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Gayana. Botánica

versión impresa ISSN 0016-5301versión On-line ISSN 0717-6643

Gayana Bot. v.66 n.1 Concepción  2009 

Documento sin título

Cayana Bot. 66(1): 58-70, 2009




Mariela A. González, Ana Silvia Cifuentes & Patricia I. Gómez

Departamento de Botánica, Facultad de Ciencias Naturales y Oceanógraficas. Universidad de Concepción,
Casilla 160-C, Concepción. Chile.


Haematococcus pluvialis is a unicellular green microalga cultivated on a large scale as a natural source of astaxanthin, a ketocarotenoid of high commercial value due to its colorant and antioxidant properties. The aim of this study was to compare growth and total carotenoids among four strains of H. pluvialis isolated from different microhabitats in two geographical locations in Chile. Growth was carried out under autotrophic and mixotrophic conditions and under two photon flux densities (PFD) (20 and 85 umol nrV1). Total carotenoid content was estimated on day 45. Most of the strains grew better under the autotrophic conditions; the highest exponential growth rates were exhibited at the high PFD in all the strains (ranging from 0.73 to 1.20 div day"1) with the exception of CCM-UDEC 023 which showed the same exponential growth rate with either PFD (0.73 div day"1). However, the cell density estimated on day 14 was higher at the low PFD in CCM-UDEC 022 and CCM-UDEC 023 (4.4 x 105 and 8.9 x 104 cells ml"1, respectively). The mixotrophic condition slightly improved the growth rate of the strain CCM-UDEC 021 at the high PFD (from 1.04 div day"1 at autotrophic condition to 1.25 and 1.14 div day"1 at 2mM and 1 OmM sodium acetate, respectively). The algal dry weight estimated on day 14 was not significantly correlated with the cell density, but it was, to a certain extent, related to the proportion and size of the different cell types quantified on that day. The strain with the highest dry weight at the end of the experimental period and under all the assayed conditions was CCM-UDEC 023. It was also the strain that produced the highest total carotenoid content under both autotrophic (5.6 mg l"1 and 95.6 pg cell"1 at the high PFD) and mixotrophic (with 2mM acetate) conditions (10.8 mg l"1 and 297 pg cell"1 at the high PFD). Ahigh intraspecific variability in the physiological attributes analyzed existed among the strains under study. Even though the mixotrophic condition assayed did not substantially improve the growth rate of any strain, it did improve the total carotenoid yield in the strain CCM-UDEC 023.

Keywords: Batch culture, Haematococcus pluvialis, intraspecific physiological differences.


Haematococcus pluvialis es una microalga unicelular verde cultivada masivamente como fuente natural de astaxantina, un cetocarotenoide de alto valor comercial debido a sus propiedades como colorante y antioxidante. El objetivo de este estudio fue comparar el crecimiento y el contenido de carotenoides totales en 4 cepas de H. pluvialis aisladas de diferentes microhabitats de dos regiones geográficas de Chile. El crecimiento se llevó a cabo en condiciones auto tróficas y mixotróficas a dos densidades de flujo fotónico (DFF) (20 y 85 umol nrV1). El contenido de carotenoides totales se estimó el día 45. La mayoría de las cepas crecieron mejor en condiciones autotróficas; las más altas tasas de crecimiento exponencial se presentaron a la mayor DFF en todas las cepas (fluctuó entre 0,73 y 1,20 div día"1) a excepción de la cepa CCM-UDEC 023 la cual mostró la misma tasa de crecimiento exponencial a cualquier DFF (0,73 div día"1). Sin embargo, la densidad celular estimada el día 14 fue mayor a la menor DFF en CCM-UDEC 022 y CCM-UDEC 023 (4,4 x 105 y 8,9 x 104 céls mi"1, respectivamente). La condición mixotrófica mejoró levemente la tasa de crecimiento de la cepa CCM-UDEC 021 a la mayor DFF (de 1,04 div día"1 en condición autotrófica a 1,25 y 1,14 div día"1 a 2mM y 1 OmM de acetato de sodio, respectivamente). El peso seco algal estimado el día 14 no mostró correlación significativa con la densidad celular, pero sí, en un cierto sentido, con la proporción y el tamaño de los diferentes tipos celulares a ese día. La cepa que presentó el mayor peso seco al final del periodo experimental y bajo todas las condiciones ensayadas fue CCM-UDEC 023. Esta fue también la cepa que produjo la cantidad de carotenoides totales más alta, tanto en condiciones auto tróficas (5,6 mg l"1 y 95,6 pg cél"1 a la mayor DFF) como mixotróficas (con2mM acetato) (10,8 mg l"1 y 297 pg cél"1 a la mayor DFF). Las cepas en estudio presentaron una alta variabilidad intraespecífica en los atributos fisiológicos analizados. Aún cuando las condiciones mixotróficas ensayadas no aumentaron sustancialmente las tasas de crecimiento de alguna de las cepas (CCM-UDEC 020, CCM-UDEC 022), esta condición sí mejoró la producción de carotenoides totales en la cepa CCM-UDEC 023.

Palabras clave: Cultivo estático, Haematococcuspluvialis, diferencias fisiológicas intraespecíficas.


Haematococcus pluvialis Flotow is a green microalga which is considered one of the richest biological sources of astaxanthin (Boussiba et al. 1999, Borowitzka 1999). The species inhabits small natural or artificial ephemeral freshwater bodies which are formed by granite or other material such as marble, cement or plastic and periodically filled with rain or tap water. H. pluvialis has a complex life cycle (Elliott 1934) which includes flagellated cells, nonmotile cells ("palmella" stage) containing a variable number of cells and the typical resting cell or cyst. The size of all these cell types is extremely variable during the life cycle.

Although considerable information exists regarding the factors that promote growth (i.e. Kobayashieia/. 1991,1993,Kakizonoe?a/. 1992, Barbera et al. 1993,Zlotnike?a/. 1993, Fane? al. 1994, Lee & Ding 1995, Harker et al. 1996, Gong & Chen 1997, Triphathi etal. 1999, Hageneia/. 2001, Orosa etal. 2001, García-Malea etal. 2005,2006, Jeoneia/. 2006) and astaxanthin accumulation (review in Boussiba 2000, Dominguez-Bocanegra etal. 2004, García-Malea et al. 2005, Orosa et al. 2005) in H. pluvialis, most of the studies have looked at single strains mainly from culture collections (i.e., UTEX, NIES, CCAP, ATCC, SAG NIVA) and examinedunder a wide range of culture conditions.

The aim of this study was to compare growth rates and total carotenoid content among four strains recently isolated from different microhabitats in the Bio-Bio and Los Lagos Regions of Chile, grown under two sodium acetate concentrations and two irradiances, in batch mode. The frequencies of the different cell types in the culture during growth and in the stationary growth phase were also compared. The results will show if physiological differences exist among the strains and if some of the mixotrophic conditions under low light improve the growth of any of the strains when compared to growth under the autotrophic conditions.


Algal strains and culture conditions The four strains of H. pluvialis studied (1CCM-UDEC 020, CCM-UDEC 021, CCM-UDEC 022 and CCM-UDEC 023) were isolated by single-cell isolation by micropipette and/or streaking cells across agar plates (Hoshaw & Rosowski 1973) from field samples obtained in the Bio-Bio and Los Lagos Regions of Chile. CCM-UDEC 020 was taken from a small, granitic bird bath in the backyard of a house in Puerto Varas(41°29'S;73°00'W). CCM-UDEC 021 and CCM-UDEC 022 were collected in the cemetery in the city of Concepción (36°51 'S; 72°59'W): CCM-UDEC 021 was isolated from a reddish liquid contained in a metal flower pot and CCM-UDEC 022 was taken from a dry red cyst layer on the side of an ornamental marble pot. The strain CCM-UDEC 023 was taken in liquid state from a small water fountain in the campus of the Universidad de Concepción.

After isolation, unialgal cultures were maintained in tubes with Bristol's medium (Starr & Zeikus 1993), at a photon flux density (PFD) of 15-20 mmol m-2 s-1 (measured by a Model LI-250 Quantum/Radiometer/ Photometer Light Meter manufactured by LI-COR Inc. U.S.A.) and at a temperature of 22 ± 1 °C.

For the experimental trials, the strains were grown in Bristol's medium under autotrophic and mixotrophic conditions (Bristol's with addition of 2 and 10 mM of sodium acetate) in 500 ml flasks with 200 ml of culture medium, under two different continuous PFD: 20 and 85 mmol m2 s-1 (suppliedby cool fluorescent daylight lamps), at 22 ± 1 °C, without aeration and agitated manually twice a day. Exponentially growing cells from stock cultures were used as inocula, and the initial cell density was of 1,000 cells ml-1.

