Applications of stepselection functions in ecology and conservation
 Henrik Thurfjell^{1}Email author,
 Simone Ciuti^{1, 2}Email author and
 Mark S Boyce^{1}Email author
DOI: 10.1186/2051393324
© Thurfjell et al.; licensee BioMed Central Ltd. 2014
Received: 15 August 2013
Accepted: 3 February 2014
Published: 7 February 2014
Abstract
Recent progress in positioning technology facilitates the collection of massive amounts of sequential spatial data on animals. This has led to new opportunities and challenges when investigating animal movement behaviour and habitat selection. Tools like Step Selection Functions (SSFs) are relatively new powerful models for studying resource selection by animals moving through the landscape. SSFs compare environmental attributes of observed steps (the linear segment between two consecutive observations of position) with alternative random steps taken from the same starting point. SSFs have been used to study habitat selection, humanwildlife interactions, movement corridors, and dispersal behaviours in animals. SSFs also have the potential to depict resource selection at multiple spatial and temporal scales. There are several aspects of SSFs where consensus has not yet been reached such as how to analyse the data, when to consider habitat covariates along linear paths between observations rather than at their endpoints, how many random steps should be considered to measure availability, and how to account for individual variation. In this review we aim to address all these issues, as well as to highlight weak features of this modelling approach that should be developed by further research. Finally, we suggest that SSFs could be integrated with statespace models to classify behavioural states when estimating SSFs.
Keywords
Step Selection Function SSF Resource Selection Function RSF Resource Selection Probability Function RSPF GPS telemetry Statespace model Broken stick model Habitat selection Geographic Information System GIS Remote sensing Individual modellingIntroduction
Step selection functions, SSFs – statistical models of landscape effects on movement probability
Quantifying movement using SSFs
Recent progress in positioning technology has facilitated the collection of large amounts of spatial data on animals. This has led to new opportunities to investigate resource selection by animals [1, 2], but also new challenges related to the development of proper tools for the analysis of these large amounts of information [3–5]. Resource Selection Functions (RSFs) and Resource Selection Probability Functions (RSPFs) are routinely used to model habitat selection by animals using data from Very High Frequency (VHF) and Global Positioning System (GPS) locations [6–9]. A RS(P)F is defined as any statistical model deployed to estimate the relative probability of selecting a resource unit versus alternative possible resource units [6]. Satellite telemetry allows collection of accurate relocations less than 1 minute apart [10]. Spatial data collected at such high frequency open new scenarios because they contain important information about behaviour and decisions made by animals while moving through the environment [11]. Studies using such finescale data and dealing with animal movement and resource selection can be used to answer fundamental ecological questions related to species distributions and diversity [6, 11–13], home range formation [14], and can result in important management tools for identifying movement corridors [15], key habitats [16], and responses to disturbance [17].
which corresponds to f_{u}/f_{a} for any x. To avoid misconception, selection is clearly based on used and available resource units, and not on used and unused ones. Compared to a RSF, a RSPF yields the actual probability that an available resource unit is selected and can be estimated using weighted distribution theory [18].
The aim of this paper is to review the SSF modelling approach, its applications and developments. In this first section, we clarify principal aspects of the technique. In the second section, we discuss the decisions practitioners’ face when using SSFs. In the final sections, we identify aspects of SSFs that should see further development.
Review
Features of stepselection functions
Here we briefly introduce main features of stepselection functions that will be fully discussed in later sections of this review.
Fix rate
Review of studies that used step selection functions to model landscape effects on movement probability
Study species  Fixrate  # random steps  Lengths and turning angles of random steps  Modelling approach  Model validation  Ref. 

