In the first part of this article we survey general similarities and differencesbetween biological and social macroevolution. In the second (and main) part, we consider a concrete mathematical model capable of describing importantfeatures of both biological and social macroevolution. In mathematical modelsof historical macrodynamics, a hyperbolic pattern of world population growtharises from non-linear, second-order positive feedback between demographic growth and technological development. Based on diverse paleontological dataand an analogy with macrosociological models, we suggest that the hyperbolic character of biodiversity growth can be similarly accounted for by non-linear,second-order positive feedback between diversity growth and the complexity of community structure. We discuss how such positive feedback mechanisms can be modelled mathematically.