'pointwise envelopes not including Theoretical line Foxall J

I am computing pointwise envelopes for the Foxall's J function to investigate the whether some point patterns of interest are clustered, avoid or are independent from other point patterns or polygons.

I am doing this using spatstat with a syntax similar to this:

evelope(my_pattern_of_interest, fun=Jfox, funargs=list(Y=my_other_patten),...)

I am calculating the envelopes for several replicated patterns (i.e., different transects) and then plotting the pooled (i.e., pool) the envelopes.

So far, whenever the Jfox is calculated between 2 point patterns, the shaded area representing the simulation envelope includes the theoretical line (i.e., represented by red dashes), as in this example:

Figure 1 Figure 1

Instead, when Jfox is calculated between a point pattern and polygons, it is frequent that the envelope area does not include the Theroretical line (at least in some regions). Like in this example:

Figure 2 Figure 2

What does this means?

From my understanding so far, if - or rather "where" since these are pointwise envelopes - the observed line (solid black) is within the shaded area, it means that the observed pattern (say clustering as in Figure 2) is not significantly different from what could be observed at random. Alternatively, if/where the observed line is out of the shaded area, then I have a significant difference.

What does the fact that the theoretical line lays outside the shaded area mean? Is it giving me another piece of information? How should I interpret this?

Thank you.



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