RESUMEN
To better understand the evolution of
dispersal in spatially heterogeneous landscapes, we study difference equation models of populations
that reproduce and disperse
in a landscape consisting
of $k$ patches.
The connectivity of the patches and costs
of dispersal are determined by a $k\times
k$ column substochastic matrix $S$, where $S_{ij}$ represents the fraction of dispersing individuals
from patch $j$ that end
up in patch $i$.
Given $S$, a dispersal strategy is a $k\times 1$
vector whose $i$th entry gives the
probability $p_i$ that individuals disperse from patch $i$.
If all of
the $p_i$'s are the same, then
the dispersal strategy is called
unconditional; otherwise
it is called
conditional. For two competing populations
of unconditional dispersers, we prove that the
slower dispersing population (i.e., the population with the smaller dispersal
probability) displaces the
faster dispersing population. Alternatively, for populations of conditional dispersers without any dispersal costs
(i.e., $S$ is column stochastic and all patches can support a population), we prove that there
is a one parameter family of strategies that
resists invasion attempts by all other strategies.