Growth and relative number of cell types Cell growth was monitored over a 14-day period by cell counting using 1 ml Utermohl chambers and a Zeiss inverted microscope. Growth rate k (divisions per day) was calculated using the formula: k= (3,322/ t2- t1) x log N2/N1 (t= time, N=number of cells. Subscripts denote values at different times) (Guillard 1973). A maximal growth rate, kmax, during the exponential phase of growth was calculated. The algal dry weight and the relative number (%) of motile cells and cysts were determined on day 14 as in Cifuentes etal. (2003).

Total carotenoid analysis Total carotenoids and cell density were both estimated on day 45. The number of motile cells and cysts were also recorded on that day. Raw extracts of pigments were obtained by grinding the algal cell pellet, utilizing either a manual tissue homogenizer or a mortar with liquid nitrogen. Then, the pigments were extracted with 90% acetone and left overnight at 4 °C in darkness. The extracts were centrifuged and the carotenoid content was calculated from the extracts' absorbance at 480 nm (UV-VIS Spectrophotometer, Shimadzu, Tokyo), according to Strickland and Parsons (1972).

Statistical analysis

All of the experiments were carried out in triplicate. A three-way analysis of variance (ANOVA) with the strain, irradiance and sodium acetate concentration as independent variables was applied to cell biomass (number of cells ml-1 and cell dry weight) and total carotenoids. The Tukey test was used for multiple comparisons. Differences were considered to be significant at a probability of 5% (P= 0.05). Correlation analysis was also carried out between cell density and cell dry weight at day 14 using Pearson's correlation coefficient. Statistical analyses were performed with the SigmaStat software program, version 2.03.


Growth rates

Maximal growth rates fluctuated between 0.57 div day1 and 1.25 div day1. The CCM-UDEC 021 and CCM-UDEC 022 strains exhibited the highest maximal growth rates of 1.25 and 1.14 div day1 at the high PFD (85mmol m2s-1), under mixotrophic (with 2mM acetate) and autotrophic conditions, respectively (Table I a and 1b).

Under autotrophic conditions, the maximum growth rate of all strains was higher at the high light (85 umol m-V), except for CCM-UDEC 023, which exhibited growth during the first six days that was very similar at either PFD (Fig. 1 d). The mixotrophic condition slightly increased the growth rate of the CCM-UDEC 021 strain at both acetate concentrations and light conditions and the CCM-UDEC 023 strain at 2mM acetate and low light. On the other hand, the CCM-UDEC 020 and CCM-UDEC 022 strains grew better in the autotrophic mode.

Cell density (N° cells ml-1) and dry weight (mg l-1) At day 14 the values of biomass measured both as cell density and as dry weight were significantly different among all the strains (P= 0.05). The acetate concentration significantly influenced both parameters, whereas PFD affected only growth estimates of cell density. The three-way ANOVA analysis indicated that the strain, PFD and acetate concentration interacted significantly. The interaction between strain identity and PFD was dependent on the acetate concentration in the medium. For both parameters of growth (cell density and dry weight), the strain identity was the most important factor in determining the magnitude of the variation reported on day 14 (2F = 53.282 and F= 51.936 for cell density and dry weight, respectively), while acetate was the most important factor determining the cell density on day45(F= 137.872).

At day 14, the highest cell density was attained by the CCM-UDEC 022 strain (4.4 x 105 cells ml-1) under autotrophic conditions at the low PFD. The CCM-UDEC 023 strain, on the other hand, showed the highest cell density (1.2 to 1.3 x 105 cells ml-1) under mixotrophic conditions (20mM acetate) at either PFD.

The CCM-UDEC 023 strain exhibited higher cell dry weights than the other strains in most of the experimental conditions, with maximum values under both mixotrophic conditions assayed (383 and 305 mg l-1 at 2mM and 1 OmM acetate and under the low and the high PFD, respectively) (see Table 1 b and 1 c). On the contrary, CCM-UDEC 022 showed the highest cell dry weight under the autotrophic conditions (227 mg) at the high PFD. No significant correlation (Pearson's coefficient= -0.189; P>0.05) was found between the cell density and the respective cell dry weight when compared among all the strains.

