  In this paper, we study the dynamics of a two-species competition model with
two different free boundaries in heterogeneous time-periodic environment, where
the two species adopt a combination of random movement and advection upward or
downward along the resource gradient. We show that the dynamics of this model
can be classified into four cases, which forms a spreading-vanishing
quartering. The notion of the minimal habitat size for spreading is introduced
to determine if species can always spread. Rough estimates of the asymptotic
spreading speed of free boundaries and the long time behavior of solutions are
also established when spreading occurs. Furthermore, some sufficient conditions
for spreading and vanishing are provided.
