lattice-automaton bioturbation simulator (labs): implementation for small deposit feeders

Computers & Geosciences 28 (2002) 213–222

Lattice-automaton bioturbation simulator (LABS):implementation for small deposit feeders

Jae Choia, Fr!eederique Francois-Carcailletb, Bernard P. Boudreaua,c,*aDepartment of Oceanography, Dalhousie University, Halifax, NS B3H 4J1, Canada

bObservatoire Oc !eeanologique de Banyuls, Universit !ee Pierre et Marie Curie (Paris VI), CNRS Laboratoire Arago,

BP 44-66651 Banyuls-sur-mer Cedex, FrancecUniversity of Southampton, School of Ocean and Earth Science, Southampton Oceanography Centre, European Way,

Southampton S014 3ZH, UK

Received 17 January 2001; received in revised form 24 May 2001; accepted 25 May 2001

Abstract

A new model for biological activity and its effects in sediments is presented. Sediment is represented as a random 2Dcollection of solid and water ‘‘particles’’, distributed on a regular lattice with individually assigned chemical, biologicaland physical properties, e.g. food versus inert material. Model benthic organisms move through the lattice (the virtual

sediment) as programmable entities, i.e., automatons, by displacing or ingesting–defecating particles. Each type ofautomaton obeys a different set of rules, both deterministic and stochastic, designed to mimic real infauna. In thepresent version of the model code, the organisms are simple small deposit feeders, resembling capitellids.

The results from the model are 2D visualizations of the movement of the animals and the particles with time. Thelatter provide immediate appreciation of the consequences of animal actions on sediment fabric and composition,including both the mixing, traditionally associated with bioturbation, and the development of biologically-inducedheterogeneities, which are observed in real sediments. The output is readily amenable to presentation as computer-

generated (QuickTimeTM) movies, for which links are provided to such examples. As a particular case, we present asimulation of the mixing of a sand plug in a muddy sediment which shows that this is process not accomplished bycounter-diffusion of sand and mud but by displacement and dilution of the sand with mud that is defecated as feces

therein; this mode of mixing appears to be far more favorable to preservation of this sand feature than traditionaldiffusive models. r 2002 Elsevier Science Ltd. All rights reserved.

Keywords: Bioturbation; Automatons; Mixing; Particle-lattice; Deposit feeders

1. Introduction

The activities of infauna are, without doubt, some ofthe most influential processes that occur during early

diagenesis of sediments. For example, sediment fabricand structure are modified and biogenic heterogeneitiesare created that change the acoustic response andgeotechnical properties; contaminants at the sediment-

water interface can be removed to depth far more

rapidly than by burial alone, while ‘‘capped’’ pollutantscan be transported to the surface and re-introduced tothe environment; the preserved geological/geochemical

record can be fundamentally altered in terms of bothtiming and intensity of events, clouding our under-standing of climate and paleoceanography; finally, (bio-)geochemical reactions can be instigated or significantly

promoted, such as the dissolution of carbonates andredox reactions.

Past models of infaunal activities are largely 1D

deterministic representations of the overall effects ofinfauna on sediment components, particularly tracers,

*Corresponding author. Department of Oceanography,

Dalhousie University, Halifax, NS B3H 4J1, Canada. Fax:

+1-902-494-3877.

E-mail address: [email protected] (B.P. Boudreau).

0098-3004/02/$ - see front matter r 2002 Elsevier Science Ltd. All rights reserved.

