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Beverton–Holt Model
The Beverton–Holt model is a classic discrete-time population model which gives the expected number ''n'' ''t''+1 (or density) of individuals in generation ''t'' + 1 as a function of the number of individuals in the previous generation, : n_ = \frac. Here ''R''0 is interpreted as the proliferation rate per generation and ''K'' = (''R''0 − 1) ''M'' is the carrying capacity of the environment. The Beverton–Holt model was introduced in the context of fisheries by Beverton & Holt (1957). Subsequent work has derived the model under other assumptions such as contest competition (Brännström & Sumpter 2005), within-year resource limited competition (Geritz & Kisdi 2004) or even as the outcome of a source-sink Malthusian patches linked by density-dependent dispersal (Bravo de la Parra et al. 2013). The Beverton–Holt model can be generalized to include scramble competition (see the Ricker model, the Hassell model and the Mayna ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discrete Time And Continuous Time
In mathematical dynamics, discrete time and continuous time are two alternative frameworks within which variables that evolve over time are modeled. Discrete time Discrete time views values of variables as occurring at distinct, separate "points in time", or equivalently as being unchanged throughout each non-zero region of time ("time period")—that is, time is viewed as a discrete variable. Thus a non-time variable jumps from one value to another as time moves from one time period to the next. This view of time corresponds to a digital clock that gives a fixed reading of 10:37 for a while, and then jumps to a new fixed reading of 10:38, etc. In this framework, each variable of interest is measured once at each time period. The number of measurements between any two time periods is finite. Measurements are typically made at sequential integer values of the variable "time". A discrete signal or discrete-time signal is a time series consisting of a sequence of quantities. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hassell Model
Hassell is a multidisciplinary architecture, design and urban planning practice with offices in Australia, China, Singapore, and the United Kingdom. Founded in 1937/8 in Adelaide, South Australia, the firm's former names include Claridge, Hassell and McConnell; Hassell, McConnell and Partners; and Hassell and Partners Pty. Ltd. They are particularly known for the Adelaide Festival Centre complex, which opened in 1973. History Hassell was founded in Adelaide, South Australia in 1938. From 1937, Colin Hassell worked with Philip R. Claridge and Associates, with Claridge, Hassell and McConnell being established as a partnership which included Jack McConnell. Hassell served in the Australian Army during the Second World War, resuming his place in the firm in 1945. After Claridge retired in 1949, the firm became Hassell, McConnell and Partners, and established offices in Melbourne and Canberra. In 1962 John Morphett joined the practice, who was very influenced by the Bauhaus and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Biostatistics
Biostatistics (also known as biometry) are the development and application of statistical methods to a wide range of topics in biology. It encompasses the design of biological experiments, the collection and analysis of data from those experiments and the interpretation of the results. History Biostatistics and genetics Biostatistical modeling forms an important part of numerous modern biological theories. Genetics studies, since its beginning, used statistical concepts to understand observed experimental results. Some genetics scientists even contributed with statistical advances with the development of methods and tools. Gregor Mendel started the genetics studies investigating genetics segregation patterns in families of peas and used statistics to explain the collected data. In the early 1900s, after the rediscovery of Mendel's Mendelian inheritance work, there were gaps in understanding between genetics and evolutionary Darwinism. Francis Galton tried to expand Mendel's ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Demography
Demography () is the statistical study of populations, especially human beings. Demographic analysis examines and measures the dimensions and dynamics of populations; it can cover whole societies or groups defined by criteria such as education, nationality, religion, and ethnicity. Educational institutions usually treat demography as a field of sociology, though there are a number of independent demography departments. These methods have primarily been developed to study human populations, but are extended to a variety of areas where researchers want to know how populations of social actors can change across time through processes of birth, death, and migration. In the context of human biological populations, demographic analysis uses administrative records to develop an independent estimate of the population. Demographic analysis estimates are often considered a reliable standard for judging the accuracy of the census information gathered at any time. In the la ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pierre Verhulst
