Eryngium viviparum is a small biennial aquatic plant that belongs to Apiaceae family, endemic to the European Atlantic region and with distribution in NW France, NW Portugal and NW Spain (Romero et al., 2004). Their natural habitat is flat areas subjected to seasonal flooding, living submerged for 7–9 months of the year. Aquatic plants are one of the most threatened groups in the European flora, mainly due to anthropic habitat alteration and destruction (Romero et al., 2004; Ramil-Rego and Dominguez-Conde, 2006; Magnanon et al., 2012). In 1997, E. viviparum was classified as vulnerable by International Union for Conservation of Nature (IUCN) and included in red list of threatened plants (Walter and Gillett, 1998). Moreover, E. viviparum has been listed in Annex I of the Berne Convention and considered by Directive 92/43/EEC as a priority species (Annex II). Its classification has recently been changed to endangered due to the loss of many subpopulations, the drastic reduction of the area of occupancy (<80 km² in the world) and the decrease in the quality of its habitat and of the number of individuals (Lansdown, 2011).

The main threats for endangered plants are human pressure over the territory, competition with other species, overgrazing and collecting that cause degradation, fragmentation, and massive reduction of their natural habitats (Ramil-Rego and Dominguez-Conde, 2006; González-Benito and Martín, 2011; Lansdown, 2011; Magnanon et al., 2012). Although high protection and access restrictions to their natural habitats have been implemented, for in situ conservation, the situation is critical for some species as E. viviparum. New ex situ conservation strategies, such as in vitro propagation are needed and should be urgently designed and implemented in order to protect them. Different micropropagation procedures have been developed for endangered and endemic plants in the past 30 years and, also for this particular species (Ba-ares et al., 2004; González-Benito and Martín, 2011). The critical population size of E. viviparum does not allow sufficient material from its natural habitat for micropropagation. Therefore, Fay (1992) has proposed its seeds as the material of choice for ex situ conservation, which allows preserving their biodiversity.

Many species of Apiaceae family are well known by a non-uniform and asynchronized seed germination (Mozumder and Hossain, 2013), which promotes germination rates lower than 10% and limits their in situ conservation. Moreover, low germination in Apiaceae is due to several kind of dormancy state in seeds and by the presence of high amount of non-viable seeds (Robinson, 1954; Ojala, 1985). Different strategies have been developed to overcome dormancy problems in several Apiaceae, including cold and/or warm stratification (Necajeva and Ievinsh, 2013), the use of plant growth regulators such as gibberellic acid (GA₃) and kinetin (KIN) (Mozumder and Hossain, 2013) or the incubation temperature (Finch-Savage and Leubner-Metzger, 2006). As far as we know no studies have addressed the low germination rate problem in E. viviparum, which remains a challenge.

In recent years, several artificial intelligence tools have been applied to model and predict the effect of different variables in plant tissue culture (Zielinska and Kepczynska, 2013), monitoring seed growth and vigor (Chaugule, 2012) or testing germination (Dell'Aquila, 2004). In this work, neurofuzzy logic has been applied to investigate the cause-effect relationships between several germination factors (dormancy breaking stratification and germination conditions) and seed germination responses (percentage of germination, embryo seed rate, etc.). Neurofuzzy logic is a hybrid approach that combines the adaptive learning capabilities from artificial neural networks with the generality of representation from fuzzy logic through simple “IF-THEN” rules. This methodology has been previously and successfully used as advanced decision support tool (Gallego et al., 2011; Gago et al., 2014).

On this purpose, this study attempts to get insight on the germination of E. viviparum seeds and the causes of its low germination rate. Neurofuzzy logic is applied to model germination results as a function of several germination conditions in order to find the key factors that control or stimulate the embryo development, facilitating the completion of germination. Understanding the physiological mechanism responsible for seed germination should help to design new procedures for any other endangered plant with low germination rates.

