Recent research has addressed evidence for theuse of spatial memory in wild primates [see review:Janson & Byrne, 2007]. In many cases, foragingdecisions appear to be informed by mental represen-tations of the spatial relationships of objects, foodpatches, and significant locations in the environment,combined with estimations of the current condition offood rewards available in these locations [Boesch &Boesch, 1984; Garber, 1989; Garber & Paciulli, 1997;Janson, 1996, 1998; Menzel, 1973, 1991; Normand &Boesch, 2009]. These mental representations, re-ferred to as spatial or mental maps [O’Keefe &Nadel, 1978; Tolman, 1948], are not unique toprimates, and have been supported for a wide varietyof taxa, from insects to birds and mammals [Chapuis& Varlet, 1987; Dyer, 1994; Gallistel, 1989; Gallistel& Cramer, 1996; Gould, 1986; Gould‐Beierle &Kamil, 1996; Hitchcock & Sherry, 1990; Suzukiet al., 1980; Tolman, 1948; Tomback, 1980].
The degree and form of spatial informationattributed to different primate taxa varies. Wild
chimpanzees, for example, are reported to useEuclidean maps, which store spatial relationshipsof key objects, allowing chimpanzees to generatenovel, direct routes among pairs of feeding siteswithout relying on landmarks to guide their naviga-tion [Normand & Boesch, 2009]. Other primatesappear to rely on the stored memories of routes andlandmarks, referred to as topological or networkmaps [Byrne, 2000], rather than information aboutdistance and direction, to navigate large‐scale space,
Contract grant sponsor: National Science Foundation;contract grant sponsor: Leakey Foundation
�Correspondence to: Scott A. Suarez, Anthropology Department,120 Upham Hall, Miami University, Oxford, OH 45056.E‐mail: [email protected]
Received 4 November 2010; revised 11 September 2013; revisionaccepted 15 September 2013
DOI: 10.1002/ajp.22222Published online 25 October 2013 in Wiley Online Library(wileyonlinelibrary.com).
such as over an entire home range [Di Fiore &Suarez, 2007; Garber, 1989; Luhrs et al., 2009;MacKinnon, 1974; Noser & Byrne, 2007a,b; Sigg &Stolba, 1981]. Still other species are suggested to usesome combination of Euclidean and topological mapsto navigate large‐scale space, depending on thenature of the feeding sites [Presotto & Izar, 2010].
When presenting evidence for spatial memory,whatever the form, it is necessary to first reject thenull hypothesis that behavior attributed to spatialknowledge might be just as easily explained byforaging or navigation that relies on little or nospatial information [Janson & Byrne, 2007]. Forexample, in primates, straight‐line travel is frequent-ly cited as evidence for travel informed by spatialinformation about the relative locations of differentfeeding sites [Janson & Byrne, 2007]. However, birdsforaging for worms and ants for aging for dead insectsappear to have no a priori expectation of thedistribution of food items and consequently tend tomaintain a single direction in their search paths toavoid revisiting previously searched areas [Cody,1971; Fourcassie & Traniello, 1994; Smith, 1974].When food items are expected to be clumped, as whena hummingbird discovers a clump of flowers or whenants discover nectar, they will increase turningfrequency to intensify search effort in a profitablespace, and therefore to enhance food discovery[Fourcassie & Traniello, 1994; Pyke, 1981]. Each ofthese strategies improves the chances of food discov-ery, but does not rely on knowledge of the location ofspecific food items.
In small‐scale space, such as the area within afeeding patch, the null hypothesis that primatesmight rely on chance to discover food hidden atplatforms has been tested experimentally using theexpected probability of particular behavior patterns.For example, white‐faced capuchins (Cebus capuci-nus), using memory of recent feeding success atbaited feeding platforms found food rewards moreoften than by chance alone [Garber & Paciulli, 1997].In larger‐scale space, however, such as when a groupof primates forage within their home range among alarge number of potential feeding sites, the probabil-ity of choosing particular feeding sites is practicallyimpossible to calculate [Janson, 1998]. It is in thesecases that computer models that simulate theforaging behavior of primates become necessary[Janson & Byrne, 2007], permitting the researcherto generate quantitative data that can be statisticallycompared to the observed behavior of foragingprimates.
