ABSTRACT Nitrogen (N) is essential to the fertilization of coffee. The fertilizer most used to meet this demand is urea, although it has high rates of N loss due mainly to ammonia volatilization. To reduce this loss, fertilizers with increased efficiency have emerged. Thus, the aim was to select the most appropriate nonlinear regression model to describe N loss attributable to ammonia volatilization in slow- and controlled-release fertilizers applied to coffee plants and to compare the different fertilizers based on the parameters of the selected model. The data studied are controlled-release fertilizers: urea + sulfur + polymer (U+S+P), urea + plastic resin (U+PR), urea + polymer insoluble in water (U+PIW) and slow-release fertilizer: urea formaldehyde (UF) applied to coffee. The Gompertz, Brody, and von Bertalanffy Logistics models were fit by the least squares method. The goodness of fit was assessed using the adjusted coefficient of determination, mean absolute deviation, and Akaike's information criterion. The von Bertalanffy model was the most appropriate for describing the data in most cases. After selecting the best model for the means, the parameters of the von Bertalanffy model were estimated again for each repetition of treatments. With the repetitions of the parameter estimates of these models, the F test of analysis of variance (ANOVA) and Tukey's test were applied. In the F test, p < 0.05 for all parameters. In the Tukey's test, the UF fertilizer reached the asymptote more quickly and presented a lower accumulated loss of N in the coffee tree. The fertilizers U+S+P and U+PIW have later inflection points (IP). (N emerged Thus slow controlledrelease controlled release U+S+P, USP , U S P (U+S+P) U+PR, UPR U+PR PR (U+PR) UPIW PIW (U+PIW slowrelease (UF Gompertz Brody method determination deviation Akaikes Akaike s criterion cases means treatments ANOVA (ANOVA Tukeys Tukey 005 0 05 0.0 tree IP. IP . (IP) (U+S+P (U+PR 00 0. (IP

Resumen Los pinos tropicales son importantes por la cantidad de madera que producen en periodos cortos de tiempo. Para ello, se requieren de funciones alométricas para predecir la altura total de los árboles, ya que es una de las variables indispensables para calcular el volumen total y comercial. El objetivo de la investigación fue desarrollar una función alométrica local y una generalizada para modelar la relación altura total-diámetro normal (at-dn) de Pinus caribaea var. hondurensis y del hibrido Pinus caribaea var. hondurensis × Pinus tecunumanii en la Sierra Norte de Puebla, México. Para analizar las relaciones se usaron 1 232 pares de datos de at-dn. Se ajustaron modelos alométricos con tres parámetros con el 80% de los datos y se validaron con el 20%. El mejor modelo fue el que presentó el menor sesgo promedio, raíz del error medio cuadrático y Criterio de Información de Akaike, así como el de mayor coeficiente de determinación ajustado. Los modelos explicaron más del 58.55% de la variabilidad en la at observada en los árboles. El modelo Logístico y de Weibull obtuvieron los mejores desempeños en el ajuste y validación, y estimaron con menor incertidumbre la at de los pinos tropicales. Las funciones alométricas ajustadas son confiables para predecir la at de los árboles, por lo que puede contribuir al manejo sustentable de plantaciones comerciales de pinos tropicales en la región de estudio.

Abstract Tropical pines are important because of the amount of wood they produce in short periods. However, it requires allometric functions to predict the total tree height, since it is one of the critical variables to estimate both, it is the total and commercial volume. Accordingly, we aimed to develop a local and a generalized allometric function for model the total height-diameter (h-d) relationship of Pinus caribaea var. hondurensis and hybrid Pinus caribaea var. hondurensis × Pinus tecunumanii in the Sierra Norte of Puebla, México. In order to analyze the relationships, 1 232 h-d pairs were used. The allometric models were fitted with three parameters totaling 80% of the data and validated with 20%. The best model had the lowest average bias, root mean square error, and Akaike’s Information Criterion, as well as of the highest adjusted coefficient of determination. The models explained over 58.55% of the variability in observed total tree height. Nonetheless, the Gompertz and Weibull models obtained the best performances in fit and validation, and estimated h of tropical pines with less uncertainty. In consequence, the fitted allometric functions are reliable for predicting tree h; therefore, it can contribute to the sustainable management of commercial tropical pine plantations in the study region.

