Population Projection - Logistics Curve

Population growth follows a mathematical relationship, which establishes an S-shaped curve.

The population tends asymptotically to a saturation value.

The parameters can also be estimated by non-linear regression.

Required conditions:

• P0 < P1 < P2 e e P0.P2 < P1^2
• The inflection point on the curve occurs at time [to-ln(c)/K1] and with Pt=Ps/2
• To apply the formulas, the data must be equidistant in time.

• First Census
  • Year of the First Census - Year of the First Census
    (FirstCensusYear)
  • Population at First Census - Population at First Census
    (FirstCensusPop)
• Intermediate Census
  • MidCensusPop - MidCensusPop
  • MidCensusYear - MidCensusYear
• Second Census
  • Year of the Second Census - Year of the Second Census
    (SecondCensusYear)
  • Population at the Second Census - Population at the Second Census
    (SecondCensusPop)
• Start of the Project
  • Initial Year - Year the project started operating
    (StartYear)
  • Initial Population - Population at the beginning of the project
    (StartPop)
• Population Projection
  • Growth Rate - growth rate of the curve
    (kPop)
    kPop = (2 * FirstCensusPop * MidCensusPop * SecondCensusPop - (MidCensusPop^2) * (FirstCensusPop + SecondCensusPop)) /
    (FirstCensusPop * SecondCensusPop - MidCensusPop ^ 2)
  • Year of Projection - Year of End of Project
    (EndYear)
  • Final Population - Population at the end of the project
    (EndPop)
    EndPop = kPop / (1 + (kPop - FirstCensusPop) / FirstCensusPop * Math.Exp(coefK1 * (EndYear - StartYear)))
  • K1 coefficient - auxiliary coefficient
    (coefK1)
    coefK1 = 1.0 / (SecondCensusYear - MidCensusYear) * Math.Log((FirstCensusPop * (kPop - MidCensusPop)) /
    (MidCensusPop * (kPop - FirstCensusPop)))