Aim: Two of the oldest observations in plant geography are the increase in plant diversity from the poles towards the tropics and the global geographic distribution of vegetation physiognomy (biomes). The objective of this paper is to use a process-based vegetation model to evaluate the relationship between modelled and observed global patterns of plant diversity and the geographic distribution of biomes. Location: The global terrestrial biosphere. Methods: We implemented and tested a novel vegetation model aimed at identifying strategies that enable plants to grow and reproduce within particular climatic conditions across the globe. Our model simulates plant survival according to the fundamental ecophysiological processes of water uptake, photosynthesis, reproduction and phenology. We evaluated the survival of an ensemble of 10,000 plant growth strategies across the range of global climatic conditions. For the simulated regional plant assemblages we quantified functional richness, functional diversity and functional identity. Results: A strong relationship was found (correlation coefficient of 0.75) between the modelled and the observed plant diversity. Our approach demonstrates that plant functional dissimilarity increases and then saturates with increasing plant diversity. Six of the major Earth biomes were reproduced by clustering grid cells according to their functional identity (mean functional traits of a regional plant assemblage). These biome clusters were in fair agreement with two other global vegetation schemes: a satellite image classification and a biogeography model (kappa statistics around 0.4). Main conclusions: Our model reproduces the observed global patterns of plant diversity and vegetation physiognomy from the number and identity of simulated plant growth strategies. These plant growth strategies emerge from the first principles of climatic constraints and plant functional trade-offs. Our study makes important contributions to furthering the understanding of how climate affects patterns of plant diversity and vegetation physiognomy from a process-based rather than a phenomenological perspective.