RESUMO: O objetivo deste trabalho foi avaliar algumas distribuições associadas ao erro na modelagem não linear bayesiana na descrição do acúmulo de matéria seca total da planta (MSTP) de Allium sativum em função dos dias após o plantio (DAP). Pelo critério DIC os modelos Logístico e Gompertz que utilizam a distribuição do erro t de Student apresentaram a melhor qualidade de ajuste, sendo que o modelo Logístico apresentou o maior DIC com a distribuição de erro Logística. No geral, a diferença de DIC em todos os cenários não apresentou valores superiores a cinco. Pelo critério do Fator de Bayes (FB), não houve diferença no ajuste do modelo Logístico e Gompertz quando se utilizam as quatro distribuições para os erros, sendo que os valores de FB não superaram 2. As distribuições a posteriori e os estimadores usuais dos parâmetros dos modelos Logístico e Gompertz apresentaram semelhanças mesmo variando a distribuição do erro. Em suma não houve diferença na utilização das quatro distribuições associadas ao erro na modelagem do crescimento planta de alho pelo fator de Bayes, sendo que os resultados mostram que alternar entre as distribuições dos erros altera de forma significativa o número de iterações de MCMC. RESUMO MSTP (MSTP DAP. DAP . (DAP) Logística geral cinco FB, , (FB) 2 MCMC (DAP (FB

ABSTRACT: This study assessed distributions associated with Bayesian nonlinear modeling error in the description of total plant dry matteraccumulation (TDMA) of Allium sativumas a function of days after planting (DAP). According to the DIC criterion, Logistic and Gompertzmodels that use student’s t distribution error exhibited the highest DIC with logistic error distribution. In general, the difference of DIC in all the scenarios was not more than 5.The Bayes factor (BF) criterion showed no difference in the Logistic and Gompertzmodel fit when four distributions are used for the errors, where BF values do not exceed 2. Posterior distributions and the usual estimators of Logistic and Gompertz model parameters were similar even forvaried error distribution. In summary, there was no difference in the use of 4 distributions associated with the modeling error of garlic plant growth by the Bayes factor, whereby the results showed that alternating between error distributions significantly changes the number of Markov Chain Monte Carlo (MCMC) iterations. ABSTRACT TDMA (TDMA DAP. DAP . (DAP) students student s general 5The The 5 (BF errors 2 summary MCMC (MCMC iterations (DAP

RESUMO: Diante da importância de descrever o acúmulo de matéria seca total em acessos de alho e a vantagem dos Modelos Não Lineares Mistos (MNLM) nesse processo, o presente trabalho teve como objetivo comparar quatro equações não lineares (Gompertz, Logístico, Richards e von Bertalanffy) no ajuste do acúmulo de matéria seca total por planta de 30 acessos de alho. O objetivo também foi identificar os melhores acessos de acordo com cada parâmetro de crescimento, estimando os efeitos aleatórios em torno da média através do melhor entre os modelos. A análise foi realizada com o uso do software R. O melhor modelo foi o Logístico segundo os critérios utilizados para comparação (AIC, BIC, R a j . 2, EQM e EAM), apresentando estimativas mais próximas dos valores reais observados. De acordo com os efeitos aleatórios estimados por este modelo, que representam desvios da média, os acessos que apresentaram maior peso assintótico foram 4505, 4826 e 4500, enquanto os acessos 4826, 4837 e 4491 demoraram mais para atingir o ponto de inflexão da curva. A abordagem NLME utilizou apenas um ajuste por equação para obter informações sobre todos os indivíduos da amostra, ajustando eficientemente a matéria seca total acumulada e identificando os melhores acessos de acordo com os efeitos aleatórios estimados de seus parâmetros. RESUMO MNLM (MNLM processo Gompertz, Gompertz (Gompertz Bertalanffy 3 crescimento modelos AIC, AIC (AIC BIC 2 EAM, EAM , EAM) observados 4505 482 4500 483 449 curva amostra parâmetros 450 48 44 45 4

ABSTRACT: Given the importance of describing the accumulation of total dry matter in garlic accessions and the advantage of Nonlinear Mixed Effect Models (NLME) in this process, the present work research compared four nonlinear equations (Gompertz, Logistic, Richards, and von Bertalanffy) in the fit of accumulation of total dry matter per plant of 30 garlic accessions. The objective was also to identify the best accessions according to each growth parameter by estimating the random effects around the mean through the best among the models. The analysis was carried out using the R software. The best model was the Logistic according to the criteria used for comparison (AIC, BIC, R a j . 2, MSE and MAE), presenting estimates closer to the actual observed values. According to the random effects estimated by this model, which represent deviations from the mean, the accessions that showed the highest asymptotic weight were 4505, 4826 and 4500, while accessions 4826, 4837 and 4491 took longer to reach the inflection point of the curve. The NLME approach used one fit per equation to obtain information on all individuals in the sample, efficiently adjusting the accumulated total dry matter and identifying the best accessions according to the estimated random effects of its parameters. ABSTRACT (NLME process Gompertz, Gompertz (Gompertz Richards Bertalanffy 3 models software AIC, AIC (AIC BIC 2 MAE, MAE , MAE) values 4505 482 4500 483 449 curve sample parameters 450 48 44 45 4

