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<blockquote data-quote="Nathal" data-source="post: 2141835" data-attributes="member: 1809"><p>I was reading a bunch of webpages as I researched this, and I felt like I was going down into a rabbit hole. One early theorist, named Malthus of England wrote in 1798: </p><p></p><p>"It may be safely asserted, therefore, that population, when unchecked, increases in a geometrical progression of such nature as to double itself every twenty-five years. This statement, of course, refers to the general result, and not to each intermediate step of the progress. Practically, it would sometimes be slower, and sometimes faster."</p><p></p><p>But...also according to this site:</p><p></p><p>"Demographers typically measure human population growth rates as annual growth rates. They calculate the annual birth rate per 1,000 people, and the annual death rate per 1,000 people. For example a birth rate of 18 per 1,000 people, and a death rate of 8 per 1,000 people, gives a net gain of 10 people per 1,000. This is then expressed as a 1% growth rate. </p><p></p><p>So, at a constant annual growth rate of 1% a human population will double roughly every 70 years, and at a constant 2% a population will double roughly every 35 years. You could just as easily calculate the population tripling or quadrupling times, but demographers prefer to use doubling times.</p><p></p><p>To attain the 25 year population doubling time used by Malthus, a population would have to sustain a growth rate of 2.8%."</p><p></p><p>The same site (<a href="http://members.optusnet.com.au/exponentialist/DoublingMech.htm" target="_blank">http://members.optusnet.com.au/exponentialist/DoublingMech.htm</a>) goes on to read:</p><p></p><p>"Constant Growth Rate versus Variable Growth Rate</p><p></p><p>Note that a variable positive growth rate (known as variable compound interest) will also result in doubling your population, which is why our global population has been growing exponentially (see below). It is a common fallacy to assume that a constant growth rate is required for exponential growth. This is what Malthus had to say in "A Summary View on The Principle Of Population", published in 1830:</p><p></p><p>"The immediate cause of the increase of population is the excess of the births above deaths; and the rate of increase, or the period of doubling, depends upon the proportion which the excess of the births above the deaths bears to the population."</p><p></p><p>Logic alone should be enough to show that, if a constant 1% growth rate doubles a population in 70 years, and a constant 2% growth rate doubles a population in 35 years, then a population which experiences variable growth rates falling from 2% to 1% will double somewhere between 70 and 35 years. "</p><p></p><p>In other words Population grows geometrically rather than arithmetically. </p><p></p><p>...</p><p></p><p>Anyway, I'm thinking that of my original 100 immigrants from Earth (from wales in the 13th century), that the average birth rate was 7 children per women in her lifetime. Average life expectancy was 60 due to some bit of magic. It seems to simple to me to double the population every 25 years without knowing the death rate. With magic, I am certain there would be excess of the births above deaths, so a high growth rate could be expected...</p><p></p><p>I'm looking at a region about 240,000 square miles.</p></blockquote><p></p>
[QUOTE="Nathal, post: 2141835, member: 1809"] I was reading a bunch of webpages as I researched this, and I felt like I was going down into a rabbit hole. One early theorist, named Malthus of England wrote in 1798: "It may be safely asserted, therefore, that population, when unchecked, increases in a geometrical progression of such nature as to double itself every twenty-five years. This statement, of course, refers to the general result, and not to each intermediate step of the progress. Practically, it would sometimes be slower, and sometimes faster." But...also according to this site: "Demographers typically measure human population growth rates as annual growth rates. They calculate the annual birth rate per 1,000 people, and the annual death rate per 1,000 people. For example a birth rate of 18 per 1,000 people, and a death rate of 8 per 1,000 people, gives a net gain of 10 people per 1,000. This is then expressed as a 1% growth rate. So, at a constant annual growth rate of 1% a human population will double roughly every 70 years, and at a constant 2% a population will double roughly every 35 years. You could just as easily calculate the population tripling or quadrupling times, but demographers prefer to use doubling times. To attain the 25 year population doubling time used by Malthus, a population would have to sustain a growth rate of 2.8%." The same site ([url]http://members.optusnet.com.au/exponentialist/DoublingMech.htm[/url]) goes on to read: "Constant Growth Rate versus Variable Growth Rate Note that a variable positive growth rate (known as variable compound interest) will also result in doubling your population, which is why our global population has been growing exponentially (see below). It is a common fallacy to assume that a constant growth rate is required for exponential growth. This is what Malthus had to say in "A Summary View on The Principle Of Population", published in 1830: "The immediate cause of the increase of population is the excess of the births above deaths; and the rate of increase, or the period of doubling, depends upon the proportion which the excess of the births above the deaths bears to the population." Logic alone should be enough to show that, if a constant 1% growth rate doubles a population in 70 years, and a constant 2% growth rate doubles a population in 35 years, then a population which experiences variable growth rates falling from 2% to 1% will double somewhere between 70 and 35 years. " In other words Population grows geometrically rather than arithmetically. ... Anyway, I'm thinking that of my original 100 immigrants from Earth (from wales in the 13th century), that the average birth rate was 7 children per women in her lifetime. Average life expectancy was 60 due to some bit of magic. It seems to simple to me to double the population every 25 years without knowing the death rate. With magic, I am certain there would be excess of the births above deaths, so a high growth rate could be expected... I'm looking at a region about 240,000 square miles. [/QUOTE]
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