A+Maximum+Entropy+and+Least+Cost+Path+Model+of+Bearded+Capuchin+Monkey+Movement+in+Northeastern+Brazil+Incorporating+ERDAS+Subpixel+Classification+Analysis+of+WorldView 2+Imagery

7/28/2019 A+Maximum+Entropy+and+Least+Cost+Path+Model+of+Bearded+Capuchin+Monkey+Movement+in+Northea

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A Maximum Entropy andLeast Cost Path Model

of Bearded CapuchinMonkey Movement inNortheastern BrazilIncorporating ERDAS Subpixel Classification Analysis

of WorldView-2 Imagery

Allison HowardSergio Bernardes, M.S., Co-Author

University of GeorgiaAthens, Georgia



A Maximum Entropy and Least Cost Path Model of Bearded Capuchin Monkey Movement in Northeastern Brazil

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Abstract

Movement patterns of bearded capuchin monkeys (Cebus (Sapajus) libidinosus) in Northeastern Brazilare likely impacted by environmental features such as vegetation density or vegetation type. Habitat

preferences of these monkeys provide insights regarding the impact of environmental features on speciesecology and the degree to which they incorporate these features in movement decisions. In order toevaluate environmental features influencing movement patterns and predict areas suitable and unsuitablefor movement, we employed an ERDAS IMAGINE Subpixel Classification module and a MaximumEntropy modeling approach using observation points along capuchin monkey daily routes as speciespresence points. Subpixel Analysis was used to generate fraction images that represent greenvegetation, soil and dark endmember in the study area. We generated two MaxEnt models (1 -vegetation, soil, and dark endmember; 2 vegetation and soil) with the preferred model including the

vegetation and soil endmembers. This models predictive power (test AUC) was 0.653. Percent greenvegetation was the greatest contributor to model AUC. Least cost path models using the inverse of theMaxEnt model as a cost layer demonstrate that this technique is suitable for estimation of capuchinroute choice, and least cost paths closely approximate observed travel. This work has implications forpredicting daily movement patterns of all mobile animals, as high-resolution imagery and subpixelanalysis in conjunction with habitat modeling represent significant improvements to previous attemptsto link species occurrence or animal behavior with environmental variables.

1. Introduction

1.1 Animal Movement and Environmental Features

Since organisms have a limited supply of time and energy and, since time and energy conserved whiletraveling can be applied to other survival activities, it is likely that animals demonstrate cost-minimizingstrategies when traveling to resource sites (Pyke, Pulliam & Charnov, 1977). Primate body weights arenegatively correlated with their mean daily planimetric travel distance (i.e., straight-line distance travelednot considering topography) (e.g., baboons; Muruthi et al., 1991), and primate groups are theorized to

reach a maximal size when the ratio of travel costs to energy intake per individual reaches its outermostsustainable limit (e.g., Wrangham et al., 1993). Primate spatial decisions not only affect the inclusivefitness of the traveling primate, but these choices may also impact the ecology of the environments inwhich these animals move, since nonhuman primates serve as key seed dispersers for fruiting plants(Chapman & Onderdonk, 1998) and play a role in the maintenance of diversity of important ecosystems(Link & DiFiore, 2006).

Field experiments have focused on the behavioral sensitivity of capuchins to the tradeoff between travelcost and reward (Janson, 2007). However, the metrics commonly used to quantify the costs to primatesincurred by their routes have been limited to the travel distance of observed routes or route segmentsdivided by the linear distance between the beginning and end of the route (e.g., Noser & Byrne, 2007;Garber, 1989; Janson, 1998). This approach assumes that animals are most sensitive to the distancethey travel as the crow flies, and ignore any other landscape variables of their travel routes (e.g.,

microhabitat preferences). Considering that animals have limited time and energy for foraging and otheractivities (MacArthur & Pianka, 1966), we expect capuchins to incorporate landscape variables into theirroute preferences. Previous analyses of primate route choice have been remarkably void of landscapefeatures such as land cover, likely due to the difficulties of quantifying landscape features across largeareas and at a scale compatible with animal movement.

