Population - Revision history

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	~~The most recent and complete demographic model documentation is available on~~ Pardee~~'s [http~~://pardee.du.edu/ifs-population-model-documentation website]. Although the text in this interactive system is, for some IFs models, often significantly out of date, you may still find the basic description useful to you.		Please cite as: Hughes, Barry B. 2014. "IFs Population Model Documentation." Working paper 2014.03.05.b. Pardee Center for International Futures, Josef Korbel School of International Studies, University of Denver, Denver, CO. Accessed DD Month YYYY <https://pardee.du.edu/wiki/Population>

	The population sub-model of IFs uses the cohort component analysis approach of many population models, including the studies done by the United Nations (United Nations, 1956<ref>United Nations, Department of Economic and Social Affairs. 1956. Methods of Population Projections by Sex and Age. New York: United Nations, ST/SOA Series A.</ref> and 1977). The structure of the IFs population model drew initially on the World Integrated Model (WIM) or the second generation Mesarovic-Pestel Model (Hughes, 1980)<ref>Hughes, Barry B. 1980. World Modeling. Lexington, Mass: Lexington Books.</ref>, but has changed much over time. In particular, José Solórzano and Randall Kuhn have made many contributions to its development.		The population sub-model of IFs uses the cohort component analysis approach of many population models, including the studies done by the United Nations (United Nations, 1956<ref>United Nations, Department of Economic and Social Affairs. 1956. Methods of Population Projections by Sex and Age. New York: United Nations, ST/SOA Series A.</ref> and 1977). The structure of the IFs population model drew initially on the World Integrated Model (WIM) or the second generation Mesarovic-Pestel Model (Hughes, 1980)<ref>Hughes, Barry B. 1980. World Modeling. Lexington, Mass: Lexington Books.</ref>, but has changed much over time. In particular, José Solórzano and Randall Kuhn have made many contributions to its development.
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	<span style="font-size:small"><span style="font-size:small"><span style="font-size:small">Often they present their data values in 5 year categories (1950-1955, . . . , 2095-2099).  To obtain values at specific 5-year intervals, such as 1960 or 2010, we average the values for the two 5-year categories that bracket that year.  To estimate annual values for all years from such categories, for instance for migration numbers, we used a Sprague algorithm to spread the 5 year data (1950-1955, . . . , 2095-2099). With respect to migration, to obtain net migration rates we divided their annualized numbers by annual population data'''.'''</span></span></span>		<span style="font-size:small"><span style="font-size:small"><span style="font-size:small">Often they present their data values in 5 year categories (1950-1955, . . . , 2095-2099).  To obtain values at specific 5-year intervals, such as 1960 or 2010, we average the values for the two 5-year categories that bracket that year.  To estimate annual values for all years from such categories, for instance for migration numbers, we used a Sprague algorithm to spread the 5 year data (1950-1955, . . . , 2095-2099). With respect to migration, to obtain net migration rates we divided their annualized numbers by annual population data'''.'''</span></span></span>

Wikiadmin at 20:56, 26 July 2018

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	<span style="font-size:small"><span style="font-size:small"><span style="font-size:small">In the long-term future, urbanization must saturate as the portion of the population urbanized approaches 100%. Moreover, there is a relationship between income levels of countries and urbanization level that should affect the growth of urban population. Thus, a function estimated cross-sectionally against GDP per capita at PPP was used to provide a target (PopUrbanTar) for urbanization that could gradually replace the value of growing urban population (PopUrbanGro) calculated by use of the growth rate –countries with very high levels of GDP per capita have already begun to approach saturation; algorithmic modifications help assure that the target is reasonable and also that it approaches saturation smoothly. </span></span></span>		<span style="font-size:small"><span style="font-size:small"><span style="font-size:small">In the long-term future, urbanization must saturate as the portion of the population urbanized approaches 100%. Moreover, there is a relationship between income levels of countries and urbanization level that should affect the growth of urban population. Thus, a function estimated cross-sectionally against GDP per capita at PPP was used to provide a target (PopUrbanTar) for urbanization that could gradually replace the value of growing urban population (PopUrbanGro) calculated by use of the growth rate –countries with very high levels of GDP per capita have already begun to approach saturation; algorithmic modifications help assure that the target is reasonable and also that it approaches saturation smoothly. </span></span></span>

