Simple Population Measurement Models

[S2 and up - Geography / S3 and up - Additional Maths]

In terms of how populations are measured, it's not always an easy feat. Sometimes, extenuating factors can affect the overall outcome of the desired model projection, so while the models we work with may approximate towards an ideal outcome, the actual outcome is prone to some deviance from the model.

You might notice the similarities this has with calculus - And you would be right. One could say that both Isaac Newton and Gottfried Leibniz (the two founders of calculus among many other things they accomplished together/separately), in their desire to understand the rate at which change occurs, inevitably arrived at the tools and methods required to understand it better.

This sort of pattern accurately indicates the relationship of many cycles in nature - In the video, you have a small glimpse into what the relationship between one type of predator and one type of prey is. There are, of course, external factors that were not mentioned to make it simpler to understand - There could be 17 different types of prey (cockroaches, fruit flies, grasshoppers, butterflies etc.) and 3 primary predators (pigeons, mynahs and cats, for example), yet the 17 prey could be competing for plants and food among each other as well - The model is a simplification, but the underlying patterns remain the same.

From this, you can guess at how natural selection and extinction comes into play - When there are too many types of predators after one type of prey, where that specific type of prey literally drops to 0 while the predators can simply move on to other types of prey to keep themselves alive.

This was exactly what happened to the Dodo bird (depiction shown here):

There were too many animals introduced to the Dodo bird's island - Cats, rats and macaques plundered their nests for the eggs, thereby reducing their population; dogs were sent by huntsmen to procure them for dinner; and pigs ate anything from berries to truffles, thereby reducing the amount of food they had access to.

Those animals were already capable of a form of ecological stability by themselves - Rats would eat grains and plants, cats would eat them etc. Their stability meant that the lack of predators taking out cats, dogs (and in some cases, their protection) and macaques represented a predator population that would not scale down with the dodo. (since I doubt you would willingly cut your cat up as food to eat, or burn your dog alive like people from mainland China do)

Actions could have compounding consequences, and it's with mathematics & models like these which help us better understand what we're really doing to the world.