I have a question about how best to visualise the predicted direction of migration given a set of points with estimated ages.
Imagine I have a set of geo coordinates, representing communities. For each point, I have an estimate of the age of that community. I want to draw an arrow on the map that indicates the most likely direction of general migration over time. I also want the magnitude of the arrow to represent how consistent the gradient is / how confident we are that there's a meaningful alignment between time and space. I'm not asking about the theory of the process of migration, just about how you would decide on the angle, position and magnitude of the arrow.
For example, below red points are older than green points. In the first box, it looks like a sensible conclusion that migration was South-East. In the second box, there's no clear pattern, so the arrow is smaller.
Is there a standard, principled way of doing this? One way I thought of was to draw a vector between the oldest point and the 2nd oldest, then between the 2nd oldest and 3rd oldest, and so on. Then sum the vectors (but how to decide the start location?). Or maybe you need to take the vectors between all pairs of points and weight them by the relative ages? Or maybe I need to work out the contours, then draw a path that starts at the highest point and heads downhill?
An R-based solution would be ideal.