Population dynamics is the type of mathematics used to model and study the size and age composition of populations as dynamical systems .
76-432: This is a demography of the population of Guinea-Bissau including population density , ethnicity , education level, health of the populace, economic status, religious affiliations and other aspects of the population. The population of Guinea-Bissau is ethnically diverse with distinct languages, customs, and social structures. Most Guineans, 99%, are Black people — mostly Fula and Mandinka -speakers concentrated in
152-457: A Chinese minority, including Macanese people of mixed Portuguese and Cantonese blood from Macau . Most people are farmers. 38%-45% are Muslims - this makes Guinea-Bissau the only Portuguese-speaking nation with a sizable Muslim population. Most Muslims are Sunnis . The rest of the population are pagans , principally the Balanta , and Christians , mostly Roman Catholics . According to
228-468: A significant comparison, numbers must be altered for the size of the population that is under study. For example, the fertility rate is calculated as the ratio of the number of births to women of childbearing age to the total number of women in this age range. If these adjustments were not made, we would not know if a nation with a higher rate of births or deaths has a population with more women of childbearing age or more births per eligible woman. Within
304-401: A country (or other entity) contains Population t persons at time t . What is the size of the population at time t + 1 ? Natural increase from time t to t + 1: Net migration from time t to t + 1: These basic equations can also be applied to subpopulations. For example, the population size of ethnic groups or nationalities within a given society or country is subject to
380-778: A logistic population, we assume the N t is the same for both models, and we expand to the following equality: N 0 e r t = N 0 λ t e r t = λ t r t = t ln ( λ ) {\displaystyle {\begin{aligned}N_{0}e^{rt}&=N_{0}\lambda ^{t}\\e^{rt}&=\lambda ^{t}\\rt&=t\ln(\lambda )\end{aligned}}} Giving us r = ln ( λ ) {\displaystyle r=\ln(\lambda )} and λ = e r . {\displaystyle \lambda =e^{r}.} Evolutionary game theory
456-460: A new product, and to analyze certain dynamics of a company's workforce. Choosing a new location for a branch of a bank, choosing the area in which to start a new supermarket, consulting a bank loan officer that a particular location would be a beneficial site to start a car wash, and determining what shopping area would be best to buy and be redeveloped in metropolis area are types of problems in which demographers can be called upon. Standardization
532-498: A period of transition where in demography emerged from statistics as a separate field of interest. This period included a panoply of international 'great demographers' like Adolphe Quetelet (1796–1874), William Farr (1807–1883), Louis-Adolphe Bertillon (1821–1883) and his son Jacques (1851–1922), Joseph Körösi (1844–1906), Anders Nicolas Kaier (1838–1919), Richard Böckh (1824–1907), Émile Durkheim (1858–1917), Wilhelm Lexis (1837–1914), and Luigi Bodio (1840–1920) contributed to
608-1858: A population is the time required for the population to grow to twice its size. We can calculate the doubling time of a geometric population using the equation: N t = λ N 0 by exploiting our knowledge of the fact that the population ( N ) is twice its size ( 2 N ) after the doubling time. N t d = λ t d N 0 2 N 0 = λ t d N 0 λ t d = 2 {\displaystyle {\begin{aligned}N_{t_{d}}&=\lambda ^{t_{d}}N_{0}\\2N_{0}&=\lambda ^{t_{d}}N_{0}\\\lambda ^{t_{d}}&=2\end{aligned}}} The doubling time can be found by taking logarithms . For instance: t d log 2 ( λ ) = log 2 ( 2 ) = 1 ⟹ t d = 1 log 2 ( λ ) {\displaystyle t_{d}\log _{2}(\lambda )=\log _{2}(2)=1\implies t_{d}={1 \over \log _{2}(\lambda )}} Or: t d ln ( λ ) = ln ( 2 ) ⟹ t d = ln ( 2 ) ln ( λ ) {\displaystyle t_{d}\ln(\lambda )=\ln(2)\implies t_{d}={\ln(2) \over \ln(\lambda )}} Therefore: t d = 1 log 2 ( λ ) = 0.693... ln ( λ ) {\displaystyle t_{d}={\frac {1}{\log _{2}(\lambda )}}={\frac {0.693...}{\ln(\lambda )}}} The half-life of
684-829: A population is the time taken for the population to decline to half its size. We can calculate the half-life of a geometric population using the equation: N t = λ N 0 by exploiting our knowledge of the fact that the population ( N ) is half its size ( 0.5 N ) after a half-life. N t 1 / 2 = λ t 1 / 2 N 0 ⟹ 1 2 N 0 = λ t 1 / 2 N 0 ⟹ λ t 1 / 2 = 1 2 {\displaystyle N_{t_{1/2}}=\lambda ^{t_{1/2}}N_{0}\implies {\frac {1}{2}}N_{0}=\lambda ^{t_{1/2}}N_{0}\implies \lambda ^{t_{1/2}}={\frac {1}{2}}} where t 1/2
760-560: A population will grow (or decline) exponentially . This principle provided the basis for the subsequent predictive theories, such as the demographic studies such as the work of Benjamin Gompertz and Pierre François Verhulst 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