One significant challenge when studying animal movement is the identification and quantification of

relevant associated landscape elements over space and time. In particular, the representation of Earth ssurface using thematic spatio-temporal continua is often limited by the reduced data collection and




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synthesis capability of field methods alone. The use of integrative research methods is a necessity,especially in high-complexity areas with intergradational physiographic features. Among these integrativeapproaches, the use of remotely-sensed imagery has led to numerous discoveries, with particularlysignificant contributions to landscape characterization in animal ecology studies (e.g., Willems et al.,2009; Stickler & Southworth, 2008). Despite its high potential, the use of remotely-sensed data to studyfine-scale animal movement patterns has been limited. When used in this field, products derived fromremote sensing are usually restricted to hard classifications of land cover or to the analysis of vegetationindices, such as the Normalized Difference Vegetation Index (NDVI) developed from freely distributed,coarse resolution remote sensing imagery. These products often provide an incomplete depiction of thelandscape, limiting our ability to adequately represent the fuzziness and natural gradations of mostenvironments (Gao et al., 2000; Elmore et al., 2000; Small, 2004). Subpixel Analysis in ERDAS Imaginesoftware, a well-tested remote sensing technique, provides a representation of areal coverage andgradients of chosen key primary landscape descriptors, often vegetation, soil and dark endmember(e.g., shade or water). When compared to hard classifications and vegetation indices, products derivedfrom this type of process provide a more complete and accurate representation of complex landscapes(e.g., Small, 2004).

1.2 Maximum Entropy Modeling

Many mathematical modeling tools have been developed to link observed species presence points withenvironmental variables for the purpose of creating a species distribution model (SDM) from speciesoccurrence data (e.g., BioClim, DOMAIN, GARP). These tools create geographic distributions for a givenspecies based upon areas of similar environmental composition to the input observation points. MaxEnt,a software package developed for modeling species distributions using environmental layers, speciespresence points, and background points (Phillips et al., 2006), performs well when compared with otherSDM techniques (Elith et al., 2011). MaxEnt creates a continuous species distribution map where thevalue of each pixel of the modeled area represents a probability of presence of the study species inthat pixel.

Generally, SDMs are developed for relatively large geographic areas, and the resultant areal distributionis used in predictions of where a species may have its range (Elith & Leathwick, 2009). Species presencedata used for the development of these models is frequently collected using systematic surveys (e.g.,

Fleishman et al., 2001) or from relatively sparse location acquisitions of radio-collared animals (e.g.,Wirsing et al., 2002). However, in modeling species movement over a much finer spatial scale, we believethat a similar technique can be applied effectively to represent the habitat characteristics animals preferfor movement. The data collected for this type of modeling must be representative of animal movementsover fine scale space, and therefore requires following the study animal and acquiring geographiccoordinates of their routes at frequent time intervals. Fine-scale representation of animal habitats is alsoa challenge for researchers using environmental data collected in the field or freely-distributed satelliteimagery of coarse resolution. Optimally, high-resolution satellite imagery at a scale compatible withanimal movement would be used to quantify environmental features for habitat modeling. Wecharacterize the habitat preferences for the movements of bearded capuchin monkeys ( Cebus (Sapajus)libidinosus) based on the environmental features of the habitat in which they move using a subpixel

analysis of landcover from DigitalGlobes WorldView-2 multispectral imagery of the study region. Theseenvironmental layers serve as inputs to the MaxEnt model of capuchin movement within our study sitein northeastern Brazil.

1.3 Path Modeling

To provide a biologically meaningful measure of efficiency of travel, we implemented a cost-of-pathanalysis within a GIS framework. Contrasted with path linearity, cost-of-path analysis considers landscapevariables in defining a maximally efficient route. Cost of path analysis creates a grid-based layer witheach cell of the grid representing a geographically referenced area of the home range of the monkeys.The values of each cell in this grid are calculated based on the cost incurred to arrive at that particular




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cell from a specified start location. Costs may be based on many factors, including topographic distance,algorithms for caloric expenditure, and observed habitat suitability. This technique has previously beenimplemented largely in the study of landscape genetics (e.g., Wang et al., 2008) and habitat connectivity(e.g., Graham, 2001; Driezen et al., 2007) where each grid cell was assigned a resistance value relatedto the study animals reluctance of moving through that particular cell. Connectivity between habitatfragments is measured by summing these resistance values for a least-cost path between patches(Adriaensen et al., 2003). For the animal, resistance may signify mortality costs, reproductive costs,energetic costs, physical resistance, thermal stress, or habitat suitability (Sawyer et al., 2011).