ABSTRACT Adana dewlap pigeons are a special kind of pigeon bred in the Adana region of Turkey. These pigeons differ from other pigeon species due to their flight characteristics. In this study, the mathematical models that explain the growth dynamics of Adana pigeons were examined and the one capable of the best predictions was determined. The incubation period of pigeons happens two or three times per year. For this reason, only one or two pairs of pigeons can be yearly reared from an adult pair of pigeons. The hatchlings die before they reach adulthood for various reasons. In this study, 43-day body weight measurements of 88 pigeons reared over a 7-year period were used. The study was carried out by taking the average of the 43-day weight measurements of these 88 pigeons. Special Matlab codes were developed to estimate the parameters in the mathematical growth models used. The performance of the most commonly used growth models when explaining the growth dynamics of Adana pigeons is discussed in this study, an issue that to the best of our knowledge had not yet been studied. Among these growth models, the Richards growth function gave the best results. The new data set obtained from 43-day weight measurements of 88 pigeons was considered as a time series. For this purpose, a discrete-time stochastic Gompertz model (DTSGM) was used to explain the growth dynamics, and modeling was done to explain the growth of Adana pigeons. It is assumed that the unknown parameter in this model changes with time. The Kalman filter (KF) was used for the time-varying estimation of this parameter. The aim of the study was to investigate whether the model and estimation method considered in this way is suitable for explaining the growth dynamics of these birds. The results obtained by considering DTSGM and estimating its parameter with KF showed that MSE provides a good analysis tool for modeling daily weight in terms of mean absolute percent error (MAPE) and R 2 criteria. It is suggested that the use of DTSGM and KF is appropriate. Turkey characteristics determined year reason reasons 43day day 43 8 7year 7 studied series purpose discretetime discrete (DTSGM (KF timevarying varying birds MAPE (MAPE criteria appropriate 4

RESUMEN El aumento de la demanda de energía en el mundo hace necesaria la búsqueda de fuentes alternativas de energía. Considerando la amplia actividad agroindustrial y agropecuaria en Colombia, la generación de energía a partir de residuos de biomasa es una opción promisoria para satisfacer las necesidades energéticas del país. La digestión anaerobia (DA) es una buena alternativa para aprovechar estos residuos. En este estudio se identificaron varios sustratos potenciales para la generación de biogás utilizando sistemas de DA a través de una revisión de la literatura. Las vinazas, los residuos de la industria del aceite de palma, el estiércol porcino, los residuos de la industria del café y los desechos sólidos municipales se consideraron como sustratos potenciales para la DA. Considerando factores como la composición, la cantidad de residuos producidos, la disponibilidad y su relación con importantes actividades económicas colombianas, se seleccionaron tres sustratos para realizar experimentos de potencial bioquímico de metano (BMP). Los sustratos seleccionados fueron estiércol porcino (SM), efluente de la industria de aceite de palma (POME) y residuos de café (CR). Los valores de BMP obtenidos fueron 240, 465 y 314 y NmLCH4/g SV respectivamente. Se realizó un análisis de parámetros cinéticos para los experimentos de BMP con base en los modelos logístico y de Gompertz. Se vio que la digestión anaerobia de SM inicia más rápido que en los otros sustratos evaluados. Sin embargo, la tasa de producción de metano fue más alta para POME, seguida por CR. SM tuvo la tasa más baja de producción de metano. Los valores obtenidos de BMP, parámetros cinéticos y los recolectados durante la revisión de la literatura pueden ser de utilidad para el diseño e implementación de sistemas AD en Colombia. Aún más, debe prestarse atención a los sustratos como POME, que presentan un alto potencial de producción de energía.

ABSTRACT Increasing energy demands around the globe require alternative sources of energy. Considering the large amount of agro-industrial and agriculture-related activities in Colombia, energy generation from biomass waste is a promising option to meet the energy needs of the country. Anaerobic digestion (AD) is a good alternative to use these wastes. In this study, several potential substrates for biogas generation using AD systems were identified through a literature review. Vinasses, palm oil industry residues, swine manure, coffee industry residues, and municipal solid wastes were found as potential substrates for AD. Considering factors such as composition, the amount of waste production, availability, and their relationship with important Colombian economic activities, three substrates were selected to perform biochemical methane potential (BMP) experiments. The selected substrates were swine manure (SM), palm oil mill effluent (POME), and coffee residues (CR). The obtained BMP values were 240, 465, and 314 NmLCH4/g VS, respectively. An analysis of kinetic parameters analysis was conducted for the BMP experiments, based on the logistic and Gompertz models. It was seen that the AD of SM starts faster than in the other evaluated substrates. Nevertheless, the overall methane production rate was the highest for POME, followed by CR. SM had the lowest methane production yield. The obtained values of BMP, kinetic parameters, and those collected during the literature review can be useful for the design and implementation of AD systems in Colombia. Moreover, attention should be paid to substrates such as POME, which have a high energy production potential.