PII: S 0 0 9 8 - 3 0 0 4 ( 0 1 ) 0 0 0 6 4 - 4

e.g. Goldberg and Koide (1963), Guinasso and Schink(1975), Fisher et al. (1980), Aller (1982), Boudreau

(1986a, b, 1998), Robbins (1986), Boudreau and Im-boden (1987), and Smith et al. (1993). Biology andecology are, in truth, largely absent from these models in

that the models contain neither direct representations ofthe organisms nor any true biological parameters, e.g.,rates of ingestion or locomotion, population composi-tion, or densities, etc., notwithstanding the efforts of

Boudreau (1986a), Wheatcroft et al. (1990), and Smith(1992) to alleviate that situation. Instead, these determi-nistic models usually produce explicit mathematical

expressions with phenomenological constants, e.g. bio-diffusivity, or nonlocal exchange parameters, etc., whichcan be easily and pleasingly fit to data. Heterogeneities,

e.g. porosity anomalies, surface structures, and food andtracer anomalies, are conveniently averaged out of suchmodels (Boudreau, 1986a, 1997), while they are the

essence of real sediments, The traditional models alsoact as high-pass filters (Guinasso and Schink, 1975), sothat the preservation of sediment heterogeneities anddiscontinuities is difficult to explain. Finally, the effects

of changes to sediments during passage through ananimal’s guts are difficult to program in traditionalmodels.

A radically new type of model that overcomes theseproblems is needed if we are to truly understand howbiology, ecology and mixing are quantitatively related

and how sediment fabric, including heterogeneities,develops and are preserved. Such a model must notonly recognize organisms, they must be an explicit andfundamental part of such a model; furthermore, it

cannot predetermine the nature of the mixing (e.g.,diffusion).

2. Strategy for a new model

The philosophical basis of our model is to embracethe discrete nature of sediments and organisms, ratherthan to average it away (see Boudreau, 1986a). Within

this framework, biologically active sediment is repre-sented as a random collection of solid and water‘‘particles’’, placed on a regular lattice, with individually

assigned chemical, biological and physical properties,e.g. food versus inert material, etc. These model particlesare not true individual sediment grains, as that would benumerically onerous, but idealized bodies of sufficient

number and small size to be statistically equivalent androughly comparable to the sediment parcels manipu-lated by organisms. Particles can be added to the model

by sedimentation and removed by burial, while compac-tion guarantees the existence of a sediment-waterinterface and the slow disintegration of some biologi-

cally generated features. Model benthic organisms movethrough the lattice as programmable entities, i.e.

automatons, by displacing or ingesting-defecating par-ticles. Each automaton obeys a set of rules, both

deterministic and stochastic, designed to mimic realinfaunal behavior (see below). At this point in itsdevelopment, the model only contains small deposit

feeders, similar to some capitellids (L. Mayer andP. Jumars, Univ. Maine, pers. commun.). This lattice-automaton bioturbation simulator is christened with theacronym LABS.

To provide substance to this general description,consider the mock-up of a 2D-particle lattice given inFig. 1, where brown rectangles are movable sediment

‘‘particles’’, while the blue rectangles are water‘‘particles’’. Note the existence of a water column, whichallows for the possibility of sediment-boundary layer

dynamics, as well as bioturbation. This paper reportsonly on 2D problems, but fully 3D simulations areplanned for the future. The 2D model can be considered

to be a slice through a 3D model that is symmetric alongone of its horizontal axes; this may seem, at firstunreasonable, but it is in fact a tried method, success-fully employed for describing a wide variety of

phenomena from flow over wings to diffusion andreaction around animal burrows. Few of these applica-tions are truly 2D, but the inaccuracies are not

damaging while the gain in computational reduction isoverwhelming.

If a worm wishes to move, it must do so by either

displacement of particles or ingestion–egestion (Fig. 2;

Fig. 1. Mock up of particle lattice with no animal present.

Brown particles are solid sediment, whereas blue ones are

water. Sediment-water interface is evident, and movement into

water column is possible, if required.

