Movement ecology of human resource users: using net squared displacement, biased random bridges and resource utilization functions to quantify hunter and gatherer behaviour

Authors

Errata

This article is corrected by:

  1. Errata: Erratum Volume 5, Issue 2, 200, Article first published online: 13 February 2014

Summary

1. Understanding human resource extraction is crucial for conservation science, allowing accurate assessments of system sustainability and testing key assumptions about human resource users.

2. We apply ecological methods and principles to Global Positioning System (GPS) data on human movement to investigate the ecological and behavioural differences between human hunters and non-hunters, a method which can be reproduced with any species which routinely return to a central place. The integration of movement ecology and habitat selection can greatly augment the applicability and scope of both disciplines, and we explore the issues that arise from integration, because of the differing data types and methods used by each approach.

3. We propose an adaptable methodological framework which can be used to combine movement ecology and habitat selection when using data from GPS tracking devices, whether from human or animal foragers. The methodology is based on three steps and can be implemented in the free downloadable statistical program R, using the full code in the Data S1.

4. First, we show that net squared displacement, coupled with nonlinear mixed-effects models, is suitable for quantifying characteristics of small-scale movement, such as daily travel patterns, and extracting parts of these journeys for analysis.

5. Secondly, having extracted part of a journey, biased random bridges use the auto-correlated GIS tracking data to create a utilization distribution (UD) for each individual. This method includes movement between known locations to estimate use intensity in an area.

6. Finally, the UD can be analysed by a resource utilization function which relates the intensity of use to landscape features of an area to identify habitats selected by an individual. This can be used to predict use of the landscape at larger scales for both individuals and an entire population.

7. This methodological framework is a flexible method to accurately assess human and animal resource use and movement through the natural environment.

Introduction

The study of how animals and plants move from one place to another, or movement ecology, is a growing field, which recognizes the contribution of internal states like hunger, and external factors such as resource distribution, to animal movement. Habitat selection research examines how organisms use their environment, by focusing on identifying features associated with use of an area. In spite of overlapping areas of interest, integration of movement ecology and habitat selection has been slow (Holyoak et al. 2008), partly hampered by differences in data treatments and requirements, and the lack of a methodological framework to tackle these differences (Holyoak et al. 2008; Calenge, Dray, & Royer-Carenzi 2009; Cagnacci et al. 2010). Incorporating the two disciplines can move movement ecology past a purely mechanistic understanding and aid more accurate assessment of habitat selection. A combined approach would benefit both ecological studies of non-human animals and studies in conservation.

Conservation science frequently uses models of human behaviour to investigate hunting and sustainable resource use (e.g. Rowcliffe, Cowlishaw, & Long 2003), but outside a small number of studies on recreational hunters in temperate zones (e.g. Kaltenborn & Andersen 2009; Lange et al. 2010), human hunter movement and habitat selection have not been quantified. Humans are central place foragers: they extract resources from an area around a central place, usually a community (Houston 2011). Research on the sustainability of wild meat hunting frequently uses estimates of the area of resource extraction to calculate sustainability indices (i.e. Hill & Padwe 2000; Levi et al. 2009). These studies usually use the furthest distance travelled by members of the community and assume a uniform circular area of extraction around a community or assume that use is most intense in areas closest to the community, but this is rarely demonstrated through empirical research. Accurate assessment of areas of extraction and habitat preferences will improve these estimations and aid prediction of areas individuals use outside a specific study area. Source-sink dynamics is another commonly used theory in conservation science (i.e. Hill & Padwe 2000), which assumes that unexploited areas can act as sources of new individuals for exploited, or sink, areas. Accurate estimation of exactly which areas are used and unused by humans, coupled with ecological information such as dispersal distance of exploited species, would help estimate the relevance of source areas to the dynamics of different exploited species.

Detailed information about an individual’s location can most easily be gained through Global Positioning System (GPS) tracking (Cagnacci et al. 2010), which records an individual’s location at set intervals. Whereas gaining location data for animals involves stressful, potentially dangerous and expensive trapping and tagging, humans can be asked to carry small inexpensive GPS receivers which record locations. Given the ease with which GPS information can be gathered for humans, the development of appropriate methodology is crucial, particularly as some characteristics of human movement ecology mean that traditional habitat selection methods are harder to apply. First, humans are often central place foragers – they collect resources in a single day, starting from and returning to a community. Secondly, like some other animals, humans often repeatedly use the same paths, for instance along ridges or cuttings through dense forests. Finally, when hunting, humans are like many other predators and so should select for prey presence rather than specific landscape features. As human hunters usually hunt a wide spectrum of prey animals, there are less likely to be specific landscape features associated with the various target species than there are for more specialist predators.