Elk (Cervus elaphus)  5hour  200  Drawn from 2 distributions established from observations of monitored individuals.  Conditional logistic regression  No  [11] 
Cougar (Puma concolor)  15min  35  Step length equal to the mean of all movement segments recorded during the same period of time. Turning angles generated at 10° increments around the starting point.  Compositional analysis  No  [22] 
Roe deer (Capreolus capreolus)  2hour and 6hour  10  Drawn from 2 distributions established from observations of monitored individuals.  Conditional logistic regression  No  [46] 
Elk (Cervus elaphus)  5hour  20  Pairs of steplengths and turning angles jointly sampled with replacement from empirical distributions.  Conditional logistic regression  No  [20] 
Moose (Alces alces)  2 hour  10  Drawn from 2 distributions established from observations of monitored individuals.  Conditional logistic regression  Yes (sensu Boyce et al. [59])  [24] 
Grizzly bear (Ursus Arctos)  4hour  20  Drawn from 2 distributions established from observations of monitored individuals considering different period of the day.  Conditional logistic regression  No  [17] 
Snowshoe Hares (Lepus americanus)  10bound segment along hare trails left on snow  2  Drawn from 2 distributions established from observations of monitored individuals.  Conditional logistic regression  No  [28] 
North Island robin (Petroica longipes)  1day  10  Single dispersal step (obtained with several 1day locations) was matched with a random walk of the same length.  Conditional logistic regression  No  [23] 
Wolf (Canis lupus)  2hour  25  Drawn from 2 distributions established from observations of monitored individuals at the seasonal scale.  Conditional logistic regression  No  [25] 
Barred Antshrike (Thammophilus doliatus); Rufousnaped Wren (Campylorhynchus rufinucha)  15min  20  Drawn from 2 distributions established from observations of monitored individuals.  Conditional logistic regression  No  [47] 
Moose (Alces alces)  2hour  2  Random turning angle (circular distribution). Random step length lower than the 99% quantile of the observed step lengths.  Conditional logistic regression  No  [64] 
Moose (Alces alces)  1hour  5  Drawn from 2 distributions established from observations of monitored individuals at the seasonal scale.  Conditional logistic regression  Yes (sensu Boyce et al. [59])  [26] 
Grizzly bear (Ursus arctos)  1 hour  20  Drawn from 2 distributions established from observations of monitored individuals.  Conditional logistic regression (individual modelling)  No  [27] 
Lynx (Lynx canadensis)  30min  5  Step length and turning angle data drawn from movement paths to distinguish activity bouts from resting bouts (i.e. clusters of GPS locations).  Conditional logistic regression (individual modelling)  Yes (sensu Boyce et al. [59])  [16] 
Random steps
Fortin et al. [11] defined random steps from two distributions established from observation of step lengths and turning angles of monitored individuals. Later researchers using SSFs (Table 1) limited the distributions of observed length and turning angles in an attempt to select random steps matching used steps depending on season [16, 24–26], time of day [17, 22, 27], or behaviour [16, 23, 24]. Selection of length and turning angle for random steps is likely the most critical aspect of SSFs that needs to be further developed by future research (discussed in “Choosing the appropriate scale & Calculating available steps”).
Number of random steps
Studies deploying SSFs have used various numbers of random steps matched with used steps (Table 1), ranging from 2 [28] to 200 [11] (discussed in “Choosing the number of random steps”).
Predictor covariates
Predictor covariates recorded for both used and random steps may be assessed differently depending on the research question and/or the behaviour of the species. A thorough understanding of the ecology of the species and data exploration are necessary to evaluate which attributes of the environment should be considered to explain spatial behaviours. Also, special care should be given to predictor covariates that vary both in space and time. Habitats are measured either as categorical variables such as vegetation type [11], continuous variables such as terrain ruggedness or canopy cover [11, 24], distance measures such as linear distance to roads [17, 25], or variables converted into other types of measures, e.g., resistance values [23] (discussed in “Measuring environmental covariates, along or at endpoints of steps”).