	:<span style="font-size:small"><span style="font-size:small"><span style="font-size:small"><math>POPURBAN_{r}=ConvergeOverTime(PopUrbanGro,PopUrbanTar)</math></span>		:<span style="font-size:small"><span style="font-size:small"><span style="font-size:small"><math>POPURBAN_{r}=ConvergeOverTime(PopUrbanGro,PopUrbanTar)</math></span></span></span>

	<span style="font-size:small"><span style="font-size:small"><span style="font-size:small">''where''</span></span></span>		<span style="font-size:small"><span style="font-size:small"><span style="font-size:small"><span style="font-size:small"><span style="font-size:small">''where''</span></span></span></span></span>

	:<span style="font-size:small"><span style="font-size:small"><span style="font-size:small"><math>PopUrbanGro=POPURBAN_{r,t-1}*(1+POPURBGR_{r,t-1})</math></span></span></span>		:<span style="font-size:small"><span style="font-size:small"><span style="font-size:small"><span style="font-size:small"><span style="font-size:small"><math>PopUrbanGro=POPURBAN_{r,t-1}*(1+POPURBGR_{r,t-1})</math></span></span></span></span></span>

	<span style="font-size:small"><span style="font-size:small"><span style="font-size:small">''and''</span></span></span>		<span style="font-size:small"><span style="font-size:small"><span style="font-size:small"><span style="font-size:small"><span style="font-size:small">''and''</span></span></span></span></span>

	:<span style="font-size:small"><span style="font-size:small"><span style="font-size:small"><math>PopUrbanPor=AnalFunc(GDPPCP_{r})</math></span></span></span>		:<span style="font-size:small"><span style="font-size:small"><span style="font-size:small"><span style="font-size:small"><span style="font-size:small"><math>PopUrbanPor=AnalFunc(GDPPCP_{r})</math></span></span></span></span></span>

	:<span style="font-size:small"><span style="font-size:small"><span style="font-size:small"><math>PopUrbanTar=POP_{r}*PopUrbanPor</math> with algorithmic modifications for smooth behavior over time and as saturation is approached.</span></span></span>		:<span style="font-size:small"><span style="font-size:small"><span style="font-size:small"><span style="font-size:small"><span style="font-size:small"><math>PopUrbanTar=POP_{r}*PopUrbanPor</math> with algorithmic modifications for smooth behavior over time and as saturation is approached.</span></span></span></span></span>

	<span style="font-size:small"><span style="font-size:small"><span style="font-size:small">Once the urban population has been updated in each time cycle, it is possible to compute the actual growth rate (POPURBGR), which will then be the starting point for growing urban population (PopUrbanGro) in the next time cycle.</span></span></span>		<span style="font-size:small"><span style="font-size:small"><span style="font-size:small"><span style="font-size:small"><span style="font-size:small">Once the urban population has been updated in each time cycle, it is possible to compute the actual growth rate (POPURBGR), which will then be the starting point for growing urban population (PopUrbanGro) in the next time cycle.</span></span></span></span></span>

	:<span style="font-size:small"><span style="font-size:small"><span style="font-size:small"><math>POPURBGR_{r}=(\frac{POPURBAN_{r}}{POPURBAN_{r,t-1}}-1)*100</math></span></span></span>		:<span style="font-size:small"><span style="font-size:small"><span style="font-size:small"><span style="font-size:small"><span style="font-size:small"><math>POPURBGR_{r}=(\frac{POPURBAN_{r}}{POPURBAN_{r,t-1}}-1)*100</math></span></span></span></span></span>

	== <span style="font-size:x-large;">Household Size</span> ==		== <span style="font-size:x-large;">Household Size</span> ==

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	<span style="font-size:small"><span style="font-size:small"><span style="font-size:small">In the long-term future, urbanization must saturate as the portion of the population urbanized approaches 100%. Moreover, there is a relationship between income levels of countries and urbanization level that should affect the growth of urban population. Thus, a function estimated cross-sectionally against GDP per capita at PPP was used to provide a target (PopUrbanTar) for urbanization that could gradually replace the value of growing urban population (PopUrbanGro) calculated by use of the growth rate –countries with very high levels of GDP per capita have already begun to approach saturation; algorithmic modifications help assure that the target is reasonable and also that it approaches saturation smoothly. </span></span></span>		<span style="font-size:small"><span style="font-size:small"><span style="font-size:small">In the long-term future, urbanization must saturate as the portion of the population urbanized approaches 100%. Moreover, there is a relationship between income levels of countries and urbanization level that should affect the growth of urban population. Thus, a function estimated cross-sectionally against GDP per capita at PPP was used to provide a target (PopUrbanTar) for urbanization that could gradually replace the value of growing urban population (PopUrbanGro) calculated by use of the growth rate –countries with very high levels of GDP per capita have already begun to approach saturation; algorithmic modifications help assure that the target is reasonable and also that it approaches saturation smoothly. </span></span></span>

