Linear Response Plateau Model Research Articles

Optimal treatment placement for on-farm experiments: pseudo-Bayesian optimal designs with a linear response plateau model

Optimal treatment placement for on-farm experiments: pseudo-Bayesian optimal designs with a linear response plateau model

Use of statistical models to determine the optimal concentration of metabolizable energy for growth performance of broiler chickens

The formulation of diets that adequately meet energy requirements in the different phases of broiler chicken production is of the utmost importance. The objective of this study was to determine the optimal content of metabolizable energy (ME) for broiler chickens in various production phases using different statistical models. A total of 900 broiler chickens were assigned to 5 treatments with 9 replicates of 20 broiler chickens each from 21 to 42 d of age in a completely randomized design. Experimental diets were based on corn and soybean meal and formulated to meet the nutritional requirements of broiler chickens, except for ME requirements. Dietary treatments consisted of 5 pelleted/crushed diets with increasing levels of ME: T1 to T5 (2,850 to 3,250 kcal/kg), divided into grower (21 to 35 d) and finisher (35 to 42 d) phases. Feed intake (FI), body weight gain (BWG), feed conversion ratio (FCR), total energy intake, efficiency of energy use for BWG, and carcass and cuts yields were determined. The ideal ME content for best FCR was determined with the use of quadratic polynomial (QP), segmented, and linear response plateau models (LRP). In all evaluated periods, BWG was not influenced by ME, whereas FI and FCR decreased linearly with increasing ME. Total energy intake increased and the energy use efficiency for BWG decreased with greater ME (P < 0.05). Neither carcass nor cuts yields were influenced by dietary ME. The ideal dietary ME content differed between statistical models. In conclusion, based on FCR results, the QP regression model presented the best fit of the data in the grower phase, indicating an optimal content of metabolizable energy for feed conversion of 3,264 kcal/kg, whereas LRP presented the best data adjustment in the finisher phase, indicating 3,224 kcal/kg of ME as optimal.

Rice bran as a substitute for soy protein and erythorbate in chicken nuggets

The aim of this work was to compare three methods of estimating the optimal plot size for evaluating fresh matter in the IPR91-Baili and IPR92-Altar cultivars of buckwheat (Fagopyrum esculentum Moench). Sixteen uniformity trials (blank experiments) were conducted, eight with the IPR91-Baili cultivar and eight with the IPR92-Altar cultivar. The trials were carried out at eight different sowing times. The fresh matter was evaluated in 576 basic experimental units (BEU), each 1 m × 1 m in size (36 BEU per trial). The optimal plot size was determined using the method of modified maximum curvature, the linear response plateau model and the quadratic response plateau model. The optimal plot size differs between methods, and decreases in the following order: quadratic response plateau model, linear response plateau model and modified maximum curvature. The optimal plot size for evaluating fresh matter in the IPR91-Baili and IPR92-Altar cultivars of buckwheat is 7.60 m2. This size can be used as a reference for future experiments with buckwheat.

Methods for Estimating Optimum Plot Size for ‘Gigante’ Cactus Pear

The optimum plot size for &amp;lsquo;Gigante&amp;rsquo; cactus pear can be estimated by several methods; thus, ultimately aiming for efficiency, simple use and high precision, the objective of this study was to compare methods for estimating plot sizes: modified maximum curvature method, Hatheway&amp;rsquo;s convenient plot size method, linear and quadratic response plateau models, and comparison of variances method for evaluating phenotypic characteristics in experiments with &amp;lsquo;Gigante&amp;rsquo; cactus pear. Plot sizes were estimated by conducting a uniformity trial. Estimated optimum plot sizes varied with the method and vegetative characteristic. The quadratic response plateau regression estimated the largest plot sizes, whereas Hatheway&amp;rsquo;s method estimated the smallest plot sizes. Comparison of variances method estimated intermediate plot sizes in comparison with the other methods for most measured characteristics. Plots sizes estimated by modified maximum curvature method are more consistent with results reported by studies on &amp;lsquo;Gigante&amp;rsquo; cactus pear. 10 basic unit plot sizes estimated by the linear response plateau model can be used with high precision and practical feasibility for growing cactus pear, thereby improving the use of resources.

