Overview
Habitat selection is fundamentally about how animals use their environment relative to what is available to them, rather than about where they occur in absolute terms (Figure 1). Just as a diner’s restaurant choice depends on which venues are open and close enough to walk or drive to, an animal can only “prefer” a habitat if it had multiple habitats to choose from and selected some over, or more often than, others.
A simple way to express this is to write:
\[\text{Selection} = \frac{\text{Use}}{\text{Availability}}\]
Here, use refers to the locations where animals were recorded, whereas availability refers to the parts of the landscape they could have realistically accessed. Because availability is almost never known exactly, it must be approximated (statistically).
Resource selection functions (RSFs)
Much of the early habitat selection literature used resource selection functions (RSFs) to carry out this approximation. RSFs are statistical models that compare the habitat characteristics (or environmental conditions) at used locations with those at a set of randomly chosen available locations (also known as controls, pseudo-absences, quadrature, or background points). Typically, it is up to the analyst to decide how many available points should be used and where these should be placed. As a result, RSFs tell us which habitats are selected more strongly than others, but not the absolute probability that a particular habitat will be chosen.
To see why, consider a simple example where an animal truly prefers habitat A over habitat B, and in the tracking data recorded from that animal, we observe 80 locations that fall within habitat A and 20 locations that fall within habitat B. Suppose that we generate 100 available points, and that for simplicity, these fall in each habitat in equal proportions (i.e., 50 in habitat A and 50 in habitat B). The RSF ratios are therefore:
Habitat A: 80 / 50 = 1.6
Habitat B: 20 / 50 = 0.4
This suggests that habitat A is selected four times more strongly than habitat B (as 1.6 / 0.4 = 4). If we repeat the same analysis with 10,000 available points instead of 100 (so that 5,000 fall in each habitat), the ratios now become:
Habitat A: 80 / 5000 = 0.016
Habitat B: 20 / 5000 = 0.004
The numerical values of these selection ratios have drastically changed, even though the behaviour of the animal remains identical. However, habitat A is still selected four times more often than habitat B (0.016 / 0.004 = 4), so the ranking of habitats remains the same.
When several habitat variables are considered at once, an RSF estimates how each of them contributes to relative habitat selection. Some variables may make a location more attractive, while others may make it less attractive. The combined influence of all variables included in the model is expressed as:
Relative selection = effect of habitat 1 + effect of habitat 2 + ... etc.
This is the same structure used across many statistical models. In practice, RSFs are commonly estimated using a form of regression model called case-control logistic regression, where used points (cases) are coded as one and available points (controls) as zero. For statistical reasons, the calculations are performed on a mathematical scale called the log-odds scale, but the estimated coefficients can still be interpreted in terms of how each habitat variable affects relative selection. The intercept has no biological meaning because it depends entirely on the ratio of used to available points, which is subjective and defined by the analyst.
Inhomogeneous Poisson point process (IPP)
More sophisticated statistical frameworks that model availability continuously in space have been proposed to avoid arbitrary choices about the number and placement of available points. One widely used approach is the inhomogeneous Poisson point process (IPP), which models the spatial distribution of observed points such as nest locations, sightings, or GPS fixes. Instead of modelling the presence or absence of a species at a set of fixed sites, a point process treats all observed points themselves as the data. The expected density of points across different parts of the landscape is described by what is called an intensity surface, which is typically labelled as \(\lambda\) in the literature.
Put simply, the intensity describes how densely observations are expected to occur: areas with higher intensity are expected to contain more observations per unit area.
In an IPP, this intensity varies across space depending on habitat conditions:
log(\(\lambda\)) at location \(s\) = baseline density + habitat effects
The baseline term describes the expected density of points when the habitat variables have no effect, or when they are at their average values if the covariates have been centred around their means.
IN SHORT
The IPP is useful when the goal is to describe how the expected density of observations varies continuously across an area, rather than representing availability using a finite set of randomly sampled points as in an RSF.
