Nonlinear models which incorporate one or more density dependent feedbacks on plant population growth have been used previously to interpret or project past or future population performance. Under controlled conditions, it may be possible to isolate and estimate the effects of neighbor density on per capita survival or fitness. However, these feedbacks can interact with other unmeasured factors in natural populations and result in over- or underestimation of density effects at different plant densities. We followed the survival and reproduction of individuals of the invasive weed Alliaria petiolata (garlic mustard Brassicaceae) from 13 natural study populations in Illinois and Michigan, USA, from 2004 to 2007 and evaluated the strength and relative importance of density feedbacks on four demographic transitions, including fecundity and survival in 3 life stages, across a natural density gradient spanning over three orders of magnitude. Using mixed-effects models, we evaluated the strength and direction of direct density dependence. By explicitly modeling the variance in survival as an exponential function of plant density, we show that the relative importance of density dependence is itself a density dependent function.
Results/Conclusions
The recruitment phase is most affected by plant density in our study populations and was the only stage with a significant mean response to the fixed effect of density. In all transitions the variance in both survival and fecundity decay exponentially as functions of initial plant density. At low plant densities, seedling, summer, and winter survival probabilities range from 0 to 1, and fecundity ranges from 0 to over 2500 seeds plant-1. As population density increases, the variation around the mean survival probabilities and fecundity declines exponentially such that survival probabilities rarely exceed 0.5, and fecundity does not exceed 500 seeds plant-1 at the highest population densities observed. The demographic rates in these models thus effectively transition from behaving like stochastic variables to behaving in a more deterministic fashion as density increases. These results suggest that nonlinear models parameterized from natural populations may benefit from treating density dependent feedbacks on demographic transitions as processes whose mean and variance simultaneously respond to changes in population density.
