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Spatial models are used in a variety of research areas, such as environmental sciences, epidemiology, or physics. A common phenomenon in such spatial regression models is spatial confounding. This phenomenon is observed when spatially indexed covariates modeling the mean of the response are correlated with a spatial random effect included in the model, for example, as a proxy of unobserved spatial confounders. As a result, estimates for regression coefficients of the covariates can be severely biased and interpretation of these is no longer valid. Recent literature has shown that typical solutions for reducing spatial confounding can lead to misleading and counterintuitive results. In this article, we develop a computationally efficient spatial model that explicitly correlates a Gaussian random field for the covariate of interest with the Gaussian random field in the main model equation and integrates novel prior structures to reduce spatial confounding. Starting from the univariate case, we extend our prior structure also to the case of multiple spatially confounded covariates. In simulation studies, we show that our novel model flexibly detects and reduces spatial confounding in spatial datasets, and it performs better than typically used methods such as restricted spatial regression. These results are promising for any applied researcher who wishes to interpret covariate effects in spatial regression models. As a real data illustration, we study the effect of elevation and temperature on the mean of monthly precipitation in Germany. Deutsche Forschungsgemeinschaft http://dx.doi.org/10.13039/501100001659

Circular data can be found across many areas of science, for instance meteorology (e.g., wind directions), ecology (e.g., animal movement directions), or medicine (e.g., seasonality in disease onset). The special nature of these data means that conventional methods for non-periodic data are no longer valid. In this paper, we consider wrapped Gaussian processes and introduce a spatial model for circular data that allow for non-stationarity in the mean and the covariance structure of Gaussian random fields. We use the empirical equivalence between Gaussian random fields and Gaussian Markov random fields which allows us to considerably reduce computational complexity by exploiting the sparseness of the precision matrix of the associated Gaussian Markov random field. Furthermore, we develop tunable priors, inspired by the penalized complexity prior framework, that shrink the model toward a less flexible base model with stationary mean and covariance function. Posterior estimation is done via Markov chain Monte Carlo simulation. The performance of the model is evaluated in a simulation study. Finally, the model is applied to analyzing wind directions in Germany.

Plant growth is almost always limited by light availability and competition. However, plants are generally plastic and can change their morphology and biomass allocation to optimize growth under suboptimal conditions. We set up a controlled pot experiment with three light availability levels (10%, 20%, and 50%) to study the effect of light and competition on the biomass allocation and leaf morphology in monospecific and mixed pots of recently planted European beech (Fagus sylvatica L.), Norway spruce (Picea abies (L.) Karst.), and Douglas fir (Pseudotsuga menziesii (Mirb.) Franco) saplings using a quantile regression model. Specific leaf area (SLA) showed the strongest reaction and increased with decreasing light availability. Woody aboveground mass fraction (AMF) increased with decreasing light availability, but the effect of light on biomass allocation was less pronounced than on SLA. The SLA, woody AMF, and root mass fraction (RMF) of the two conifer species and European beech varied greatly, with European beech having a higher SLA and RMF than the two conifer species. The associated effect of plant size on biomass allocation was small, and the strength of the association was not meaningful on a practical level. The competitor’s effect on biomass allocation was minor overall and only present for some species, suggesting that species’ functional dissimilarity does not greatly affect allocational patterns in early tree development stages.

It is widely accepted that spatial dependencies have to be acknowledged appropriately in data that are spatially aligned. However, most spatial models still assume that the dependence structure does not vary over space, i.e., it is stationary. While assuming stationarity considerably facilitates estimation, it is often too restrictive when describing atmospheric phenomena such as precipitation. Nonetheless, the applicability of non-stationary models is often hindered, as their use reveals to be cumbersome and improvements over stationary models can be hard to identify. The stochastic partial differential equation (SPDE) approach to spatial modelling allows for flexible specifications of non-stationary models. In particular, given the German orographic diversity, it makes sense to investigate potential non-stationarity in precipitation patterns. Taking such potential non-stationarities into account may, in particular, leads to improved smoothing of the observed precipitation pattern taken on a finite set of measurement stations, and therefore to improved inputs to hydrological models. We suggest an SPDE-based model where the mean and dependence structure are allowed to vary with elevation, as well as a more flexible non-parametric alternative based on multivariate B-Splines. As factors such as wind may cause higher dependence in a given direction, we include anisotropy in the model. Results show that, according to the widely applicable Bayesian information criterion, a non-stationary model provides a better fit to the data. Taking German monthly precipitation as a motivation, we set up a simulation study to explore the ability of the elevation and spline-based models to correctly identify non-stationarity.

