Prior modeling work has found that pure winner and loser effects (i.e., cha
nging the estimation of your own fighting ability as a function of direct p
rior experience) can have important consequences for hierarchy formation. W
ere these models are extended to incorporate "bystander effects." When byst
ander effects are in operation, observers (i.e., bystanders) of aggressive
interactions change their assessment of the protagonists' fighting abilitie
s (depending on who wins and who loses). Computer simulations demonstrate t
hat when bystander winner effects alone are at play, groups have a clear om
ega (bottom-ranking individual), while the relative position of other group
members remains difficult to determine. When only bystander loser effects
are in operation, wins and losses are randomly distributed throughout a gro
up (i.e., no discernible hierarchy). When pure and bystander winner effects
are jointly in place, a Linear hierarchy, in which all positions (i.e., al
pha to delta when N = 4) are clearly defined, emerges. Joint pure and bysta
nder loser effects produce the same result. In principle one could test the
predictions from the models developed here in a straightforward comparativ
e study. Hopefully, the results of this model will spur on such studies in
the future.