In autotrophic conditions, cell densities estimated on day 45 indicated that most of the strains continued growing after day 14 (Table I), with maximal cell densities of 4.7 x 105 and3.5 x 105 cells ml"1 in CCM-UDEC 023 and CCM-UDEC 021, respectively. In mixotrophic conditions, on the contrary, the cell densities achieved on day 14 increased slightly in some strains at 2mM acetate, but were barely maintained or, as occurred in most strains, decreased substantially by day 45 at 20mM acetate and at the high PFD (see Table I).

Relative number of motile cells and cysts in the culture

Although the data analyzed include the four strains, the results presented in Figure 2 summarize the results of the two strains presenting the greatest contrast: CCM-UDEC 022 and CCM-UDEC 023. At day 14, the cultures of most of the strains showed a predominance of motile cells, while CCM-UDEC 023 formed cysts very early under almost all experimental conditions (Fig. 2a). At day 45, motile cells had decreased in most of the strains, with a predominance of cysts principally under mixotrophic conditions. The clearest exception occurred in the CCM-UDEC 022 strain, in which the proportion of motile cells was mostly higher than 80% (except at 1 OmM acetate and low light) at day 45 (see Fig. 2b).

The statistical analysis applied to these results (three-way ANO VA) showed significant differences in the proportions of the two cell types among all the strains, both on day 14 and on day 45, and under all experimental conditions (P= 0.05). Even though strain, PFD and acetate concentration significantly influenced this proportion on day 14, strain was the most important factor determining this variation (F= 248.176 and F=237.626 for motile cells and cysts, respectively). At day 45, on the contrary, acetate concentration was the single factor significantly affecting the proportion of these cell types (F=l85.264 and F=l70.783 for motile cells and cysts, respectively).

Total carotenoid accumulation When compared with the other strains, CCM-UDEC 023 was the most carotenogenic strain under all the conditions, except at 10 mM acetate. Under this condition, the amount of carotenoids accumulated by all the strains were very low. The maximum amount of total carotenoids per volume in CCM-UDEC 023 occurred under autotrophic conditions (3.3 and 5.6 mg 1-1) and at 2mM acetate (10.1 and 10.8 mgl-1), at the two PFD, respectively (Table I).

The three-way ANOVA analysis revealed significant differences in the total amount of carotenoids per volume accumulated on day 45 among all the strains, under all the culture conditions (P= 0.05). The acetate concentration (F=602.804) and the PFD (F=203.404) significantly influenced this parameter. The three factors -strain, PFD and acetate concentration- interacted significantly, and the effect of the interaction between strain identity and PFD was dependent on the acetate concentration.

When carotenoid accumulation was expressed on a cell basis, the amount accumulated by CCM-UDEC 023 at 2mM acetate was much greater (217 pg cell-1 and 296 pg cell-1 at 20 and 85 mmol m-2 s-1, respectively) than the amount accumulated by the other strains (8.5 to 62.6 pg cell-1). The two-way ANOVA analysis, with PDF and strain as variable factors, revealed that strain was the main factor in determining carotenoid accumulation on a cell basis (F=68.459), and that there were significant differences (P=0.001) in the amount of carotenoid accumulation per cell between the strain CCM-UDEC 023 and the other three strains.

Figure 1. Comparison of growth (indicated by cell density) of four strains of Haematococcus pluvialis in Bristol's medium under different concentrations of sodium acetate (NaAc) (2mM and 1 OmM) and photon flux densities (20 and 80 mmol m-2 s-1). (a) CCM-UDEC 020 strain, (b) CCM-UDEC 021 strain, (c) CCM-UDEC 022 strain and (d) CCM-UDEC 023 strain.

Figura 1. Comparación del crecimiento (como densidad celular) de cuatro cepas de Haematococcus pluvialis en medio Bristol bajo diferentes condiciones de acetato de sodio (NaAc) (2mM y 10 mM) y de densidades de flujo fotónico (20 y 80 mmol m-2 s-1). (a) cepa CCM-UDEC 020, (b) cepa CCM-UDEC 021, (c) cepa CCM-UDEC 022 y (d) cepa CCM-UDEC 023.

