Synchronous update revisited

red ball Directed Paths in Random Media (DPRM): Least energy paths obtained recursively (transfer matrix, dynamic programming)

yellow ballSynchronous growth with variable size is equivalent to DPRM leads to similar statistics of sectors and ancestry:

yellow ball"Evolution in range expansions with competition at rough boundaries,"

S. Chu, M.Kardar, D.R. Nelson, & D.A. Beller, Journal of Theoretical Biology 478, 153 (2019). (off-line)

red ballFitness and Mutation may serve as an alternative interpretation for optimal energy and random landscape:

yellow ball What is the distribution of fitness at the front of range expansion?       

yellow ball The stepping stone model predics a (non-Gaussian) Tracy-Widom distribution:       

yellow ball Different fitness distributions are likely for different areas of competition:      

yellow ball "The  Mother Machine"

 

versus

yellow ball "The Long term evolution experiment"