Garber & Hannon [1993] used computer simu-lations to test the null hypothesis that mustachedtamarins (Saguinus mystax) and saddle‐back tamar-ins (Saguinus fuscicollis) might follow the odor of ripefruits to discover and navigate to feeding trees. Bymodeling the way odor plumes disperse in a forest,and how tamarins typically move when foraging,
Garber & Hannon [1993] demonstrated that themovement patterns of tamarins relying on odorplumes from one or more feeding trees wereinconsistent with characteristics of the travel pat-terns of wild tamarins.
Janson built on Garber and Hannon’s model, andused two different computer simulations to test thenull hypothesis that brown capuchins (Cebus apella)might apply a simple foraging rule‐of‐thumb such asa tendency to travel in a forward direction thatminimized backtracking when searching for un-known food sources [Janson, 1998]. One model, astep model, simulated the movement of capuchins inspace as they searched for food items, while anotherhad the simulated capuchins travel in straight linesuntil their search field allowed the discovery of foodsources. Simulated capuchins in neither the stepmodel nor the straight‐line model were able to matchthe foraging efficiency of observed brown capuchinsexcept when their search fields were expanded tounrealistic values of 225–350m [Janson, 1998].Variations of Janson’s step and straight‐line comput-er simulationmodels have been also used to reject thenull hypothesis that white‐faced saki monkeys(Pithecia pithecia) and white‐handed gibbons (Hylo-bates lar) forage without the use of knowledge of thelocations of feeding trees [Asensio et al., 2011;Cunningham & Janson, 2007].
While previous computer‐generated null modelshave shown that they do not predict the movementand foraging behavior of wild primates whensimulated monkeys are free to wander around theirentire home ranges, a modified version of the modelmay be necessary when primate movement is con-strained. A number of primates have been observedhabitually traveling along a system of paths, referredto as a route network, to navigate among differentparts of their home range. In many cases, these routenetworks consist of a broad path that follows localgeological features such as ridges or rivers [Di Fiore&Suarez, 2007; Presotto & Izar, 2010; Sigg &Stolba, 1981]. In a few cases, there is some suggestionthat primates might even follow and reuse veryspecific branch‐to‐branch paths through the forest[MacKinnon, 1974;Moffett, 1993]. Presumably, theseroute networks allow primates to reduce energyexpenditure by minimizing increased energy expen-diture associated with traveling up and down ridgesrather than along them [Di Fiore & Suarez, 2007]. Inseveral cases, these route networks have beensuggested to be consistent with the use of topologicalspatial maps, rather than Euclidean maps.
While not all primates who use route networksare entirely constrained to route travel [Presotto &Izar, 2010], long‐term studies of spider monkeys(Ateles belzebuth) in the Yasuní National Park,Ecuador, demonstrate that this population con-strains most of its ranging behavior to a routenetwork that follows the tops of the ridges
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characterizing the terrain in the area, and that theseroutes are persistent from year after year [Di Fiore &Suarez, 2007]. Ninety‐five percent of location datapoints collected across several years for this speciesfell with 50m of the tops of ridges when the monkeysnavigated in large‐scale space while movements insmall‐scale space were much less constrained,perhaps guided by visual detection, memory of locallandmarks, or local Euclidean spatial memory [DiFiore & Suarez, 2007; Poucet, 1993]. The overalleffect of the route system is that, once on a segment ofthe route system, travel is relatively straight,limiting the circuitous travel that is often character-istic of the movement of simulated monkeys inpreviously described step models. This limitation ofcircuitous movement should reduce backtracking, bydefault decreasing the overall distance traveled andenergy expended compared to a monkey with noknowledge of the location of feeding trees.
For studies of spatial knowledge in primatesusing a route network to navigate large‐scale spacewithin their home range, a more realistic null modelis required. Here we examine the hypothesis that theuse of a route network might be sufficient to allowYasuní spider monkeys to forage efficiently. To thisend, we created a computer model that allowssimulated monkeys to follow the route system thatwe observed in wild spider monkeys. The simulatedmonkeys in the model use no knowledge of thelocation of feeding trees to forage, but travel along thesame route network observed inwild spidermonkeys,and discover feeding sites opportunistically. Wecompare the results of the foraging success ofsimulated monkeys in a route model to that ofsimulated monkeys foraging in a less‐constrainedstep model, as well as to the foraging behavior of wildspider monkeys, and discuss the significance of thesecomparisons.
