3.1 Description of Individual Model Sectors
3.1.6 The Population Sector
Two basic dynamics of the society-biosphere-climate-economy-energy system of the Earth and biosphere are exhibited in a) the tendency in all human populations towards exponential growth, and b) the long delay in the adaptive response of a population to changing external conditions (Meadows et al., 1974). The actual rate of growth, the nature of the adaptive response, and the length of delay all vary, depending on many different factors in the total system.
When any biological population grows, the pattern of growth over time tends to be exponential. In the twentieth century, rapid exponential growth has been exhibited not only by the global human population but by nearly every national and regional population as well (Meadows et al., 1974). The total increase in the global population during any time period is determined at least partially by the size of the population of reproductive age in that time period. For the global population, migration is not a factor, as there is no consideration of spatial distribution of the population.
There is often significant delay in demographic responses to new external conditions brought about by changes in the birth and death rates. The two major sources of the delay are the age structure of the population and the inherent slowness of social change. It takes at least 15 years for a newborn child to mature and become a parent (Figure 3.15). There is a delay of more than 50 years before the child reaches the age of highest probability of death. The long delays inherent in the biological processes of maturation and aging give every human population a strong momentum, the tendency to keep following the same dynamic behaviour that it has followed in the past (Meadows et al., 1974). Because of the momentum, a population that has been growing rapidly will continue to grow for decades, even after fertility has fallen to the equivalent of two surviving children per married couple. Similarly, a population that has experienced a fertility rate that is lower
than the replacement level may continue to decrease in size for some time after the fertility rate has again risen to the replacement level.
Figure 3.15: Model structure of the ANEMI version 2 population sector
The population sector includes a four-level population model, which means the population is divided into 4 age groups (0 to 14 yr; 15 to 44yr; 45 to 64yr; and 65 to 65 plus). For initial stocks values, the UN data (DESA, 2011) of 1980 is used.
Causal Structure of the ANEMI Version 2 Population Sector
The population sector of the ANEMI model version 2 is based on the WORLD3 population model (Meadows et al., 1974). It represents continuous dynamic interactions among the human population, climate and global resources (Figure 3.16). The population sector model contains numerous feedback loops representing demographic and technological-economic means of achieving a favourable balance between the population size and the supply of resources. In this model crowding, pollution, availability of food,
Population:
age 0 to 14 age 15 to 44Population:
Population: age 45 to 64 Population: age 65 plus births Matured 14 to 15 Matured 44 to 45 Matured 64 to 65 Deaths 65 plus Deaths 45 to 64 Deaths 15 to 44 Deaths 0 to 14 Deaths Reproductive lifetime Mortality 45 to 64 Mortality 65 plus Mortality 15 to 44 Mortality 0 to 14 Total fertility Population Birth rate <Life expectancy> Total temperature related death 65+ Population growth rate Total temperature related death 0-14
and household income affect average life expectancy. Life expectancy and extreme temperature determine the population death rate. Fertility is determined by a number of factors, including fertility control effectiveness, capital allocation, and desired family size. Birth and death rates are the only two direct variables used in the population computation.
Figure 3.16: Causal loop structure of the ANEMI version 2 population sector
Mathematical Description of the ANEMI Version 2 Population Sector
Many factors affect the population‘s average level of health or life expectancy, and it is by no means easy to assess the role of each particular factor or how each one interacts with the others. Sometimes one variable of interest appears to depend on a number of others, and in such cases one can use statistical interface techniques to find out the relative importance of the variables in question. In the case of life expectancy, Kusukawa (1967) carried out just such a statistical analysis. Here, however, the empiricalEnergy- Economy Sector Carbon Sector Food Production Sector Population Deaths Life expectancy Pollution Crowding Food per capita Births Fertility Fertility control effectiveness Desired total fertility Maximum total fertility
Need for fertility control
Family planning service per capita
GDP Food production water stress extreme temperature Water Quality Sector Climate Sector
relationship between food per capita and life expectancy is adopted from both Meadows et al. (1974) and Keyfitz and Flieger (1971).
Four factors: (i) food, (ii) health services, (iii) crowding, and (iv) pollution are incorporated in the equation for life expectancy as modifiers, or multipliers, of a ‗normal‘ life expectancy. The normal life expectancy can be set at any arbitrary value as long as the four multipliers are all defined properly with respect to that value.
where LE is the life expectancy, LEN is the life expectancy normal, and LMF is the lifetime
multiplier from food. Lifetime multiplier from health service, persistent pollution, and crowding are respectively represented as LMHS, LMP, and LMC.
In the population sector the number of deaths per year is expressed as the total number of people of a specific age group multiplied by the mortality of the same group.
where mortality is a function of life expectancy. This functional relationship is expressed in Meadows et al. (1974, page 170-172) as:
The thermal stress related mortality should increase due to the climate change. It has been established that 16 to 30 degree Celsius is the comfortable temperature zone. A 1 percent increase in the death rate could happen for 1 degree drop in temperature below 16 degree Celsius. On the other hand a 1.4 percent increase in the death rate may be experienced per degree temperature rise above 30 degree Celsius (Martens, 1998). As children and the elderly (people above 65 years of age) are mainly vulnerable to extreme climate, so temperature related death is incorporated in the ANEMI model version 2 for two age categories (0-14 and 65 plus). The Equation (3.75) therefore changes as follows:
The Equation (3.51) is still valid for the population between 15 to 64 years of age. The number of births per year is calculated from (i) a purely demographic factor, (ii) from the number of fertile women in the population (half of the total population between the 15 to 44 age group), and (iii) from a socio-economic factor, the average number of births per women per year.
where is the total fertility, is the reproductive lifetime of 30 years, and is the total population between age 15 and 44.
Total fertility is computed from the maximum total fertility , desired total fertility and fertility control effectiveness :