Distinguishing Passive and Driven Trait Evolution in the presence of Boundaries

Quantifying the dynamics of macroevolutionary trends, such as changes in body size and complexity, is vital for understanding the processes that have shaped patterns of extant and extinct biodiversity. For example, whilst maximum body size may tend to increase within lineages (the Cope-Depéret rule), it is still unclear whether such patterns are driven by selection preferentially operating in one direction or are passive outcomes of diffusive processes. Increasingly, empirical studies reveal the need for better models of these processes, especially when phylogenies are incomplete or unavailable. Here, we present a flexible, non-phylogenetic model that captures key macroevolutionary processes—speciation, extinction and both passive (unbiased) and driven (biased) trait evolution—whilst accounting for physical and biological constraints. Our model incorporates three types of boundary condition: Dirichlet, Neumann and zero-flux, to represent real-world limits on trait evolution, such as biomechanical constraints on body size. We demonstrate the utility of our modelling approach by applying it to two distinct datasets: the body mass distribution of extant mammals and the size evolution of bivalves and brachiopods over geological time. In mammals, we detect driven trait evolution towards smaller body masses, but this is counteracted by passive diffusion, bounded by a lower mass limit, resulting in increased modal, mean and maximum body masses over time. In bivalves and brachiopods, the model captures a consistent evolution towards larger body sizes, revealing that both modern bivalves and brachiopods appear limited by an upper size boundary. Notably, the Permian-Trassic mass extinction triggered a significant shift in brachiopod evolutionary dynamics, emphasising how environmental upheavals can alter trait evolution. These results demonstrate how a small number of mechanisms can model the processes producing various trait distributions when boundaries are imposed to limit the range of possible traits. Importantly, our approach allows us to detect multiple, overlapping processes, apparently acting in opposition.