Knowledge of species' geographic distributions is critical for understanding and forecasting population dynamics, responses to environmental change, biodiversity patterns, and conservation planning. While many suggestive correlative occurrence models have been used to these ends, progress lies in understanding the underlying population biology that generates patterns of range dynamics. Here, we show how to use a limited quantity of demographic data to produce demographic distribution models (DDMs) using integral projection models for size-structured populations. By modeling survival, growth, and fecundity using regression, integral projection models can interpolate across missing size data and environmental conditions to compensate for limited data. To accommodate the uncertainty associated with limited data and model assumptions, we use Bayesian models to propagate uncertainty through all stages of model development to predictions. DDMs have a number of strengths: 1) DDMs allow a mechanistic understanding of spatial occurrence patterns; 2) DDMs can predict spatial and temporal variation in local population dynamics; 3) DDMs can facilitate extrapolation under altered environmental conditions because one can evaluate the consequences for individual vital rates. To illustrate these features, we construct DDMs for an overstory perennial shrub in the Proteaceae family in the Cape Floristic Region of South Africa. We find that the species' population growth rate is limited most strongly by adult survival throughout the range and by individual growth in higher rainfall regions. While the models predict higher population growth rates in the core of the range under projected climates for 2050, they also suggest that the species faces a threat along arid range margins from the interaction of more frequent fire and drying climate. The results (and uncertainties) are helpful for prioritizing additional sampling of particular demographic parameters along these gradients to iteratively refine projections. In the appendices, we provide fully functional R code to perform all analyses.
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