Agent-based modelling of clonal plant propagation across space: Recapturing fairy rings, power laws and other phenomena

Many plants reproduce clonally through vegetative extensions (spacers). This results in a patch of clones connected through a network of spacers. The resulting network has a nontrivial spatial pattern that can be an important determinant of survival and fitness of the clonal plant. Here, we develop general growth rules that dictate how individual clones under local density-dependent conditions add spacers, giving rise to emergent population-level spatial patterns. A population subject to these growth rules is simulated using a stochastic individual-based model. The dependence of network structure on various architectural parameters is explored. The growth rules generate networks similar to those observed in natural populations, and can replicate real-world phenomena such as central die-back with regeneration, ‘fairy rings', and branch entrapment. A shorter spacer length results in higher population density (which may confer resistance to invasion in real populations), while longer spacer length allows the population to spread more quickly. The lateral branching angle, node-by-node angle, and spacer length appear to be the most influential parameters for determining the spatial architecture of the clonal patch. The number of daughter branches per mother branch follows a power law distribution in a diverse set of simulated networks. Continually growing computational power will make such simulation models increasingly useful for understanding the spatial growth of clonal plants, and power law behaviour may be a very common feature of both simulated and real clonal plant populations.