A conceptual and mechanistic approach for bridging the fields of macroecology (ecological biogeography) and historical biogeography has been a long-term aim in Evolutionary Biology. Such a bridge could increase our understanding on the processes governing the spatial and temporal generation of biodiversity distribution patterns. This aim has been recently approached from the perspective of evolutionary biogeographic inferential statistical models, within a maximum likelihood or Bayesian framework, which incorporates the contribution of environmental factors as scaling parameters. Here, we describe a new approach that builds on a spatially-explicit, forward-time, computer simulation (“automat”) model. The model sets a series of rules by which speciation, extinction, and dispersal of lineages are governed within an environmentally heterogeneous, two-dimensional gridded landscape. Unlike some previous approaches, niche conservatism is assumed but the model allows for environmental conditions to vary both spatially and temporally, by letting the model run over three time-series of actual palaeoclimate data, spanning the last 20 million years of geological history. Speciation is governed by a global speciation rate, whereas the background extinction rate is made dependent on abiotic (palaeoenvironmental conditions) and biotic (species density per grid cell) factors, hence giving a local background extinction rate. Also, we propose a novel mechanistic approach in which species are not the result of unique, independent events but linked through evolutionary history from a single evolutionary origin. We set different rules to generate the resulting phylogenies to test different factors (time, environment) that govern the inheritance of range distributions. Dispersal follows a simple Poisson kernel model, with higher probability of migration to contiguous grid cells and rare long-distance movements to distant cells. We also describe ways in which the presence of temporal dispersal barriers could modify the resultant spatial patterns. Evaluation of model accuracy and fit is based on comparison of simulated spatial patterns with observed, empirical ones. We use statistic dependent variables such as the spatial distribution of species in the landscape, species’ geographic range size and location, and the shape of the resultant phylogenies. Finally, we propose that this spatially-explicit simulation model could be used to evaluate the role played by niche conservatism, ecological vicariance and climatic-driven extinction in the generation of disjunct continental patterns, such as the presence of sister-lineages in numerous families of angiosperms forming a ring in the continental margins of the African continent, the Rand Flora pattern.