The seeds of H. persicum were manually harvested from a Saharan bioclimatic zone in Tunisia, i.e., Kebili (33°40′N, 08°59′E; 60 m a.s.l.). As described by Emberger (1971), this region is characterized by an arid climate, with hot and dry summers (temperatures exceeding 40.0°C), an average annual rainfall of 100 mm, a very high evapotranspiration of 1700 mm, an annual average temperature of >20.0°C, and an extreme aridity index of 8.40 (Ferchichi, 1996).

In January 2023, ten healthy H. persicum species with the height of 2.00-4.00 m were selected in Kebili, and seeds with an approximate diameter of 2.00 mm were then randomly chosen. Finally, 9430 freshly matured seeds were collected. After removing debris, these seeds were air dried and stored at 2.0°C until further use.

To determine the proportion of embryoless seeds, we evenly divided 100 seeds into 4 groups (25 seeds per group) and viewed them using a Zoom Trinocular Stereoscope (Optech Optical Technology, München, Germany) as described by Zanetti et al. (2020). Following the International Rules for Seed Testing (ISTA, 2013), we measured embryo viability in the experiments by counting viable and non-viable seeds after a 6-d incubation period (Krichen et al., 2023). The percentage of seeds with developing embryos or growing cotyledons was used to calculate embryo viability. Seeds with degradation or brown/black stains were deemed unviable. The tests were repeated 4 times with 50 seeds each (Ma et al., 2016). Three replicates of 1000 seeds were weighed digitally to specify thousand seed weight.

Additionally, a sample of 30 seeds was randomly picked and analyzed using image analysis software ImageJ (National Institutes of Health, Bethesda, the United States) to determine seed area and seed diameter (Chen et al., 2022). Three replicates of 100 fresh seeds were weighed and then oven-dried at 70.0°C for 3 d before being reweighed. Seed water content (SWC; %) was calculated using the equation listed below (Krichen et al., 2023).

where FW is the fresh weight (g); and DW is the dry weight (g).

To prevent fungal infection, the seeds were surface sterilized for 2 min in a 5.00% sodium hypochlorite solution. Then, they were rinsed three times with distilled water (Nosrati et al., 2014).

All statistical analyses were accomplished using the R statistical package (version 4.2.1). Nonparametric two-way analysis of variance (ANOVA) was used to analyze the variation between groups utilizing the ''nparLD'' package in R (Noguchi et al., 2012). Bonferroni post-hoc test at P<0.05 level was applied to check the differences between temperature and osmotic potential. The thermal time model and hydrotime model methods were conducted using the ''seedr'' package in R. The asymmetric correlation matrix assessed the relationship between the seed functional traits and seed parameters using the ''heatmap with pheatmap'' package in R.

For the investigated H. persicum population, 1000 seeds had an average weight of approximately 3.15 g, with a remarkably low coefficient of variation (0.95%), showing a consistent weight distribution throughout all seed samples (Table 1). These seeds had spherical shape, brownish-grey shade, spirally twisted embryos, and an average diameter of around 2.00 mm. The coefficient of variation for seed diameter was only 0.20%, indicating that the diameter is consistent throughout all examined seeds. Additionally, 22.51% of the seeds lacked embryos, while embryo viability was around 74.33%. Furthermore, SWC was around 14.76% and seed area was approximately 3.14 mm².

The results of the germination kinetics are expressed as germination curves (Fig. 1), which represent the evolution of the cumulative percentage of germinated seeds as a function of time. The seed germination of H. persicum was significantly (P<0.05) affected by temperature. The seeds could germinate at a temperature range between 10.0°C and 35.0°C. The maximum GP was recorded at 25.0°C with a value of 80.00% (Fig. 1), followed by 72.00% at 20.0°C. The medium GP was recorded at 15.0°C, 30.0°C, and 35.0°C by a value of around 50.00%. The lowest GP was noticed at 10.00°C with a final value of about 33.00%.

The maximum GR was observed at 25.0°C (0.39/d), enlightening a full rapid germination ability at this temperature, followed by 20.0°C (0.37/d), 30.0°C (0.30/d), and 35.0°C (0.30/d). Further, the GR declined at 15.0°C and 10.0°C, with the values of 0.12/d and 0.07/d, respectively.

