Perhaps the calamity is due to an infectious disease or, in the case of some human
populations, to war. We leave out natural causes like earthquake and meteor
impacts because these disasters are not brought on by the population itself. Likewise as some argue, a larger population causes an inventive focus to alleviate some
of the human dilemma. We need to express the death rate in such a way that both the
negative and the beneficial effects of rising population can be felt. The question is:
when the birth rate is higher than the nominal death rate, what are the population
dynamics when higher populations can have the effect of increasing and at other
times decreasing the death rate? The answer is rather surprising.
Let us set the birth rate to a constant rate of 7 %. To mimic unanticipated changes
in the death rate, we introduce a nominal death rate, NOMINAL DR, which we set to
NOMINAL DR ¼ :04
ð3:1Þ
We make use of this nominal death rate as the mean value in a normal distribution, DR DISTRIBUTION. To specify a normal distribution with a mean of
nominal death rate we make use of the built-in function NORMAL. We must
specify the mean and standard deviation as its arguments. We define
DR DISTRIBUTION ¼ NORMAL NOMINAL DR, 0:005 Ã POPULATION
ð
Þ
ð3:2Þ
with an arbitrarily set standard deviation of 0.005 * POPULATION. Thus, as the
POPULATION increases, so does the standard deviation around the mean
NOMINAL DR.
Next we define a death rate signal, DR DIST CONTROL that constrains the
normally distributed DR DISTRIBUTION between 0.01 and 1:
DR DIST CONTROL ¼ IF DR DISTRIBUTION ! 0:01
ð
Þ AND
DR DISTRIBUTION 1
ð
Þ
THEN DR DISTRIBUTION ELSE 0:01
ð3:3Þ
We assume that the absolute minimum of the death rate is 0.01.
Finally, the DEATH RATE itself is set up to allow the following three test cases:
(a) The DR DIST CONTROL is defined in Eq. (3.3) above,
(b) A case where the standard deviation is allowed to only increase the death
rate, and
(c) An exponentially declining nominal death rate whose standard deviation
(0.005 * POPULATION) is allowed to only increase the death rate.
For the first case, we define
DEATH RATE ¼ DR DIST CONTROL
ð3:4Þ
Consequently, the death rate varies with normal distribution from 0.01 to 1
in every time period (e.g., year, decade, generation) with the nominal death rate
42
3 Risky Population
populations, to war. We leave out natural causes like earthquake and meteor
impacts because these disasters are not brought on by the population itself. Likewise as some argue, a larger population causes an inventive focus to alleviate some
of the human dilemma. We need to express the death rate in such a way that both the
negative and the beneficial effects of rising population can be felt. The question is:
when the birth rate is higher than the nominal death rate, what are the population
dynamics when higher populations can have the effect of increasing and at other
times decreasing the death rate? The answer is rather surprising.
Let us set the birth rate to a constant rate of 7 %. To mimic unanticipated changes
in the death rate, we introduce a nominal death rate, NOMINAL DR, which we set to
NOMINAL DR ¼ :04
ð3:1Þ
We make use of this nominal death rate as the mean value in a normal distribution, DR DISTRIBUTION. To specify a normal distribution with a mean of
nominal death rate we make use of the built-in function NORMAL. We must
specify the mean and standard deviation as its arguments. We define
DR DISTRIBUTION ¼ NORMAL NOMINAL DR, 0:005 Ã POPULATION
ð
Þ
ð3:2Þ
with an arbitrarily set standard deviation of 0.005 * POPULATION. Thus, as the
POPULATION increases, so does the standard deviation around the mean
NOMINAL DR.
Next we define a death rate signal, DR DIST CONTROL that constrains the
normally distributed DR DISTRIBUTION between 0.01 and 1:
DR DIST CONTROL ¼ IF DR DISTRIBUTION ! 0:01
ð
Þ AND
DR DISTRIBUTION 1
ð
Þ
THEN DR DISTRIBUTION ELSE 0:01
ð3:3Þ
We assume that the absolute minimum of the death rate is 0.01.
Finally, the DEATH RATE itself is set up to allow the following three test cases:
(a) The DR DIST CONTROL is defined in Eq. (3.3) above,
(b) A case where the standard deviation is allowed to only increase the death
rate, and
(c) An exponentially declining nominal death rate whose standard deviation
(0.005 * POPULATION) is allowed to only increase the death rate.
For the first case, we define
DEATH RATE ¼ DR DIST CONTROL
ð3:4Þ
Consequently, the death rate varies with normal distribution from 0.01 to 1
in every time period (e.g., year, decade, generation) with the nominal death rate
42
3 Risky Population