Animal Population Spatial Analysis - The Elk of Bannf Nationa Park

Introduction

What is Spatial Ecology and Why It Matters

Spatial ecology examines how ecological processes are shaped by spatial patterns and environmental variation. It helps explain species distributions, movement behaviour, and ecosystem functions (Fletcher 2018). The field integrates both endogenous processes—such as dispersal, population growth, and behaviour—and exogenous factors like habitat structure and human disturbance (Ovaskainen et al. 2017; Massol et al. 2011). Together, these dynamics shape how species interact with their environment across spatial and temporal scales (Nathan et al. 2008).
Technological advances such as GPS telemetry, remote sensing, and spatial analysis tools (e.g., RStudio and QGIS) have allowed ecologists to collect and analyse high-resolution spatial data. These tools support a Lagrangian approach, allowing individual-based movement analysis at fine spatial and temporal scales (Nathan et al. 2008). As a result, ecologists can estimate home ranges, evaluate resource selection, identify behavioural responses to environmental stimuli, and model movement patterns over time with exceptional precision (Seidel et al. 2018).
Spatial ecology is essential for conservation management. It provides key insights into species’ space use and habitat needs, helps identify and protect movement corridors in fragmented landscapes, and supports adaptive responses to anthropogenic and climate-driven pressures. Through understanding the dynamics of habitat selection, home range variability, and movement behaviour, conservation decisions can be based on robust ecological evidence.

Context and Aims

Elk (Cervus elaphus), also known as wapiti in North America, are large-bodied, social ungulates (hoofed mammal) that are native to forested and mountainous regions of the Northern Hemisphere. In North America they are primarily found in the Rocky Mountains. In our study area, in and around Banff National Park, Alberta, Canada, Cervus elaphus serves as a keystone species influencing plan communities, predator-prey dynamics, and nutrient cycling (Hobbs 2006; Ripple and Larsen 2001).
Cervus elaphus, from here on referred to as “elk”, have strong seasonal patterns driven by resource availability, climate, and risk avoidance. In their mountainous habitats they usually migrate between lower-elevation winter ranges and higher-elevation summer ranges (Hebblewhite, Merrill, and McDermid 2008). Elk prefer open meadows for foraging and forested areas for refuge and for resting and rutting (Mark S. Boyce et al. 2003; Ciuti, Muhly, et al. 2012).
Elk exhibit crepuscular activity (active during dawn and dusk), but studies have shown that they easily shift their behavioural patterns to avoid areas of high human use and activity (Ciuti, Muhly, et al. 2012). In areas with active elk hunting, such as our study area, elk have been shown to change their use of space and movement behaviour and some populations have shown to avoid humans and have selection for wariness, especially among females (Thurfjell, Ciuti, and Boyce 2017a).
This study uses spatial ecology tools to assess movement data from 16 elk in and around Banff National Park, Alberta, Canada. This elk population is exposed to seasonal environmental change and anthropogenic pressure, especially from hunting in autumn. Understanding their spatial ecology under such pressures is critical for developing effective conservation strategies.
The study aims to analyse elk spatial behaviour using a combination of home range estimation, resource selection modelling, and movement behaviour analysis. The research applies multiple spatial methodologies—including Minimum Convex Polygon (MCP), Kernel Density Estimation (KDE), Autocorrelated KDE (AKDE), Resource Selection Functions (RSFs), Step Selection Functions (SSFs), and Hidden Markov Models (HMMs)—to examine how elk respond to seasonal variation, habitat structure, and anthropogenic influence.

The main research questions being explored in this study:

• RQ1: Home Range Estimation – How do elk home range sizes vary across individuals and seasons, and how do different estimation methods (MCP, KDE, AKDE) influence the interpretation of spatial usage under hunting pressure?

• RQ2: Resource Selection – How does elk (Cervus elaphus) resource selection vary across seasons, and are these patterns influenced by sex and age under hunting pressure?