The mean germination time varied significantly among all temperatures, from 9.36 to 13.18 d (P<0.05; Table 2). The initial germination time at 10.0°C and 15.0°C was 12.00 and 6.00 d, respectively, revealing a medium germination speed. However, at 25.0°C, the initial germination time was only 1.50 d, and at 20.0°C, 30.0°C, and 35.0°C, it was 2.00 d. The final germination time varied between 13.00 and 15.00 d at the optimal temperature range (15.0°C-25.0°C), while it was 10.00 and 11.00 d at the highest temperatures (30°C and 35.0°C, respectively). The most extended germination period was observed at 10.0°C with a final germination time of 20.00 d. This variability reflects that environmental factors greatly influence the germinative capacity of H. persicum's seeds, underlining the significance of knowing the ecophysiological needs for effective germination at regulated temperatures.

When seeds were exposed to PEG₆₀₀₀ or NaCl solutions with different concentrations, the impact of temperature on seed germination decreased significantly (P<0.05; Fig. 2). The final GP of H. persicum was also affected considerably by osmotic potentials. It was more sensitive to osmotic stress caused by PEG₆₀₀₀ (or NaCl) than by temperature. Specifically, it decreased significantly with the decreasing osmotic potential (P<0.05) at all temperatures (15.0°C, 20.0°C, 25.0°C, and 30.0°C). With the decrease of osmotic potential, the seeds of H. persicum could germinate at all temperatures.

Meanwhile, under the PEG₆₀₀₀ and NaCl treatments, all the seeds could germinate at all temperatures. For example, at the optimal temperature (25.0°C), the final GP decreased from 80.00% at the osmotic potential of 0.00 MPa under the control treatment to 42.00% at the osmotic potential of -2.00 MPa under the PEG₆₀₀₀ treatment, followed by 20.0°C (decreasing from 71.00% to 24.00%), 30.0°C (decreasing from 58.00% to 9.00%), and 15.0°C (decreasing from 48.00% to 5.00%) (Fig. 2a). At the highest NaCl concentration (osmotic potential of -2.00 MPa), the best final GP was recorded at 25.0°C to reach a value of 27.33%, followed by 20.0°C with a value of about 23.00%, 30.0°C with a value of 10.67%, and 15.0°C with a value of 7.33% (Fig. 2b). These results enlightened the idea that the seeds could germinate under different osmotic potential conditions, thus confirming its invasive potential.

Temperature, water stress, and salt stress are all factors that significantly influence the seed germination pattern of H. persicum (P<0.0001; Table 3). The two-way ANOVA results exhibited significant differences among these factors. Their interaction also greatly affected the final GP (P<0.0001).

Based on the predicted thermal time model, T_b was about 8.4°C, T_o was estimated as 25.5°C with a suboptimal θ_T(50)(g) (the median θ_T(g)) of about 37.23 MPa, and T_c was around 58.3°C with a supraoptimal estimated θ_T(50)(g) of about 75.06 MPa at the osmotic potential of 0.00 MPa under the control treatment. In addition, the suboptimal model had a thermal time constant of 37.23 MPa with a standard deviation of 97.58 MPa and a coefficient of determination (R²) of 0.55. In contrast, the supraoptimal model showed a thermal time constant of 75.06 MPa with a standard deviation of 110.58 MPa and a higher R² of 0.72.

Table 4 and Figure 3 illustrate a successful relationship between the germination behavior of H. persicum and osmotic potentials of all PEG₆₀₀₀ and NaCl solutions at different temperatures (15.0°C, 20.0°C, 25.0°C, and 30.0°C).

This relationship was assessed using a hydrotime model with R² ranging from 0.48 to 0.76. The Ψ_b(50) increased with the decreasing temperature (Table 4). Under the water stress treatments, the Ψ_b(50) values revealed a minimum fluctuation varying from -7.74 to -4.14 MPa at the suboptimal temperatures (15.0°C, 20.0°C, and 25.0°C). In contrast, the θ_H values decreased as increasing temperature. At 30.0°C, the predicted Ψ_b(50) recorded the lowest value while the θ_H reached its highest value.

Under the salt stress, the predicted Ψ_b(50) was from -7.03 to -4.66 MPa at the temperature range of 20.0°C-30.0°C (Table 4). In addition, the θ_H highlighted the lowest values of 14.50 and 20.30 MPa•d at 15.0°C and 30.0°C, respectively. The highest θ_H was recorded at 20.0°C, with the value of 25.84 MPa•d. The predicted σΨ_b(g) varied considerably between 1.26 and 5.63 MPa under all water and salt stress treatments. The lowest σΨ_b(g) was recorded at 15.0°C, with the values of 1.26 and 2.07 MPa, respectively, under the water and salt stress treatments. These results proved that the invasive H. persicum can tolerate water stress better than salt stress.