	:<span style="font-size:small"><span style="font-size:small"><span style="font-size:small"><math>POPURBAN_{r}=ConvergeOverTime(PopUrbanGro,PopUrbanTar)</math~~></span></span~~></span>		:<span style="font-size:small"><span style="font-size:small"><span style="font-size:small"><math>POPURBAN_{r}=ConvergeOverTime(PopUrbanGro,PopUrbanTar)</math></span>

	<span style="font-size:small"><span style="font-size:small"><span style="font-size:small">''where''</span></span></span>		<span style="font-size:small"><span style="font-size:small"><span style="font-size:small">''where''</span></span></span>

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	<span style="font-size:small"><span style="font-size:small"><span style="font-size:small">Often they present their data values in 5 year categories (1950-1955, . . . , 2095-2099).  To obtain values at specific 5-year intervals, such as 1960 or 2010, we average the values for the two 5-year categories that bracket that year.  To estimate annual values for all years from such categories, for instance for migration numbers, we used a Sprague algorithm to spread the 5 year data (1950-1955, . . . , 2095-2099). With respect to migration, to obtain net migration rates we divided their annualized numbers by annual population data'''.'''</span></span></span>		<span style="font-size:small"><span style="font-size:small"><span style="font-size:small">Often they present their data values in 5 year categories (1950-1955, . . . , 2095-2099).  To obtain values at specific 5-year intervals, such as 1960 or 2010, we average the values for the two 5-year categories that bracket that year.  To estimate annual values for all years from such categories, for instance for migration numbers, we used a Sprague algorithm to spread the 5 year data (1950-1955, . . . , 2095-2099). With respect to migration, to obtain net migration rates we divided their annualized numbers by annual population data'''.'''</span></span></span>

	~~----~~

	= References  =		= References  =

	<references />		<references />

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	<span style="font-size:small">Humans as individuals within households interact in larger demographic systems or structures. The computer model should represent the behavior of such households, such as decisions to have children or to emigrate. And it should represent the larger demographic structures that incorporate the decisions of millions of such households. A typical approach to representing such demographic systems is through age-sex cohort distributions (see the figure below showing an example from the model). IFs also uses fertility and mortality distributions by age and sex and tracks migration across countries.[[File:Pop1.png\|frame\|center\|Population pyramid for India (2010).]]</span>		<span style="font-size:small">Humans as individuals within households interact in larger demographic systems or structures. The computer model should represent the behavior of such households, such as decisions to have children or to emigrate. And it should represent the larger demographic structures that incorporate the decisions of millions of such households. A typical approach to representing such demographic systems is through age-sex cohort distributions (see the figure below showing an example from the model). IFs also uses fertility and mortality distributions by age and sex and tracks migration across countries.[[File:Pop1.png\|frame\|center\|Population pyramid for India (2010).]]</span>

	<span style="font-size:small">Demographers have widely accepted the representation of demographic systems and the development of demographic models with cohort-component structures. In fact, the United Nations, the U.S. Census Bureau, and the International Institute for Applied Systems Analysis (IIASA), pre-eminent demographic forecasting institutions, all use cohort-component modeling (O’Neill and Balk 2001).</span>		<span style="font-size:small">Demographers have widely accepted the representation of demographic systems and the development of demographic models with cohort-component structures. In fact, the United Nations, the U.S. Census Bureau, and the International Institute for Applied Systems Analysis (IIASA), pre-eminent demographic forecasting institutions, all use cohort-component modeling (O’Neill and Balk 2001)<ref>O’Neill, B. C., & Balk, D. (2001). World population futures (Vol. 56). Population Reference Bureau. Retrieved from http://auth.prb.org/Source/ACFAC56.pdf</ref>.</span>

	= <span style="font-size:xx-large;">Dominant Relations: Population</span> =		= <span style="font-size:xx-large;">Dominant Relations: Population</span> =

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	:<math>MALNCHIL_r=(AGEDST_{r,c=1,p}+AGEDST_{r,c=2,p})*MALNCH_r/100</math>		:<math>MALNCHIL_r=(AGEDST_{r,c=1,p}+AGEDST_{r,c=2,p})*MALNCH_r/100</math>