• RQ3: Movement Behaviour – How does elk movement behaviour vary across seasons and landscapes, and to what extent do step-based movement patterns and behavioural state transitions reflect responses to environmental and anthropogenic pressures?

Objectives

• Estimate seasonal home range sizes using MCP, KDE, and AKDE, and evaluate inter-individual and seasonal variation

• Model habitat selection using RSFs, considering terrain, vegetation, roads, and demographic variables

• Characterise movement using SSFs and HMMs, exploring behavioural changes under hunting pressure

• Integrate methods to inform conservation strategies for elk movement, habitat, and space-use models to inform conservation strategies for elk and other large herbivores

Methods

Home Range Estimation

Spatial Use vs Home Range:

Home range literature differentiates between space use and home range, both of which help to understand how animals interact with their environment:

Space Use:

• Describes where an animal spends its time, often visualised through utilisation distributions (UDs) or density maps. Spatial use is usually analysed over shorter time periods (weeks or days) and is used for assessing habitat use and behavioural responses to both endo- (dispersal, population growth, and behaviour) and exogenous factors (habitat and human disturbance).

Home Range:

• Refers to the area an animal uses to satisfy its “life-history” requirements (foraging, resting, breeding) over longer periods, such as seasons or a year (Burt 1943).

Estimation Methods:

• MCP: Encloses all points in the smallest convex polygon around all known locations (Mohr 1947). However, it is very sensitive to outliers, and does not account for physical boundaries, such as lakes, rivers, and inhabitable areas within the landscape, and can be ineffective at calculating home range estimations with small sample sizes (Noonan et al. 2019; Mukomberanwa et al. 2024). Regardless of these limitations, MCP was still used a baseline data set for comparison between the other methods.
  
• KDE: Uses density of locations to estimate a utilisation distribution, which is the probability of where an animal is to be found within the space based on the pattern of its GPS locations. It is useful for identifying core use areas (Worton 1989). assumes that the GPS locations are independent and identically distributed (IID), whereas the ecological reality is that the data is usually nearly always autocorrelated (C. H. Fleming et al. 2015).

Tip

It is best to think of autocorrelation as “momentum”. The animals don’t teleport from one location to the next. They move gradually, so their recent locations usually influence where they go next! The more clustered the locations are in space and time, the more similar they tend to be! (Silva et al. 2021)

• AKDE: Improves KDE by accounting for the autocorrelation in the data. This autocorrelation within KDE estimates is what causes most estimates to be biased and underestimate home ranges (Hansteen, Andreassen, and Ims 1997). It better represents true home ranges from irregularly sampled GPS data (C. H. Fleming et al. 2015; Silva et al. 2021).

Important

AKDE was chosen over dBBMM due to elk data containing inconsistent fix intervals (~120 minutes) and anomalies, which limited dBBMM performance. Hansteen et al., (Hansteen, Andreassen, and Ims 1997) explains that with increasing time intervals the degree of autocorrelation will decrease as the sample size decreases.

Implementation

Telemetry data was cleaned, seasonally split (pre-hunting and hunting), and analysed by individuals. MCP, KDE, and AKDE home ranges were calculated using R packages adehabitatHR and ctmm, with contours at 50%, 75%, and 95% to represent core to total space use. AKDE, which accounts for autocorrelation and sampling frequency (Christen H. Fleming and Calabrese 2017), provided refined seasonal range estimates. This multi-method approach enabled comparison of spatial responses to hunting pressure across individuals.

Note

You can explore the different methods of home range methodologies and their outputs in Figure 1

Figure 1: Interactive Home Range Method Map.

Resource Selection Function (RSF)

What is RSF?

A Resource Selection Function (RSF) models the likelihood of an animal selecting a resource (e.g., habitat type) by comparing used GPS locations with random available ones that were not used (D. H. Johnson 1980). Fitted using binomial generalized linear model (GLM) with logistic regression, RSFs relate selection to both abiotic and biotic variables (Mark S. Boyce et al. 2002; C. J. Johnson et al. 2006). Individual ID is included as a random effect to avoid pseudoreplication (the same animal’s data being used more than once). and account for demographic variation individuals (e.g., sex, age) [Gillies2006].

