Edge-focused network-based approach: an improved kernel density estimator for home range

O_LIOne of the central challenges in ecology and animal behaviour is to generate animal home range estimations. Kernel density estimate for home range has been one of the most widely used estimates these last few decades, despite its limitations. More recently a network-based kernel density (NKDE) approach has been proposed, which uses Delaunay triangulation. C_LIO_LIHere we show that NKDE has a discontinuous kernel density. We then develop a new network-based method that emphasises entirely on the edges, instead of the nodes in the network. We call this Edge-Focused Network-based Kernel Density Estimation (EFNKDE). In this method, a unit weight is distributed uniformly along each edge of the network and Euclidean distance is used to compute the contribution of each segment of the edge to the kernel density at a given point. C_LIO_LIThis is a network based method that leads to a continuous and differentiable kernel density. An analytical expression for the same is obtained for the Gaussian kernel. By taking concrete examples and studying different methods and through different perspectives across a range of bandwidths, we show that EFNKDE has many advantages over other methods. We present a model that provides a theoretical basis to the effectiveness of EFNKDE in linear regimes. C_LIO_LIEFNKDE is easy to apply, can work with minimal data, provides a smooth kernel density that highlights the network and does not overemphasise the data. This method is most suitable for estimating home ranges with narrow corridors and forbidden regions. C_LI