METHODS
We compare the observed behavior of spidermonkeys foraging among a set of feeding trees to twocomputer models of simulated monkeys foragingamong a variety of feeding tree densities.We considerthree characteristics of a travel path as indicators ofpath efficiency: total distance traveled, directness oftravel, and the difference (or error) between originaltravel direction and direction of the goal path. For thefirst analysis, simulated monkeys forage among thesame sets and distributions of feeding trees observedfor wild monkeys. In the second analysis, wemanipulate the number and locations of the feedingtrees, and ask at which density is simulated behaviormost similar to that of wild monkeys. Computersimulations were repeated 5,000 times for each treeset tested, allowing the creation of frequency dis-tributions for each characteristic. These distributionsthen allow us to quantitatively compare the efficiency
of the models, as well as to compare each todistributions generated from the observed data.
Research Site and Behavioral Data
The behavioral aspect of this research wasconducted at the Proyecto Primates Research Site(PPRS: approximately 75°280E, 0°420S), located in theYasuní National Park, eastern Ecuador. The re-search site itself is overlaid with a trail system, witheach trail marked every 25m. In addition to allmarked trail points, more than 1,500 feeding treeshave been marked, mapped, and assigned UTMcoordinates.
Behavioral data were collected on individualparous female monkeys (N¼ 3) from a single commu-nity (N¼ 16 individuals) of white‐bellied spidermonkeys (A. belzebuth) whose entire 300ha homerange is encompassed within the Proyecto PrimatesResearch Site [Suarez, 2006]. All community mon-keys were recognizable individually by variations infacial patterns and coat color. Research methods forthis project were approved under the IACUCproject #98‐1001 at StonyBrookUniversity, compliedwith thelaws and regulations of the Government of Ecuador,and adhered to the American Society of Primatolo-gists’ Principles for the Ethical Treatment ofPrimates.
Spidermonkeyswere followed from dawn to dusk(typically from 5:45 am to 6:00 pm) for a periodvarying from 10 to 14 days. SS conducted ten suchfollows, divided among three focal females, fromMarch 1999 to June 2000, resulting in 1,268hr and144 days of behavioral data [Suarez, 2006]. Duringfollows, SS mapped the location of the focal subjectrelative to mapped trail points via instantaneoussampling at 5‐min intervals. These are the same focalsubjects and same ranging data used for analysis ofroute‐use [Di Fiore & Suarez, 2007]. SS recorded allfeeding bouts by the focal subject, mapped thelocation of the feeding tree, and assigned it a uniqueidentification number.
Computer Models
Two different computer simulations are pre-sented here. Each simulation was programmed usingCþþ. The first model is a random‐walkmodel (RWM)in which a simulated monkey adopts travelingcharacteristics (distance traveled before turning,and probability of turning a particular direction)derived from observed spider monkeys, and searchesfor feeding trees within a predefined territory using arandom‐walk strategy based. ‘Random’ here impliesthat the movement patterns are “independent of thespatial and temporal distribution” of particularresources [Kiester & Slatkin, 1974, p.2]. In thesecond model, a route model (RM), a simulatedmonkey’s random walk is constrained to travel paths
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defined by a route network derived from datacollected in 1999 and 2000 [Di Fiore & Suarez,2007]. Each of these simulations is built upon thelogic used for step models developed by Janson in astudy of capuchin foraging [Janson, 1998]. For eachsimulation of the RM, we ran an “equivalent”simulation of the RWM; the starting point for eachcompared run of the model is the same. This allowedus to directly compare a specific run of a search foreach model.
In each run of the RWM, a simulated monkeyleaves a designated starting point in a directionderived from a distribution of turning angles ob-served in wild spider monkeys (Fig. 1), travels a steplength of 100m, and scans for a feeding patch. If onehappens to be within the search distance (40m)anywhere along that step, the monkey is consideredto have found the food patch, and travels directly to itfrom the point of discovery. If no feeding patch isdiscovered, the monkey takes a step in a newdirection, derived from a distribution of turningangles observed in real spider monkeys. If a stepleads themonkey outside of the search area, that stepis nullified, and new turning angles are generateduntil the next step remains inside the boundaries ofthe search area (Fig. 2a).