• Used points: GPS telemetry locations from each elk
  
• Available points: Randomly generated within a buffered 100% MCP representing accessible habitat

Covariates used in the models:

• Land cover class (ESA WorldCover Consortium 2021)
• Elevation (m) (extracted using the elevatr package)
• Ruggedness (terrain roughness calculated using terra::terrain())
• Patch area (derived using landscapemetrics) (Hesselbarth et al. 2019)
• Tree cover (%) (Hansen et al. 2013)
• Distance to roads (m) (calculated as Euclidean distance to nearest road)
• Season, sex, and age class as fixed effects

Model evaluation:

• AIC (Akaike Information Criterion) was used to compare model fit and select top models
• AUC (Area Under the Curve) was calculated to assess model predictive performance

Important

RSF models were interpreted using log-odds coefficients and visualised with confidence intervals. These results were mapped and compared across seasons to understand how elk respond to hunting-related disturbance.

Step Selection Function (SSF)

What is SSF?

Step Selection Functions (SSFs) analyse how animals make movement decisions by comparing each observed step to a set of randomly generated alternative steps the animal could have taken (Fortin et al. 2005; Thurfjell, Ciuti, and Boyce 2014). This approach links movement paths to environmental factors, allowing interpretation on how features like habitat type, terrain, and human presence influence behaviour. In this study, SSFs were fitted using the amt package, incorporating covariates such as elevation, distance to roads, step length, and turning angle. Mixed-effects logistic regression models included individual ID as a random intercept, with model performance assessed using AIC and AUC.

Implementation

Using the amt package, SSFs were fit using GPS data sampled every 2 hours. Covariates included those in RSFs, also:

• Step Length (log-transformed)
• Turning Angle (cosine-transformed)

Models were fit using glmer() with individual elk ID included as a random intercept to account for variation between animals. A second random effect, representing unique step pairings, was initially included but later removed because it showed no variation and contributed nothing to the model. Model fit was evaluated using AIC and AUC metrics.

Hidden Markov Models (HMMs)

What is HMM?

Hidden Markov Models (HMMs) infer hidden behavioural states from movement data (e.g., GPS tracks) by modelling transitions based on step length and turning angle patterns(McClintock and Michelot 2018). Using the momentuHMM package, elk movements were classified into two states: ‘Encamped’ (slow, winding movement) and ‘Travelling’ (longer, directed steps). These models computed state durations and transitions across seasons.

Tip

HMMs are commonly used in movement ecology to uncover hidden behaviour — like resting or foraging — based on how an animal moves through space (Seidel et al. 2018).

Implementation

Using momentuHMM, two-state models were fitted:

• State 1: Encamped (slow, tortuous movement)
• State 2: Travelling (longer, straighter steps)

Important

Step lengths >1000 m were filtered out to improve model stability. Initial parameters were selected based on distribution summaries (see Figure 2 & Figure 3)

Figure 2: Raw step length distribution before filtering

Figure 3: Step Length Distribution after filtering >1000m

Results

RQ1: Home Range Estimation

Home range sizes varied across individuals and seasons. AKDE, which adjusts for autocorrelation, showed distinct behavioural responses to hunting compared to MCP and KDE, which tended to overestimate space use (@fig-home_range)

• E004: Range contracted from 167 ha (Pre-Hunting) to 127 ha (Hunting), suggesting restricted movement under pressure.

• E007: Expanded dramatically from 39 ha to 721 ha, possibly indicating displacement or increased exploratory movement.

• E009: Maintained a small, consistent range (<15 ha), implying stable behaviour.

Figure 4

AKDE estimates were derived using pHREML, providing confidence intervals and more realistic spatial estimates than MCP or KDE.

