Standardised empirical dispersal kernels emphasise the pervasiveness of long-distance dispersal in European birds.

Dispersal is a key life-history trait for most species and is essential to ensure connectivity and gene flow between populations and facilitate population viability in variable environments. Despite the increasing importance of range shifts due to global change, dispersal has proved difficult to quantify, limiting empirical understanding of this phenotypic trait and wider synthesis. Here, we introduce a statistical framework to estimate standardised dispersal kernels from biased data. Based on this, we compare empirical dispersal kernels for European breeding birds considering age (average dispersal; natal, before first breeding; and breeding dispersal, between subsequent breeding attempts) and sex (females and males) and test whether different dispersal properties are phylogenetically conserved. We standardised and analysed data from an extensive volunteer-based bird ring-recoveries database in Europe (EURING) by accounting for biases related to different censoring thresholds in reporting between countries and to migratory movements. Then, we fitted four widely used probability density functions in a Bayesian framework to compare and provide the best statistical descriptions of the different age and sex-specific dispersal kernels for each bird species. The dispersal movements of the 234 European bird species analysed were statistically best explained by heavy-tailed kernels, meaning that while most individuals disperse over short distances, long-distance dispersal is a prevalent phenomenon in almost all bird species. The phylogenetic signal in both median and long dispersal distances estimated from the best-fitted kernel was low (Pagel's λ < 0.25), while it reached high values (Pagel's λ >0.7) when comparing dispersal distance estimates for fat-tailed dispersal kernels. As expected in birds, natal dispersal was on average 5 km greater than breeding dispersal, but sex-biased dispersal was not detected. Our robust analytical framework allows sound use of widely available mark-recapture data in standardised dispersal estimates. We found strong evidence that long-distance dispersal is common among European breeding bird species and across life stages. The dispersal estimates offer a first guide to selecting appropriate dispersal kernels in range expansion studies and provide new avenues to improve our understanding of the mechanisms and rules underlying dispersal events.

La dispersión es un rasgo clave del ciclo vital de la mayoría de las especies y es esencial para garantizar la conectividad y el flujo genético entre poblaciones y contribuir a la viabilidad de la población en contextos de ambiente variable. A pesar de que la dispersión es clave para estudiar los cambios en el área de distribución de las especies debido al cambio global, la dispersión es difícil de cuantificar, lo que limita la comprensión empírica de este rasgo fenotípico y su síntesis más amplia. Aquí introducimos un marco de trabajo estadístico para estimar de manera estandarizada los kernels de dispersión a partir de datos sesgados. Basándonos en este marco, comparamos los kernels de dispersión empíricos para las aves reproductoras europeas considerando la edad (dispersión media vital; natal, antes de la primera reproducción; y dispersión reproductora, entre los intentos de reproducción posteriores) y el sexo (hembras y machos), además de explorar si las diferentes propiedades de dispersión se conservan filogenéticamente. Estandarizamos y analizamos los datos de una extensa base de datos de anillamiento de aves en Europa (EURING), basada en voluntarios, teniendo en cuenta los sesgos relacionados con los diferentes umbrales de comunicación de las anillas entre países y con los movimientos migratorios. A continuación, ajustamos, en un marco bayesiano, cuatro funciones de probabilidad ampliamente utilizadas para comparar y proporcionar las mejores descripciones estadísticas de los diferentes kernels de dispersión por edad y sexo para cada especie de ave. Los movimientos de dispersión de las 234 especies de aves europeas analizadas se explicaron estadísticamente mejor mediante kernels de cola pesada, lo que significa que, aunque la mayoría de los individuos se dispersan en distancias cortas, la dispersión a larga distancia es un fenómeno prevalente en casi todas las especies de aves. La señal filogenética tanto en las distancias de dispersión medias como en las largas estimadas a partir del kernel mejor ajustado fue baja (λ de Pagel < 0,25), mientras que alcanzó valores altos (λ de Pagel >0,7) al comparar las estimas de distancia de dispersión para los kernels de cola pesada. Como se esperaba en las aves, la dispersión natal fue en promedio 5 km mayor que la dispersión reproductiva, pero no se detectó una dispersión sesgada por sexo. Nuestro robusto marco analítico permite un buen uso de los datos de marcaje y recaptura disponibles para la estimación estandarizada de las distancias de dispersión. Hemos encontrado pruebas sólidas de que la dispersión a larga distancia es común entre las especies de aves reproductoras europeas y en todas las etapas de la vida. Las estimas de dispersión ofrecen un primer paso para seleccionar los kernels de dispersión adecuados para los estudios de expansión del rango de distribución y proporcionar nuevas vías de investigación para mejorar nuestra comprensión de los mecanismos y procesos que subyacen a los eventos de dispersión.

