, Volume 238, Issue 4, pp 771–784

Characterizing Ipomopsis rubra (Polemoniaceae) germination under various thermal scenarios with non-parametric and semi-parametric statistical methods

Original Article

DOI: 10.1007/s00425-013-1935-8

Cite this article as:
Pérez, H.E. & Kettner, K. Planta (2013) 238: 771. doi:10.1007/s00425-013-1935-8


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 demonstrate 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 indicated highly significant differences in temporal germination patterns for seeds exposed to fluctuating or constant temperatures. Extended Cox regression models specified an inverse relationship between temperature and the hazard of germination. Moreover, temperature and the temperature × day interaction had significant effects on germination response. Comparisons to reference temperatures and linear contrasts suggest that summer temperatures (33/24 °C) play a significant 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 analysis procedures to address various topics in seed biology and more widespread use is encouraged.


Cox regressionHazard ratioHeat stressKaplan–MeierViability



Slope coefficient


Hazard function


Baseline hazard


Pearson’s χ2 test statistic


General association test statistic


Survivor function

\( \hat{S}(t) \)

Kaplan–Meier estimator


Time in days for germination of the 50th (median) percentile of the seed population


Germination rate


2,3,5-Triphenyl tetrazolium chloride


Germination uniformity


Cramér’s V


Cohen’s w index

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of Environmental Horticulture, Plant Conservation and Restoration Horticulture Research ConsortiumUniversity of FloridaGainesvilleUSA
  2. 2.Undergradaute Program, Department of Horticultural SciencesUniversity of FloridaGainesvilleUSA
  3. 3.Andrew Smith CompanyIndiantownUSA