Final answer:
A geographer reasoning that spatial interaction is linked to population size and inversely to distance is engaging in spatial analysis based on Tobler's First Law of Geography.
Step-by-step explanation:
If a geographer reasons that spatial interaction is directly related to the size of the populations and inversely related to the distance between them, (s)he is making use of concepts from spatial analysis that are rooted in Tobler's First Law of Geography which states that "everything is related to everything else, but near things are more related than distant things."
This law suggests that spatial interactions, such as trade, communication, and migration, are more likely to occur between areas with large populations and those that are geographically close to each other, due to the "friction of distance" that tends to reduce interaction as distance increases.
The spatial analysis considers factors such as the range of a good or service, which is the maximum distance people will travel to obtain it, and the tendency for a predictable hierarchy of villages, towns, and cities to emerge based on this and other socio-economic interactions. This analysis also includes looking at how phenomena are co-located and may indicate causal relationships - for example, a consistent link between air pollution and lung cancer rates in a specific area.
Geographers make use of tools like Moran's I to measure spatial autocorrelation or clustering on a map, and nearest neighbor analysis to compare and contrast the distributions of observed points vs. randomly distributed ones. These methods are part of the broader discipline of Spatial Statistics, a key subfield in geography.