RESÚMEN Tradicionalmente se ha utilizado el modelo de von Bertalanffy como patrón único en el estudio del crecimiento de los peces, considerándolo a priori como el único modelo que se ajusta a los datos de longitud-edad de las especies; una consideración que genera incertidumbres en los valores de los parámetros de crecimientos que son estimados, por cuanto se sabe que existen otros modelos de crecimiento que podrían ajustarse igualmente a los datos de longitud-edad. En este sentido, en la región del Orinoco Medio se hizo anteriormente un estudio del crecimiento de Brachyplatystoma rousseauxii utilizando el modelo tradicional de von Bertalanffy, y los resultados fueron usados posteriormente para evaluar la población; de ahí que el objetivo del presente trabajo fue validar los resultados del trabajo anterior, ajustando los mismos datos de longitud-edad a los modelos de crecimiento de la familia U Richards, y seleccionando el de mejor ajuste usando el Criterio de la Información de Akaike (AIC). Tal como se demostró en el primer trabajo, el modelo tradicional de von Bertalanffy se ajustó a los datos longitud-edad retro calculados, pero solo en un 35,4 %; mientras que la mayoría (64,6 %) se adaptó a los modelos U von Bertalanffy, U Logístico y U Gompertz, sin superioridad alguna de ninguno de ellos en el ajuste. Los parámetros de crecimiento estimados a partir de un modelo promedio fueron algo diferente a los obtenidos en el trabajo anterior, y por lo tanto se hace necesario reevaluar el recurso, para conocer realmente su nivel de explotación en el Orinoco Medio.

ABSTRACT Traditionally, the von Bertalanffy model has been used as the only standard in the study of fish growth, considering it a priori as the only model that fits the length-age data of the species; a consideration that generates uncertainties in the values of the growth parameters that are estimated, since it is known that other growth models could also fit the length-age data. In this sense, in the Middle Orinoco region, a study of Brachyplatystoma rousseauxii growth was previously done using the traditional von Bertalanffy model, and the results were subsequently used to evaluate the population; hence the objective of the present work was to validate the results of the previous work, fitting the same length-age data to the growth models of the U Richards family, and selecting the best fit using the Akaike Information Criterion (AIC). As demonstrated in the first paper, the traditional von Bertalanffy model fitted the back-calculated length-age data, but only 35;4 %; while the majority (64,6 %) fitted the U von Bertalanffy, U Logistic, and U Gompertz models, with no superiority of any of them in the fit. The growth parameters estimated from na average model were somewhat from those obtained in the previous work, and therefore necessary to re-evaluate the resource to know its level of exploitation in the Middle Orinoco.

Resumen El objetivo fue el ajuste de un modelo no lineal (MNL) para evaluar la curva de crecimiento en bovinos Limousin, en pureza de raza (PRZ) y cinco grados de cruzamiento (GPZ; 1/2, 3/4, 7/8, 15/16, 31/32 de Limousin). Se analizó el peso vivo, el intervalo de peso al nacer a 500 días de edad. Se evaluaron cuatro MNL: Brody, Bertalanffy, Gompertz y logístico. Se estimaron parámetros de crecimiento: peso adulto (PAD); tasa de crecimiento (TAC); edad (EPI; meses) y peso (PPI; kg) al punto de inflexión; edad (meses; E50M) para alcanzar 50% de madurez y madurez a 15 meses (GM15). Con el MNL seleccionado en PRZ se caracterizó la curva de crecimiento en GPZ. El modelo de mejor ajuste fue Bertalanffy. El PAD para machos PRZ fue 566.1, para GPZ estuvo en el intervalo de 446.9 a 527.4; para hembras, en GPZ estuvo en el intervalo de 374.5 a 419.9, en PRZ fue 443.0. Los MNL presentaron correlaciones por debajo de -0.75 entre PAD y TAC. En vaquillas de PRZ, EPI se estimó a 3.7 con 131.2 para PPI; en GPZ, EPI y PPI estuvieron en los intervalos de 2.9 a 3.7 y 110.9 a 124.4, respectivamente. E50M para hembras, en PRZ fue a 10.6 y para GPZ en el intervalo de 8.9 a 10.5. GM15 para hembras, en GPZ el promedio fue 90.5 % en PRZ fue de 87.9 %. Los machos en PRZ alcanzan E50M a partir de 13 meses.