Methodological framework

We present a combination of three methods to integrate movement ecology and habitat selection for GPS track data. Although this methodology was developed to overcome issues specific to data collected from human hunters, the framework is applicable to other study species which use central places. Resource extraction of central place foragers is made up of three components: the outward journey, a period of resource extraction and the return journey (Orians & Pearson 1979). Central places are points to which an individual returns on a regular basis. This includes many species, such as fish returning annually to spawning grounds, human hunters returning daily to their community or diving mammals who return to the surface to breathe. We propose using net squared displacement (NSD) combined with nonlinear mixed models to estimate the distance travelled and the area of resource extraction. Biased random bridges (BRB) are then used to define utilization distributions (UD), and resource utilization functions (RUF) identify habitat features associated with greater use (Fig. 1). The combination of these methods creates a flexible framework which can overcome issues associated with integrating movement ecology and habitat selection.

Figure 1.

 Methodological framework outline and potential outcomes of each step.

Distance, Duration and Speed: Net Squared Displacement

Net squared displacement calculates the squared distance between each GPS location in an individual’s track and the individual’s original location. Distances are squared to remove directional information. NSD has previously been used to study yearly movement cycles of migratory and dispersing animals (Bunnefeld et al. 2011; Börger & Fryxell in press). Although its appropriateness at smaller temporal and spatial scales has not been demonstrated, the approach is scale independent and we test here its applicability to tackle ecological questions of habitat selection during different movement states. Plotting the NSD over time gives a curve starting at zero when an animal is at the central place, with NSD increasing until it reaches a maximum location. NSD can then remain relatively constant until the animal starts to return to the central place, when NSD will gradually decrease until the animal reaches the central place, where NSD = 0 (Fig. 2a). From modelling NSD, key parameters such as distance travelled, duration and speed can be mathematically defined. Single trips can be compared to the population mean, or comparisons made between different individuals or classes of individual within a population. If animals make multiple trips to and from the central place in a single day, such as birds caring for young in a nest or defending key central resources such as mating display areas, each trip in the day can be modelled separately. A double logistic function (eqn 1) can be used to model trips, as outlined in Bunnefeld et al. (2011).

Figure 2.

 Measures used when modelling net squared displacement (NSD) using eqn 1. δ = asymptotic height, θa = time when half the asymptotic height is reached on the outward journey, θr = time when half the asymptotic height is reached on the return journey ϕa = time taken to travel between half and approximately three quarters of the asymptotic height on the outward journey, ϕr = time taken to travel between half and approximately three quarters of the asymptotic height on the return journey. For this figure, δ = 20, θa = 75, θr = 325, ϕa = 20, ϕr = 20. (b) Three different definitions of NSD using a double logistic model, demonstrating the flexibility of non-linear models. Solid line: δ = 40, θa = 140, θr = 200, ϕa = 10, ϕr = 10. Dotted line δ = 30, θa = 150, θr = 350, ϕa = 40, ϕr = 10. Dashed line δ = 20, θa = 100, θr = 300, ϕa = 10, ϕr = 10.

image(eqn 1)

where δ is the asymptotic height of the distance travelled from the community, θa and θr are the times at which half the asymptotic height is reached on the away and return journeys, respectively. ϕa and ϕr model the time between reaching one half and inline image of the trip on the away and return journeys and thus define trip duration (Fig. 2a). Number of minutes since the trip started is represented by t. Different parameters for the away and return journeys allow the timing and speed of travel to differ on the two elements of the trip (Fig. 2b). Representative speeds of away and return journeys can be calculated using one quarter of the asymptotic height divided between the time taken to travel between one half and three quarters of the trip: inline image. By modelling NSD with nonlinear models, the parts of the journey can be mathematically defined and separated for analysis. The part of the journey which is separated for analysis will depend on the study system and specific research questions. For example, in animals which use central places, such as nests or dens, only an outward journey may be of interest as the return journey is a function of central place location. In human hunters, hunting is more likely to occur on the outward journey, as hunters return to their community once successful. Thus, the outward journey is a searching phase, as hunters search for an animal they can successfully kill, followed by resource extraction. In contrast, the return journey (though likely similar to the outward journey) will be of less interest. An additional issue for species which use central places is that analysis of raw data would produce a strong preference for the habitat type where the central place is located (Benhamou 2011).

