  While the overarching pattern of biannual avian migration is well understood,
there are significant questions pertaining to this phenomenon that invite
further study. Necessary to any analysis of these questions is an understanding
of how a given species' spatial distribution evolves in time. While studies of
animal movement are often conducted using telemetry data, the collection of
such data can be time- and resource-intensive, frequently resulting in small
sample sizes. Ecological surveys of animal populations are also indicative of
species distribution trends, but may be constrained to a limited spatial
domain. Within this article we utilize crowd-sourced observations from the
eBird database to model the abundance of migratory bird species in space and
time. While crowd-sourced observations are individually less reliable than
those produced by experts, the sheer size and spatial coverage of the eBird
database make it attractive for use in this setting. We introduce a hidden
Markov model for observed bird counts utilizing a novel transition structure
developed using principles from circuit theory. After illustrating model
properties we fit it to observations of Baltimore orioles and yellow-rumped
warblers within the eastern United States and discuss insight it provides into
the migratory patterns for these species.
