Our Model
We found that the best way to represent world population was with a logistic function, which we calculated based on 23 data points from the U.S. Census Bureau International Programs. Our data is evenly spaced every three years from midyear 1951 to 2017 (in the scale of our graph, our data ranges from 0.5 to 66.5). We originally included data points further into the past, but these are less accurate (since we have less information from which to infer values further in the past), and they therefore made our function less accurate for more recent years. Including data points going further back into history can make the regression more accurate during that time period, but since we wanted to maximize the accuracy of our future predictions, we chose to include only relatively recent data.
We chose to use a logistic regression since the y growth rate of our data decreases as it approaches 66.5 (our last data value), showing that population growth is slowing. Our regression has an R² value of .9997, which indicates that our function models the world's population relatively accurately.
Using our regression, we predicted when the population would exceed the carrying capacity. We decided on a carrying capacity of 10 billion after taking into account various different scientists' estimates. We found estimates ranging from 500 million to 100 sextillion, but in the end we decided that 10 billion was around the average of most credible estimates. (To read more about how we found the carrying capacity, visit our groups section under resources). Based on this carrying capacity and our function, we have predicted that the world population will exceed carrying capacity in 2062.
According to our model, we have 45 years left until we reach our carrying capacity. Of course, this does not mean that the world will end in less than five decades, but rather shows us when it will be difficult to sustain population growth with our available food sources and natural resources. We have looked further into the causes and consequences of population growth, as well as some solutions to it. Read about our research into these topics under consequences and solutions.
We chose to use a logistic regression since the y growth rate of our data decreases as it approaches 66.5 (our last data value), showing that population growth is slowing. Our regression has an R² value of .9997, which indicates that our function models the world's population relatively accurately.
Using our regression, we predicted when the population would exceed the carrying capacity. We decided on a carrying capacity of 10 billion after taking into account various different scientists' estimates. We found estimates ranging from 500 million to 100 sextillion, but in the end we decided that 10 billion was around the average of most credible estimates. (To read more about how we found the carrying capacity, visit our groups section under resources). Based on this carrying capacity and our function, we have predicted that the world population will exceed carrying capacity in 2062.
According to our model, we have 45 years left until we reach our carrying capacity. Of course, this does not mean that the world will end in less than five decades, but rather shows us when it will be difficult to sustain population growth with our available food sources and natural resources. We have looked further into the causes and consequences of population growth, as well as some solutions to it. Read about our research into these topics under consequences and solutions.
Logistic Population Growth over Time
To view our raw data or to further investigate our predictions, visit the graph on desmos using the button on the bottom right of the graph. Try changing the carrying capacity to see how our prediction changes!
This counter shows the current worldwide population, based on our regression. We wrote a program in JavaScript & html which, once per second, uses the current time to calculate the population based on our logistic function. It's pretty shocking how fast the population grows; seeing it in real time really puts the problems of overpopulation in perspective!
current population
based on our logistic regression