User decisions
Choosing the appropriate scale
SSFs can be used to analyse resource selection from the second order of selection (home ranges in the landscape by monitoring dispersing individuals) [23] – to third or fourth order selection – e.g., patches within home ranges and food items within patches [29]. Both temporal and spatial scales are fundamental when modelling resource selection by animals [7], and understanding their effects is key in resource selection studies [30]. Spatial studies are strictly limited by the resolution and spatiotemporal extent of data, and it is possible to include predictor covariates measured at different scales [7]. The appropriate spatial extent in resource selection analyses depends on the research question and on the knowledge of the ecology of the target species [7, 31]. The scale needs to be fine enough to capture the ecological process or behaviour of interest, and have sufficient extent to observe the entire process or behaviour and not just a part of it. Habitatuse patterns can vary daily [32], seasonally [33], and across years [34], and the temporal extent of the analysis could be set accordingly. Boyce [7] suggested selecting the best scale by comparing alternative models, i.e., each model built using different spatial or temporal scales, by how well they predict patterns of use of the landscape. When the aim is to detect factors that limit species distributions across scales of space, multiscale RSF modelling is strongly recommended [35]. Some processes such as predation and dispersal may consist of several processes that take place at different scales and can be depicted by RSFs estimated at multiple scales [8, 23, 36]. An example could be predator avoidance by prey that may consist of general avoidance of more risky habitats, direct avoidance of predators, or certain defence or flight strategies.
The spatial grain or resolution of spatial covariates is crucial, and spatial heterogeneity occurring at fine spatial scales can be obliterated if the resolution or grain size is too large [7, 37]. Selecting the size of sample units can be arbitrary and problematic, e.g., when one assigns to both used and available resource units a measure of road density estimated in areas of 1 ha, 1 km^{2}, and 10 km^{2}. Also in these cases, alternative models might be built with covariates recorded at different spatial scales and then evaluated using metrics such as the Akaike Information Criterion (AIC) [7]. If spatial data are too fine scaled, selection that takes place on a larger scale might be difficult to detect. Also, there is a temporal aspect to some spatial covariates (e.g., vegetation productivity in a given pixel of the landscape), and both sampling and model building must accommodate spatial covariates varying in time [38].
Calculating available steps
Because SSFs compare use versus availability, the methods for generating available steps are crucial. Random steps can be generated either from empirical or parametric distributions [20], or possibly simulated within the framework of movement models (see “New directions for developing SSFs” for further discussion).
Relationship between step lengths and turning angles along movement path recorded for cougars and elk
Species  Fixrate  Mean r^{2}  Max r^{2}  N  Method  Sign of the relationship  Source 

Cougar^{1}  3hour  0.11  0.16  4  Linear regression^{4}    Banfield et al., unpublished data 
Cougar^{1}  15min  0.17  0.22  7  Linear regression^{4}    Banfield et al., unpublished data 
Elk^{2}  5hour  NA  < 0.03  11  Correlation  NA  [11] 
Elk^{3}  2hour  0.02  0.07  73  Linear regression^{4}    Thurfjell et al., unpublished data 
Some researchers have instead chosen to sample available locations based on parametric distributions [20]. This assumes that animals make their movement choices based on the distribution used. A uniform circular distribution for the angle would for example assume animals have knowledge of everything within the distance of a step in all directions. Different choices on how to select step length and turning angle will affect the analysis or quantification of selection. Forester et al. [20] showed that less realistic sampling is more biased and that inclusion of step length as a predictor covariate reduces this bias, therefore recommending that step length is always included. We believe that striving for the strongest selection coefficients may not always be the answer to biologically relevant questions. The results that come out of realistic distributions, i.e., paired turning angles and step lengths or a more realistic parametric distribution might reflect the choices made by the animals better [20], even if the selection coefficients are weaker. For future studies we therefore recommend that the correlation between step length and turning angle be estimated before fitting the SSF. If the correlation is high, as might be the case with high fix rate or predators patrolling the environment (Table 2), step length and turning angle should be drawn in pairs [20].