Figure 3 elucidates the relationship between the probit germination model and Ψ_b(g) via the ''seedr'' package. Probit germination, representing the cumulative probability of seed germination, showed a distinct positive correlation with Ψ_b(g). The probability of germination declined with increasing Ψ_b(g) at all measured temperatures, demonstrating that a decrease in water availability has a negative impact on germination success under both water stress (PEG₆₀₀₀) and salt stress (NaCl) treatments.

Figure 4 represents a heat map correlation between seed germination parameters and seed functional traits of H. persicum at 25.0°C. A strong negative correlation was highlighted between GR and thousand seed weight (r= -0.96) and between mean germination time and thousand seed weight (r= -0.96). In contrast, a strong positive correlation between GP and thousand seed weight (r=0.96) suggested that heavier seeds may have higher GP. Moreover, a strong positive correlation existed between GR and embryo viability (r=0.87) and between mean germination time and embryo viability (r=0.87). Furthermore, a negative correlation was found between GP and embryo viability (r= -0.87).

Conversely, the negative correlation between GP and percentage of embryoless seeds (r= -0.96) showed that the higher the percentage of embryoless seeds, the lower the GR. In addition, the negative correlation between GP and seed area (r= -0.87) indicated that seeds with larger extensive surface areas had lower GP. The positive relationship between mean germination time and seed area (r= -0.87) indicated that seeds with larger extensive surface areas have longer mean germination time. At last, the negative correlation between mean germination time and SWC (r= -0.94) indicated that seeds with higher water content can germinate faster. On the contrary, the positive correlation between GP and SWC (r=0.94) showed that seeds with higher water content have significant high final GP.

Under harsh environmental conditions in the arid bioclimate zones of North Africa, seed germination appears to be key to the establishment of plant populations, especially for invasive species whose seed germination may significantly affect native species. The invasive species use germinated seeds as a viable method for successful colonization and settlement (Guido et al., 2017), specifically in desertic regions. When investigating the seed functional traits of H. persicum, we noticed that SWC was around 14.76%. According to Tangney et al. (2019), this low content suggested that this species could survive at higher temperatures. Moreover, thousand seed weight of H. persicum was around 3.15 g with a low coefficient of variation being 0.95%, confirming the uniformity within the treated populations. This result was in line with the findings of Chen et al. (2022) for the seeds of Salsola species. The spirally twisted embryo shape and color of seeds are characteristics of the Chenopodiaceae family (Shepherd et al., 2005). Sarcocornia blackiana belongs to Salicornioideae, a sub-family of Chenopodiaceae; its seed has a peripheral embryo with the outer edge aligned with the inner surface of the bitegmic seed coat, limiting evaporative losses (Shepherd et al., 2005). Besides, understanding ecological processes in plants and the coexistence among species relies heavily on the link between seed functional characteristics. Functional traits are essential indicators of the metabolism and life cycle of plant species (Visser et al., 2016), especially for seeds, to study their source, usage, storage, and improvement strategies, resulting in lower costs and higher seedling establishing success (Zanetti et al., 2020).

Temperature represents a significant germination inhibitor (Notarnicola et al., 2023). An important abiotic stressor negatively impacts seed germination for several plant species (Bakhshandeh and Jamali, 2020). Our results suggested that the seeds of H. persicum can germinate at temperatures from 10.0°C to 35.0°C with different speeds (Table 2). Such a flexibility may offer H. persicum competitive benefits across crop-growing seasons in varied environments. The maximum GP was recorded at 25.0°C (P<0.0001; Fig. 1), with a high germination speed (1.00 d) and the highest GP (0.39/d) under the control treatment (osmotic potential of 0.00 MPa), knowing that the species of Chenopodiaceae are characterized by a high germination speed, which could vary from several hours to a few days (Baskin et al., 2014). Similar results were reported previously for Dioscorea dregeana (Kulkarni et al., 2007) and Stachys mouretii (Ismaili et al., 2023). Seed form influences germination speed based on the environment, life cycle strategy, and climate (Vandelook et al., 2012). Besides, several studies have demonstrated that invasive plants may germinate earlier or more quickly under different conditions (Ozaslan et al., 2017; Gioria et al., 2018; Nešić et al., 2022). Additionally, Tobe et al. (2000) affirmed that the T_o of H. persicum growing in a non-saline area in China was 20.0°C. This variation of T_o may result from different climatic zones (Vázquez et al., 2017). The Mediterranean climate characterizes Tunisia with hot and dry summers and mild and humid winters (Bouatrous et al., 2022). China, on the other hand, has a climate with moderate temperatures and obvious seasonal variations (Wang et al., 2019). Seeds germinating optimally at 20.0°C in China may benefit from cold conditions (Li et al., 2006). In comparison, those H. persicum plants that grow in Tunisia (with T_o of 25.0°C) have to adapt to hotter and drier climate conditions, which can pose challenges under climate change scenarios (Rejili et al., 2010). In this concern, several studies on the seed germination of plant species in the Saharan bioclimatic zones found the same temperature range (Derbel and Chaieb, 2007; Hayder et al., 2024).