836-426: A standardized mortality rate (SMR) or standardized incidence rate (SIR). Population change is analyzed by measuring the change between one population size to another. Global population continues to rise, which makes population change an essential component to demographics. This is calculated by taking one population size minus the population size in an earlier census . The best way of measuring population change
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#1732801921433912-405: 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
988-499: A variety of demographic methods for modelling population processes. They include models of mortality (including the life table , Gompertz models , hazards models , Cox proportional hazards models , multiple decrement life tables , Brass relational logits), fertility (Hermes model, Coale -Trussell models, parity progression ratios ), marriage (Singulate Mean at Marriage, Page model), disability ( Sullivan's method , multistate life tables), population projections ( Lee-Carter model ,
1064-471: Is a useful demographic technique used in the analysis of a business. It can be used as an interpretive and analytic tool for the comparison of different markets. These organizations have interests about the number and characteristics of their clients so they can maximize the sale of their products, their outlook on their influence, or the ends of their power, services, and beneficial works. Population dynamics Population dynamics has traditionally been
1140-401: Is also called the finite rate of increase. Therefore, by induction , we obtain the expression of the population size at time t : N t = λ t N 0 {\displaystyle N_{t}=\lambda ^{t}N_{0}} where λ is the finite rate of increase raised to the power of the number of generations. This last expression is more convenient than
1216-417: Is because developed countries have proportionally more older people, who are more likely to die in a given year, so that the overall mortality rate can be higher even if the mortality rate at any given age is lower. A more complete picture of mortality is given by a life table , which summarizes mortality separately at each age. A life table is necessary to give a good estimate of life expectancy. Suppose that
1292-786: Is in Guinea-Bissau not complete. The Population Departement of the United Nations prepared the following estimates. Demographic statistics according to the World Population Review in 2022. The following demographic are from the independent Guinea-Bissau Statistical Service and from the CIA World Factbook unless otherwise indicated. Muslim 46.1%, folk religions 30.6%, Christian 18.9%, other or unaffiliated 4.4% (2020 est.) definition: age 15 and over can read and write note: on 21 March 2022,
1368-431: Is likely to continue to rise. Populations can change through three processes: fertility, mortality, and migration. Fertility involves the number of children that women have and is to be contrasted with fecundity (a woman's childbearing potential). Mortality is the study of the causes, consequences, and measurement of processes affecting death to members of the population. Demographers most commonly study mortality using
1444-494: Is seen as the intellectual father of ideas of overpopulation and the limits to growth. Later, more sophisticated and realistic models were presented by Benjamin Gompertz and Verhulst . In 1855, a Belgian scholar Achille Guillard defined demography as the natural and social history of human species or the mathematical knowledge of populations, of their general changes, and of their physical, civil, intellectual, and moral condition. The period 1860–1910 can be characterized as
1520-426: Is the population size , r is the intrinsic rate of natural increase , and K is the carrying capacity of the population. The formula can be read as follows: the rate of change in the population ( dN / dt ) is equal to growth ( rN ) that is limited by carrying capacity (1 − N / K ) . From these basic mathematical principles the discipline of population ecology expands into a field of investigation that queries
1596-554: Is the case in much of the developing world, and most of historical demography . One of these techniques in contemporary demography is the sister method, where survey researchers ask women how many of their sisters have died or had children and at what age. With these surveys, researchers can then indirectly estimate birth or death rates for the entire population. Other indirect methods in contemporary demography include asking people about siblings, parents, and children. Other indirect methods are necessary in historical demography. There are
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#17328019214331672-432: Is the half-life. The half-life can be calculated by taking logarithms (see above). t 1 / 2 = 1 log 0.5 ( λ ) = − ln ( 2 ) ln ( λ ) {\displaystyle t_{1/2}={1 \over \log _{0.5}(\lambda )}=-{\ln(2) \over \ln(\lambda )}} Note that as
