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This activity uses Map Viewer. ResourcesMapTeacher guide Student worksheetGet startedOpen the map.Use the teacher guide to explore the map with your class or have students work through it on their own with the worksheet.New to GeoInquiriesTM? See Getting to Know GeoInquiries.StandardsCCSS: MATH.CONTENT.HSF.LE.A.1 – Distinguish between situations that can be modeled with linear functions and with exponential functions.CCSS: MATH.CONTENT.HSF.IF.B.4 – For a function that models a relationship between two quantities, interpret key features of graphs & tables in terms of the quantities, & sketch graphs showing key features given a verbal description of the relationship.Learning outcomesStudents will investigate rates of population growth and decline. Students will compare linear and exponential growth rates.More activitiesAll Mathematics GeoInquiriesAll GeoInquiries

A system of differential equations is proposed as a model of dispersion between two populations in habitats separated by a barrier.

Investigate rates of population growth and decline with US Census data. THE GEOINQUIRIES™ COLLECTION FOR MATHEMATICShttp://www.esri.com/geoinquiriesThe GeoInquiry™ collection for Mathematics contains 15 free, standards-based activities that correspond and extend spatial concepts found in course textbooks frequently used in introductory algebra or geometry classes. The activities use a common inquiry-based instructional model, require only 15 minutes to deliver, and are device/laptop agnostic. Each activity includes an ArcGIS Online map but requires no login or installation. The activities harmonize with the Common Core math national curriculum standards. Activities include:· Rates & Proportions: A lost beach· D=R x T· Linear rate of change: Steady growth· How much rain? Linear equations· Rates of population change· Distance and midpoint· The coordinate plane· Euclidean vs Non-Euclidean· Area and perimeter at the mall· Measuring crop circles· Area of complex figures· Similar triangles· Perpendicular bisectors· Centers of triangles· Volume of pyramids

Teachers, GeoMentors, and school administrators can learn more at http://www.esri.com/geoinquiries.

Utilizing survey research, 186 university students completed measures of math anxiety, math self-efficacy, statistics anxiety, and statistics self-efficacy.

BackgroundIn a given population the age pattern of mortality is an important determinant of total number of deaths, age structure, and through effects on age structure, the number of births and thereby growth. Good mortality models exist for most populations except those experiencing generalized HIV epidemics and some developing country populations. The large number of deaths concentrated at very young and adult ages in HIV-affected populations produce a unique ‘humped’ age pattern of mortality that is not reproduced by any existing mortality models. Both burden of disease reporting and population projection methods require age-specific mortality rates to estimate numbers of deaths and produce plausible age structures. For countries with generalized HIV epidemics these estimates should take into account the future trajectory of HIV prevalence and its effects on age-specific mortality. In this paper we present a parsimonious model of age-specific mortality for countries with generalized HIV/AIDS epidemics.Methods and FindingsThe model represents a vector of age-specific mortality rates as the weighted sum of three independent age-varying components. We derive the age-varying components from a Singular Value Decomposition of the matrix of age-specific mortality rate schedules. The weights are modeled as a function of HIV prevalence and one of three possible sets of inputs: life expectancy at birth, a measure of child mortality, or child mortality with a measure of adult mortality. We calibrate the model with 320 five-year life tables for each sex from the World Population Prospects 2010 revision that come from the 40 countries of the world that have and are experiencing a generalized HIV epidemic. Cross validation shows that the model is able to outperform several existing model life table systems.ConclusionsWe present a flexible, parsimonious model of age-specific mortality for countries with generalized HIV epidemics. Combined with the outputs of existing epidemiological and demographic models, this model makes it possible to project future age-specific mortality profiles and number of deaths for countries with generalized HIV epidemics.

A discrete mathematical model was developed to study the population dynamics after a time-varying environmental disaster (R4.x261.000:0008). A 5-stage-structure matrix includes parameters for stage-specific survival and transition rates, as well as annual fecundity. This model can be used to examine the sensitivity and elasticity of the model, as well as demographic and environmental stochasticity, and many others.

A mathematical model including dynamical systems, statistical models and differential equations involves variety abstract structures. Population growth is one of the main issues in India and China which are located in Asia.

List of Top Authors of Mathematical Population Studies sorted by citations.

