Covariates
The following spatial covariates were used as explanatory variables in
the model:
- Distance to primary roads (meters)
- Land lot density (number of lots per square kilometre)
- Mean temperature of the hottest month (centigrade)
- Mean temperature of the coldest month (centigrade)
- Precipitation of the driest month (millimetres)
- Precipitation of the wettest month (millimetres)
- Mean elevation from the sea level (meters)
- Foliage projective cover (proportion)
The covariate Distance to primary roads was considered to only
influence spatio-temporal bias associated with these sightings
(Dissanayake, Stevenson, Allavena and Henning 2019), since it quantifies
the easiness of access to koala habitat by an observer. The other
covariates can be assumed to mostly influence observed koala sightings
density. These covariates were obtained from online spatial databases
(http://qldspatial.information.qld.gov.au,
http://www.bom.gov.au) and included as raster maps with a 1 square
kilometre resolution.
Spatio-temporal modelling of koala
sighting
density
The koala sightings were modelled as a realisation of a spatio-temporal
point process model (STPP) model (Baddeley, et al. 2016). STPPs are a
useful statistical tool that allow to model the spatial and temporal
variation of sightings within a region and time window of interest.
Within this modelling framework two main methods can be distinguished:
(1) mechanistic models, where subject matter knowledge is used to inform
the probability that a sighting will occur at a particular location and
a particular time point; and (2) empirical models, where the objective
is to use observational data to inform estimates of koala density. The
approach used here is a combination of the two methods.
More specifically, we assumed that the koala density at a particular
location and a particular time is dependent on the three groups of
variables: (a) variables that relate to the spatio-temporal detection
bias; (b) spatio-temporally referenced variables that are known to be
associated with koala density; and (c) variables that reflect
well-established knowledge on the home range of koalas. The main
mechanistic component of the model is the third group of variables,
while the first two are modelled as a log-linear regression of koala
density. A partial likelihood approach was used to fit the model
(Diggle, et al. 2010).
Three factors were considered in the spatio-temporal modelling of koala
density: spatio-temporal detection bias \(b\left(x,t\right)\),
observed koala density \(q(x,\ t)\), and clustering
r(x,t|Ht).
Let \(\mathcal{H}_{t}\) denote the full story of the process up to yeart. We assumed that conditionally on \(\mathcal{H}_{t}\), the
intensity \(\lambda\) of the process is at a location x in yeart was given by: