We construct a state-and-transition model for mammals in tropical savannas in northern Australia to synthesize ecological knowledge and understand mammalian declines. We aimed to validate the existence of alternative mammal assemblage states similar to those in arid Australian grasslands, and to speculate on transition triggers. Based on the arid grassland model, we hypothesized that assemblages are partitioned across rainfall gradients and between substrates. We also predicted that assemblages typical of arid regions in boom periods would be prevalent in savannas with higher and more regular rainfall. Data from eight mammal surveys from the Kimberley region, Western Australia (1994 to 2011) were collated. Survey sites were partitioned across rainfall zones and habitats. Data allowed us to identify three assemblage states: State 0:- low numbers of mammals, State II:- dominated by omnivorous rodents and State III:- dominated by rodents and larger marsupials. Unlike arid grasslands, assemblage dominance by insectivorous dasyurids (State I) did not occur in savannas. Mammal assemblages were partitioned across rainfall zones and between substrates as predicted, but - unlike arid regions - were not related strongly to yearly rainfall. Mammal assemblage composition showed high regional stability, probably related to high annual rainfall and predictable wet season resource pulses. As a consequence, we speculate that perpetually booming assemblages in savannas allow top-down control of the ecosystem, with suppression of introduced cats by the dingo, the region's top predator. Under conditions of low or erratic productivity, imposed increasingly by intense fire regimes and introduced herbivore grazing, dingoes may not limit impacts of cats on native mammals. These interacting factors may explain contemporary declines of savanna mammals as well as historical declines in arid Australia. The cat-ecosystem productivity hypothesis raised here differs from the already-articulated cat-habitat structure hypothesis for mammal declines, and we suggest approaches for explicit testing of transition triggers for competing hypotheses.