Pierre is a masculine given name. It is a French form of the name Peter. Pierre originally meant "rock" or "stone" in French (derived from the Greek word πέτρος (''petros'') meaning "stone, rock", via Latin "petra"). It is a translation of Aramaic כיפא (''Kefa),'' the nickname Jesus gave to apostle Simon Bar-Jona, referred in English as Saint Peter. Pierre is also found as a surname. People with the given name * Abbé Pierre, Henri Marie Joseph Grouès (1912–2007), French Catholic priest who founded the Emmaus Movement * Monsieur Pierre, Pierre Jean Philippe Zurcher-Margolle (c. 1890–1963), French ballroom dancer and dance teacher * Pierre (footballer), Lucas Pierre Santos Oliveira (born 1982), Brazilian footballer * Pierre, Baron of Beauvau (c. 1380–1453) * Pierre, Duke of Penthièvre (1845–1919) * Pierre, marquis de Fayet (died 1737), French naval commander and Governor General of Saint-Domingue * Prince Pierre, Duke of Valentinois (1895–1964), father ... [...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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logistic Function
A logistic function or logistic curve is a common S-shaped curve (sigmoid function, 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 functions, 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nonlinear
In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other scientists because most systems are inherently nonlinear in nature. Nonlinear dynamical systems, describing changes in variables over time, may appear chaotic, unpredictable, or counterintuitive, contrasting with much simpler linear systems. Typically, the behavior of a nonlinear system is described in mathematics by a nonlinear system of equations, which is a set of simultaneous equations in which the unknowns (or the unknown functions in the case of differential equations) appear as variables of a polynomial of degree higher than one or in the argument of a function which is not a polynomial of degree one. In other words, in a nonlinear system of equations, the equation(s) to be solved cannot be written as a linear combination of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Maynard Smith
John Maynard Smith (6 January 1920 – 19 April 2004) was a British 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 well-known 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 Darwinian evolutionary theory and mathematics, after having read the work of old Etonian J. B. S. Haldane, whose books were in the school's library d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ricker Model
The Ricker model, named after Bill Ricker, is a classic discrete population model which gives the expected number ''N'' ''t''+1 (or density) of individuals in generation ''t'' + 1 as a function of the number of individuals in the previous generation, : N_ = N_t e^.\, Here ''r'' is interpreted as an intrinsic growth rate and ''k'' as the carrying capacity of the environment. The Ricker model was introduced in 1954 by Ricker in the context of stock and recruitment in fisheries. The model can be used to predict the number of fish that will be present in a fishery. Subsequent work has derived the model under other assumptions such as scramble competition,Brännström and Sumpter(2005) within-year resource limited competition or even as the outcome of source-sink Malthusian patches linked by density-dependent dispersal.Bravo de la Parra et al (2013) The Ricker model is a limiting case of the Hassell modelGeritz and Kisdi (2004) which takes the form : N_ = k_1 \frac. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Population Modeling
A population model is a type of mathematical model that is applied to the study of population dynamics. Rationale Models allow a better understanding of how complex interactions and processes work. Modeling of dynamic interactions in nature can provide a manageable way of understanding how numbers change over time or in relation to each other. Many patterns can be noticed by using population modeling as a tool. Ecological population modeling is concerned with the changes in parameters such as population size and age distribution within a population. This might be due to interactions with the environment, individuals of their own species, or other species. Population models are used to determine maximum harvest for agriculturists, to understand the dynamics of biological invasions, and for environmental conservation. Population models are also used to understand the spread of parasites, viruses, and disease. Another way populations models are useful are when species become enda ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scramble Competition
In ecology, scramble competition (or complete symmetric competition or exploitation competition) refers to a situation in which a resource is accessible to all competitors (that is, it is not monopolizable by an individual or group). However, since the particular resource is usually finite, scramble competition may lead to decreased survival rates for all competitors if the resource is used to its carrying capacity. Scramble competition is also defined as " finite resource hatis shared equally amongst the competitors so that the quantity of food per individual declines with increasing population density".Den Berg, V., Rossing, W., and Grasman, J. (2006). "Contest and Scramble Competition and the Carry-Over Effect in Globodera spp. In Potato-Based Crop Rotations Using an Extended Ricker Model". Journal of Nematology, 38(2):210-220. A further description of scramble competition is "competition for a resource that is inadequate for the needs of all, but which is partitioned equally amo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