An important contribution of movement ecology to habitat selection would be the identification and separation of travelling and non-travelling periods (Börger, Dalziel, & Fryxell 2008), and this can be achieved by modelling NSD. Non-travelling periods are often equated with foraging or feeding periods and can normally only be separated from travelling periods when time between recorded locations is expected to be shorter than the non-travelling periods. Most studies using GPS tracks use the relationship of distance travelled between recorded locations (step length) and relative angle between three consecutive locations (turning angle) to distinguish behavioural changes in individuals movement (Gurarie, Andrews, & Laidre 2009). Individuals are assumed to be foraging when step lengths are shorter, and turning angles more tortuous, and travelling when turning angles are less tortuous and step lengths are longer. Cut-off values for separating the step lengths and turning angles into travelling and non-travelling periods can be determined through statistical exploration of the data (Gurarie, Andrews, & Laidre 2009), but if GPS location error is greater than the cut-off length, non-travelling periods could be incorrectly classified as travelling periods (Frair et al. 2010). Therefore, these methods are only appropriate in animals where non-travelling periods are longer than recorded location intervals, and travelling between location intervals is expected to be greater than location error. This greatly reduces the species for which this method can be applied. In contrast, when modelling NSD with nonlinear models, it is not necessary to define cut-off points for step length and turning angle, but travelling and non-travelling periods can be identified, mathematically defined and separated. Furthermore, nonlinear models of NSD can extrapolate between recorded locations and so are robust to missing locations, a frequent problem in GPS tagging studies. Finally, these models can be applied to a wide variety of species, ecological questions and various location intervals.

If the area of resource extraction is assumed to be represented by the peak area of the curve because hunters return to the community once they are successful (Fig. 2a), it too can be simply identified and isolated. The peak area is not identical to the asymptotic height δ, which, by definition, is never reached, but can be derived from the parameter estimates of the nonlinear mixed model. The extent to which δ approximates the peak of the curve should be checked, and the difference may be significant in some situations. In these cases, and when other properties of the double logistic function are unlikely to be appropriate (such as gradual acceleration and deceleration close to the central attractor), alternatives to the double logistic function (for example, double asymptotic functions) should be explored, though the methodological framework remains valid.

Area, Intensity of Use and Selection of Landscape Features: Biased Random Bridge Utilization Distributions (BRB) and RUF

Multiple locations of a single individual recorded by GPS units are non-independent, as the location of the next position in the sequence at any time-scale is bound by the animals’ potential for movement within the given period. Locations are also non-independent as nearby locations are often more similar to one another than more distant locations (Boyce et al. 2010). Both of these factors mean that data are autocorrelated, which is a problem for studies based on parametric statistics. One method to reduce autocorrelation is data thinning (Swihart & Slade 1985), but this can remove real patterns of animal behaviour, particularly in resource selection studies. For example, an animal will show high autocorrelation if locations are recorded every 10 min, and they ‘select’ to stay in the same area (the definition of ‘same area’ also varying with spatial scale and normal daily geographical extent of animal) for an hour (Fig. 3). If data are thinned to one point every hour (circled locations, Fig. 3) to reduce autocorrelation, the selection of this area is lost in analyses. Data thinning also occurs when methods require locations to be recorded at equal time intervals. Missing locations are common in GPS tracks, because of landscape features blocking satellite signals (DeCesare, Squires, & Kolbe 2005), and these missing locations mean unequal intervals between locations. In these cases, biologically important information is lost to make data conform to the assumptions of habitat use methods. The proposed methodological framework does not require data thinning to remove autocorrelation and can interpolate missing location from recorded locations.

Figure 3.

 Example animal trajectory, showing strong selection of riverside areas in the raw data, and the potential loss of this relationship when locations are sub-sampled (circled locations).

