dorsal/arxiv
View SchemaHierarchical population model with a carrying capacity distribution
| Authors | J. O. Indekeu, K. Sznajd-Weron |
|---|---|
| Categories | |
| ArXiv ID | physics/0212001 |
| URL | https://arxiv.org/abs/physics/0212001 |
| DOI | 10.1103/PhysRevE.68.061904 |
Abstract
A time- and space-discrete model for the growth of a rapidly saturating local biological population $N(x,t)$ is derived from a hierarchical random deposition process previously studied in statistical physics. Two biologically relevant parameters, the probabilities of birth, $B$, and of death, $D$, determine the carrying capacity $K$. Due to the randomness the population depends strongly on position, $x$, and there is a distribution of carrying capacities, $\Pi (K)$. This distribution has self-similar character owing to the imposed hierarchy. The most probable carrying capacity and its probability are studied as a function of $B$ and $D$. The effective growth rate decreases with time, roughly as in a Verhulst process. The model is possibly applicable, for example, to bacteria forming a "towering pillar" biofilm. The bacteria divide on randomly distributed nutrient-rich regions and are exposed to random local bactericidal agent (antibiotic spray). A gradual overall temperature change away from optimal growth conditions, for instance, reduces bacterial reproduction, while biofilm development degrades antimicrobial susceptibility, causing stagnation into a stationary state.
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"abstract": "A time- and space-discrete model for the growth of a rapidly saturating local\nbiological population $N(x,t)$ is derived from a hierarchical random deposition\nprocess previously studied in statistical physics. Two biologically relevant\nparameters, the probabilities of birth, $B$, and of death, $D$, determine the\ncarrying capacity $K$. Due to the randomness the population depends strongly on\nposition, $x$, and there is a distribution of carrying capacities, $\\Pi (K)$.\nThis distribution has self-similar character owing to the imposed hierarchy.\nThe most probable carrying capacity and its probability are studied as a\nfunction of $B$ and $D$. The effective growth rate decreases with time, roughly\nas in a Verhulst process. The model is possibly applicable, for example, to\nbacteria forming a \"towering pillar\" biofilm. The bacteria divide on randomly\ndistributed nutrient-rich regions and are exposed to random local bactericidal\nagent (antibiotic spray). A gradual overall temperature change away from\noptimal growth conditions, for instance, reduces bacterial reproduction, while\nbiofilm development degrades antimicrobial susceptibility, causing stagnation\ninto a stationary state.",
"arxiv_id": "physics/0212001",
"authors": [
"J. O. Indekeu",
"K. Sznajd-Weron"
],
"categories": [
"physics.bio-ph",
"q-bio"
],
"doi": "10.1103/PhysRevE.68.061904",
"title": "Hierarchical population model with a carrying capacity distribution",
"url": "https://arxiv.org/abs/physics/0212001"
},
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