The focus of the paper is to address the temporal discrepancies in long-term rainfall trend results in South Africa, by evaluating a systematic range of observation periods over the century-long analysis period of 1921-2022. Available long-term climate projections show that significant parts of South Africa are expected to experience progressively drier conditions, mainly in the west. To assess long-term rainfall trends over the country, historical trends should be determined - the results of published studies for which are not consistent. Arguably the most significant reason for these inconsistencies is the length of analysis period. This study investigates this effect on the magnitude and statistical significance of historical annual rainfall trends over hydrological years, with the data of 94 homogeneous rainfall districts. Trends of annual rainfall were determined for all periods up to 2022, from the 1921-2022 period up to the last 30 years, i.e. 1993-2022. The annual rainfall trends over the longest analysis period show significantly positive trends over most of the central and western parts and significant drying over extensive parts of mainly the far north-east. However, the most recent period (1993-2022) shows significantly drying trends over extensive parts of the west, south and east. Among the main findings is that the change in trends shows a consistent spatial pattern of significant negative change over most of the southwestern half, and mostly significantly positive trends over the north-eastern sector. These results are in large agreement with future rainfall projections, particularly for the western half. Ultimately, the study emphasizes the wide range of long-term trends in South Africa, both spatially and temporally, and the importance of considering a range of historical analysis periods in the detection of long-term rainfall changes. In effect, the eventual results provide increased confidence to predicted future rainfall scenarios.

RESUMO Compreender o solo, os atributos das plantas e a dinâmica das culturas de cenoura é vital para otimizar praticas de manejo a sitio especifico e melhorar o rendimento das culturas e a qualidade do solo. Este estudo teve como objetivo verificar a dependência e a variabilidade espacial entre a produtividade da cenoura irrigada e os atributos físicos do solo em um Latossolo Argiloso. A pesquisa ocorreu durante a safra 2021 em uma área comercial de produção de cenoura em Campos Altos, MG, Brasil. Foram estabelecidos cem pontos amostrais dentro da área irrigada, distribuídos em uma área quadrada de 40.000 m², posicionados nos centros de grades de 20 x 20 m. O estudo revelou alta produtividade na cultura da cenoura irrigada (99,74 t ha-1) com variabilidade moderada. Os atributos do solo apresentaram uma gama de heterogeneidade, variando de baixa a extremamente alta, dependendo da variável avaliada, determinada pelo coeficiente de variação. Dentre as variáveis que apresentam dependência espacial, a densidade de partículas apresentou alcance mínimo de 40 m, o que é recomendado para futuros estudos de cultivo de cenoura irrigada em Latossolo Argiloso. A disponibilidade total de água no solo demonstrou correlação espacial positiva e mostrou-se a variável recomendada para estimar a variabilidade espacial da produtividade da cultura da cenoura. Argiloso 202 Altos MG Brasil 40000 000 40.00 m² m 2 99,74 9974 99 74 (99,7 ha1 ha 1 ha-1 moderada heterogeneidade avaliada variação 4 mostrouse mostrou se 4000 00 40.0 99,7 997 9 7 (99, ha- 400 0 40. 99, (99 (9 (

ABSTRACT Understanding soil, plant attributes, and carrot crop dynamics is vital for optimizing site-specific management practices and enhancing crop yield and soil quality. This study aimed to ascertain the dependence and spatial variability between irrigated carrot yield and soil physical attributes in a clayey Oxisol. The research took place during the 2021 growing season in a commercial carrot production area in Campos Altos, MG, Brazil. One hundred sampling points were established within the irrigated area, distributed across a square expanse of 40,000 m², positioned at the centers of 20 × 20 m grids. The study revealed high yield in the irrigated carrot crop (99.74 t ha-1) with moderate variability. Soil attributes displayed a range of heterogeneity, ranging from low to extremely high, contingent on the variable assessed, as determined by the coefficient of variation. Among the variables exhibiting spatial dependence, particle density exhibited a minimum range of 40 m, which is recommended for further studies on irrigated carrot cultivation in a clayey Oxisol. Total soil water availability demonstrated a positive spatial correlation and proved to be the recommended variable for estimating the spatial variability of carrot crop yield. sitespecific site specific quality Oxisol 202 Altos MG Brazil 40000 000 40,00 m² 2 grids 99.74 9974 99 74 (99.7 ha1 ha 1 ha-1 heterogeneity assessed variation 4 4000 00 40,0 99.7 997 9 7 (99. ha- 400 0 40, 99. (99 (9 (