Abstract The objective was to fit a non-linear model (NLM) to evaluate the growth curve in purebred (PB) Limousin cattle and in five degrees of crossbreeding (DCBs: 1/2, 3/4, 7/8, 15/16, 31/32 Limousin). Live weight, the birth weight interval at 500 d of age, was analyzed. Four NLMs were evaluated: Brody, Bertalanffy, Gompertz, and logistic. Growth parameters were estimated: adult weight (ADW); growth rate (GR); age (AIP; months) and weight (WIP; kg) at inflection point; age (months; A50M) to reach 50 % maturity and degree of maturity at 15 mo (DM15). The growth curve in DCB was characterized using the NLM selected for BP. The best-fitting model was Bertalanffy. The ADW for purebred (PB) males was 566.1, for crossbred (CB) males it was in the range of 446.9 to 527.4; for CB females it was in the range of 374.5 to 419.9, and for PB females, it was 443.0. The NLMs exhibited correlations below -0.75 between ADW and GR. In PB heifers, AIP was estimated at 3.7, and WIP, at 131.2; in CB heifers, AIP and WIP were in the ranges of 2.9 to 3.7 and 110.9 to 124.4, respectively. A50M for PB females was 10.6, and for CB females, within the range of 8.9 to 10.5. DM15 for CB females, the average was 90.5 %, and 87.9 % for PB females. PB males reach A50M at the age of 13 mo.

Resumen El presente trabajo tiene como objetivo caracterizar y modelar el crecimiento microbiano de una bebida probiótica fermentada no láctea a base de extracto vegetal de tarwi. Se empleó la metodología de molienda húmeda para obtener el Extracto Vegetal de Tarwi (EVQ), luego se procedió a formular las mezclas con sacarosa (6 y 12 %) e inóculo de Saccharomyces boulardii (2 y 4 %) y se obtuvo así cuatro tratamientos (A1 - A4) con réplicas; la inoculación fue realizada a 37 °C con agitación constante a 20 RPM durante 24 horas. Se realizaron las lecturas del incremento de biomasa con un microscopio y una cámara de neubauer, expresado en (ufc/ml) en intervalos de 3 horas; se construyó curvas y parámetros cinéticos de crecimiento microbiano con el modelo matemático de Gompertz; se realizó un monitoreo de °Brix, densidad, pH, y % de acidez; se aplicó un análisis de regresión lineal; finalmente se realizó el ajuste del modelado matemático. Los resultados de la cinética de crecimiento microbiano mostraron las fases de crecimiento microbiano en todos tratamientos, sin embargo, A1 mostró el mejor ajuste en los parámetros cinéticos (C = 0.652, B = 1.296, M = 0.408). Por otro lado, se observó en la regresión lineal de las propiedades fisicoquímicas pendientes negativas con respecto a los °Brix, densidad, pH, y una pendiente positiva en la acidez. El comportamiento de la cinética de crecimiento microbiano y los cambios fisicoquímicos presentaron buenos parámetros y características propia de una bebida probiótica.

Abstract The present study, had the purpose of developing a fermented non-dairy probiotic drink based on tarwi, for this purpose the legume was unmarked, and then obtained Tarwi Vegetable Extract (EVQ) by blending it, then proceeded to make mixtures with sucrose (6 and 12%) and inoculum of Saccharomyces boulardii (2 and 4%) thus obtaining a total of 4 treatments (A1 - A4), the inoculation was performed at 37 ° C with constant agitation at 20 RPM for a period of 24 hours; where at three-hour intervals readings of the biomass increase were made with a microscope and a neubauer chamber expressed in (cfu / ml) at intervals of 3 hours, curves and kinetic parameters of microbial growth were constructed with the mathematical model of Gompertz, a monitoring of ° Brix, density, pH, and% of acidity was carried out, a linear regression analysis was applied; finally the adjustment of the mathematical modeling was carried out. The results of the microbial growth kinetics showed the stages of microbial growth in all treatments, however, A1 showed the best fit in the kinetic parameters (C = 0.652, B = 1.296, M = 0.408). On the other hand, negative slopes with respect to ° Brix, density, pH, and a positive slope in acidity were observed in the linear regression of the physicochemical properties. The behavior of the kinetics of microbial growth and the physicochemical changes presented good parameters and characteristics of a probiotic drink.

