Representing Cumulative Germination.

“…Although splines are suitable for curve-fitting by LMs, germination time-courses are frequently modeled as continuous curves according to a few sigmoidal functions that have been shown to be specifically valuable for this scope but are not suitable to fitting by LMs [50]. Modeling the whole germination progress curve can be more informative than considering time a categorical variable or using splines, but it can require stronger assumptions.…”

Section: Considering Time As a Continuous Variable Requires Parametrimentioning

confidence: 99%

Basic Features of the Analysis of Germination Data with Generalized Linear Mixed Models

Gianinetti¹

2020

Data

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Germination data are discrete and binomial. Although analysis of variance (ANOVA) has long been used for the statistical analysis of these data, generalized linear mixed models (GzLMMs) provide a more consistent theoretical framework. GzLMMs are suitable for final germination percentages (FGP) as well as longitudinal studies of germination time-courses. Germination indices (i.e., single-value parameters summarizing the results of a germination assay by combining the level and rapidity of germination) and other data with a Gaussian error distribution can be analyzed too. There are, however, different kinds of GzLMMs: Conditional (i.e., random effects are modeled as deviations from the general intercept with a specific covariance structure), marginal (i.e., random effects are modeled solely as a variance/covariance structure of the error terms), and quasi-marginal (some random effects are modeled as deviations from the intercept and some are modeled as a covariance structure of the error terms) models can be applied to the same data. It is shown that: (a) For germination data, conditional, marginal, and quasi-marginal GzLMMs tend to converge to a similar inference; (b) conditional models are the first choice for FGP; (c) marginal or quasi-marginal models are more suited for longitudinal studies, although conditional models lead to a congruent inference; (d) in general, common random factors are better dealt with as random intercepts, whereas serial correlation is easier to model in terms of the covariance structure of the error terms; (e) germination indices are not binomial and can be easier to analyze with a marginal model; (f) in boundary conditions (when some means approach 0% or 100%), conditional models with an integral approximation of true likelihood are more appropriate; in non-boundary conditions, (g) germination data can be fitted with default pseudo-likelihood estimation techniques, on the basis of the SAS-based code templates provided here; (h) GzLMMs are remarkably good for the analysis of germination data except if some means are 0% or 100%. In this case, alternative statistical approaches may be used, such as survival analysis or linear mixed models (LMMs) with transformed data, unless an ad hoc data adjustment in estimates of limit means is considered, either experimentally or computationally. This review is intended as a basic tutorial for the application of GzLMMs, and is, therefore, of interest primarily to researchers in the agricultural sciences.

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“…where IMBT is the cumulative imbibition at time T; M is an asymptote for the cumulative imbibition and represents the maximum IMB-value for each batch of seeds; l (lag of imbibition) is a location parameter that estimates the latest time at which imbibition is strictly zero, which in practice represents the time that is necessary for at least one seed start imbibing; k (rate of imbibition) is a scale parameter estimating the rate of imbibition completion over time with l + k estimating the time that is necessary for the completion of 63% of cumulative imbibition; and, c is a dimensionless shape parameter estimating the symmetry of the distribution of imbibition over time, with 3.25 ≤ c ≤ 3.61 showing symmetry and representing a good approximation to the normal distribution, c < 3.25 positive asymmetry, and c > 3.61 negative asymmetry [20][21][22]. The fitted equations were only accepted after a consistency check of parameter estimates and imbibition predictions against the original data [23].…”

Section: Data Analysesmentioning

confidence: 99%

Imbibition, Germination, and Early Seedling Growth Responses of Light Purple and Yellow Seeds of Red Clover to Distilled Water, Sodium Chloride, and Nutrient Solution

Costa

Dias

2019

Sci

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The seeds of red clover are heteromorphic and two color morphs can be visually recognized, light purple and yellow, resulting from heterozygosity and recessive homozygosity at two loci. Here, we report the responses of seed imbibition, seed germination, and early seedling growth of the two morphs to distilled water, sodium chloride, and complete nutrient solution. The sensitivityof red clover seeds to treatments increased with the stage of development in what seems to be a cumulative process. No differences were found in seed imbibition between morphs or between treatments. In seedling growth, on the contrary, treatments were always effective, but differences between morphs were only observed in seeds that were treated with nutrient solution, whereas in the intermediate stage of seed germination, the effects by treatments were observed together with the appearance of differences between morphs in distilled water and in the treatment by sodium chloride solution. Simultaneously, the superior performance of the yellow morph that was found in germination, which appears to be a trait stable across cultivars of red clover seeds, turned into a superior performance of the light purple morph in seedling growth.

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Representing Cumulative Germination.

Cited by 176 publications

References 20 publications

Study the Effect of Organic and Inorganic Sources of Nitrogen on Growth and Yield of Kharif Pearlmillet

Study the Effect of Organic and Inorganic Sources of Nitrogen on Growth and Yield of Kharif Pearlmillet

Basic Features of the Analysis of Germination Data with Generalized Linear Mixed Models

Imbibition, Germination, and Early Seedling Growth Responses of Light Purple and Yellow Seeds of Red Clover to Distilled Water, Sodium Chloride, and Nutrient Solution

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