Resumen Los modelos de proyección estructurados (MPE) son una herramienta poderosa para investigar la dinámica de las poblaciones estructuradas, lo que los hace ideales para estudiar las especies vegetales, abarcando su variedad de formas de vida, tamaños, longevidad y complejidad del ciclo de vida. Los MPE son una de las herramientas más versátiles de la ecología vegetal, con cientos de especies estudiadas y una gran variedad de formulaciones alternativas para diferentes preguntas y objetivos. Revisamos algunas consideraciones conceptuales y metodológicas sobresalientes sobre la construcción y uso de los MPE, incluyendo los modelos matriciales de proyección, que son discretos, y los modelos integrales de proyección, que son continuos. Discutimos la selección de la variable de estado y la estimación de parámetros, especialmente aquellos que involucran transiciones difíciles de observar, tales como la cuantificación de la reproducción y la mortalidad de los individuos hacia el final de su ciclo de vida. Debido a la creciente importancia de investigar las tendencias poblacionales en un mundo que cambia rápidamente, destacamos el uso de los MPE tanto en un contexto ambiental como cuando las poblaciones se alejan de su equilibrio. El papel de la densodependencia recibe especial atención debido a que suele correlacionarse con el ambiente, potencialmente confundiendo ambos efectos. De igual modo, desentrañar los diferentes efectos ambientales plantea complicaciones propias, dificultando la comprobación de las relaciones de causalidad. Las alternativas disponibles se ilustran considerando la selección de variables, muestreo y tipos de modelos adecuados para diferentes propósitos.

Abstract Structured projection models (SPMs) are a powerful tool to investigate the dynamics of structured populations, which makes them ideal for the study of plant species spanning their range of life forms, sizes, longevity, and life cycle complexity. They are one of the most versatile tools in plant ecology, with hundreds of species studied so far and a wide variety of alternative formulations for different questions and purposes. We revise some of the most salient conceptual and methodological issues in the construction and use of SPMs including both discrete matrix projection models and continuous integral projection models. Consideration is given to the selection of the state variable and the estimation of parameters, especially those involving transitions difficult to observe in the field, such as the quantification of offspring production and the rarely observed mortality of individuals towards the end of the life cycle. Due to the growing importance of investigating population trends in a rapidly changing world, we highlight the use of SPMs for populations under a variety of environmental influences and/or away from their expected equilibrium. The presumed role of population density receives special attention because it often correlates with features of the environment, thus potentially confounding the two effects. Similarly, disentangling the various environmental effects poses challenges of its own, making it difficult to prove causality. The alternatives available are illustrated considering the selection of variables, samples, and model type suitable for specific purposes.

Resumen Los modelos digitales de elevación mejoran la precisión en el análisis del terreno. Este trabajo tuvo como objetivo comparar diferentes métodos de interpolación utilizando criterios estadísticos en un levantamiento topográfico de 339 puntos levantados con estación total en la zona de San Juan de Lagunillas (Venezuela). Se documentó la existencia de un proceso de tendencia significativa con autocorrelación espacial modelada mediante un semivariograma gaussiano isotrópico. Los kriging consiguieron residuales menores a un error mínimo tolerable igual 0.1 m. El kriging residual fue el mejor evaluado en la validación cruzada con exclusión (error medio absoluto de 0.71 m). El kriging disyuntivo tuvo menor media del error pero un amplio rango del error y el mayor error medio absoluto (12.8 m). Los otros kriging tienen medias de la varianza del error superiores a 1.3 m y errores mínimos absolutos superiores a 0.85 m. Debido a la alta dependencia en la forma de especificación de los modelos se recomiendan las ayudas gráficas para un mejor ajuste.

Abstract Digital Elevation Models improve accuracy in terrain analysis. This work compared different interpolation methods using statistical criteria in a topographic survey of 339 points raised with a total station in the “San Juan de Lagunillas” area (Venezuela). The existence of a signiftablaicant trend process with spatial autocorrelation modeled by an isotropic Gaussian semivariogram was documented. The kriging allowed to obtain residuals less than a minimum tolerable error equal to 0.1 m. The residual kriging was the best evaluated in cross validation with exclusion (absolute mean error of 0.71 m). The disjunctive kriging showed a lower error average but a wider error range and the highest mean absolute error (12.8 m). The other kriging showed mean error variance greater than 1.3 m and absolute minimum errors greater than 0.85 m. Due to the high dependence on the model specification form, graphics are recommended for a better fit.

