From the Gastric to Global: a Computational Environment forEvaluating Effects of Foraging Choice on Landscape

Composition

Paul W. Box, Assistant Professor of Geography;Frederick D. Provenza, Professor of Rangeland Resources

Utah State Universitypaulbox@cc.usu.edu, stan@cc.usu.edu

Abstract. Ecosystem diversity is largely a story of multiple interactions. One example of these complex interactions isbetween grazing animals and the plants that they graze on. Herbivores select forage based on needs for nutrients andmitigation of toxins, managing a complex mix in the gut. Interaction of chemicals may dictate intentional ingestion oftoxic plants to allow for access to other nutrients. The grazing behavior in turn affects the composition of plantcommunities through selective cropping and trampling, in ways that may not be predictable from short-termobservation. Both plants and grazers adapt over time, eliciting counter-adaptations in a cycle that can produce verycomplex webs of dependencies. What happens inside stomachs has measurable, and often unpredictable effects at thelandscape level. Ample literature exists on both stomach and landscape dynamics, but far less that explicitly links thetwo. A computational design is presented here that allows for singular integration of dynamic landscape processessuch as plant succession (modeled using cellular automata), interaction of foragers (using agent-based models) andnutritional cues (using embedded digestive models in the foragers) to investigate the interaction of chemicalcomposition of the foragers' stomach contents with the composition of the plant communities in the landscapes theyinhabit. It will be demonstrated how use of the Swarm libraries and Kenge GIS extensions allow for embedding modelsand scheduling mechanisms within one another, giving relatively easy integration of the different modelingmethodologies implied in the integration across scales.

1. INTRODUCTION

The idea that ecosystem stability is a function ofdiversity is not new, but there has been continuingdebate on the subject (Kaiser, 2000). Diversity is centralto ecological theory, even though the mechanisms bywhich diversity creates stability are not well understood,nor techniques on how to manage ecosystems topromote such diversity. Understanding how herbivoresinfluence plant diversity and visa versa is a criticalcomponent for comprehending basic ecologicalprocesses for managing ecosystems.

The influence of herbivores on plant species richnesshas attracted more attention than the complexinteractions governing plant biochemical diversity andherbivores (Landsberg et al., 1999). Herbivores havetraditionally been viewed as simple consumers of plants,and herbivore populations have been portrayed as mereoutputs of plant communities (reviewed by Hobbs(1996)). However, foraging is a dynamic process that isinfluenced by animals' evolutionary and culturalhistories and experiences (Provenza, 1995b,a; Provenzaet al., 1998). There are many feedbacks betweenbiochemical properties of plants and behavioral motivesof herbivores which can have important implications onefforts to model such interactions.

In a modeling exercise to re-create the dynamics ofherbivores and plant communities, one must be able tosuccessfully represent the actions that plants andgrazers will take in response to changes in their world.

With an individual plant, the rules can be simple: theplant grows in response to moisture, soil nutrients, andlevel of disturbance (trampling, grazing, lightdeprivation, etc.). With a herbivore in the same system,one needs to be able to model the most likely forage thatthe herbivore will take as it eats. If there is a choicebetween different things to eat, one needs to be able tomodel the decision process that the herbivore uses inselecting forage.

Optimal Foraging Theory would seem to give a simple,yet logical decision rule for a herbivore to select itsforage. Optimal Foraging Theory assumes that aherbivore will forage in a manner that maximizes energyintake per unit effort (Stephens and Krebs, 1986). Aherbivore foraging by that assumption should either eator ignore forage based on the quality (energy supply) ofthe forage. ``High quality'' forage would always be betterthan ``low quality'' forage; given a choice, the herbivoreshould always go for the high quality forage and shunthe low quality stuff. By this logic, partial preference forforage of differing ``quality'' should not exist.

Partial preference is exhibited by most herbivores(Stephens and Krebs, 1986; Belovsky and Schmitz,1999,1991). Partial preference may simply be a result of aherbivore's inability to discriminate between plantspecies (Illius et al., 1999), or it could be that partialpreferences are the best way to meet nutritional needs(Westoby, 1978) or help herbivores avoid toxins(Freeland and Janzen, 1974). More likely, flavors,nutrients, toxins, and dietary experiences all influence

partial preference (Provenza, 1996,1995a; Provenza et al.,1998).

This interaction of flavor, dietary experience, etc., hasbeen expressed by Provenza et al. (2001) in a ``satietyhypothesis'' as explanation as to why partial preferenceswould be observed in herbivores. This hypothesis linkspalatability of foods with a preference for variety in diet(partial preference). In Provenza (1995a) an interactionbetween flavor of a food and feedback to the animal isdiscussed. Flavor integrates odor, taste, and texture withpostingestive effects of nutrients and toxins. The senseshelp animals in discriminating between foods, andpostingestive feedback relates sensory experience with afood's utility.

