A Minimal CA-Based Model Capturing Evolutionarily Relevant Features of Biological Development

Miguel Brun-Usan (), Javier de Juan García and Roberto Latorre
Additional contact information
Miguel Brun-Usan: CABD-Centro Andaluz de Biología del Desarrollo, CSIC-Universidad Pablo de Olavide, Campus UPO, 41013 Seville, Spain
Javier de Juan García: Departamento Ingeniería Informática, Escuela Politécnica Superior, Universidad Autónoma de Madrid, 28049 Madrid, Spain
Roberto Latorre: Departamento Ingeniería Informática, Escuela Politécnica Superior, Universidad Autónoma de Madrid, 28049 Madrid, Spain

Mathematics, 2025, vol. 13, issue 19, 1-24

Abstract: Understanding how complex biological forms emerge and evolve remains a central question in evolutionary and developmental biology. To explore this complexity, we introduce a minimal two-dimensional, cellular automaton (CA)-based model that captures key features of biological development—such as spatial growth, self-organization, and differentiation—while remaining computationally tractable and evolvable. Unlike most abstract genotype–phenotype mapping models, our approach generates emergent morphological complexity through spatially explicit rule-based interactions governed by a simple genetic vector, resulting in self-organized patterns reminiscent of biological morphogenesis. Using simulations, we show that, as observed in empirical studies, the resulting phenotypic distribution is highly skewed: simple forms are common, while complex ones are rare. The model exhibits a strongly non-linear genotype-to-phenotype mapping in such a way that small genetic changes can lead to disproportionately large morphological shifts. Notably, transitions toward complexity are less frequent than regressions to simplicity, reflecting evolutionary asymmetries observed in natural systems. We further demonstrate that, by allowing for mutations in the generative rules, our model is capable of adaptive evolution and even reproducing generic features of tumoral growth. These findings suggest that even minimal developmental rules can give rise to rich, hierarchical patterns and complex evolutionary dynamics, positioning our CA-based model as a powerful tool for investigating how developmental constraints and biases shape morphological evolution.

Keywords: cell automaton; self-organization; genotype-phenotype-map; spatial pattern; complexity; evolvability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/19/3238/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/19/3238/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:19:p:3238-:d:1767578

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().