According to literature review, no disinfection or general antiseptic procedures such as ethanol 70% for 30 s followed by sodium hypochlorite at low concentration 1% for 5–10 min were enough for surface seed sterilization in Apiaceae family (Walmsley and Davy, 1997; Vandelook et al., 2008; Thiem et al., 2013). Those typical procedures did not work at all for E. viviparum seeds. All seeds revealed severe contamination by fungi during germination and none were able to germinate. Only after application of strong antiseptic procedures including sulfuric acid, a method commonly used to surface-sterilize seeds heavily contaminated with fungi (Latchs and Christensen, 1985; Siegel et al., 1987), we succeeded in achieving the total elimination of fungal contamination.

Poor germination rate is a common problem in the Apiaceae family (Robinson, 1954; Ojala, 1985; Baskin and Baskin, 2014). Eryngium genus is not an exception. Eryngium maritimum (Walmsley and Davy, 1997; Necajeva and Ievinsh, 2013), Eryngium planum (Thiem et al., 2013) and Eryngium foetidum (Mozumder et al., 2011; Mozumder and Hossain, 2013), have shown lower than 20, 12, and 10% germination respectively, without dormancy breaking treatments. Little information on Eryngium viviparum is available. Our results ranging from 0 to 27% of germination are in agreement with Magnanon and coworkers that reported low germination percentages (10–40%) on populations from France and Spain (Magnanon et al., 2012).

Low germination rates in the Apiaceae family have been correlated with the next three causes (Robinson, 1954; Ojala, 1985; Baskin and Baskin, 2014): (1) presence of high percentage of non-viable seeds without embryo; (2) presence of high percentage of seed with underdeveloped embryos; and (3) presence of dormant seeds.

In agreement with the first cause our results showed a high non-viable seeds percentage (62.5%) close to other Apiaceae as Anethum graveolens (ranged 39–62%; Robinson, 1954) or Anthriscus caucalis (49%; Rawnsley et al., 2002). Among the potential causes for non-viable seeds (zygote degeneration, death of embryo, mutations, etc.; Baskin and Baskin, 2014), two have been described for Apiaceae family: (1) insect infestation; these seeds have an endosperm but not embryo (Flemion and Henrickson, 1949) and (2) self-pollinated umbels; seeds produced in these umbels are usually empty (without endosperm and embryo; Ojala, 1985). In this work, the high percentage of non-viable seeds have been described as embryoless (25.5% EL) and empty (37% EM), supporting the hypothesis that the poor germination percentage of E. viviparum seeds can be explained as a consequence of the high percentage of non-viable seeds due to insect infestation and self-pollinated umbels.

The second cause of low germination in Apiaceae is the presence of underdeveloped embryos at the moment of dispersal (Martin, 1946). The embryo needs to grow up to a critical length before germination. E:S ratio was investigated to check the presence of underdeveloped embryos in E. viviparum (Table 3). The E:S ratio seeds stored during 12 weeks at 4°C in darkness, used as control, averaged 0.31, similar to those values found for other Apiaceae species as Torilis japonica with a ratio 0.25, Angelica sylvestris with 0.29, or Selinum carvifolia with 0.31 at harvest. However, after 20 weeks at 5°C, those embryos growth until 0.29, 0.39, and 0.34, respectively, a little higher than the E:S ratio at harvest (Vandelook et al., 2007a, 2008). This delay in seed germination due to the underdeveloped and differentiated embryo is called morphology dormancy (MD, Nikolaeva, 1977), and those Apiaceae has been characterized as MD seed (Vandelook et al., 2007a,b, 2008). Our results, clearly demonstrated a high percentage 30.4% of underdeveloped embryo seeds suggesting that E. viviparum also showed MD dormancy, in agreement with other Eryngium sp. (Necajeva and Ievinsh, 2013). Seeds with MD, as Apiaceae, need specific conditions as a moist substrate, suitable temperature and photoperiod as growth embryo requirements (Baskin and Baskin, 2014). If seeds remain under these conditions, embryos should growth and germinate in 4 weeks or less. No precise protocol to overcome this problem (the need of right conditions enabling embryo growth and development until reach a critical size to germinate) has been previously described in the literature for E. viviparum.