J. Choi et al. / Computers & Geosciences 28 (2002) 213–222214

solid particles in brown). Note that particles that aretaken within the animals (pink) can be chemically,

physically or even biologically altered before defecation,but this is not done in the simulations discussed below.Either through animal-induced displacement or inges-

tion–egestion, particles are displaced to new positions inthe lattice. If displacement moves a particle across a leftor right (vertical) border, then the particle simply

appears on the other side (Fig. 3) in order to conservethe number of particles. Particles can leave the bottomof the lattice by sedimentation (advection) or be pushedout by bioturbational movements or the bottom can act

as a reflector for bioturbational displacements. Care istaken not to perturb the local average porosityinordinately by these actions. As to the sediment-water

interface, it is not a rigid lid, and biological structures,i.e., 2D pits and mounds, can form through biologicalactivities; as a result, the porosity near the interface

increases somewhat with time to a greater average value.As we develop better compaction and pellet formation/decomposition algorithms, we will be able to create,rather than impose, better predictions of porosity

gradients.

The model and its components are not described bydifferential equations, as in traditional models of

bioturbation (Schink and Guinasso, 1975; Boudreau,1986a,b). Instead, there is a simple accounting forparticle (and tracer) conservation, but otherwise the

model is governed by rules and chance, as determined bya random number generator. At each time step, thebehavior of the automatons (animals) is controlled by aset of rules, such as:

* Move at a velocity (distance time�1) of (fill in theblank);

* Consume ( )% of particles encountered;* Consume food at probability ( ) at each time step;* Defecate when ( )% filled or ( ) times per day;* Change direction to ( 1) with a probability ( ) at

this time step;* Turn ‘‘upward’’ at angle ( 1) with probability ( ) at

this step;* Etc.

Fig. 2. Key: solid sediment particles in brown, water in blue,

animal in black with H for head and B for body, and ingested

particles in pink within animal. Left-hand diagram: small

worm, i.e., capitellid-like, moving by particle displacement

forward and upward in matrix at three successive time steps.

Animal must push aside particles to proceed in desired

direction, i.e., vertically in top panel and laterally in middle

panel. Right-hand diagram: example of forward movement of

worm by (selective) ingestion.

Fig. 3. Illustration of movement of particle at edge of domain

when it is displaced laterally, i.e., red particle. This displaced

particle will move out of domain on left-hand side and re-

appear at same height position on right-hand side, displacing

any solid particle already there, using displacement rules.

Particle moving from right-hand side of lattice will do same, but

in opposite direction. Thus, no particles are lost from this type

of motion, nor is there any net effect on particle (porosity)

distribution from this type of motion.

J. Choi et al. / Computers & Geosciences 28 (2002) 213–222 215

The sediment particles must act consistently accordingto their own set of rules, such as:

* New particles enter the top at a rate of ( ) (i.e.,sedimentation);

* Composition of a particle will change to ( ) for

organic C, 210Pb,y;* Etc.

A good random-number generator, generic to For-

tran90/95, is employed to resolve the probabilities.Whereas the use of a 2D lattice to model sediment

mixing is arguably not in itself truly innovative, the useof automatons to perform the mixing is definitely

original. Specifically, the 2D transition matrix approachdeveloped by Hanor and Marshall (1971), Foster (1985),and Trauth (1998) can be interpreted to be a particle

matrix method for mixing, although it could as well beargued that this is a finite form of the Boudreau (1986b)and Boudreau and Imboden (1987) non-local models;

however, the automaton model contains independentcausal agents for the mixing, i.e. the worms. The actionsof the worm(s) cannot be reduced a priori to a transition

matrix of probabilities once the simulation startsbecause such a matrix for LABS is dynamic andcontinuously being recalculated by the automatonsthemselves, independent of the user. In addition, as

Foster (1985) states, the transition matrix approach isnot ‘‘a model for a specific process of bioturbation’’,whereas LABS is just such a model. Another technique

to overcome the lack of biology using a 2D (or 3Dmatrix) has been the functional-group model advancedby Francois et al. (1997). Although this model does

contain real biological elements, they are static and themode of mixing they produce is generally predeter-mined; yet, it is certainly a step in the right direction andcan be considered a precursor to LABS.

