Matrix models are a common tool used to project the population dynamics of plant species.  Recently, these have become increasingly common for problems in conservation biology.  Models are created for rare plant species to determine which factors contribute to population growth rate and elasticity analyses have been used to pinpoint which demographic vital rates should be targeted for management to improve population growth.  Likewise, matrix models have been created for invasive plants to determine which factors regulate population growth and to pinpoint which demographic vital rates should be targeted for control to reduce population growth.  Here, I present a quantitative review of matrix models and ask whether the elasticities differ among rare, common and invasive plant species.  I examine the relationship between population growth rate and its sensitivity to changes in annual fertility; this relationship is significantly positive, and those species that have faster population growth rates are more sensitive to changes in their fertility.  However, the population growth rates of invasive plant species are comparatively more sensitive to fertility, even when their higher growth rates are accounted for.  Thus, invasive plants are demographically distinct from their native counterparts.  One possible reason for this is that invasives may be ruderal species which are predisposed to becoming invasive.  Another explanation is that the factors that regulate their population growth rates differ from those that regulate population growth of native plants species, and these factors result in a shift in the elasticity structure.  I examine this further in analyses that control for plant life span and evolutionary history.