# Spatial decomposition of predation risk using resource selection functions: an example in a wolf–elk predator–prey system

> Is an elk in danger simply wherever wolves roam? By following wolf trails for about 1250 km in the snow around Banff National Park, researchers mapped where wolves crossed elk tracks and where elk were actually killed. Wolves mostly found elk in valley bottoms, but pine forest made elk easier to kill once found, while grasslands helped them escape.

Summary by Kersey Lawrence, Original Wisdom. Updated 9 November 2026. Page: https://www.originalwisdom.com/tracking-literature/2005-hebblewhite-merrill-spatial-decomposition-predation-risk/

## Citation and access

- **Authors:** M. Hebblewhite, E. H. Merrill and T. L. McDonald
- **Year published:** 2005
- **Journal or source:** Oikos
- **Full citation:** Hebblewhite, M., Merrill, E. H. and McDonald, T. L. 2005. Spatial decomposition of predation risk using resource selection functions: an example in a wolf–elk predator–prey system. Oikos 111(1): 101–111.
- **DOI:** 10.1111/j.0030-1299.2005.13858.x
- **Access status:** Publisher link only
- **Where to find it:** https://doi.org/10.1111/j.0030-1299.2005.13858.x

## Tags

- **Species:** Mammals > Elk; Mammals > Grey wolf
- **Region:** North America > Canada
- **Tracking:** Kill sites; Snow tracks; Tracking; Tracks; Tracks and signs identification; Trailing
- **Behaviour and ecology:** Behaviour; Habitat selection; Hunting; Predation; Predation risk
- **Methods and technology:** Akaike Information Criterion (AIC); Geographic Information System (GIS); Logistic regression; Radio telemetry; Resource selection function; Telemetry
- **Data type:** Modelling or theoretical; New field data
- **Observer qualification:** Not reported
- **Discipline:** Behaviour and ecology; Wildlife tracking
- **Year published:** 2005

## Detailed keywords

- **Species:** Studied: gray wolf (Canis lupus), the Cascade pack, and elk or wapiti (Cervus elaphus). Prey killed by wolves: 119 elk (29 adult females, 52 adult males, 7 yearlings, 9 calves and 31 of unknown female age class; these add up to 128, not 119). Named in the background and discussion but not studied: moose (Alces alces), wild turkey (Meleagris gallopavo), sparrowhawk (Accipiter nisus), redshank (Tringa totanus), caribou (Rangifer tarandus), mountain caribou, desert tortoise (Gopherus agassizii), common raven (Corvus corax) and deer (Odocoileus spp.).
- **Location and habitat:** The Cascade wolf pack territory in and next to Banff National Park (6641 km²), Alberta, Canada, on the eastern slope of the continental divide in the Canadian Rocky Mountains (1400 to 3400 m). Two main elk winter ranges (Ya Ha Tinda and Bow Valley) and several smaller ones. Closed lodgepole pine forest with riparian Engelmann spruce and willow, aspen parkland and dry grasslands at low elevations; Engelmann spruce and subalpine fir forest, willow-shrub meadows, subalpine grasslands, avalanche terrain and alpine meadows higher up. Cover types used in the models: pine, closed conifer, open conifer, avalanche path, alpine, grassland, shrub and rock/ice.
- **Topics:** predation risk; splitting predation into search, encounter and kill stages; probability of encounter and probability of death given an encounter; Holling’s functional response and Lima and Dill’s predation risk formula; predator habitat use versus true predation risk; habitat and topography effects on predation; distance to roads and trails (human access); predation risk mapping; predator–prey models; elk group size and dilution effects (discussed); caribou conservation and roads (discussed).
- **Statistics or models:** Resource selection functions (RSF, used-available design) and a resource selection probability function (RSPF, used-unused design), both fitted with logistic regression; odds ratios with 90% confidence intervals (significance at P = 0.10); model selection with Akaike’s Information Criterion corrected for small samples (AICc), Akaike weights and summed weights to rank covariates; collinearity screening with tolerance scores; standard errors clustered by individual elk; k-fold cross-validation (five folds) with Spearman rank correlation; likelihood ratio tests and Nagelkerke’s pseudo R²; predation risk surface P(k) = 1 − exp(−a·d·T) built in ArcGIS 8.2 at 30 m resolution; analyses in STATA 7.0. Inconsistencies in the paper: (1) the abstract says encounter odds were 1.3 times higher in pine and 4.1 times lower in grassland, and kill odds in pine rose by 1.2, but Table 3 gives encounter odds ratios of 1.07 for pine and 1.86 for grassland, and the Results text compares kill odds in grassland (1.34) with an encounter value of 7.65, which is the elk occurrence value in Table 3, not the encounter value; (2) the text gives the elk open conifer coefficient as 1.65, which matches the odds ratio in Table 3 (1.635) rather than a beta coefficient; (3) the kill model’s likelihood ratio P-value is 0.12 in the text and 0.07 in Table 2; (4) the paper reports 119 kills, Figure 3 shows 118, and the age classes add up to 128; (5) Table 2 sample sizes (1190 for the wolf model, 189 for the kill model) do not match 119 + 1000 and 77 + 119.
- **Data type:** New field data: winters (15 October to 15 April) 1997 to 2001, described as four winters. Also a modelling framework. Elk telemetry data were provided by Parks Canada.

## Synopsis

### 1. What they did

Predation risk is often treated as simply “where the predators are”. The authors argue that it is more than that. A predator first has to find, or encounter, its prey, and then has to succeed in killing it. Landscape features can affect these two stages differently. Building on Holling’s functional response and Lima and Dill’s formula for predation risk, they show how to map each stage separately with resource selection functions (RSF), statistical models that compare places that were used with places that were available, and then combine the two into one map of predation risk.

