There are some interesting thoughts about this in the paper: Miller W(III). 2014. Mystery of the graphoglyptids. Lethaia 47(1): 1-3

Also note the other papers by A.A. Ekdale and James Lehane on this page about the per in Researchgate.

https://www.researchgate.net/publication/259553951_Mystery_of_the_graphoglyptids

robably this helps a bit, pointing int the direction for literature worth reading and lookig for about this subject.

Article Mystery of the graphoglyptids

Thank you, Jens: I was familiar with William Miller's paper but I have not been able to locate any confirmed reports of living agrichnial relationships in either shallow or deep water. This appears to be a huge gap in our knowledge of modern aquatic-benthic ecosystems.

Mark:

Have a look at this link, which you may find interesting. However, I am not familiar with any modern analogues.

Best

Syed

 http://www.academia.edu/2634162/Fractal_analysis_of_graphoglyptid_trace_fossils

I am not sure about your question, is this publication in Nature an answer to your question?

NATURE | NEWS

Overharvesting leaves ‘Himalayan Viagra’ fungus feeling short

Rising demand for yarsagumba threatens to cause ecological damage.

Hi Mark! The obvious agrichnial activity on land is of course leaf-cutter ants, and I believe they create distinctive chambers for the purposes of fungus-growing. I'm not aware of any equivalents in marine settings, unfortunately...

Adolf Seilacher described modern Paleodictyon in Mid-Atlantic deepsea bottoms, interpreted as farms of bacteria which possible use methano.

Seilacher, A. 2007. Trace fossil analysis. Springer.

Maria:

You are right that Adolf Seilacher did make serious attempt to explore deep sea in Mid-Atlantic to actually find the creature which made such wonderful regular hexagonal design in fractal dimensions. But unfortunately, no creature has been found so far. Moreover, it is difficult to say whether it is the same creature which made Paleodictyon like trace in modern deep sea and in ancient flysch deposits and whether they were meant for bacterial farming. 

Best

Syed

For researchers following this question, please see Chapter 5 ("Mat farmers") and Chapter 12 ("Parenting Skills") in Dynamic Paleontology (2016):

http://www.springer.com/us/book/9783319227764