**6. Methodology**

Potatoes (*Solanum tuberosum L)* and yeast (*Saccharomyces cereviceae)* contain more than 60% of protein, this consumption by the post- larva is consistent with the protein requirement, and also this source contains immune system stimulant compounds such as β-glucan, nucleic acids like manna oligosaccharides that increase the immune response (Champagne et al., 2009). When yeast gets attached to the intestine of the larvae, on their 27th day after birth, it produces a higher secretion of amylase and this stimulates the enzymes located on the membrane cells in the brush border shape (Austin & Brunt, 2009, as cited in Montet & Ray, 2009).

Potatoes (*Solanum tuberosum L*) have been used as a nutrient because they play an energetic roll due to their high levels of starch (60% – 80%), of the dry matter is starch. In addition, the potato is low in fat and rich in several micronutrients, especially vitamin C. It is also a good source of vitamins B1, B3, B6, folate, pantothenic acid, riboflavin and minerals, such as potassium, phosphorus and magnesium, Potatoes also contain dietary antioxidants, which may play a part in preventing diseases related to ageing (Murniece et al., 2011; FAO, 2008a).

The enrichment with flour provides protein (50%) and high level of lecithin to the living food. Few authors have shown the incidence in growth and intestine morphology improvement including soy oatmeal (Murray et al., 2010). Despite its limitations, the incidence of scoliosis and mouth twisting in the larvae is reduced with the addition of lecithin Salze et al., 2010). Gutiérrez-Espinoza and Vásquez-Torres (2008), confirm that soy in different presentations has a high digestibility index in White Cachama juveniles (*Piaractus brachypomus*) and can be used without restrictions on this specie (Guillaume et al., 2004; Sealey et al., 2009).

The mutual action of these three nutrients over the productive and reproductive parameters of Daphnia magna can be demonstrated with this research, thorough its exposition to eight diets. These diets include yeast, potato and soy oatmeal, with 15 and 30 ppm concentrations of nutrient and enrichment compound, determining productive and reproductive parameters, creation of life history and comparing populations under stress conditions.

Daphnia magna was used, with two populations: one with adults and the other with young breeders (32 specimens / population). *Daphnia magna* was seeded individually (1 Daphnia/tank) in multicells with 24 tanks, each one with 3 mL capacity, covered with parafilm. The compartments were fully filled with the culture medium according to the treatment. The daily exchange for a culture medium was 50%. Concentrations of 30 mg/L and 15 mg/L were prepared for the culture medium for each of the nutrient with discolored water. The treatments used were the following:

Treatment 1: 15 ppm *S. cereviceae*, 15 ppm potato, 15 ppm soy oatmeal flour.

Treatment 2: 15 ppm *S. cereviceae*, 15 ppm potato, 30 ppm soy oatmeal flour.

Treatment 3: 15 ppm *S. cereviceae*, 30 ppm potato, 15 ppm soy oatmeal flour.

Treatment 4: 15 ppm *S. cereviceae*, 30 ppm potato, 30 ppm soy oatmeal flour.

Treatment 5: 30 ppm *S. cereviceae*, 15 ppm potato, 15 ppm soy oatmeal flour.

Treatment 6: 30 ppm *S. cereviceae*, 15 ppm potato, 30 ppm soy oatmeal flour.

Treatment 7: 30 ppm *S. cereviceae*, 30 ppm potato, 15 ppm soy oatmeal flour.

Treatment 8: 30 ppm *S. cereviceae*, 30 ppm potato, 30 ppm soy oatmeal flour.

The whole production was preserved in a laboratory with the following environmental conditions: 1.200 masl (meters above the sea level), 22 ± 3 °C room temperature, 12 light hours, 12 dark hours, 7.0 ± 0.6 pH water, during 20 days. Eight treatments were used with four replica/treatment.

These are the productive and reproductive parameters of Daphnia magna:

#### **6.1 Growth and corporal weight: Productive variables**

Maximum density (Dmax):

$$\text{Dmáx} = \frac{\text{Final population}}{\text{Volume}} \equiv \left[ \frac{\text{Individulas}}{\text{Volume}} \right] \tag{1}$$

Daily average density (Dmd):

$$\text{Dmd} = \frac{\text{Final population}}{\text{T}} \equiv \left[ \frac{\text{Individulas}}{\text{Time}} \right] \tag{2}$$

Doubling Time (Td):

250 Aquaculture

in different presentations has a high digestibility index in White Cachama juveniles (*Piaractus brachypomus*) and can be used without restrictions on this specie (Guillaume et al.,

The mutual action of these three nutrients over the productive and reproductive parameters of Daphnia magna can be demonstrated with this research, thorough its exposition to eight diets. These diets include yeast, potato and soy oatmeal, with 15 and 30 ppm concentrations of nutrient and enrichment compound, determining productive and reproductive parameters, creation of life history and comparing populations under stress conditions.

