Mathematical models for evolutionary dynamics in biological populations
Vaishali Latkevaishali.latke@pccoer.inDepartment of Computer EngineeringPimpri Chinchwad Education Trust’sPimpri Chinchwad College of Engineering & ResearchPune, Maharashtra, 412101, IndiaView full profile → , *Radha ChauhanCorresponding authorDepartment of MicrobiologyNoida International UniversityGreater Noida, Uttar Pradesh, 201312, IndiaView full profile → , Chandrashekhar Ramesh Ramtirthkarchandrashekhar.ramtirthkar@vit.eduDepartment of Mechanical EngineeringVishwakarma Institute of TechnologyPune, 411037, Maharashtra, IndiaView full profile → , Mayank Srivastavamayank.shrivastava@gla.ac.inDepartment of Computer Engineering & ApplicationsGLA UniversityMathura, Uttar Pradesh, 281406, IndiaView full profile → , Dikshit Sharmadikshit.sharma.orp@chitkara.edu.inCentre for Research Impact and Outcome (CRIO)Chitkara UniversityRajpura, Punjab, 140401, IndiaView full profile → , A. Saravanansaravanan.a@adityauniversity.inDepartment of Mechanical EngineeringAditya UniversitySurampalem, Andhra Pradesh, 533437, IndiaView full profile → , Bogolu Rupabogolurupa@outlook.comDepartment of Computer Science and Engineering (Data Science)Vardhaman College of EngineeringHyderabad, Telangana, 501218, IndiaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 01 Apr 2026
- Published Online:
- 27 Oct 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-2823
- Pages:
- 3109–3121
Abstract
The dynamics of biological populations is a complex process that includes selection, mutation, inheritance, migration and random genetic variation, and predicting the dynamics is difficult. The issue of quantifying these interaction mechanisms in a single functional mathematical model is tackled in this work. The goal is to create mathematical models that will enable the description of the evolution of population states and long time behavior of the model. The approach utilized is based on nonlinear differential equations, replicator dynamics, mutation selection equations, equilibrium analysis and numerical simulation. Under various parameter conditions, the stability, convergence, fitness of populations, variation in allele frequencies and evolutionary trajectory are analyzed. Results show that the extent of selection and mutation rates have a significant effect on the establishment of an equilibrium, population diversities, and adaptation. Findings show that the results vary with stable, unstable and coexistence states under different evolutionary scenarios. The innovations are the combination of several evolutionary mechanisms within a tractable computational framework. The study provides quantitative tools for predicting population adaptation, and also concludes that mathematical modeling can provide a characterization of the complex evolutionary dynamics.
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References
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