They tested the approach on gray wolves hunting elk in winter, in and next to Banff National Park, Alberta, Canada, from 1997 to 2001, using the Cascade wolf pack (about eight wolves). They asked two questions:

- Do the places where wolves occur differ from the places where wolves encounter and kill elk?

- At which stage of predation (search, encounter or kill) do landscape features have their greatest effect?

To answer them they collected four kinds of data:

- Search: weekly aerial locations of radio-collared wolves.

- Encounters: following wolf tracks in the snow and recording each place where wolf tracks crossed the tracks of an elk group.

- Kills: elk killed by wolves, found while snow tracking and through telemetry.

- Elk: weekly locations of radio-collared female elk, from the air or the ground.

For each data set they measured distance to roads and trails, slope, elevation, aspect and vegetation cover in a Geographic Information System (GIS). They built four models with the same six landscape features (elk, wolf search, encounter and kill), compared them, and turned the encounter and kill models into maps.

### 2. What they found

The data

- 119 wolf locations at least 24 hours apart, from six wolves.

- About 1250 km of wolf trails followed in the snow, with 77 elk groups encountered.

- 119 elk killed by wolves, more adult males (52) than any other class.

- 4890 locations from 104 collared adult female elk.

- After an encounter, elk were chased an average of 262 m (range 10 to 1700 m) before being killed.

The models

- Six features stayed in the best models for every stage: distance to roads and trails, slope, elevation, grassland, pine and open conifer.

- The elk, wolf and encounter models fitted the data well. The kill model fitted poorly, and many features did not predict where elk were killed once encountered.

Where elk and wolves were

- Elk were more likely near roads, at lower elevations and on gentler slopes, and used grasslands and open conifer more and pine forest less.

- Wolves were also more likely near roads and at lower elevations and on gentler slopes, and used grasslands and pine forest more and open conifer less.

Encounters and kills

- Wolves avoided high, steep ground more than elk did, so encounters were concentrated in valley bottoms. Topography (slope and elevation) drove encounters.

- Once an elk was encountered, habitat mattered most. Elk were more likely to be killed in pine forest, and less likely in grasslands and open conifer, than the encounter stage suggested.

- Distance to roads and slope steepness had the same effect on encounters and kills.

- If predation risk had been defined simply as where wolves were, risk would have been overestimated by about 60% in grasslands and open conifer, and underestimated by about 20% in pine forest and at higher elevations.

### 3. What they concluded

- Predation risk is not the same as where predators are found. Landscape features can make prey more or less vulnerable once they have been encountered, and a feature can affect the encounter and kill stages differently.

- If a feature lowers the chance of encounter but raises the chance of being killed, studies that do not separate the stages can miss it, because the two effects cancel out.

- Separating the stages lets researchers form and test ideas about why risk differs. For example, safety in grasslands may come from better predator detection, vigilance or larger elk groups; in pine forest, shorter sight lines or fallen timber may slow fleeing elk (fallen timber was not measured).

- The risk map applies only to the Cascade pack and to the season studied. Total risk also depends on predator numbers, so with several packs, each pack’s map could be weighted by pack size.

- Where encounters cannot be recorded, comparing kill sites with available habitat can approximate risk, but cannot show which stage is responsible.

- The authors suggest these risk maps could be used in spatial predator–prey models, for example to spread a known number of kills across a landscape.

### 4. How tracking was or was not used

Tracking was central to the study. Radio-collared wolves were located from the air, and these locations were used to start continuous snow-tracking sessions. Field teams then followed (backtracked) wolf trails in the snow for about 1250 km in total. They recorded:

- Encounters: each place where wolf tracks crossed the tracks of an elk group. The authors note this is a spatial encounter, not necessarily the exact time and place the animals met.

- Chases: the distance elk were chased after an encounter, read from the tracks.

- Kills: elk killed by wolves found along the trail.

The authors assume that wolves were always hunting while travelling. They also name snow tracking, alongside direct observation and Global Positioning System (GPS) collars, as one way to estimate encounters in other studies.

### 5. Tracker or observer certification

Not reported. The paper thanks “the dozens of field assistants who made this study possible” but does not say who did the snow tracking or how their skill was assessed. This matters because both the encounter and kill models rest on reading wolf and elk tracks correctly.

### 6. Other technologies, skills or innovations

- Radio collars on wolves and elk, with aerial and ground relocation (fixed-wing aircraft).

- Mapping in ArcGIS 8.2: a digital elevation model, a human-use atlas of roads and trails, and two merged land cover maps.

- A method for turning separate encounter and kill models into a single predation risk map.

### 7. Implications for conservation (from the paper)

- Knowing which stage of predation a landscape feature affects can focus conservation on the stage with the greatest effect or the most room for management.

- For endangered mountain caribou, it matters whether roads and trails make wolves more likely to find caribou, or make caribou easier to kill once found: these may need different actions.

- Studies that assume predation risk equals predator habitat use may be misleading.

### 8. Implications for tracking (Original Wisdom's observations)

_These are Original Wisdom's observations, not the authors'._

- Collars showed where wolves were, but only the tracks in the snow showed where wolves actually crossed paths with elk and how far they chased them. The study’s main finding, that encounters and kills happen in different places, depends on tracks and signs evidence.

- Because the encounter and kill data come from tracking, reporting who did the tracking and how their skill was checked would make the results easier to judge.

## Cite this summary

Lawrence, K. 2026. Summary of: Spatial decomposition of predation risk using resource selection functions: an example in a wolf–elk predator–prey system (Hebblewhite and Merrill et al., 2005). Original Wisdom, Tracking Literature. https://www.originalwisdom.com/tracking-literature/2005-hebblewhite-merrill-spatial-decomposition-predation-risk/