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Economic growth is associated with the diversification of economic activities, which can be observed via the evolution of product export baskets. Exporting a new product is dependent on having, and acquiring, a specific set of capabilities, making the diversification process path-dependent. Taking an agnostic view on the identity of the capabilities, here we derive a probabilistic model for the directed dynamical process of capability accumulation and product diversification of countries. Using international trade data, we identify the set of pre-existing products, the product Ecosystem, that enables a product to be exported competitively. We construct a directed network of products, the Eco Space, where the edge weight corresponds to capability overlap. We uncover a modular structure, and show that low- and middle-income countries move from product communities dominated by small Ecosystem products to advanced (large Ecosystem) product clusters over time. Finally, we show that our network model is predictive of product appearances.