Daphnia magna was used, with two populations: one with adults and the other with young breeders (32 specimens / population). *Daphnia magna* was seeded individually (1 Daphnia/tank) in multicells with 24 tanks, each one with 3 mL capacity, covered with parafilm. The compartments were fully filled with the culture medium according to the treatment. The daily exchange for a culture medium was 50%. Concentrations of 30 mg/L and 15 mg/L were prepared for the culture medium for each of the nutrient with discolored

The whole production was preserved in a laboratory with the following environmental conditions: 1.200 masl (meters above the sea level), 22 ± 3 °C room temperature, 12 light hours, 12 dark hours, 7.0 ± 0.6 pH water, during 20 days. Eight treatments were used with

≡

≡

Individuals

Individuals

Volume <sup>൨</sup> (1)

Time <sup>൨</sup> (2)

Treatment 1: 15 ppm *S. cereviceae*, 15 ppm potato, 15 ppm soy oatmeal flour. Treatment 2: 15 ppm *S. cereviceae*, 15 ppm potato, 30 ppm soy oatmeal flour. Treatment 3: 15 ppm *S. cereviceae*, 30 ppm potato, 15 ppm soy oatmeal flour. Treatment 4: 15 ppm *S. cereviceae*, 30 ppm potato, 30 ppm soy oatmeal flour. Treatment 5: 30 ppm *S. cereviceae*, 15 ppm potato, 15 ppm soy oatmeal flour. Treatment 6: 30 ppm *S. cereviceae*, 15 ppm potato, 30 ppm soy oatmeal flour. Treatment 7: 30 ppm *S. cereviceae*, 30 ppm potato, 15 ppm soy oatmeal flour. Treatment 8: 30 ppm *S. cereviceae*, 30 ppm potato, 30 ppm soy oatmeal flour.

These are the productive and reproductive parameters of Daphnia magna:

Dmáx= Final population Volume

Dmd= Final population T

**6.1 Growth and corporal weight: Productive variables** 

2004; Sealey et al., 2009).

four replica/treatment.

Maximum density (Dmax):

Daily average density (Dmd):

water. The treatments used were the following:

$$\text{Td} = \frac{0.693}{\text{k}} \equiv \text{[días]} \tag{3}$$

Specific growth rate (k):

$$\mathbf{k} = \frac{\text{Ln(final population)} \cdot \text{Ln(PobblInitial population inicial)}}{\text{TiempoTime}} \equiv \left[ \frac{1}{\text{day}} \right] \tag{4}$$

Performance (r):

$$\mathbf{r} = \frac{\text{(Final population)} \cdot \text{(Initial population)}}{\text{Time}} \equiv \left[ \text{individuals}^\* \frac{1}{\text{Time}} \right] \tag{5}$$

Numeric growth (PN):

$$P\_{\mathcal{N}} = \mathsf{b}^\* \overline{\mathsf{N}} \equiv \left[ \# \text{ individuals} \ast \frac{1}{\text{Time}} \right] \tag{6}$$

N̅= individual media number

b= birth rate population, in a period of time.

Birth rate (b) (Edmodson equation):

$$\mathbf{b} = \ln(\mathbf{E}/\mathbf{D} + 1) \equiv [\# \text{ neurons}] \tag{7}$$

E= egg number /female D= egg development time (days).

Another way to calculate the birth rate is:

$$\mathbf{k} = \mathbf{b} + \mathbf{d} \tag{8}$$

therefore:

$$\mathbf{b} = \mathbf{k} \cdot \mathbf{d} \tag{9}$$

Individuals average number (N�):

$$\bar{\mathbf{N}} = \frac{(\text{No} + \text{N}\_t)}{2} \tag{10}$$

No=individuals initial number Nt=individual number after a period of time t

Biomass productivity (Pw):

$$\mathbf{P}\_{\mathcal{W}} = \mathbf{b}^\* \overline{\mathbf{N}}^\* \overline{\mathbf{W}} \equiv \left[ \frac{\text{Biomass}}{\text{Volume}} \ast \frac{1}{\text{Time}} \right] \tag{11}$$

W̅=Final weight at the end of the period. N̅= Individuals media number b= birth rate population, in a period of time.

Mortality rate (d):

$$\text{Ind} = \frac{\text{Ln(Final pop. of encounters)} \cdot \text{Ln(Initial pop. of encounters)}}{\text{T}} \equiv \left[\frac{\text{1}}{\text{day}}\right] \tag{12}$$

Biomass (B):

$$\text{B} = \frac{\text{(Average number)\*(Final weight)}}{\text{T}} \equiv \left[\frac{\text{Biomass}}{\text{Volume}}\right] \tag{13}$$

Production rate (I de P):

$$\text{I de P=} \frac{\text{P}}{\text{B}}\tag{14}$$

Final weight (pf) was determined as dry weight. Every Daphnia was dried up with tissue paper (analytical scale, 0.0001g. precision), expressed in mg/L.

#### **6.2 Reproductive variables**

Egg number/female (HPP). The egg number/female was determined in the microscope (10x and 40x).

Neonate number/female (NPP). This count was made directly.

