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Vaynu, Kasia, Isaiah, Joseph
Population Models and Carrying Capacity Projection
Our group (Vaynu, Kasia, Isaiah, Joseph from Ithaca High School) created two models using both logistic and exponential functions. Our data comes from the United Nations for data points from 1900 to 1940, and the US Census Bureau for data from 1940 to 2010 (data is in intervals of 10 years). An additional data point was included for the world population of 2017.
Our logistic model had a relative k value of approximately 9.51 billion. An important thing to note, however, is that carrying capacities are not necessarily the k value of the logistic function. According to Edward O. Wilson, a socio-biologist at Harvard University, the carrying capacity is approximately 10 billion, based on the limits of the world's food source.
Although the logistic function had a better fit with a higher R² value, we decided that the exponential function would be better to predict when the carrying capacity would be reached. This is because, as the following video will explain, humans are constantly exploiting resources and technology to continually increase the population. Therefore an exponential function would be a better fit for the nearer future, and would predict when the population would reach the projected carrying capacity more accurately.
Based on our model, the carrying capacity of 10 billion would be reached 135.9 years after 1900, or approximately the year 2026.
Although the logistic function had a better fit with a higher R² value, we decided that the exponential function would be better to predict when the carrying capacity would be reached. This is because, as the following video will explain, humans are constantly exploiting resources and technology to continually increase the population. Therefore an exponential function would be a better fit for the nearer future, and would predict when the population would reach the projected carrying capacity more accurately.
Based on our model, the carrying capacity of 10 billion would be reached 135.9 years after 1900, or approximately the year 2026.
CHRIS\ROWAN\SARA\KIERAN
Data for our model was collected from http://www.lithoguru.com/gentleman/data/population.xls, with some supplemental data supplied from worldpopulation.org for years after 2014. We used data points from after 1950, due to the great increase, seemingly, in the reliability, and frequency of census data after this year. Although it was clear that the population was growing exponentially, it was not initially clear whether
an exponential or logistic model should be used to model the growth.
Our group, Chris, Rowan, Kieran, and Sara decided that a logistical model would best fit the data we selected. This was mainly due to the logistical model resulting in the year accounting for 99.6% of the variation population, which is a better fit than the exponential model, which resulted in the year accounting for only 96% of the variability population. We decided on a carrying capacity of 10,000,000,000, which would result in the carrying capacity being reached in 2025, which is only 7 years away. This value was decided on as it was in the middle of what most reasonable ecologists and scientists predicted, with over 20 studies supporting the 10,000,000,000 number.
OWEN • PATRICK • RYAN • LAURA
Our group, Owen, Patrick, Ryan, and Laura (Ithaca High School) created a logistic regression from fifteen points representing the global human population on a constant time interval (5 years) since 1950. The R^2 coefficient, representing the “fit” of the equation to the data, was 0.9997. The carrying capacity mentioned in the logistic equation (k) is realistic, seeing as the human population growth in the past 50 years has started to increase exponentially but will eventually plateau as we run out of resources. Since 1950 the population appears to increase exponentially, making it unlikely that the acclaimed 10-billion-people limit is a good (k) value in a logistic equation. However, the 10-billion-people carrying capacity takes in other factors such as resource consumption and nonrenewable resource quantity into account. The point (103.081, 10) where our model intersects with 10 billion is a point where problems may occur. 103.081 years after 1950, the population will intersect with 10 billion, the carrying capacity many scientists suggest. This will occur in about 2053 CE. We have 36 years left.
Hayk - Sam - Julius - Tilden
Our group has created an exponential regression to determine when the Earth will reach our estimated population capacity - 10 billion - based on our data. The Y-axis represents world population in billions, and the x-axis is years since 1900, as data from that year appear to be most accurate than the ones prior. Our model equation, as seen above, has a correlation coefficient of determination (r^2) is .991, meaning that 99.1% of the variability in population is explained by year since 1900, making it fairly reliable model for estimation.
By our estimations, using the rate at which the population has been growing in the last 100 years, the Earth will reach its carrying capacity in only about 15 years, in 2032. Only time will tell if humanity is able to deal with this quickly growing issue in such a short amount of time.
By our estimations, using the rate at which the population has been growing in the last 100 years, the Earth will reach its carrying capacity in only about 15 years, in 2032. Only time will tell if humanity is able to deal with this quickly growing issue in such a short amount of time.