The third cause for low germination rates in Apiaceae is the existence of an additional physiological mechanism of dormancy, which also inhibits germination (Baskin and Baskin, 2004). Some Apiaceae present both dormancies morphological (MD) and physiological (PD) at the same time, known as morphophysiological dormancy (MPD), and need a considerably longer period for germinate than MD seeds (Baskin and Baskin, 2004). The combination of cold and warm stratification can be effective for break MPD dormancy and allow the embryo to growth. Warm stratification was effective in some species of Osmorhiza and Erythronium genus (Baskin et al., 1995). In addition, short warm stratification increases the seed sensitivity to GA₃ improving germination rate in E. maritimum and suggesting a key role of GA₃ to overcome the dormancy (Vandelook et al., 2008; Necajeva and Ievinsh, 2013). E. viviparum presents low percentage of seeds (mean 7.1%) that germinate after breaking the MPD. Interesting, some treatment, such as 2, reached 27.3%G and 100%RG, which means that all viable seeds were able to break MPD dormancy and germinate.

To understand the physiological mechanism of dormancy breaking, a representative study of seed germination require test several factors, which implies many different treatments and replicates, and finally large batches of seeds. Those requirements are essential for an accurate interpretation of the cause-effect of those factors and their interactions on seed germination (International Seed Testing Association, 1985). As stated above, E. viviparum is an endangered species and therefore, no large seed batches are available. Based on these limitations, two experiments including just 27 treatments were proposed. We test the most important factors well known as dormancy breaking in Apiaceae such as cold and warm stratification and two PGR (GA₃ and KIN) well known as inducers of embryo development (Vandelook et al., 2008; Mozumder and Hossain, 2013; Necajeva and Ievinsh, 2013). The authors are aware that the design space was not well-sampled, which hinders a conventional statistical treatment to analyse the results and draw conclusions. Neural networks has demonstrated to be a practical approach to deciphering the key factors in several biological process and an excellent alternative to conventional statistical methods (Gago et al., 2010a,b; Gallego et al., 2011; Nezami-Alanagh et al., 2014; Arab et al., 2016). Advantageously, neurofuzzy logic technology allows working with not well-defined design spaces and different kind data at the same time (Nezami-Alanagh et al., 2017). In this paper, that technology was used to reduce the number of treatments and therefore, the needed seeds, without losing key information to extract scientific conclusions.

Neurofuzzy logic succeeded in modeling all outputs simultaneously with high predictability and accuracy (Table 3). Additionally, it allowed obtaining a set of rules that explain the cause-effect among the factors (inputs) and the germination parameters obtained (Table 4). The model pinpointed that the factor time of incubation was the most significant factor for Eryngium seed germination; long periods (around 20 weeks) are strongly recommended to obtain high %G, low %NG, low %EL, high E:S, and high %RG, but in this case in combination with low warm stratification. In fact only after 20 weeks of incubation the highest real germination rates can be reached (see treatment 2 and 4; Table 3). Interesting, also with high incubation periods a high percentage of empty seeds was obtained, suggesting a high correlation between endosperm degradation and duration of the germination period. The model also identified the important role of the interaction between incubation temperature and GA₃ concentration. If temperature is around 24°C and 1 mg L⁻¹ GA₃ is present, the highest real germination and E:S was obtained. The third most important factor was the factor stratification at 25°C. Low period of warm stratification (4 weeks) is preferred to obtain the highest % of real germination and E:S ratio (1.00 membership). Some authors (Necajeva and Ievinsh, 2013) demonstrated that seed of E. maritimum seed germinated to a high final germination percentage only after 12–16 weeks cold stratification. Our model suggests that E. viviparum presents seeds with MDP, and needs to break dormancy. Long incubation time (20 weeks) combined with low warm stratification (4 weeks) at continuous high temperature 24°C and 1 mg L⁻¹ GA₃ are strongly recommended.

MA: Performed the experiments; PR-R: Contributed with reagents/materials; ML and PG: Contributed modeling/analysis tools; PG and MB: Conceived and designed the experiments. All authors contributed to writing of the manuscript.