Estimation and comparison of flowering curves

Background: Many researchers have simply recorded first flowering dates, while others have recorded the full extent of flowering. Such flowering curves show the rate of increase and decrease in flowering, as well as the day on which flowering is a maximum. Aim: To develop objective statistical methods for the estimation and comparison of flowering curves, with particular emphasis on the date of maximal flowering. Methods: We considered data collected either as percentages or as actual counts of numbers of flowers. We developed appropriate techniques for fitting regression curves involving non-linear least squares and Poisson regression, including a new generalisation of the epsilon-skew-normal curve. Results: Our generalised regression curve was found to be sufficiently flexible to provide good estimates of flowering in a wide variety of situations. The five parameters of this curve have a direct and straightforward interpretation, namely the date and magnitude of maximum flowering, along with the spread, skewness and kurtosis of flowering. The method of maximum likelihood was used to provide estimates and confidence limits for the parameters and to compare Crocosmia flowering curves over eight consecutive years. Conclusions: Regression curves, particularly those of the generalised skew-normal, give an effective, practical and objective procedure for estimating and comparing flower curves.