Behavioural movement strategies in cyclic models

The spatial segregation of species is fundamental to ecosystem formation and stability. Behavioural strategies may determine where species are located and how their interactions change the local environment arrangement. In response to stimuli in the environment, individuals may move in a specific direction instead of walking randomly. This behaviour can be innate or learned from experience, and allow the individuals to conquer or the maintain territory, foraging or taking refuge. We study a generalisation of the spatial rock-paper-scissors model where individuals of one out of the species may perform directional movement tactics. Running a series of stochastic simulations, we investigate the effects of the behavioural tactics on the spatial pattern formation and the maintenance of the species diversity. We also explore a more realistic scenario, where not all individuals are conditioned to perform the behavioural strategy or have different levels of neighbourhood perception. Our outcomes show that self-preservation behaviour is more profitable in terms of territorial dominance, with the best result being achieved when all individuals are conditioned and have a long-range vicinity perception. On the other hand, invading is more advantageous if part of individuals is conditioned and if they have short-range neighbourhood perception. Finally, our findings reveal that the self-defence strategy is the least jeopardising to biodiversity which can help biologists to understand population dynamics in a setting where individuals may move strategically.

Nothing in evolution makes sense except in the light of parasites

The emergence of parasites in evolving replicating systems appears to be inevitable. Parasites emerge readily in models and laboratory experiments of the hypothesised earliest replicating systems: the RNA world. Phylogenetic reconstructions also suggest very early evolution of viruses and other parasitic mobile genetic elements in our biosphere. The evolution of such parasites would lead to extinction unless prevented by compartmentalisation or spatial pattern formation, and the emergence of multilevel selection. Today and apparently since the earliest times, many intricate defence and counter-defence strategies have evolved. Here we bring together for the first time automata chemistry models and spatial RNA world models, to study the emergence of parasites and the evolving complexity to cope with the parasites. Our system is initialised with a hand-designed program string that copies other program strings one character at a time, with a small chance of point mutation. Almost immediately, short parasites arise; these are copied more quickly, and so have an evolutionary advantage. Spatial pattern formation, in the form of chaotic waves of replicators followed by parasites, can prevent extinction. The replicators also become shorter, and so are replicated faster. They evolve a mechanism to slow down replication, which reduces the difference of replication rate of replicators and parasites. They also evolve explicit mechanisms to discriminate copies of self from parasites; these mechanisms become increasingly complex. Replicators speciate into lineages and can become longer, despite the fitness cost that entails. We do not see a classical co-evolutionary arms-race of a replicator and a parasite lineage: instead new parasite species continually arise from mutated replicators, rather than from evolving parasite lineages. Finally we note that evolution itself evolves, for example by effectively increasing point mutation rates, and by generating novel emergent mutational operators. The inevitable emergence of parasites in replicator systems drives the evolution of complex replicators and complex ecosystems with high population density. Even in the absence of parasites, the evolved replicators outperform the initial replicator and the early short replicators. Modelling replication as an active computational process opens up many degrees of freedom that are exploited not only to meet environmental challenges, but also to modify the evolutionary process itself.

Endogenous spatial pattern formation from two intersecting ecological mechanisms: the dynamic coexistence of two noxious invasive ant species in Puerto Rico

Endogenous (or autonomous, or emergent) spatial pattern formation is a subject transcending a variety of sciences. In ecology, there is growing interest in how spatial patterns can ‘emerge’ from internal system processes and simultaneously affect those very processes. A classic situation emerges when a predator's focus on a dominant competitor releases competitive pressure on a subdominant competitor, allowing coexistence of the two. If this idea is formulated spatially, two interesting consequences immediately arise. First, a spatial predator/prey system may take the form of a Turing instability, in which an activator (the dispersing prey population) is contained by a repressor (the more rapidly dispersing predator population) generating a spatial pattern of clusters of prey and predators, and second, an indirect intransitive loop (where A beats B beats C beats A) emerges from the simple fact that the system is spatial. Two common invasive ant species, Wasmannia auropunctata and Solenopsis invicta, and the parasitic phorid flies of S. invicta commonly coexist in Puerto Rico. Emergent spatial patterns generated by the combination of the Turing mechanism and the indirect intransitive loop are likely to be common here. This theoretical framework and the realities of the natural history in the field could explain both the long-term coexistence of these two species, and the highly variable pattern of their occurrence across a large landscape.

A theory of centriole duplication based on self-organized spatial pattern formation

In each cell cycle, centrioles are duplicated to produce a single copy of each preexisting centriole. At the onset of centriole duplication, the master regulator Polo-like kinase 4 (Plk4) undergoes a dynamic change in its spatial pattern around the preexisting centriole, forming a single duplication site. However, the significance and mechanisms of this pattern transition remain unknown. Using super-resolution imaging, we found that centriolar Plk4 exhibits periodic discrete patterns resembling pearl necklaces, frequently with single prominent foci. Mathematical modeling and simulations incorporating the self-organization properties of Plk4 successfully generated the experimentally observed patterns. We therefore propose that the self-patterning of Plk4 is crucial for the regulation of centriole duplication. These results, defining the mechanisms of self-organized regulation, provide a fundamental principle for understanding centriole duplication.