IPP approximations (gridded, down-weighted & infinitely weighted Poisson)
Because the IPP represents the intensity continuously through space, evaluating the entire surface would in principle require calculations at an infinite number of locations, which is impossible. Approximations are therefore preferred in practice. One solution is to divide the study region into many small grid cells and treat the number of points in each of those cells as a Poisson count. The Poisson distribution is commonly used to describe how many events occur within a fixed unit of time or space. Here, the “events” are observed locations, and the model describes how many of those locations we expect to fall within each grid cell based on the intensity in that cell. The actual number can of course be somewhat higher or lower, and the Poisson distribution describes natural variation around this expected count.
For each grid cell, the expected number of points is given as:
Expected count in a cell = surface area of the cell x intensity in that cell
Taking the logarithm gives: log (expected count) = log (cell area) + log(intensity)
This is known as a gridded Poisson approximation. The smaller the grid cells, the more closely the results of this approximation will match those of the continuous-space IPP. Instead of dividing the landscape into grid cells, we can also approximate the IPP using a large number of background points spread across the study area. Two commonly used approaches do this in slightly different ways:
Down‑weighted Poisson regression, treats each background point as a tiny portion of the landscape. Because many such points are used, each one receives only a small weight (hence the term down-weighted). Adding up all these weighted points approximates the full amount of space available across the study area. An intuitive way to think about this is that each point in down-weighted Poisson regression is like a small tile in a mosaic: every tile contributes a little, and together they reconstruct the whole picture.
Infinitely weighted logistic regression, instead treats background points as a sample representing the entire available landscape. As more background points are added, the model gives this sample increasingly large overall weight, so that it provides an increasingly accurate representation of continuous availability across the study area.
Although the mathematics differ, both approaches use the same basic information and converge on the same habitat selection coefficients as the IPP when enough background points are used. The main difference is that infinitely weighted logistic regression only indicates which habitats are preferred relative to others, whereas down-weighted Poisson regression can additionally estimate the expected density of observations across the landscape. This difference arises because infinitely weighted logistic regression retains the logistic regression structure of an RSF, whereas down-weighted Poisson regression explicitly accounts for how much area the background points represent. In practice, the choice between them is often driven more by computational convenience and software availability than by biological considerations.
However, a key assumption of the IPP is that habitat alone explains why some areas are used more than others. After accounting for the effects of habitat in the model, any remaining clustering of locations is assumed to be random. In reality, ecological data often show additional clustering because animals revisit the same places over time, interact socially, aggregate as part of key behaviours (e.g., swarming, flocking) or simply respond to (unmeasured) environmental features that have not been included in the model and are themselves spatially clustered (for example, patchily distributed prey or broad temperature gradients).
Log-Gaussian Cox processes (LGCPs)
Log‑Gaussian Cox process (LGCP) models address this by including an additional term called a spatial random effect, which takes the form of a smooth surface that increases or decreases \(\lambda\) locally, allowing the model to capture spatial clustering that is not explained by the measured habitat variables. LGCP models are therefore direct extensions of the IPP:
LGCP intensity = habitat effects (as in the IPP) + unexplained spatial structure (via random effect)
IN SHORT
LGCPs are useful when habitat variables do not fully explain spatial patterns in the data.
Step selection functions (SSFs)
The models above can be used when observations are treated primarily as a collection of points in space, without explicitly modelling how an animal moved from one location to the next. Tracking data pose an additional challenge because successive locations form a movement path. In particular, successive GPS locations represent repeated snapshots of the same individual animal moving continuously; as such, they tend to be strongly autocorrelated, meaning that where the animal is at one time strongly constrains where it can be at the next. Ignoring this dependence can cause movement-driven clustering to be mistaken for habitat selection:
Distant habitats may appear “avoided” simply because they were never reachable.
Habitats near the animal’s track may appear strongly “selected” because they were always accessible.
In other words, availability is dynamic and changes through time.
