BSi: biogenic silica; POM: particulate organic matter; TEP: transparent exopolymeric particles

1 2 3 4101

102

AR0.5 1

CSF100

TEP mass (%)101 102

BSi mass (%)101 102

POM mass (%)40

0 5010

1

102

Avg cell length (µm)0 50 100

Type 1 (%)50 100

Type 2 (%)

E-3F-L

E-4WE-4E

A3-2

E-5

Avg:39±21%

Avg:15±13%

Avg:18±18%

Avg:44±24%

100 m d–1

A B C D

G H

E

F Avg:48±12µm

Avg:43±25µm

Type 1: chain diatoms without setae

Type 2: small setae-forming diatoms

SV

(m d

–1)

100 0

Stations

Fig. 8. Influence of shape, chemical composition and phytoplankton morphology on sinking velocity (SV). (A–E) Aspect ratio(AR), Corey shape factor (CSF), transparent exopolymer particles (TEP), biogenic silica (BSi), and particulate organic matter(POM) mass proportion in solid content, respectively. (F) Average cell length in aggregates; (G,H) proportion in aggregates ofchain diatoms without setae (type 1; Fragilariopsis spp. and Eucampia antarctica) and small setae-forming diatoms (type 2;Chaeroceros spp.), respectively. There is no clear influence of shape or chemical composition. Data clustering of morphologi-cal properties of phytoplankton at each station suggests a control by phytoplankton cell type. High proportions of type 1 (39 ±21%) and low proportions of type 2 (18 ± 18%) diatoms are observed in aggregates sinking faster than 100 m d−1. The opposite

is found for aggregates sinking slower than 100 m d−1 (type 1: 15 ± 13%; type 2: 44 ± 24%)

Mar Ecol Prog Ser 520: 35–56, 2015

tained in average cells having similar length (mean ±SD: 48 ± 12 and 43 ± 25 µm, respectively). However,aggregates sinking faster than 100 m d−1 had highproportions of Eucampia antarctica and Fragilariop-sis spp. (type 1; mean ± SD: 39 ± 21%) and low pro-portions of Chaetoceros spp. (type 2; 18 ± 18%). Incontrast, aggregates sinking slower than 100 m d−1

had low proportions of type 1 (15 ± 13%) and highproportions of type 2 (44 ± 24%).

DISCUSSION

Our image analyses suggested that the structure ofaggregates produced in roller tanks were similar tothose of natural aggregates collected in gel traps dur-ing KEOPS2. The fractal numbers DF1 and DF2 wereclose to those of natural particles, suggesting thataggregation processes in the roller tanks were some-what similar to those acting in the water column. Thisis an encouraging result toward the applicability ofthis experiment to natural conditions, but needs con-siderable caution, especially since roller tank experi-ments have been previously shown to poorly simu-late natural aggregation processes and should not beused for quantitative studies (Jackson 1994). Aggre-gates formed in the roller tanks were consistentlybigger than natural aggregates collected in gel traps.One major feature of roller tank experiments whichdiffers from natural conditions is that fast-sinkingparticles cannot escape from the tank and tend toform continuously larger particles until completeclearing of the water. Thus, the size of aggregatesformed in roller tank experiments depends mainly onthe duration of incubation. However, the main objec-tive here was to form marine snow aggregates from anatural mixture of phytoplankton and test if varia-tions in their composition and structure was relatedto sinking velocity variations. Even if aggregatesformed in this experiment were far from natural par-ticles encountered at the same sites (which does notseem to be the case according to our observations),they still can serve as model aggregates to identifyfactors altering the size−sinking velocity relationship.

While the overall correlation between sinking velo -city and particle size is quite weak in our results, sev-eral sites exhibited reasonably tight correlations(Fig. 3C) and with slopes reasonably close to thoseexpected from general sinking velocity models. Thissuggests that differences in the initial compositionsmight be responsible for the overall weak correlationobserved when combining all aggregates from dis-tinct sites. A match between size−sinking velocity

model curves and experimental data from each sitewas obtained by varying the fractal dimension, indi-cator of particle compactness. In combination, these 2results suggest that distinct particle sources sampledat different sites formed aggregates having differentcomposition, structure and sinking velocity. Also, thesize−sinking velocity relationship appears to be pre-served for the most compact aggregates, suggestingthat a reduction of the porosity could restore size as acontrolling factor. Iversen & Ploug (2010) comparedsize−sinking velocity relationships for different typesof aggregates formed from different primary parti-cles. They also noted a correlation of sinking velocitywith size only within homogeneous sources of aggre-gates, but when compared across different aggre-gate composition, the sinking velocity appeared size-independent.

