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Macroevolutionary theory posits three processes leading to lineage diversification and the formation of regional biotas: dispersal (species geographic range expansion), speciation (species lineage splitting), and extinction (species lineage termination). The Theory of Island Biogeography (TIB) predicts species richness values using just two of these processes; dispersal and extinction. Yet most species on Earth live on continents or continental shelves, and the dynamics of evolutionary diversification at regional and continental scales are qualitatively different from those that govern the formation of species richness on biogeographic islands. Certain geomorphological processes operating perennially on continental platforms displace barriers to gene flow and organismal dispersal, and affect all three terms of macroevolutionary diversification. For example, uplift of a dissected landscape and river capture both merge and separate portions of adjacent areas, allowing dispersal and larger geographic ranges, vicariant speciation and smaller geographic ranges, and extinction when range sizes are subdivided below a minimum persistence threshold. The TIB also does not predict many biogeographic and phylogenetic patterns widely observed in continentally distributed taxa, including: (i) power function-like species-area relationships; (ii) log-normal distribution of species geographic range sizes, in which most species have restricted ranges (are endemic) and few species have broad ranges (are cosmopolitan); (iii) mid-domain effects with more species toward the geographic center, and more early-branching, species-poor clades toward the geographic periphery; (iv) exponential rates of net diversification with log-linear accumulation of lineages through geological time; and (v) power function-like relationships between species-richness and clade diversity, in which most clades are species-poor and few clades are species-rich. Current theory does not provide a robust mechanistic framework to connect these seemingly disparate patterns. Here we present SEAMLESS (Spatially Explicit Area Model of Landscape Evolution by SimulationS) that generates clade diversification by moving geographic barriers on a continuous, neutral landscape. SEAMLESS is a neutral Landscape Evolution Model (LEM) that treats species and barriers as functionally equivalent with respect to model parameters. SEAMLESS differs from other model-based biogeographic methods (e.g., Lagrange, GeoSSE, BayArea, and BioGeoBEARS) by modeling properties of dispersal barriers rather than areas, and by modeling the evolution of species lineages on a continuous landscape, rather than the evolution of geographic ranges along branches of a phylogeny. SEAMLESS shows how dispersal is required to maintain species richness and avoid clade-wide extinction, demonstrates that ancestral range size does not predict species richness, and provides a unified explanation for the suite of commonly observed biogeographic and phylogenetic patterns listed above. SEAMLESS explains how a simple barrier-displacement mechanism affects lineage diversification under neutral conditions, and is advanced here toward the formulation of a general theory of continental biogeography. [Diversification, extinction, geodispersal, macroevolution, river capture, vicariance.].