Choice of statistics in resource and habitat use studies has been discussed in numerous review papers (e.g. Conner, Smith, & Burger 2003; Johnson et al. 2006; Millspaugh et al. 2006; Thomas & Taylor 2006). Most approaches compare characteristics of locations where a species is observed to be present to characteristics of absent or available locations in a study area. Comparisons between observed and available locations are considered more robust because of difficulties in identifying absent locations (Johnson et al. 2006). Other authors (Thomas & Taylor 2006) have argued that available locations are also difficult to identify, because of uncertainty about the accessibility of locations to a species, and temporal differences in environmental variables such as vegetation cover. For both these types of study, categorical characteristics such as ‘heathland’ are assigned to each location. Locations can, however, be misclassified if GPS location error is great (Frair et al. 2010). Conner, Smith, & Burger (2003) found that categories were less able to identify the importance of edge habitats than distance-based analyses where a continuous measure of distance to each habitat feature of interest is calculated for each location. However, using continuous variables creates new problems. If a species is selecting a particular habitat type, observed locations should show smaller variance in distance to this habitat than for all available locations, making it difficult to use parametric analyses (that require homogeneity of variance across conditions). For example, human hunters frequently follow paths through the forest, but will sometimes leave paths to pursue animals or explore new areas. Areas away from paths should be considered as available habitat as they are sometimes, though less frequently, used. If random locations are generated in this landscape to represent the available landscape, a much higher variance in distance to path would be expected for these locations than observed hunter locations. Equal variance in this case would a priori lead to the conclusion that hunters are not selecting for paths, thus making testing redundant.

Resource utilization functions can be used to examine resource use by relating landscape features to a probability distribution of an individual or species use of the landscape. These probabilities, or UD, are frequently used in movement ecology, but are not often linked to landscape features or used for habitat selection studies. Using UDs, area of use and overlap between individuals or types of individuals can be calculated. Kernel methods smooth observed locations of a species or individual to create an average probability of use for each square in a gridded area. This probability of use for each grid square is then converted to a value between 0 and 100 in which lower value grid squares are more intensively used. Bridging kernel methods are considered an improvement on traditional kernel methods (Benhamou & Cornélis 2010), as they place a kernel function between successive locations rather than over known locations. This means that the area used to move between points is considered and all observed locations of an individual are connected. Traditional kernel methods could leave disconnected use areas in home range estimates of terrestrial animals, which is not ecologically realistic, as it must be assumed that individuals use corridors linking areas. Kernel bridges can also bridge gaps where locations are missing (Benhamou 2011). In the BRB method, movement is biased towards the next location, an improvement over existing kernel bridging methods which use random movement to model this process (Calenge 2011). An additional advantage of BRB is its ability to incorporate natural boundaries into the calculation of UD, such as constraining estimations so that terrestrial animals never use lakes. Furthermore, the smoothing factor for BRB, a significant source of error in kernel studies (Millspaugh et al. 2006) can be automatically estimated from the data. Using BRB to interpolate between known locations means that missing locations are estimated from the data and thinning of the GPS data is not required.

Resource utilization functions assume that increased height of the UD in a grid square represents selection and uses multiple regression to relate use intensity of all the grid squares in the study area to landscape features, such as distance to a river. The probability of use for each grid square is subtracted from 100 to give a log-normal distribution. Thus, if grid squares closer to the river are more intensively used, then the RUF will output this as a positive coefficient estimate. As the use intensity and landscape features of any grid square will be correlated with that of adjacent squares, a Matern correlation function is used to account for the spatial correlation of the grid cells (Marzluff et al. 2004). The Matern correlation function has two parameters (i) ρ, the range of spatial dependence in metres, and (ii) θ, the smoothness of the UD surface. This method can be used to compare habitat selection between different individuals, compare the relative importance of various environmental variables in explaining use intensity, and develop predictive models of species distribution. Although continuous variables should be normally distributed to be included in an RUF, non-normal variables can be transformed and/or changed to categorical variables (Marzluff et al. 2004). RUFs can only identify increased or decreased use associated with features within a researcher defined study area, but as analysis is based only on observed locations, there are reduced errors from generating random locations. As it is not necessary to generate random or unused location for analysis, uncertainty about whether areas are truly unused or random is removed, and it is not necessary to ensure equal variance between the two sets of locations.

The outlined methodological framework, combining NSD, BRB and RUF methods, is flexible and can be applied to track data to address various questions of ecology, conservation and human behaviour. Each step uses the most biologically realistic methods available, and this three-step combination can account for missing locations and spatiotemporal autocorrelation (Table 1). Additional information on all three methods can be found in Appendix S1. We demonstrate the use of this framework by using GPS tracking data to determine whether movement ecology and habitat selection differs between hunters and non-hunter.

Table 1.  Strengths, limitations and assumptions of combined methodology using net squared displacement, biased random bridges and resource utilizations functions
StrengthsLimitationsAssumptions
  1. GPS, Global Positioning System; UD, utilization distribution. *Benhamou & Cornélis (2010).