3. Structure and detailed functioning of the LABS code

3.1. Initialization

The following two key scaling parameters are

specified in the files Parameters.in and Organisms.in,and their values are used to re-scale the other parametersof the simulation. 1. The size of a pixel, as defined atrun-time: this size must be smaller than the size of the

smallest organism (head width). 2. The duration of onetime step, which is taken as the time required movingacross one pixel by the fastest moving organism. All

other organisms move proportionately to this parametervalue in discrete time and space. The simulation area isinitially divided into two regions: the lower sediment

area and a section of water overlying the sediments. Thesediment area is randomly filled with particles while

maintaining a prescribed porosity distribution, e.g.,uniform with depth, as used here.

Currently, the code tracks the following particle traits:(1) The initial time of appearance of each particle; (2) theinitial and current co-ordinates of the particles, used to

track displacement; (3) the initial and current activitylevel of a tracer, e.g., 210Pb, on each particle, to providemixing profiles; and (4) the initial and current lability ofa particle, if it is designated as organic matter/food.

Currently there are five classes of organic matter/food,ranging from the most labile, i.e., class 5, to the leastlabile, i.e., class 1. While the deposit feeders can be placed

anywhere at the beginning of a simulation, we start allour simulations with them randomly placed in the watercolumn adjacent to the water-sediment interface.

3.2. Main program flow

For each organism, a sinusoidal probability functionis calculated at each time step, which is used to mimicyearly and daily cycles of locomotion and feeding rates.

This forces activity (motion and ingestion/egestion) tovary from a maximum of 100% probability of beingactive to a lower threshold of 20% probability of beingactive. The ratio of amplitudes of yearly to daily

variations in these probabilities were arbitrarily assumedto be 9 : 1, but this can be user modified.

If biological activity is possible, the current rate of

locomotion is then computed as a running average witha window of one-day duration. Movement in the nexttime step is allowed if the current rate of locomotion

does not exceed its allowed maximum. If movement isnot possible, then control is passed to the next organism,or the next time step, i.e., the organism pauses.

If movement is possible, the current rate of ingestion

is computed as a running average with a window of one-day duration. Ingestion is allowed in the next time step ifthe current rate of ingestion does not exceed its

maximum potential ingestion rate. If the organism isnot able to ingest particles, then movement proceedswithout ingestion by pushing (clearing) the particles

adjacent to the head.If, however, the organism is able to ingest particles,

then the likelihoods of ingestion and egestion of particles

are computed as a linear function of the relative fullnessof the organism’s gut. That is, when the gut iscompletely full, there is a 0% probability that theorganism will try to ingest particles and a 100%

probability that it will egest, and vice-versa. If the gutis not full, selected particles adjacent to the head areingested and any non-ingested particles are cleared

(pushed) away prior to the move.The allowable directions of motion are then deter-

mined based upon the following criteria. (1) Is

a direction blocked by an immobile object, such as abody part (including that of another organism) or


a particle that is defined as being immobile? (2) Does adirection lead to an impermeable/impenetrable bound-

ary (top or bottom of the matrix)? Of the allowable setof directions, the preferable set is selected based uponthe following criteria: (1) When depth avoidance is a

constraint, the probability of turning away from thebottom increases as a prescribed function of the depth ofthe head, e.g., linearly with depth. (2) If an organism’sposition is above the initial sediment-water interface, the

local porosity of the sediments in the vicinity of the headis determined; if this local porosity is less than thecritical porosity (arbitrarily set at 90% porosity), it turns

away from the upwards orientation with a probability of99%. (3) An organism will otherwise follow a roughlystraight-line path; however, there is a user defined

probability (currently set at 25%) of turning away fromthis path. (4) The direction with the highest averageparticle labilities in the sensory range of the head

(currently set as the length of the head) is the preferreddirection of motion.

Each of the above four rules carry an equal weightand the preferred direction is selected from the

maximum of the combined product, i.e., this assumesthe processes to be independent. A further 25% randomerror in the selection of the preferred direction is added

to the simulation. The head is rotated in that directionand then translated one pixel in the chosen direction,with the rest of the body following the head.

