The Influence of Demographic Stochasticity on Population Dynamics

1. Front Matter

   Pages i-xvii

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2. Introduction

   • Tommaso Biancalani

   Pages 1-17

3. Methods

   • Tommaso Biancalani

   Pages 19-30

4. Noise-Induced Bistability

   • Tommaso Biancalani

   Pages 31-61

5. Stochastic Waves on Regular Lattices

   • Tommaso Biancalani

   Pages 63-82

6. Stochastic Waves on Complex Network

   • Tommaso Biancalani

   Pages 83-98

7. Conclusions

   • Tommaso Biancalani

   Pages 99-105

8. Back Matter

   Pages 107-113

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The dynamics of population systems cannot be understood within the framework of ordinary differential equations, which assume that the number of interacting agents is infinite. With recent advances in ecology, biochemistry and genetics it is becoming increasingly clear that real systems are in fact subject to a great deal of noise. Relevant examples include social insects competing for resources, molecules undergoing chemical reactions in a cell and a pool of genomes subject to evolution. When the population size is small, novel macroscopic phenomena can arise, which can be analyzed using the theory of stochastic processes. This thesis is centered on two unsolved problems in population dynamics: the symmetry breaking observed in foraging populations and the robustness of spatial patterns. We argue that these problems can be resolved with the help of two novel concepts: noise-induced bistable states and stochastic patterns.

• Fluctuation in Small Populations
• Fokker-Planck Equation
• Gillespie Algorithm
• Noise-induced Bistability
• Population Dynamics and Noise
• Robustness of Spatial Patterns
• Stochastic Patterns
• Symmetry Breaking in Foraging Populations
• Van Kampen Expansion
• data-driven science, modeling and theory building

• Department of Physics, University of Illinois at Urbana-Champaign, Urbana, USA

  Tommaso Biancalani

Tommaso Biancalani is currently a post-doctoral researcher with a joint appointment at the NASA Astrobiology Institute and the Department of Physics at the University of Illinois. He is working on the evolutionary theory of the origin of life. Previously, he contributed to the fields of non-equilibrium statistical mechanics and population dynamics. He has obtained a PhD in theoretical physics from the University of Manchester in 2013, under the supervision of Prof. Alan McKane.

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