1 3 Planta DOI 10.1007/s00425-013-1935-8 ORIGINAL ARTICLE Characterizing Ipomopsis rubra (Polemoniaceae) germination under various thermal scenarios with non-parametric and semi-parametric statistical methods Hector E. Pérez · Keith Kettner Received: 20 May 2013 / Accepted: 19 July 2013 © Springer-Verlag Berlin Heidelberg 2013 interaction had significant effects on germination response. Comparisons to reference temperatures and linear contrasts suggest that summer temperatures (33/24 °C) play a sig- nificant role in differential germination responses. Similarly, simple and complex comparisons revealed that the effects of elevated temperatures predominate in terms of components of seed viability. In summary, the application of non- and semi- parametric analyses provides appropriate, powerful data anal- ysis procedures to address various topics in seed biology and more widespread use is encouraged. Keywords Cox regression · Hazard ratio · Heat stress · Kaplan–Meier · Viability Abbreviations β i Slope coefficient h(t) Hazard function h o (t) Baseline hazard Q P Pearson’s χ 2 test statistic Q General association test statistic S(t) Survivor function ˆ S(t ) Kaplan–Meier estimator t 50 Time in days for germination of the 50th (median) percentile of the seed population 1·t -1 50 Germination rate TZ 2,3,5-Triphenyl tetrazolium chloride U Germination uniformity V Cramér’s V w Cohen’s w index Introduction Seed germination is a multi-phase process, bounded by imbibition and emergence of the embryonic axis through its Abstract Time-to-event analysis represents a collection of relatively new, flexible, and robust statistical techniques for investigating the incidence and timing of transitions from one discrete condition to another. Plant biology is replete with examples of such transitions occurring from the cellular to population levels. However, application of these statistical methods has been rare in botanical research. Here, we dem- onstrate the use of non- and semi-parametric time-to-event and categorical data analyses to address questions regarding seed to seedling transitions of Ipomopsis rubra propagules exposed to various doses of constant or simulated seasonal diel temperatures. Seeds were capable of germinating rapidly to >90 % at 15–25 or 22/11–29/19 °C. Optimum temperatures for germination occurred at 25 or 29/19 °C. Germination was inhibited and seed viability decreased at temperatures ≥30 or 33/24 °C. Kaplan–Meier estimates of survivor functions indi- cated highly significant differences in temporal germination patterns for seeds exposed to fluctuating or constant tempera- tures. Extended Cox regression models specified an inverse relationship between temperature and the hazard of germi- nation. Moreover, temperature and the temperature × day H. E. Pérez (*) Department of Environmental Horticulture, Plant Conservation and Restoration Horticulture Research Consortium, University of Florida, P.O. Box 110675, Gainesville, FL 32611-0675, USA e-mail: heperez@ufl.edu K. Kettner Undergradaute Program, Department of Horticultural Sciences, University of Florida, P.O. Box 110690, Gainesville, FL 32611-0690, USA Present Address: K. Kettner Andrew Smith Company, P.O. Box 717, Indiantown, FL 34956, USA