#### 3.1. Experimental Material

The accuracy of determining the mean value of a given physical parameter can be inferred from the standard error of the estimate based on the sample size, standard deviation of the analyzed trait and Student t-values at the adopted significance level. In this study, each sample comprised 101 to 118 seeds; therefore, the standard error of the estimate of the mean values of the physical properties of fir seeds did not exceed: 0.2 m s^{−1} for terminal velocity, 0.1 mm for seed thickness, 0.2 mm for seed width, 0.3 mm for seed length, 1° for the angle of external friction, and 0.5 mm (balsam fir) to 2.5 mm (Forrest’s fir) for seed mass.

The physical properties of the analyzed seeds are presented in

Table 1. The average terminal velocity ranged from 4.8 m s

^{−1} (balsam fir) to 7.1 m s

^{−1} (silver fir). The following fir species formed homogeneous groups in terms of terminal velocity: (1) balsam fir and subalpine fir, (2) grand fir, Japanese fir and Sierra white fir, (3) corkbark fir and Sierra white fir, (4) corkbark fir, Forrest’s fir and Korean fir. The average terminal velocity of silver fir seeds was comparable to that presented by Kaliniewicz et al. [

28], and somewhat higher than that determined by Tylek [

29,

30] in seeds from southern Poland.

The average seed thickness ranged from 1.76 mm (Korean fir) to 3.22 mm (silver fir). In turn, the average seed width ranged from 3.29 mm (balsam fir) to 5.57 mm (silver fir), and the average seed length—from 5.44 mm (balsam fir) to 11.06 mm (noble fir). Seeds characterized by similar values of the three basic dimensions were noted only in grand fir and Sierra white fir. The seeds of silver fir were somewhat larger than those analyzed by Tracz and Barzdajn [

31], Tylek [

30] and Kaliniewicz et al. [

28], but their dimensions were within the range of average values noted in Poland [

16]. The evaluated seeds were similar to selected batches of Normann fir seeds in terms of length [

14,

32], and they were similar to pindrow fir seeds in terms of length and width [

33]. The analyzed Korean fir seeds were approximately 10% larger than those studied by Song et al. [

34].

Relatively minor variation was noted in the values of the angle of external friction which ranged from 26° (corkbark fir) to 33° (balsam fir). Six fir species formed a homogeneous group in terms of the angle of external friction: Forrest’s fir, Korean fir, noble fir, Sierra white fir, silver fir and white fir. Balsam fir seeds differed most considerably from the remaining fir species in this respect.

In the studied fir species, seed mass (

Figure 2,

Table 1) ranged from 2.8 mg (balsam fir) to 78.6 mg (silver fir), and average seed mass ranged from 7.9 to 48.3 mg. The following fir species formed homogeneous pairs in terms of seed mass: (1) Korean fir and subalpine fir, (2) grand fir and Sierra white fir, (3) Forrest’s fir and noble fir. According to the literature [

16,

20,

35,

36,

37], seed mass is largely influenced by environmental conditions, genetic traits, tree age and, above all, geographic location. If the above factors are not taken into account, the average mass of silver fir seeds is somewhat lower than that reported by Tylek [

38], Balian [

20] and Gradečki-Poštenjak and Ćelepirović [

37], and similar to that noted by Skrzyszewska and Chłanda [

13] and Kaliniewicz et al. [

28]. The average mass of Sierra white fir and subalpine fir seeds was somewhat lower (by approx. 17% and 3%, respectively), whereas the average mass of grand fir seeds was higher (by approx. 32%) than that observed by Veech et al. [

39] in the corresponding species.

Silver fir was characterized by the largest seeds (geometric mean diameter—5.77 mm), and balsam fir produced the smallest seeds (geometric mean diameter—3.16 mm) (

Table 2). No significant differences in the values of the geometric mean diameter were noted between the following species: (1) balsam fir and Korean fir, (2) corkbark fir and subalpine fir, (3) grand fir and Sierra white fir, (4) Forrest’s fir and white fir.

The average aspect ratios were determined in the following range of values:

T/W—from od 43.76% (Forrest’s fir) to 59.83% (noble fir);

T/L—from 20.78% (Japanese fir) to 32.80% (balsam fir);

W/L—from 40.11% (noble fir) to 60.58% (balsam fir). Aspect ratios were similar in the seeds of grand fir, Sierra white fir and white fir, i.e., species that belong to the section

Grandis [

2].

The highest values of the sphericity index were determined in balsam fir (58.20%), and the lowest values—in Japanese fir (43.86%). Eight homogeneous groups were identified in terms of the sphericity index, and the following species formed common groups: (1) grand fir, Sierra white fir and white fir, (2) silver fir and subalpine fir.

The average specific mass of fir seeds varied widely from 2.48 g m^{−1} (balsam fir) to 8.29 g m^{−1} (silver fir). The above indicates that balsam fir and silver fir seeds were characterized by the largest and smallest proportions of the seed coat, respectively, in seed mass, and that they contained empty spaces not filled with parenchymal tissue. The following species formed homogeneous pairs in terms of average seed mass: (1) Korean fir and subalpine fir, (2) silver fir and white fir.

