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Direct PNAS a is article This interest. of the conflict no wrote declare C.T.R. authors and The B.W., and L.P.C., R.H., and M.F.R., data; C.C.-L., analyzed paper. B.W., C.T.R. L.P.-C., research; research; performed C.T.R. designed L.P.-C. contributions: Author ARS encounter-conditional of data model These Bayesian setting. a fit natural to a of used in Nahua are location of searching and follows foragers time focal mushroom the data—GPS during on encounters—recorded GPS waypoints item encounter-annotated food GPS with of then paired database tor- We tracks encounter. and a an slow on following a enacted which We draw be for literatures. should lags for ARS time-step ARS tuous predictions of and numerical number provides optimal MVT the MVT the the link that demonstrate to heuristics search https://github.com/ctross/mushrooming owo orsodnesol eadesd mi:[email protected]. Email: addressed. be should correspondence whom To work. this to equally contributed C.T.R. and L.P.-C. a nvria earzn,Xlp,Vrcu 19,Mexico; 91090, Veracruz Xalapa, Veracruzana, Universidad ´ ıa, eernefo osrainbooyt ooi design. explained robotic to method biology the conservation dis- from of academic range here applications across potential interest the widespread effi- ciplines: of organisms how is Elucidating search patch. ciently given should test a foragers to inside long used remain how be they concerning can time way predictions model of This theoretical function the encounter. a change resource as last and speed since and detect direction can adjusting behav- by foraging foragers search of which model in analytical ior time an known present balance within searching We to and patches. patches forager new a for while search searching requires spent resources efficiently costs distributed traveling foragers patchily collec- reducing experienced Locating mushroom how resources. Nahua for study followed to we tors trackers, GPS Using Significance dcs nvria ainlAut Nacional Universidad edicas, ´ ee eueamdlo dpie encounter-conditional adaptive, of model a use we Here, y c c etoTacl eBiolog de Tlaxcala Centro acsF Rosetti F. Marcos , | a 1 2019 21, May . y y ). nm eM de onoma d ´ y . Cetv omn Attribution-NonCommercial- Commons Creative y oy Hudson Robyn , y ad aCnut,Universidad Conducta, la de ´ ıa | o.116 vol. y www.pnas.org/lookup/suppl/doi:10. xc,Mxc iy04510, City Mexico exico, ´ | o 21 no. d , ´ v ihsor flights evy | b 10339–10347 y Graduate

APPLIED ANTHROPOLOGY MATHEMATICS trajectories. The empirical estimates of “giving-up time” impediment to empirical tests and technological applications of (GUT)—a measure of “intrapatch” search duration—from this the MVT (41). Methods of analysis that mitigate the need to model are numerically concordant with predictions of the same make a discrete map of patches have the potential to broaden the quantity derived from the MVT. More generally, we illustrate scope for empirical evaluations of the MVT and related theory a method of analysis for testing the MVT in natural settings (e.g., ref. 50). that does not require an independent definition or mapping of patches—expanding the empirical scope of the MVT to cases Integrating ARS Models and the MVT to Explain the Search Pat- where quantitative data on patch boundaries and their respective terns of Nahua Mushroom Foragers. To generalize the insights of food item densities are unavailable or impossible to obtain. the MVT to the case of sessile food items that are distributed continuously over an environment with spatial autocorrelation Theory on Search in Continuous Environments (i.e., patchiness), we use recent mathematical and statistical ARS. A central focus in movement ecology is how mobile preda- approaches developed in the ARS literature (19, 22, 26, 34) to tors can most efficiently locate randomly distributed food items. estimate the number of time-step lags for which turning-angle A body of literature on the Lévy flight foraging hypothesis has and step-size changes are associated with encounters with food suggested that foragers should search for randomly distributed items. We use encounter-annotated GPS data to make these esti- food items using approximations to Lévy flights (18, 23, 24), since mates. The number of time-step lags for which these effects are they are frequently more efficient than Brownian movement significant multiplied by the length of each time-step yields an at encountering sparse, randomly distributed food items. More estimate of the GUT (42, 51) for a local patch (22). Although recent work on intermittent and two-stage search has exam- GPS tracks annotated with behavioral observations on encoun- ined how encounters with food items (22, 25, 26) can trigger ters with food items can themselves be difficult to acquire, such ARS behavior (27–34) in which search velocity and turning- data have been collected in nonhuman animals using clever angle (35) are modified for some interval of time. This work research designs (e.g., refs. 29 and 30), as well as in humans (e.g., demonstrates that foragers of patchily distributed resources can ref. 34); increasingly powerful and simple-to-use GPS units will use a simple heuristic—search with slower and more tortuous undoubtedly make production of such data easier. movement after a recent encounter with a food item (intrapatch In the following sections, we first introduce the field-site search) and move with more rapid and linear movement otherwise and foraging context. After this, we provide the mathemati- (“interpatch” search)—to improve search efficacy. These models cal details describing how