1748-481: Is the maximum theoretical rate of increase of a population per individual – that is, the maximum population growth rate. The concept is commonly used in insect population ecology or management to determine how environmental factors affect the rate at which pest populations increase. See also exponential population growth and logistic population growth. Population dynamics overlap with another active area of research in mathematical biology: mathematical epidemiology ,
1824-404: Is the total number of individuals in the specific experimental population being studied, B is the number of births and D is the number of deaths per individual in a particular experiment or model. The algebraic symbols b , d and r stand for the rates of birth, death, and the rate of change per individual in the general population, the intrinsic rate of increase. This formula can be read as
1900-432: Is today widely taught in many universities across the world, attracting students with initial training in social sciences, statistics or health studies. Being at the crossroads of several disciplines such as sociology , economics , epidemiology , geography , anthropology and history , demography offers tools to approach a large range of population issues by combining a more technical quantitative approach that represents
1976-510: Is used in a wide variety of contexts. For example, it is often used in business plans, to describe the population connected to the geographic location of the business. Demographic analysis is usually abbreviated as DA. For the 2010 U.S. Census, The U.S. Census Bureau has expanded its DA categories. Also as part of the 2010 U.S. Census, DA now also includes comparative analysis between independent housing estimates, and census address lists at different key time points. Patient demographics form
2052-421: Is using the intercensal percentage change. The intercensal percentage change is the absolute change in population between the censuses divided by the population size in the earlier census. Next, multiply this a hundredfold to receive a percentage . When this statistic is achieved, the population growth between two or more nations that differ in size, can be accurately measured and examined. For there to be
2128-807: The International Union for the Scientific Study of Population , or a national association such as the Population Association of America in the United States, or affiliates of the Federation of Canadian Demographers in Canada . Population composition is the description of population defined by characteristics such as age, race , sex or marital status . These descriptions can be necessary for understanding
2204-666: The Leslie Matrix ), and population momentum ( Keyfitz ). The United Kingdom has a series of four national birth cohort studies, the first three spaced apart by 12 years: the 1946 National Survey of Health and Development , the 1958 National Child Development Study , the 1970 British Cohort Study , and the Millennium Cohort Study , begun much more recently in 2000. These have followed the lives of samples of people (typically beginning with around 17,000 in each study) for many years, and are still continuing. As
2280-516: The Middle Ages , Christian thinkers devoted much time in refuting the Classical ideas on demography. Important contributors to the field were William of Conches , Bartholomew of Lucca , William of Auvergne , William of Pagula , and Muslim sociologists like Ibn Khaldun . One of the earliest demographic studies in the modern period was Natural and Political Observations Made upon
2356-572: The United States and much of Europe ), registry statistics are the best method for estimating the number of births and deaths. A census is the other common direct method of collecting demographic data. A census is usually conducted by a national government and attempts to enumerate every person in a country. In contrast to vital statistics data, which are typically collected continuously and summarized on an annual basis, censuses typically occur only every 10 years or so, and thus are not usually
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2432-426: The demographics of real populations and tests these results against the statistical models. The field of population ecology often uses data on life history and matrix algebra to develop projection matrices on fecundity and survivorship. This information is used for managing wildlife stocks and setting harvest quotas. The rate at which a population increases in size if there are no density-dependent forces regulating