ABSTRACT Soil nitrogen (N) variability affects the effective application of N fertilizers. The objective of this research was to determine and assess the spatial dependence of soil N in two different soils using spatial sampling and geostatistics fundamentals. An optimized nested sampling design was applied in two sites, using 16 main stations from where soil samples (0 - 23 cm) were obtained at 1.5, 4.5, 13.5, 40.5, and 121.5 m, at random directions. Soil samples were collected from an Andisol and an Inceptisol (2 x n = 98), and the potentially available N (PAN) was measured by anaerobic soil incubation for 7 days at 40oC (PAN = NH4+ day 7 - NH4+ day 1). The PAN variance components from each distance were calculated by residual maximum likelihood (REML), and then accumulated to plot an approach to the variogram. The results showed a wide range of values for PAN at both sites. The Andisol site registered high PAN levels, with a mean value of 32.92 mg NH4+ kg soil-1, which was five times larger than in the Inceptisol soil, probably associated with a larger soil organic matter content. The limit of the spatial dependence was 13.5 m for the Andisol, and 40.5 m for the Inceptisol soil, corresponding to the 59% and 35% of the process variance, respectively.

RESUMEN La alta variabilidad del nitrógeno (N) en el suelo afecta la aplicación efectiva de fertilizantes nitrogenados. El objetivo de esta investigación fue determinar y evaluar la dependencia espacial del N en dos tipos de suelo. Para ello se utilizó un diseño espacial anidado optimizado, con 16 estaciones de muestreo, y en direcciones aleatorias se tomaron muestras de suelo (0-23 cm) a intervalos de distancia de 1,5; 4,5; 13,5; 40,5; y 121,5 m. Los suelos evaluados fueron un Andisol y un Inceptisol (2 x n = 98), en los que se midió el potencial de nitrógeno disponible (PND) a través de incubación anaeróbica de suelo por 7 días a 40oC (PND = NH4+ día 7 - NH4+ día 1). La dependencia espacial del PND en cada uno de los sitios fue establecida mediante la acumulación de varianza de cada distancia, calculada a través de un análisis de máxima probabilidad residual (REML), y posterior aproximación al variograma. Los resultados mostraron un rango amplio de valores en ambos sitios. El sitio Andisol registró un elevado PND, con un valor promedio de 32,92 mg NH4+ kg-1, cinco veces mayor que en el Inceptisol, lo que se explicó principalmente por un mayor contenido de materia orgánica. La dependencia espacial del PND para ambos sitios se obtuvo a intervalos de 13,5 y 40,5 m, logrando cuantificar un 59% de la variabilidad del proceso en el sitio Andisol, y tan sólo un 35% en el sitio Inceptisol.

ABSTRACT Spatial and temporal variation of the physical and chemical conditions of coastal karst wetland ecosystems, which annually range from flooded to completely dry, generate a very dynamic fish community structure. We assessed the relative influence of spatial dependence and environmental factors on fish community structure in a seasonally flooded tropical karst system on the north-western coast of the Yucatan Peninsula, Mexico. Sampling was carried out between November 2009 and April 2010, while the area was inundated by seasonal floodwater. Fish biomass, abundance and species richness, as well as environmental variables and geographic location, were recorded. A variation partitioning analysis was performed to assess the influence of the spatial and environmental variables on the fish community using multiple regression, and a principal coordinates analysis of neighbor matrices (PCNM). Spatial factors had a greater influence on the changes in the community structure than the environmental factors. After spatial variation, environmental effects from conductivity, oxygen saturation, temperature and depth further shaped the community. These results imply that, despite the diversity of niches and wide variation in environmental conditions, the structuring force of the community is the spatial dynamic probably linked to species dispersal mechanisms and reproductive strategies.