The ability to choose efficient routes to goal sites may be indicative of knowledge of the distribution of

environmental features in ones home range and route planning capacity (Shettleworth, 1998), and manyprevious studies have attempted to present evidence for route planning of nonhuman primates using avariety of route metrics (e.g., Janson, 1998; Normand & Boesch, 2009; Asensio et al., 2011). Oneessential challenge to drawing conclusions about route planning is the quantification and characterizationof animal routes in relation to the landscape. Many conclusions about primate navigation and spatialcognition have been drawn based on route linearity (e.g., Janson, 1998, 2007; Normand & Boesch,2009). Researchers have argued that route linearity is indicative of cognitive capacities, including spatialmemory, external (i.e., allocentric) strategies for reasoning about location, and even complex Euclideanor cognitive maps (Janson, 1998; Presotto & Izar, 2010; Normand & Boesch, 2009), since routeefficiency is presumably facilitated by an accurate mental representation of ones environment (Janson,

2000). Nonhuman primates efficiency in choosing multi-destination routes has been studied using bothlaboratory and field observation methods (e.g., Menzel, 1974; Janson, 2007) with often conflicting results(e.g., compare apparent limitations in navigational skill seen in Pot, 2000 with evidence for strategic routeplanning in Janson, 2007). Capuchin monkeys in particular have demonstrated the capacity to plan routeson computerized maze tasks (Pan et al., 2010), yet we argue that there is inconclusive evidence for routeplanning around environmental features for capuchin monkeys in the wild (although see Janson, 2007 forevidence of route planning irrespective of environmental features). The disparity between results fromlaboratory experiments and results from field observations on efficiency of routes chosen by primates maybe due to the limitations of previously employed analysis techniques for the field data.

As highly encephalized, quadrupedal primates living in a savanna habitat and spending over 30% of theirtime on the ground (Biondi, 2010), bearded capuchin monkeys represent an important model species tocompare to ancestral humans as well as to other extant nonhuman primates. As partially terrestrial

animals, the costs of capuchin travel may prove to be similar to the costs incurred by baboons,chimpanzees, extinct hominids, and other terrestrial species. Previous studies have investigated thenavigation of baboons and chimpanzees, analyzing the linearity of their daily routes and demonstratinga greater linearity of routes when resources were scarce (baboons: Noser & Byrne, 2007) or when theywere traveling in a familiar area (chimpanzees: Normand & Boesch, 2009). The results of theseinvestigations have been taken as evidence that these animals possess sophisticated spatial orientationmechanisms such as episodic memory and a cognitive or Euclidean map of their home range. However,it is to date unknown whether the animals studied in these investigations are choosing linear routes inorder to minimize the environmental costs of their travel to a known goal location, or because they haveno knowledge of the location of resources, such that the most efficient movement strategy is to continuein a straight line until reaching a resource site (Janson, 2000).

The work completed here analyzed capuchin routes using novel methodology which incorporated

environmental features in the estimation of route efficiency. Subpixel classification of environmentalvariables in the monkeys homerange was followed by Maximum Entropy modeling of the probability ofcapuchin presence. This probability was then used to predict paths of least cost through the landscapeand this least cost path was compared to observed capuchin travel.