ABSTRACT The present study was executed to evaluate the effect of lighting programs for meat quails on their bone growth and development. A total of 1500 sexed European quails (Coturnix coturnix coturnix) were distributed using a completely randomized design in a 2 × 3 factorial arrangement, with two sexes and three lighting programs (natural, intermittent, and continuous) with five replicates of 50 quails. The lighting programs were applied in the period from 7 to 49 d of age. Weekly slaughterings were performed to remove the tibiotarsus and femur and subsequently determine weight, length, dry and mineral matter content. The growth and deposition curves of dry and mineral matter in the bones were obtained using the Gompertz model. There was no significant interaction between lighting programs and sex for the estimates of the Gompertz curve parameters of all variables studied. There was an effect of the lighting programs only on the time needed to reach the maximum deposition rate of the growth curve and dry and mineral matter deposition. Females showed higher weight and deposition of mineral matter at maturity, and took longer to reach the maximum deposition rate value for these variables. There was influence of the lighting programs on resistance and bone deformity of the tibiotarsus. For quails raised in the tropical region, a natural or intermittent lighting program must be used, as it does not compromise the development of bones and assures bone quality. 150 Coturnix arrangement natural, (natural continuous 5 4 age length content model studied maturity region used quality 15 1

Resumen La producción de palma de aceite es muy importante en Colombia. La marchitez letal de la palma de aceite es una enfermedad muy limitante en la zona oriental colombiana. Algunos modelos empleados en el análisis de estas epidemias se basan en el supuesto de que existe un área constante donde el hospedante llega a enfermarse al final de ellas (incidencia máxima de la enfermedad = 100 %). El análisis de tres epidemias diferentes demostró el error que se comete en la aplicación del modelo que mejor se ajusta a los datos observados, con una máxima incidencia de la enfermedad (Kmax) por debajo de la asumida. El ajuste de los modelos monomolecular, logístico y Gompertz se hizo con diferentes incidencias, incluida la máxima observada (y 1 + 0,1). Los datos se sometieron a análisis de regresión lineal y de varianza y distribución de los residuales. La calidad del ajuste se midió mediante los coeficientes de determinación (R2), el análisis de regresión lineal y los criterios de información Akaike (CIA) y bayesiano (CIB). Se evidenció la sensibilidad del modelo monomolecular cuando la incidencia máxima de la enfermedad se asumió por encima del valor real, contrario a lo observado en los modelos logístico y Gompertz, cuyos valores se mantuvieron estables independientemente del aumento de la Kmax evaluada. Las consecuencias de asumir una Kmax con valores igual a 1 no solamente se reflejan en la estimación errónea de parámetros como el y 0 y el r, sino que también conduce a una mala interpretación del comportamiento de la epidemia.

Abstract The production of oil palm is a major agricultural activity in Colombia. Lethal wilt (LW) of the oil palm is one of the most devastating diseases in the Eastern zone of the country. Several epidemiological models used in epidemic analyses assume that there is a constant area where the host will become diseased at the end of the epidemic (maximum incidence of disease = 100%). Based on the analysis of three different epidemics, we demonstrated the error in the application of the model that best fits the observed data when the maximum incidence of the disease (Kmax) is below the assumed. We assessed the fit of the monomolecular, logistic, and Gompertz models at different final incidence values of the disease including the maximum observed (y1 + 0.1). We analyzed the data with linear regression and residuals variance and distribution. We measured the relative quality level of fit of the model for each Kmax by determining coefficients (R2) and the Akaike and Bayesian information criteria (AIC & BIC). The monomolecular model showed a tendency to increase the level of adjustment when Kmax assumed values were close to 1 while the logistic and Gompertz models remained stable regardless of the evaluated Kmax values. The consequences of assuming a Kmax with values equal to 1 reflected not only the erroneous estimation of parameters such as y 0 and r but also gave rise to a misinterpretation of the temporal behavior of the epidemic.

Resumen Se evaluó el comportamiento de modelos no lineales y no lineales mixtos en la descripción de la cinética de producción de gas in vitro de alimentos para rumiantes. Para ello se utilizaron los modelos logístico, Gompertz y Groot. Los análisis incluyeron la adición de efectos aleatorios al parámetro asintótico de cada modelo, pues dicho parámetro fue el que más varió entre las botellas de incubación. Cada efecto aleatorio se asoció con una fuente probable de variabilidad del experimento. Los parámetros se estimaron con el proc NLMIXED del programa SAS. Para la selección del modelo de mejor ajuste, se tuvo en cuenta el R2aj, σ2, AIC y BIC. Además, se valoró el cumplimiento de los supuestos básicos para los residuos y la relación entre ajuste matemático, simplicidad e interpretación biológica de los parámetros. Se concluye que los modelos no lineales mixtos permitieron obtener mejores R2aj, BIC y σ2. Los efectos aleatorios no tuvieron efecto considerable en el cumplimiento de los supuestos de autocorrelación y aleatoriedad de los residuos. El efecto aleatorio botella en el tiempo permitió determinar los horarios en los que hubo falta de ajuste. A pesar de las limitaciones de los modelos analizados, el logístico, sin la incorporación del efecto aleatorio, fue el más adecuado según criterio de parsimonia.