Methods are biologically meaningful and give uncertainty associated with parameter estimationsAll three methods require large numbers of locationsSpecies movement highly influenced by central places
Can be applied to GPS tracks of any collection frequency and spatial scale that is expected to detect an individual’s relocationNot able to identify multiple resource use areas in a single tripSampling frequency more frequent than duration of resource extraction bouts
Can be applied when GPS locations are missingNet squared displacement needs all parts of the curve to have enough dataMissing locations randomly distributed
Journeys and resource extraction can be separatedNot able to identify areas of resource extraction in species without central placesThe peak of the curve is the area of resource extraction and only one extraction period occurs before return to the central place
Movement between locations is included>200 locations/individual required for an accurate assessment of UD*Area used during the study represents true use intensity for an individual
Considers use intensity, rather than just useCannot identify characteristics of areas which are never usedFeatures of unused areas do not explain habitat selection
All analyses can be completed in single, free to download, statistical programAnalyses can be computationally time consumingResearcher knowledge of statistical program R

Materials and methods

Data Collection

Data on movement during forest trips were collected from 12 individuals in a small Waorani community inside Yasuní National Park, Amazonian Ecuador (0°41′S latitude, 76°24′W longitude) which with the adjacent Waorani Reserve covers 1·6 million hectares. Ridges of 25–40 m are separated by streams which flow into rivers running east to join the Napo and Amazon rivers. The canopy is 10–25 m with 30–40 m emergents, evergreen and without large disturbances on terre firme, excepting swamps and the flood plains of larger rivers. Rainfall and temperature are seasonal; average monthly rainfall is <100 mm and monthly temperatures vary between 22° and 34°C (Valencia et al. 2004). When going on a forest trip, members of the community were asked to carry a Mio 168 PDA loaded with Cybertracker (http://cybertracker.org/) and programmed to record a location every 10 s. The aim of this study was to determine whether there were behavioural differences between hunters and non-hunters which could potentially be recognized and utilized by prey species to avoid hunting pressure. One point per minute was extracted for analysis to speed processing time. All trips started and ended at the community. Individuals in the community went on forest trips to hunt, fish, gather plants and collect cultivated plants from small forest clearings. For all trips, individuals returned with a single resource (e.g. three monkeys of the same species, or a basket of fish), further supporting the assumption that only a single bout of resource extraction occurred during a trip.

Predictor Variables

A small questionnaire was completed before and after each trip and used to divide trips into ‘hunting’ and ‘non-hunting’. Hunting trips were any trip in which any member of the group carried a gun or blowpipe, regardless of hunting success. The single trip in which an individual took hunting dogs into the forest was also classified as a hunting trip. All non-hunting trips returned without meat and included a variety of activities: fishing, collecting wild plants and cultivated plants from small areas of cleared forest, in 14 of 17 non-hunting trips individuals took fishing equipment and returned with fish. As mean GPS location error was 30 ± 47 m, the study area was divided into 100 × 100 m (1 ha) squares. This scale allows for fine-scale analysis and meant recorded locations would be within one square of their actual location. Landscape features were measured as the distance in metres from the centre of each 100 × 100 m grid square to the community and nearest stream and river. Rivers were permanent bodies of water, >10 m across, whereas streams were smaller, not navigable by canoe year round, and <5 m wide. Shapefiles were imported into the statistical software R (version 2.13, R Core development team 2001), and distances calculated using the nncross function in the package spatstat 1.23. (Baddeley and Turner, http://www.jstatsoft.org).

Modelling Methods

Thirty-nine trips were recorded, but gaps in point collection were common because of the variable forest cover, and any trip where less than 10 points were recorded was excluded (three trips). This left 36 trips for analysis, made up of 19 hunting trips and 17 non-hunting trips. These trips had between 15 and 283 GPS locations, representing 32·4 ± 25·5% of expected locations given trip duration. The exact start and end time was identified using questionnaires, and a single point at the centre of community was added at the recorded start and end time for each trip. These additional points meant that NSD was calculated from the same point for each trip, and trips were constrained to return to the community even if the end of the trip was not accurately recorded because of battery failure of the PDA unit (six occasions).

Data were modelled using the nlme package (Pinheiro et al., 2011) in R. Trip was nested within individual as a random effect to account for individual differences and multiple trips undertaken by the same individual. All variables and combinations were modelled to vary with the random effects. Models were rejected if estimates for any parameter were outside the range of the data, for example, if θr was estimated to occur after the longest trip in the data set had finished. Models which did not violate these conditions were evaluated using Akaike Information Criteria (Burnham & Anderson 2002), whereby lower AIC values suggest a model better explains the data. After selecting a random effects structure, two models were compared: one in which the NSD varied between hunting and non-hunting trips, and a second in which NSD did not vary with trip type. The peak of the curve, which represents the furthest distance travelled, was derived from the parameter estimates of the nonlinear mixed model.