Abstract Introduction. Dairy production in tropical zones is characterized by a high dependence on the forage resource, which makes it sensitive to climatic variables of which there is limited information on their effect on the performance of specialized dairy breeds. Objective. The objective of this study was to evaluate the association between temperature and humidity index (THI) and daily milk production (kgl) of cows breeds Holstein, Jersey, and their crosses. Materials and methods. The study was conducted in the northern and central regions of Costa Rica, with data collected between 1990 and 2015. THI values were obtained using linear predictive models and spatial autocorrelation models, applied to 3,547 monthly records of maximum temperature and relative humidity from seventeen weather stations. 6,478,582 kgl records from 418 dairy herds were analyzed, using a generalized mixed linear model (GLMM), which considered the fixed effects of breed, year and month, birth number, lactation stage, breed × lactation stage, ENSO (Effect “El Niño”), ITH and breed×ITH, in addition to a random effect of the cow. Results. All factors had a highly significant effect (p<0.0001) on kgl. For the ITH range between 72-88, linear reductions of 0.41 (r2=0.94), 0.36 (r2=0.95) and 0.29 (r2=0.82) kg day-1 were estimated for Holstein, Holstein×Jersey and Jersey, respectively. No significant trends were observed for kgl when ITH <72. The economic losses attributable to the greater stress exposure in the north compared to the central region were estimated at $680, $587 and $477 per lactation and cow for Holstein, Holstein×Jersey and Jersey, respectively. Conclusion. There was an inverse relationship between temperature and humidity index and milk production in Holstein, Jersey and crossbreed cows for this tropical region.

Resumen Introducción. La producción lechera en zonas tropicales se caracteriza por una alta dependencia del recurso forrajero, lo que la hace sensible a las variables climáticas, de las cuales existe información limitada sobre su efecto en el rendimiento de razas lecheras especializadas. Objetivo. El objetivo del presente estudio fue evaluar la asociación entre el índice de temperatura y humedad (ITH) y la producción diaria de leche (kgl) de vacas de razas Holstein, Jersey y sus cruces. Materiales y métodos. El estudio se efectuó en las regiones Norte y Central de Costa Rica, con datos recolectados entre 1990 y 2015. Los valores de ITH se obtuvieron mediante modelos predictivos lineales y modelos espaciales de autocorrelación, ajustados sobre 3547 registros mensuales de temperatura máxima y humedad relativa de diecisiete estaciones meteorológicas. Se analizaron 6 478 582 registros de kgl provenientes de 418 hatos lecheros, mediante un modelo lineal mixto generalizado (GLMM), que consideró los efectos fijos de la raza, el año y el mes calendario, número de parto, etapa de lactancia, raza×etapa de lactancia, ENOS (Efecto “El Niño”), ITH y raza×ITH, además del efecto aleatorio de la vaca. Resultados. Todos los factores presentaron efecto altamente significativo (p<0,0001) sobre la kgl. Para el rango de ITH entre 72-88 se estimaron reducciones lineales de 0,41 (r2=0,94), 0,36 (r2=0,95) y 0,29 (r2=0,82) kg día-1 para Holstein, Holstein×Jersey y Jersey, respectivamente. No se observaron tendencias significativas en los kgl para ITH <72. Las pérdidas económicas atribuibles a la mayor exposición al estrés en la región norte comparada con la región central se estimaron en $680, $587 y $477 por lactancia por vaca para Holstein, Holstein×Jersey y Jersey, respectivamente. Conclusión. Hubo relación inversa entre el índice de temperatura y humedad, y la producción de leche en vacas Holstein, Jersey y sus cruces, en esta región tropical.

Resumo: O estudo teve como objetivos descrever a distribuição espacial do rastreamento por mamografia entre áreas geográficas pequenas (microrregiões) no Brasil, além de investigar se as diferenças observadas estavam associadas a inequidades espaciais nas condições socioeconômicas, na prestação de assistência à saúde e no uso de serviços de saúde. Este foi um estudo ecológico de base territorial, comparando a cobertura do rastreamento por mamografia em 2010-2011 com fatores socioeconômicos e de cuidados de saúde. O estudo usou 438 microrregiões sanitárias brasileiras como as unidades analíticas. Foram utilizados modelos de regressão espacial para estudar as associações. Houve uma importante variabilidade na cobertura por mamografia entre microrregiões (mediana = 21,6%; variação interquartil: 8,1%-37,9%). A análise multivariada identificou: forte desigualdade na renda familiar, número baixo de radiologistas/100 mil habitantes, número baixo de aparelhos de mamografia/10 mil habitantes e número baixo de mamografias realizadas com cada aparelho enquanto correlatos independentes da baixa cobertura mamográfica no nível microrregional. Houve evidência de forte dependência espacial nessas associações, em que as mudanças em uma microrregião afetavam as microrregiões vizinhas, além de heterogeneidade geográfica. O estudo revelou importantes inequidades no acesso ao exame de mamografia entre microrregiões brasileiras em 2010-2011, com cobertura mais alta nas microrregiões com menor desigualdade de renda e melhor acesso geral aos cuidados de saúde.