Comprehensive population and demographic data for Rini Math Village

This is a hybrid gridded dataset of demographic data for the world, given as 5-year population bands at a 0.5 degree grid resolution.

This dataset combines the NASA SEDAC Gridded Population of the World version 4 (GPWv4) with the ISIMIP Histsoc gridded population data and the United Nations World Population Program (WPP) demographic modelling data.

Demographic fractions are given for the time period covered by the UN WPP model (1950-2050) while demographic totals are given for the time period covered by the combination of GPWv4 and Histsoc (1950-2020)

Method - demographic fractions

Demographic breakdown of country population by grid cell is calculated by combining the GPWv4 demographic data given for 2010 with the yearly country breakdowns from the UN WPP. This combines the spatial distribution of demographics from GPWv4 with the temporal trends from the UN WPP. This makes it possible to calculate exposure trends from 1980 to the present day.

To combine the UN WPP demographics with the GPWv4 demographics, we calculate for each country the proportional change in fraction of demographic in each age band relative to 2010 as:

\(\delta_{year,\ country,age}^{\text{wpp}} = f_{year,\ country,age}^{\text{wpp}}/f_{2010,country,age}^{\text{wpp}}\)

Where:

- \(\delta_{year,\ country,age}^{\text{wpp}}\) is the ratio of change in demographic for a given age and and country from the UN WPP dataset.

- \(f_{year,\ country,age}^{\text{wpp}}\) is the fraction of population in the UN WPP dataset for a given age band, country, and year.

- \(f_{2010,country,age}^{\text{wpp}}\) is the fraction of population in the UN WPP dataset for a given age band, country for the year 2020.

The gridded demographic fraction is then calculated relative to the 2010 demographic data given by GPWv4.

For each subset of cells corresponding to a given country c, the fraction of population in a given age band is calculated as:

\(f_{year,c,age}^{\text{gpw}} = \delta_{year,\ country,age}^{\text{wpp}}*f_{2010,c,\text{age}}^{\text{gpw}}\)

Where:

- \(f_{year,c,age}^{\text{gpw}}\) is the fraction of the population in a given age band for given year, for the grid cell c.

- \(f_{2010,c,age}^{\text{gpw}}\) is the fraction of the population in a given age band for 2010, for the grid cell c.

The matching between grid cells and country codes is performed using the GPWv4 gridded country code lookup data and country name lookup table. The final dataset is assembled by combining the cells from all countries into a single gridded time series. This time series covers the whole period from 1950-2050, corresponding to the data available in the UN WPP model.

Method - demographic totals

Total population data from 1950 to 1999 is drawn from ISIMIP Histsoc, while data from 2000-2020 is drawn from GPWv4. These two gridded time series are simply joined at the cut-over date to give a single dataset covering 1950-2020.

The total population per age band per cell is calculated by multiplying the population fractions by the population totals per grid cell.

Note that as the total population data only covers until 2020, the time span covered by the demographic population totals data is 1950-2020 (not 1950-2050).

Disclaimer

This dataset is a hybrid of different datasets with independent methodologies. No guarantees are made about the spatial or temporal consistency across dataset boundaries. The dataset may contain outlier points (e.g single cells with demographic fractions >1). This dataset is produced on a 'best effort' basis and has been found to be broadly consistent with other approaches, but may contain inconsistencies which not been identified.

The portion of the budget, consumed by defectors is and the relative amount spent for regulators is . Countries are classified according to their distance from equilibrium defined by expression (46).

This dataset provides annual population projections for the 50 states and the District of Columbia by age, sex, and race for the years 1986 through 2010. The projections were made using a mathematical projection model called the cohort-component method. This method allows separate assumptions to be made for each of the components of population change: births, deaths, internal migration, and international migration. The projections are consistent with the July 1, 1986 population estimates for states. In general, the projections assume a slight increase in the national levels of fertility, an increasing level of life expectancy, and a decreasing level of net international migration. Internal migration assumptions are based on the annual state-to-state migration data for the years 1975-1986.