Figure 2. Relative number (%) of motile cells and cysts in the CCM-UDEC 022 and CCM-UDEC 023 strains, in cultures grown under different sodium acetate (NaAc) concentrations (2 mM and lOmM) and photon flux densities (20 and 80 mmol m-2 s-1). (a) on day 14 and (b) on day 45.

Figura 2. Número relativo (%) de células móviles y cistos en las cepas CCM-UDEC 022 y CCM-UDEC 023, en cultivos que crecieron con diferentes concentraciones de acetato de sodio (NaAc) (2 mM y lOmM) y a dos densidades de flujo fotónico (20 y 80 mmol m-2 s-1).
(a) el día 14 y (b)
el día 45.


The variability of the responses obtained from the different strains ofH. pluvialis cultured under the same conditions are evidence of the difficulty of establishing effective experimental conditions for promoting growth and total carotenoid accumulation which are valid for all the strains. Growth patterns differed even among those strains taken from the same location (CCM-UDEC 021 and CCM-UDEC 022), similar to findings for strains of Dunaliella salina Teod. (Gómez & González 2005). Like Dunaliella salina, H. pluvialis inhabits temporary isolated pools with extreme environmental conditions that vary within a wide range. The strains must adapt to these conditions with great celerity.

In contrast to Dunaliella salina, Haematococcus pluvialis exhibits a more complex life cycle. A predominance of green motile cells in the culture is a sign that the alga is still growing (i.e., the number of cells is increasing). A higher proportion of cysts than motile cells in the cultures is on the other hand an indicator of aging and/or unfavorable environmental conditions for the cells. Although the formation of cysts has been related to the cessation of cell growth (Borowitzka et al. 1991, Boussiba & Vonshak 1991, Kobayashi et al. 1991), in old cultures (i.e., two months old or more) it has been found that the cysts can grow either by increasing their cell size or by internal cell division, giving rise to new non-motile cells.

The strains that exhibited the most varied results were CCM-UDEC 022 and CCM-UDEC 023. In fact, CCM-UDEC 022 showed the highest division rates (0.97 div day-1 and the highest cell densities (4.4 x 105 cells ml-1) under autotrophic conditions on day 14; both parameters were much higher than the normal range found in the literature for the species (0.5-0.7 div day-1 and 1.5-2.5 x 105 cell ml-1, Hagen et al. 1993,2001, Lee & Ding 1994,1995,Harkere?a/. 1996, Orosa etal. 2001). The CCM-UDEC 023 strain, in contrast, exhibited lower division rates than CCM-UDEC 022 (ca. 0.73 div day-1) under all conditions, reaching a maximum cell density of 1.2 to 1.3 x 105 cells ml-1 under mixotrophic conditions (10 mM acetate) and independent of the irradiance.

The acetate concentrations assayed in the present study (2 and 10 mM), in relation to improving growth in motile cells, could be considered low in comparison to the concentrations utilized by other authors for other strains [i.e., 12 mM in ATCC 30453 (Barbera et al. 1993), 20 mM in UTEX 16 (Gong & Chen 1997) and 30.5 mM in CCAP 34/7 (Orosa et al. 2001)] with the same objective. Preliminary growth assays carried out in our laboratory with a wide range of acetate concentrations (2-60 mM) showed that acetate concentrations higher than 10 mM did not support good growth of motile cells in the four studied strains (unpublished data); on the contrary, they triggered the settling of cells and a slow growth of nonmotile cells ("palmella stage"). These findings agree with the studies done by Orosa et al. (2005) and Jeon et al. (2006) which found that the effect of acetate on growth depends on the acetate concentration. Even though the growth rates estimated in the CCM-UDEC 023 and CCM-UDEC 021 strains were a little higher when they were grown with 2 mM acetate than under autotrophic conditions (Table 1 ), the biomass estimated as cell dry weight showed a marked increment in CCM-UDEC 023 under both mixotrophic conditions. In general, the strains attained higher cell dry weight in media with low concentrations of acetate (2mM) irrespective of the PFD, with the exception of CCM-UDEC 022. This latter strain achieved its maximum growth rate and growth (cell number and dry weight) under autotrophic conditions.