Resumen: Los objetivos de este estudio fueron describir la distribución espacial de la cobertura del cribado mamográfico, a través de pequeñas áreas geográficas (microrregiones) en Brasil, y examinar si las diferencias observadas estuvieron asociadas con inequidades espaciales, en términos de condiciones socioeconómicas, sistema de atención de salud, y utilización de servicios de salud. Se trata de un estudio ecológico, basado en áreas incluidas en la cobertura de cribado mamográfico durante 2010-2011 y relacionadas con variables socioeconómicas y de salud. Las unidades de análisis fueron 438 microrregiones de salud en Brasil. Se utilizaron modelos de regresión espacial para estudiar estas relaciones existentes. Hubo una variabilidad marcada en relación con la cobertura mamográfica a través de las microrregiones (media = 21.6%; rango intercuartílico: 8,1%-37,9%). Los análisis multivariables identificaron una alta inequidad en los ingresos por hogar, bajo número de radiólogos/100,000 habitantes, bajo número de máquinas de mamografía/10.000 habitantes, y un bajo número de mamografías realizadas por cada máquina, lo que está independiente correlacionado con la baja cobertura de mamografías en el nivel de microrregión. Hubo evidencias de una dependencia espacial fuerte de estas asociaciones, con cambios en una microrregión afectando a microrregiones vecinas, y también de heterogeneidades geográficas. Hubo inequidades sustanciales en el acceso al cribado mamográfico a través de las microrregiones en Brasil, en 2010-2011, con una cobertura superior en aquellas con pequeñas inequidades respecto a la riqueza y mejor acceso a los servicios de salud.

Abstract: Our objectives with this study were to describe the spatial distribution of mammographic screening coverage across small geographical areas (micro-regions) in Brazil, and to analyze whether the observed differences were associated with spatial inequities in socioeconomic conditions, provision of health care, and healthcare services utilization. We performed an area-based ecological study on mammographic screening coverage in the period of 2010-2011 regarding socioeconomic and healthcare variables. The units of analysis were the 438 health micro-regions in Brazil. Spatial regression models were used to study these relationships. There was marked variability in mammographic coverage across micro-regions (median = 21.6%; interquartile range: 8.1%-37.9%). Multivariable analyses identified high household income inequality, low number of radiologists/100,000 inhabitants, low number of mammography machines/10,000 inhabitants, and low number of mammograms performed by each machine as independent correlates of poor mammographic coverage at the micro-region level. There was evidence of strong spatial dependence of these associations, with changes in one micro-region affecting neighboring micro-regions, and also of geographical heterogeneities. There were substantial inequities in access to mammographic screening across micro-regions in Brazil, in 2010-2011, with coverage being higher in those with smaller wealth inequities and better access to health care.

Abstract: Due to high variability of chemical characteristics, soil sampling is one of the major sources of error in a correction and fertilization program. This critical review aimed to analyze the theoretical foundations that define the soil sampling types used for different cropping systems, assessing the degree of influence of variations in chemical characteristics conferred by each situation. Confronting information from the studies reviewed, we determined that the range of spatial dependence of soil chemical properties is dependent on the distance between previous sampling points. Land stratification in sampling units reduces the occurrence of spatial dependence caused by environmental factors associated with long-distance variations (macro-dependence), but does not prevent the occurrence of spatial dependence at short distances in positions within the stratum itself (meso-dependence). The option to use composite sample analysis from homogeneous field (average fertility) or the soil fertility maps for recommendation of lime and fertilizer, is primarily due to economic issues. The collection of single samples of small volume to calculate local averages, or the formation of composite samples from these “single samples” tends to increase the effectiveness and reliability of fertility maps.