Habitat Selection

The best model for NSD was used to extract locations of resource extraction for hunting and non-hunting trips. When hunting, an individual can be considered searching for prey at any point on the outward journey, only returning when they achieve success. Therefore, only the outward journey is part of resource extraction and locations which were part of the return journey were not included (approximated using inline image). In contrast, for non-hunting trips, it was assumed that both the out and return journeys were travel to the point of extraction, rather than resource extraction events. Therefore, locations which were part of the outward and return journeys were excluded (approximated using inline image). Separate UDs for hunting and non-hunting trips were calculated to assess use at the community level, using the biased random bridge method (Benhamou 2011). For the two individuals with more than 200 locations who conducted hunting trips, and two with more than 200 locations who conducted non-hunting trips, separate UDs using the BRB method were calculated for use with RUFs. If there were no locations for more than 2 h, a kernel function was not modelled between the two locations, effectively meaning each trip by an individual was separately modelled. The diffusion coefficient, or smoothing factor, which determines the degree of uncertainty in the location of the kernels between two locations, was calculated from the data using the function BRB.D in the package adehabitathr version 3.2.2-CAPI-1.6.2 (Calenge, http://www.faunalia.it/animove/trac/). The resulting UDs were analysed using the RUF package version 1.5-1 in R. Following the methods of Kertson & Marzluff (2010), grid squares with use intensity <99 were selected and the natural log of (100-UD) was used as the response variable to give a normal distribution, whereby larger values meant higher use. The number of grid squares used to estimate the RUF is equal to the 99% probability area of use in hectares, as 1 hectare = 1 100 × 100 m grid cell. The square root of the explanatory variables, distance to community (CM), distance to the nearest river (RV) and stream (ST), was used for analysis. These three variables were chosen to give a simple example of using these methods to study habitat selection in humans. Rivers are often used for transport throughout the Amazon region, whereas streams are used for fishing, thus increased use may be expected for non-hunting trips only. Distance from the community was included as most models of human behaviour assume either a uniform circular pattern around the community or increased use close to the community. Other variables were not included for varying reasons. Not all hunting paths within the study area were mapped, and so hunting paths were not included in the analysis as a variable, and no part of the forest had suffered significant degradation, excepting areas close to the road. Distance to the road was significantly correlated with distance to the community, and community was considered a more informative variable for inclusion in the models. Altitude and slope were digitalized from a paper map, but the variations in altitude within the area used by the community were small (220–300 m), and the paper map did not include sufficiently fine detail to accurately estimate topographical features such as slope, aspect and altitude. Unstandardized coefficient estimates from RUFs can be used to map predicted occurrence of the study organisms within the larger landscape, but standardized coefficients are presented here to show direction of selection and the relative importance of the three explanatory variables. Further details and code for all methods are given in the Data S1.

Results

Net Squared Displacement

Variation in the random effects was mostly due to variation in ϕr, the time at which individuals had completed half the return journey (39·02% of variation explained by differences in ϕr between individuals, and 42·06% by variation within individuals). Differences in the asymptotic height between individuals accounted for <0·01% of overall variation, and differences within individuals in asymptotic height accounted for 15·89% of overall variation. For the fixed effects, a lower AIC was found when two separate curves were fitted to hunting and non-hunting trips (ΔAIC: same curve, 507; separate curves, 0). Hunting trips had a higher peak, indicating individuals travelled further when hunting, and also showed a greater time difference between the away and return mid-points, most likely because they were travelling further from the community (Fig. 4, Table 2). Duration of both away and return journeys was shorter for non-hunting trips, but this is to be expected as they travelled less far from the village. In fact, non-hunting trips had a faster travel speed (3·3 km/h for away and return sections) than hunting trips (2·52 km/h when travelling away from the community, and 2·22 km/h on the return portion).

Figure 4.

 Net squared displacement of hunting and non-hunting trips. The grey points connected by lines represent single trips, and the black line superimposed above shows the fitted model.

Table 2.  Estimated trip parameters, with 95% confidence intervals, for hunting and non-hunting trips, determined by modelling net squared displacement with nonlinear mixed-effects models.
ParameterTrip type
HuntingNon-hunting
  1. NSD, net squared displacement.

