Population dynamicsPopulation dynamics is the type of mathematics used to model and study the size and age composition of populations as dynamical systems. Population dynamics is a branch of mathematical biology, and uses mathematical techniques such as differential equations to model behaviour. Population dynamics is also closely related to other mathematical biology fields such as epidemiology, and also uses techniques from evolutionary game theory in its modelling.
Frequency-dependent selectionFrequency-dependent selection is an evolutionary process by which the fitness of a phenotype or genotype depends on the phenotype or genotype composition of a given population. In positive frequency-dependent selection, the fitness of a phenotype or genotype increases as it becomes more common.In negative frequency-dependent selection, the fitness of a phenotype or genotype decreases as it becomes more common.
EvolutionChange in the heritable traits of populationsEvolution is the change in the heritable characteristics of biological populations over successive generations. It happens when individuals in a population vary in their genetic characteristics and in the numbers of their surviving offspring. Mutation introduces new genetic variation, and processes such as genetic drift, gene flow, and natural selection result in some genetic variants becoming more or less common over time.
Fitness (biology)Fitness (often denoted w{\displaystyle w} or ω in population genetics models) is a quantitative representation of what tends to be favored by natural selection. Fitness can be defined either with respect to a genotype or to a phenotype in a given environment or time. The fitness of a genotype is manifested through its phenotype, which is also affected by the developmental environment. The fitness of a given phenotype can also be different in different selective environments.Evolutionary game theoryEvolutionary game theory (EGT) is the application of game theory to evolving populations in biology. It defines a framework of contests, strategies, and analytics into which Darwinian competition can be modelled. It originated in 1973 with John Maynard Smith and George R. Price's formalisation of contests, analysed as strategies, and the mathematical criteria that can be used to predict the results of competing strategies.
PhenotypeIn genetics, the phenotype (from Ancient Greek (phaínō)'to appear, show' and (túpos)'mark, type') is the set of observable characteristics or traits of an organism. The term covers all traits of an organism other than its genome, however transitory: the organism's morphology (physical form and structure), its developmental processes, its biochemical and physiological properties whether reversible or irreversible, and all its behavior, such as a peacock's display.
EcologyEcology (from Ancient Greek οἶκος (oîkos) 'house' and -λογία (-logía) 'study of') is the natural science which studies the interactions between organisms and their environments. Ecology considers organisms at the community, ecosystem, and biosphere levels. Ecology overlaps with the sciences of biogeography, evolutionary biology, genetics, and ethology.
Phenotypic traitA phenotypic trait, simply trait, or character state is any distinct variant of a phenotypic, or observable, characteristic of an organism; it may be either inherited or determined environmentally but typically occurs as a combination of the two. For example, having eye color is a character of an organism, while blue, brown and hazel versions of eye color are traits.
ParameterA parameter (from Ancient Greek (pará)'beside, subsidiary' and (métron)'measure'), generally, is any characteristic that can help in defining or classifying a particular system (meaning an event, project, object, situation, etc.).
Expression (mathematics)In mathematics, an expression is an arrangement of symbols following the context-dependent, syntactic conventions of mathematical notation. Symbols can denote numbers, variables, operations, and functions. Other symbols include punctuation marks and brackets, used for grouping where there is not a well-defined order of operations.
Asexual reproductionAsexual reproduction is a type of reproduction that does not involve the fusion of gametes or change in the number of chromosomes. The offspring that arise by asexual reproduction from either unicellular or multicellular organisms inherit the full set of genes of their single parent and thus the newly created individual is genetically and physically similar to the parent or an exact clone of the parent.
Differential equationType of functional equation (mathematics) In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two.*As an Amazon Associate I earn from qualifying purchases.