The satiety hypothesis attributes changes in palatabilityto transient food aversions due to eating a food toooften or in too large an amount Provenza (1996,1995a).That aversion can be pronounced in food that has toxinsor is nutritionally unbalanced, but can occur in food thatis perfectly nutritious if the animal is satiated or has anexcess of what that food has to offer (in other words, theanimal can get sick even the most delicious forage). Thistransient aversion to any one food, even ``high quality''food, encourages animals to forage a variety of foods ata variety of locations.

While many of the assertions about stomach chemistry,plant response to selective cropping, behavioralresponse of grazers to nutritional cues, and effects ofgrazing behaviors on plant community structure can betested through direct experimentation, there are otherassertions that can only be tested by putting the piecestogether into a bigger picture. For example, to whatextent does behavior of grazers contribute to plantcommunity diversity? To what extent does plantcommunity diversity contribute to stability orrobustness of the community? Nested within thesequestions are issues about subtle differences ofherbivore choice when grazing, and how thosedifferences affect the ultimate composition of the plantcommunity. This system has many feedbacks, and manyopportunities to create the combinations of thresholdsthat are typical of complex adaptive systems, asdiscussed in popular books like Kauffman (1995) andAuyang (1998).

To answer these questions, models must be constructedthat place the known (directly testable) processestogether in an interacting system, and then a way mustbe developed to interpret the results of theseinteractions in terms of the ``big picture'' assertions. Toconsider the feedback loop between plant nutritionalvalue, to consumption by grazing animal, to digestionand biochemical reactions within the gut of the grazer, tonutritional cues that direct the grazer to consume otherplants, we envision a modeling method that cansimultaneously represent processes at the molecular,organismal, community, and landscape scale.Additionally, one needs to be able to representprocesses in terms of minutes or hours for grazer

behavior and digestive processes, days or weeks forplant response dynamics, and months to years forcommunity and landscape processes.

In this collection of processes, the grazer's motivationcan be reduced to nutritional cues. A grazer who issimply an optimal forager will have different motivationas it moves through the landscape than a grazer who islooking to satiate on different nutritional components,and a grazer who is attempting to balance nutrition withtoxic intakes will have further subtle differences in how itinteracts with the landscape. By creating acomputational model that allows for differentnutritionally motivated herbivore behaviors in anotherwise identical landscape, a suite of hypotheses canbe tested to explore these interactions between behaviorand environment. An added layer of complexity is thatthe landscape itself is a dynamic entity, with its own setof rules and potentially complex interactions.

We propose to do this with a hierarchical representationof models in an agent-based simulation. Some aspectswill require nesting of models within models (rumenswithin herbivores, plants within parcels of land), andothers will require concurrent activity of agents (eachindividual herbivore, plant, and components of thelandscape) who may or may not have awareness of otheragents in their system. While this kind of system issimple enough to describe, in practice thisimplementation must be done through (a large amountof) computer programming. Typically, this is donethrough some customized code, which becomes verycomplex in itself, and may or may not correctly addressthe programming issues involved. The implementationsfrom programmers can sometimes be of very highquality, but the quality can be impossible to evaluate(Box, 2000).

We propose to avoid many of these issues by using anestablished set of ``building blocks'' or tool kits forworking with agent-based models and spatial data. Byusing these tool kits, we anticipate our efforts will befocused on the model itself rather than details of thecomputer code.

2. THE SWARM AND KENGE LIBRARIES

The Swarm simulation libraries (Minar et al., 1998) weredeveloped originally at the Santa Fe Institute, NewMexico, as a tool for studying artificial life or lifelikesystems. Responsibility for maintenance anddevelopment of the software libraries was later spun offto a non-profit organization (www.swarm.org), withsupport coming largely from the user community.

Swarm was developed as a platform for specifying andimplementing agent-based systems, where the actors oragents interact in the world at their own rates andagendas, who have little or no information about otheragents in the system, but are nevertheless affected bythem. Examples of such systems are traffic jams and birdflocks (Resnick, 1996; Reynolds, 1987), where each bird

or car interacts as an independent entity, yet the multipleinteractions of all these entities form some coherent,emergent whole. Specifying the rules for each individual,and specifying that all the individuals should do theiractions simultaneously, is simple enough. Translatingthe actions to a computer program, where all instructionsare processed sequentially through a single processor,is tricky and involves many computer science issues,such as virtual concurrent parallel processes, that gowell beyond the scope of the intended model. Swarm isan environment for reconciling the myriad concurrentprocesses into the sequential processing environment ofthe computer chip.