theoretical GUTs are calculated and demonstrate that ARS can outperform nonconditional Lévy or how empirical GUTs are estimated. We then demonstrate the Brownian movement by minimizing search time (25), increasing main results that: (i) encounter-annotated GPS tracking data encounter rate, and decreasing risk of starvation (22). However, show that Nahua mushroom foragers respond adaptively to it remains unclear how the parameters governing encounter- encounters with food items by increasing turning-angle between conditional ARS trajectories can be tuned to improve encounter time-steps and decreasing search velocity, and (ii) this response rates in a given environment. In this paper, we draw on the leads to distinct forms of intrapatch and interpatch search behav- MVT to provide some important—but partial—insights into the ior. Intrapatch search transitions to interpatch search after an effective tuning of such parameters. average of 6 to 13 time steps, representing 3.0 to 6.5 min, since the last encounter with a harvested mushroom—an estimate that The MVT. Efficient foragers searching in a patch—a localized coincides closely with the theoretically derived GUT of 8 to 21 aggregation of resource items—face a declining rate of return time-steps under the MVT. We conclude with a discussion of the as they continue to harvest (36). As resources are depleted or relevance of our results for future studies of human and nonhu- their availability is depressed, a forager faces the question of man foraging behavior and then comment on the applicability of how long it should remain in its current patch before seeking our model to a range of applied problems. out a fresh patch to harvest. Assuming a discrete set of patches, Charnov’s MVT (11) predicts that a forager should transition Fieldwork into interpatch search when the marginal encounter rate in its The database used here consists of focal follows conducted by current patch drops to the overall encounter rate averaged over authors L.P.-C. and C.C.-L. with mushroom foragers from a interpatch search and intrapatch harvest. Nahua community in 2006 and 2007 within La Malinche National Despite the sometimes “daunting” data requirements (37, p Park, Tlaxcala, Mexico (49, 52, 53). L.P.-C. and C.C.-L. main- 257) involved in testing the MVT, studies of human (38–41) tained a position 1 to 2 m from the focal forager during slow and nonhuman (14, 42, 43) foragers have found some evidence movement or rest and 2 to 5 m during rapid movement. GPS consistent with MVT predictions. Venkataraman et al. (41), for positions were recorded at 30-s intervals using a Garmin GPS example, use extensive, daily records of Batek foraging returns V Personal Navigator; the data are analyzed at this resolution. to fit resource-depletion curves and show that camp-relocation Table 1 provides descriptive statistics for each of the 34 foraging events generally conform to MVT predictions. trips in the sample. Nonetheless, testing if a given group of foragers actually In total, L.P.-C. and C.C.-L. recorded 141.5 h of focal fol- use MVT-predicted GUTs is complicated. The overall forag- lows consisting of 16,979 GPS data points. Annotated points of ing encounter-rate is among the easier variables to observe and interest were recorded on the GPS unit for each of the 1,485 measure (11, 44, 45). It is considerably more difficult to pro- mushroom encounters. Fig. 1A plots each recorded search path duce the independent information required to delineate the key and encounter in the database. Fig. 1B plots a higher-resolution features of patches—their locations, boundaries, resource lev- section of a single path. Focal foragers were selected opportunis- els, and responses to exploitation. In controlled experimental tically on each day of research with the constraint that the sample designs, patch-specific data are not generally prohibitively dif- be balanced by sex. Informed consent was obtained from each ficult to acquire. However, food items growing in natural settings forager before data collection. are seldom distributed in discrete, easily defined patches (46–49). Mushroom gathering is a rainy season (June–September) Rather, they are typically distributed continuously and, even if activity for families living in La Malinche. Foraging bouts are clustering or spatial autocorrelation in their distribution is high, frequent (three to five per week) among the families that com- the “boundaries” between high- and low-density regions can be mercialize mushrooms. Our encounter-annotated GPS tracks fuzzy. The difficulty associated with partitioning continuous envi- reflect the behavioral patterns of single foragers on these ronmental variation into discrete patches thus has been a key trips; however, mushroom foraging is at least partially a social

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APPLIED ANTHROPOLOGY MATHEMATICS AB

Fig. 1. Focal follow GPS recordings of Nahua mushroom foragers, 2006–2007. Shown in A are smoothed, low-resolution, and sometimes overlapping paths for all trips in the dataset. At this large scale, searches appear fairly linear. Shown in B is a high-resolution image of the red-shaded area in A. At this scale, it becomes evident that encounters with mushrooms (black dots) are associated with changes in search mode (shorter step-sizes and increased turning-angles). Note that the paths are colored by time since last encounter with a mushroom of interest. The orange regions, representing search periods of at least 10 min postencounter, are mostly linear. The green regions, representing search periods shortly after an encounter, are more tortuous (B).

