Evolutionary singular strategies and the adaptive growth
and branching of the evolutionary tree

S.A.H. Geritz, E. Kisdi, G. Meszena and J.A.J. Metz

Summary

We present a general framework for modeling the adaptive
trait dynamics in which we integrate various concepts and 
techniques from modern ESS-theory. The concept of 
evolutionary singular strategies is introduced as a 
generalization of the ESS concept. We give a full 
classification of the singular strategies in terms of ESS
stability, convergence stability, the ability of the singular 
strategy to invade other populations if initially rare itself,
and the possibility of protected polimorphisms occuring within
the singular strategy's neighborhood. Of particular interest
is a type of singular strategy that is an evolutionary 
attractor from a large distance, but once in its neighborhood
a population becomes dimorphic and undergoes disruptive
selection leading to evolutionary branching. Modelling the
adaptive growth and branching of the evolutionary tree thus
can be considered as a major application of the framework. A
haploid version of Levene's "soft selection" model is developed
as a specific example in order to demonstrate evolutionary
dynamics and branching in monomorphic and polymorpic
populations.