The optimum valine: lysine ratios on performance and carcass traits of male broilers based on different regression approaches

ABSTRACTThree different regression approaches were applied to determine the optimal digestible (d.) and analyzed Val:Lys ratios for broiler performance and carcass yield. One-day-old male Cobb 500 broilers (n = 960) were assigned to 1 of 8 diets, with 6 pens/diet and 20 birds/pen, for 42 days. The negative control consisted of the basal diet with a d.Val:d.Lys ratio of 0.63 and with 93% of the required d.Lys. The positive control consisted of the basal diet with a d.Val:d.Lys of 0.80, with no reduction in d.Lys content. The other (test) diets contained a range of d.Val:d.Lys ratios, all with 93% of the required d.Lys. Data on feed intake (FI), body weight gain (BWG), and feed conversion ratio (FCR) were submitted to regression analysis, applying quadratic polynomial (QP), exponential asymptotic (EA), and linear response plateau (LRP) models. Since Val did not affect carcass or breast meat yield, no regression was performed. Digestible and analyzed Val:Lys ratios were similar based on the regression models. The intercept between the QP and LRP models was used to determine the optimum Val:Lys ratio. Overall, the ideal d.Val:d.Lys ratio will vary according to the main goal of poultry production, i.e., BWG or FCR. For BWG, the ideal ratio was found to be 0.78 (0 to 12 d), 0.73 (0 to 28 d), and 0.76 (0 to 35 or 0 to 42 d). For FCR, the optimum d.Val:d.Lys was found to be 0.80 (0 to 12 d), 0.75 (0 to 28 d), and 0.78 (0 to 35 or 0 to 42 d). The optimum analyzed Val:Lys ratio was slightly higher. For instance, for BWG the optimum ratio was 0.80 (0 to 12 d), 0.76 (0 to 28 d), and 0.79 (0 to 35 or 0 to 42 d). For FCR, the optimum Val:Lys was 0.81 (0 to 12 d), 0.79 (0 to 28 d), and 0.81 (0 to 35 or 0 to 42 d). Valine did not affect carcass or breast meat yield.

Optimum experimental plot size in the castor bean

Optimum plot size is of fundamental importance for the results, precision and cost-effectiveness of experiments. The aim of this study therefore, was to estimate optimum plot size in a strain of the castor bean by means of the Linear Response Plateau Model (LRPM). The experiment consisted of a test for uniformity, carried out in Cruz das Almas, in the State of Bahia, Brazil. The UFRB-222 strain was used, which was planted at a spacing of 3 m x 1 m, in 10 rows of 37 plants each. The eight central rows were considered, each with 35 plants per row giving a total of 280 plants and a working area of 840 m2. For the evaluations, each plant was taken as one basic unit (bu) with an area of 3 m2, resulting in 280 bu. The characteristics under evaluation were the number of racemes harvested, the mean length of the first three racemes, number of seeds per raceme, seed weight per raceme, raceme weight per plant, number of seeds per plant and productivity. For productivity and its components, the optimum plot size is 11 experimental units in an area of 33 m2, at a spacing of 3 m between rows and 1 m between plants.

Phosphorus requirements of tambaqui juveniles

The aim of this study was to determine the requirement of digestible phosphorus in diets for juvenile tambaqui (Colossoma macropomum). 300 juveniles (26.4 ± 0.68 g) were used in a completely randomized design, consisting of six treatments with five replicates and 10 fish per experimental unit. The treatments consisted of six isoprotein, isonitrogenous, and isocalcium rations, with different levels of digestible phosphorus: 0.27; 0.46; 0.67; 0.91; 1.04; and 1.14%. The fish were kept in 30 polyethylene tanks (500 L) with a closed water circulation system and fed six meals per day for 49 days. Parameters of performance and feed efficiency, daily protein, and fat, ash, and phosphorus deposition rates were evaluated. The elevation of digestible phosphorus provided a quadratic increase in feed consumption to a level of 0.92%, linear increase in the consumption of digestible phosphorus, and quadratic reduction in the efficiency of digestible phosphorus for weight gain. The linear response plateau model was the best fit for weight gain and specific growth rate, estimated at 0.55% and 0.56% digestible phosphorus, respectively. The feed conversion and protein efficiency for weight gain improved quadratically up to an estimated level of 0.84% of digestible phosphorus. Body fat deposition improved quadratically up to an estimated level of 0.90% of digestible phosphorus. The linear response plateau model was the best fit for body deposition of protein, ash, and phosphorus, estimated at 0.55%, 0.46%, and 0.59% of digestible phosphorus, respectively. To optimize weight gain, the recommended level of digestible phosphorus in diets for juvenile tambaqui is 0.55%, which corresponds to an estimated level of 0.87% of total phosphorus.

