  The Fisher-Stefan model involves solving the Fisher-KPP equation on a domain
whose boundary evolves according to a Stefan-like condition. The Fisher-Stefan
model alleviates two practical limitations of the standard Fisher-KPP model
when applied to biological invasion. First, unlike the Fisher-KPP equation,
solutions to the Fisher-Stefan model have compact support, enabling one to
define the interface between occupied and unoccupied regions unambiguously.
Second, the Fisher-Stefan model admits solutions for which the population
becomes extinct, which is not possible in the Fisher-KPP equation. Previous
research showed that population survival or extinction in the Fisher-Stefan
model depends on a critical length in one-dimensional Cartesian or
radially-symmetric geometry. However, the survival and extinction behaviour for
general two-dimensional regions remains unexplored. We combine analysis and
level-set numerical simulations of the Fisher-Stefan model to investigate the
survival-extinction conditions for rectangular-shaped initial conditions. We
show that it is insufficient to generalise the critical length conditions to
critical area in two-dimensions. Instead, knowledge of the region geometry is
required to determine whether a population will survive or become extinct.
