Modelling axial and circular data for vegetation stripes at Marion Island

Abstract

In this study, a bivariate model is proposed to analyse the joint distribution of Marion Island’s vegetation stripe and wind direction data. The objective is to investigate whether wind contributes to the formation of these irregular vegetation stripe patterns. Using a copula-based approach, the joint density function is modelled with a bivariate wrapped Cauchy circular component combined with various circular and axial distributions. Due to multimodality in the data, a finite mixture model is proposed to accurately model the overall density. This finite mixture model incorporates the slope angle and cone aspect as concomitant variables. The results indicate that a three latent component finite mixture model with von Mises and axial normal distributions as marginals provides the best fit. Using the proposed model it was determined that wind influences vegetation stripe orientation on the southern sides of cones, while no clear relationship is observed on the northern sides, likely due to harsher wind and sunlight exposure. These findings highlight the role of wind and other environmental factors, such as cone aspect and slope, in shaping vegetation patterns.