REPRESENTING MIGRATION PATTERNS AND CONSTRUCTING PHYLOGENETIC TREES USING A PERCOLATION MODEL: A CASE STUDY OF FAMILY CAMELIDAE

Computational methods have received increased attention as powerful tools for morphological and molecular data processing and phylogenetic tree reconstruction in paleobiology and evolutionary biology. Numerous techniques from fractal geometry have been adapted to model network distributions and reconstruct branching patterns. Percolation theory is one of the theories related to fractal geometry, which focuses on phase transitions. It is widely incorporated in studies of groundwater flow, hydraulic fracturing (“fracking”), and the spread of epidemics. Patterns associated with such models mimic the geometry of trees. In this study, we have adapted invasion percolation methods to model both phylogenetic trees and patterns of biogeographic dispersal, using the Family Camelidae as an empirical case study.

We begin by generating a null model tree, which results in a network that forms at the initial point and growth outwards based on the randomly assigned connection probabilities. The nodes within the network diagram represent species in Camelidae. The next step is to modify our model to incorporate a pattern of migration and dispersal of Camelidae out of North America, relying on the relationship between speciation and geographic isolation. Allopatric speciation is considered to be a common mode of cladogenesis requiring geographic isolation. New species are formed by the migration of populations away from the center of origin, and further divergence prevents later interbreeding with the parent population. Therefore, we modify our null model by adjusting the probability field to reflect stratigraphic and geographic fossil occurrence data, both of which serve as controlling parameters to steer the network’s progression through space and time. In the end, the resulting patters from null and modified models are reconfigured as branching diagrams, and are compared to a morphological cladogram of Camelidae obtained from the literature. Given the wide variety of processes that can generate similar types of branching patterns in nature, modeling these different topologies and comparing them quantitatively can reveal the similarities and differences among the empirical and simulated patterns. Such can allow paleontologists to better understand bursts of diversification in time and space.