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Age distribution dynamics with stochastic jumps in mortality.

Salvatore Calabrese1, Amilcare Porporato1,2, Francesco Laio3

  • 1Department of Civil and Environmental Engineering, Princeton University, Princeton, NJ, USA.

Proceedings. Mathematical, Physical, and Engineering Sciences
|December 12, 2017
PubMed
Summary

This study introduces a stochastic model for population dynamics, incorporating random birth and mortality events. It provides solutions for age distribution and population moments, with applications in soil science.

Keywords:
M’Kendrick–von Foerster equationPoisson jumpsage distribution dynamicsstochastic mortalitystochastic soil salinity

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Area of Science:

  • Mathematical Biology
  • Stochastic Processes
  • Soil Science

Background:

  • Deterministic age distribution models are widely used, but the impact of stochasticity in birth and mortality remains understudied.
  • External events causing sudden population losses (jumps in mortality) are not well-integrated into existing models.

Purpose of the Study:

  • To analyze a stochastic M'Kendrick-von Foerster equation with mortality jumps.
  • To derive explicit solutions for population age distribution, total population, and their moments.
  • To apply the developed framework to model salt distribution in the soil root zone.

Main Methods:

  • Developed a stochastic M'Kendrick-von Foerster equation incorporating mortality jumps.
  • Derived analytical solutions for probability density functions (PDFs) of age distribution and total population.
  • Calculated temporal dynamics for population moments, mean age, and harmonic mean age.
  • Applied the model to a soil science problem involving salt accumulation and loss.

Main Results:

  • Obtained explicit solutions for the PDFs of age distribution and total population.
  • Characterized the temporal dynamics of population moments, mean age, and harmonic mean.
  • Successfully applied the stochastic framework to model salt distribution in the soil root zone, considering deposition, uptake, and percolation losses.

Conclusions:

  • Stochasticity, particularly mortality jumps, significantly influences population dynamics and age structure.
  • The developed stochastic model provides a robust framework for analyzing populations with sudden losses.
  • The model's application to soil salinization demonstrates its versatility in addressing complex environmental processes.