A Delay-Based Theory of Pigeon Population Growth (DBTPPG): Biological Foundations, Mathematical Modelling, and Econometric Extensions

Classical population growth models predominantly rely on instantaneous reproduction and density-dependent regulation, often failing to explain why populations remain seemingly stable for extended periods before undergoing rapid and unexpected expansion. This study introduces the Delay-Based Theory of Pigeon Population Growth (DBTPPG) as a new, mechanism-driven population growth theory that places reproductive delay at the centre of population dynamics. Grounded in avian life-history biology, discrete-time delay difference mathematics, econometric lag structures, and statistical systems analysis, DBTPPG demonstrates that nonlinear and potentially explosive population growth can emerge even under constant fertility and zero mortality, purely through the accumulation of reproductively mature cohorts over time. The theory is formalised using a deterministic delay difference equation representing a six-month maturation period, and its implications are examined through month-wise simulation, sensitivity analysis, and structural extensions incorporating mortality, carrying capacity, and stochastic shocks. Results reveal a distinct phase structure—latency, acceleration, and explosion—highlighting why short-term observations and delayed policy interventions systematically underestimate long-term growth potential. Econometric interpretation further shows that population control is subject to inertia analogous to lagged accumulation processes in dynamic economic systems. While developed using pigeons as an empirical reference, DBTPPG is shown to be generalizable to a wide class of biological and socio-economic systems characterised by maturation delay and continuous output. By elevating delay from a secondary modifier to a primary causal driver, this study advances population theory and offers critical insights for urban ecology, public health planning, and proactive population governance. Keywords: Delay-based population theory; Pigeon population dynamics; Delay difference equations; Urban ecology; Lagged accumulation; Nonlinear growth dynamics