Prior to any translational movement (see above), thespace in front of the head is cleared of particles via twoprocesses: (1) ingestion of labile particles, if ingestion ispossible, or (2) pushing them away. The ingestion of

particles is probabilistically accomplished with only a setproportion of labile particles being ingested, based uponthe relative selectivity of the organism. All remaining

particles are pushed away laterally or in the forwarddirection with probabilities of 0.4 : 0.4 : 0.2 (left : right : -forward). Such pushing extends from particle to

adjacent particle until an element of water is ‘‘pushed’’,’’, whereupon the water is ‘‘squeezed’’ out of thesimulation. (No water is actually removed as the lattice

position occupied by a part of a worm becomes eitherwater or egested particles upon passage of the organism.On average this all balances out.) If the particles arriveupon the lateral boundaries of the simulation, the

pushing sequence continues by wrapping-around to theopposite side.

If the current location of the head (the top left point,

in the frame of reference of the organism) is on a lateralboundary, the organism is ‘‘wrapped-around’’ to theopposite side, whereupon motion is constrained to be

lateral until the head clears the edge. If an organism isscheduled to move but is blocked by some cause/constraint from movement, it attempts to back out. If

the organism is forced to back out n-steps (wherenXhead length) then the head and tail are swapped and

movement continues, as an escape sequence. If motion iscompletely blocked for a specified period, e.g., 1/4 year,

the organism is considered ‘‘dead’’ and is moved to thesediment-water interface and re-initialized. Any particlesin the gut are randomly released to the space that had

been occupied by the organism.Upon completion of the movement, the empty space

at the tail end of the organism is filled with particles thatare ‘‘egested’’ by the organism or water if no egestion

occurs. The organic matter particles that are so egestedare ‘‘degraded’’ by shifting down one lability class. Thus,for example, lability class 5 (most labile) particles

become lability class 4 particles (less labile), down tominimum of class 1 (inert minerals). The user can alterthis scheme. The first particles ingested are the first to be

egested.At specified intervals of time (ranging from every year

to every 1/4 year), new particles are sedimented onto the

surface of the water-sediment interface. This is accom-plished by moving a particle down or diagonallyuntil the local porosity above and below the sedimentingparticle are approximately the same. These particles

have prescribed lability class distributions, and wehave set them to be identical to those of the initialconditions of the simulation. The total number of

particles in the simulation may be forced to be constantor to vary within a specified tolerance. When too manyparticles are sedimented into the simulation, the

particles at the bottom row of the matrix are removedand all elements of the simulation are shifted down onepixel.

3.3. Data input

The following are the user-specified pieces of informa-tion that need to be input for a simulation. Within file

Parameters.in, the information about the dimensions ofthe simulation and output options must be set.

1. Is the output a continuous movie (true) or user

defined series of pictures (false)?2. Is depth avoidance on (true) or off (false)?3. Are the lability searching and degradation functions

turned on (true) or off (false)?4. Are the particle sedimentation functions turned on

(true) or off (false)?5. Is mixing localFdisplacement onlyF(true) or non-

local (false)?6. Are data to be saved to disk (true/false)?7. Is a color representation of the matrix to be created

(true/false)?8. Is a locally averaged representation of the porosity

to be created (true/false)?

9. Is a locally averaged representation of the tracer,e.g. 210Pb activity, to be created (true/false)?


10. Shall the variation of porosity as a function of thelength scale be quantified and output (true/false)?

11. The total number of organisms in the simulation(integer).

12. The depth of the simulation (sediments and water,

inclusive, in cm; integer).13. The width of the simulation (cm; integer).14. The size of particles (cm; real).15. The sedimentation rate (in cm yr�1; e.g., w=0.1,

0.01, 0.001 cmyr�1; real).16. The average density of sediment particles (in g cm�3;

real; default=2.5 g cm�3).