The measurement of the rest of the variables was taken directly from the data base, such as:

Egg development time (tm), number of days passed between the appearance of the egg in the incubation chamber and the presence of the neonate.

Offspring number (NC)

First reproduction age (EPR), in days.

Production frecuency (FR), in hours.

The born individuals were moved to another tank with the same treatment. Neonate mortality was evaluated here.

#### **6.3 Life history parameters**

Daily measurements were made in 32 young breeders and in 32 adults, keeping a follow up during the 21 days (duration of the research). The frequency of the observation was 12 hours to differentiate seeded population and produced population.

The reproduction net rate (Ro) and the generation time (Tc), were calculated according to the Lotta equation (1913).

$$\sum\_{\mathbf{x}=0}^{n} \mathbf{l}\_{\mathbf{x}} \mathbf{m}\_{\mathbf{x}} \text{(exp}^{\text{-}\text{rx}}) = \mathbf{1} \tag{15}$$

lx= survival in a specific time starting in the birth period. mx= fertility in a specific period x=period (from 0 to 21 days) r= intrinsic grow rate

Net reproduction rate (Ro):

252 Aquaculture

Ln�Final pop. of neonates)-Ln�Initial pop. of neonates)

I de P= P B

Final weight (pf) was determined as dry weight. Every Daphnia was dried up with tissue

Egg number/female (HPP). The egg number/female was determined in the microscope (10x

The measurement of the rest of the variables was taken directly from the data base, such as: Egg development time (tm), number of days passed between the appearance of the egg in

The born individuals were moved to another tank with the same treatment. Neonate

Daily measurements were made in 32 young breeders and in 32 adults, keeping a follow up during the 21 days (duration of the research). The frequency of the observation was 12 hours

The reproduction net rate (Ro) and the generation time (Tc), were calculated according to

B= �Average number)\*�Final weigth)

paper (analytical scale, 0.0001g. precision), expressed in mg/L.

Neonate number/female (NPP). This count was made directly.

the incubation chamber and the presence of the neonate.

to differentiate seeded population and produced population.

<sup>T</sup> � � <sup>1</sup>

<sup>T</sup> � �Biomass

day� (12)

(14)

Volume � (13)

W̅=Final weight at the end of the period.

b= birth rate population, in a period of time.

N̅= Individuals media number

d=

Production rate (I de P):

**6.2 Reproductive variables** 

Offspring number (NC)

mortality was evaluated here.

**6.3 Life history parameters** 

the Lotta equation (1913).

First reproduction age (EPR), in days. Production frecuency (FR), in hours.

Mortality rate (d):

Biomass (B):

and 40x).

$$\mathbf{R\_o = \sum\_{\chi=0}^{n} 1\_{\chi} \mathbf{m\_{\chi}}} \tag{16}$$

Generation time (Tc):

$$\mathbf{T} = \mathbf{1} \Big/\_{\mathbf{R}\_o} \sum\_{\mathbf{x}=\mathbf{0}}^{\mathbf{n}} \mathbf{1}\_{\mathbf{x}} \mathbf{m}\_{\mathbf{x}} \mathbf{x} \tag{17}$$

Where Ro= net reproductive rate and Tc= generation time.

#### **6.4 Statistical methodology**

An experimental classification design was used, fully randomized, fixed effect, symmetric, balanced, 23 factorial arrangement, with 4 replicas, n=32 to each population. The results were compared through ANOVA and Tukey test with α=0.05. An exploratory descriptive analysis, one-dimensional for each condition type, was established. Data transformation to the square root function was used on egg number/female and neonates number variables. For survival and mortality percentages, arcsine transformation was applied. SAS version 9.1 Statistical package was used.

$$\mathbf{T} = \mathbf{1}\_{\parallel} \Big|\_{\mathbf{R}\_{\odot}} \sum\_{\mathbf{x}=\mathbf{0}}^{n} \mathbf{1}\_{\times} \mathbf{m}\_{\times} \,\mathrm{X}$$

$$Y\_{ij:k} = \mu + L\_i + P\_j + E\_s + LP\_{ij} + LE\_{is} + PE\_{js} + LPE\_{ijs} + \mathcal{E}\_{k\{js\}} \tag{18}$$

Where*Yijsk* : represented de number variable of *Daphnia magna.* 

: Experiment average effect

*Li* : Yeast effect

*Pj* : Potato dosage effect

*Es* : Enrichment effect

*k ijs* ( ) : Experimental error Additionally, a comparison test with adult population and young breeders was made. To do this, the Mann Whitney test was applied, for the productive variables: daily average density (Dmd), doubling time (Td), specific growth rate (k), performance (r) and biomass productivity (Pw) and for reproductive parameters: egg number/female (HPP), neonates number/female (NPP), litter number (NC), net reproduction rate (Ro) and generation time (Tc). A correlation analysis was completed between the variables. For reproduction net rate and generation time, one way analysis of the variance and the Tukey test took place, in order to compare the life history parameters between the different diets.
