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Evolutionary Dynamics
Evolutionary dynamics is the study of the mathematical principles according to which biological organisms as well as cultural ideas evolve and evolved. This is mostly achieved through the mathematical discipline of population genetics, along with evolutionary game theory. Most population genetics considers changes in the frequencies of alleles at a small number of gene loci. When infinitesimal effects at a large number of gene loci are considered, one derives quantitative genetics. Traditional population genetic models deal with alleles and genotypes, and are frequently stochastic. In evolutionary game theory, developed first by John Maynard Smith, evolutionary biology concepts may take a deterministic mathematical form, with selection acting directly on inherited phenotypes. These same models can be applied to studying the evolution of human preferences and ideologies. Many variants on these models have been developed, which incorporate weak selection, mutual population structur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), Mathematical analysis, analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of mathematical object, abstract objects that consist of either abstraction (mathematics), abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to proof (mathematics), prove properties of objects, a ''proof'' consisting of a succession of applications of in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Evolution
Evolution is the change in the heritable Phenotypic trait, characteristics of biological populations over successive generations. It occurs when evolutionary processes such as natural selection and genetic drift act on genetic variation, resulting in certain characteristics becoming more or less common within a population over successive generations. The process of evolution has given rise to biodiversity at every level of biological organisation. The scientific theory of evolution by natural selection was conceived independently by two British naturalists, Charles Darwin and Alfred Russel Wallace, in the mid-19th century as an explanation for why organisms are adapted to their physical and biological environments. The theory was first set out in detail in Darwin's book ''On the Origin of Species''. Evolution by natural selection is established by observable facts about living organisms: (1) more offspring are often produced than can possibly survive; (2) phenotypic variatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Population Genetics
Population genetics is a subfield of genetics that deals with genetic differences within and among populations, and is a part of evolutionary biology. Studies in this branch of biology examine such phenomena as Adaptation (biology), adaptation, speciation, and population stratification, population structure. Population genetics was a vital ingredient in the emergence of the Modern synthesis (20th century), modern evolutionary synthesis. Its primary founders were Sewall Wright, J. B. S. Haldane and Ronald Fisher, who also laid the foundations for the related discipline of quantitative genetics. Traditionally a highly mathematical discipline, modern population genetics encompasses theoretical, laboratory, and field work. Population genetic models are used both for statistical inference from DNA sequence data and for proof/disproof of concept. What sets population genetics apart from newer, more phenotypic approaches to modelling evolution, such as evolutionary game theory and evolu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Allele
An allele is a variant of the sequence of nucleotides at a particular location, or Locus (genetics), locus, on a DNA molecule. Alleles can differ at a single position through Single-nucleotide polymorphism, single nucleotide polymorphisms (SNP), but they can also have insertions and deletions of up to several thousand base pairs. Most alleles observed result in little or no change in the function or amount of the gene product(s) they code or regulate for. However, sometimes different alleles can result in different observable phenotypic traits, such as different pigmentation. A notable example of this is Gregor Mendel's discovery that the white and purple flower colors in pea plants were the result of a single gene with two alleles. Nearly all multicellular organisms have two sets of chromosomes at some point in their biological life cycle; that is, they are diploid. For a given locus, if the two chromosomes contain the same allele, they, and the organism, are homozygous with re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gene
In biology, the word gene has two meanings. The Mendelian gene is a basic unit of heredity. The molecular gene is a sequence of nucleotides in DNA that is transcribed to produce a functional RNA. There are two types of molecular genes: protein-coding genes and non-coding genes. During gene expression (the synthesis of Gene product, RNA or protein from a gene), DNA is first transcription (biology), copied into RNA. RNA can be non-coding RNA, directly functional or be the intermediate protein biosynthesis, template for the synthesis of a protein. The transmission of genes to an organism's offspring, is the basis of the inheritance of phenotypic traits from one generation to the next. These genes make up different DNA sequences, together called a genotype, that is specific to every given individual, within the gene pool of the population (biology), population of a given species. The genotype, along with environmental and developmental factors, ultimately determines the phenotype ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Locus (genetics)
In genetics, a locus (: loci) is a specific, fixed position on a chromosome where a particular gene or genetic marker is located. Each chromosome carries many genes, with each gene occupying a different position or locus; in humans, the total number of Human genome#Coding sequences (protein-coding genes), protein-coding genes in a complete haploid set of 23 chromosomes is estimated at 19,000–20,000. Genes may possess multiple variants known as alleles, and an allele may also be said to reside at a particular locus. Diploid and polyploid cells whose chromosomes have the same allele at a given locus are called homozygote, homozygous with respect to that locus, while those that have different alleles at a given locus are called heterozygote, heterozygous. The ordered list of loci known for a particular genome is called a gene map. Gene mapping is the process of determining the specific locus or loci responsible for producing a particular phenotype or biological trait. Association ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Infinitesimal