17. The porosity of sediment at the sediment/waterinterface (e.g., 0.8=80% H2O; real).

18. The tracer half-life (e.g., t ¼ 22:3 yr for 210Pb; real).

19. The depth at which organisms have B0 probabilityof being found (cm; real).

20. The time at which the first data output is to be made

(days; integer).21. The time at which the simulation ends (days;

integer).22. The time steps to be used if the output is to be a

movie (days; real).

Likewise, in the file Organisms.in, the informationabout each individual deposit feeder must be stated, i.e.;

1. identification number (integer),2. organism width (cm; real),3. organism length (cm; real),

4. specific density of the organism (g cm�3; real and1.2 g cm�3 default),

5. feeding type (D=deposit feeder; others to be defined

in the future),6. locomotion speed (cm day�1; real),7. ingestion rate (mass specific; day�1; real),8. ingestion selectivity towards ‘‘food’’, i.e., ranging

from 0 for no selectivity to 1 for ingestion only offood, regardless of lability class (in this version).

4. Model results and discussion

In a real model run (e.g., Figs 4 and 5), large numbers

of particles are employed (>45,000) in order to assuregood statistics with regard to the particle population.The initial distribution is usually chosen to be purelyrandom (Fig. 4-top), but consistent with the prescribed

porosity function, i.e., constant in this situation at 0.8.The model sediment section is adjustable, but in allexamples illustrated here, it is 50 cm in width and 14 cm

thick, with a mixed layer depth of 12 cm. The ‘‘particles’’are about 0.5mm in diameter.

The yellow and orange mass in these figures is a single

automaton, with its head indicated in orange. Thenumber of organisms can be either preset or dynamic,

and it is the translation of this number into 3D animaldensities that perhaps poses the greatest conceptual

challenge to comparing the model to real sediments. Thekey to resolving this quandary is to understand what the2D model represents. Specifically, it is a cut through a

3D volume of sediment in which activity and distribu-tions are independent of one of the lateral directions, saythe y-direction. We encounter the same idea with a 1Ddiagenetic model (Berner, 1980), i.e., a sediment has a

1D representation when the actual 3D distributions canbe represented by a single, vertical profile because lateralgradients are negligible. In 2D the idea arises in Aller’s

tube model (Aller, 1980): each vertical slice of the tubethat includes the vertical axis is identical, i.e., no angulardependence, even though natural processes and distribu-

tions are indeed 3D; however, assuming symmetry inthe angular direction is a reasonable approximation.Thus, in the example of a 2D lattice model, it is assumed

that any 2D (vertical) slice of a 3D sediment looks thesame, on average. This assumption may not appearrealistic at first, however, representative results can beobtained, as attested by Aller’s tube model (Aller, 1980,

1982).Again, the areas in Figs. 4 and 5 are slices through a

3D volume that shows no variation in the direction

perpendicular to the plane of the figure (the y-direction).The animals (automatons) in LABS are not of zerothickness; however, in every z–x plane of the model

volume, each animal is present in the same place, withthe same shape, and doing the same thing. To convertthe 2D animal densities (numbers) to 3D animaldensities (numbers), let us start by assuming, a

50 cm� 50 cm lateral area for the volume. This meansthat each model animal extends 50 cm in the y-direction.If real animals are 2mm thick in the y-direction, then we

divide 50 cm per 2D animal by 0.2 cm for each 3Danimal to arrive at the number of equivalent 3D animalsfor that one 2D animal, i.e., 250 equivalent D animals. If

four animals exist in the 2D slice, then the total numberof 3D animals in the area is 4� 250=1000 animals. A50 cm� 50 cm is 1/4 of a m2, so that the density is

1000� 4=4000 3D animals m�2, which is large but notunreasonable for capitellid-like worms.

