These equations are useful but they arent true

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These equations are useful, but they aren’t true.
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Variable birth and death rates One way to make them more accurate is to relax the assumption that b and d are constants. Instead let’s assume that b and d vary as functions of population size, such that b = b o k b N d = d o + k d N where b o and d o are birth and death rates at low population sizes and k b and k d are slopes of the relationship between population size and birth/death rates.
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Logistic Equation Also, we can define r o = b o d o where r o is the population growth rate at low population size. Another definition K is the population size at which births are equal to deaths, so where: b o k b N = d o + k d N You could take these definitions and derive a new population growth equation: dN/dt = r o N((K-N)/K)
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Metapopulation Theory An overall population could consist of many isolated subpopulations each of which has density-independent (unregulated) population growth, with occasional migration between them. Then, with some assumptions (infinite number of patches, each of them equal in likelihood of colonization and extinction) you can calculate the change in the proportion of potential habitats occupied as: dp/dt= (c*p*(1-p)) e*p where p is the proportion of potential habitats occupied, c is the migration (colonization) rate, and e is the extinction rate. At equilibrium, the proportion of habitats occupied will be 1-(e/c)
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Human Population Growth
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Population Growth in Italy
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Human Life Tables Age Pre-industrial Developed world x lx mx lxmx S lxmx lx mx lxmx S lxmx 10 .5 0 0 .98 0 0 20 .45 .67 .3 .97 .1 .097 30 .40 1.5 .6 .96 .4 .384 40 .36 .33 .12 .95 .5 .475 50 .3 0 0 .94 .1 .094 60 .2 0 0 .92 0 0 > 60, who cares? Unless you want to figure out social security… 1.02 1.05
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Human Age Structure, France and India
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Human Population Management in China
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