Choosing the number of random steps
A small number of available samples can influence coefficient estimates potentially causing misinterpretations of habitat selection patterns [45]. However, this is not a concern in resource selection analyses using conditional regression approaches, such as for SSFs, for which the number of available samples (i.e., random steps) can be low with no effect on parameter estimation. Fortin et al. [11] used 200 random steps because their research question was to detect selection for rare habitats; however, such a large number of available random steps is generally not needed to estimate a SSF [45]. If sample size is relatively large, a large number of random steps can make the size of the database excessive, resulting in computational limitations imposed by computer power and processing time. Because most datasets generated by GPS radiotelemetry have a large number of locations per animal, often thousands, we suggest that for most cases a low number or even one random step per used step could be sufficient [45].
Measuring environmental covariates, along or at endpoints of steps
Steps can be characterised by the lines between locations, the average of continuous variables along the step [11], extreme values of continuous variables along the step [11], the proportion of habitats along the step [11], or with habitats measured at intervals along the step [46]. Another way to characterise steps is by the environmental features of the endpoint of the step [11, 17, 47]. Buffers also can be applied to steps or endpoints and covariates measured within those buffers [22, 46].
In most studies largescale maps, remote sensing or satellite imagery with low resolution are used as a source of environmental variables for obvious practical reasons and limited budgets, especially when target species are relocated across large regions. To answer more finescaled questions however, these data layers may not have the necessary resolution [48]. Modern realtime GPS radiotracking allows frequent downloads of data which in turn can be analysed in SSFs throughout the study. This enables researchers to collect field data from real and random steps by visiting them and measuring, e.g., biomass, vegetation species composition, etc. (close in time to avoid seasonal changes in environmental covariates). Care must be taken not to disturb radiocollared individuals during data collection because this might obviously skew the results.
Statistical tools for SSFs
where β _{ 1 } to β _{ p } are coefficients estimated by conditional logistic regression for associated covariates x _{1} to x _{ p }, respectively [11]. Steps with a higher SSF score w( x ) have a higher likelihood of being chosen by the tracked animal. For two normal distributions (i.e., distributions of available and used resources), the exponential model provides the correct form of the RSF, but for other distributions, logistic or probit models might best fit the data (see [9]).
Almost all studies to date have built SSFs using conditional logistic regression (Table 1), with only a few exceptions (e.g., compositional analysis [22]). Duchesne et al. [50] showed the importance of using mixed conditional logistic regression in matched useavailable habitat selection designs. Specifically, Duchesne et al. [50] showed how mixed conditional logistic regression could be used in the presence of amongindividual heterogeneity in selection, and when the assumption of independence from irrelevant alternatives (IIA, [51]) is violated. Despite their suggestions, since their publication no studies to date have used mixed conditional logistic regression to model SSF  but see Gillies et al. [47] and Forester et al. [20] who took into account amongindividual variation. This could be related to the limited availability of software for calculating mixed conditional regression: this can be done in Matlab [50] or in R [52] by i) doing a reparameterization of a lmer (linear mixed model lmer, lme4 package) to a conditional model, i.e., a model with no intercept where the variables are expressed as the difference between the paired used and available, ii) using the coxme function (coxme package) by setting time equal to 1 for all data points, or using the mclogit package.
An alternative to mixedmodelling is individual modelling, as done by Squires et al. [16] and Northrup et al. [27] for SSFs. Individual differences in behaviour, including habitat choices, have become a key target of research with important ramifications for ecology and evolution [53]. Resource selection can have strong interindividual variability within a population in response to several factors [54]. With abundant relocations, GPS units generate enough data to fit individual models.
A method for fitting individual resourceselection models, and to obtain models for inference at the population level, is the twostage modelling approach [4]. The first stage involves fitting, ranking [55] and averaging a priori models [4, 56, 57] separately for individual animals. The second stage is to average regression coefficients across individuals to estimate populationlevel selection [57]. This can be done either manually or using routines provided by the TwoStepClogit package in R. Fieberg et al. [4] recommend the twostage approach as a practical method to account for correlation within individuals in habitatselection studies.