Overall, our results suggested a poor contributionfrom size, shape or chemical composition in ag -gregate sinking velocity variation among sites. Themultiple regression analyses performed (Table 3)showed that among all the aggregate propertiestested in our experiment, phytoplankton cell typeseemed the best property to explain sinking velocityvariation. The 2 distinct morphological categoriesthat we selected (type 1: Eucampia antarctica andFragilariopsis spp.; and type 2: Chaetoceros spp.)could have influenced the sinking velocity either byballast effect (Waite et al. 1997a, Ploug et al. 2008,Iversen & Ploug 2010, Miklasz & Denny 2010), or byinfluencing aggregate structure through distinctaggregation processes. The absence of correlationbetween BSi mass fraction in aggregate solid content(Fig. 8D) suggests that a ballast effect did not explaina large part of sinking velocity variation; the ob -served increase in BSi with aggregate volume (Fig. 6),as expected for diatom aggregates, suggesting reli-able measurements for this component.

Setae are known to promote phytoplankton coagu-lation by increasing the efficiency of ‘mechanical’sticking upon contact (Alldredge & Gotschalk 1989,Kiorboe et al. 1990). Stickiness (i.e. the probabilitythat 2 particles become attached upon collision) hasbeen demonstrated to be species-specific (Kiorboe etal. 1990, Alldredge et al. 1995, Crocker & Passow1995), and Waite et al. (1997b) noted that spine for-mation, cell surface bound sugars, and TEP con-trolled phytoplankton cell stickiness and played arole in determining aggregate structure via coagula-tion processes. High sticking efficiency is not subjectonly to cell morphology and depends on variousother factors including TEP production, which playsa central role in coagulation (Kiorboe & Hansen 1993,

52

Laurenceau-Cornec et al.: Phytoplankton controls on sinking velocity

Dam & Drapeau 1995, Jackson 1995, Thornton 2002).Cell concentration and size have also been demon-strated to be critical parameters for coagulation pro-cesses during algal blooms (Jackson 1990); high algalconcentration increases the probability of encounter,and thus a high coagulation efficiency, provided thatcell stickiness is sufficiently high and the cells aresufficiently large.

Logan & Wilkinson (1990) used fractal geometry totest if colloidal aggregation mechanisms, well de -scribed for inorganic particles, were applicable tomarine snow aggregates. They suggested that differ-ent types of aggregates form as a function of differentparticle stickiness and thus collision efficiencies. Ifthe probability of sticking upon collision is high, cellswill efficiently stick when they encounter and formhighly porous and tenuous structures (diffusion- limited aggregation or DLA). In contrast, if severalcollisions are required, then more solid and compactaggregates are formed (reaction-limited aggregationor RLA). Meakin (1991) suggested that the processesforming marine aggregates are likely to correspondclosely to the diffusion- and reaction-limited clus-ter−cluster aggregation mechanisms described forcolloids. Aggregates formed through these 2 mecha-nisms may thus have distinct compactness affectingtheir sinking velocity.

To explore further the hypothesis that species- specific coagulation efficiencies were responsiblefor different aggregate compactness influencing thesinking velocity, we widened our morphological classification (type 1 and 2) to include the mostand second most abundant phytoplankton genera inour samples (Table 2). Overall, 6 species dominatedaggregate composition: Chaetoceros (Hyalo chaete)spp., Pseudo-nitzschia spp., Fragilariopsis spp., E.antarctica, Thalassionema nitzschioides and smallcentrics. Chaetoceros (Hyalochaete) spp. was clas -sified as type 2, along with Pseudo-nitzschia spp.,(even though not producing setae) due to their morphology facilitating attachment upon collision;Fragilariopsis spp., E. antarctica, T. nitzschioides andsmall centric diatoms were classified as type 1. Astrong linear relationship was found between the av-erage proportion of phytoplankton cells of type 2 andthe average sinking velocity recorded at each station(Fig. 9; Stn E-4E was considered an outlier, rejectedat 95% confidence and excluded from the fit). In con-trast to other aggregates, Stn E-4E particles containeda relatively large abundance of fecal pellets (Fig. 7D).Because fecal pellets are tightly packaged materialformed by biological ag gregation, this may have in-creased aggregate density and compactness and thus

altered the relation between dominant phytoplanktontypes and aggregate sinking velocity. Certainly fecalpellets on their own are known to have high densitiesand sinking velocities (Fowler & Small 1972, Small etal. 1979, Yoon et al. 2001). This result emphasizes thecomplexity of controls on the sinking velocities ofmarine snow and the importance of ecological con-siderations, suggesting that controlling factors mayvary at very small spatio-temporal scales.