In mathematics, an infinitesimal number is a non-zero quantity that is closer to 0 than any non-zero real number is. The word ''infinitesimal'' comes from a 17th-century Modern Latin coinage ''infinitesimus'', which originally referred to the "infinity- th" item in a sequence. Infinitesimals do not exist in the standard real number system, but they do exist in other number systems, such as the surreal number system and the hyperreal number system, which can be thought of as the real numbers augmented with both infinitesimal and infinite quantities; the augmentations are the reciprocals of one another. Infinitesimal numbers were introduced in the development of calculus, in which the derivative was first conceived as a ratio of two infinitesimal quantities. This definition was not rigorously formalized. As calculus developed further, infinitesimals were replaced by limits, which can be calculated using the standard real numbers. In the 3rd century BC Archimedes used what ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantitative Genetics
Quantitative genetics is the study of quantitative traits, which are phenotypes that vary continuously—such as height or mass—as opposed to phenotypes and gene-products that are Categorical variable, discretely identifiable—such as eye-colour, or the presence of a particular biochemical. Both of these branches of genetics use the frequencies of different alleles of a gene in breeding populations (gamodemes), and combine them with concepts from simple Mendelian inheritance to analyze inheritance patterns across generations and descendant lines. While population genetics can focus on particular genes and their subsequent metabolic products, quantitative genetics focuses more on the outward phenotypes, and makes only summaries of the underlying genetics. Due to the continuous distribution of phenotypic values, quantitative genetics must employ many other statistical methods (such as the ''effect size'', the ''mean'' and the ''variance'') to link phenotypes (attributes) to gen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stochastic
Stochastic (; ) is the property of being well-described by a random probability distribution. ''Stochasticity'' and ''randomness'' are technically distinct concepts: the former refers to a modeling approach, while the latter describes phenomena; in everyday conversation, however, these terms are often used interchangeably. In probability theory, the formal concept of a '' stochastic process'' is also referred to as a ''random process''. Stochasticity is used in many different fields, including image processing, signal processing, computer science, information theory, telecommunications, chemistry, ecology, neuroscience, physics, and cryptography. It is also used in finance (e.g., stochastic oscillator), due to seemingly random changes in the different markets within the financial sector and in medicine, linguistics, music, media, colour theory, botany, manufacturing and geomorphology. Etymology The word ''stochastic'' in English was originally used as an adjective with the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Evolutionary Game Theory
Evolutionary 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 Darwinism, 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. Evolutionary game theory differs from classical game theory in focusing more on the dynamics of strategy change. This is influenced by the frequency of the competing strategies in the population. Evolutionary game theory has helped to explain the basis of altruism (biology), altruistic behaviours in Darwinian evolution. It has in turn become of interest to economists, sociologists, anthropologists, and philosophers. History Classical game theory Classical non-cooperative game theory was conceived by John von Neumann to determine optimal strategies i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Maynard Smith
John Maynard Smith (6 January 1920 – 19 April 2004) was a British mathematical and theoretical biology, theoretical and mathematical evolutionary biologist and geneticist. Originally an aeronautical engineer during the Second World War, he took a second degree in genetics under the biologist J. B. S. Haldane. Maynard Smith was instrumental in the application of game theory to evolution with George R. Price, and theorised on other problems such as the evolution of sex and signalling theory. Biography Early years John Maynard Smith was born in London, the son of the surgeon Sidney Maynard Smith, but following his father's death in 1928, the family moved to Exmoor, where he became interested in natural history. Quite unhappy with the lack of formal science education at Eton College, Maynard Smith took it upon himself to develop an interest in Darwinism, Darwinian evolutionary theory and mathematics, after having read the work of old Etonian J. B. S. Haldane, whose books were ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Deterministic
Determinism is the metaphysical view that all events within the universe (or multiverse) can occur only in one possible way. Deterministic theories throughout the history of philosophy have developed from diverse and sometimes overlapping motives and considerations. Like eternalism, determinism focuses on particular events rather than the future as a concept. Determinism is often contrasted with free will, although some philosophers claim that the two are compatible. A more extreme antonym of determinism is indeterminism, or the view that events are not deterministically caused but rather occur due to random chance. Historically, debates about determinism have involved many philosophical positions and given rise to multiple varieties or interpretations of determinism. One topic of debate concerns the scope of determined systems. Some philosophers have maintained that the entire universe is a single determinate system, while others identify more limited determinate systems. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