Step selection functions (SSFs) address this by focusing on each movement the animal makes in turn. For every observed movement, or step, an SSF compares where the animal actually went with a number of other places it could reasonably have reached during the same time interval. These alternative movements are usually generated to resemble the animal’s typical movement behaviour, for example in terms of how far it tends to travel and how sharply it tends to turn (Figure 2).
This means that the habitats considered “available” are restricted to those the animal could realistically have reached from its current location. Availability therefore changes from one step to the next as the animal moves through the landscape. Habitat selection is then estimated by asking how the environmental conditions at the location the animal chose differ from those at the alternative locations it could have chosen. Although only a finite number of alternative locations are generated for each step, these can be thought of as a sample from the much larger range of possible locations the animal could have reached given its movement constraints.
IN SHORT
SSFs are useful when the habitats available to an animal change from one movement to the next. They estimate habitat selection by comparing where the animal actually was with other locations it could realistically have reached at that moment.
Space–time point process models (STPPs)
A closely related class of models, known as space–time point process models (STPPs), takes a similar idea but represents the animal’s possible next locations as a continuous surface rather than as a finite set of alternative steps. In other words, rather than sampling a handful of places the animal could have moved to, an STPP describes the full range of possible locations continuously across space. At each time interval, this surface describes where the animal could realistically have moved, based on where it started, how much time it had to move, and its typical movement behaviour. Like an SSF, availability therefore changes as the animal moves through the landscape. Unlike an SSF, however, that availability is represented as a continuous surface rather than by a sample of alternative locations. In this sense, STPPs extend the IPP framework through time rather than assuming that the same availability surface applies throughout the study.
In this sense, STPPs extend the IPP framework through time by allowing the set of available locations to change as the animal moves. For tracking data, the STPP intensity can therefore be separated into two components:
One describing habitat selection
Another describing availability constrained by movement
In an STPP:
Intensity at location \(s\) and time \(t\) = habitat effects at location \(s\) and time \(t\) x movement-based availability at location \(s\) and time \(t\)
The movement-based availability term is defined using a model of how the animal moves. Different movement models can be used (e.g., Brownian motion, ecological diffusion, Ornstein–Uhlenbeck), each describing movement in a different way and therefore producing a different surface of locations the animal could potentially reach. Because STPPs consider each observation separately, they can relate an animal’s location to the environmental conditions present at the exact time it was recorded. This makes them particularly useful for studying fine-scale habitat relationships, but also computationally demanding because the movement-based availability surface must be calculated again at every time step.
IN SHORT
STPPs are useful when availability changes through time and we want to represent the full range of locations an animal could have reached at each moment as a continuous surface.
Marginalised space–time point processes (mSTPPs)
STPPs provide a detailed picture of availability at each moment in time, but repeatedly calculating a new availability surface for every observation can be computationally expensive and can make the resulting habitat relationships closely tied to the particular movement path that was observed. Marginalised STPPs (mSTPPs) provide a broader-scale alternative by combining movement-based availability across the entire tracking period.
In an mSTPP:
Intensity at location \(s\) = habitat effects x time averaged availability
This broader availability surface is obtained by combining the movement-based availability surfaces from all movement intervals. Rather than asking what was available at one particular moment, it describes which parts of the landscape were generally accessible over the tracking period. This approach:
- avoids repeating the full STPP calculation at every time step,
- represents a broader range of environmental conditions within a single availability surface, and
- can make habitat relationships more transferable to new areas or time periods.
IN SHORT
mSTPPs are useful when the goal is broad-scale habitat selection inference while still accounting for movement constraints.
Conclusion
Although the models described above differ in their statistical formulation, they are all trying to answer the same basic biological question: how does an animal’s use of the landscape relate to the habitats that were available to it? They differ primarily in how they represent that availability. RSFs represent it using a sample of points from a broadly defined available area; IPPs represent it continuously across space; LGCPs additionally allow for unexplained spatial clustering; and SSFs and STPPs recognise that availability changes as an animal moves. mSTPPs then combine this movement-based availability over time to support broader-scale inference. Moving from one model to the next therefore means progressively changing how realistically space, movement and availability are represented, rather than changing the fundamental question being asked.