In the RM, a simulated monkey starts at anarbitrarily selected intersection of two routes (thispoint is also used as the starting point for the pairedRWM) and randomly selects a direction to begintraveling along the pre‐defined paths. The monkeydiscovers a feeding patch if at any time it comeswithin the search distance (40m) of that patch (either
while at a route intersection, or while traveling alonga route), and immediately travels directly to it. If themonkey reaches a new intersection of route segmentswithout discovering a feeding patch it again random-ly selects a new direction for travel from its route‐defined options (forbidden only from directly back-tracking), and searches along that route (Fig. 2b).
For each encountered feeding patch, we recordedthe travel distance from the starting point to thefeeding patch, and used this to calculate a circuityindex (CI) [index of circuity: Garber & Hannon, 1993]calculated as the ratio of the distance the monkeytraveled from its starting point to the straight‐linedistance from the starting point.We also recorded thedirection in which the monkey departs a startingpoint, and then compared this to the true directionfrom the start point to the discovered feeding tree.Janson [1998] referred to this difference as theangular deviation (AD), which is a measure of the“correctness” of the direction chosen when travelingto a feeding tree.
Test runs of the models showed that simulatedmonkeys were sometimes able to travel hundreds orthousands of kilometerswithout discovering a feedingtree. Simulated monkeys in the random‐walk modelsometimes searched treeless corners of themap,whileRM monkeys sometimes searched repeatedly alongtreeless routes. To avoid skewing comparisons of runsbetween the twomodels by the inclusion of abnormal-ly large and unproductive travel distances, weeliminated all paired runs in which either simulatedmonkeywas observed to travelmore than 8,000m.Weselected 8,000m, as this was slightly longer than the
Observed Turning Angles
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Fig. 1. Distribution of turning angles after 100‐m steps, derived from observations of wild spider monkeys. This distribution of anglesprovides the likelihood of turning in any particular direction formonkeys in the RWM.Nearly all of the turning angles result in simulatedmonkeys traveling forward, with a slight chance of reversing directions.
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longest daily travel distance observed for these spidermonkeys [Suarez, 2006].
Selection of Variables Used in Models
To approximate the distance at which a spidermonkey would be likely to discover an unknownfeeding tree, we relied on a field experiment thatdemonstrated that capuchins have a 50% chance ofdiscovering unknown feeding sites at a distance ofabout 25m from the nearest group member, and thatthe discovery distance increased with patch size[Janson & DiBitetti, 1997]. Spider monkeys in smallparties generally travel in single file, suggesting thata 25‐m detection distance would be appropriate formodeled monkeys. However, spider monkey feedingtrees were larger than the platforms used in Jansonand DiBitetti’s study (unpublished data). To accountfor a probable increased detection distance due tolarger patch size, we selected 40m as a reasonableestimate of the distance at which the monkeys woulddetect unknown feeding patch.
We determined the step length used in the spidermonkey step model by examining ten randomlyselected maps of spider monkey daily path lengths,and measured the distance between obvious changesin direction. In general, spider monkeys traveled amedian distance of 97m before altering their direc-tion of travel (mean¼ 108.9�SD 65.9, N¼ 202).Because of this, we selected 100‐m step lengths asan appropriate approximation for use in the comput-er model.
We noted that the spider monkeys generallytravel forwards, but occasionally reversed directionentirely during their daily travel. To account for thisin the RWM, we allowed the computer monkeys toselect different turning angles (including reversals)with the same probability observed for real spidermonkeys. We calculated the turning angle distribu-tions by randomly selecting 1 day from each of the ten2‐week focal follows. For each day, we restructuredthe daily paths into a series of 100‐m steps (to matchtheRWM) and calculated the turning angle from eachsequential step, creating a frequency distributionfrom the 262 resulting turning angles (Fig. 1). Thisfrequency distribution then determined the newdirection selected after each step in the RWM.
In the first analysis, simulated monkeys foragedamong sets of feeding trees that replicated thenumber and locations of feeding trees determinedby observed monkeys. Observed monkeys werefollowed for ten 2‐week follows, each with a uniqueset of feeding trees (mean¼ 71.2 per follow, SD¼ 32.2). Simulatedmonkeys searched among each setof trees, with 5,000 paired runs for each set, resultingin 50,000 runs. Foraging behavior of observedmonkeys foraging among the same set of trees wasstatistically compared distributions derived from thetwo models.
