We use a simple stage-structured model to investigate the influence of resource-dependent rates on population dynamics, and discuss the demography of two contrasting types of cycle that can occur – large amplitude cycles with a period shorter than the juvenile development time and smaller amplitude cycles with a period longer than the generation time. For certain parameter combinations, there are multiple attractors with both types of cycle possible, depending on initial histories.  The resulting cyclic patterns of resource dynamics have a strong impact on natural selection. Small-amplitude consumer-resource cycles lead to lower rates of natural selection than do large-amplitude consumer-resource cycles. We parameterize the model for a laboratory Daphnia-algal system, for which multiple periodic attractors have been previously reported (McCauley et al. Nature 402: 653-656, 1999), and use the model to test whether resource-dependent life-history can explain the recently published observation that selection among Daphnia genotypes changed depending on the pattern of resource fluctuations (Nelson et al. Nature 433: 413-417, 2005). Our results reveal that the common ecological features of resource-dependent life-history and ontogenetic size-structure may contribute to population stability and to the maintenance of diversity, phenomena traditionally discussed in terms of density dependence and intra- or inter-specific competition.  The model provides a context for addressing conceptual questions on how to characterize inter-size-class competition.