Agent-Based Modeling of Locust Foraging and Social Behavior

Locust swarms contain millions of individuals and are a threat to agriculture on four continents. At low densities, locusts are solitary foragers; however, when crowded, they undergo an epigenetic phase change to a gregarious state in which they are attracted to other locusts. It is believed that this is an evolutionary adaptation that optimizes the seeking of resources. We have developed an agent-based model based on the solitary-gregarious transition and foraging behaviors due to hunger levels. A novel feature of our model is that it treats food resources as a dynamic variable in the environment. We discuss how social interaction strategies influence the efficiency of foraging and the effect of heterogeneous distributions of resources on the solitary-gregarious phase transitions

On the Chow and cohomology rings of moduli spaces of stable curves

In this paper, we ask: for which $(g, n)$ is the rational Chow or cohomology ring of $\overline{\mathcal{M}}_{g,n}$ generated by tautological classes? This question has been fully answered in genus $0$ by Keel (the Chow and cohomology rings are tautological for all $n$) and genus $1$ by Belorousski (the rings are tautological if and only if $n \leq 10$). For $g \geq 2$, work of van Zelm shows the Chow and cohomology rings are not tautological once $2g + n \geq 24$, leaving finitely many open cases. Here, we prove that the Chow and cohomology rings of $\overline{\mathcal{M}}_{g,n}$ are isomorphic and generated by tautological classes for $g = 2$ and $n \leq 9$ and for $3 \leq g \leq 7$ and $2g + n \leq 14$. For such $(g, n)$, this implies that the tautological ring is Gorenstein and $\overline{\mathcal{M}}_{g,n}$ has polynomial point count.Comment: 42 pages, comments welcome