Planar graphIn graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints. In other words, it can be drawn in such a way that no edges cross each other. Such a drawing is called a plane graph or planar embedding of the graph. A plane graph can be defined as a planar graph with a mapping from every node to a point on a plane, and from every edge to a plane curve on that plane, such that the extreme points of each curve are the points mapped from its end nodes, and all curves are disjoint except on their extreme points.
Population dynamics of fisheriesA fishery is an area with an associated fish or aquatic population which is harvested for its commercial or recreational value. Fisheries can be wild or farmed. Population dynamics describes the ways in which a given population grows and shrinks over time, as controlled by birth, death, and migration. It is the basis for understanding changing fishery patterns and issues such as habitat destruction, predation and optimal harvesting rates. The population dynamics of fisheries is used by fisheries scientists to determine sustainable yields.
Graph (discrete mathematics)In discrete mathematics, and more specifically in graph theory, a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related". The objects correspond to mathematical abstractions called vertices (also called nodes or points) and each of the related pairs of vertices is called an edge (also called link or line). Typically, a graph is depicted in diagrammatic form as a set of dots or circles for the vertices, joined by lines or curves for the edges.
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.
Cascade effect (ecology)An ecological cascade effect is a series of secondary extinctions that are triggered by the primary extinction of a key species in an ecosystem. Secondary extinctions are likely to occur when the threatened species are: dependent on a few specific food sources, mutualistic (dependent on the key species in some way), or forced to coexist with an invasive species that is introduced to the ecosystem. Species introductions to a foreign ecosystem can often devastate entire communities, and even entire ecosystems.
Freshwater molluscFreshwater molluscs are those members of the Phylum Mollusca which live in freshwater habitats, both lotic (flowing water) such as rivers, streams, canals, springs, and cave streams (stygobite species) and lentic (still water) such as lakes, ponds (including temporary or vernal ponds), and ditches. This article is about freshwater Mollusca in general; for information on one particular family of freshwater molluscs, please follow the appropriate links in the lists below.
Petersen graphIn the mathematical field of graph theory, the Petersen graph is an undirected graph with 10 vertices and 15 edges. It is a small graph that serves as a useful example and counterexample for many problems in graph theory. The Petersen graph is named after Julius Petersen, who in 1898 constructed it to be the smallest bridgeless cubic graph with no three-edge-coloring. Although the graph is generally credited to Petersen, it had in fact first appeared 12 years earlier, in a paper by .
MusselMussel (ˈmʌsəl) is the common name used for members of several families of bivalve molluscs, from saltwater and freshwater habitats. These groups have in common a shell whose outline is elongated and asymmetrical compared with other edible clams, which are often more or less rounded or oval. The word "mussel" is frequently used to mean the bivalves of the marine family Mytilidae, most of which live on exposed shores in the intertidal zone, attached by means of their strong byssal threads ("beard") to a firm substrate.
Lake ecosystemA lake ecosystem or lacustrine ecosystem includes biotic (living) plants, animals and micro-organisms, as well as abiotic (non-living) physical and chemical interactions. Lake ecosystems are a prime example of lentic ecosystems (lentic refers to stationary or relatively still freshwater, from the Latin lentus, which means "sluggish"), which include ponds, lakes and wetlands, and much of this article applies to lentic ecosystems in general. Lentic ecosystems can be compared with lotic ecosystems, which involve flowing terrestrial waters such as rivers and streams.
Comparability graphIn graph theory, a comparability graph is an undirected graph that connects pairs of elements that are comparable to each other in a partial order. Comparability graphs have also been called transitively orientable graphs, partially orderable graphs, containment graphs, and divisor graphs. An incomparability graph is an undirected graph that connects pairs of elements that are not comparable to each other in a partial order.
