and \(u(x)\) is the square root of the koala home range (in km2) at location \(x\). In Equation 4 the parameter \(\theta(t)\) regulates the strength and direction of the spatial interaction between sightings:\(0\ <\ \theta(t)\ <\ 1\) corresponds to an inhibitory point-process; \(\theta(t)\ =\ 1\) is the case of no interaction; and\(\theta(t)\ >\ 1\) represents the situation where koala sightings are spatially aggregated. We let \(\theta(t)\) vary between the mating and non-mating seasons as we expected a stronger spatial interaction of koalas and thereby potential aggregations of sightings during the former period. This seasonality was included as binary variable with 1 being assigned the for mating season \(\theta 2\ \) (August to September (de Oliveira, Murray, de Villiers and Baxter 2014)) and 0 representing the non-mating season \(\theta 1\ \text{for\ rest\ of\ the\ year\ }\)We fit the model using partial likelihood (Lp) given by to estimate koala sightings density for the observation period of 17 years: