Population dynamics
Overview
Population dynamics is the branch of life sciences
Life sciences
The life sciences comprise the fields of science that involve the scientific study of living organisms, like plants, animals, and human beings. While biology remains the centerpiece of the life sciences, technological advances in molecular biology and biotechnology have led to a burgeoning of...

 that studies short-term and long-term changes in the size and age composition of population
Population
A population is all the organisms that both belong to the same group or species and live in the same geographical area. The area that is used to define a sexual population is such that inter-breeding is possible between any pair within the area and more probable than cross-breeding with individuals...

s, and the biological
Biology
Biology is a natural science concerned with the study of life and living organisms, including their structure, function, growth, origin, evolution, distribution, and taxonomy. Biology is a vast subject containing many subdivisions, topics, and disciplines...

 and environmental
Environment (biophysical)
The biophysical environment is the combined modeling of the physical environment and the biological life forms within the environment, and includes all variables, parameters as well as conditions and modes inside the Earth's biosphere. The biophysical environment can be divided into two categories:...

 processes influencing those changes. Population dynamics deals with the way populations are affected by birth
Birth rate
Crude birth rate is the nativity or childbirths per 1,000 people per year . Another word used interchangeably with "birth rate" is "natality". When the crude birth rate is subtracted from the crude death rate, it reveals the rate of natural increase...

 and death rates, and by immigration
Immigration
Immigration is the act of foreigners passing or coming into a country for the purpose of permanent residence...

 and emigration
Emigration
Emigration is the act of leaving one's country or region to settle in another. It is the same as immigration but from the perspective of the country of origin. Human movement before the establishment of political boundaries or within one state is termed migration. There are many reasons why people...

, and studies topics such as ageing populations or population decline
Population decline
Population decline can refer to the decline in population of any organism, but this article refers to population decline in humans. It is a term usually used to describe any great reduction in a human population...

.

The mathematical model often viewed as the best to govern the population dynamics of any given species is called the exponential model.
Encyclopedia
Population dynamics is the branch of life sciences
Life sciences
The life sciences comprise the fields of science that involve the scientific study of living organisms, like plants, animals, and human beings. While biology remains the centerpiece of the life sciences, technological advances in molecular biology and biotechnology have led to a burgeoning of...

 that studies short-term and long-term changes in the size and age composition of population
Population
A population is all the organisms that both belong to the same group or species and live in the same geographical area. The area that is used to define a sexual population is such that inter-breeding is possible between any pair within the area and more probable than cross-breeding with individuals...

s, and the biological
Biology
Biology is a natural science concerned with the study of life and living organisms, including their structure, function, growth, origin, evolution, distribution, and taxonomy. Biology is a vast subject containing many subdivisions, topics, and disciplines...

 and environmental
Environment (biophysical)
The biophysical environment is the combined modeling of the physical environment and the biological life forms within the environment, and includes all variables, parameters as well as conditions and modes inside the Earth's biosphere. The biophysical environment can be divided into two categories:...

 processes influencing those changes. Population dynamics deals with the way populations are affected by birth
Birth rate
Crude birth rate is the nativity or childbirths per 1,000 people per year . Another word used interchangeably with "birth rate" is "natality". When the crude birth rate is subtracted from the crude death rate, it reveals the rate of natural increase...

 and death rates, and by immigration
Immigration
Immigration is the act of foreigners passing or coming into a country for the purpose of permanent residence...

 and emigration
Emigration
Emigration is the act of leaving one's country or region to settle in another. It is the same as immigration but from the perspective of the country of origin. Human movement before the establishment of political boundaries or within one state is termed migration. There are many reasons why people...

, and studies topics such as ageing populations or population decline
Population decline
Population decline can refer to the decline in population of any organism, but this article refers to population decline in humans. It is a term usually used to describe any great reduction in a human population...

.

The mathematical model often viewed as the best to govern the population dynamics of any given species is called the exponential model. With the exponential model, the rate of change of any given population is proportional to the already existing population.

History

Population dynamics has traditionally been the dominant branch of mathematical biology
Mathematical biology
Mathematical and theoretical biology is an interdisciplinary scientific research field with a range of applications in biology, medicine and biotechnology...

, which has a history of more than 210 years, although more recently the scope of mathematical biology has greatly expanded. The first principle of population dynamics is widely regarded as the exponential law of Malthus, as modelled by the Malthusian growth model
Malthusian growth model
The Malthusian growth model, sometimes called the simple exponential growth model, is essentially exponential growth based on a constant rate of compound interest...

. The early period was dominated by demographic
Demography
Demography is the statistical study of human population. It can be a very general science that can be applied to any kind of dynamic human population, that is, one that changes over time or space...

 studies such as the work of Benjamin Gompertz
Benjamin Gompertz
Benjamin Gompertz was a British self educated mathematician and actuary, who became a Fellow of the Royal Society...

 and Pierre François Verhulst
Pierre François Verhulst
Pierre François Verhulst was a mathematician and a doctor in number theory from the University of Ghent in 1825...

 in the early 19th century, who refined and adjusted the Malthusian demographic model.

A more general model formulation was proposed by F.J. Richards in 1959, further expanded by Simon Hopkins, in which the models of Gompertz, Verhulst and also Ludwig von Bertalanffy
Ludwig von Bertalanffy
Karl Ludwig von Bertalanffy was an Austrian-born biologist known as one of the founders of general systems theory . GST is an interdisciplinary practice that describes systems with interacting components, applicable to biology, cybernetics, and other fields...

 are covered as special cases of the general formulation.
The Lotka–Volterra predator-prey equations are another famous example. The computer game SimCity
SimCity
SimCity is a critically acclaimed city-building simulation video game, first released in 1989, and designed by Will Wright. SimCity was Maxis' first product, which has since been ported into various personal computers and game consoles, and spawned several sequels including SimCity 2000 in 1994,...

 and the MMORPG
MMORPG
Massively multiplayer online role-playing game is a genre of role-playing video games in which a very large number of players interact with one another within a virtual game world....

 Ultima Online
Ultima Online
Ultima Online is a graphical massively multiplayer online role-playing game , released on September 24, 1997, by Origin Systems. It was instrumental to the development of the genre, and is still running today...

, among others, tried to simulate
Computer simulation
A computer simulation, a computer model, or a computational model is a computer program, or network of computers, that attempts to simulate an abstract model of a particular system...

 some of these population dynamics.

In the past 30 years, population dynamics has been complemented by evolutionary game theory
Evolutionary game theory
Evolutionary game theory is the application of Game Theory to evolving populations of lifeforms in biology. EGT is useful in this context by defining a framework of contests, strategies and analytics into which Darwinian competition can be modelled. It originated in 1973 with John Maynard Smith...

, developed first by John Maynard Smith
John Maynard Smith
John Maynard Smith,His surname was Maynard Smith, not Smith, nor was it hyphenated. F.R.S. was a British theoretical 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....

. Under these dynamics, evolutionary biology concepts may take a deterministic mathematical form. Population dynamics overlap with another active area of research in mathematical biology: mathematical epidemiology
Mathematical modelling in epidemiology
It is possible to mathematically model the progress of most infectious diseases to discover the likely outcome of an epidemic or to help manage them by vaccination...

, the study of infectious disease affecting populations. Various models of viral spread have been proposed and analysed, and provide important results that may be applied to health policy decisions.

Fisheries and wildlife management

In fisheries and wildlife management
Wildlife management
Wildlife management attempts to balance the needs of wildlife with the needs of people using the best available science. Wildlife management can include game keeping, wildlife conservation and pest control...

, population is affected by three dynamic rate functions.
  • Natality or birth rate
    Birth rate
    Crude birth rate is the nativity or childbirths per 1,000 people per year . Another word used interchangeably with "birth rate" is "natality". When the crude birth rate is subtracted from the crude death rate, it reveals the rate of natural increase...

    , often recruitment, which means reaching a certain size or reproductive stage. Usually refers to the age a fish can be caught and counted in nets
  • Population growth rate, which measures the growth of individuals in size and length. More important in fisheries, where population is often measured in biomass.
  • Mortality
    Mortality rate
    Mortality rate is a measure of the number of deaths in a population, scaled to the size of that population, per unit time...

    , which includes harvest mortality and natural mortality. Natural mortality includes non-human predation, disease and old age.


If N1 is the number of individuals at time 1 then
N1 = N0 + B - D + I - E

where N0 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 and time 1.

If we measure these rates over many time intervals, we can determine how a population's density changes over time. Immigration and emigration are present, but are usually not measured.

All of these are measured to determine the harvestable surplus, which is the number of individuals that can be harvested from a population without affecting long term stability, or average population size. The harvest within the harvestable surplus is considered compensatory mortality, where the harvest deaths are substituting for the deaths that would occur naturally. It started in Europe. Harvest beyond that is additive mortality, harvest in addition to all the animals that would have died naturally. These terms are not the universal good and evil of population management, for example, in deer, the DNR are trying to reduce deer population size overall to an extent, since hunters have reduced buck competition and increased deer population unnaturally.

Intrinsic rate of increase

The rate at which a population increases in size if there are no density-dependent forces regulating the population is known as the intrinsic rate of increase.



Where (dN/dt) is the rate of increase of the population and N is the population size, r is the intrinsic rate of increase. This is therefore the theoretical maximum rate of increase of a population per individual .
The concept is commonly used in insect population biology to determine how environmental factors affect the rate at which pest populations increase. See also exponential population growth and logistic population growth.

External links

  • GreenBoxes code sharing network. Greenboxes (Beta) is a repository for open-source population modelling and PVA code. Greenboxes allows users an easy way to share their code and to search for others shared code.
  • The Virtual Handbook on Population Dynamics. An online compilation of state-ot-the-art basic tools for the analysis of population dynamics with emphasis on benthic invertebrates.
  • Creatures! High School interactive simulation program that implements an agent based simulation of grass, rabbits and foxes.
The source of this article is wikipedia, the free encyclopedia.  The text of this article is licensed under the GFDL.
 
x
OK