Pólya-splitting distributions as stationary solutions of multivariate birth-death processes under extended neutral theory.

Multivariate count distributions are crucial for the inference of ecological processes underpinning biodiversity. In particular, neutral theory provides useful null distributions allowing the evaluation of adaptation or natural selection. In this paper, we build a broader family of multivariate distributions: the Polya-splitting distributions. We show that they emerge naturally as stationary distributions of a multivariate birth-death process. This family of distributions is a consistent extension of non-zero sum neutral models based on a master equation approach. It allows considering both total abundance of the community and relative abundances of species. We emphasize that this family is large enough to encompass various dependence structures among species. We also introduce the strong closure under addition property that can be useful to generate nested multi-level dependence structures. Although all Pólya splitting distributions do not share this property, we provide numerous example verifying it. They include the previously known example with independent species, and also new ones with alternative dependence structures. Overall, we advocate that Polya-splitting distribution should become a part of the classic toolbox for the analysis of multivariate count data in ecology, providing alternative approaches to joint species distribution framework. Comparatively, our approach allows to model dependencies between species at the observation level, while the classical JSDM's model dependencies at the latent process strata.

Integrative models for joint analysis of shoot growth and branching patterns.

Plants exhibit dependences between shoot growth and branching that generate highly structured patterns. The characterization of the patterning mechanism is still an open issue because of the developmental processes involved with both succession of events (e.g. internode elongation, axillary shoot initiation and elongation) and complex dependences among neighbouring positions along the parent shoot. Statistical models called semi-Markov switching partitioned conditional generalized linear models were built on the basis of apple and pear tree datasets. In these models, the semi-Markov chain represents both the succession and lengths of branching zones, whereas the partitioned conditional generalized linear models represent the influence of parent shoot growth variables on axillary productions within each branching zone. Parent shoot growth variables were shown to influence specific developmental events. On this basis, the growth and branching patterns of two apple tree (Malus domestica) cultivars, as well as of pear trees (Pyrus spinosa) between two successive growing cycles, were compared. The proposed integrative statistical models were able to decipher the roles of successive developmental events in the growth and branching patterning mechanisms. These models could incorporate other parent shoot explanatory variables, such as the local curvature or the maximum growth rate of the leaf.

Item response models for the longitudinal analysis of health-related quality of life in cancer clinical trials.

BACKGROUND: The use of health-related quality of life (HRQoL) as an endpoint in cancer clinical trials is growing rapidly. Hence, research into the statistical approaches used to analyze HRQoL data is of major importance, and could lead to a better understanding of the impact of treatments on the everyday life and care of patients. Amongst the models that are used for the longitudinal analysis of HRQoL, we focused on the mixed models from item response theory, to directly analyze raw data from questionnaires. METHODS: We reviewed the different item response models for ordinal responses, using a recent classification of generalized linear models for categorical data. Based on methodological and practical arguments, we then proposed a conceptual selection of these models for the longitudinal analysis of HRQoL in cancer clinical trials. RESULTS: To complete comparison studies already present in the literature, we performed a simulation study based on random part of the mixed models, so to compare the linear mixed model classically used to the selected item response models. As expected, the sensitivity of the item response models to detect random effects with lower variance is better than that of the linear mixed model. We then used a cumulative item response model to perform a longitudinal analysis of HRQoL data from a cancer clinical trial. CONCLUSIONS: Adjacent and cumulative item response models seem particularly suitable for HRQoL analysis. In the specific context of cancer clinical trials and the comparison between two groups of HRQoL data over time, the cumulative model seems to be the most suitable, given that it is able to generate a more complete set of results and gives an intuitive illustration of the data.

New insights for estimating the genetic value of segregating apple progenies for irregular bearing during the first years of tree production.

Because irregular bearing generates major agronomic issues in fruit-tree species, particularly in apple, the selection of regular cultivars is desirable. Here, we aimed to define methods and descriptors allowing a diagnostic for bearing behaviour during the first years of tree maturity, when tree production is increasing. Flowering occurrences were collected at whole-tree and (annual) shoot scales on a segregating apple population. At both scales, the number of inflorescences over the years was modelled. Two descriptors were derived from model residuals: a new biennial bearing index, based on deviation around yield trend over years and an autoregressive coefficient, which represents dependency between consecutive yields. At the shoot scale, entropy was also considered to represent the within-tree flowering synchronicity. Clusters of genotypes with similar bearing behaviours were built. Both descriptors at the whole-tree and shoot scales were consistent for most genotypes and were used to discriminate regular from biennial and irregular genotypes. Quantitative trait loci were detected for the new biennial bearing index at both scales. Combining descriptors at a local scale with entropy showed that regular bearing at the tree scale may result from different strategies of synchronization in flowering at the local scale. The proposed methods and indices open an avenue to quantify bearing behaviour during the first years of tree maturity and to capture genetic variations. Their extension to other progenies and species, possible variants of descriptors, and their use in breeding programmes considering a limited number of years or fruit yields are discussed.