Resumo: Devido à elevada variabilidade de determinadas características químicas, a amostragem de solo é uma das mais importantes fontes de erro em um programa de correção e adubação. O objetivo dessa revisão foi analisar criticamente os fundamentos teóricos que definem os tipos de amostragem de solo utilizados para diferentes sistemas de cultivo, avaliando o grau de influência das variações de características químicas conferidas por cada situação. Confrontando informações dos trabalhos consultados, foi possível inferir que a estratificação do terreno em unidades de amostragem diminui a ocorrência de dependência espacial causada por fatores do ambiente associados às variações de longa distância (macrodependência), mas não impede a ocorrência de dependência espacial a curtas distâncias em locais dentro do próprio estrato (mesodependência). A opção de se utilizar a análise da amostra composta por unidade de amostragem (fertilidade média) ou os mapas de fertilidade do solo, para recomendação de corretivos e fertilizantes, deve-se especialmente a questões econômicas. A coleta de amostras simples de pequeno volume e obtenção de médias locais, ou a formação de amostras compostas a partir destas “amostras simples”, tende a incrementar a efetividade e a confiabilidade dos mapas de fertilidade.

RESUMEN Las enfermedades "pudrición negra del fruto" y "moniliasis" son reportadas como limitantes en plantaciones de cacao en Colombia. Fueron evaluados los patrones espaciales de incidencia para estas dos enfermedades en un cultivo de cacao durante un monitoreo de trece semanas en campo. Semivariogramas e interpolación kriging fueron usados para analizar el comportamiento espacial de "pudrición negra del fruto", los estadísticos Join Count e Indice de Moran se emplearon para estudiar el comportamiento espacial de "moniliasis". La incidencia de "pudrición negra del fruto" presentó estructura de dependencia espacial de acuerdo a los semivariogramas durante el tiempo de evaluación, mientras que la autocorrelación espacial de sitios de infección de "moniliasis" se distribuyó de forma aleatoria entre las plantas de cacao según el Indice de Moran. El rango de dispersión estimado de "pudrición negra del fruto" varió entre 21,74 y 40,23 m y los mapas kriging evidenciaron el progreso espacio-temporal de la enfermedad durante las semanas evaluadas. Las condiciones experimentales dadas y la aproximación de los análisis espaciales, contribuyeron al entendimiento de la dinámica espacial de dos enfermedades limitantes en tres clones de cacao en la Orinoquía Colombiana.

ABSTRACT "Black pod" and "frosty pod" diseases are reported as limiting in cocoa plantations in Colombia. Spatial patterns of incidence for these two diseases were evaluated during a thirteen weeks long period of monitoring in the field. Semivariogram and kriging interpolation were used to analyze the spatial behavior of "black pod" and Join Count and Moran's Index statistics were used to analyze the spatial behavior of "frosty pod". The incidence of "Black pod" has a spatial dependence structure according to semivariogramas during the evaluation time, while spatial autocorrelation of "moniliasis" infection sites was randomly distribuited among cocoa plants according to the Moran's Index. The estimated dispersion range of "Black pod" was from 21.74 to 40.23 m y the kriging maps showed the spatio-temporal progression of the disease during the evaluated weeks. The experimental conditions given and spatial analysis approach, contributed to the understanding of the spatial dynamics of two limiting diseases in three clones of cocoa in the Colombian Orinoquia.

Resumen: En este trabajo analizamos algunos límites cosmológicos dados por una solución FLRW para la gravedad masiva. Encontramos los límites para datos observacionales recientes de H(z) y mostramos que los mejores ajustes para los valores de los parámetros cosmológicos concuerdan con el modelo ɅCDM e indican una curvatura espacial aproximadamente abierta, como se espera. También se analiza la variación de la masa del gravitón con las constantes α 3 y α4 relacionadas con los términos lagrangianos adicionales del modelo, y se obtiene una fuerte dependencia de tales parámetros. Sin embargo, la condición m g ≃ H 0 -1 parece dominar en un intervalo amplio de los parámetros α 3 y α4.

Abstract: In this work we analysed some cosmological bounds concerning an open FLRW solution oí massive gravity. The constraints from recent observational H(z) data are found and the best fit values for the cosmological parameters are in agreement with the ɅCDM model, and also point to a nearly open spatial curvature, as expected from the model. The graviton mass dependence with the constant parameters α 3 and α4 related to the additional lagrangians terms of the model, are also analysed, and we obtain a strong dependence on such parameters, although the condition m g ≃ H 0 -1 seems dominant for a large range of the parameters α 3 and α4.

