  We analyze the properties of population spreading in environments with
spatial anisotropy within the frames of a lattice model of asymmetric (biased)
random walkers. The expressions for the universal shape characteristics of the
instantaneous configuration of population, such as asphericity $A$ and
prolateness $S$ are found analytically and proved to be dependent only on the
asymmetric transition probabilities in different directions. The model under
consideration is shown to capture, in particular, the peculiarities of invasion
in presence of an array of oriented tubes (fibers) in the environment.