and when to look for mushrooms, as well as how to modulate points (x[t], y[t]) and (x[t−1], y[t−1]), and θ[t] ∈ (−π, π) gives the search mode upon encounter with a patch, is critical to optimiz- corresponding heading-angle: ing the time and energy spent in the forest—as well as the cash q income associated with foraging. 2 2 r[t] = (x[t] − x[t−1]) + (y[t] − y[t−1]) [1] Modeling Forager Movement ? (y[t] − y[t−1]) Estimating Theoretical GUTs. The MVT predicts that foragers θ[t] = arctan , [2] should make the switch between intrapatch search-and-harvest (x[t] − x[t−1]) and interpatch search for an undepleted locale when the arctan? arctan marginal encounter-rate within the current patch declines below where the function is the standard function the average encounter-rate inclusive of within and between patch after adjusting the angle for the quadrant of the point in costs (11). To test this prediction, we calculate the predicted Cartesian space (57). Then, we transform heading-angle (an number of time-steps with no encounters that would be required absolute direction) into turning-angle, by considering the dif- to decrease the intrapatch encounter-rate to or less than the ference in heading-angle between time-steps. The unit-scaled δ overall mean encounter-rate. This value is known as the GUT turning-angle, [t], is: and is a classic metric from the MVT literature used to mea- ∆(θ[t], θ[t−1]) sure patch leaving (14, 42). We then compare this value to the δ[t] = , [3] empirically estimated number of time-step lags of intrapatch π search following an encounter before a forager fully resumes an where the ∆(a, b) function returns the minimum of: |a − b| and interpatch search pattern. 2π − |a − b|, since a 90◦ right turn is the same as a 270◦ left To arrive at a numerical prediction for our case study, we turn, for example. Division by π radians yields a value on the first determine that the mean rate of encounters across for- unit interval. aging trips is 0.09 (interquartile range: 0.04, 0.12) encounters Since turning-angle is a unit-constrained variable, we can most per time-step (Table 1). Then, we evaluate when a horizon- effectively model its distribution using a Beta regression model tal line with this value intersects the graph of y = 1 , where x+1 (see ref. 58 for a formal justification): the value x indicates how many time-steps with no encounters have occurred after the most recent encounter, and the value y δ[t] ∼ Beta(µ[t]ν, (1 − µ[t])ν). [4] gives the encounter rate since last encounter, inclusive of that encounter. Given the average empirical encounter rate of 0.09 The mean of the Beta distribution at time t is then given by µ[t]: encounters per time-step and the interquartile range of 0.04 to 0.12 encounters per time-step, the MVT predicts that ∼8 to 21 S ! −1 X time-steps without an encounter should cause mushroom for- µ[t] = logit ψ[0] + ψ[s]E[t−s] , [5] agers to transition from an intrapatch into an interpatch search s=1 mode (Fig. 2). and the dispersion of the distribution for a fixed µ is controlled + Estimating Empirical GUTs. To calculate an empirical estimate of by ν ∈ R . E[t] is an indicator variable of whether a food item S+1 GUT using encounter-annotated GPS tracks, we use a Bayesian was encountered at time-step t, ψ ∈ R is a vector of unknown model linking encounters and forager movement patterns (22). parameters estimating the effects of encounters on turning-angle The data represent a forager’s search path as a sequence of dis- over S time-step lags, and logit−1 is the inverse logit function. crete points in space, (x[t], y[t]), with a constant separation of 30 s. Eq. 5 allows us to estimate how encounters with mushrooms at These data are easily converted into a more theoretically relevant lagged time-steps affect turning-angle in the current time-step. form via Cartesian-to-polar mapping (57). We can parameter- Regarding the distribution of step-sizes, we use a log-normal + ize the data so that r[t] ∈ R gives the linear distance between model, as information theoretic model comparison of step-size