Using the distribution and number of feedingpatches in themodels raises potential biases. Feedingtrees and travel routes were derived from the sameset of behavioral observations, potentially biasinglocation of known trees to be alongside the routenetwork. Therefore, in the second analysis werandomly generated the locations of feeding treesbefore each simulation run, all restricted to arectangular boundary encompassing the equivalentof the entire home range with the same treedistribution used for paired RWM and RM runs.Additionally, because the set of observed availablefeeding trees used by wild spider monkeys in alllikelihood did not include all feeding trees availablein the habitat [Janson & Byrne, 2007], and becausewe lacked an independent measure of all availablefeeding trees within the habitat during any follow, weran a number of simulations for each model, varyingthe number of randomly placed trees from10 to 1,000,by increments of 10. Results for each model werederived from 5,000 searches at each feeding treedensity (resulting in 500,000 runs permodel), with alldata pooled for analysis.
Statistical AnalysisIn the first analysis we compared foraging
characteristics of modeled monkeys searching amongthe same sets of feeding trees used by observedmonkeys. We compared distance traveled, circuityindex, and angular deviation between paired runs ofcomputer simulations at the density of trees recordedfor wild monkeys. For these we used Student’s pairedt tests [Sokal & Rohlf, 1995]. For comparisonsbetween computer simulations and observed behav-ior, we used t tests to compare means [Sokal &Rohlf, 1995]. All tests are two‐tailed. Statisticalanalyses were carried out in JMP 8.0.1 (Copyright2009 SAS Institute Incorporated). To examine differ-ences between the RWM and the RM, we comparedvalues of foraging characteristics across an increas-ing number of feeding trees, varying from 10 to 1,000,in the modeled home range. To this we compared thefeeding characteristics observed in wild primates at71.2 trees, the mean tree density derived fromobservation, and asked at what feeding densitywouldmodeledmonkeys be able to replicate observedbehavior.
RESULTS
We compared the foraging success of monkeys inthe RWM to the RM for 5,000 runs at the density offeeding trees used by observed monkeys in eachfollow. When the feeding tree densities matchedthose observed for wild spider monkeys, simulatedRWM monkeys traveled 20% farther before finding afeeding tree when searching at random versus whensearching along a route among the same tree sets
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(Table I) (Student’s paired t‐test T¼�29.7, df¼ 38,153, P< 0.0001). Simulated monkeys also trav-eled more directly (index of circuity) to feedingsources when following a route system than whenrandomly searching for feeding trees (Table I)(Student’s paired t‐test: T¼�6.3769, df¼ 38,153,P< 0.0001). Additionally, simulated monkeysstarted traveling in the direction of a feeding treemore often in the RM than when randomly searching(Table I) (Student’s paired t‐test: T¼�3.73528,df¼ 38,153, P< 0.0002). Together, these resultssuggest that monkeys foraging among sets ofunknown feeding trees do so twice as efficientlywhen foraging along a route system than whenforaging at random.
We then compared the foraging characteristics ofsimulated monkeys across 10 tree sets when using aRM to the foraging characteristics of observedmonkeys foraging among the same sets of feedingtrees to determine whether following a route systemexplains observed behavior. In all characteristics,observed monkeys outperformed simulated monkeys(Table I). Observed monkeys consistently traveledshorter distances between trees (t‐test: T¼�99.66896, df¼ 1580.19, P< 0.0000), traveled moredirectly (t‐test: T¼�61.33745, df¼ 1766.655,P< 0.0000), and started off in the correct directionmore often than did simulated monkeys (t‐test:T¼ 28.10781, df¼ 711.2894, P< 0.0001). Figures 3–5present the cumulative distributions for the results oftwo models and the observed behavior.
We then compared the foraging success ofobservedmonkeys to those of RWMand RMmonkeysat a variety of feeding tree densities. We assessedtravel distance, CI and AD from each model acrossdensities of 10–1,000 randomly placed trees acrossthe equivalent of a 300ha search area (Fig. 6). Forboth simulation models, travel distance, CI, and ADdecreased as feeding tree density increased. Fortravel distance, RWM monkeys matched observedtravel distance (292.8m) between patches at adensity of almost 400 trees, while RM monkeysmatched that distance at a density of about 300 trees.RWM monkeys matched the travel directness ofobserved monkeys (1.4) at a density of 600 feedingtrees, and RM monkeys approached that of observedmonkeys at a density close to 700 feeding trees. Forangular deviation, RWMmonkeys matched observeddeviation (41) at a density of about 330 trees, whileRM monkeys matched it at about 250 trees. Taken
together, neither model appears to approximate theforaging behavior of spider monkeys at Yasuní for allthree variables below a density of 700 feeding trees.
