Why biennials delay flowering: an optimization model and field data on Cirsium vulgare and Cynoglossum officinale

A model is developed to calculate the population growth rate of different lineages within a biennial species, in a density-independent situation. The types differ in the minimum size they require for flowering. The environment is stochastic in the sense that each year a value for combined seed and early seedling survival was drawn from a probability distribution. Other probabilities of survival and growth were entered into the model as fixed rates, which are only dependent on the size of the plant. From demographic data on the delayed biennials Cirsium vulgare and Cynoglossum officinale, the model predicts that for both species (1) there exists a unique, optimal value of minimum size or weight w* for flowering, i.e. delayed flowering is profitable, (2) there is weak selection against flowering at sizes larger than optimal w* but strong selection against flowering at sizes smaller than optimal w*, and (3) that optimal w* is 2 g or more. In the field the size requirement was between 1 and 2 g for both species. The optimal value of w* is mostly determined by the fact that delayed flowering results in an increase in the expected number of seeds and less by delayed flowering resulting in averaging of variable recruitment over the years.