The Swarm environment also presents a structure forspecifying what agents interact in a model, andschedules of when they do their things (what happensat each time step). The two most compelling reasons forusing established software packages when creating amodel are convenience (complex models can bedeveloped quickly) and, most importantly, replicability.Given a published description of the agents and actions,another researcher should be able to replicate a set ofexperiments conducted via an individual-based modelwithout using the original experimenter's source code.This latter issue is often overlooked in simulationliterature, though its importance is discussed inMcMullen (1997), Grimm (1999), and Lorek andNonnenschein (1999).

The Kenge template (Box, 2001a,1999) is a way to importspatial data from various geographic information system(GIS) formats into Swarm, and create landscaperepresentations that perform cellular automata (CA) orcellular stochastic functions on the landscape. Thislandscape can then serve as both a dynamicrepresentation of a landscape, and a ``stage'' upon whichthe agents of an agent-based simulation interact. Theprinciples behind the Kenge template are described inBox (2001b).

The Kenge template is derived from an object known asa grid2d (two-dimensional grid) from the Swarm libraries,which is essentially a primitive for raster graphicstructures. Additions were made to allow each cell (orpixel, if you're thinking in terms of graphics) to containmore than a single value (figure 1). Each cell (pixel) wasrepresented as a cell object in Swarm's object-orientedhierarchy (figure 2). Through this same object structure,cells are also able to contain functions (called methodsin object-oriented programming), where one can definehow the cells communicate with other cells, the world,and agents moving around in the world. By populating araster structure with such cell objects, a virtuallandscape is formed (figure 3).

Figure 1: Cell with multiple attributes

Figure 2: A cell object with attributes andfunctions

Figure 3: A cell surface occupied by many cellobjects

Figure 4: Cell surface with models in cells

Since swarm allows for potentially infinite nesting ofentire models within objects, it's possible for the cells inthis virtual landscape to have sub-models executing

within them (figure 4). For example, if one is setting up alandscape for fire behavior, each pixel could encapsulatea model on how that part of the landscape burns. Thefact that one pixel represents a grassy field, the next aconifer stand, and the third a building implies not justdifferences in the amount of burnable material, butfundamental differences in how they react to fire.

3. THE COMPUTATIONAL ENVIRONMENT

To address the issues in section 1, we propose to use ahierarchical set of objects to represent the grazers andtheir environment. To properly understand the matchbetween biochemical reactions in the gut of grazers,grazer behavior, plant succession, and landscapecommunity development, we would like to have a modelthat represents all of these objects. Swarm's librarystructure will be used to define the objects, and managethe relationship of objects to each other, as well asschedule execution of objects' activities at the varyingtime scales. Kenge templates will be used to managespatially explicit parts of the model, as well as handle GISinput and output.

3.1 Model Objects

Currently, the model is proposed to have the followingobjects: a population of grazers, rumens embeddedwithin each grazer, a landscape, and plant communitiesliving within the landscape.

1.1.1. Grazer

The grazing animal is one of the fundamental objects ofstudy in this modeling exercise. While it is discussedhere in terms of a general object, in practice the objectwill be extended to be ``real'' grazing animals (goats,cows, sheep, elk, etc.). The grazing animal has the abilityto walk around on a landscape surface, locate andconsume plants, modify other plants in the landscape(through trampling, etc.), and possibly modify thelandscape itself (compacting soil).

There will be some rudimentary models of cognitivefunctions within the grazers, as much of grazer behaviorcomes from their perception of the landscape and abilityto interpret environmental cues. Other parts of grazerbehavior are heavily influenced by social dynamicswithin the herd, other grazers, avoidance of predators,memories of past encounters with various locations, andlearned behavior by mentors. The grazer will carry withinit an embedded model of the landscape that it hasconstructed from its own experiences, that it willcontinuously update based on its experiences in the``real'' world. Some considerations for allowing forcognition of agents and their landscapes have beenpresented in Gimblett et al. (1996a), Gimblett et al.(1996b), and Deadman and Gimblett (1994).

The grazer will also have a rumen embedded within it,which will store food that the grazer consumes (up to a

limit specified by stomach size), digest the food byextracting out nutritional components, and sendingwaste components out. Since not all food is uniform, thiswill allow specification of a more complex diet for thegrazer. The grazer, after a meal, may be satiated withcarbohydrates, but still feel the need for salt, vitamins, ortrace minerals that it needs in its diet. The grazer willrespond to these needs by searching out andconsuming plants that it thinks to be rich in the neededelements. Since the grazer is not simply an amoebablindly feeling its way around the surface, it needs tomake decisions about where the best supply for the foodit needs is, how is the best place to get there, and thesuitability of potential sites for exposure to predationand difficulty of getting there.

