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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 beco ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Model
A mathematical model is an abstract and concrete, abstract description of a concrete system using mathematics, mathematical concepts and language of mathematics, language. The process of developing a mathematical model is termed ''mathematical modeling''. Mathematical models are used in applied mathematics and in the natural sciences (such as physics, biology, earth science, chemistry) and engineering disciplines (such as computer science, electrical engineering), as well as in non-physical systems such as the social sciences (such as economics, psychology, sociology, political science). It can also be taught as a subject in its own right. The use of mathematical models to solve problems in business or military operations is a large part of the field of operations research. Mathematical models are also used in music, linguistics, and philosophy (for example, intensively in analytic philosophy). A model may help to explain a system and to study the effects of different components, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vito Volterra
Vito Volterra (, ; 3 May 1860 – 11 October 1940) was an Italian mathematician and physicist, known for his contributions to Mathematical and theoretical biology, mathematical biology and Integral equation, integral equations, being one of the founders of functional analysis. Biography Born in Ancona, then part of the Papal States, into a very poor Jewish family: his father was Abramo Volterra and his mother, Angelica Almagià. Abramo Volterra died in 1862 when Vito was two years old. The family moved to Turin, and then to Florence, where he studied at the Dante Alighieri Technical School and the Galileo Galilei Technical Institute. Volterra showed early promise in mathematics before attending the University of Pisa, where he fell under the influence of Enrico Betti, and where he became professor of rational mechanics in 1883. He immediately started work developing his theory of functional (mathematics), functionals which led to his interest and later contributions in integra ... [...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 (biophysical), environment, such as birth rate, 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 statistics, 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 Community ecology, synecology—the study of groups of species in relation to the environment. The term autecology (from Ancient Greek language, Ancient Greek: :wikt:αὐτο, αὐτο, ''aúto'', "self"; ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Population Dynamics Of Fisheries
A 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. The basic accounting relation for population dynamics is the BIDE (Birth, Immigration, Death, Emigration) model, shown as: : ''N''1 = ''N''0 + ''B'' − ''D'' + ''I'' − ''E'' where ''N''1 is the number of individuals at time 1, ''N''0 is the number of individuals at time 0, ''B'' is the number of individuals born, ''D'' the number that died, ''I'' the number that immigrated, and ''E'' the number that emigrated between time 0 a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Population Dynamics
Population dynamics is the type of mathematics used to model and study the size and age composition of populations as dynamical systems. Population dynamics is a branch of mathematical biology, and uses mathematical techniques such as differential equations to model behaviour. Population dynamics is also closely related to other mathematical biology fields such as epidemiology, and also uses techniques from evolutionary game theory in its modelling. History Population dynamics has traditionally been the dominant branch of mathematical biology, which has a history of more than 220 years,Malthus, Thomas Robert. An Essay on the Principle of Population: Library of Economics 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. According to Malthus, assuming that the conditions (the environment) remain constant ('' ceteris pari ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logical Deterministic Individual-based Cellular Automata Model Of Interspecific Competition For A Single Limited Resource
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure of arguments alone, independent of their topic and content. Informal logic is associated with informal fallacies, critical thinking, and argumentation theory. Informal logic examines arguments expressed in natural language whereas formal logic uses formal language. When used as a countable noun, the term "a logic" refers to a specific logical formal system that articulates a proof system. Logic plays a central role in many fields, such as philosophy, mathematics, computer science, and linguistics. Logic studies arguments, which consist of a set of premises that leads to a conclusion. An example is the argument from the premises "it's Sunday" and "if it's Sunday then I don't have to work" leading to the conclusion "I don't have to work." Premises ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Species–area Relationship
The species–area relationship or species–area curve describes the relationship between the area of a habitat, or of part of a habitat, and the number of species found within that area. Larger areas tend to contain larger numbers of species, and empirically, the relative numbers seem to follow systematic mathematical relationships.Preston, F.W. 1962. The canonical distribution of commonness and rarity: Part I. Ecology 43:185–215 and 410–432. The species–area relationship is usually constructed for a single type of organism, such as all vascular plants or all species of a specific trophic level within a particular site. It is rarely if ever, constructed for all types of organisms if simply because of the prodigious data requirements. It is related but not identical to the species discovery curve. Ecologists have proposed a wide range of factors determining the slope and elevation of the species–area relationship.Rosenzweig, M.L. 1995. Species Diversity in Space and Time ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Island Biogeography
Insular biogeography or island biogeography is a field within biogeography that examines the factors that affect the species richness and diversification of isolated natural communities. The theory was originally developed to explain the pattern of the species–area relationship occurring in oceanic islands. Under either name it is now used in reference to any ecosystem (present or past) that is isolated due to being surrounded by unlike ecosystems, and has been extended to mountain peaks, seamounts, oases, fragmented forests, and even natural habitats isolated by human land development. The field was started in the 1960s by the ecologists Robert H. MacArthur and E. O. Wilson, who coined the term ''island biogeography'' in their inaugural contribution to Princeton's Monograph in Population Biology series, which attempted to predict the number of species that would exist on a newly created island. Definitions For biogeographical purposes, an insular environment or "islan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Competitive Lotka–Volterra Equations
The competitive Lotka–Volterra equations are a simple model of the population dynamics of species competing for some common resource. They can be further generalised to the generalized Lotka–Volterra equation to include trophic interactions. Overview The form is similar to the Lotka–Volterra equations for predation in that the equation for each species has one term for self-interaction and one term for the interaction with other species. In the equations for predation, the base population model is exponential. For the competition equations, the logistic equation is the basis. The logistic population model, when used by ecologists often takes the following form: = rx\left(1-\right). Here is the size of the population at a given time, is inherent per-capita growth rate, and is the carrying capacity. Two species Given two populations, and , with logistic dynamics, the Lotka–Volterra formulation adds an additional term to account for the species' interactions. ... [...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 the equation f(x) = \frac where The logistic function has domain the real numbers, the limit as x \to -\infty is 0, and the limit as x \to +\infty is L. The exponential function with negated argument (e^ ) is used to define the standard logistic function, depicted at right, where L=1, k=1, x_0=0, which has the equation f(x) = \frac and is sometimes simply called the sigmoid. It is also sometimes called the expit, being the inverse function of the logit. 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. There are various generalizations, depending on the field. History The logistic function was introduced in a series of three papers by Pierre F ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ecology
Ecology () is the natural science of the relationships among living organisms and their Natural environment, environment. Ecology considers organisms at the individual, population, community (ecology), community, ecosystem, and biosphere levels. Ecology overlaps with the closely related sciences of biogeography, evolutionary biology, genetics, ethology, and natural history. Ecology is a branch of biology, and is the study of abundance (ecology), abundance, biomass (ecology), biomass, and distribution of organisms in the context of the environment. It encompasses life processes, interactions, and adaptations; movement of materials and energy through living communities; ecological succession, successional development of ecosystems; cooperation, competition, and predation within and between species; and patterns of biodiversity and its effect on ecosystem processes. Ecology has practical applications in fields such as conservation biology, wetland management, natural resource m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