Crude protein levels in diets for two growth stages of Nile tilapia (Oreochromis niloticus) in a biofloc system

Biofloc technology (BFT) provides an additional feed source for aquatic organisms through the conversion of waste in microbial flocs. Because of this, the suitable protein level in a diet for animals in this system could be different from those in conventional systems. Our objective was to determine the suitable protein level in the diet of Nile tilapia juveniles reared with BFT. Two experiments were carried out with tilapia weighing ~10 g (first experiment) and about 50 g (second experiment) during 61 and 98 days respectively. Five crude protein (CP) levels (within 17% and 33%) were tested. The increment of CP resulted in a reduction in dissolved oxygen, pH, alkalinity and an increase in dissolved phosphorus, total suspended solids and total ammonium nitrogen. The crude protein level had a significant effect (p < 0.05) on animal performance. The linear response plateau model was the best fit for the final weight and weight gain data in the two growth phases. In conclusion, tilapia juveniles of 10–60 g and 60–230 g in biofloc can be fed on diets with 28% of CP (26% of digestible protein) and 22% CP (20% of digestible protein) respectively.

Energy coefficients of plant foods for broiler chickens at different ages

In order to determine the apparent metabolizable energy (AME), the AME corrected for nitrogen balance (AMEn), the apparent coefficients of metabolization (ACM) of gross energy and the ACM corrected for nitrogen balance (ACMn), an experiment was conducted to evaluate five different plant foods (corn, soybean meal, deactivated full-fat soybean, wheat bran and soybean oil) for broilers at different ages (1-8, 11-18, 21-28, 31-38 and 41-48 days). The method of total excreta collection was used, divided into five metabolism assays. The birds were housed in metabolic cages in a completely randomized design, with five treatments and five replicates per treatment, totaling 25 experimental units. The AME and AMEn values increased with the age of the birds for most foods, except soybean meal. The smaller AMC and AMCn of gross energy were obtained for wheat bran. There was adjustment of the equation to the linear response plateau model for the ACM of corn, soybean meal and deactivated full-fat soybean. The wheat bran and soybean oil were adjusted to the linear regression model. The equations show that the digestibility of energy tends to increase with age, except for soybean meal, which had higher metabolization with younger birds. We conclude that the age of the birds influences the determination of the metabolizable energy of feed.

Digestible tryptophan to lysine ratios for weaned piglets at 26 days of age

With the objective of determining the optimal digestible tryptophan to lysine ratios (Trp : Lys) in feed, 192 crossbred piglets were weaned at 26.3 ± 2.0 days, with initial weights of 8 ± 0.360 kg. The piglets were blocked by bodyweight and randomly allotted into six treatments, eight repetitions and four piglets per experimental unit. The treatments included five ratios of digestible Trp : Lys of 0.15, 0.17, 0.19, 0.21 and 0.23 with 1.26% digestible lysine and one positive control treatment (C+) with a Trp : Lys ratio of 0.19 and digestible lysine of 1.33%. The piglet’s performance and other characteristics were evaluated in phases: Phase I lasted from weaning up to Day 14 of the experiment, and Phase II lasted from weaning up to Day 21 of the experiment. The feed intake during Phase I, including the protein and fat deposition rates, the kidney relative weights and carcass yield were not influenced by the Trp : Lys ratios (P &gt; 0.05). The Trp : Lys ratios had a linear effect on the liver and kidney absolute weights (P &lt; 0.05). The ratio also had a linear effect (P &lt; 0.01) on the bodyweight, the average daily gain, the gain : feed ratio of the piglets during Phases I and II and on the feed intake during Phase II (P &lt; 0.05). The effect of the Trp : Lys ratios on the digestible lysine level (P = 0.04) demonstrated that digestible lysine was a limiting factor. The Linear Response Plateau model indicated that the best Trp : Lys ratio (P = 0.04) was 0.20 during Phase I and 0.22 (P &lt; 0.01) during Phase II. Thus, the optimal digestible Trp : Lys ratio for piglets during the initial growth phase (from 26 to 47 days of age) is 0.22.

