  This paper considers a multi-patch model, where each patch follows a logistic
law, and patches are coupled by asymmetrical migration terms. First, in the
case of perfect mixing, i.e when the migration rate tends to infinity, the
total population follows a logistic equation with a carrying capacity which in
general is different from the sum of the n carrying capacities, and depends on
the migration terms. Second, we determine, in some particular cases, the
conditions under which fragmentation and asymmetrical migration can lead to a
total equilibrium population greater or smaller than the sum of the carrying
capacities. Finally, for the three-patch model, we show numerically the
existence of at least three critical values of the migration rate for which the
total equilibrium population equals the sum of the carrying capacities.
