Each student is directly above his doctoral advisor or advisors.
See this site and this site for notes about individual entries on this and similar sites. Automatic translations of the German Wikipedia entries are available for Richelot and Dirksen. Note that one must be careful not to confuse these scientists with others having similar names, such as the elder Johann Tobias Mayer, the jurist Anton Friedrich Justus Thibaut, and the elder Christian August Hausen.
For good measure, my Erdös chain is (and has been, since 1998):
Had I collaborated with my principal advisor, the chain would have been far shorter, but not nearly as interesting.
Here's the missing piece of the above tree:
| Gerard van Swieten | Albrecht von Haller | ||||||
| Herman Boerhaave | J. G. Duvernoy | ||||||
| Burchard de Volder | Wolferd Senguerdius | J. P. Tournefort | |||||
| Johannes de Bruyn | Franciscus de le Boë Sylvius | Johannes de Raey | J. P. Magnal | ||||
| Daniel Berckringer | Jacobus Stupaeus | Jean Baptiste Van Helmont | Adriaan Heereboord | Henricus Regius | J. P. Laugier | ||
| Martinus del Rio | Adam Haslmayr | Franck Burgersdijk | P. R. Belleval | ||||
| Gilbert Jacchaeus | |||||||