BackgroundAn increase in the average age of dengue hemorrhagic fever (DHF) cases has been reported in Thailand. The cause of this increase is not known. Possible explanations include a reduction in transmission due to declining mosquito populations, declining contact between human and mosquito, and changes in reporting. We propose that a demographic shift toward lower birth and death rates has reduced dengue transmission and lengthened the interval between large epidemics.Methods and FindingsUsing data from each of the 72 provinces of Thailand, we looked for associations between force of infection (a measure of hazard, defined as the rate per capita at which susceptible individuals become infected) and demographic and climactic variables. We estimated the force of infection from the age distribution of cases from 1985 to 2005. We find that the force of infection has declined by 2% each year since a peak in the late 1970s and early 1980s. Contrary to recent findings suggesting that the incidence of DHF has increased in Thailand, we find a small but statistically significant decline in DHF incidence since 1985 in a majority of provinces. The strongest predictor of the change in force of infection and the mean force of infection is the median age of the population. Using mathematical simulations of dengue transmission we show that a reduced birth rate and a shift in the population's age structure can explain the shift in the age distribution of cases, reduction of the force of infection, and increase in the periodicity of multiannual oscillations of DHF incidence in the absence of other changes.ConclusionsLower birth and death rates decrease the flow of susceptible individuals into the population and increase the longevity of immune individuals. The increase in the proportion of the population that is immune increases the likelihood that an infectious mosquito will feed on an immune individual, reducing the force of infection. Though the force of infection has decreased by half, we find that the critical vaccination fraction has not changed significantly, declining from an average of 85% to 80%. Clinical guidelines should consider the impact of continued increases in the age of dengue cases in Thailand. Countries in the region lagging behind Thailand in the demographic transition may experience the same increase as their population ages. The impact of demographic changes on the force of infection has been hypothesized for other diseases, but, to our knowledge, this is the first observation of this phenomenon.Please see later in the article for the Editors' Summary

Comprehensive population and demographic data for Math Adam Village

Comprehensive population and demographic data for Math Toi Village

This dataset tracks annual math proficiency from 2011 to 2023 for Washington G High School vs. Illinois and Chicago Public Schools District 299

Equations for steady states and critical parameter values. (PDF)

Using a fictitious population of Rocs, a mythical species of giant raptor, students accomplish two broad objectives: 1) they undertake the process of building a first mathematical model of a population, and 2) they begin to develop their understanding of the product of a scientific model. Students accomplish these objectives by engaging deeply with a system of linked scientific practices: developing scientific models collaboratively, to explain or predict observations, to multiple audiences using multiple representations. The lesson is scalable from large introductory biology courses to upper-division courses in population ecology or biological modeling. The scenario unfolds within as little as a single 50-minute class period and requires no prior preparation of students. During and after the class meeting, students work in collaborative teams to build a simple, but non-trivial spreadsheet model. Students then use their model to engage in several modeling-related activities: they use their model to make predictions, conduct a sensitivity analysis, make decisions, and communicate their model results to non-experts. This lesson invites both students and instructors to collaborate, as students work to master concepts of population growth, and scientific practices of modeling, working with data, communication, and collaboration.

This is a hybrid gridded dataset of demographic data for China from 1979 to 2100, given as 21 five-year age groups of population divided by gender every year at a 0.5-degree grid resolution.

The historical period (1979-2020) part of this dataset combines the NASA SEDAC Gridded Population of the World version 4 (GPWv4, UN WPP-Adjusted Population Count) with gridded population from the Inter-Sectoral Impact Model Intercomparison Project (ISIMIP, Histsoc gridded population data).

The projection (2010-2100) part of this dataset is resampled directly from Chen et al.’s data published in Scientific Data.

This dataset includes 31 provincial administrative districts of China, including 22 provinces, 5 autonomous regions, and 4 municipalities directly under the control of the central government (Taiwan, Hong Kong, and Macao were excluded due to missing data).

Method - demographic fractions by age and gender in 1979-2020

Age- and gender-specific demographic data by grid cell for each province in China are derived by combining historical demographic data in 1979-2020 with the national population census data provided by the National Statistics Bureau of China.