Tamanho ótimo da parcela experimental de abacaxizeiro 'Vitória'

No planejamento experimental, a parcela experimental é um fator determinante para o sucesso da pesquisa. Portanto, é necessário que o pesquisador defina adequadamente a constituição da parcela ou unidade experimental, no intuito de aumentar a eficiência do experimento e diminuir o erro experimental. Em decorrência da grande variabilidade no tamanho da parcela encontrada nos experimentos com abacaxizeiro, realizou-se uma pesquisa objetivando estimar o tamanho ótimo para parcelas experimentais, considerando diferentes características. Os dados utilizados para este trabalho foram coletados em 100 plantas de abacaxizeiro 'Vitória'. Foram coletados 100 frutos e 100 folhas "D" de plantas cultivadas na mesma área experimental e submetidas às mesmas práticas de cultivo. Foram avaliados nos frutos: o comprimento, o diâmetro e a massa. Na folha "D", foram avaliados o comprimento e a massa, além dos teores de N, P e K. As estimativas do tamanho da parcela foram baseadas nos métodos do modelo linear de resposta a platô e da curvatura máxima. O tamanho ótimo da parcela para a avaliação do abacaxizeiro 'Vitória' é de 15 a 20 unidades experimentais por parcela, para as características dos frutos e das folhas, pelo método do modelo linear de resposta a platô. Para a avaliação dos teores de N, P e K, 10 folhas representam o tamanho ótimo da parcela pelo método do modelo linear de resposta a platô. Por outro lado, o tamanho ótimo da parcela para avaliação dos frutos e das folhas do abacaxi 'Vitória' é de 1,7 a 2,8 unidades experimentais pelo método da curvatura máxima. Enquanto, para os teores de N, P e K, 3 a 5 unidades experimentais representam o tamanho ótimo da parcela pelo método da curvatura máxima.

Positioning and number of nutritional levels in dose-response trials to estimate the optimal-level and the adjustment of the models

The aim of this research was to evaluate the influence of the number and position of nutrient levels used in dose-response trials in the estimation of the optimal-level (OL) and the goodness of fit on the models: quadratic polynomial (QP), exponential (EXP), linear response plateau (LRP) and quadratic response plateau (QRP). It was used data from dose-response trials realized in FCAV-Unesp Jaboticabal considering the homogeneity of variances and normal distribution. The fit of the models were evaluated considered the following statistics: adjusted coefficient of determination (R²adj), coefficient of variation (CV) and the sum of the squares of deviations (SSD).It was verified in QP and EXP models that small changes on the placement and distribution of the levels caused great changes in the estimation of the OL. The LRP model was deeply influenced by the absence or presence of the level between the response and stabilization phases (change in the straight to plateau). The QRP needed more levels on the response phase and the last level on stabilization phase to estimate correctly the plateau. It was concluded that the OL and the adjust of the models are dependent on the positioning and the number of the levels and the specific characteristics of each model, but levels defined near to the true requirement and not so spaced are better to estimate the OL.

Reduction of the crude protein content of diets supplemented with essential amino acids for piglets weighing 15 to 30 kilograms

Two experiments were carried out to evaluate the reduction of crude protein (CP) in diets supplemented with synthetic amino acids for piglets of 15 to 30 kg. In the performance assay (Exp I), 60 piglets with initial weight of 15.34±0.87 kg and final weight of 30.08±1.59 kg were distributed in a randomized block design with six replicates, five treatments and two animals per experimental unit. The treatments consisted of five diets in which the CP was reduced by 1.5 percentage points, resulting in low-protein diets (19.24, 17.74, 16.24, 14.74 and 13.24%), meeting the requirements of amino acids with inclusion of L-lysine, DL-methionine, L-threonine, L-tryptophan, L-valine and L-isoleucine. The average daily gain and feed conversion according to the Linear Response Plateau model (LRP) were estimated at 14.23 and 14.79% of CP, respectively. As the CP levels were reduced, there was an increase in the essential:non-essential amino acids ratio. The plasma urea concentration decreased linearly, indicating that there was a better use for amino acids with the CP reduction. In the nitrogen balance (Exp II), 30 crossbred barrow piglets with average weight of 21.69±4.46 kg were housed in metabolic cages, distributed in a completely randomized design with five treatments and six replicates, and the experimental unit consisted of a piglet. The biological protein value in the diets remained above the ideal (70%), in which the level of 13.24% CP corresponded to the highest value. There was no difference in levels of urea in blood and urine. Reduction of protein levels is efficient in decreasing the pollution effect in the excreta, with lower nitrogen excretion in feces and urine.

