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Maximum Sustainable Yield
In population ecology and economics, maximum sustainable yield (MSY) is theoretically, the largest yield (or catch) that can be taken from a species' stock over an indefinite period. Fundamental to the notion of sustainable harvest, the concept of MSY aims to maintain the population size at the point of maximum growth rate by harvesting the individuals that would normally be added to the population, allowing the population to continue to be productive indefinitely. Under the assumption of logistic growth, resource limitation does not constrain individuals' reproductive rates when populations are small, but because there are few individuals, the overall yield is small. At intermediate population densities, also represented by half the carrying capacity, individuals are able to breed to their maximum rate. At this point, called the maximum sustainable yield, there is a surplus of individuals that can be harvested because growth of the population is at its maximum point due to the l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Population Ecology
Population ecology is a sub-field of ecology that deals with the dynamics of species populations and how these populations interact with the environment, such as birth and death rates, and by immigration and emigration. The discipline is important in conservation biology, especially in the development of population viability analysis which makes it possible to predict the long-term probability of a species persisting in a given patch of habitat. Although population ecology is a subfield of biology, it provides interesting problems for mathematicians and statisticians who work in population dynamics. History In the 1940s ecology was divided into autecology—the study of individual species in relation to the environment—and synecology—the study of groups of species in relation to the environment. The term autecology (from Ancient Greek: αὐτο, ''aúto'', "self"; οίκος, ''oíkos'', "household"; and λόγος, ''lógos'', "knowledge"), refers to roughly the same ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
United Nations Convention On The Law Of The Sea
The United Nations Convention on the Law of the Sea (UNCLOS), also called the Law of the Sea Convention or the Law of the Sea Treaty, is an international agreement that establishes a legal framework for all marine and maritime activities. , 167 countries and the European Union are parties. The Convention resulted from the third United Nations Conference on the Law of the Sea (UNCLOS III), which took place between 1973 and 1982. UNCLOS replaced the four treaties of the 1958 Convention on the High Seas. UNCLOS came into force in 1994, a year after Guyana became the 60th nation to ratify the treaty. It is uncertain as to what extent the Convention codifies customary international law. While the Secretary-General of the United Nations receives instruments of ratification and accession and the UN provides support for meetings of states party to the Convention, the United Nations Secretariat has no direct operational role in the implementation of the Convention. A UN specialized agen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Positive Feedback
Positive feedback (exacerbating feedback, self-reinforcing feedback) is a process that occurs in a feedback loop which exacerbates the effects of a small disturbance. That is, the effects of a perturbation on a system include an increase in the magnitude of the perturbation. That is, ''A produces more of B which in turn produces more of A''.Keesing, R.M. (1981). Cultural anthropology: A contemporary perspective (2nd ed.) p.149. Sydney: Holt, Rinehard & Winston, Inc. In contrast, a system in which the results of a change act to reduce or counteract it has negative feedback. Both concepts play an important role in science and engineering, including biology, chemistry, and cybernetics. Mathematically, positive feedback is defined as a positive loop gain around a closed loop of cause and effect. That is, positive feedback is in phase with the input, in the sense that it adds to make the input larger. Positive feedback tends to cause system instability. When the loop gain is pos ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modeling Population Growth
A model is an informative representation of an object, person or system. The term originally denoted the plans of a building in late 16th-century English, and derived via French and Italian ultimately from Latin ''modulus'', a measure. Models can be divided into physical models (e.g. a model plane) and abstract models (e.g. mathematical expressions describing behavioural patterns). Abstract or conceptual models are central to philosophy of science, as almost every scientific theory effectively embeds some kind of model of the physical or human sphere. In commerce, "model" can refer to a specific design of a product as displayed in a catalogue or show room (e.g. Ford Model T), and by extension to the sold product itself. Types of models include: Physical model A physical model (most commonly referred to simply as a model but in this context distinguished from a conceptual model) is a smaller or larger physical copy of an object. The object being modelled may be smal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pierre François Verhulst