With increasing fix rate, positional data of animals also becomes increasingly autocorrelated in time [58]. This will not affect the beta estimates but will result in underestimated variance for these estimates [7]. Fortin et al. [11] dealt with temporal autocorrelation by calculating and correcting the confidence intervals based on rarefied data where locations are no longer correlated. Another way to account for temporal autocorrelation is to include an autocorrelative structure [26] or the temporal variables as predictor covariates. Often the autocorrelated nature of the landscape explains the autocorrelation in the data and one can evaluate this by fitting the model and examining the residuals for autocorrelation. In many instances we have found that the residuals are not autocorrelated.
Before applying such models in management and conservation plans [59], evaluation of model performance is a necessary but commonly neglected procedure in resourceselection studies, and this applies to SSF studies as well (Table 1). Although a number of methods are available for presenceabsence data (e.g., [60, 61]), these evaluation approaches are not appropriate for presenceavailable designs because presence sites are derived from the distribution of available sites [59, 62, 63]. A kfold crossvalidation method should be appropriate for SSF designs and could be used to verify the accuracy of predictions such as previously done for RSFs [59, 63]. We encourage further research to develop new evaluation methods to ensure that predictions from SSFs models are robust before using them to plan conservation actions.
Applications of SSFs in ecology and conservation
Predictions of SSF portrayed in the GIS environment are probably one of the most promising tools in ecology, management and conservation. SSFs are a powerful technique for identifying the habitats that animals choose to move through, expanding our knowledge of animal decisionmaking at finer spatial and temporal scales. This approach has the potential to be widely used to understand animal behaviour within humandominated landscapes, e.g. to assess the effect of human disturbance on wildlife [64, 65], to predict movement corridors in humandominated landscapes [16, 17, 23], and to plan management and conservation strategies accordingly. SSFs are particularly useful for understanding the effects of humanrelated features such as roads and associated vehicle traffic [11, 17, 27]), the use by wildlife of manmade linear features [25], and relationships between temporal patterns in human activity and consequent disruption of animal behavioural patterns [64, 65]. SSFs combined with costdistance modelling can assess functional landscape connectivity [23] and dispersal behaviour [17] by considering entire dispersal events and a random walk of similar properties as the alternative step(s) [23]. Squires et al. [16] used RSFs to find potential animal home ranges, and then SSFs and leastcostpath models to define movement corridors between the potential home ranges by mapping SSFs. The map identified dispersal corridors for Canada lynx (Lynx canadensis) made by plotting the SSFvalues, rescaled to relative probability of use between 0 and 1, excluding the 5% highest and lowest values to remove outliers [16]. This is a promising development of the technique, with great potential for management and conservation planning. Parameters of SSFs could be artificially modified to create scenarios within GIS framework for conservation plans, e.g., by artificially increasing road density or deforestation and to verify how habitat selection predicted by SSFs changes.
New directions for developing SSFs
There are several other potential ways in which steps could be calculated for assessing functional landscape connectivity. For example spatial graphtheoretic approaches such as Brownian bridges or circuit theory might be used to define steps instead of the straight lines between observations, and could be used for generating random steps as well [43]. Brokenstick models [66], transition equations [44], and statespace models SSMs [67] are approaches taking into account that different behaviours shape movement parameters. These approaches can be integrated with SSF designs to develop new resourceselection models within the same framework. Specifically, they could be excellent methods for defining the length and turning angle of random steps depending on the state or behaviour of the animal. This is likely the most critical point of SSF models, because it is clear that selection patterns depend on how we choose available resources.
