Spatial distribution and movement models

Understanding animal habitat preferences and movement patterns is key to effective conservation. We develop new types of spatial and movement models (see also Spatial models for understanding the distribution of animals and plants).


Splines

Describing relationships between two (or more) variables

Splines are clever ways to characterise often complex relationships between one or more covariates and some response of interest. For instance, we might be interested in complex spatial patterns such as how giraffe in Namibia distribute themselves across Etosha National Park and patterns like these are often heavily 'clumped'. To add to this, the spatial patterns can be quite similar in some areas of the park but vary wildly in others (e.g. in the relatively popular areas). Alongside these features, there are some 'no-go' areas in the park for giraffe such as large salt pans which are either muddy when it rains (where they can get stuck) or barren when they are dry (and where little food is to be found).

Spline based analyses can accommodate both far reaching trends in spatial patterns and more localised patterns (e.g. in and around water sources) whilst considering surface features such as 'no-go' areas - this requires the distances which underpin these surfaces to respect the fact that the animals must move around objects rather than cross them. Dr. Lindesay Scott-Hayward and Dr. Monique Mackenzie work on developing methods such as these (Complex Region Spatial Smoother; CReSS) and with colleagues (Dr. Walker in Auckland, NZ) developing automated model selection methods.


An equation for the shape of the relationship

The particular equation given here is for a two-dimensional smooth and is an exponential radial basis function. This uses the distance between two points (h) and a range parameter (r) to describe the shape. The range aspect is particularly useful when areas of the smooth are 'no-go' areas. For example, there may be land masses which a marine mammal cannot cross. When this occurs, we use geodesic distance for h (as the fish swims) rather than Euclidean distance (as the crow flies). This Complex Region Spatial Smoother (CReSS) is described in this paper.

spline

Animal densities in time and space

When constructing spatial distribution maps (see our pages spatial and dsm for more details), we use splines to describe non-linear relationships. An example of such a smooth relationship might be how the density of animals changes with the month of the year (see figure). This is an example of a one-dimensional spline, however, we also use two-dimensional splines to describe the relationship between two continuous covariates. The commonest two-dimensional smooth is of space (x and y coordinates).

partialplot

Example: estimated change in animal density from January (month 1) to December (month 12). The red lines show 95% confidence intervals for this estimated relationship. The relationship was found using B-splines.

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