Arce Guillen, R.; Pohle, J.; Jeltsch, F.; Roeleke, M.; Reineking, B.; Klappstein, N.; Schlägel, U.

Habitat selection analysis includes resource selection analysis (RSA) and step selection analysis (SSA). These frameworks are used in order to understand space use of animals. Particularly, the SSA approach specifies the space availability of sequential locations through a movement kernel. This movement kernel is typically defined as the product of independent parametric distributions of step lengths (SLs) and turning angles (TAs). However, this assumption may not always be plausible for real data where short SLs are often correlated with large TAs and vice versa. The objective of this paper is to relax the need for parametric distributions using generalized additive models (GAMs) and the R-package mgcv, based on the work of Klappstein et al. (2024). For this, we propose to specify the movement kernel as a bivariate tensor product, rather than independent distributions of SLs and TAs. In addition, we account for residual spatial autocorrelation in this GAM-approach. Using simulations, we show that the tensor product approach accurately estimates the underlying movement kernel and that the fixed effects of the model are not biased. In particular, if the data are simulated with a copula distribution for SL and TA, i.e. if the independence assumption for SL and TA does not hold, the GAM approach produces better estimates than the classical approach. In addition, including a bivariate tensor product in the model leads to a better uncertainty estimation of the model parameters and a higher predictive quality of the model. Incorporating a bivariate tensor product solves the problem of assuming parametric distributions and independence between SLs and TAs. This offers greater flexibility and makes the analysis of real data more reliable.