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Spinal study of a population model for colonial species with interactions and environmental noise

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  • Billiard, Sylvain
  • Medous, Charles
  • Smadi, Charline

Abstract

We introduce and study a stochastic model for the dynamics of colonial species, which reproduce through fission or fragmentation. The fission rate depends on the relative sizes of colonies in the population, and the growth rate of colonies is influenced by intrinsic and environmental stochasticities. Our setting thus captures the effect of an external noise, correlating the trait dynamics of all colonies. In particular, we study the effect of the strength of this correlation on the distribution of resources between colonies. We then extend this model to a large class of structured branching processes with interactions in which the particle type evolves according to a diffusion. The branching and death rates are general functions of the whole population. In this framework, we derive a ψ-spine construction and a Many-to-One formula, extending previous works on interacting branching processes. Using this spinal construction, we also propose an alternative simulation method and illustrate its efficiency on the colonial population model. The extended framework we propose can model various ecological systems with interactions, and individual and environmental noises.

Suggested Citation

  • Billiard, Sylvain & Medous, Charles & Smadi, Charline, 2026. "Spinal study of a population model for colonial species with interactions and environmental noise," Stochastic Processes and their Applications, Elsevier, vol. 196(C).
    • Handle: RePEc:eee:spapps:v:196:y:2026:i:c:s0304414926000554
    DOI: 10.1016/j.spa.2026.104923
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    References listed on IDEAS

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    1. Hardy, Robert & Harris, Simon C., 2006. "A conceptual approach to a path result for branching Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 116(12), pages 1992-2013, December.
    2. Monique Jeanblanc & Marc Yor & Marc Chesney, 2009. "Mathematical Methods for Financial Markets," Springer Finance, Springer, number 978-1-84628-737-4, October.
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