Home Range Comparison for Selected Elk (AKDE, KDE, MCP)
Elk ID	AKDE Pre-Hunting (ha)	AKDE Hunting (ha)	KDE Pre-Hunting (ha)	KDE Hunting (ha)	MCP Pre-Hunting (ha)	MCP Hunting (ha)
E004	166.7	126.7	9647.4	8092.3	4926.8	5043.2
E007	39.3	720.6	3427.4	25692.3	2127.6	15788.9
E009	9.6	397.6	954.8	21731.2	692.8	14169.3

RQ2: Resource Selection (RSF Models)

Over 20 RSF models were evaluated using AIC and AUC (see Table 1) Top models revealed consistent elevation and tree cover selection, with behavioural changes under hunting pressure.

Table 1: Table of Model Ranking by AIC and AUC

	Model Performance Metrics
Model	AIC	AUC	Rank	Performance
H1.4 Grassland x Season x Elevation	61611.08	0.748	1	Fair (>0.7)
H4.4 Road x Season x Elevation	61683.41	0.744	2	Fair (>0.7)
H3.5 Age x Season x Elevation	62092.04	0.738	3	Fair (>0.7)
H2.4 Sex Season x Elevation	62174.82	0.739	4	Fair (>0.7)
H4.3 Sex and Road Interaction	65161.34	0.708	5	Fair (>0.7)
H1.2 Patch x Season	65535.99	0.698	6	Poor (>0.6)
H1.3 Grassland x Season	65556.16	0.698	7	Poor (>0.6)
H4.2 Road and Season Interaction	65784.93	0.692	8	Poor (>0.6)
H3.3 Age and Season Interaction + Road	65901.59	0.694	9	Poor (>0.6)
H2.3 Sex And Season Interaction + Elevation	65925.00	0.693	10	Poor (>0.6)
H3.4 Age and Ruiggedness Interaction	66312.27	0.682	11	Poor (>0.6)
H3.2 Age and Season Interaction	66316.37	0.683	12	Poor (>0.6)
H2.2 Sex And Season Interaction	66343.86	0.681	13	Poor (>0.6)
H1.1 Season Behaviour	69500.86	0.639	14	Poor (>0.6)
H2.1 Sex Based Differences	70034.05	0.621	15	Poor (>0.6)
H3.1 Age Class Differences	70181.04	0.619	16	Poor (>0.6)
H4.1 Anthropogenic Avoidance	70901.69	0.602	17	Poor (>0.6)

Habitat Preferences:

• Elevation: Strong positive effect across models (β ≈ 0.31–0.40).

• Tree Cover: Strongest selection driver (β ≈ 2.6–2.7).

• Grassland: Selected most during Pre-Hunting, reduced during Post-Hunting when interacted with elevation (β = -0.217 in H1.4).

• Patch Area: Negative across models (e.g., β = -0.17), suggesting elk avoid small or fragmented patches.

Seasonal and Demographic Effects:

• Season: Selection scores were lower during hunting periods.

• Sex: Males selected less for elevation (β = -0.23) and had lower overall selection probabilities (β = -0.60).

• Age: Juveniles showed weaker selection (β = -0.48) and significant seasonal interactions.

Anthropogenic Features:

• Roads: Unexpected positive effect (β = 0.13–0.21), possibly reflecting constrained landscapes or habituation. A significant season × elevation × road interaction (H4.4) suggested complex risk trade-offs.

RQ3: Movement Behaviour – Step Selection Function (SSF)

We fitted a suite of SSF models grouped into four hypothesis categories (H1–H4), each exploring the effects of seasonal dynamics, sex, age, and landscape context on elk movement decisions.

Across all models, AUC values ranged from 0.511 to 0.548, indicating poor model performance. The top-performing models were:

• Models including land cover and patch metrics outperformed terrain-only models (see Table 3).

