Physics 434, 2015: Project 5
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How should we model population growth in humans rather than in bacteria?
Start with the world human population size data from the textbook web site. Notice that there are also other estimates out there -- maybe it's worthwhile looking for them. A simple model of growth for bacteria (and humans) would be an exponential growth, where . That is each person gives rise to people over a certain time. But humans have two sexes, and the growth rate should be proportional to the rate of pair encounters in the population. Change the model appropriately -- does it fit the data better?
It probably doesn't -- why is that? Think of whether human-human encounters actually happen in proportion to the square of the number of humans. And does each human actually participate in the production of offsprings, or just half?
But humans are also different from bacteria and simple organisms. For example, there's a certain time it take for us to develop, and hence the largest number of offsprings that we can produce. Try to model this limitation on the growth rate. Further, our childhood survival rates have gone way up. This is because of accumulation of knowledge and the overall development of the society. Maybe we should model the growth rate of the human population as proportional not just to the number of people, but to the amount of accumulated knowledge, which, in turn, depends on contacts among people. Try to develop models of this type. Do they fit the world population data better than exponential models? Does the fit become even better if you account for the effects of the world wars on the population growth?