Single species evolutionary dynamics

Not long after the introduction of evolutionary stable strategy (ESS) concept, it was noticed that dynamic selection did not always lead to the establishment of the ESS. The concept of continuously stable strategy (CSS) was thereafter developed. It was generally accepted that dynamic selection leads to the establishment of an ESS if it is a CSS. Examination of an evolutionary stability concept which is called neighborhood invader strategy (NIS) shows that it may be impossible for an ESS to be established through dynamic selection even if it is a CSS and no polymorphisms occur. We will examine the NIS concept and its implications for two evolutionary game models: root-shoot allocation in plant competition and Lotka-Volterra competition. In the root-shoot model we show that an ESS will be attained through dynamic selection if it is a NIS. Similarly for the Lotka-Volterra model, we show that an ESS will be attained through dynamic selection even if protected dimorphisms occur during the evolutionary process if it is an NIS.