Temperature, osmotic potentials, and their combinations significantly impact the seed germination of the invasive H. persicum. Their interactions showed the potential invasive character of this species in the Saharan bioclimatic zones of Tunisia. Our results proved that H. persicum could germinate at different osmotic potentials of PEG₆₀₀₀ and NaCl solutions, as it could grow even at the osmotic potential of -2.00 MPa for both PEG₆₀₀₀ and NaCl solutions to attend the minimum final GP of 5.00% and 7.00%, respectively, at 15.0°C. On the other hand, at the optimal temperature (25.0°C), the minimum GP was recorded at the osmotic potential of -2.00 MPa (274 mmol/L for NaCl concentration), with the values of 27.33% and 42.33% for PEG₆₀₀₀ and NaCl solutions, respectively (Fig. 3). The maximum salt concentration necessary for seed germination and recovery after NaCl exposure indicates a species' resistance to high salinity levels (Hinojosa et al., 2018). Also, according to the results found in our research, the seeds of H. persicum showed better tolerance to PEG₆₀₀₀ solutions than NaCl solutions (Fig. 3). It is proven that H. persicum has more flexibility to water stress than salt stress under different concentrations. Our results corroborated the findings of Duan et al. (2004), who proved that the seed germination of Chenopodium glaucum (Chenopodiaceae) was lower in NaCl solutions than in iso-osmotic PEG₆₀₀₀ solutions with an osmotic potential less than -0.50 MPa. Conversely, our findings opposed those of Song et al. (2005), who showed that PEG₆₀₀₀ treatments had a more potent inhibitory impact on the seed germination of H. persicum than iso-osmotic NaCl treatments. Indeed, Song et al. (2005) emphasized that seedlings that underwent PEG₆₀₀₀ treatments did not experience ion toxicity. The final GP values were 43.00%, 48.00%, and 76.00% lower at the osmotic potentials of -1.34, -2.24, and -3.13 MPa under the PEG₆₀₀₀ treatments, respectively, compared to iso-osmotic NaCl treatments (Song et al., 2005). Moreover, Tobe et al. (2000) asserted that the GR of H. persicum decreased with increasing NaCl concentrations, with a final GR of 64.00% at the osmotic potential of -3.00 MPa (667 mmol/L for NaCl concentration). In addition, the leaves of H. persicum are tiny, allowing them to retain and preserve water. This capacity results from tremendous photosynthetic efficiency and high resistance to drought (Alsahli et al., 2015). However, the capacity for the seeds of H. persicum to germinate at high salinity levels may represent an adaptive strategy that allows this species to maintain its populations under extreme salt conditions. Thereby, it was emphasized by Ruan et al. (2006) that during drought period, the cells of H. persicum quickly accumulate solutes, such as proline, to prevent water loss and restore cell turgescence, which is maintained by osmotic adjustment. Hence, this mechanism can improve the drought tolerance of H. persicum. Indeed, Ozturk et al. (2021) further affirmed that this is the most effective stress-coping mechanism of all. The synthesis and accumulation of the osmoregulating chemicals (proline, betaine, polyols, soluble sugars, and seed starch) promote the rapid seed germination of halophytic species under salt conditions (Kumari et al., 2015).

