A generalized, coupled system of finite-difference equations is used to describe a population in which one generation depletes the carrying capacity of a subsequent one. It is shown through graphical presentation of numerically defined stability characteristics that the general consequence of this interaction is severe instability. Potential evolutionary strategies which restore system stability are examined by modifying the original set of equations and repeating the analysis. It is concluded from these results that there are at least two general types of stabilizing strategies: refuge and reduction of intergenerational flow. The latter strategy is further subdivided into diversion and dispersion tactics. These strategies may be ranked according to their tendency toward stable, single-point equilibrium as follows: Diversion > Refuge > Dispersion. Biological attributes of species illustrating these methods are outlined. Finally, the significance of these findings to other evolutionary strategies (e.g., r and K selection) is discussed.