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APPLIED ANTHROPOLOGY MATHEMATICS AB

Fig. 3. Effects of encounters on turning-angle and step-size. Both A and B depict medians and 90% credible intervals. A shows ψ[s]—the lagged effect of encounters on turning-angle—and B shows φ[s]—the lagged effect of encounters on step-size, for lags s ∈ {1, ... , 30}. Lagged encounters significantly affect both turning-angle and step-size, with effects lasting ∼6 to 9 time-steps (3.0 to 4.5 min) for turning angle, and ∼8 to 13 time-steps (4.0 to 6.5 min) for step-size. Each bar in the plot illustrates the value of the increment or decrement in turning-angle or step-size (y axis) as a function of the number of lags since last encounter (x axis). The number of lags for which the increment or decrement is significant is indicative of the length of time for which an encounter affects search mode. soil or detritus from the growth of mushrooms below, or symbi- variation in return-rate over trips. Alternatively, if mean return- otic trees or plants—using a linear and high-velocity interpatch rate is well explained by year, season, individual, or some other search mode. Once they detect an edible mushroom, they quickly characteristic—and the dataset is large—predictions and sta- cut it off at its base and, then, using a slower and more tortu- tistical evaluations could be made more precise by structuring ous intrapatch search mode, closely scan the surrounding area analyses by such variables. (1 to 5 m) to find the “brother” mushrooms. After depleting a Second, significant handling or processing time of resources local area of the easily located mushrooms, the foragers resume might confound the interpretation of model parameters. If pro- an interpatch search mode until they spot another mushroom or cessing time after an encounter is large relative to the GPS sam- microhabitat clue signaling the presence of mushrooms. pling rate, then the parameters giving the effects of encounters on movement dynamics might reflect the behavioral response of Qualifications and Potential Issues. We note three potential item processing rather than intrapatch search over some range issues affecting our model and analysis. First, since the mean of lags. In the case of mushroom foraging, processing time is encounter-rate is quite variable over trips in our data, we generally very brief, involving nothing more than the removal acknowledge that a fairly wide range of numerical predictions of attached soil or pine needles from the bottom of a harvested for optimal GUT—i.e., predictions of 8 to 21 time-step lags— fruiting body, so it is unlikely to confound our inferences beyond are all plausible. More precise evaluations of the MVT using a possible elevation of the effect sizes of parameters at a single our methods could be conducted in systems where there is less lag. In some cases, foragers first place collected mushrooms into

Fig. 4. Continuous relationship between search mode and encounter-rate since last encounter. A shows the relationship between the log encounter-rate 1 since last encounter, log( s+1 ), and the log of the regression coefficients giving the lagged effect of encounters on turning-angle, log(ψ[s]), for the lags with 1 reliable effects, s ∈ {1, ... , 9}. B shows the relationship between the log encounter-rate since last encounter, log( s+1 ), and the log of the absolute value of the regression coefficient giving the lagged effect of encounters on step-size, log(|φ[s]|), for the lags with reliable effects, s ∈ {1, ... , 13}. A and B show a strong continuous relationship between search mode s time-steps after encounter with a food item and the encounter-rate since that last encounter. A indicates that when the encounter-rate is relatively high, turning-angle changes are higher. This produces tortuous ARS when in a patch, and efficient, unidirectional movement when outside of a patch. B indicates that when the encounter rate is relatively high, step-size decrements are higher. This yields a slower search mode when in a patch and a higher velocity mode when outside of a patch.

