Progress in understanding the relationship between lineage diversity, morphological diversity, and morphospace dynamics has been hampered by the lack of an appropriate null model of morphospace occupation. In this article, we introduce a simple class of models based on branching random walks (BRWs) for continuous traits. We show that many of the observed patterns of morphospace occupation might be simply a consequence of the dynamics of BRWs and therefore might not require special explanations. We also provide expected patterns of morphospace occupation according to a number of different conditions. In particular, we model BRWs on neutral landscapes and demonstrate that clumping in morphospace is possible even in the absence of adaptive landscapes with well-defined peaks and valleys. The quantitative definition of the BRW provides a means to analyze, both computationally and analytically, patterns of morphospace occupation according to different hypotheses.
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