Spatially Inhomogeneous Populations with Seed-Banks: I. Duality, Existence and Clustering

We consider a system of interacting Moran models with seed-banks. Individuals live in colonies and are subject to resampling and migration as long as they are active. Each colony has a seed-bank into which individuals can retreat to become dormant, suspending their resampling and migration until they become active again. The colonies are labelled by $${\mathbb {Z}}^d$$ Z d , $$d \ge 1$$ d ≥ 1 , playing the role of a geographic space. The sizes of the active and the dormant population are finite and depend on the location of the colony. Migration is driven by a random walk transition kernel. Our goal is to study the equilibrium behaviour of the system as a function of the underlying model parameters. In the present paper, under a mild condition on the sizes of the active populations, the system is well defined and has a dual. The dual consists of a system of interacting coalescing random walks in an inhomogeneous environment that switch between an active state and a dormant state. We analyse the dichotomy of coexistence (= multi-type equilibria) versus clustering (= mono-type equilibria) and show that clustering occurs if and only if two random walks in the dual starting from arbitrary states eventually coalesce with probability one. The presence of the seed-bank enhances genetic diversity. In the dual this is reflected by the presence of time lapses during which the random walks are dormant and do not move.

The “Missing Link”

The inauguration of a steamship route between Canada and Australia, described as the “missing link,” was envisaged to complete Britain's imperial circuit of the globe. This article examines the early proposals and projects for a service between Vancouver and Sydney, which finally commenced in 1893. The route was more than a means of physically bridging the gulf between Canada and Australia. Serving as a conduit for ideologies and expectations, it became a key element of aspirations to reconfigure the Pacific as a natural domain for the extension of settler-colonial power and influence. In centering the “white” Pacific and relations between white colonies in empire, the route's early history, although one of friction and contestation, offers new insights into settler-colonial mobilities beyond dominant themes of metropole–colony migration.