In brokenstick models, each step can be assigned to a behaviour such as intrapatch foraging, interpatch movement or migration [66]. With transition equations, the possibility of an animal changing behavioural state from one to another is calculated [44]. In statespace models, the previous step of the animal determines the likelihood of the next step, based on its location and on the properties of previous steps, usually via a Markov chain [67]. Statespace models also have the advantage of accounting for the observational/locational error in the observation model [67]. SSFs can be improved by combining these models in several ways. A brokenstick model can objectively distinguish different types of behaviours [66], and the distribution of random step lengths and turning angles can be drawn within those behaviours [16]. This could account for the correlation between step length and turning angle because they would be drawn from populations of observations within each behaviour, and one SSF could be produced per behaviour (see [16] for an example where a single behaviour was tested).
Another approach would be to estimate the random steps within the framework of the statespace model [67] by estimating the random steps based on previous steps to determine the behaviour distribution (D_{n}) from which the random steps should be drawn. If a vector of distributions (D) represent one behaviour each, and a number of transition equations (T) represents the chance of an animal going from one behavioural state to another given a number, n, of previous locations (u _{ t1}…u _{ tn }). The function of available units could look like f(a _{ u }(t1, tn)_{,} D,T). This would associate each step with random steps accounting for the possibilities that the animal continues with its current behaviour or changes to a new behaviour [44]. In this way each position is associated with the choices the animal is faced with. An example would be a lion (Panthera leo) that has just eaten, as shown by the properties of the steps. The probability for the following steps to be searching for prey is low and for resting and digesting is high. As the time from the feeding increase, the probability of steps belonging to a search behaviour increases because the lion will get hungrier.
Conclusions
SSFs have a distinct advantage over regular RSFs because they include the serial nature of animal relocations and can associate parameters of movement rules with landscape features, and they can model the choices actually presented to the animal as it moves through the landscape [15]. However, as strong as the tool might be, there are several pitfalls that must be avoided in order to accurately capture behaviours and ecological processes. The properties and scale (fix rate) of steps (lines or endpoints), and the habitat measurements that are taken must be able to capture the relevant behavioural processes, and we recommend that analyses are carried out after thorough data exploration and with good knowledge of the behaviour and ecology of the target species.
So far few studies have taken into account the differences among individual animals. Mixed conditional models are one way to deal with this source of variability, especially if the sample size is moderate. However, if the data are sufficient to allow it, we believe individual modelling has more advantages, is simpler to carry out in conventional software, and has the potential to capture ecological processes that are considered random variation in conditional mixedeffects models.
A fix rate that has both the resolution and temporal extent to capture the studied behaviours is necessary, and we strongly recommend that researchers start by considering which scale they are interested in and at which scale they will access the covariate data. Then they can try with a fixrate that is slightly high and do several preliminary analyses with rarefied data. Then they could reset the fix rate to balance the trade off between a high fix rate and a long battery life of the GPS unit. As fix rate increases, the probability of autocorrelation between step length and turning angle will increase, and the influence of positional errors increase. This needs to be tested before further analysis is carried out; we recommend either to include this correlation in the process of selecting random steps or to assign behaviours to each step as per the brokenstick model and estimate one SSF per behaviour. In the future we believe that these processes could be integrated by using SSMs in the process of selecting random steps and thus to estimate SSFs where selection of a movement path depends on the positional locations themselves and the state of the animal.
Abbreviations
 SSF:

Step selection function
 RSF:

Resource selection function
 RSPF:

Resource selection probability function
 VHF:

Very high frequency
 GPS:

Global positioning system
 GIS:

Geographic information system
 SSM:

State space model.
Declarations
Funding
We thank the Natural Sciences and Engineering Research Council of Canada (NSERC –CRD grants), Alberta Conservation Association (ACA – Grant Eligible Conservation Fund), Shell Canada, and Carl Tryggers Foundation for Scientific Research (Swedish Postdoc grant) for funding and support. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. We thank three anonymous reviewers for thorough reviews that greatly improved the quality of this manuscript and Joshua Killeen for revising the English.
Authors’ Affiliations
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