2508-666: The life table , a statistical device that provides information about the mortality conditions (most notably the life expectancy) in the population. Migration refers to the movement of persons from a locality of origin to a destination place across some predefined, political boundary. Migration researchers do not designate movements 'migrations' unless they are somewhat permanent. Thus, demographers do not consider tourists and travellers to be migrating. While demographers who study migration typically do so through census data on place of residence, indirect sources of data including tax forms and labour force surveys are also important. Demography
2584-672: The natural number t is the index the generation ( t=0 for the first generation, t=1 for the second generation, etc.). The letter t is used because the index of a generation is time. Say N t denotes, at generation t , the number of individuals of the population that will reproduce, i.e. the population size at generation t . The population at the next generation, which is the population at time t+1 is: N t + 1 = N t + B t − D t + I t − E t {\displaystyle N_{t+1}=N_{t}+B_{t}-D_{t}+I_{t}-E_{t}} where For
2660-433: The social dynamics from historical and comparative research. This data is often compared using a population pyramid . Population composition is also a very important part of historical research. Information ranging back hundreds of years is not always worthwhile, because the numbers of people for which data are available may not provide the information that is important (such as population size ). Lack of information on
2736-516: The 2022 revision of the world factbook the total population was 2,026,778 in 2022. The proportion of children below the age of 14 in 2020 was 43.17%, 53.75% was between 15 and 65 years of age, while 3.08% was 65 years or older. The proportion of the population below the age of 15 in 2010 was 41.3%, 55.4% were aged between 15 and 65 years of age, while 3.3% were aged 65 years or older. Population Estimates by Sex and Age Group (01.VII.2019) (Data refer to national projections.): Registration of vital events
2812-751: The Application of Probabilities to Life Contingencies (1838). In 1755, Benjamin Franklin published his essay Observations Concerning the Increase of Mankind, Peopling of Countries, etc. , projecting exponential growth in British colonies . His work influenced Thomas Robert Malthus , who, writing at the end of the 18th century, feared that, if unchecked, population growth would tend to outstrip growth in food production, leading to ever-increasing famine and poverty (see Malthusian catastrophe ). Malthus
2888-564: The Bills of Mortality (1662) by John Graunt , which contains a primitive form of life table . Among the study's findings were that one-third of the children in London died before their sixteenth birthday. Mathematicians, such as Edmond Halley , developed the life table as the basis for life insurance mathematics. Richard Price was credited with the first textbook on life contingencies published in 1771, followed later by Augustus De Morgan , On
2964-662: The US Centers for Disease Control and Prevention (CDC) issued a Travel Alert for polio in Africa; Guinea-Bissau is currently considered a high risk to travelers for circulating vaccine-derived polioviruses (cVDPV); vaccine-derived poliovirus (VDPV) is a strain of the weakened poliovirus that was initially included in oral polio vaccine (OPV) and that has changed over time and behaves more like the wild or naturally occurring virus; this means it can be spread more easily to people who are unvaccinated against polio and who come in contact with
3040-425: The accuracy of the census information gathered at any time. In the labor force , demographic analysis is used to estimate sizes and flows of populations of workers; in population ecology the focus is on the birth, death, migration and immigration of individuals in a population of living organisms, alternatively, in social human sciences could involve movement of firms and institutional forms. Demographic analysis
3116-616: The assumption of no external influence. Models can be more mathematically complex where "...several competing hypotheses are simultaneously confronted with the data." For example, in a closed system where immigration and emigration does not take place, the rate of change in the number of individuals in a population can be described as: d N d t = B − D = b N − d N = ( b − d ) N = r N , {\displaystyle {\mathrm {d} N \over \mathrm {d} t}=B-D=bN-dN=(b-d)N=rN,} where N
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3192-467: The basic demographic equation holds true by definition, in practice the recording and counting of events (births, deaths, immigration, emigration) and the enumeration of the total population size are subject to error. So allowance needs to be made for error in the underlying statistics when any accounting of population size or change is made. The figure in this section shows the latest (2004) UN ( United Nations ) WHO projections of world population out to