DISCUSSION
Because the assessment of primate behavior forcognitive mapping skills should begin with therejection of simpler, non‐goal‐directed behavioralstrategies, we created a computer‐generated nullmodel to simulate the foraging behavior of monkeyssearching for food using simple foraging rules that donot rely on specific or general information about thelocation of feeding trees. While similar null modelshave been used to simulate randomized foraging,generating quantifiable measurable movement char-acteristics for statistical comparison with observedbehavior [Cunningham & Janson, 2007; Garber &Hannon, 1993; Janson, 1998; Janson & Byrne, 2007],our null model is different in that it was created tosimulate the constrained movement characteristic ofprimates using a network system for navigating theirenvironments [Di Fiore & Suarez, 2007]. We feel thisis a more appropriate null model for assessing goal‐directed foraging for primates whose travel may beconstrained to route networks.
We used our computer‐generated model (and anadaptation of earlier step‐based models) to simulatenon‐goal‐directed behavior in spider monkeys (Atelesbelzebuth) foraging in the Yasuní National Park. Ourmodel allowed us to input a route‐network system,which we derived from observations of wild Yasuníspider monkeys [Di Fiore & Suarez, 2007], sets offeeding trees used by the spider monkeys, and othercharacteristics such as search distance, step length,and turning angles.We quantified the characteristicsof non‐goal‐oriented foraging in spider monkeys,generating distributions of measurable outputs.Measurable outputs included the distance a simulat-ed monkey traveled before it discovered its firstfeeding tree (total distance), the directness of travelto that tree (CI), and the difference between thecompass direction of its first step and the compassdirection from the starting point to the discoveredtree (angular deviation).
Our research had two primary goals. The firstgoal was to determine whether constraining themovement of simulated monkeys to a route networkmirroring that observed in real monkeys would makefor a more appropriate null model against which to
TABLE I. Comparisons of Simulations Models to Observed Behavior at Observed Feeding Tree Density
Total distance Circuity index Angular deviation Sample size
Random foraging model 1993.8�SD 2110.9 4.8�SD 7.7 95.5�SD 93.7 50,000Route model 1428.0�SD 1540.6 3.6�SD 5.1 87.4�SD 85.8 50,000Scrambled route model 1188.3�SD 1357.7 3.3�SD 5.0 77.1�SD 80.0 50,000Observed behavior 292.8�SD 229.3 1.4�SD 0.7 40.6�SD 41.0 639
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assess the behavior of wild monkeys, assessed bydetecting improvement in foraging. The second goalwas to examine whether either null model couldaccount for the foraging behavior of observed Yasuníspider monkeys.
In both sets of comparisons of the route model tothe random‐walk model, at nearly all feeding densi-ties (with the exception of very high or very lowdensities), RMmonkeys foragedmore efficiently thandid RWM. Simulated monkeys employing a random‐walk strategy traveled asmuch as 30% farther to findfeeding trees compared to monkeys searching forthose same treeswith a route‐based search (Fig. 3). Inmany primate studies, travel distance is frequentlyused as a proxy for energy expended [Steudel, 2000].Using this measure, RM monkeys spent less energyfinding a feeding tree.
RM monkeys (CI of 3.6) traveled more directly tofeeding trees than did RWM monkeys (CI¼ 4.8). Thereduction in circuitous paths is almost certainly aresult of the nature of the route system itselfcompared to the less constrained movement in theRWMmodel. In many cases, RMmonkeys discoveredfeeding trees along the first route segment theytraveled, resulting in many straight‐line paths.Although RWM monkeys did tend to maintain aforward momentum when they traveled, their pathswere more tortuous (Fig. 2a,b). In addition, underconditions in which several feeding trees lie close to ahabitual route system, monkeys searching for foodscan minimize revisiting areas that they had previ-ously searched.