  Table 2: AUC Summary for SSF Models

  Model	AUC
  H1_1_season_patch	0.540
  H1_2_complex_season	0.548
  H1_3_season_ruggedness	0.511
  H1_4_season_logsl	0.548
  H1_5_season_costa	0.538
  H1_6_season_woodland	0.541
  H2_1_treecov_sex_season	0.538
  H2_2_complex_sex	0.547
  H2_3_road_sex_season	0.511
  H3_1_patch_area_age	0.534
  H3_2_road_age_season	0.535
  H3_3_complex_age_road	0.547
  H4_1_habitat	0.541
  H4_2_hab_mov	0.542
  H4_3_road_season	0.511
  H4_4_elev_season	0.511

• Seasonal variation (H1) was the strongest driver:

  • Elk selected tree cover and larger patches during Pre-Hunting.

  • Selection declined in Post-Hunting (see Figure 5).

Figure 5. Coefficient plots of H1 Models

• Sex × Season (H2) and Age × Season (H3) models showed weak interaction effects:

  • Most sex and age coefficients overlapped zero (see Figure 6, Figure 7).

    

    Figure 6. Coefficient plots of H2 Models

    

    Figure 7. Coefficient plots of all H3 models

• Landscape × Season (H4) models confirmed:

  • Consistent avoidance of built-up, bare ground, and water.

  • Positive selection for woodland and tree cover across seasons (see Figure 8).

    

    Figure 8. Coefficient plots of H4 models

• Overall, elk responded most strongly to seasonal changes in vegetation and land cover, with subtler variation by sex and age.

Movement Dynamics:

• Turning Angle: Significant (β = -0.042, p < 0.001), indicating straighter movement in high-risk conditions.

• Step Length: Not significant, possibly due to high individual variability

RQ3: Movement Behaviour – Hidden Markov Models (HMMs)

HMMs revealed distinct movement states and behavioural shifts (Figure 9):

• State 1 (Encamped): Short, slow steps with high turning frequency.

• State 2 (Traveling): Long, directed steps.

Figure 5: Step Length Distribution by State

Model Refinement:

• The initial model (with full step length range) classified nearly all fixes as travelling.

• Filtering out steps >1000 m improved classification, allowing both states to emerge clearly.

State Parameters (Filtered Model):

• Encamped: Shape = 1.53, Scale = 9.15

• Travelling: Shape = 0.83, Scale = 172.6

• Angle Concentration: Higher in travelling, suggesting directional persistence.

Covariate Effects – Model Comparison

Ten HMMs were compared using AIC:

• Best model (HMM8): ~season + sex + age

• Close contenders: HMM10 (~season * age + sex) and HMM9 (~season * sex + age)

• Baseline model (HMM1): Performed worst, confirming covariate importance

HMM Model Selection Summary
Model	AIC	Log-Likelihood	Formula	ΔAIC	Akaike Weight	Rank
HMM8	392,588.6	−196,277.3	~season + sex + age	0.0	0.754	1
HMM10	392,591.2	−196,274.6	~season * age + sex	2.6	0.208	2
HMM9	392,594.7	−196,276.4	~season * sex + age	6.1	0.036	3
HMM5	392,601.0	−196,281.5	~season * sex	12.3	0.002	4
HMM6	392,756.9	−196,359.4	~season * age	168.2	0.000	5
HMM7	392,784.0	−196,377.0	~sex * age	195.3	0.000	6
HMM3	392,798.1	−196,388.1	~sex	209.5	0.000	7
HMM4	392,872.3	−196,425.1	~age	283.6	0.000	8
HMM1	393,200.0	−196,591.0	~1	611.3	0.000	9
HMM2	393,201.9	−196,588.0	~season	613.3	0.000	10

Discussion

RQ1: Home Range Analysis and Model Performance

AKDE analysis revealed large individual variation in home range size across seasons. Some elk contracted their ranges (e.g., E004), while others expanded them (e.g., E007). These divergent strategies likely reflect different responses to risk—either reducing exposure or increasing mobility (Benz et al. 2016). AKDE clearly outperformed MCP and KDE by correcting for autocorrelation and irregular sampling (Christen H. Fleming and Calabrese 2017), providing more realistic estimates.