3268-696: The best source of data on births and deaths. Analyses are conducted after a census to estimate how much over or undercounting took place. These compare the sex ratios from the census data to those estimated from natural values and mortality data. Censuses do more than just count people. They typically collect information about families or households in addition to individual characteristics such as age, sex, marital status, literacy/education, employment status, and occupation, and geographical location. They may also collect data on migration (or place of birth or of previous residence), language, religion, nationality (or ethnicity or race), and citizenship. In countries in which
3344-483: The birth and death rates do not depend on the time t (which is equivalent to assume that the number of births and deaths are effectively proportional to the population size). This is the core assumption for geometric populations, because with it we are going to obtain a geometric sequence . Then we define the geometric rate of increase R = b t - d t to be the birth rate minus the death rate. The geometric rate of increase do not depend on time t , because both
3420-446: The birth rate minus the death rate do not, with our assumption. We obtain: N t + 1 = ( 1 + R ) N t . {\displaystyle {\begin{aligned}N_{t+1}&=\left(1+R\right)N_{t}.\end{aligned}}} This equation means that the sequence (N t ) is geometric with first term N 0 and common ratio 1 + R , which we define to be λ . λ
3496-518: The category of standardization , there are two major approaches: direct standardization and indirect standardization. A stable population does not necessarily remain fixed in size. It can be expanding or shrinking. The crude death rate as defined above and applied to a whole population can give a misleading impression. For example, the number of deaths per 1,000 people can be higher in developed nations than in less-developed countries, despite standards of health being better in developed countries. This
3572-553: The core of the data for any medical institution, such as patient and emergency contact information and patient medical record data. They allow for the identification of a patient and their categorization into categories for the purpose of statistical analysis. Patient demographics include: date of birth , gender , date of death , postal code, ethnicity, blood type , emergency contact information, family doctor, insurance provider data, allergies , major diagnoses and major medical history. Formal demography limits its object of study to
3648-498: The core of the discipline with many other methods borrowed from social or other sciences. Demographic research is conducted in universities, in research institutes, as well as in statistical departments and in several international agencies. Population institutions are part of the CICRED (International Committee for Coordination of Demographic Research) network while most individual scientists engaged in demographic research are members of
3724-528: The development of demography and to the toolkit of methods and techniques of demographic analysis. Demography is the statistical and mathematical study of the size, composition, and spatial distribution of human populations and how these features change over time. Data are obtained from a census of the population and from registries: records of events like birth , deaths , migrations, marriages, divorces , diseases, and employment . To do this, there needs to be an understanding of how they are calculated and
3800-649: The distribution and abundance of organisms. As it relates to organizations and demography, organizations go through various liabilities to their continued survival. Hospitals, like all other large and complex organizations are impacted in the environment they work. For example, a study was done on the closure of acute care hospitals in Florida between a particular time. The study examined effect size, age, and niche density of these particular hospitals. A population theory says that organizational outcomes are mostly determined by environmental factors . Among several factors of
3876-474: The dominant branch of mathematical biology , which has a history of more than 220 years, 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 paribus ),
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#17328019214333952-408: The family. The causes of turnover can be split into two separate factors, one linked with the culture of the organization, and the other relating to all other factors. People who do not fully accept a culture might leave voluntarily. Or, some individuals might leave because they fail to fit in and fail to change within a particular organization. A basic definition of population ecology is a study of
4028-427: The full, routine polio vaccine series receive a single, lifetime booster dose of polio vaccine. Demographics Demography (from Ancient Greek δῆμος ( dêmos ) 'people, society' and -γραφία ( -graphía ) 'writing, drawing, description') is the statistical study of human populations : their size, composition (e.g., ethnic group, age), and how they change through
