Determination of germination potential is one of the most important measurement when the quality of seeds is evaluated, and it represents the germination when seeds are exposed to appropriate conditions, expressed as the speed rate with which the germination process occurs (germination rate GR). For international seed trade, it is very useful to have a common standard for evaluating germination potential.

The reliability of calculation of a germination parameter is necessarily linked to the number of seeds evaluated. Increased numbers produce more accurate results; however, if the number is too high, there may be an unnecessary increase in the cost of the research and the time required to complete it.

Based on the above, the International Seed Testing Association (ISTA) developed criteria to define minimum sample sizes in the germination tests of different species, mainly from the temperate zone. According to this organization, the evaluation of commercial seeds should be based on a quantity of 400 seeds divided into four replicates of 100 units each, although less seeds could be used depending on their size and collection difficulties (

While GP represents seed viability, GR is a parameter that reflects the vigor of the seed and varies depending on the time required for the germination process to occur. Groups of seeds with similar GP may differ significantly in their GR.

A formula widely used for the calculation of GR in seed studies was developed by

Despite the rationale presented by

Germination rate, as proposed by

In the tests, it is inferred that Maguire used 100 seeds, but in the numerator of his formula he placed "number of seedlings" instead of "percentage of seedlings", as it should be according to the concept correctly indicated by him. However, in the text, he made clear that his calculations referred to 100 seeds. Obviously, in his case, the "number of seedlings" was exactly the same as the percentage of seedlings.

The use of number of seedlings instead of percentage of seedlings in many of the subsequent seed studies where the sample size differed from 100 seeds has led to serious inconsistencies in the reported results and the impossibility of direct comparison with those of other studies.

In a review of the pertinent bibliography of articles of recent decades referring to seed germination, it can be observed that different formulas have been used to calculate the seed germination rate. Since in several cases errors have been detected in the application of these formulas, the present study reviewed an important number of publications related to seed germination in order to determine the frequency of occurrence of inaccuracies in the application of the aforementioned formula. The aim of this study is to present statistical information regarding the inconsistencies found in these publications and the errors that these imply when interpreting the vigor of the seeds of many botanical materials.

A search was conducted through Google Scholar and the databases of the Web of Science and Scopus, utilizing a filter that included only articles from the last 25 years (1994 to 2018). This produced a total of 216 articles that involved the word germination in the title and, of these, 152 articles were selected that cited the article by

Articles that did not present numerical results or in which the methodology was not clearly indicated were excluded, along with those that, despite having determined germination parameters, used different representations of the germination rate or had incorrectly transcribed Maguire's formula. This filtering process left a total of 124 articles, which were those ultimately used in this study.

We evaluated the articles in which there would be some form of imprecision when applying the formula developed by Maguire or that had not followed the recommendation of

A linear regression analysis was carried out between the number of seeds used in each paper and the mean value reported for the germination rate. When a paper stated that measurements had been converted to percentages, the independent variable was considered as 100, regardless of the actual number of seeds tested. A total of 107 papers were used for this analysis, with 17 papers discarded because their results were unclear or highly variable. The regression was developed by means of the SAS v.9.1 program (Cary, NC, USA).

The regression analysis detected a highly significant effect (
^{2}
= 0.3983), but can be attributed to the high and predictable natural variability that existed between the germination rates of the different plant species considered.

It is notable that the values reported for the germination rate tended to diminish with lower numbers of seeds evaluated in the tests, which corresponds to the magnitude of the error in the application of Maguire´s formula. Long time ago,

The number of studies that met the requirements for this study increased as we examined more recent publications (

The papers that featured objectionable application of the formula came mainly from the field of forestry (

The geographical distribution of the origin of the articles evaluated has predominance in Brazil (57 papers), country where a large number of papers on seed germination are produced. It was followed by China, Iran, USA, and México, with 13, 12, 8 and 5 papers, respectively. Other countries contributed only with three or less articles: Argentina, Colombia, and Peru (for America), France, Greece, Poland, and Sweden (for Europe), Arab Emirates, Bangladesh, Japan, Jordan, Pakistan, Saudi Arabia, and Turkey (for Asia), and Nigeria, South Africa, and Zimbabwe (for Africa). Objectionable papers among countries varied from 31 to 75 %.

A significantly smaller number of articles used other units of measurement, catalogued as indices or rates. In others, the authors used the term "germination rate" to refer to "germination percentage". Likewise, it was observed in a moderate number of articles that germination rate was expressed as "mean germination time" (

In the study, some articles claimed to have used Maguire's formula, despite having mentioned the term IVE (speed of emergence index), or its translated equivalent, in the article. There were also articles that used the formula but cited it through other published references.

It should be emphasized that only a few of the evaluated papers presented sufficient details of the application of the formula that would allow us to precisely verify its correct use. The majority of papers judged as "objectionable" were therefore those that reported calculations based on the "number of germinated seeds". In contrast, some papers that did not mention the "number of seeds" but, instead, mentioned "the counts", were given the benefit of the doubt and were classified as not objectionable.

A second identified source of error was the use of the total percentage of seeds germinated in each evaluation, when the appropriate value for use would have been that of the difference between the current and previous measurements. For this reason, it is good practice in trials to discard all newly germinated seedlings immediately after measurement, so that there is no possibility of confusion when carrying out the subsequent measurement. While

The results of our study show that, in terms of the application of Maguire's formula, 68 out of 124 papers (54.8 %) were considered objectionable. This represents a considerable number of articles that we can assume to have calculated the GR erroneously. These errors would have occurred for one of the following two reasons:

a) Incorrect use in the formula of number of seeds instead of percentage of seeds in cases where the tests were conducted using less than 100 seeds (in this case, between 10 and 50 seeds per replicate).

b) Failure to eliminate germinated seeds in each count in order to avoid readings of seedlings that had already been recorded in previous readings.

The inconsistencies found in these publications indicate that errors of considerable magnitude exist when interpreting the seed vigor of certain botanical material, and the incorrect application of the formula for calculating the GR makes it impossible to compare the results of different studies.

Examples of two cases in which there were inaccuracies in relation to the number of seeds used or the erroneous counting of seedlings already recorded in previous readings are shown in Tables 2 and 3 [suppl.]. For both cases, the published and corrected results are presented, detailing the expected procedure.

For many years, numerous papers have featured an incorrect application of Maguire´s formula to estimate seed vigor by calculating the rate or speed of germination. This has caused inconsistencies when comparing the values of this index among different plant species, leading to erroneous results. With respect to the application of Maguire's formula, 54.8 % of the papers examined in this study, mainly from the field of forestry, were considered objectionable.

To the CDCHT of the UCLA for supporting this investigation.