Abstract The performance of non-linear and mixed non-linear models was evaluated in the description of in vitro gas production kinetics of ruminant feeds. For this, the logistic, Gompertz and Groot models were used. The analyzes included the addition of random effects to the asymptotic parameter of each model, since this parameter was the one that varied the most among the incubation bottles. Each random effect was associated with a probable source of variability in the experiment. The parameters were estimated with the NLMIXED proc of SAS program. For the selection of the best fit model, the R2aj, σ2, AIC and BIC were considered. In addition, compliance with the basic assumptions for the residuals and the relationship among mathematical fit, simplicity and biological interpretation of the parameters were assessed. It is concluded that the non-linear mixed models allowed to obtain better R2aj, BIC and σ2. The random effects had no significant effect on the fulfillment of the assumptions of autocorrelation and randomness of residuals. The random effect bottle over time allowed to determine the times in which there was a lack of fit. Despite the limitations of the analyzed models, the logistic, without the inclusion of the random effect, was the most appropriate according to the parsimony criterion.

ABSTRACT This study examined the effect of different supplementation strategies for ewes in the last third of gestation, kept on a deferred Brachiaria brizantha cv. Marandu pasture, on their performance and the growth curve of their lambs. A total of 54 ewes, of no defined breed, with an average weight of 41.10±3.10 kg, were used in a completely randomized design, divided into three groups (18 ewes per treatment). In total, 61 lambs were born, 28 females and 33 males, with 3.70±0.55 and 3.68±0.69 kg birth weight, respectively. Treatments were as follows: multiple mixture ad libitum, concentrate supplement at 0.4% live weight (LW), and concentrate supplement at 0.8% LW. Average daily weight gain (ADG, g/animal/day) and total weight gain (TWG, kg/animal) were evaluated in ewes and lambs. Reproductive efficiency indices were measured in the ewes and biometric variables in the lambs. The ADG and TWG of ewes in the last third of gestation were higher in animals supplemented at 0.8% LW. Reproductive efficiency results were superior in ewes supplemented at 0.4% LW. The effect of ewe supplementation on lamb growth curve as estimated by the Gompertz model did not reveal differences between the curves of lambs born to ewes that received supplementation at 0.4 and 0.8% LW. However, supplementing ewes with a multiple mixture induced a reduction in the growth curve parameters of their lambs. The use of concentrated supplementation, at levels of 0.4 and 0.8% of LW, provides greater productive and reproductive performance for ewes and lambs.

RESUMO: O girassol produz aquênios e óleo de qualidade, além de servir para produção de silagem, forragem e biodiesel. A modelagem de crescimento permite conhecer o padrão de crescimento da cultura e otimizar o manejo. O objetivo deste trabalho foi caracterizar o crescimento da cultivar de girassol Rhino por meio dos modelos Logístico e Gompertz e fazer considerações a respeito do manejo com base em pontos críticos. Os dados utilizados são oriundos de três ensaios de uniformidade com a cultivar de girassol confeiteiro Rhino, conduzidos na área experimental da Universidade Federal de Santa Maria, Campus Frederico Westphalen, na safra 2019/2020. Foram realizadas 14, 12 e 10 avaliações semanais de altura em 10 plantas, respectivamente, no primeiro, segundo e terceiro ensaio. Os dados foram ajustados em função da soma térmica acumulada. Os parâmetros foram estimados por meio do método dos mínimos quadrados ordinários, usando o algoritmo de Gauss-Newton. A qualidade de ajuste dos modelos aos dados foi medida pelo coeficiente de determinação ajustado, critério de determinação de Akaike, critério bayesiano de informação, e por meio da não linearidade intrínseca e paramétrica. Foram determinados os pontos de inflexão (IP), máxima aceleração (MAP), máxima desaceleração (MDP) e desaceleração assintótica (ADP). As análises estatísticas foram realizadas com Microsoft Office Excel® e o software R. Os modelos descreveram de forma satisfatória a curva de crescimento da altura do girassol, fornecendo parâmetros com interpretações práticas. O modelo Logístico apresenta melhor qualidade de ajuste, sendo o mais adequado para caracterização da curva de crescimento. Os pontos críticos estimados fornecem informações importantes para o manejo da cultura. As plantas daninhas devem ser controladas até o MAP. As aplicações de fertilizantes em cobertura devem ser realizadas entre MAP e IP. O ADP é um indicador de maturidade, após atingir este ponto, as plantas podem ser colhidas para a produção de silagem sem perda de volume e qualidade.