Professor L. Mayer (Univ. Maine, USA; pers. comm.,2000) has offered a somewhat different, but instructive

method for this conversion. He suggests that if ‘‘youassume that the animals are 2mm thick, then any 2Dcross-section must have intersected a sum of four

integral animals. In reality, you would intersect moreanimals, but most would be off-center and hencecontribute less than one integral animal to the summa-

tion. Your model then simply takes that sum, convertsthem to whole (discretized) animals and watches theirimpact in 2D. Now, a 2 mm thickness also implies that

your next summation must translate to a plane 2 mmdistant from the first plane, so that the total population


is (50/0.02)� 4 or 4000 individuals m�2.’’ Both approacheslead to the same interpretation of animal density.

Starting with an initial particle distribution, as in

Fig. 4-top, the model can be run or stopped at anyfuture time, e.g. 5 years as in Fig. 5-top. Comparison ofthese two figures reveals the effects of bioturbation;

specifically, the sediment has been completely re-workedby the worms and the fabric is similar to that of realsediments with burrows and ‘‘pellitized’’ areas. Tohighlight these effects on sediment fabric, the code also

averages on a set number of pixels to eliminate isolatedparticles of water or sediment, i.e., Figs. 4-bottom and5-bottom. Compaction is currently partially implemen-

ted in LABS, so that these results emphasize the effectsof the biology. The rules governing the rate and effectsof compaction are far more subtle than one might

initially believe, and their complete implementation willtake some time and research. In addition, this single 2Danimal (1000m�2 in 3D) has been allowed to exist for 5consecutive years, but this is more reasonable than it

first appears. Real sediment that is not subject to a

devastating event is more-or-less continuously inhabitedby infauna. Whether we let the single organism survivefive years, or let it die and be replaced by new

generations, leads to the same outcome (only detailschange). The organism does, nevertheless, change therates of its various activities as functions of diurnal and

seasonal cycles.Temporal sequences of model visualizations can be

strung together to create movies of sediment evolution,thereby providing a more concrete means of under-

standing causes and effects. A first example of themovies that may be so created can be found on theIAMG web site as the QuickTimes file 0108 8 using

Internet Explorers or Netscapes. The movie shows twoworms, the longer about 2 cm in length and the shorterabout 1 cm, as they burrow into initially random

sediment of 0.2 cm particles over a 21 d 9 h period. Themode of the formation of the burrows and thedefecation of fecal material therein becomes evident.Notice that the worms do ‘‘sense’’ the interface through

their rules and avoid leaving the sediment.

Fig. 4. Particle lattice of about 45,000 particles with four capitellid-like worms that are 1–4 cm long and about 0.05–0.2 cm in diameter.

This is 1 day into simulation. Worms are searching for food (not color coded) and have linearly decreasing chance of moving deeper

into sediment. Dimensions of lattice are 50 by 14 cm, and four worms in this 2D simulation are approximately equivalent to 4000

wormsm�2 in 3D world. Top figure is pixel-by-pixel exact representation of solid and water particles. Bottom figure is 24-pixel-area

running-average to emphasize biologically reworked areas in dense red.


Another, perhaps more informative example, isprovided on the IAMG web site as the QuickTimes

files 0108 9a and 0108 9b. These movies show thesituation where a rectangular plug of sand (lightercolored sediment) is placed in mud (see Fig. 6). The sand

contains no organic matter, and the worms cannotingest these larger particles; the latter must be moved bythe displacement mechanism, rather than ingestion–

egestion. Movie 0108 9a starts with four worms, 1–3 cmin length, and runs 9 d and 23 m; the sand plug is sharpand well-defined visually. Movie 0108 9b illustrates theconditions 100–101 days latter. Mud particles are now

present through the sand and the sand edges have beendistorted; both indications of bioturbation. However,presence and the shape of the sand plug are still evident

and the sand particles are not significantly spread intothe mud (Fig. 6).