To combine the national population census data with the historical demographics, we constructed the provincial fractions of demographic in each age groups and each gender according to the fourth, fifth and sixth national population census, which cover the year of 1979-1990, 1991-2000 and 2001-2020, respectively. The provincial fractions can be computed as:

\(\begin{align*} \begin{split} f_{year,province,age,gender}= \left \{ \begin{array}{lr} POP_{1990,province,age,gender}^{4^{th}census}/POP_{1990,province}^{4^{th}census} & 1979\le\mathrm{year}\le1990\\ POP_{2000,province,age,gender}^{5^{th}census}/POP_{2000,province}^{5^{th}census} & 1991\le\mathrm{year}\le2000\\ POP_{2010,province,age,gender}^{6^{th}census}/POP_{2010,province}^{6^{th}census}, & 2001\le\mathrm{year}\le2020 \end{array} \right. \end{split} \end{align*}\)

Where:

- \( f_{\mathrm{year,province,age,gender}}\)is the fraction of population for a given age, a given gender in each province from the national census from 1979-2020.

- \(\mathrm{PO}\mathrm{P}_{\mathrm{year,province,age,gender}}^{X^{\mathrm{th}}\mathrm{census} }\) is the total population for a given age, a given gender in each province from the X^th national census.

- \(\mathrm{PO}\mathrm{P}_{\mathrm{year,province}}^{X^{\mathrm{th}}\mathrm{census} }\) is the total population for all ages and both genders in each province from the X^th national census.

Method - demographic totals by age and gender in 1979-2020

The yearly grid population for 1979-1999 are from ISIMIP Histsoc gridded population data, and for 2000-2020 are from the GPWv4 demographic data adjusted by the UN WPP (UN WPP-Adjusted Population Count, v4.11, https://beta.sedac.ciesin.columbia.edu/data/set/gpw-v4-population-count-adjusted-to-2015-unwpp-country-totals-rev11), which combines the spatial distribution of demographics from GPWv4 with the temporal trends from the UN WPP to improve accuracy. These two gridded time series are simply joined at the cut-over date to give a single dataset - historical demographic data covering 1979-2020.

Next, historical demographic data are mapped onto the grid scale to obtain provincial data by using gridded provincial code lookup data and name lookup table. The age- and gender-specific fraction were multiplied by the historical demographic data at the provincial level to obtain the total population by age and gender for per grid cell for china in 1979-2020.

Method - demographic totals and fractions by age and gender in 2010-2100

The grid population count data in 2010-2100 under different shared socioeconomic pathway (SSP) scenarios are drawn from Chen et al. published in Scientific Data with a resolution of 1km (~ 0.008333 degree). We resampled the data to 0.5 degree by aggregating the population count together to obtain the future population data per cell.

This previously published dataset also provided age- and gender-specific population of each provinces, so we calculated the fraction of each age and gender group at provincial level. Then, we multiply the fractions with grid population count to get the total population per age group per cell for each gender.

Note that the projected population data from Chen’s dataset covers 2010-2020, while the historical population in our dataset also covers 2010-2020. The two datasets of that same period may vary because the original population data come from different sources and are calculated based on different methods.

Disclaimer

This dataset is a hybrid of different datasets with independent methodologies. Spatial or temporal consistency across dataset boundaries cannot be guaranteed.

IntroductionAfter more than 100 years of generating monoculture batch culture growth curves, microbial ecologists and evolutionary biologists still lack a reference method for inferring growth rates. Our work highlights the challenges of estimating the growth rate from growth curve data. It shows that inaccurate estimates of growth rates significantly impact the estimated relative fitness, a principal quantity in evolution and ecology. Methods and resultsFirst, we conducted a literature review and found which methods are currently used to estimate growth rates. These methods differ in the meaning of the estimated growth rate parameter. Mechanistic models estimate the intrinsic growth rate µ, whereas phenomenological methods – both model-based and model-free – estimate the maximum per capita growth rate µmax. Using math and simulations, we show the conditions in which µmax is not a good estimator of µ. Then, we demonstrate that inaccurate absolute estimates of µ are not overcome by calculating relative values. Importantly, we find that poor approximations for µ sometimes lead to wrongly classifying a beneficial mutant as deleterious. Finally, we re-analyzed four published data sets, using most of the methods found in our literature review. We detected no single best-fitting model across all experiments within a data set and found that the Gompertz models, which were among the most commonly used, were often among the worst-fitting. DiscussionOur study suggests how experimenters can improve their growth rate and associated relative fitness estimates and highlights a neglected but fundamental problem for nearly everyone who studies microbial populations in the lab.