Symbolic Formulae for Linear Mixed Models

A statistical model is a mathematical representation of an often simplified or idealised data-generating process. In this paper, we focus on a particular type of statistical model, called linear mixed models (LMMs), that is widely used in many disciplines e.g.~agriculture, ecology, econometrics, psychology. Mixed models, also commonly known as multi-level, nested, hierarchical or panel data models, incorporate a combination of fixed and random effects, with LMMs being a special case. The inclusion of random effects in particular gives LMMs considerable flexibility in accounting for many types of complex correlated structures often found in data. This flexibility, however, has given rise to a number of ways by which an end-user can specify the precise form of the LMM that they wish to fit in statistical software. In this paper, we review the software design for specification of the LMM (and its special case, the linear model), focusing in particular on the use of high-level symbolic model formulae and two popular but contrasting R-packages in lme4 and asreml

Older fathers' children have lower evolutionary fitness across four centuries and in four populations

Peer reviewe

Profile and width of rough interfaces

In the context of Landau theory and its field theoretical refinements, interfaces between coexisting phases are described by intrinsic profiles. These intrinsic interface profiles, however, are neither directly accessible by experiment nor by computer simulation as they are broadened by long-wavelength capillary waves. In this paper we study the separation of the small scale intrinsic structure from the large scale capillary wave fluctuations in the Monte Carlo simulated three-dimensional Ising model. To this purpose, a blocking procedure is applied, using the block size as a variable cutoff, and a translationally invariant method to determine the interface position of strongly fluctuating profiles on small length scales is introduced. While the capillary wave picture is confirmed on large length scales and its limit of validity is estimated, an intrinsic regime is, contrary to expectations, not observed.Comment: 18 pages, 4 Postscript figures, LaTeX2e, formulation of sec.3.2 improved, 1 reference adde

Relaxed selection and mutation accumulation are best studied empirically : reply to Woodley of Menie et al.

Correction to: replay to Woodley of Menie et al. 10.1098/rspb.2018.1427.Peer reviewe

Computing the Roughening Transition of Ising and Solid-On-Solid Models by BCSOS Model Matching

We study the roughening transition of the dual of the 2D XY model, of the Discrete Gaussian model, of the Absolute Value Solid-On-Solid model and of the interface in an Ising model on a 3D simple cubic lattice. The investigation relies on a renormalization group finite size scaling method that was proposed and successfully tested a few years ago. The basic idea is to match the renormalization group flow of the interface observables with that of the exactly solvable BCSOS model. Our estimates for the critical couplings are $\beta_R^{XY}=1.1199(1)$, $K_R^{DG}=0.6653(2)$ and $K_R^{ASOS}=0.80608(2)$ for the XY-model, the Discrete Gaussian model and the Absolute Value Solid-On-Solid model, respectively. For the inverse roughening temperature of the Ising interface we find $K_R^{Ising}= 0.40758(1)$. To the best of our knowledge, these are the most precise estimates for these parameters published so far.Comment: 25 pages, LaTeX file, no figure

Monte Carlo Methods for Estimating Interfacial Free Energies and Line Tensions

Excess contributions to the free energy due to interfaces occur for many problems encountered in the statistical physics of condensed matter when coexistence between different phases is possible (e.g. wetting phenomena, nucleation, crystal growth, etc.). This article reviews two methods to estimate both interfacial free energies and line tensions by Monte Carlo simulations of simple models, (e.g. the Ising model, a symmetrical binary Lennard-Jones fluid exhibiting a miscibility gap, and a simple Lennard-Jones fluid). One method is based on thermodynamic integration. This method is useful to study flat and inclined interfaces for Ising lattices, allowing also the estimation of line tensions of three-phase contact lines, when the interfaces meet walls (where "surface fields" may act). A generalization to off-lattice systems is described as well. The second method is based on the sampling of the order parameter distribution of the system throughout the two-phase coexistence region of the model. Both the interface free energies of flat interfaces and of (spherical or cylindrical) droplets (or bubbles) can be estimated, including also systems with walls, where sphere-cap shaped wall-attached droplets occur. The curvature-dependence of the interfacial free energy is discussed, and estimates for the line tensions are compared to results from the thermodynamic integration method. Basic limitations of all these methods are critically discussed, and an outlook on other approaches is given

Within-individual phenotypic plasticity in flowers fosters pollination niche shift

Authors thank Raquel Sánchez, Angel Caravante, Isabel Sánchez Almazo, Tatiana López Pérez, Samuel Cantarero, María José Jorquera and Germán Fernández for helping us during several phases of the study and Iván Rodríguez Arós for drawing the insect silhouettes. This research is supported by grants from the Spanish Ministry of Science, Innovation and Universities (CGL2015-71634-P, CGL2015-63827-P, CGL2017-86626-C2-1-P, CGL2017- 86626-C2-2-P, UNGR15-CE-3315, including EU FEDER funds), Junta de Andalucía (P18- FR-3641), Xunta de Galicia (CITACA), BBVA Foundation (PR17_ECO_0021), and a contract grant to C.A. from the former Spanish Ministry of Economy and Competitiveness (RYC-2012-12277). This is a contribution to the Research Unit Modeling Nature, funded by the Consejería de Economía, Conocimiento, Empresas y Universidad, and European Regional Development Fund (ERDF), reference SOMM17/6109/UGR.Phenotypic plasticity, the ability of a genotype of producing different phenotypes when exposed to different environments, may impact ecological interactions. We study here how within-individual plasticity in Moricandia arvensis flowers modifies its pollination niche. During spring, this plant produces large, cross-shaped, UV-reflecting lilac flowers attracting mostly long-tongued large bees. However, unlike most co-occurring species, M. arvensis keeps flowering during the hot, dry summer due to its plasticity in key vegetative traits. Changes in temperature and photoperiod in summer trigger changes in gene expression and the production of small, rounded, UV-absorbing white flowers that attract a different assemblage of generalist pollinators. This shift in pollination niche potentially allows successful reproduction in harsh conditions, facilitating M. arvensis to face anthropogenic perturbations and climate change. Floral phenotypes impact interactions between plants and pollinators. Here, the authors show that Moricandia arvensis displays discrete seasonal plasticity in floral phenotype, with large, lilac flowers attracting long-tongued bees in spring and small, rounded, white flowers attracting generalist pollinators in summer.Spanish Ministry of Science, Innovation and Universities (EU FEDER funds) CGL2015-71634-P CGL2015-63827-P CGL2017-86626-C2-1-P CGL2017-86626-C2-2-P UNGR15-CE-3315Junta de Andalucia P18-FR-3641Xunta de GaliciaBBVA Foundation PR17_ECO_0021Spanish Ministry of Economy and Competitiveness RYC-2012-12277Consejeria de Economia, Conocimiento, Empresas y Universidad SOMM17/6109/UGREuropean Union (EU) SOMM17/6109/UG