Brazil stands as the largest coffee producer in the world. However one of the factors capable of undermining the potential of this species is the poor quality of seeds. One tool that is being proposed for use in agriculture is the Geostatistics analysis to verify the existence and quantify the degree of spatial dependence of variables. The seeds were collected in a field with five years of age in an area of 0.8 ha, 50 sampling points. In the laboratory we used a completely randomized design (CRD) with four replicates of 25 seeds per point materialized with the aid of a total station. After removal of the scrolls, the seeds were treated with Captan (Orth Cide) to 0.1% for five minutes and subjected to the following determinations: moisture, germination first count of germination, root length and shoot length. Then the seeds were placed to develop in an incubator at temperature 20-30 °C for 60 days. In the results there was spatial dependence of the quality variables of physiological Catuaí. The lowest range for the variable length of shoot (CPA) and greater range for the variable fresh weight (MFPA).

El Brasil se destaca como el mayor productor de café del mundo. Sin embargo, uno de los factores capaces de afectar el potencial de esta especie es la mala calidad de las semillas. Una de las herramientas que se proponen para el uso en la agricultura es el análisis geoestadístico, para evaluar la existencia y cuantificar el grado de dependencia espacial de las variables estudiadas. Las semillas se recolectaron en una granja a la edad de cinco años, en un área de 0,8 ha en 50puntos del muestreo. En el laboratorio se utilizó el diseño completamente al azar (DCA), con cuatro repeticiones de 25 semillas por punto que se materializó con la ayuda de una estación total. Después del retiro de los pergaminos, las semillas fueron tratadas con Captán (Orth Cide) 0,1% durante 5 minutos y está subjeta a las siguientes determinaciones: contenido de agua (humedad), germinación, primer corte de germinación, longitud de la raíz y la longitud de la parte aérea, peso fresco de la parte aérea; peso fresco de la raíz, materia seca de la parte aérea y materia seca de la raíz. Posteriormente, las semillas se colocaron para desarrollarse en el germinador a la temperatura de 20-30 °C durante 60 días. Los resultados mostraron la dependencia espacial de las variables de calidad fisiológica de cultivar Catuaí. Siendo la gama más pequeña para la longitud variable de la parte aérea (LPA) y de mayor alcance para la variable longitud de peso fresco de la parte aérea (MFPA).

Nuestro objetivo fue el de explorar el patrón de distribución espacial de la riqueza de especies de anfibios en el departamento de Antioquia, Colombia y determinar cómo la temperatura anual, la precipitación anual y la heterogeneidad altitudinal afecta este patrón, como modelo para los Andes tropicales. Para ello, delineamos mapas de distribución de 223 especies de anfibios que habitan en Antioquia y junto a mapas de las variables ambientales se generalizaron en cuadrículas de 752 celdas que cubrían todo del departamento. La relación entre riqueza de especies y ambiente fue determinada utilizando dos modelos globales de regresión (modelo OLS y GLS) y un modelo local (modelo GWR). Se encontró una relación significativa entre la riqueza de especies y el clima (GLS r²: 0.869; GRW r²: 0.929), donde la temperatura fue la variable más importante, mientras que la heterogeneidad altitudinal no fue significativa. El modelo GLS mostró mayor eficiencia en incorporar el efecto de la autocorrelación espacial en los términos del error, mientras que el modelo GWR mostró un ajuste mayor (r²) y mejor balance entre número de parámetros y ajuste (AICc). Los coeficientes de regresión en el modelo WGR mostraron una gran variación a lo largo del área de estudio, indicando que la relación entre la riqueza de especies y las variables climáticas es espacialmente compleja. La fuerte relación entre ambiente y riqueza de especies de anfibios puede atribuirse a las características de historia de vida como la condición de ectotermos y la dependencia de humedad para la reproducción.

Our objective was to explore the spatial distribution patterns of amphibian species richness in Antioquia, as model for the tropical Andes, and determine how annual mean temperature, annual precipitation, and elevation range influence it; and to briefly compare local and global regression models for estimating the relation between environmental variables and species richness. Distribution maps for 223 amphibian species and environmental variables were generalized onto grid maps of 752 blocks each covering the entire of Antioquia. We explored the relationship between species richness and environment using two global regression models (the Ordinary Least Squares "OLS" and Generalized Linear Squares "GLS" models) and one local model (the Geographically Weighted Regression "GWR" model). We found a significant relationship between species richness and environmental variables (GLS r²: 0.869; GRW r²: 0.929). The GLS model efficiently incorporated the spatial autocorrelation effect and handled spatial dependence in the regression error terms while the GWR model showed the best fit (r²) and balance between number of parameters and fit (AICc). GWR parameters show wide variation within the study area, indicating that relationship between species richness and climate is spatially complex. Temperature was the most important variable in the GLS and GWR models, and altitude range the least significant. The strong relationship between environment and amphibian richness is possibly due to life history traits of amphibians, such as ectothermy and water dependency to complete the life cycle.