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2. METHOD

2.1 Study Site and Subjects

Bearded capuchins (Cebus (Sapajus) libidinosus) are New World primates living in a savannah habitat

and are frequently studied for their unique use of stone tools to crack nuts for food (Fragaszy et al, 2004)(Figure 1). We studied capuchin monkeys at our research site (hereafter, Boa Vista) in the state of Piau,in Northeastern Brazil (9 39 S, 45 25 W). The site encompasses the home range of several capuchingroups and the climate of the region is seasonally dry, with lowest precipitation values recorded from Aprilto September (data source: Brazilian National Water Agency-ANA). The marked dry season and thereduced moisture-holding capacity of the sandy and rocky soil contribute to the establishment of specificvegetation communities, characterized by drought tolerance and avoidance. The dominant vegetationformation type in Boa Vista is largely deciduous and transitional tropical savanna. Trees and shrubs occurover a conspicuous grassy layer, with characteristic density and structure intergrading, varying from talldense-canopy woodland to nearly-treeless grassland (Oliveira & Marquis, 2002). Ground palms arenotable species in the area, and can often be found in patches with reduced tree cover and a dominantgrassy layer. Many of these palms are associated with the unique use of stone tools and nut-crackingbehavior of the capuchin monkeys in Boa Vista (Fragaszy et al., 2004). Vegetation is expected to

represent a significant predictor of the suitability of a given area for movement, as it serves to representfood distribution and cover or escape for predator avoidance (Sawyer et al., 2011). Arboreal substratesare frequently used by our study animals for all activity types (e.g., feeding, play, rest) with the exceptionof nut cracking (Biondi, 2010).

Figure 1: Bearded capuchin monkey at the Boa Vista field site using a stone hammerto crack open a palm nut on a log anvil. This behavior is a unique form

of tool use among nonhuman primates.

2.2 Field Data Collection

In Boa Vista, route data was collected for two groups of bearded capuchin monkeys with overlappinghome ranges for a total of approximately 10 days per month (between both groups) from October 2008




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to September 2009 (except May 2009). During route data collection, an observer followed the groupstaying within 20 m of the group center and collecting GPS coordinates for the location of the monkeygroup at five-minute intervals. When the center of the group was greater than 20 meters from theobserver, the approximate distance and compass direction of the group center from the observer wasrecorded manually. Group follows were conducted from approximately 7 am to 5 pm each day of datacollection. These route coordinates (6,449 total points) were entered into a GIS (ArcGIS 10), and thedistance corrections for the point estimates were edited using right angle trigonometry (Figure 2).

Figure 2: Color composite (5R, 3G, 2B) of a WorldView-2 pan-sharpened image,resulting from fusing a set of WorldView-2 multispectral bands, at 2 m spatial resolution,with a WorldView-2 panchromatic band, at 50 cm spatial resolution. Blue points indicate

all monkey route coordinates collected from October 2008 to September 2009.

2.3 Environmental Layers and Subpixel Analysis

Two WorldView-2 multispectral images were inspected for quality and verified to meet the qualityrequirements of this project, including the absence of duplicate line artifacts and clouds. The positionalaccuracy of WorldView-2 was also analyzed by comparing the coordinates of selected landscapefeatures, retrieved from the image, with coordinates acquired in the field using a handheld GPS unit.The same GPS unit was used to record the coordinates of monkeys while foraging. Positional accuracyof the WorldView-2 image was verified to be compatible with the methods employed by this investigation.

Preprocessing of the image consisted in identifying potential backgrounds to be removed fromsubsequent procedures during the subpixel classification (i.e., signature retrieval and the classification ofthe Material of Interest-MOI). Preprocessing was followed by the automatic generation of parameters tocorrect the image for atmospheric and environmental factors. These corrections were applied mainlyaiming to compensate for atmospheric and environmental effects that could affect the identification ofMOIs, supporting in-scene signature derivation. The WorldView-2 images were inspected for clouds andverified to be cloud-free, eliminating the need for cloud identification during environmental correction.Considering that our investigation used a single image, scene-to-scene transferability and cross-scenenormalization were not a concern. The quality of the environmental correction was verified by analyzingthe two derived spectra (atmospheric correction factor [ACF] and Sun correction factor [SCF]), associatedwith the contribution of the atmosphere and the geometry of illumination, respectively. Because a deepbody of water is not available in the scene, the ACF spectrum was compared to topographic shadow

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pixels (dark pixels) produced by one of the mesas occurring in the area of the study. ACF values wereverified to be lower than the values for the dark pixels, suggesting the adequacy of the procedure.