The effect of temperature on the seed germination of H. persicum was confirmed by the thermal time model, which showed that T_o was predicted to be 25.5°C, T_b was 8.4°C, and T_c was 58.3°C. The same T_c value was found previously for Chenopodium quinoa (quinoa), i.e., 54.0°C (Oveisi, 2017). It was reported previously that T_c value varies across seeds in the population and depends on the stress level (Alvarado and Bradford, 2002; Bakhshandeh et al., 2017; Abdellaoui et al., 2019). Also, our results opposed the findings of Peng et al. (2018), who found that the Chenopodiaceae family exhibits a lower T_b. This spectrum in the T_b of seed germination may be an adaptative trait in plants, as species growing in low temperatures have relatively low T_b. This behavior could be explained by the fact that C₄ species adapt highly to the ecological conditions in arid environments characterized by high temperatures. This adaptation is a common survival strategy of Mediterranean plants with T_o ranging from 15.0°C to 30.0°C (Baskin et al., 2000). Baskin et al. (2000) mentioned that the successful seed germination observed at high temperatures enables the seeds to avoid the risk of rapid dryness in the soil during the germination period. Furthermore, temperatures around 25.0°C are optimal for C₄ photosynthetic species (Khaeim et al., 2022; Zhu et al., 2022). Our results revealed a significant variability in the germination pattern of H. persicum species compared to previous findings (Tobe et al., 2000; Soltani, 2011). Although prior research indicated an optimal germination at lower temperatures (Song et al., 2005; Soltani, 2011), our data showed that the seeds of H. persicum can germinate better at moderate temperatures, which is one of the characteristics of Tunisian Saharan bioclimate. This environmental-dependent strategy allows H. persicum to survive, adapt, and quickly germinate under harsh habitat conditions for natural regeneration (Soltani, 2011). Indeed, Le Houerou (2000) stated that the average temperature throughout the spring and autumn seasons in the Tunisian Saharan bioclimatic zones is around 20.0°C, which is the beginning temperature point for seed germination for most species. Cardinal temperatures for seed germination are frequently linked to a species' climatic range of adaption, and they link germination time with favorable conditions for seedling emergence development and growth (Krichen et al., 2023). Consequently, a time-temperature relationship could be appropriate for woodland management projection via the H. persicum populations. Likewise, according to enthalpy methods, when the temperature increases, the energy in the water rises, causing an increase in diffusion pressure. This pressure boosts simultaneously metabolic and enzymatic activity while decreasing a seed's internal potential, which enhances water absorption (Haj Sghaier et al., 2022).

The effect of low osmotic potentials on seed germination was investigated using the hydrotime model parameters estimated by the probit regression analysis with the σΨ_b(g) as an indicator of seed germination uniformity in a seed lot (Table 4; Fig. 3) (Bradford and Still, 2004). Generally, seeds require a specific moisture level to germinate, suggesting that seeds with the Ψ_b higher than the Ψ_a cannot germinate. Thus, Ψ_b shows the water stress endurance of the seed population; the more significant (less negative) the Ψ_b, the lower the seeds' resistance to water stress (Patanè et al., 2016). In line with this, our results revealed that the seeds of H. persicum are more tolerant to water stress than salt stress, exhibiting the lowest Ψ_b (-10.90 MPa) at 30.0°C, which requires a greater cumulative soil water content. This finding is supported by the probit germination fit, indicating that the variation in GR is related to the species' adaptation to its native Saharan bioclimate. Consequently, these seeds required a longer time to germinate, which could attend 13.18 d. The hydrotime model posited that GR depends on the difference between the Ψ_a and Ψ_b (Cardoso and Bianconi, 2013). It has been emphasized in a recent study by Yang and Lv (2023) that as an adaptation strategy to water stress, H. persicum enhances the content of organic acids and their derivatives, and reduces the content of lignans and their related compounds. H. persicum has a high osmoregulatory capability, reactive oxygen species detoxification, and cell membrane stability by controlling vital metabolic pathways and anabolism of related metabolites. In this regard, H. persicum can adapt to long-term dry conditions by controlling required metabolism and metabolite production pathways.

The high correlation between thousand seed weight and seed diameter (r=0.73; Fig. 4), as emphasized by Tuthill et al. (2023), facilitates the wind dispersity, such as invasive species, to expand their populations, knowing that the seeds of H. persicum are winged. Indeed, winged seeds have a boosted dispersity, especially those of the Amaranthaceae family (Baskin et al., 2014). In addition, the smaller seeds are also likely better suited for long-distance wind dispersal because they require less energy.

Our study demonstrated that H. persicum has a strong invasive potential in Tunisia. However, it has been listed as endangered species in the Red List of Threatened Species in its native habitat, where it could face several environmental issues, such as habitat degradation. Indeed, its rapid germination and reproductive advantage threatens local biodiversity. The invasive potential of this species is linked to its introduction into Tunisia, where it experiences less ecological pressures, with favorable Mediterranean climate conditions.