The study of birds species is an excellent indicator of biodiversity or productivity. Global warming and changes human land us are considered major threats to biodiversity, affecting the abundance of bird species. In this study we focus on the Mourning Dove and American Robin, the most abundant birds species in the United States. The abundances of these species can be correlated between them and they would also be similar in nearby locations. Thus we propose to model these data simultaneously through multivariate models that relies on sharing common spatial Gaussian random effect terms. In order to improve the computational efficiency, each spatial Gaussian process is approximated to the block nearest neighbor Gaussian process (block-NNGP). Since the multivariate geostatistical model belongs to the class of Latent Gaussian Models, fast Bayesian inference can be carried out through the In...