RMmonkeys found trees more often in the initialtravel direction than didRWMmonkeys searching fortrees. In both simulations, CI decreased as thenumber of available feeding patches increased, butin all cases RM monkeys outperformed random walkmonkeys. The higher the density of patches, themorelikely it was that simulated monkeys discovered onein the initial direction. Yet, in studies of wildprimates, starting travel in a correct direction issometimes cited as not only evidence of ecologicalknowledge, but also as evidence that the observedprimates are capable of calculating novel and directroutes between feeding trees [Garber, 1989, 2000;Normand & Boesch, 2009]. At any given density offeeding trees, RMmonkeys not only took their initialsteps in a direction that led to a feeding tree morefrequently than did RWM monkeys, they alsotraveled shorter distances (Fig. 6). The combinationof a starting direction leading to a feeding tree withshorter travel distances suggests that sticking to aroute system reduced the likelihood of more tortuousroutes that a random walk can generate, whilesimultaneously facilitating discovery of feeding sitesalong those routes. The discovery of a route system fortravel in primates that have been observed to traveldirectly between feeding sites could require reassess-ment of evidence for Euclidean mental maps.
The simulations with increasing densities offeeding trees revealed two interesting by‐products.First, at a density of 600 trees (2/ha), a reverse in thetrends occurred such that RWM monkeys traveledshorter distances to find feeding trees than did RM
Fig. 3. Cumulative distribution of total distance traveled for simulation models and observed behavior. Data from observed behavior(n¼639) are represented with a solid line, data from the RWM (n¼50,000) are represented with a dotted line, and data from the routemodel (n¼50,000) are represented with a sequence of dashes and dots.
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Fig. 4. Cumulative distribution of index of circuity for simulation models and observed behavior. Data from observed behavior (n¼639)are represented with a solid line, data from the RWM (n¼50,000) are represented with a dotted line, and data from the route model(n¼50,000) are represented with a sequence of dashes and dots.
Fig. 5. Distribution of angular deviations for RWM (n¼50,000), route model (n¼50,000), and observed behavior (n¼639). Box plotspresent 25th and 75th percentiles, and median, minimum, and maximum values.
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monkeys. At high feeding tree densities, RWMmonkeys were less constrained than RM, and couldfind trees in almost any direction and in fewer steps,where RM were constrained to travel along one ofonly a few travel directions, and stuck to routesegments that might not contain trees within thesight distance of the monkeys. When feeding treeswere extremely common, a random‐walk patternappeared to be more efficient in finding feeding trees,at least in terms of travel distance. Second, RWMmonkeys traveled more directly to feeding trees thandid RM monkeys when fewer than 250 trees wereavailable in the search area, while above 250 treesRMmonkeys outperformed RWM monkeys. At lowerdensities, it is less likely that therewere feeding treeslocated along segments of the route system, requiringthat monkeys travel along multiple segments toencounter feeding trees. As route segments wererelatively straight‐line paths running in differentdirections, AD would be high for monkeys searchingalong two or more segments. As density increased, itbecame more likely that feeding trees occurred alonga route segment, andmore treeswould be found alongthe initial search segment, resulting in more directtravel for the RM.
Route Model Compared to Observed Behavior
While the use of a route system improved theforaging success of simulated monkeys with noknowledge of the locations of feeding trees, realmonkeys outperformed simulated models in allmeasures. When foraging among the same sets offeeding trees, observed spider monkeys traveled only
an average of 293m from one feeding tree to the next,approximately one fourth of the mean distancetraveled by the RM simulated monkeys. Observedspider monkeys traveled an average of 3,311m eachday [Suarez, 2006], allowing them to feed in 10 or sofeeding trees. Simulated monkeys would have totravel nearly 14 km to feed in as many trees.
Observed spider monkeys also moved betweentrees in about half the distance used by simulatedmonkeys foraging along a route system. Wild spidermonkeys traveled less than twice the distancebetween feeding trees in 90% of observed cases,while this was true in only about 55% of the cases forsimulated monkeys traveling along a route system.Nearly all (98%) of the transitions between feedingtrees for wild spider monkeys fell below a circuityindex of 4, while this was only the case for 75% of theRM monkeys. Because both the simulated monkeysand the observed spider monkeys were travelingalong a route system, the more direct travel ofobserved monkeys suggests that they either havelarger search distances [Janson &DiBitetti, 1997], orused memory of the location of feeding trees toenhance navigation between feeding trees.