The mixing is fundamentally different than suggested

by the frequently used diffusive model of bioturbation.Specifically, if mixing were diffusive, one would expectthat the edges of the sand plug would become spread-out, i.e., diffuse; the plug (slowly) losing its geometric

integrity. Instead, the plug distorts, but does not become

obviously diffuse on the time scale of 100 d. Mud travelslong distance to be deposited in the sand, whereas on

this time scale, the sand particles do not stray far fromtheir original positions. The different types of particlesdo not move at the same rate, and cannot be said to

counter-diffuse as required by a diffusion theory. Over-all, the evolution in movies 0108 9a and 0108 9b appearscloser to our understanding of reality than that obtained

from popular biodiffusion models, i.e., simple diffusionat the edges.

In pure mud situations, where the mode of mixing ismore diffusive, the particles can also be tagged with

radioactive tracers, such as 210Pb, and the resulting 2Ddistribution can be integrated laterally to give a typical1D depth profile of the activity. This in turn can be fit

with, for example, a bio-diffusion model (Boudreauet al., submitted). This allows a direct link between thebiological parameters of the 2D model (i.e., feeding rate,

etc.) and the parameters familiar to geochemists, i.e., themixing coefficient DB: Boudreau et al. (submitted) havedone this and derived DB: values similar to thoseextracted from natural sediment cores, as compiled in

Boudreau (1994). This finding represents a crucial

Fig. 5. Same sediment as in Fig. 4, but 5 years into simulation. Worms do not actually live for 5 years; instead worms approximate

effects of sediment being occupied by average of four worms over that time. (Worms in water column are artifact of early version of

code; this no longer occurs.) Note that sediment surface is punctuated with biological features, as are real sediments. Bottom figure

emphasizes strongly reworked sediment in dense red, which shows that burrows and fecal deposits now dominate sediment.


validation in that it indicates that the averaged behaviorof the automatons in LABS produce the same averaged

effects as natural organisms on 1-D isotope distribu-tions, which constitutes an independent quantitativemeasure of bioturbation.

5. Final remarks

LABS constitutes a new method for obtaining a

mechanistic understanding of bioturbation and itseffects of sediments properties and their distributions.The essential individuality of benthic organisms andtheir appropriate behaviors are preserved in the model,

unlike popular deterministic models. Consequently,LABS is more ecologically and geologically realistic(see Boudreau et al., submitted). Although this program

may not be an efficient tool for fitting individual 1Dsediment property profiles, it offers instead a betterchance of discovering the relationship between actual

animal activities and their observed effects on sedimentproperties and chemical distributions.

LABS is a work in progress and must improveand expand with time to include more biology,

chemistry and sediment physics. Nevertheless, theresponse from audiences to our presentations of thismodel at international meetings has encouraged us to

release this prototype so that others many use it andparticipate in its development. We believe it to be anexcellent tool for research and teaching, although no

user-friendly interface exists at this time. Some FOR-TRAN-90 coding skills are, consequently, necessary topermit the user to run or modify the code.

Acknowledgements

We wish to thank Peter Jumars and Larry Mayer ofthe Darling Center (Univ. Maine) for their guidance oninfaunal behavior, and Jim Eckman (ONR) for his

continued support. This research was funded by USONR Grant N00014-99-1-0100 and an NSERC Re-search Grant to BPB; further development is nowsponsored by a US ONR (NICOP) Grant. Bill Fornes

and Martin Trauth are warmly thanked for their reviews.

Fig. 6. Visualizations of mixing of sand plug. Animals will not digest sand, but will displace it. Top diagram is initial distribution,

showing sand plug in white, mud in gold, animal bodies in yellow and their heads in red. There are four worms, largest about cm in

length. Bottom diagram illustrates sand and mud distributions after 100 days of animal activity. Note mud trailers, caused by egestion,

well within sand, whereas sand shows no such penetration into mud. Outline of plug is slightly distorted, but recognizable. See text on

instructions to obtain QuickTimes movies of start and finish of this numerical experiment.


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