10344 | www.pnas.org/cgi/doi/10.1073/pnas.1814476116 Pacheco-Cobos et al. ahc-oo tal. et Pacheco-Cobos a and measure, ephemeral, of or locations patch features observe the relevant to diffuse, boundaries the difficult patch the that often environ- fact are an distribution the of environment resource by classification an complicated a of is Such patches ment discretely. defined the using be methods, Environments. must tested standard Continuous effectively with to MVT be Patches could Discrete it From here. that done have way we operational- like use be data a GPS could can encounter-annotated such model forager work in Oaten’s optimal Future if ized an returns. explore increase patch; usefully to the might strategically in information prey this of individual-level overall density about information the with average the forager the because the provide can arises intra- history below encounter marginal effect declined the This has if encounter-rate. even rate benefit patch encounter might current forager patch its compli- given a in more that MVT remaining indicates considerably from deterministic but is Charnov’s the model than of Oaten’s cated (11). those Charnov from by predictions diverge generates can (50) Oaten that by developed model donment of study foragers. the from nonhuman obtained or data human similar other optimum. to MVT applied broadly that theoretical be methodology can statistical the replicable GUT a to a provide with we close Additionally, ARS parameterized of form is a that use foragers estimate these further that to to demonstrate able analysis been have we the GUTs, empirical extending and theoretical both By foraging. ARS when encounter-conditional use evidence heuristics find foragers we mushroom (34), Nahua Colombia that in Ember game of small study pursuing a hunters and (19) Dominica of wealth naturalistic a in searching foragers setting. mushroom encounter-annotated the from high-resolution, in of tracks of test GPS model quantitative database been a a the provide have using we of MVT environments Here, (41). tests natural conduct to direct in hard operating However, archeolog- foragers (62). using MVT human studies evaluated The been patches case controlled. even resource ical have experimentally where models or related cases defined nonhuman and of in easily studies be especially in can 61), influential (60, widely been foraging has MVT The Discussion (34). Ember here, hunts solitary of effect on an study embarking such similar of a evidence paralleling reliable statistically find and we Nevertheless, strong movement encounters. encounters slower mushroom which to with lead associated to events not extent waiting these potential the since the of ARS, trigger have underestimation an also cause encounters longer to mushroom in are by that engaging triggered waiting of before not periods others These movement. for interpatch some- waiting distance will time Foragers activity. spend social times partly a is hunting mushroom search examine appropriately foraging, to or trajectories. needed of handling be of cases effects may gener- the other time and for processing In account negligible, that be day. model our not the of may alizations of rest time end the handling the at and with processing at collectively items it group process do for- the not to the of did preferring of however, encounter, Many study, upon estimates. all this our in in encounters, followed shift with agers associated downward not a velocity are to slow that of leading recordings episodes GPS brief These the to backs. clean on their lead to on might carried stop periods sufficient baskets they processing wicker a into gathered, when them been pack then, have and and mushrooms buckets, of or number bags plastic hand-held ent eeta tcatcpthdpeinadaban- and depletion patch stochastic a that here note We Common- the in fishers artisanal of study a in found been has As that fact the to relates results our about concern additional An ´ Cham a ´ lwu hunters blowgun ı ´ Cham a ots the test To ´ blowgun ı mosbet en,adbhvoa ucmsms egener- be or must impractical outcomes are behavioral and patches define, discrete search to where efficient impossible cases to in lead can algorithms models and ARS MVT based the encounter-contingent Jointly, those strategies. search example, encounter-contingent models—for on contem- foraging to algorithmic models theory porary foraging early of insights the extending changes these MVT. of the like magnitude models the foraging how classic to explored relate decre- encounters. yet of and not function increments have a of as We turning-angle magnitude and overall of step-size part to the ments important is an too is so mode ARS, search time affect of length encounters the which While for GUTs. on solely based evaluations from for methodology our need. mitigates MVT, general tracks define the the GPS to test encounter-annotated from to necessary the GUTs patches be inferring of of sometimes set tests may discrete prevented, it a not Although but of (41). independent impeded, MVT is has that behavior way a forager in patches discretely environmental characterizing bounded and identifying of of study difficulty amount observational the in daunting humans, (63). least potentially At proclivities a information. and species-specific of of skills accumulation behavioral the entails its This and shelter, for needs and its capacities, food the other of and range cognitive the its to organism, relative gener- foraging defined More be (48). normally large must covered patches be ally, to range habitat potential the fefciesac eairi olbrtr etn (72). setting or nonlaboratory a transmission teaching in social on behavior of search (71) evidence effective for data of test network further developmen- foraging social could continue the with coforaging they over paired and collected period old, data