The direction selected by Yasuní spider monkeyswhen leaving one feeding patch more often led themto feeding trees compared to their simulated counter-parts. Alone, this finding may not be sufficientevidence to argue that Yasuní spider monkeys havea destination in mind when they begin traveling[Janson, 1998]. However, when paired with theobservations that they fared better in startingdirection (angular deviation), travel distance, andcircuity index, a stronger argument can be made that
Fig. 6. This graph shows the effects of increasing densities (from 10 to 700) of randomly placed feeding trees on directness of total distancetraveled, circuity index (CI) and angular deviation (AD) for simulatedmonkeys in both the random‐walkmodel (solid line) and routemodel(dashed line). For comparison, we included comparative data for observed monkeys for the highest density of observed feeding trees forany 2‐week observational period (n¼114).
Am. J. Primatol.
Simulating Foraging in Route Networks / 469
Yasuní spider monkeys are incorporating spatialinformation concerning the location of and routes tofeeding trees in their foraging decisions. If a Yasuníspider monkey decides, as it leaves a patch, that itwill travel directly to another particular patchlocated hundreds of meters away, there would belittle need to accurately predict the exact direction ofthe target patch. Instead, it would only need to knowwhich of the possible combinations of routes wouldlead it in the general location, as well as the overalldistance of each combination of routes leading to thegoal. The association of distance and directioninformation at each intersection of route segmentswould allow a monkey to choose a route leading to agoal without actually needing to know the exactdirection to that goal from any point along the route[Di Fiore & Suarez, 2007].
As one might expect, travel distance, thedirectness of travel (CI), and angular deviation(AD) for simulated monkeys in both models de-creased as feeding tree density increased. Thedensity of feeding trees needed for the two simula-tion models to replicate the foraging characteristicsof observed monkeys required tree densities thatwere 2.5–7 times as high as the estimated treedensity derived from the observation of foragingmonkeys (mean¼ 71.2 trees per follow). For exam-ple, RWMmonkeys needed a density of 600 trees (2/ha) to approach a CI of 1.4 for observed monkeys,and RM monkeys only approached a CI of 1.5 above700 trees. To match all three foraging character-istics of observedmonkeys, modeled monkeys wouldneed to forage among 600 feeding trees in the 300 hastudy area. By comparison, two groups of woollymonkeys (Lagothrix lagotricha) within the samestudy area were only observed to feed in some 800trees across a 12‐month study period, only 100–200more than modeled here for a given 2‐week period[Di Fiore, 2004].
If we assume that the number of feeding treesrecorded for the observed monkeys is approximate-ly close to the total number of available feedingtrees in the environment, and not off by a magnitudeof seven, we can draw two conclusions from thesemodels. First, the route model simulation did moreclosely approximate observed behavior than therandom‐walk model, suggesting that it was themore appropriate null model for the study group ofYasuní spider monkeys. And second, despite theimprovement in foraging characteristics as compar-ed to the RWM, the RM could not replicate thebehavior of wild Yasuní spider monkeys below afeeding tree density of 700 trees within the studyarea. This leads us to reject the null hypothesis, andsuggests that the foraging of Yasuní spider monkeysis informed by ecological information, minimally inthe form of memory for location of important feedingtrees and calculation of efficient routes amongfeeding sites.
ACKNOWLEDGEMENTS
This study was supported by doctoral disserta-tion improvements grants from the National ScienceFoundation and from the Leakey Foundation, andwas approved by the Institutional Animal Care andUse Committee at Stony Brook University. We thankScott Campbell and David Scoville for technicalassistance. S.S. thanks INEFAN and the governmentof Ecuador for permission to conduct research atYasuní. S.S. thanks the staff of the Yasuní ScientificResearchStation, and from thePontificaUniversidadCatolica del Ecuador, particularly Laura Arcos,Friedeman Koester, and Lucy Baldeon. AdditionallyS.S. thanks Christine Lucas, Sharon Stacks, andMatthew Swarner for field assistance, and LarryDew, Anthony Di Fiore, Diane Doran‐Sheehy, JohnFleagle, Paul Garber, Charles Janson, PatriciaWright and two anonymous reviewers for researchadvice and comments on this manuscript.
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