Protein and Digestible Threonine Levels in Pre Starter Diets for Broiler Chicks

This experiment was carried out in experimental poultry facilities of University of Goias to estimate digestible threonine (Thr) requirement for broiler from 1 to 21 days of age. 384 AgRoss-508 broiler chicks were allotted in a completely randomized design in a 4 x 2 factorial arrangement, with two protein levels (205 and 221 g/kg) and four digestible threonine levels (6.1, 7.1, 8.1 and 9.1 g/kg) with four replications of 12 birds each. The performance, nutrient digestibility and morfometrical index were evaluated. The polynomial regression and linear response plateau (LRP) model was used to estimate digestible, had been the Minimum Square of Deviations (MSD) utilized for choice criterion. Used polynomial regression, the results showed that a quadratic effect (p<0.05) for mean body weight at seven and 21 days of age (seven days - Y = -31.41 + 455.28x - 285.62x /21 days - Y = 510.08 + 508.91x - 324.61x ) which estimates a 7.9 and 7.1 g/kg 2 2 of digestible Thr, but LRP model showed low MSD and smaller estimates for digestible Thr levels (7.7 and 6.7 g/kg in seven and 21 days, respectively). The results showed a tendency if lower levels of digestible Thr (below to 7.1 g/kg) reduced intestinal length. The digestible Thr levels recommended for pre-starter phase vary from 7.7 at 6.7 g/kg, estimated by LRP model and 7.9 at 7.1 g/kg estimated by polynomial regression for mean body weight at seven and 21 days of age, respectively, but the LRP values presented smaller minimum square of deviations.

Níveis de lisina digestível de fêmeas suínas selecionadas para deposição de carne magra na carcaça dos 30 aos 60kg

Utilizaram-se 50 leitoas de alto potencial genético para deposição de carne magra na carcaça, com peso inicial de 30,17 ± 2,03, a fim de avaliar o efeito de níveis crescentes de lisina digestível sobre o desempenho e características de carcaça. Os animais foram distribuídos em delineamento experimental de blocos ao acaso, com cinco tratamentos (0,83; 0,93; 1,03; 1,13 e 1,23% de lisina digestível), cinco repetições e dois animais por unidade experimental. Na distribuição dos animais dentro de cada bloco foi adotado como critério o peso inicial dos animais. Não foi observado efeito dos níveis de lisina digestível sobre o consumo de ração diário e ganho de peso diário. Observou-se efeito quadrático dos tratamentos sobre a conversão alimentar, que melhorou até o nível estimado de 1,11% de lisina digestível. Foi observado efeito linear dos níveis de lisina sobre a taxa de deposição de proteína diária, entretanto, o modelo Linear Response Plateau foi o que melhor se ajustou aos dados e estimou o nível de 1,09% de lisina digestível para melhor deposição de proteína diária. Não foi observado efeito dos tratamentos sobre a taxa de deposição diária de gordura. Conclui-se que o nível de 1,11% de lisina digestível proporciona os melhores resultados de desempenho e de taxa de deposição de proteína diária na carcaça de fêmeas suínas de alto potencial genético para deposição de carne magra na carcaça, dos 30 aos 60kg.

Exigências em treonina para frangos de corte de 22 a 42 dias de idade

Um experimento foi realizado com o objetivo de estabelecer critérios de avaliação das exigências de treonina digestível para frangos de corte de 22 a 42 dias de idade utilizando-se diferentes modelos de regressão (quadrático, exponencial e de retas segmentadas ou Linear Response Plateau). Foram utilizados 1.920 frangos de corte machos com 22 dias de idade, distribuídos em delineamento inteiramente ao acaso, com seis tratamentos (seis níveis de treonina digestível: 0,5904; 0,6441; 0,6977; 0,7514; 0,8051 e 0,8588%) e oito repetições de 40 aves. Utilizou-se como padrão o nível de 0,6977% de treonina digestível. Foram avaliados dados de desempenho e características de carcaça. Com base nos dados, o nível de 0,7642% de treonina digestível, correspondente às relação treonina:lisina digestível de 71,19%, promoveu o melhor resultado de conversão alimentar de acordo com o modelo Linear Response Plateau.

Métodos de estimativa do tamanho ótimo de parcelas experimentais de híbridos de milho simples, triplo e duplo

O objetivo deste trabalho foi comparar os métodos de estimativa do tamanho ótimo de parcela e verificar a variabilidade do tamanho ótimo de parcela entre híbridos simples, triplo e duplo de milho. Para isso, foram usados os dados de produtividade de grãos de milho de 16 ensaios de uniformidade com o híbrido simples (P32R21), 16 com o híbrido triplo (DKB566) e 16 com o híbrido duplo (DKB747). Cada ensaio foi composto de quatro linhas de 6m de comprimento, dividido em unidades experimentais básicas de um metro linear. Em cada um dos 48 ensaios foi determinado o tamanho ótimo de parcela por meio dos métodos da curvatura máxima modificada, do modelo linear de resposta com platô e da curvatura máxima do modelo do coeficiente de variação. Foi utilizado o coeficiente de correlação de Spearman para verificar a associação entre os métodos e o teste t para comparar as médias. Há concordância na estimativa do tamanho ótimo de parcelas experimentais de milho simples, triplo e duplo por meio dos métodos da curvatura máxima modificada e da curvatura máxima do modelo do coeficiente de variação. Por esses métodos, o tamanho ótimo de parcela entre os híbridos de milho é de seis unidades experimentais básicas para o híbrido simples e cinco para os híbridos triplo e duplo.