Asymptotic height (δ)38·00 (26·58–49·42)9·88 (−2·0 to 21·77)
Predicted peak NSD36·119·88
Peak distance travelled (km)6·013·14
Difference between inline image and peak distance travelled (km)0·150·00
Time of journey mid-point (mins)
 Away (θa)69·58 (66·95–72·21)30·58 (25·65–35·51)
 Return (θr)356·42 (311·46–401·38)293·44 (241·15–345·74)
Duration of travel between approx 1/2 and 3/4 of asymptotic height (mins)
 Away (ϕa)36·66 (34·98–38·35)14·22 (10·40–18·03)
 Return (ϕr)41·53 (38·56–44·49)14·32 (11·67–16·97)

Of 95% confidence intervals of the parameters for hunting and non-hunting trips only overlapped for the mid-point of the return journey (θr), and these no longer overlapped at 79% confidence intervals. Locations for habitat selection analyses were extracted using parameter estimates from the model (Table 2). Locations before the 273rd min of a trip [inline image = 356·42 − (2 × 41·53)] were included for hunting trips, resulting in 1294 locations, and locations were included between the 60th and 265th minute of non-hunting trips [inline image = 30·58 – (2 × 14·22) < t < 293·44 – (2 × 14·32)], resulting in 1303 locations.

Biased Random Bridge Utilization Distribution

For one individual (referred to as individual BA in Table 3) where sufficient locations were available for both hunting and non-hunting trips, a greater area was used for non-hunting trips. However, the UD estimate for non-hunting trips by this individual was based on a greater number of trips and locations than the estimate for hunting trips (Table 3), and so is unlikely to represent true differences in area used by hunting and non-hunting trips.

Table 3.  Number of locations, trips and area of use, with estimates for standardized resource utilization functions coefficients for each individual and trip type with sufficient data. Hectares used at 99% probability is equal to the number of grid cells used to evaluate habitat selection. Estimates represent the relationship between the natural log of 100-UD and the square root of the distance to each explanatory variable. Positive values suggest increased use in areas close to the environmental variable, and negative values suggest decreased use in areas closer to the feature. Relative importance of resources is indicated by the magnitude of the estimate for each variable.
Trip typeINDNo. of tripsNo. global positioning system recorded locationsArea of 50% use (ha)Area of 99% use (ha)SmoothnessSpatial range (m)Community estimate (±SE)River estimate (±SE)Stream estimate (±SE)
HuntingMA1183819417002·3367 ± 8−0·08 ± 0·03−0·14 ± 0·03−0·06 ± 0·02
BA2258201112·6298 ± 220·51 ± 0·20−0·85 ± 0·230·35 ± 0·17
Non-huntingSS4433453961·9266 ± 150·04 ± 0·08−0·11 ± 0·08−0·29 ± 0·07
BA4386445492·0354 ± 14−0·10 ± 0·05−0·52 ± 0·05−0·26 ± 0·06

The pooled overall area for all individuals in the community which was used by hunting trips was greater than non-hunting trips (50% probability of use: 182 ha for hunting trips; 99 ha for non-hunting trips. 95% probability of use: 1395 ha for hunting trips, 689 ha for non-hunting trips, Fig. 5a,b), but this was in part because of a large contribution (both in terms of number of trips and number of locations) from one single individual (Individual MA: 838 of 1303 locations) to the hunting data set. At 50% probability of use, only 20 ha were used by both hunting and non-hunting trips, rising to 263 ha at 95% probability of use. This overlap represents between 10 and 40% of the total area used, suggesting that the majority of resource extraction is carried out areas used exclusively for one type of trip (hunting or non-hunting).

Figure 5.

 Pooled geographical distribution of resource use by all individuals for hunting trips. Areas more frequently used are darker, with 95% use (dashed line) and 50% use (solid line) contours shown.

Resource Utilization Function

The number of grid squares used to estimate the RUF for each individual varied between 111 and 1700 (Table 3). The most consistent result, for both direction of relationship and relative importance of the explanatory variables, was lower use intensity close to rivers (Table 3). Relationship with distance to streams and the community was less consistent. The autocorrelation values of smoothness and spatial range were relatively consistent between individuals, as should be expected as all were using a similar area.