Subpixel classification involved a series of steps used to select and sample each endmember consideredby this study (i.e., vegetation, soil and dark landscape component). These procedures were performedaiming to identify pixels and areas in the image which are representative of the spatial variation of eachendmember. Combinations of the primary endmember and background were identified at differentproportions and used to define multiple areas of interest inside the scene. These sampled values andassociated fractions were used during signature generation, followed by the combination of signaturesbelonging to a single signature family. Following this approach, all signatures representing the variabilityof a given endmember were combined into a single signature file. The classification of the material ofinterest was then performed using the combined signatures.

(a) (b)

Figure 3: Parameters resulting from the Automatic Environmental Correction procedure,for each multispectral band of WorldView-2: ACF (a), SCF (b).

The results of the classification were post-processed, aiming to combine the output fraction layersassociated with each signature into a single band, representing the percentage of a given endmemberinside the image pixel.

A comparative inspection of the resulting fraction images, based on our experience in the field indicatedconsistency in the identification of proportions of vegetation and soil. Open areas, including roads andareas of bare soil, were correctly identified as having zero to near zero vegetation cover. Alternatively,tree crowns and vegetation canopy presented high percentage of the vegetation endmember, withfractions approaching total cover in some areas. Similarly, more dense riparian vegetation showed higherfractions of vegetation, when compared to the grassy areas of savanna. Notable features include an areaof savanna with reduced values of vegetation fraction and high proportions of soil, occurring in thesouthern part of the area of study and possibly resulting from a fire episode. Among the endmembersselected, we observed a better representation of proportions of vegetation and soil, when compared with

the representation of fractions of dark component. Figure 3 presents the results of the Subpixel Analysis.

2.4 Maximum Entropy Modeling

MaxEnt software for species habitat modeling, version 3.3.3k,www.cs.princeton.edu/~schapire/maxent/,was used to build a model of capuchin monkey habitats for movement. To inform the model of variation inenvironmental parameters over the area of interest, 13,162 background points were generated within the50 km2-area around the mean geographic center of all route coordinates. Subpixel values for greenvegetation, soil, and dark endmember were extracted to all background and presence points. The logistic
http://www.cs.princeton.edu/~schapire/maxent/http://www.cs.princeton.edu/~schapire/maxent/http://www.cs.princeton.edu/~schapire/maxent/http://www.cs.princeton.edu/~schapire/maxent/




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MaxEnt model was created using a 20% random test percentage of presence points (5,160 trainingpoints, 1,289 test points). One MaxEnt model using vegetation, soil, and dark endmember and anothermodel using vegetation and soil alone were computed. Model results were evaluated using a ReceiverOperating Characteristic (ROC) analysis, generating the Area Under the Curve (AUC) measure of modelfit where a random model would have an AUC value of 0.50.

The inverse of the veg/soil model (1/model value) was used as a cost layer for least cost path modeling ofone daily route (January 26, 2009) of the capuchin monkeys so that the modeled least cost path and theobserved path could be compared. Least cost paths were constructed between points where capuchinmonkeys were observed to stop for 10 minutes or longer using the inverse of the MaxEnt veg/soil modelas a cost. These least cost path segments were then converted from raster to vector and visualized usingthe color composite WorldView-2 image.

Figure 4. Fraction images representing (a) vegetation; (b) soil; and (c) dark endmember. Lighter areas represent proportions of theendmember inside a pixel. Images were manipulated to enhance contrast for display purposes.

3. RESULTS

Green vegetation is an important environmental variable for capuchin monkeys, with a mean percentgreen vegetation of capuchin monkey presence points of 50.04% (minimum = 0%; maximum = 98%;

SD = 25.06%). Capuchin monkey presence points showed a lower percentage of bare soil and darkendmember than percent green vegetation, with a mean of 20.60% soil (minimum = 0%;maximum = 98%; SD = 20.60%), and a mean of 16.01% dark endmember (minimum = 0%;maximum = 98%; SD = 34.17%) (Figure 5).

Figure 5: Distribution of Bearded Capuchin monkey presence points for the three endmembers of the subpixel analysis:(a) green vegetation, (b) dark endmember, and (c) bare soil.




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The geographic distribution of the bearded capuchin MaxEnt movement model including vegetation, soil,and dark endmember is shown in Figure 6a. The training AUC value for this model was 0.660 while thetest AUC value (i.e., the measure of test data fit to model output) was 0.652. The geographic distributionof the bearded capuchin Maxent movement model including vegetation and soil is shown in Figure 6b.