	<span style="font-size:small"><span style="font-size:small"><span style="font-size:small">Relatively few models attempt to close the loop between food availability and mortality. (See, for example, Meadows, et. al., 1974 and Mesarovic and Pestel, 1974). IFs does so, while recognizing that little is actually known about the linkage. IFs treats calories as the basis for severe malnutrition- or starvation-related deaths. Regional calorie need (CLNEED) is computed by a sum across the age distribution (AGEDST), considering age specific calorie requirements (CLAGE) and an exogenous factor'' (clnf'' ) with which the user can introduce regional variation in needs (or assumptions of regional differences in ability to respond to calorie shortages). </span></span></span>		<span style="font-size:small"><span style="font-size:small"><span style="font-size:small">Relatively few models attempt to close the loop between food availability and mortality. (See, for example, Meadows, et. al., 1974<ref>Meadows, Dennis L. et al. 1974. Dynamics of Growth in a Finite World. Cambridge, Mass: Wright-Allen Press.</ref> and Mesarovic and Pestel, 1974<ref>Mesarovic, Mihajlo D. and Eduard Pestel. 1974. Mankind at the Turning Point. New York: E.P. Dutton & Co.</ref>). IFs does so, while recognizing that little is actually known about the linkage. IFs treats calories as the basis for severe malnutrition- or starvation-related deaths. Regional calorie need (CLNEED) is computed by a sum across the age distribution (AGEDST), considering age specific calorie requirements (CLAGE) and an exogenous factor'' (clnf'' ) with which the user can introduce regional variation in needs (or assumptions of regional differences in ability to respond to calorie shortages). </span></span></span>

	:<span style="font-size:small"><span style="font-size:small"><span style="font-size:small"><math>CLNEED_{r}=\sum^{C}\sum^{G}AGEDST_{r,c,p}\mathbf{clage}_{c}\mathbf{clnf}_{r}</math></span></span></span>		:<span style="font-size:small"><span style="font-size:small"><span style="font-size:small"><math>CLNEED_{r}=\sum^{C}\sum^{G}AGEDST_{r,c,p}\mathbf{clage}_{c}\mathbf{clnf}_{r}</math></span></span></span>

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	== <span style="font-size:x-large;">Nutrition</span> ==		== <span style="font-size:x-large;">Nutrition</span> ==

	<span style="font-size:small">As noted in the overview of demographics, there is an element of mortality calculations that has historically captured considerable attention from many of those interested in long-term population forecasting, going back to at least Malthus's elaboration of the negative feedback loop linking undernutrition or starvation to higher death rates.  Donella Meadows, et al. (1972) popularized this in their discussion of ''The Limits to Growth.''</span>		<span style="font-size:small">As noted in the overview of demographics, there is an element of mortality calculations that has historically captured considerable attention from many of those interested in long-term population forecasting, going back to at least Malthus's elaboration of the negative feedback loop linking undernutrition or starvation to higher death rates.  Donella Meadows, et al. (1972) popularized this in their discussion of ''The Limits to Growth.<ref>Meadows, Donella H., Dennis L. Meadows, Jørgen Randers, and William W. Behrens III. 1972. The Limits to Growth. New York: Universe Books.</ref>''</span>

	<span style="font-size:small">In the current default representation of the model, with the health model turned on, that health model computes the rate of undernutrition among children (MALNCHP), the resultant total numbers of children undernourished (MALNCHIL), and the deaths associated with undernutrition.  Undernutrition in the health model is a function of calories, but also of access to improved sanitation and clean water.  Health interventions, including those to reduce diarrhea, can supplement greater access to calories to reduce the undernutrition and associated mortality.</span>		<span style="font-size:small">In the current default representation of the model, with the health model turned on, that health model computes the rate of undernutrition among children (MALNCHP), the resultant total numbers of children undernourished (MALNCHIL), and the deaths associated with undernutrition.  Undernutrition in the health model is a function of calories, but also of access to improved sanitation and clean water.  Health interventions, including those to reduce diarrhea, can supplement greater access to calories to reduce the undernutrition and associated mortality.</span>

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	<span style="font-size:small">Change in fertility centers on the current value of the total fertility rate (TFR).  IFs determines the TFR and then imposes that on the cohort-specific fertility distribution (FERDST) of the region/country.</span>		<span style="font-size:small">Change in fertility centers on the current value of the total fertility rate (TFR).  IFs determines the TFR and then imposes that on the cohort-specific fertility distribution (FERDST) of the region/country.</span>