tal y Foraging 10 a adulthood. about for into age- are gathering GUTs they mushroom effective produce joining when learn start trips to to Children takes including type. possible it resource strategies, time given be search the of for should estimation curves an it acquisition McElreath 70), skill by specific (69, used Koster design and study individual-level longitudinal, in (70), heuristics rates search encounter effective success. of in hunting importance variation the from age. demonstrating of among arises return-rates y in hunters 40 variation the about human of at fraction Ach reached large a is 147 Moreover, effectiveness of exam- hunting database peak (69) longitudinal that Koster 20-y, and become a McElreath to required ine forager, is human learning argu- successful of the period a for and extended formation support an finding as empirical that ment as such Providing coalitions. challenges, such tactical social factors, of than evolution ecological rather brain food, by human catching that explained claim better the is support to models were tional of learning in suite investment Gonz brain, a entailed. significant exploiting enlarged and to adulthood, an of delayed commitment resources; heav- period hominin was difficult-to-acquire extended a argue high-quality, an (66) by al. skills. to shaped et due critical ily Kaplan peculiar of which dependence, experi- is acquisition juvenile how history the studying life affect of Human socialization possibility and suc- the ence shape opens History. foraging (65)—that Life cessful Tinbergen Human heuristics—sensu and proximate Age, Skill, units. Foraging autonomous be such of may design forag- engineers the MVT, from optimize the to algorithms and able heuristics better applying ARS the By like intake—with theory, deposits. areas ing dirt dirt vacuum of thoroughly denser rate more to with the movement their of their vary function slowing to units a intakes their as in speed sensors search dust can use (64) to cleaners programmed vacuum robotic be example, For real-time. in ated u prahhr,tog nopee ssilase toward step a still is incomplete, though here, approach Our away moving by improved be could however, approach, Our ycmiigtersac ehd rsne eewt the with here presented methods research the combining By ´ lzFrr n ookr 6,6)uecomputa- use 68) (67, coworkers and alez-Forero PNAS | a 1 2019 21, May | o.116 vol. u ou nthe on focus Our ´ utr,finding hunters, e | o 21 no. | 10345

APPLIED ANTHROPOLOGY MATHEMATICS Wider Importance of Search Optimization and Foraging Theory. The in applied settings ranging from the design of robotic vacuum search behaviors analyzed here are ubiquitous and consequential cleaners and product distribution warehouses to the implemen- in both ancient and modern times, for human and nonhuman tation of search and rescue efforts. Greater understanding of foragers. While the MVT and foraging theory more broadly the proximate heuristics underlying foraging decisions in patchy are instrumental to the analysis of hunter-gatherer adaptations, environments thus engages a broad array of scientific and practi- human life history, and our evolutionary origins (73), we all are cal endeavors that should benefit from greater understanding of foragers still. Software designers have looked to foraging models how encounter-conditional search heuristics can be optimized. to aid in the design of internet search engines (7). Criminologists have used foraging decision models to investigate “prey” selec- Supporting Information. SI Appendix includes the results of tion by automobile thieves (5) and the internet search behavior robustness checks and provides statistical and modeling details. of sex offenders (74). Studies guided by models of search and prey selection can serve conservation biology by estimating the Materials and Methods effects of current harvesting patterns on the middle- to long-term Methods of data collection and analysis have been fully described in the stability of prey populations (75–78). Environmental heterogene- main text. Additional methodological details and the results of robustness ity and the MVT are particularly important to studies of resource checks are included in SI Appendix. Analysis of data was conducted using exploitation because they suggest that effective foragers will R (84) and Rstan (85). The raw data and model code will be maintained at abandon a patch before fully depleting it of prey (8, 9, 79–82); https://www.github.com/ctross/mushrooming (86). our analysis illustrates that this same pattern should hold for The research protocol and consent process for this investigation were continuous resource distributions as well as those clustered in approved by the institutional committee at Posgrado Ciencias Biologicas at the National Autonomous University of Mexico. Respondents provided discrete patches. Models of patch-residency times, like the MVT, informed consent before participation. combined with models of prey choice, are well poised to play a role in increasing the efficacy of integrated pest-management ACKNOWLEDGMENTS. We are greatly indebted to the foragers who partic- strategies (10), by illuminating how decoy crops can most effi- ipated in this research project. This research was supported by Programa ciently be distributed and maintained. Cognitive scientists have Anual de Cooperacion´ Academica´ y Cultural 2015 Universidad Nacional Autonoma´ de Mexico–Universidad´ Veracruzana; the University of Califor- even used foraging theory models to examine the ways in which nia, Davis Division of Social Sciences; and the Max Planck Institute for our brains acquire and retrieve information (6, 83). It is easy Evolutionary Anthropology Department of Human Behavior, Ecology and to envision the application of high-efficiency search strategies Culture.

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