RQ2: Resource Selection under Hunting Pressure

RSF models showed that elk habitat selection varied seasonally and was influenced by sex and age. Elk consistently selected elevated, forested areas, likely using them as refuge from disturbance, as found by Ciuti et al, (Ciuti, Northrup, et al. 2012). Tree cover was the strongest predictor (β ≈ 2.6), and elevation was selected across models. Grassland was preferred pre-hunting but avoided later, especially at higher elevations—possibly to avoid detection in open terrain (Paton et al. 2017).

Sex and age also shaped selection. Males avoided higher elevation pre-hunting (β = -0.60), consistent with studies showing they take more foraging risks (Thurfjell, Ciuti, and Boyce 2017b). Juveniles used less habitat overall and avoided rugged areas, suggesting inexperience (Ciuti, Northrup, et al. 2012).

Unexpectedly, roads had a positive effect on selection. This contrasts with road avoidance patterns seen in other studies (Prokopenko, Boyce, and Avgar 2017), but may reflect habitat constraints or opportunistic foraging near edges (Killeen et al., n.d.). A significant season × elevation × road interaction indicates the importance of context in interpreting anthropogenic influences.

RQ3: Movement Behaviour under Disturbance

Movement modelling (SSF and HMM) confirmed elk shift behaviour in response to hunting. SSF results showed elk strongly avoided built-up, sparse, and wetland habitats and preferred more connected patches. They also moved more directly in risky environments (cos_ta β = -0.042), supporting the idea that elk reduce exposure through straighter paths (Ciuti, Northrup, et al. 2012; Prokopenko, Boyce, and Avgar 2017).

HMMs reinforced these patterns. After excluding extreme step lengths (>1000 m), the model clearly distinguished between two behavioural states: Encamped and Traveling. Transition probabilities indicated elk spent more time travelling during hunting seasons—likely reflecting attempts to escape or bypass risk (Ensing et al. 2014) (Ensing et al., 2014). The best-fitting model (HMM8) included additive effects of season, sex, and age, showing that all three influence movement strategy. This aligns with Ciuti (Ciuti, Muhly, et al. 2012), who reported demographic and seasonal variation in behavioural plasticity under hunting pressure.

Conservation Implications

The findings highlight the importance of preserving forested and elevated areas, particularly during hunting periods. These act as key refuge habitats. The data suggests that Elk prefer roadside habitats, however this may not reflect habitat selection, but rather limited options of spatial use, especially during hunting seasons. Targeted conservation management, such as seasonal buffer zones or habitat corridors may reduce risk and promote safe movement (Benz et al. 2016).
Management plans should consider variation among individuals, as elk respond differently to disturbance. Conservation strategies that support both movement and refuge needs are likely to be more effective in landscapes with active hunting.

Limitations and Future Work

This study relied on high-frequency GPS data, but with a limited sample of 16 elk, and average 120 minute time intervals this limited sample size and fine scale analysis, leading some results to be generalised. Covariates such as NDVI, slope, and LiDAR-derived data could improve accuracy. RSF models assumed spatial independence, which can overestimate significance (Roberts et al. 2017). HMMs used only two states; future work could include foraging/resting as a third state or use integrated step selection analysis (ISSA) (Thurfjell, Ciuti, and Boyce 2014). Finally, environmental covariates were not included in HMMs due to processing constraints. Including spatial predictors in transition probabilities would improve insights to movement behaviour.

Conclusion

By combining home range estimation, habitat selection, and movement modelling, this study revealed that elk adapt behaviour and space use in response to hunting pressure. RSFs showed elk preferred forested and elevated habitats, SSFs identified avoidance of risky areas, and HMMs confirmed behavioural state shifts during hunting. AKDE gave more reliable home range estimates than traditional methods. Together, these results highlight the importance of multi-method approaches and support context-specific conservation measures—such as protecting refuge and reducing disturbance—to ensure the long-term viability of elk in hunted landscapes.

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