  Models that capture the spatial and temporal dynamics are applicable in many
science fields. Non-separable spatio-temporal models were introduced in the
literature to capture these features. However, these models are generally
complicated in construction and interpretation. We introduce a class of
non-separable Transformed Gaussian Markov Random Fields (TGMRF) in which the
dependence structure is flexible and facilitates simple interpretations
concerning spatial, temporal and spatio-temporal parameters. Moreover, TGMRF
models have the advantage of allowing specialists to define any desired
marginal distribution in model construction without suffering from
spatio-temporal confounding. Consequently, the use of spatio-temporal models
under the TGMRF framework leads to a new class of general models, such as
spatio-temporal Gamma random fields, that can be directly used to model Poisson
intensity for space-time data. The proposed model was applied to identify
important environmental characteristics that affect variation in the abundance
of Nenia tridens, a dominant species of snail in a well-studied tropical
ecosystem, and to characterize its spatial and temporal trends, which are
particularly critical during the Anthropocene, an epoch of time characterized
by human-induced environmental change associated with climate and land use.