(a)

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Figure 6: The geographic distribution of the MaxEnt modelscreated from WorldView-2 Satellite Images and observed

capuchin monkey presence points. White dots show presencelocations used for training, while violet dots show test locations.

(A) The MaxEnt model created from veg/soil/dark(B) The MaxEnt model created from veg/soil.


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The training AUC value for this model was 0.654, while the test AUC value was 0.653 (random predictionfor both models = 0.5).

Figure 7. Jackknife plot of variable importance in the MaxEnt models of bearded capuchin movement. Dark blue bars represent theAUC value of the model using only the variable listed to the left. Light blue bars represent the AUC value of the model without the

variable of interest. The final red bar shows the AUC of the complete model, including all variables. The top jackknife plot depicts theveg/soil/dark model, while the bottom plot depicts the veg/soil model.

An analysis of the relative contributions of individual variables indicated that percent green vegetationwas the greatest predictor of capuchin presence points, contributing 71.6% to the veg/soil/dark model and72.5% to the veg/soil model, followed by percent bare soil (veg/soil/dark = 22.3%; veg/soil = 26.4%), andpercent dark endmember (veg/soil/dark = 2%). A jackknife test of variable importance (Figure 7) indicatedthat the variable that decreases model AUC most when omitted is percent green vegetation (veg).Percent green vegetation alone also has the greatest model AUC value when it is the only variableincluded in the model.

Results of the least cost path modeling indicate that the observed capuchin monkey route closelyfollowed the modeled least cost path (considering percent green vegetation) for travel on January 26,2009 (Figure 8).




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Figure 8: Least Cost Path and Observed Routes of Bearded Capuchin Monkeys for January 26, 2009.

The Least Cost Path (purple) was modeled using the MaxEnt model of probability of capuchin presencegiven the environmental variables percent green vegetation and percent bare soil.

The green line represents the actual observed path of travel of the monkey group on January 26, 2009,and the red points represent stop points where the group remained stationary for 10 minutes or longer

(e.g., goal sites such as nut-cracking sites or locations of other clumped resources).




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4. DISCUSSION

Our model suggests that the variables percent green vegetation, percent bare soil, and percent darkendmember all have an impact on the movement patterns of bearded capuchin monkeys at our field site

in Northeastern Brazil. We believe that the MaxEnt model including only percent bare soil and vegetationis more appropriate given the better representation of proportions from those two endmembers comparedto the third dark endmember. For the monkeys in our study area, daily movements were most likely tooccur in areas with 50% or greater coverage by green vegetation.

Of all environmental layers included in our model, percent green vegetation had the greatest influenceon habitat suitable for movement. We attribute the influence of green vegetation on habitat movementsuitability to the availability for substrates upon which capuchin monkeys travel. Although beardedcapuchins at our field site spend up to 30% of their time on the ground, they spend the greatestproportion of their time using arboreal substrates (Biondi, 2010). In addition, the presence of greenvegetation may serve as a vertical substrate on which to evade terrestrial predators (Gursky & Nekaris,2007). Green vegetation also serves as a potential location from which to find food resources such asthe insects and ground palm nuts upon which bearded capuchin monkeys feed at Boa Vista.

These results indicate that MaxEnt species distribution modeling can be used to create a model of habitatappropriate for species movement, and that the inverse of MaxEnt model values represents anappropriate cost layer for modeling species movement using least cost path analysis. From thepreliminary investigation of one bearded capuchin monkey route from January 26, 2009, the physicalappearance of observed capuchin monkey routes approximates that of the modeled least cost pathbetween stop points. This novel methodology for analyzing species routes has the potential to transformthe way animal paths (e.g., seasonal migration, dispersal) are analyzed by all ecologists interested inanimal paths. The scale at which fine-resolution phenomena such as animal paths can be representedusing WorldView-2 high resolution satellite imagery is not only a major improvement on previousanalyses, but absolutely necessary for scientists wishing to draw substantive conclusions regardingthe link between environmental features and animal behavior.

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