Pierre François Verhulst (28 October 1804, Brussels – 15 February 1849, Brussels) was a Belgian mathematician and a doctor in number theory from the University of Ghent in 1825. He is best known for the logistic growth model. Logistic equation Verhulst developed the logistic function in a series of three papers between 1838 and 1847, based on research on modeling population growth that he conducted in the mid 1830s, under the guidance of Adolphe Quetelet; see for details. Verhulst published in the equation: : \frac = rN - \alpha N^2 where ''N''(''t'') represents number of individuals at time ''t'', ''r'' the intrinsic growth rate, and ''\alpha'' is the density-dependent crowding effect (also known as intraspecific competition). In this equation, the population equilibrium (sometimes referred to as the carrying capacity, ''K''), N^*, is : N^* = \frac . In he named the solution the logistic curve. Later, Raymond Pearl and Lowell Reed popularized the equation, bu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Yeast
Yeasts are eukaryotic, single-celled microorganisms classified as members of the fungus kingdom. The first yeast originated hundreds of millions of years ago, and at least 1,500 species are currently recognized. They are estimated to constitute 1% of all described fungal species. Yeasts are unicellular organisms that evolved from multicellular ancestors, with some species having the ability to develop multicellular characteristics by forming strings of connected budding cells known as pseudohyphae or false hyphae. Yeast sizes vary greatly, depending on species and environment, typically measuring 3–4 µm in diameter, although some yeasts can grow to 40 µm in size. Most yeasts reproduce asexually by mitosis, and many do so by the asymmetric division process known as budding. With their single-celled growth habit, yeasts can be contrasted with molds, which grow hyphae. Fungal species that can take both forms (depending on temperature or other conditions) a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logistic Growth
A logistic function or logistic curve is a common S-shaped curve (sigmoid curve) with equation f(x) = \frac, where For values of x in the domain of real numbers from -\infty to +\infty, the S-curve shown on the right is obtained, with the graph of f approaching L as x approaches +\infty and approaching zero as x approaches -\infty. The logistic function finds applications in a range of fields, including biology (especially ecology), biomathematics, chemistry, demography, economics, geoscience, mathematical psychology, probability, sociology, political science, linguistics, statistics, and artificial neural networks. A generalization of the logistic function is the hyperbolastic function of type I. The standard logistic function, where L=1,k=1,x_0=0, is sometimes simply called ''the sigmoid''. It is also sometimes called the ''expit'', being the inverse of the logit. History The logistic function was introduced in a series of three papers by Pierre François Verhuls ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sigmoid Function
A sigmoid function is a mathematical function having a characteristic "S"-shaped curve or sigmoid curve. A common example of a sigmoid function is the logistic function shown in the first figure and defined by the formula: :S(x) = \frac = \frac=1-S(-x). Other standard sigmoid functions are given in the Examples section. In some fields, most notably in the context of artificial neural networks, the term "sigmoid function" is used as an alias for the logistic function. Special cases of the sigmoid function include the Gompertz curve (used in modeling systems that saturate at large values of x) and the ogee curve (used in the spillway of some dams). Sigmoid functions have domain of all real numbers, with return (response) value commonly monotonically increasing but could be decreasing. Sigmoid functions most often show a return value (y axis) in the range 0 to 1. Another commonly used range is from −1 to 1. A wide variety of sigmoid functions including the logistic and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Population Growth
Population growth is the increase in the number of people in a population or dispersed group. Actual global human population growth amounts to around 83 million annually, or 1.1% per year. The global population has grown from 1 billion in 1800 to 7.9 billion in 2020. The UN projected population to keep growing, and estimates have put the total population at 8.6 billion by mid-2030, 9.8 billion by mid-2050 and 11.2 billion by 2100. However, some academics outside the UN have increasingly developed human population models that account for additional downward pressures on population growth; in such a scenario population would peak before 2100. World human population has been growing since the end of the Black Death, around the year 1350. A mix of technological advancement that improved agricultural productivity and sanitation and medical advancement that reduced mortality increased population growth. In some geographies, this has slowed through the process called the demographic t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
