The weather is hot
The weather is very hot. by drawing a picture
Squirrels - you may love them or hate them - but however you feel about them, let’s talk about the maths of species conflict.
In Britain, there are two species of squirrels - the red and the gray. The gray squirrels have supplanted the red and pushed them out, primarily to Scotland and parts of North Wales. If you see a squirrel in the UK, it is likely to be a gray squirrel.
To understand how this happened, we can write down interaction equations between the two squirrel populations. We will consider the gray squirrel and the red squirrel population, and write down equations that tell us how they interact.
The gray squirrel population changes with time (T) and the red population changes with time. We can include space in this and understand how they were pushed further north, but generally we don’t need to.
We can say that the gray squirrels undergo binary competition as do the red squirrels. The equations will be similar, but we will add in a new term - Alpha gr and Beta gr. Alpha gr is the competition of the gray and the red for the gray squirrels, and Beta gr is the competition for the gray and red squirrels for the red. It is always going to be a negative effect - the competition is never going to help the species, but the size of Alpha and Beta are going to be how good they are at competing.
In order to understand this better, we can use a concept called a null cline. The null cline is where the populations aren’t changing. When we set these to zero, we have some conditions linking the red and gray squirrels which will give us some curves - the null clines.
When we rearrange these equations, we can draw a picture which will immediately show the answer to these equations. This can help to convince policy makers on how to save the red squirrel.