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 has traditionally been the dominant branch of mathematical biology, which has a history of more than 220 years, although over the last century the scope of mathematical biology has greatly expanded. The beginning of population dynamics is widely regarded as the work of Malthus, formulated as the Malthusian growth model.
Stabilizing selectionStabilizing selection (not to be confused with negative or purifying selection) is a type of natural selection in which the population mean stabilizes on a particular non-extreme trait value. This is thought to be the most common mechanism of action for natural selection because most traits do not appear to change drastically over time. Stabilizing selection commonly uses negative selection (a.k.a. purifying selection) to select against extreme values of the character. Stabilizing selection is the opposite of disruptive selection.
Weak selectionWeak selection in evolutionary biology is when individuals with different phenotypes possess similar fitness, i.e. one phenotype is weakly preferred over the other. Weak selection, therefore, is an evolutionary theory to explain the maintenance of multiple phenotypes in a stable population. Weak selection can only be used to explain the maintenance of mutations in a Moran process. A Moran process is one in which birth and death are paired events, and therefore population size remains constant.
Background selectionBackground selection describes the loss of genetic diversity at a non-deleterious locus due to negative selection against linked deleterious alleles. It is one form of linked selection, where the maintenance or removal of an allele from a population is dependent upon the alleles in its linkage group. The name emphasizes the fact that the genetic background, or genomic environment, of a neutral mutation has a significant impact on whether it will be preserved (genetic hitchhiking) or purged (background selection) from a population.
Directed evolutionDirected evolution (DE) is a method used in protein engineering that mimics the process of natural selection to steer proteins or nucleic acids toward a user-defined goal. It consists of subjecting a gene to iterative rounds of mutagenesis (creating a library of variants), selection (expressing those variants and isolating members with the desired function) and amplification (generating a template for the next round). It can be performed in vivo (in living organisms), or in vitro (in cells or free in solution).
Random graphIn mathematics, random graph is the general term to refer to probability distributions over graphs. Random graphs may be described simply by a probability distribution, or by a random process which generates them. The theory of random graphs lies at the intersection between graph theory and probability theory. From a mathematical perspective, random graphs are used to answer questions about the properties of typical graphs.
Graph operationsIn the mathematical field of graph theory, graph operations are operations which produce new graphs from initial ones. They include both unary (one input) and binary (two input) operations. Unary operations create a new graph from a single initial graph. Elementary operations or editing operations, which are also known as graph edit operations, create a new graph from one initial one by a simple local change, such as addition or deletion of a vertex or of an edge, merging and splitting of vertices, edge contraction, etc.
Symmetric graphIn the mathematical field of graph theory, a graph G is symmetric (or arc-transitive) if, given any two pairs of adjacent vertices u_1—v_1 and u_2—v_2 of G, there is an automorphism such that and In other words, a graph is symmetric if its automorphism group acts transitively on ordered pairs of adjacent vertices (that is, upon edges considered as having a direction). Such a graph is sometimes also called 1-arc-transitive or flag-transitive. By definition (ignoring u_1 and u_2), a symmetric graph without isolated vertices must also be vertex-transitive.
Line perfect graphIn graph theory, a line perfect graph is a graph whose line graph is a perfect graph. Equivalently, these are the graphs in which every odd-length simple cycle is a triangle. A graph is line perfect if and only if each of its biconnected components is a bipartite graph, the complete graph K_4, or a triangular book K_1,1,n. Because these three types of biconnected component are all perfect graphs themselves, every line perfect graph is itself perfect.
Nearly neutral theory of molecular evolutionThe nearly neutral theory of molecular evolution is a modification of the neutral theory of molecular evolution that accounts for the fact that not all mutations are either so deleterious such that they can be ignored, or else neutral. Slightly deleterious mutations are reliably purged only when their selection coefficient are greater than one divided by the effective population size. In larger populations, a higher proportion of mutations exceed this threshold for which genetic drift cannot overpower selection, leading to fewer fixation events and so slower molecular evolution.
EpistasisEpistasis is a phenomenon in genetics in which the effect of a gene mutation is dependent on the presence or absence of mutations in one or more other genes, respectively termed modifier genes. In other words, the effect of the mutation is dependent on the genetic background in which it appears. Epistatic mutations therefore have different effects on their own than when they occur together. Originally, the term epistasis specifically meant that the effect of a gene variant is masked by that of a different gene.