	<span style="font-size:small">IFs uses three key variables to drive TFR forecasts over time.  One of those accounts for the change that typically accompanies long-term development and social evolution. The two principal candidates to represent such change in the long term across all IFs models are GDP per capita at purchasing power parity (GDPPCP) and the years of formal education attained by adults (EDYRSAG15).  Our own analysis and that by Angeles (2010)<ref>Angeles, Luis. 2010. "Demographic Transitions: Analyzing the Effects of Mortality on Fertility", Journal of Population Economics 23: 99-120. DOI 10.1007/s00148-009-0255-6.</ref> both suggest that the latter is the stronger predictor for TFR.  Frequently in IFs we find (Hughes 2001) that the relationship between one of those two deep distal drivers and any specific element of social change is logarithmic (that is, social change happens especially rapidly at lower levels of income and education and then saturates) and this is the case in this instance also.  You can see the approximate form of that relationship by examining a scattergram of TFR as a function of EDYRSAG15 in the initial model year or you can look at the multivariate relationship that IFs actually uses (in Scenario Analysis/Change Selected Functions).</span>		<span style="font-size:small">IFs uses three key variables to drive TFR forecasts over time.  One of those accounts for the change that typically accompanies long-term development and social evolution. The two principal candidates to represent such change in the long term across all IFs models are GDP per capita at purchasing power parity (GDPPCP) and the years of formal education attained by adults (EDYRSAG15).  Our own analysis and that by Angeles (2010)<ref>Angeles, Luis. 2010. "Demographic Transitions: Analyzing the Effects of Mortality on Fertility", Journal of Population Economics 23: 99-120. DOI 10.1007/s00148-009-0255-6.</ref> both suggest that the latter is the stronger predictor for TFR.  Frequently in IFs we find (Hughes 2001)<ref>Hughes, Barry B. 2001. "Global Social Transformation: The Sweet Spot, the Steady Slog, and the Systemic Shift,” Economic Development and Cultural Change 49, No. 2 (January 2001): 423-458.</ref> that the relationship between one of those two deep distal drivers and any specific element of social change is logarithmic (that is, social change happens especially rapidly at lower levels of income and education and then saturates) and this is the case in this instance also.  You can see the approximate form of that relationship by examining a scattergram of TFR as a function of EDYRSAG15 in the initial model year or you can look at the multivariate relationship that IFs actually uses (in Scenario Analysis/Change Selected Functions).</span>

	<span style="font-size:small">In addition to long-term development and the deep or distal variables associated with it, societies are subject to short-term factors, most of which are in turn influenced heavily over time by the distal variables.  These more proximate variables do, however, exhibit patterns of change that are at least somewhat independent of the distal drivers and more dependent on societal choices and policies.  In the case of fertility change, two such variables often identified to be important are the rate of mortality, often infant mortality in particular (INFMORT), and the rate of use of modern contraception (CONTRUSE).</span>		<span style="font-size:small">In addition to long-term development and the deep or distal variables associated with it, societies are subject to short-term factors, most of which are in turn influenced heavily over time by the distal variables.  These more proximate variables do, however, exhibit patterns of change that are at least somewhat independent of the distal drivers and more dependent on societal choices and policies.  In the case of fertility change, two such variables often identified to be important are the rate of mortality, often infant mortality in particular (INFMORT), and the rate of use of modern contraception (CONTRUSE).</span>

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	=== <span style="font-size:medium;">Overview</span> ===		=== <span style="font-size:medium;">Overview</span> ===

	<span style="font-size:small;">The population submodel of IFs uses the cohort component analysis approach of many population models, including the studies done by the United Nations (United Nations, 1956 and 1977). The structure of the IFs population model drew initially on the World Integrated Model (WIM) or the second generation Mesarovic-Pestel Model (Hughes, 1980), but has changed much over time.</span>		<span style="font-size:small;">The population submodel of IFs uses the cohort component analysis approach of many population models, including the studies done by the United Nations (United Nations, 1956<ref>United Nations, Department of Economic and Social Affairs. 1956. Methods of Population Projections by Sex and Age. New York: United Nations, ST/SOA Series A.</ref> and 1977). The structure of the IFs population model drew initially on the World Integrated Model (WIM) or the second generation Mesarovic-Pestel Model (Hughes, 1980<ref>Hughes, Barry B. 1980. World Modeling. Lexington, Mass: Lexington Books.</ref>), but has changed much over time.</span>

