I wonder how they make the hydrocarbon chains shorter?
Steam cracking?
Seems to me that they are "breaking the chains" at the double bonds and combining with "half an ethylene" so creating two molcules that are both significantly smaller than the original FAME.
Something like: R1-CH=CH-R2 + CH2=CH2 --> R1-CH=CH2 + CH2=CH-R2 where R1 and R2 are the chains either side of the unsaturation, and R1 and R2 could also contain further unsaturation which could react further. Oleic is mono unsaturated, whereas Linoleic is doubly unsaturated and Linolenic is tripply unsaturated).
I didn't read all the detail.