4104-525: The interplay of fertility (births), mortality (deaths), and migration. 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
4180-409: The mathematical relationship below. The growth equation for exponential populations is N t = N 0 e r t {\displaystyle N_{t}=N_{0}e^{rt}} where e is Euler's number , a universal constant often applicable in logistic equations, and r is the intrinsic growth rate. To find the relationship between a geometric population and
4256-418: The measurement of population processes, while the broader field of social demography or population studies also analyses the relationships between economic, social, institutional, cultural, and biological processes influencing a population. Demographic thoughts traced back to antiquity, and were present in many civilisations and cultures, like Ancient Greece , Ancient Rome , China and India . Made up of
4332-507: The models of Gompertz, Verhulst and also Ludwig von Bertalanffy are covered as special cases of the general formulation. The Lotka–Volterra predator-prey equations are another famous example, as well as the alternative Arditi–Ginzburg equations . Simplified population models usually start with four key variables (four demographic processes ) including death, birth, immigration, and emigration. Mathematical models used to calculate changes in population demographics and evolution hold
4408-413: The nation will become a nation of immigrants. This influx is projected to rise over the next century as new immigrants and their children will account for over half the U.S. population. These demographic shifts could ignite major adjustments in the economy, more specifically, in labor markets. People decide to exit organizations for many reasons, such as, better jobs, dissatisfaction, and concerns within
4484-507: The north and northeast, the Balanta and Papel, living in the southern coastal regions, and the Manjaco and Mancanha, occupying the central and northern coastal areas. Most of the rest, 1% of its total population, are mestiços of mixed Portuguese and black descent, including Cape Verdean minority. Due to the exodus of most Portuguese settlers after independence, less than 1% of Guinea-Bissauans are pure Portuguese. The country also has
4560-410: The number of births and the number of deaths are approximately proportional to the population size. This remark motivates the following definitions. The previous equation can then be rewritten as: N t + 1 = ( 1 + b t − d t ) N t . {\displaystyle N_{t+1}=(1+b_{t}-d_{t})N_{t}.} Then, we assume
4636-458: The original data-collection procedures may prevent accurate evaluation of data quality. The demographic analysis of labor markets can be used to show slow population growth, population aging , and the increased importance of immigration. The U.S. Census Bureau projects that in the next 100 years, the United States will face some dramatic demographic changes. The population is expected to grow more slowly and age more rapidly than ever before and
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#17328019214334712-567: The population is assumed to decline, λ < 1 , so ln( λ ) < 0 . In geometric populations, R and λ represent growth constants (see 2 and 2.3 ). In logistic populations however, the intrinsic growth rate, also known as intrinsic rate of increase ( r ) is the relevant growth constant. Since generations of reproduction in a geometric population do not overlap (e.g. reproduce once a year) but do in an exponential population, geometric and exponential populations are usually considered to be mutually exclusive. However, both sets of constants share
4788-421: The population is known as the intrinsic rate of increase . It is d N d t = r N {\displaystyle {\mathrm {d} N \over \mathrm {d} t}=rN} where the derivative d N / d t {\displaystyle dN/dt} is the rate of increase of the population, N is the population size, and r is the intrinsic rate of increase. Thus r
4864-516: The prefix demo- and the suffix -graphy , the term demography refers to the overall study of population. In ancient Greece, this can be found in the writings of Herodotus , Thucydides , Hippocrates , Epicurus , Protagoras , Polus , Plato and Aristotle . In Rome, writers and philosophers like Cicero , Seneca , Pliny the Elder , Marcus Aurelius , Epictetus , Cato , and Columella also expressed important ideas on this ground. In
4940-485: The previous one, because it is explicit. For example, say one wants to calculate with a calculator N 10 , the population at the tenth generation, knowing N 0 the initial population and λ the finite rate of increase. With the last formula, the result is immediate by plugging t = 10 , whether with the previous one it is necessary to know N 9 , N 8 , ..., N 2 until N 1 . We can identify three cases: The doubling time ( t d ) of