When the relative abundance of the different cell types during growth in the culture was examined, a significant difference also appeared between CCM-UDEC 022 and CCM-UDEC 023. While CCM-UDEC 022 exhibited a predominance of motile cells (81-93%) on day 14 undermost of the experimental conditions, the CCM-UDEC 023 strain showed a similar proportion of cysts and motile cells (Fig. 2a). According to these results, the CCM-UDEC strain 023 fits well with other H. pluvialis strains studied in batch system; that is, an exponential growth period of 5 to 8 days with predominance of motile cells, followed by a linear phase with decrease of motile cells and an increment of "palmella" stages and cysts (Lee & Ding 1994, Moya et al. 1997). Many studies on H. pluvialis have been focused on trying to find culture conditions that lengthen the active growing phase (first stage, according to Kobayashi et al. 1991, Olaizola 2000), in order to improve the astaxanthin yield per dry weight at the end of the inductive phase. The CCM-UDEC 022 strain fulfilled the first requirement, i.e. an exponential growth period of 14 days, with predominance of motile cells (ca. 93%), reaching a high cell density (4.4 x 105 cells ml-1) when growing under autotrophic conditions at low light. Moreover, on day 45, this strain still exhibited a higher proportion of motile cells than cysts in 2mM acetate, both at the low and high PFD (ca. 83% and 81%, respectively) (Fig. 2b).This is a promising and uncommon characteristic of old H. pluvialis cultures (Borowitzka etal. 1991, Kobayashi et al. 1992, Lee & Ding 1994), which makes this strain very interesting from a biotechnological point of view, as long as this high cell density is coupled with high astaxanthin production once stress mechanisms are applied.

Many researchers utilize cell density to estimate growth in H. pluvialis (Borowitzka et al. 1991, Kobayashi etal. 1991, Lee & Ding 1994, Fábregas etal. 1998, 2000, 2001, Dominguez-Bocanegra et al. 2004, Orosa et al. 2005). In this study, growth was estimated as cell density and as dry weight, but correlations between both parameters were not found under any experimental condition on day 14. This is probably due to the complex life cycle of the species, where cell division and cell enlargement simultaneously occur in the culture. For example, on day 14, a dry weight of 305 mg l-1 in CCM-UDEC 023 (at 1 OmM acetate and at the high PFD) was in fact more closely related to the high proportion of cysts (43%) than to the culture cell density (1.2 x 105 cells ml-1), since the same cell density was exhibited by the CCM-UDEC 022 strain (at 2mM acetate and high PFD), with a dry weight of 115 mgl-1 and a low proportion of cysts (6%) (Table 1 and Fig. 2a). Cell density is a good estimator of biomass when motile cells are predominant in the culture, but when batch growth experiments are being planned, care should be taken to choose the adequate parameter for estimating and comparing cell growth among strains.

The levels of carotenoids (mg L) quantified on day 45 also showed considerable inter-strain variation. While in most strains the total amount of carotenoids accumulated was influenced significantly by both PFD and acetate, in CCM-UDEC 021 this parameter was only affected by the acetate concentration.

The amount of carotenoids on a per-cell basis, estimated in almost all the strains and culture conditions, may be considered low, if the full culturing period is taken into account (45 days). The only exception occurred in CCM-UDEC 023, where levels of carotenoids of 200-300 pg cell-1 were registered. Thus, strain and growth condition can result in as much as a 30-fold difference in carotenoid/ cell at 45 days. In addition, these values are in line with those reported by Harker et al. (1996) and Triphathi et al. (1999). The former found that the greatest increase in the pigment content of the cells occurred after day 40 and accumulated at a constant rate until day 90 and preferably in nonmotile cells.

Most of the large-scale cultures of H. pluvialis around the world are carried out under autotrophic growth conditions (Olaizola & Huntley 2003). However, finding strains that can achieve satisfactory growth and carotenoid accumulation in a reliable mixotrophic system would improve the outlook for commercial cultivation at higher latitudes, where integral of the natural radiation is low. The CCM-UDEC 023 strain seems to fulfill these requirements but needs additional study.

The physiological variability found among the four strains ofH. pluvialis studied have provided a strong motivation for continuing to seek new strains from the field, based on the conviction that the simple selection of strains from nature would be the easiest way to produce genetic improvement in this species.


This study was supported by a grant to M.A. González from Dirección de Investigación, Universidad de Concepción (DIUCN°


1CCM-UDEC = Colección de Cultivos de Microalgas de la Universidad de Concepción, Chile.

2F= F test statistic value.


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Recibido: 18.12.08

Aceptado: 20.03.09

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