Species pairs characterized by significant similarities in all physical parameters were not identified. The seeds of grand fir and Sierra white fir were most similar, and they did not differ significantly in the values of terminal velocity, basic dimensions, mass, geometric mean diameter, aspect ratios or sphericity index. In general, balsam fir seeds were most different, whereas Sierra white fir seeds were most similar to the seeds of the remaining fir species. Therefore, the seeds of Sierra white fir can be regarded as representative of the pine family and used to differentiate between the seeds of different fir species. The W/L aspect ratio (four homogeneous groups) was the least differentiating trait, whereas specific mass (nine homogeneous groups) was the most differentiating attribute in the analyzed fir species.

#### 3.3. Seed Separation

According to many authors [

2,

13,

33,

37,

40,

41,

42], fir seeds differ in germination capacity that can range from 0 to approximately 90% in freshly harvested seeds. The above can be attributed to the fact fir seeds are characterized by a high proportion of empty seeds [

2,

13,

20,

37,

43,

44], which can reach 70% in some cases. Empty seeds are difficult to separate because similarly to filled seeds, they contain resin globules whose specific gravity is similar to that of filled seeds. The ranges of seed mass values overlap in empty and filled seeds, but empty and filled seeds differ in average mass, and this trait can be potentially used in the separation of fir seeds [

13,

20,

30]. The mass of fir seeds was most significantly influenced by seed thickness and seed length (

Table 3). Therefore, the above parameters should be regarded as the primary distinguishing features in seed separation processes, and fir seeds should be sorted with the use of mesh sieves with longitudinal openings or with a seed grader. According to the authors of this study, a seed grader is less effective because indented pockets on the surface of the cylinder are more suitable for separating elliptical seeds [

22] rather than triangular seeds. Seed thickness should be regarded as a distinguishing feature because this parameter was highly correlated with specific mass (coefficient of determination of 0.62). Sorting operations based on seed thickness will produce seed fractions with different content of parenchymal tissue. The resulting fractions should be sown separately to improve germination rates and germination efficiency.

A detailed analysis of the linear correlations between seed mass and the remaining physical attributes of seeds (

Table 4) revealed that seeds of selected fir species can also be sorted with a pneumatic separator. The above applies particularly to the seeds of balsam fir, Forrest’s fir, grand fir, noble fir, Sierra white fir and subalpine fir. According to Załęski [

16] and Tylek [

29,

30,

38,

45], terminal velocity should be the primary distinguishing trait in the process of separating silver fir seeds.

The results of the analysis (

Table 5) indicate that fir seeds can also be effectively separated based on their terminal velocity. In most cases, the resulting seed fractions were characterized by uniform seed mass. Before sorting, the coefficient of variation of seed mass ranged from around 22% (white fir) to around 37% (Forrest’s fir), and it decreased after sorting, particularly in fractions II and III. Fraction III seeds (8 out of 11 cases) and fraction II seeds (3 out of 11 cases) were least varied in terms of mass. The coefficient of variation of seed mass in each separated fraction differed across fir species from around 12% (fraction III, noble fir) to around 36% (fraction I, Sierra white fir). Seed mass was the most reliable separation trait in noble fir seeds in fraction III (change of 54.4%) and the least reliable trait in Sierra white fir seeds in fraction I (change of 36.2% relative to unsorted material). The average increase in the homogeneity of seeds separated into three fractions based on terminal velocity ranged from approximately 4.1% (Sierra white fir) to approximately 32.5% (noble fir).

In most cases (excluding three cases in fraction I), seed thickness was also a reliable parameter for sorting seeds into fractions with similar mass (

Table 6). The coefficient of variation of seed thickness differed across fir species from around 16% (fraction III, silver fir) to around 35% (fraction I, Forrest’s fir), and silver fir seeds in fraction III were characterized by the most uniform thickness (change of 40% relative to unsorted material). The average increase in the homogeneity of seeds separated into three fractions based on seed thickness ranged from around 2.6% (grand fir) to around 24.7% (Japanese fir).

The homogeneity of fir seeds separated into three fractions based on terminal velocity or seed thickness indicates that a pneumatic separator should be potentially used for sorting balsam fir, corkbark fir, Forrest’s fir, grand fir, noble fir and white fir seeds, whereas a mesh sieve with longitudinal openings is most suitable for sorting Japanese fir, Korean fir, Sierra white fir, silver fir and subalpine fir seeds. A mesh sieve appears to be the preferred solution for sorting fir seeds because the resulting fractions do not have to be dewinged before storage (seed wings do not disrupt the separation process), whereas dewinging operations increase the risk of damage to resin ducts and make seeds more susceptible to infection [

38]. It should also be noted that the elimination of resin globules, for example during rapid dewinging, leads to a rapid deterioration in seed quality [

2,

9,

46].

The obtained seed fractions should be analyzed for germination capacity and sown in the most appropriate locations. Seeds of fractions I and II, with the potentially lowest germination capacity, can be sown in rows or broadcast in conventional nurseries (by choosing the most appropriate sowing rate), whereas fraction III seeds can be sown individually in beds or containers.