Natural selection favors the evolution of brains that can capture fitness-relevant features of the environment's causal structure. We investigated the evolution of small, adaptive logic-gate networks ("animats") in task environments where falling blocks of different sizes have to be caught or avoided in a 'Tetris-like' game. Solving these tasks requires the integration of sensor inputs and memory. Evolved networks were evaluated using measures of information integration, including the number of evolved concepts and the total amount of integrated conceptual information. The results show that, over the course of the animats' adaptation, i) the number of concepts grows; ii) integrated conceptual information increases; iii) this increase depends on the complexity of the environment, especially on the requirement for sequential memory. These results suggest that the need to capture the causal structure of a rich environment, given limited sensors and internal mechanisms, is an important driving force for organisms to develop highly integrated networks ("brains") with many concepts, leading to an increase in their internal complexity.