Understanding the evolution of dispersal is an important issue in evolutionary
ecology. For continuous time models in which individuals disperse throughout their
lifetime, it has been shown that a balanced dispersal strategy, which results in an ideal
free distribution, is evolutionary stable in spatially varying but temporally constant
environments. Many species, however, primarily disperse prior to reproduction (natal
dispersal) and less commonly between reproductive events (breeding dispersal). As
demographic and dispersal terms combine in a multiplicative way for models of natal
dispersal, rather than the additive way for the previously studied models, we develop new
mathematical methods to study the evolution of natal dispersal for continuous-time and
discrete-time models. A fundamental ecological dichotomy is identified for the non-trivial
equilibrium of these models: (i) the per-capita growth rates for individuals in all patches
is equal to zero, or (ii) individuals in some patches experience negative per-capita growth
rates, while individuals in other patches experience positive per-capita growth rates. The
first possibility corresponds to an ideal-free distribution, while the second possibility
corresponds to a "source-sink" spatial structure. We prove that populations with a
dispersal strategy leading to an ideal-free distribution displace populations with
dispersal strategy leading to a source-sink spatial structure. When there are patches which
can not sustain a population, ideal-free strategies can be achieved by sedentary
populations, and we show that these populations can displace populations with any
irreducible dispersal strategy. Collectively, these results support that evolution selects
for natal or breeding dispersal strategies which lead to ideal-free distributions in
spatially heterogenous, but temporally homogenous, environments.