Concept
Population dynamics
Related concepts (22)
Mathematical and theoretical biology
Mathematical and theoretical biology, or biomathematics, is a branch of biology which employs theoretical analysis, mathematical models and abstractions of the living organisms to investigate the principles that govern the structure, development and behavior of the systems, as opposed to experimental biology which deals with the conduction of experiments to prove and validate the scientific theories. The field is sometimes called mathematical biology or biomathematics to stress the mathematical side, or theoretical biology to stress the biological side.
Population model
A population model is a type of mathematical model that is applied to the study of population dynamics. 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.
Evolutionary invasion analysis
Evolutionary invasion analysis, also known as adaptive dynamics, is a set of mathematical modeling techniques that use differential equations to study the long-term evolution of traits in asexually reproducing populations. It rests on the following four assumptions about mutation and natural selection in the population under study: Individuals reproduce clonally. Mutations are infrequent, and natural selection acts quickly. The population can be assumed to be at equilibrium when a new mutant arises.
Gompertz function
The Gompertz curve or Gompertz function is a type of mathematical model for a time series, named after Benjamin Gompertz (1779–1865). It is a sigmoid function which describes growth as being slowest at the start and end of a given time period. The right-side or future value asymptote of the function is approached much more gradually by the curve than the left-side or lower valued asymptote. This is in contrast to the simple logistic function in which both asymptotes are approached by the curve symmetrically.
Malthusian growth model
A Malthusian growth model, sometimes called a simple exponential growth model, is essentially exponential growth based on the idea of the function being proportional to the speed to which the function grows. The model is named after Thomas Robert Malthus, who wrote An Essay on the Principle of Population (1798), one of the earliest and most influential books on population. Malthusian models have the following form: where P0 = P(0) is the initial population size, r = the population growth rate, which Ronald Fisher called the Malthusian parameter of population growth in The Genetical Theory of Natural Selection, and Alfred J.
Mathematical constant
A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a special symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. Constants arise in many areas of mathematics, with constants such as e and pi occurring in such diverse contexts as geometry, number theory, statistics, and calculus. Some constants arise naturally by a fundamental principle or intrinsic property, such as the ratio between the circumference and diameter of a circle (pi).
Benjamin Gompertz
Benjamin Gompertz (5 March 1779 – 14 July 1865) was a British self-educated mathematician and actuary, who became a Fellow of the Royal Society. Gompertz is now best known for his Gompertz law of mortality, a demographic model published in 1825. He was the brother of the early animal rights activist and inventor Lewis Gompertz and the poet Isaac Gompertz. Of the German Jewish family of Gompertz of Emmerich, he was born in London, where his father and grandfather had been successful diamond merchants.
Steady state
In systems theory, a system or a process is in a steady state if the variables (called state variables) which define the behavior of the system or the process are unchanging in time. In continuous time, this means that for those properties p of the system, the partial derivative with respect to time is zero and remains so: In discrete time, it means that the first difference of each property is zero and remains so: The concept of a steady state has relevance in many fields, in particular thermodynamics, economics, and engineering.
Biostatistics
Biostatistics (also known as biometry) is a branch of statistics that applies 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. Biostatistical modeling forms an important part of numerous modern biological theories. Genetics studies, since its beginning, used statistical concepts to understand observed experimental results.
R/K selection theory
In ecology, r/K selection theory relates to the selection of combinations of traits in an organism that trade off between quantity and quality of offspring. The focus on either an increased quantity of offspring at the expense of individual parental investment of r-strategists, or on a reduced quantity of offspring with a corresponding increased parental investment of K-strategists, varies widely, seemingly to promote success in particular environments.