Genomic Prediction Using Bayesian Regression Models With Global-Local Prior.

Bayesian regression models are widely used in genomic prediction for various species. By introducing the global parameter τ, which can shrink marker effects to zero, and the local parameter λ k , which can allow markers with large effects to escape from the shrinkage, we developed two novel Bayesian models, named BayesHP and BayesHE. The BayesHP model uses Horseshoe+ prior, whereas the BayesHE model assumes local parameter λ k , after a half-t distribution with an unknown degree of freedom. The performances of BayesHP and BayesHE models were compared with three classical prediction models, including GBLUP, BayesA, and BayesB, and BayesU, which also applied global-local prior (Horseshoe prior). To assess model performances for traits with various genetic architectures, simulated data and real data in cattle (milk production, health, and type traits) and mice (type and growth traits) were analyzed. The results of simulation data analysis indicated that models based on global-local priors, including BayesU, BayesHP, and BayesHE, performed better in traits with higher heritability and fewer quantitative trait locus. The results of real data analysis showed that BayesHE was optimal or suboptimal for all traits, whereas BayesHP was not superior to other classical models. For BayesHE, its flexibility to estimate hyperparameter automatically allows the model to be more adaptable to a wider range of traits. The BayesHP model, however, tended to be suitable for traits having major/large quantitative trait locus, given its nature of the "U" type-like shrinkage pattern. Our results suggested that auto-estimate the degree of freedom (e.g., BayesHE) would be a better choice other than increasing the local parameter layers (e.g., BayesHP). In this study, we introduced the global-local prior with unknown hyperparameter to Bayesian regression models for genomic prediction, which can trigger further investigations on model development.

Hierarchical Bayes approach for subgroup analysis.

In clinical data analysis, both treatment effect estimation and consistency assessment are important for a better understanding of the drug efficacy for the benefit of subjects in individual subgroups. The linear mixed-effects model has been used for subgroup analysis to describe treatment differences among subgroups with great flexibility. The hierarchical Bayes approach has been applied to linear mixed-effects model to derive the posterior distributions of overall and subgroup treatment effects. In this article, we discuss the prior selection for variance components in hierarchical Bayes, estimation and decision making of the overall treatment effect, as well as consistency assessment of the treatment effects across the subgroups based on the posterior predictive p-value. Decision procedures are suggested using either the posterior probability or the Bayes factor. These decision procedures and their properties are illustrated using a simulated example with normally distributed response and repeated measurements.

Investigating a Weakly Informative Prior for Item Scale Hyperparameters in Hierarchical 3PNO IRT Models.

The half-t family has been suggested for the scale hyperparameter in Bayesian hierarchical modeling. Two parameters define a half-t distribution: the scale s and the degree-of-freedom ν. When s is set at a finite value that is slightly larger than the actual standard deviation of the parameters, the half-t prior density can be vaguely informative. This paper focused on such densities, and applied them to the hierarchical three-parameter item response theory (IRT) model. Monte Carlo simulations were carried out to investigate the performance of such specifications in parameter recovery and model comparisons under situations where the actual variability of item parameters varied, and results suggest that the half-t family does offer advantages over the commonly adopted uniform or inverse-gamma prior density by allowing the variability for item parameters to be either very small or large. A real data example is also provided to further illustrate this.