Modeling population growth of a proto-city: A new urban accretion growth hypothesis and its P-CPAG model

The population growth of a proto-city (P–C, the initial stage of city-forming) is fundamental for shaping the subsequent pattern of population growth in city evolution. This study proposed a mathematical model, the P–C Population Accretion Growth (P-CPAG) model, to simulate key processes of population growth over a P–C period, based on the Urban Accretion Growth hypothesis (the UAG hypothesis). In the P-CPAG model, several parameters, e.g., natural increase rate of population(k), accretion rate (ρ), accretion radius(r), and initial population size (Pt0o), are vital for population growth. In the model examination, we determined the potential value for all parameters by the universal laws and the collected literature about the worldwide ancient cities. Based on observation and evaluation of 64 simulation scenarios, a promising plan of optimal parameters was suggested, that is, k = 0.008, ρ = 0.01, kρ = 0.003, Pt0o = 2000, Pt0i = 3.6, r = 5, N = 200000, Ni = 300. The proposed P-CPAG model sheds new light on population simulation in the critical but limited-mentioned P–C stage and has the potential to simulate population growth in other periods of city evolution. The unique perspectives on urban accretion growth and the P-CPAG model are meaningful for understanding the complicated and mysterious history of cities' evolution back about 5000 years ago.