Nonlinear Birth-Death Models

  • James H. Matis
  • Thomas R. Kiffe
Part of the Lecture Notes in Statistics book series (LNS, volume 145)


Consider now modeling the single population of sizeX(t)with population rates
$$ \lambda _X = \left\{ \begin{gathered} a_1 X - b_1 X^{s + 1} for X < (a_1 /b_1 )^{1/s} \hfill \\ 0 otherwise \hfill \\ \end{gathered} \right. $$
$$ \mu _X = a_2 X + b_2 X^{s + 1} $$
for integers >1. These are called nonlinear rates in ecological population modeling because the per capita rates, i.e.Ax/X, are obviously functions ofX, as discussed in Section 3.7. The aiare called the intrinsic rates, and are interpreted as the per-capita birth and death rate coefficients for small initial population sizes, before population density pressures are of any practical consequence. Theb i are the crowding coefficients which add density-dependency to the model. Their inclusion may in principle yield long-term, equilibrium solutions for the model.


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Copyright information

© Springer-Verlag New York, Inc. 2000

Authors and Affiliations

  • James H. Matis
    • 1
  • Thomas R. Kiffe
    • 2
  1. 1.Department of StatisticsTexas A&M UniversityCollege StationUSA
  2. 2.Department of MathematicsTexas A&M UniversityCollege StationUSA

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