The variations in the dominance of the 2 phyto-plankton types appears to have some relationship tobiomass levels at the different stations, and perhapsto the intensity of iron fertilization. For instance,Stns A3-2 and E-4W, where the genus Chaetocerossubgenus Hyalochaete was dominant, displayedhigh biomass — characteristic of bloom conditions —and are known to be under the influence of naturaliron fertilization (Bowie et al. 2014, van der Merweet al. 2014, Quéroué et al. 2015). Conversely, Stn E-3was largely dominated by the ribbon-chain diatomFragilariopsis spp. and was in a central region ofmoderate biomass with less iron enrichment.

53

0 20 40 60 80 1000

50

100

150

200

250

Type 2 phyto. cells in agg. (%)

y = –1.48x + 168(n = 5; r2 = 0.98; p < 0.005)

E-3

F-L

E-5A3-2

E-4W

E-4E

SV

(m d

–1)

Fig. 9. Relationship between the average sinking velocity(SV) of aggregates from each station and the average pro-portion of phytoplankton (phyto.) cells in aggregates thathad a morphology facilitating attachment upon collision(type 2; see ‘Discussion’). Stn E-4E was excluded from best

fit line calculation. Error bars: 1 SD

Mar Ecol Prog Ser 520: 35–56, 2015

Evaluating the generality of our results will requireobservations on aggregates across varying levels oftotal biomass and ecological community structure.When comparing these environments, it is importantto note that phytoplankton community compositionand total biomass can have somewhat independenteffects on aggregate sinking velocities; i.e. even forsetae-forming species, if biomass is sufficient foraggregation to continue until very large particles areformed, then high sinking velocities can still beobtained. This could explain the EIFEX iron fertili -zation experiment results, during which the setae-forming diatom C. dichaeta was abundant, and forwhich transmissometry profiles were interpreted asrepresenting cm-sized aggregates sinking at rates>500 m d−1 (Smetacek et al. 2012). These results arecompatible with the perspectives developed here, tothe extent that the very large size of the aggregatescould have outweighed the expectation of low sink-ing velocities for aggregates formed from this spe-cies. Without any direct observations on either theaggregates or their sinking velocities during EIFEX,it is of course possible that other factors were at play,such as the myriad of influences on sinking velocitiesas summarized in the introduction, and the diversenature of deep ocean particles, including living orga -nisms (Silver & Gowing 1991).

From a cautionary perspective, this study empha-sizes that predictions of marine snow sinking velocityshould not be based only on size parameterizations,and certainly should not assume that sinking velo -cities will always increase with size. Further studiesmay eventually identify those phytoplankton typeswhich are most readily assembled into rapid sinkingaggregates, by either physical or biological aggrega-tion, as a path towards greater predictability of car-bon export and biological pump efficiencies.

Acknowledgements. This work received support from theAustralian Commonwealth Cooperative Research CentresProgram to the ACE CRC, and the Australian National Network in Marine Science via UTAS IMAS. We thank thepersonnel of the RV ‘Marion Dufresne’, Institut Paul EmileVictor, Institut National des Sciences de l’Univers, and theKEOPS2 voyage leader Bernard Queguiner and KEOPS2science team for assistance at sea. Stephen Bray (ACE CRC),Peter Jansen (IMOS), and David Cherry (CSIRO) preparedthe free-drifting sediment trap arrays. The MODIS (NASA)satellite ocean-colour image is courtesy of Francesco d’Ovidio (Univ. Paris). The altimeter and colour/temperatureproducts for the Kerguelen area were produced bySsalto/Duacs and CLS with support from CNES. We thankSimon Wotherspoon (IMAS) for his precious insights intostatistical analysis. We thank the 3 anonymous reviewers fortheir constructive and thorough comments which helpedimprove the manuscript.

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Editorial responsibility: Graham Savidge, Portaferry, UK

Submitted: December 10, 2013; Accepted: November 13, 2014Proofs received from author(s): January 20, 2015