5016-566: The questions they answer which are included in these four concepts: population change , standardization of population numbers, the demographic bookkeeping equation, and population composition. There are two types of data collection —direct and indirect—with several methods of each type. Direct data comes from vital statistics registries that track all births and deaths as well as certain changes in legal status such as marriage, divorce, and migration (registration of place of residence). In developed countries with good registration systems (such as
5092-479: The rate of change in the population ( dN / dt ) is equal to births minus deaths ( B − D ). Using these techniques, Malthus' population principle of growth was later transformed into a mathematical model known as the logistic equation : d N d t = r N ( 1 − N K ) , {\displaystyle {\mathrm {d} N \over \mathrm {d} t}=rN\left(1-{N \over K}\right),} where N
5168-439: The sake of simplicity, we suppose there is no migration to or from the population, but the following method can be applied without this assumption. Mathematically, it means that for all t , I t = E t = 0 . The previous equation becomes: N t + 1 = N t + B t − D t . {\displaystyle N_{t+1}=N_{t}+B_{t}-D_{t}.} In general,
5244-417: The same sources of change. When dealing with ethnic groups, however, "net migration" might have to be subdivided into physical migration and ethnic reidentification ( assimilation ). Individuals who change their ethnic self-labels or whose ethnic classification in government statistics changes over time may be thought of as migrating or moving from one population subcategory to another. More generally, while
5320-447: The samples have been drawn in a nationally representative way, inferences can be drawn from these studies about the differences between four distinct generations of British people in terms of their health, education, attitudes, childbearing and employment patterns. Indirect standardization is used when a population is small enough that the number of events (births, deaths, etc.) are also small. In this case, methods must be used to produce
5396-458: The stool or respiratory secretions, such as from a sneeze, of an "infected" person who received oral polio vaccine; the CDC recommends that before any international travel, anyone unvaccinated, incompletely vaccinated, or with an unknown polio vaccination status should complete the routine polio vaccine series; before travel to any high-risk destination, CDC recommends that adults who previously completed
5472-453: 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. The mathematical formula below is used to model geometric populations. Such populations grow in discrete reproductive periods between intervals of abstinence , as opposed to populations which grow without designated periods for reproduction. Say that
5548-404: The theory, there are four that apply to the hospital closure example: size, age, density of niches in which organizations operate, and density of niches in which organizations are established. Problems in which demographers may be called upon to assist business organizations are when determining the best prospective location in an area of a branch store or service outlet, predicting the demand for
5624-478: The vital registration system may be incomplete, the censuses are also used as a direct source of information about fertility and mortality; for example, the censuses of the People's Republic of China gather information on births and deaths that occurred in the 18 months immediately preceding the census. Indirect methods of collecting data are required in countries and periods where full data are not available, such as
5700-533: The year 2150 (red = high, orange = medium, green = low). The UN "medium" projection shows world population reaching an approximate equilibrium at 9 billion by 2075. Working independently, demographers at the International Institute for Applied Systems Analysis in Austria expect world population to peak at 9 billion by 2070. Throughout the 21st century, the average age of the population
5776-798: Was first developed by Ronald Fisher in his 1930 article The Genetic Theory of Natural Selection . In 1973 John Maynard Smith formalised a central concept, the evolutionarily stable strategy . Population dynamics have been used in several control theory applications. Evolutionary game theory can be used in different industrial or other contexts. Industrially, it is mostly used in multiple-input-multiple-output ( MIMO ) systems, although it can be adapted for use in single-input-single-output ( SISO ) systems. Some other examples of applications are military campaigns, water distribution , dispatch of distributed generators , lab experiments, transport problems, communication problems, among others. Population size in plants experiences significant oscillation due to
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