Relationship of methionine plus cystine with lysine in diets for laying Japanese quails

The objective of this work was to evaluate the relationships of methionine plus cystine with lysine for Japanese quails in the laying phase. Thus, it was used 480 birds at initial age of 65 days, distributed in randomized block design with 6 treatments, 10 replicates and 8 birds per experimental unit. The treatments consisted of basal diet deficient in methionine plus cystine (0.65%), with 19.6% of crude protein and 2800 kcal of metabolizable energy/kg of ration, supplemented with six levels of DL-methionine 98% (0.116; 0.167; 0.218; 0.269; 0.320 and 0.371%), corresponding to methionine plus cystine with lysine ratio of 0.65, 0.70, 0.75, 0.80, 0.85 and 0.90, and the digestible lysine set at a suboptimal level of 1.00. The parameters studied were: feed intake, egg production per hen day, egg production per housed hen, commercial egg production, egg weight, egg mass, feed conversion per egg mass, feed conversion per dozen eggs, viability of birds, weight of the egg components (yolk, albumen and shell), percentage of components of eggs, diameter and height of the eggs and specific gravity. It was observed an increasing linear effect for feed intake, egg diameter, shell weight and percentage of yolk. For eggshell percentage, it was observed a decreasing linear effect. For the weight of the eggs, the best adjustment was obtained by using the Linear Response Plateau model. A quadratic effect was observed for egg mass, feed conversion per egg mass, egg production per hen day, egg production per housed hen, yolk weight, albumen weight and height of the eggs. The relationship of methionine plus cystine with lysine of 0.84 which corresponds to the consumption of 221.0 mg/bird/day of methionine + cystine provides better performance and satisfactory quality of Japanese quail eggs.

Effects of Applying Nitrogen on Yield of Introduced Perennial Summer Grass Cultivars in Oklahoma

Effects of Applying Nitrogen on Yield of Introduced Perennial Summer Grass Cultivars in Oklahoma

Níveis de lisina digestível em rações para alevinos de tilápia-do-nilo

Avaliaram-se níveis de lisina digestível em rações para alevinos de tilápia-do-nilo (Oreochromis niloticus), linhagem tailandesa, com base no conceito de proteína ideal. Utilizaram-se 432 alevinos com peso inicial de 0,98 ± 0,03 g, distribuídos em delineamento inteiramente casualizado, com 6 tratamentos, 6 repetições e 12 peixes por unidade experimental. Os tratamentos constaram de seis rações isoenergéticas (3.000 kcal de ED/kg de ração) e isoproteicas (39,14% de PB) contendo 1,50; 1,66; 1,82; 1,98; 2,14 ou 2,30% de lisina digestível. Foram avaliados o consumo de ração, o consumo de lisina digestível, o ganho de peso, a taxa de crescimento específico, a taxa de sobrevivência, a conversão alimentar, as taxas de deposição diária de proteína e gordura corporais, a composição química corporal (teores de umidade, proteína e gordura corporais) e a eficiência de retenção de nitrogênio. O consumo de lisina digestível, a conversão alimentar, a porcentagem de proteína corporal e a deposição de proteína corporal melhoraram de forma linear de acordo com o nível de lisina digestível. O modelo Linear Response Plateau foi o de melhor ajuste para consumo de ração, ganho de peso, taxa de crescimento específico e eficiência de retenção de nitrogênio e estimou em 2,06; 2,17; 2,14 e 2,12%, respectivamente, os níveis de lisina digestível para melhorar cada um desses parâmetros. A exigência de lisina digestível e total em rações para alevinos de tilápia-do-nilo é, respectivamente, de 2,17% (0,723%/Mcal de energia digestível) e de 2,32% (0,773%/Mcal de energia digestível) para atender às principais características de desempenho e de carcaça utilizando-se o conceito de proteína ideal na formulação das rações.