Evolutionarily stable cleistogamy

Abstract Cleistogamy, the production of closed flowers providing obligatory selfed seeds, has evolved repeatedly in more than 50 botanical families. Usually associated with chasmogamy, open flowers producing potentially outcrossed seeds in various proportion is an iconic example of mixed self-fertilization.Here, I develop an analytical Evolutionarily Stable Strategies (ESS) model for the evolution of cleistogamy. The model considers the role of inbreeding depression and the dependence of pollen export to chasmogamous flowers. Three generic functional relationships between pollen export and cleistogamy are considered. The model reveals that the classical inbreeding depression threshold of 0.5 no longer applies in the evolution of cleistogamy. Evolutionarily stable mixed cleistogamy is possible when inbreeding depression is low (below 0.5) and when pollen export per flower decreases with the rate of chasmogamy, consistent with the higher physiological cost of open flowers relative to closed flowers. Beyond the cost of flower types, the model points out the major impact of cleistogamy rate on gene transmission through pollen in the evolution of cleistogamy.