ABSTRACT: Sunflower produces achenes and oil of good quality, besides serving for production of silage, forage and biodiesel. Growth modeling allows knowing the growth pattern of the crop and optimizing the management. The research characterized the growth of the Rhino sunflower cultivar using the Logistic and Gompertz models and to make considerations regarding management based on critical points. The data used come from three uniformity trials with the Rhino confectionery sunflower cultivar carried out in the experimental area of the Federal University of Santa Maria - Campus Frederico Westphalen in the 2019/2020 agricultural harvest. In the first, second and third trials 14, 12 and 10 weekly height evaluations were performed on 10 plants, respectively. The data were adjusted for the thermal time accumulated. The parameters were estimated by ordinary least square’s method using the Gauss-Newton algorithm. The fitting quality of the models to the data was measured by the adjusted coefficient of determination, Akaike information criterion, Bayesian information criterion, and through intrinsic and parametric nonlinearity. The inflection points (IP), maximum acceleration (MAP), maximum deceleration (MDP) and asymptotic deceleration (ADP) were determined. Statistical analyses were performed with Microsoft Office Excel® and R software. The models satisfactorily described the height growth curve of sunflower, providing parameters with practical interpretations. The Logistics model has the best fitting quality, being the most suitable for characterizing the growth curve. The estimated critical points provide important information for crop management. Weeds must be controlled until the MAP. Covered fertilizer applications must be carried out between the MAP and IP range. ADP is an indicator of maturity, after reaching this point, the plants can be harvested for the production of silage without loss of volume and quality.

Resumo Objetivou-se descrever a curva de crescimento de pêssegos “Aurora 1”, utilizando dados de altura e diâmetro do fruto ao longo do tempo, através de modelos sigmoidais difásicos contruídos a partir de oito combinações dos modelos: Brody, Gompertz e Logístico. Os dados deste estudo foram obtidos de um experimento realizado em 2005, no município de Vista Alegre do Alto, São Paulo, Brasil. Os parâmetros dos modelos foram ajustados pelo método de mínimos quadrados, utilizando o algoritmo de Gauss-Newton, implementados no software R. Os pressupostos de normalidade, homogeneidade e independência dos resíduos foram verificados com base nos testes de Shapiro-Wilk, Breush e Pagan e Durbin-Watson, respectivamente. A comparação dos ajustes dos modelos foi verificada de acordo com o critério de informação de Akaike corrigido (AICc), desvio padrão residual (DPR), índice de ajuste da assíntota (IA) e medidas de não linearidade. Todos os modelos ajustados para ambas as variáveis altura e diâmetro do fruto atenderam às pressuposições de normalidade, independência e homocedasticidade dos erros. Além disso, todos eles apresentam boa qualidade de ajuste aos dados de altura e diâmetro do fruto, visto que apresentaram valores de IA próximos de um e baixos valores do DPR e de medidas de não linearidade. Contudo, o modelo duplo Gompertz (GG) e o modelo Logístico + Gompertz (LG) apresentaram, respectivamente, a melhor qualidade de ajuste aos dados de altura e diâmetro do fruto, em relação aos demais modelos avaliados. Conclui-se que todos os modelos sigmoidais difásicos avaliados apresentaram bom ajuste aos dados de altura e diâmetro e podem ser utilizados para a descrição da curva de crescimento de pêssegos “Aurora-1”, segundo os critérios de qualidade de ajuste. No entanto, é importante destacar que os modelos GG e LG apresentaram a melhor qualidade de ajuste e podem ser preferidos para descrever o crescimento em altura e diâmetro dos frutos de pêssego “Aurora 1”, respectivamente, com crescimento máximo esperado próximos de 63 mm de altura e 48 mm de diâmetro.

Abstract The aim of this study was to describe the growth curve of “Aurora 1” peaches using fruit height and diameter data over time through diphasic sigmoidal models constructed from eight combinations of the following models: Brody, Gompertz and Logistic. Data were obtained from an experiment carried out in 2005 in the municipality of Vista Alegre do Alto, São Paulo, Brazil. The parameters of models were adjusted by the least squares method using the Gauss-Newton algorithm implemented in the R software. Assumptions of normality, homogeneity and independence of residues were verified based on Shapiro-Wilk, Breush and Pagan and Durbin-Watson tests, respectively. The goodness of fit of models was verified according to the corrected Akaike information criterion (AICc), residual standard deviation (RSD), asymptote adjustment index (AI) and nonlinearity measures. All models adjusted for both fruit height and diameter variables met the assumptions of normality, independence and homoscedasticity of errors. In addition, all of them present good quality of fit to fruit height and diameter data, since they presented AI values close to one and low RSD values and non-linearity measures. However, the double Gompertz (GG) and the Logistic + Gompertz (LG) models presented, respectively, the best quality of fit to fruit height and diameter data in relation to the other models. It could be concluded that all diphasic sigmoidal models evaluated showed good fit to height and diameter data and can be used to describe the growth curve of “Aurora-1” peaches, according to goodness of fit criteria. However, it is important to highlight that GG and LG models presented the best quality of fit and can be selected to describe the height and diameter growth of “Aurora 1” peach fruits, respectively, with maximum expected growth close to 63 mm in height and 48 mm in diameter.