There might be useful methods to borrow from network theory. If we take overlap (0-1) as analogous to interaction strength, or the presence of an edge linking two nodes...
Starting with just the binary, edge/no edge, ESS/H would predict communities with clusters/modules that are interconnected but not connected to each other. If all species are distinct, that'd give S modules of 1 member each (I'm not sure if the network folks still call that a module). If species are all smushed together, you'd get a chain or a cloud.
I'm not as familiar with how network folks have handled interaction matrices with strength as opposed to just 0/1, but that seems especially promising? They inherently understand the meaning of the 0-1 scale, and they've been dealing with the kind of difficult-to-see issue of many comparisons. And they get at these kind of multi-component clouds better than is intuitive from a basically 1-d histogram.
There might be useful methods to borrow from network theory. If we take overlap (0-1) as analogous to interaction strength, or the presence of an edge linking two nodes...
Starting with just the binary, edge/no edge, ESS/H would predict communities with clusters/modules that are interconnected but not connected to each other. If all species are distinct, that'd give S modules of 1 member each (I'm not sure if the network folks still call that a module). If species are all smushed together, you'd get a chain or a cloud.
I'm not as familiar with how network folks have handled interaction matrices with strength as opposed to just 0/1, but that seems especially promising? They inherently understand the meaning of the 0-1 scale, and they've been dealing with the kind of difficult-to-see issue of many comparisons. And they get at these kind of multi-component clouds better than is intuitive from a basically 1-d histogram.