	<span style="font-size:small;">The approach relies upon age, fertility, and mortality distributions for each country/region with 22 cohorts - one for infants, 20 of 5-year size, and one for all individuals of age 100 or older. A major advantage of 5-year cohorts is that data sources generally present demographic data in that form. Ideally, however, the cohort size should correspond to the model time step so as to avoid "numerical diffusion," the propagation of change from a five-year cohort to an adjoining cohort in a single year. To prevent such numerical diffusion, IFs actually runs an age distribution with 100 single-year cohorts and advances that over time, collapsing to 22 cohorts only for the calculations of births and deaths.</span>		<span style="font-size:small;">The approach relies upon age, fertility, and mortality distributions for each country/region with 22 cohorts - one for infants, 20 of 5-year size, and one for all individuals of age 100 or older. A major advantage of 5-year cohorts is that data sources generally present demographic data in that form. Ideally, however, the cohort size should correspond to the model time step so as to avoid "numerical diffusion," the propagation of change from a five-year cohort to an adjoining cohort in a single year. To prevent such numerical diffusion, IFs actually runs an age distribution with 100 single-year cohorts and advances that over time, collapsing to 22 cohorts only for the calculations of births and deaths.</span>

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	The most recent and complete demographic model documentation is available on Pardee's [http://pardee.du.edu/ifs-population-model-documentation website]. Although the text in this interactive system is, for some IFs models, often significantly out of date, you may still find the basic description useful to you.		The most recent and complete demographic model documentation is available on Pardee's [http://pardee.du.edu/ifs-population-model-documentation website]. Although the text in this interactive system is, for some IFs models, often significantly out of date, you may still find the basic description useful to you.

	The population sub-model of IFs uses the cohort component analysis approach of many population models, including the studies done by the United Nations (United Nations, 1956 and 1977). The structure of the IFs population model drew initially on the World Integrated Model (WIM) or the second generation Mesarovic-Pestel Model (Hughes, 1980), but has changed much over time.  In particular, José Solórzano and Randall Kuhn have made many contributions to its development.		The population sub-model of IFs uses the cohort component analysis approach of many population models, including the studies done by the United Nations (United Nations, 1956<ref>United Nations, Department of Economic and Social Affairs. 1956. Methods of Population Projections by Sex and Age. New York: United Nations, ST/SOA Series A.</ref> and 1977). The structure of the IFs population model drew initially on the World Integrated Model (WIM) or the second generation Mesarovic-Pestel Model (Hughes, 1980)<ref>Hughes, Barry B. 1980. World Modeling. Lexington, Mass: Lexington Books.</ref>, but has changed much over time. In particular, José Solórzano and Randall Kuhn have made many contributions to its development.

	The approach relies upon age, fertility, and mortality distributions for each country/region with 22 cohorts: one for infants, 20 of five-year size, and one for all individuals of age 100 or older. A major advantage of five-year cohorts is that data sources generally present demographic data in that form. Ideally, however, the cohort size should correspond to the model time step so as to avoid "numerical diffusion," the propagation of change from a five-year cohort to an adjoining cohort in a single year. To prevent such numerical diffusion, IFs actually runs an age distribution with 100 single-year cohorts and advances that over time, collapsing to 22 cohorts only for the calculations of births and deaths.		The approach relies upon age, fertility, and mortality distributions for each country/region with 22 cohorts: one for infants, 20 of five-year size, and one for all individuals of age 100 or older. A major advantage of five-year cohorts is that data sources generally present demographic data in that form. Ideally, however, the cohort size should correspond to the model time step so as to avoid "numerical diffusion," the propagation of change from a five-year cohort to an adjoining cohort in a single year. To prevent such numerical diffusion, IFs actually runs an age distribution with 100 single-year cohorts and advances that over time, collapsing to 22 cohorts only for the calculations of births and deaths.

	Because extensions of life expectancy are occurring steadily and there is at least the possibility of substantial breakthroughs, the IFs project has also created the option of extending the number of cohorts from 22 up to as many as 42 (allowing separate representation of age categories up to 200+).  The capability is normally turned off, but instructions for turning on extended aging can be found [[Population#Demographic_Flow_Charts\|here]].		Because extensions of life expectancy are occurring steadily and there is at least the possibility of substantial breakthroughs, the IFs project has also created the option of extending the number of cohorts from 22 up to as many as 42 (allowing separate representation of age categories up to 200+). The capability is normally turned off, but instructions for turning on extended aging can be found [[Population#Demographic_Flow_Charts\|here]].

	= <span style="font-size:xx-large;">Structure and Agent System: Demographic</span> =		= <span style="font-size:xx-large;">Structure and Agent System: Demographic</span> =