Dissertação de Mestrado, Biologia Marinha, Especialização em Pescas e Aquacultura, Faculdade de Ciências e Tecnologia, Universidade do Algarve, 2009 Os cavalos marinhos estão incluídos no género Hippocampus, o qual é um dos muitos pertencentes á família Syngnathidae. Entre as diversas características que os distinguem dos outros géneros, estes apresentam a particularidade de ser o macho que desempenha os cuidados parentais, incluindo o período de gestação. Esta característica tem levado regularmente a estudos acerca do comportamento reprodutivo de algumas espécies pertencentes ao género, e do papel de cada um dos sexos na reprodução. Na sequência de estudos anteriores foi desenvolvido uma experiência acerca do comportamento reprodutivo do cavalo marinho de focinho comprido, Hippocampus guttulatus, uma das duas espécies de cavalo marinho existentes na Ria Formosa. Numa primeira fase, este estudo comportamental foi desenvolvido de forma a caracterizar o comportamento de corte desta espécie, assim como os papéis desempenhados por cada um dos sexos no processo reprodutivo. Seguidamente, foi feita a delimitação temporal das várias etapas que constituem o ciclo reprodutivo desta espécie, analisou-se a sua estratégia reprodutiva e o potencial reprodutivo de cada um dos sexos. O conhecimento destes factores será uma ferramenta útil no desenvolvimento de um protocolo adequado de cultivo e manutenção, em cativeiro. H. guttulatus apresenta papéis sexuais convencionais, nos quais, são os machos que competem pelo acesso à parceira e consequentemente, cabe às fêmeas a selecção do parceiro. Em situações onde a proporção sexual de machos disponíveis é superior à de fêmeas, o período total de corte tende a diminuir, por diminuição do tempo de inactividade entre cortes, pelo que a competição induz um aceleramento no processo reprodutivo e, quer o período de corte, como todas as outras etapas que constituem o ciclo reprodutivo desta espécie, parecem estar condicionados pelas alterações da temperatura verificadas. O parto é um processo descontínuo e o número máximo de descendentes atingido por gestação foi de 678 juvenis. Os intervalos de latência entre acasalamentos consecutivos apresentam uma maior duração para os machos, pelo que, as fêmeas em situações onde não há limitação de machos disponíveis tendem a acasalar com outro macho, antes da conclusão do período de gestação do macho inicial. Desta forma, a espécie H. guttulatus não revelou monogamia estrita para uma época reprodutiva, o que provocou uma desigualdade no potencial reprodutivo de machos e fêmeas, ocorrendo uma prevalência das fêmeas em relação aos machos no número total de descendentes produzidos por época reprodutiva. Seahorses are included in the genus Hippocampus, which is one of many included in the family Syngnathidae. Among the several features that distinguish them from other genera, they have the distinction of being the male performs parental care, including the period of gestation. This feature has led to regular studies on the reproductive behavior of some species of the genus and about the role of each sex for reproduction. Following previous studies was conducted an experiment on the reproductive behavior of the long snouted seahorse, Hippocampus guttulatus, one of two species of seahorse existing in the Ria Formosa. At first this behavioral study was carried out to characterize the courtship behavior of this species as well as the roles played by each sex in the reproductive process. It was subsequently made time delimitation of the various steps that constitute the reproductive cycle of this specie; we analyzed its reproductive strategy and reproductive potential of each sex. The knowledge of these factors will be a useful tool in the development of a protocol suitable for the cultivation and maintenance in captivity. H. guttulatus has conventional sex roles, in which males are competing for access to the partner and therefore it is up to the selection of the female partner. In situations where the sex ratio of available males is higher than in females, the total courtship, tends to decrease by decreasing downtime between courtship behavior interactions, so that competition leads to an acceleration in the reproductive process and shortened the courtship, like all the other steps that constitute the reproductive cycle of this species seem to be driven by changes in temperature observed. The birth of juveniles is a batch process and the maximum number of juveniles by pregnancy was 678. The intervals of latency between consecutive matings have a longer duration for the males, so that the females in situations where there is no limitation of available males tend to mate with another male before the end of the gestation period of the initial male. Thus, the H. guttulatus revealed no strict monogamy to a reproductive season and has led to inequality in reproductive potential of males and females, occurring a prevalence of females compared to males in the total number of offspring produced by reproductive season.