1.1.2. Rumen

The rumen is a model (collection of objects andschedules) that takes in food, breaks it down intocomponent parts, and sends the components to eitherthe host organism (grazer) or out of the waste passage.Those components that have been sent to the organismremain in ``storage bins'', which the organism draws onthrough its live processes. As different bins getdepleted, then the organism will get ``hungry'' for thatparticular component, and search out food that willsatiate it. The storage bin can be seen as a metaphor forthe organism's degree of satiation in respect to thatcomponent.

Since any food that the organism takes will have otheringredients as the components it wishes, it must haveways of dealing with that. For example, if the grazer eatsa toxic plant with some nutritive values, it will get thecorresponding amounts of calories and vitamins, but willalso ingest toxins. In this case, the rumen's storage mayhave enough calories and vitamins to be satiated inthose components, but now have a level of toxins in itssystem that need to be dealt with. In that case, it maynext search out a plant with chemicals that can mitigatethe effect of the toxin, regardless of other nutritivevalues that the plant has. Whether the grazer learnedthis behavior through trial and error, observing othergrazers, or simply had the effect as a ``hard-wired''instinct is beyond the scope if this discussion, but all ofthose are possible.

Since the rumen is embedded within the grazer, thegrazer will be sending all input messages to the rumen(food intake) and accept all output from it (nutritionalinformation). The rumen will be a major factor indetermining the grazer's behavior.

1.1.3. Landscape

In one sense, the landscape is the ``stage'' upon whichthe grazers act. In another sense, the landscape itself is adynamic model with its own rules and processes thattake place regardless of the presence of grazers or otherorganisms. For this model, a landscape minimally has

topography (slope, aspect, elevation), soil properties(such as porosity and organic content), and a plantcommunity, represented by a number of plant objects(described in next section). The landscape isconstructed from the Kenge template, and consists ofthe following hierarchy of objects, as described insection 2 and in Box (2001a):

• Cell, which contains all ``interesting'' behavior

• Cell Surface, which knows location (swarmand geographic), and knows neighbors of eachcell

• Datafile, which reads and writes GIS data layers

The cell surface is essentially a platform to support cellobjects, and the cell is a platform to host plantcommunities.

1.1.4. Plant

The plant is an object that grows in a place in thelandscape, utilizes resources in the landscape to grow(water, soil nutrients, etc.), and possibly replacesnutrients into the soil if all or part of it dies. As plantsget modified by grazers (eating and trampling), theirgrowth rules change.

It is important in this part of the model to take great careon how plants compete with each other. Specifically,plant growth rules will be implemented by fundamentalproperties of the plants (growth rates, accessibility toresources, water availability, etc.); competition betweenplants will come from competition to resources. If twoplants are occupying the same parcel of land, one plantwill gain competitive advantage through processes suchas water uptake (simply using the available water beforethe other plant can access it), light deprivation, or otherknown mechanistic or biological functions. Rules suchas ``plant A will stop growing if plant B is present'' willnot be implemented specifically, but rather ``plant A andplant B will draw on available water to grow;'' if plant Btakes all the water, plant A has no water to draw on, andwill not grow. Reasons for maintaining such emergentproperties of the simulation are discussed in Railsback(2001).

3.2 Schedules

This model will have the following processes happeningconcurrently. At each time step, the following actionswill take place:

• Each rumen digests its' contents

o process food that has come in

o fills ``bins'' with stocks of nutritionalcomponents

o if one or more bin is running low,inform the grazer to find more

• Each cow metabolizes rumen contents, takescurrent nutritional status, and forages

o decides on what nutrients are needed

o decides where in landscape suchnutrient is available

o decides best way to get there

o decides if it is practical to get there

o once decision is made, heads for thatarea

o decides what to eat in immediate area,and eat

§ reduces plant's biomass bycertain amount

§ send same amount to rumenfor processing

o modify cell that it occupies

§ trample soil and plants

§ defecate

§ drop seeds if any areattached

• Each plant grows

o draw on appropriate resources inparcel (water, nutrients, etc.), asproportion of present size, andconvert to new plant

o attempt to colonize neighboring cells ifit's a species that spreads that way

o attach seeds to grazers if it reproducesthat way

• Each cell updates itself

o replenish water supply if possible

o lose soil to erosion if exposed

4. CONCLUSION

Considerable effort is placed here in representingprocesses at their most fundamental level, in order forhigher level processes to emerge without being explicitlycoded into the model. This is in line with a fundamentalbelief about the natural system that we are studying,that what we observe in nature is the result of many

disjoint, but interconnected processes. It is anticipatedthat many of the results will be impossible to anticipatewithout explicitly coding into a simulation.

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