Curvas espacialmente correlacionadas están presentes en un amplio rango de disciplinas aplicadas. En este trabajo se describe el paquete R geofd que implementa predicción por kriging ordinario para este tipo de datos. Inicialmente las curvas son suavizadas usando bases de funciones de Fourier o B-splines. Posteriormente la dependencia espacial entre las curvas es estimada por la función traza-variograma. Finalmente los parámetros del predictor kriging ordinario son estimados resolviendo un sistema de ecuaciones basado en la estimación de la función traza-variograma. Se ilustra el paquete analizando datos reales y simulados.

Spatially correlated curves are present in a wide range of applied disciplines. In this paper we describe the R package geofd which implements ordinary kriging prediction for this type of data. Initially the curves are pre-processed by fitting a Fourier or B-splines basis functions. After that the spatial dependence among curves is estimated by means of the trace-variogram function. Finally the parameters for performing prediction by ordinary kriging at unsampled locations are by estimated solving a linear system based estimated trace-variogram. We illustrate the software analyzing real and simulated data.

Los procesos y atributos que influyen sobre el desempeño de los cultivos varían en el espacio y tiempo. Su magnitud y estructura espacial es específica para cada lote y su cuantificación es necesaria para la aplicación del manejo sitio-específico de cultivos (MSEC). Nuestro objetivo fue examinar la variabilidad espacial intra-lote de atributos químicos y físicos del horizonte superficial de un Argiudol típico del centro de Santa Fe para la implementación del MSEC. En una parcela de 475 x 100 m se tomaron 60 muestras distribuidas en 3 transectas de 20 puntos separados cada 25 m y 50 m entre transecta. En cada muestra perturbada (0-20 cm) se determinó N de nitratos (N-NO3), C orgánico total (COT), N total (Nt); P extractable (P), arena, arcilla, reacción del suelo (pH). La densidad aparente del suelo (Ds) se determinó a partir de muestras no perturbadas de las profundidades 0-10 y 10-20 cm. Se calcularon estadísticas descriptivas y se analizó la dependencia espacial de los atributos mediante variogramas empíricos y sus límites obtenidos por permutación (envelopes). Los coeficientes de variación (CV) para COT, Nt, Arena, Arcilla, Ds 0-10, Ds 10-20 y pH fueron bajos (CV < 15%) mientras que para P y N-NO3 fueron moderados (15 < CV < 35%). La dependencia espacial del N-NO3 fue moderada con un rango de 96 m, mientras que el resto de los atributos no presentó autocorrelación producto de la variación que ocurre a distancias menores a la utilizada en el muestreo. En este estudio no fue posible modelar la distribución espacial de los atributos ni obtener mapas de la condición de suelo confiables que permitan orientar el uso de MSEC debido a la escasa variabilidad y ausencia de estructura espacial de las propiedades del suelo evaluadas.

The processes and properties that regulate crop performance and yield vary in space and time. The assessment of the magnitude and spatial structure of their variation is required in order to apply site-specific crop management (SSCM). Our aim was to assess the intra-field spatial variability of some chemical and physical topsoil properties of a typic Argiudoll of the center of Santa Fe for the use of the SSCM. Sixty soil samples of the top layer (0-20 cm depth) were taken in a 475 x 100 m plot. Sampling was distributed in three transects separated by 50 m with 20 points every 25 m. Disturbed soil samples were used to analyze N of nitrates (NNO 3), total organic C (COT), total N (Nt); available P (P), sand (Arena), clay (Arcilla) and soil reaction (pH). Soil bulk density (Ds) was determined on non-disturbed soil samples taken at 0-10 and 10-20 cm depths. Summary statistics were calculated and the spatial dependence was determined with sample variograms and envelopes obtained by permutations. Coefficients of variation (CV) for COT, Nt, Arena, Arcilla, Ds 0-10, Ds 10-20, and pH were low (CV < 15%) while they were moderate for P and N-NO3 (15 < CV < 35%). Moderate spatial dependence with a range of 96 m was only observed for N-NO3. The other soil properties had no autocorrelation because their variation occured at distances shorter than 25 m. In this study, the low variability and lack of spatial dependence of the soil properties did not allow modeling their spatial distribution as well as the development of reliable soil maps that would allow the use of the SSCM.