Evolutionary distributions and competition by way of reaction-diffusion and by way of convolution
- Resource Type
- Authors
- Yosef Cohen; Gonzalo Galiano
- Source
- Bulletin of mathematical biology. 75(12)
- Subject
- General Mathematics
Immunology
Population
Population Dynamics
Context (language use)
Biology
Models, Biological
General Biochemistry, Genetics and Molecular Biology
Evolutionarily stable strategy
Competitive exclusion principle
Animals
Humans
Statistical physics
Selection, Genetic
education
Selection (genetic algorithm)
General Environmental Science
Pharmacology
education.field_of_study
Natural selection
General Neuroscience
Computational Biology
Mathematical Concepts
Biological Evolution
Genetics, Population
Phenotype
Computational Theory and Mathematics
Population model
Kernel (image processing)
Evolutionary biology
Genetic Fitness
General Agricultural and Biological Sciences
- Language
- ISSN
- 1522-9602
Evolution by natural selection is the most ubiquitous and well understood process of evolution. We say distribution instead of the distribution of the density of populations of phenotypes across the values of their adaptive traits. A phenotype refers to an organism that exhibits a set of values of adaptive traits. An adaptive trait is a trait that a phenotype exhibits where the trait is subject to natural selection. Natural selection is a process by which populations of different phenotypes decline at different rates. An evolutionary distribution (ED) encapsulates the dynamics of evolution by natural selection. The main results are: (i) ED are derived by way of PDE of reaction-diffusion type and by way of integro-differential equations. The latter capture mutations through convolution of a kernel with the rate of growth of a population. The kernel controls the size and rate of mutations. (ii) The numerical solution of a logistic-like ED driven by competition corresponds to a bounded traveling wave solution of population models based on the logistic. (iii) Competition leads to increase in diversity of phenotypes on a single ED. Diversity refers to change in the number of local maxima (minima) within the bounds of values of adaptive traits. (iv) The principle of competitive exclusion in the context of evolution depends, smoothly, on the size and rate of mutations. (v) We identify the sensitivity—with respect to survival—of phenotypes to changes in values of adaptive traits to be an important parameter: increase in the value of this parameter results in decrease in evolutionary-based diversity. (vi) Stable ED corresponds to Evolutionary Stable Strategy; the latter refers to the outcome of a game of evolution.