A new method for the estimation of variance matrix with prescribed zeros in nonlinear mixed effects models

We propose a new method for the Maximum Likelihood Estimator (MLE) of nonlinear mixed effects models when the variance matrix of Gaussian random effects has a prescribed pattern of zeros (PPZ). The method consists in coupling the recently developed Iterative Conditional Fitting (ICF) algorithm with the Expectation Maximization (EM) algorithm. It provides positive definite estimates for any sample size, and does not rely on any structural assumption on the PPZ. It can be easily adapted to many versions of EM.Comment: Accepted for publication in Statistics and Computin

Sward structure of marandu palisadegrass subjected to continuous stocking and nitrogen-induced rhythms of growth

Acceleration of the growth rhythm of plants using nitrogen fertiliser alters the rates of physiological processes like growth and senescence and may cause significant changes in sward structure, interfering with plant and animal responses. The objective of this experiment was to evaluate sward structure of marandu palisadegrass (Brachiaria brizantha) maintained at 30 cm under continuous stocking and subjected to contrasting rhythms of growth from January 2007 to April 2008. These were generated using or not nitrogen fertiliser, and comprised four experimental treatments as follows: control (non-fertilised), 150, 300 and 450 kg ha-1 of N. Acceleration of the growth rhythm of plants was associated with increases in leaf and stem bulk density, and resulted in larger LAI and total bulk density on swards subjected to faster (fertilised with 300 and 450 kg ha-1 of N) than those subjected to slower rhythms of growth (non-fertilised or fertilised with 150 kg ha-1 of N). Variations in dead material bulk density were associated with seasonal variations in climatic conditions, and were not influenced by growth rhythms. During autumn/winter and early spring (dry period of the year) swards subjected to faster, relative to those subjected to slower rhythms of growth, had larger proportion of leaves on the top horizons. On the other hand, sward structure did not vary among rhythms of growth at times of the year when there was no limitation in the availability of climatic growth factors (late spring and summer), indicating that when control of the grazing process is efficient, changes in sward structure are basically a function of seasonal variations in climatic growth conditions and phenological state of plants.A aceleração do ritmo de crescimento das plantas por meio da adubação nitrogenada altera a velocidade dos processos fisiológicos, atuando sobre o crescimento e a senescência, podendo refletir-se em alterações importantes sobre a estrutura do dossel. Avaliou-se a estrutura do dossel forrageiro de pastos de capim-marandu (Brachiaria brizantha) mantidos a 30 cm de altura por meio de lotação contínua e submetidos a ritmos de crescimento contrastantes de janeiro de 2007 a abril de 2008. Os distintos ritmos de crescimento foram criados por meio da utilização de adubação nitrogenada, segundo os tratamentos: sem adubação (controle), 150, 300 e 450 kg ha-1 de N. A aceleração do ritmo de crescimento dos pastos resultou em aumentos de densidade volumétrica de folhas e de colmos, refletindo em maior IAF e densidade volumétrica total em pastos submetidos aos ritmos de crescimento mais acelerados (adubados com 300 e 450 kg ha-1 de N) relativamente àqueles submetidos a ritmos de crescimento mais lentos (pastos não adubados e/ou adubados com 150 kg ha-1 de N). Variações em densidade volumétrica do material morto estiveram associadas a flutuações estacionais das condições climáticas, e não foram influenciadas pelos ritmos de crescimento avaliados. Na época da seca (outono/inverno e início de primavera), os pastos submetidos aos ritmos de crescimento mais acelerados apresentaram maior proporção de folhas no horizonte superior do dossel. Por outro lado, a estrutura do dossel não variou entre os ritmos de crescimento nas épocas de maior disponibilidade de fatores de crescimento (final de primavera e verão), indicando que quando o controle do processo de pastejo é feito de maneira eficiente, mudanças em estrutura são função basicamente de variações estacionais em condições climáticas e estádio fenológico das plantas

Growth increments and stability over time in fast-growing forest tree species

Zamudio, F. Facultad de Ciencias Forestales, Universidad de Talca, PO Box 747, 2 Norte 685, Talca, Chile.We review an analytical procedure useful for measuring the influence of time on the phenotypic expression of cumulative growth. It consists of separating the genetic control into two meaningful components: the cumulative genetic effect of growth increments and the effect of genotype × time interaction. The analysis is performed via a hierarchical mixed linear model. Data from three Pinus tecunumanii Eguiluz & J.P. Perry provenance–progeny trials established by the CAMCORE Cooperative in South America were used to assess the practical application of the method. Results suggest that the simple observation of age–age correlations for cumulative growth can be misleading, because they hide the effects of family and within-family variation. The partition of cumulative growth into mutually exclusive growth increments can help to discriminate covariance components, which are also useful to predict the degree of association between growth at different ages and the potential value for early selection