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I'm attempting to learn various methods for summarizing spatial statistics, and I'm struggling to understand how to interpret the value of the pair correlation function. This link gives a nice qualitative description of how the PCF is different from Ripley's K function, but it doesn't go into how the value itself can be informative. The documentation on pcf() from spatstat in R has some insight, telling me how to interpret $g(r)$ values above and below 1 (the value of $g(r)$ corresponding to CSR), but no more granularity than that. My question: How do I interpret the value of the pair correlation function?

As some further context, here are two graphs of the PCF for two different species in a given observational area:

Plot 1

And a second species: enter image description here

At a distance of 50 meters, Species 1 has a g(r) value of ~1.5 while Species 2 has a g(r) value of ~1.25. Can I infer anything about the two species from those values? For example, is it appropriate to say that at 50m, Species 1 is 120% as dense as Species 2?

As always, many thanks for any assistance folks can provide.

---Edit after further research--- After reading some more, particularly this, pg 620, it seems I can consider the $g(r)$ as a ratio of the density at a given distance to the total average density across the window of observation? Further, since CSR is $g_{poiss}(r)=1$, $g(r)$ is the ratio of density to a Poisson CSR?

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You should remember that everything is related to pairs of points. So in your example at 50m it is more likely to observe pairs of species 1 separated by 50m than pairs of species 2 separated by 50m. For species 1 you could say that observing pairs separated by 50m is 1.5 times more likely for the process generating species 1 than complete spatial randomness with the same average density of points.

You can read more about the pair correlation function in chapter 7 of the book Spatial Point Patterns: Methodology and Applications with R I have recently co-authored with Adrian Baddeley and Rolf Turner.

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  • $\begingroup$ Ah, fantastic. Thank you for your help and the link. I'll read through that. $\endgroup$
    – Ashe
    Commented Dec 1, 2015 at 22:33

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