Discussion

Differences between Hunters and Non-Hunters

We use nonlinear models to describe NSD and distinguish movement patterns of hunting and non-hunting trips, with the results showing that treating these two types of trips as distinct is justified by the differences in distance, speed and duration of stay at the furthest point. Asymptotic height varied more within individuals than between individuals, but duration of trip varied both within and between individuals. Insufficient data were available to draw firm conclusions about the nature of area use, overlap and habitat selection in hunters and non-hunters, but these preliminary results suggest that humans do not use a uniform circular area around the community for resource extraction. Furthermore, the few individuals tested suggest that use may not be most intense closest to the community. Both hunters and non-hunters showed less intensive use of areas close to rivers. This is surprising, given the ease of travel along rivers by canoe, and the resources for extraction close to rivers, such as fish and animals such as tapir (Tapirus terrestris) and capybara (Hydrochoerus hydrochaeris), which use river banks and are eaten in the study area (S. Papworth, unpublished data). These preliminary data suggest more research is required into use of space and habitat selection in human resource users. The purpose of this paper, however, is not to draw firm conclusions about human resource extraction, but rather to demonstrate the use of this methodological framework and its applications.

Net squared Displacement

In this example, we used NSD to select locations we considered associated with resource use, but this method could also be used to select other trip characteristics such as removing locations within a certain distance of a central place, or comparing habitat characteristics of the central place and maximum displacement. The modelling process for NSD is flexible, and equations other than the double logistic function (eqn 1) can be used to describe movement. For example, Bunnefeld et al. (2011) use the double logistic function, a single logistic function and a linear model to describe NSD and distinguish between migrating, dispersing, and nomadic moose (Alces alces) and individuals remaining in a single home range throughout the year. Alternate curves could similarly be used to describe the movement of central place foragers. The advantages of NSD over step length and turning angle methods are its ability to account for missing locations, and its definition of cut-points from the data itself. This said, NSD cannot pick up on finer-scale variations or pauses in movement, and constant NSD does not mean that an individual is stationary, rather it could be moving equidistant around the point of origin.

Utilization Distribution Built with BRB

To accurately estimate a UD using the BRB method, Benhamou & Cornélis (2010) recommend a minimum sample size of a few hundred serially correlated locations. For the presented data set, this condition is only fulfilled by a few individuals. This high sample of locations needed to estimate UD using BRB is a drawback, but not necessarily a major issue as GPS tracks can generate thousands of locations over the course of a study. The BRB is an improvement over existing kernel methods, as it can incorporate geographical boundaries, estimates a smoothing parameter from the data, and uses algorithms for calculating bridges based on realistic animal movement patterns. Using UD methods which incorporate movement to study human resource users can highlight areas with scant use, which may potentially be acting as source areas in a sink-source system. Calculating overlap between individuals can also help identify whether the landscape is being used as a common resource, or whether particular areas are only used by certain individuals or types of individuals.

Resource Utilization Functions

Resource utilization functions can identify features associated with both increased and decreased use intensity, which can either be used to describe habitat selection or create predictive maps of use intensity. As RUFs only use presence data, they reduce some of the uncertainty associated with estimation of habitat selection, as neither available nor absent locations are used for comparison. Furthermore, RUFs associate landscape features with not just observed locations of an individual or species, but also incorporate use intensity, identifying features associated with both increased and decreased use. As these landscape features can be either continuous measures or categorical labels, RUFs offer a very flexible way to determine habitat selection.

Conclusions

Although these methods have been applied to previous studies (NSD: Bunnefeld et al. 2011; BRB: Benhamou 2011; RUF: Marzluff et al. 2004; Kertson & Marzluff 2010; Long et al. 2009), they have not previously been used together. This methodological framework tackles some of the major issues for incorporating movement data into studies of resource use. The authors consider these three methods the best currently available to study movement ecology and habitat selection where GPS tracking data are available to study human behaviour, but a further advantage of this framework is its flexibility to incorporate methodological advances. For example, if a new method is developed for estimating utilization distributions, this can be substituted for the BRB within the framework. Alternatively, if a study has fewer than the 200 relocations per individual recommended for BRB, a simpler UD estimation method can likewise be substituted. The use of these methods has demonstrated how differences between hunters and non-hunters in a single community can be quantified and provided preliminary results which suggest further research is required into some of the assumptions about human resource users. We encourage the use of the methodological framework outlined here in future studies.

Acknowledgements

Many thanks to the individuals who participated in this study, especially the field assistants in Yasuní National Park. Particular thanks also to two anonymous reviewers, Bernardo Garcia Carreras and the Natural Environment Research Council and Economical and Social Research Councils who funded the interdisciplinary studentship which made this research possible. NB and EJMG were supported by the European Commission under the HUNT project of the 7th Framework Programme for Research and Technological Development.

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