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1. Ecological Modeling

   Linked via "statistical regression"

   Mechanistic models (or process-based models) attempt to explicitly represent the underlying biological, physical, and chemical processes governing system behavior. For instance, a Lotka-Volterra predator-prey model explicitly defines per-capita growth rates, consumption rates, and mortality rates based on hypothesized interactions. These models are highly dependent on accurate parameterization of underlying ecological theory.
   Empirical models rely primarily on observed inp…

2. Empirical Model

   Linked via "statistical regression"

   Historical Development and Context
   The formal recognition of empirical modeling as a distinct discipline within applied mathematics began in the early 19th century's, spurred by advancements in precision measurement in fields like astronomy and early geology. While curve fitting has ancient roots, the systematic application of statistical regression to create robust predictive frameworks gained traction after the standardization of [least squares methods](/e…