Forward and inverse modeling studies of the relationship between tree ring width and bivariate climate are performed using a model called VS-Lite. The monthly time-step model incorporates two simple but realistic nonlinearities in its description of the transformation of climate variability into ring width index. These features ground VS-Lite in scientific principles and make it more complex than empirically-derived statistical models commonly used to simulate tree ring width. At the same time, VS-Lite is vastly simpler and more efficient than pre-existing numerical models that simulate detailed biological aspects of tree growth. A forward modeling validation study shows that VS-Lite simulates a set of observed chronologies across the continental United States with comparable or better skill than simulations derived from a standard, linear regression based approach. This extra skill derives from VS-Lite's basis in mechanistic principles, which makes it more robust than the statistical methodology to climatic nonstationarity. A Bayesian parameterization approach is also developed that incorporates scientific information into the choice of locally optimal VS-Lite parameters. The parameters derived using the scheme are found to be interpretable in terms of the climate controls on growth, and so provide a means to guide applications of the model across varying climatologies. The first reconstructions of paleoclimate that assimilate scientific understanding of the ring width formation process are performed using VS-Lite to link the proxy data to potential climate histories. Bayesian statistical methods invert VS-Lite conditional on a given dendrochronolgy to produce probabilistic estimates of local bivariate climate. Using VS-Lite in this manner produces skillful estimates, but does not present advantages compared another set of probabilistic reconstructions that invert a simpler, linear, empirical forward model. This result suggests that future data-assimilation based reconstructions will need to integrate as many data sources as possible, both across space and proxy types, in order to benefit from information provided by mechanistic models of proxy formation.